Intelligent Control and Automation: International Conference on Intelligent Computing, ICIC 2006, Kunming, China, August, 2006 (Lecture Notes in Control and Information Sciences)

Lecture Notes in Control and Information Sciences 344 Editors: M. Thoma, M. Morari

De-Shuang Huang, Kang Li, George William Irwin (Eds.)

Intelligent Control and Automation International Conference on Intelligent Computing, ICIC 2006 Kunming, China, August 16–19, 2006

ABC

Series Advisory Board F. Allgöwer, P. Fleming, P. Kokotovic, A.B. Kurzhanski, H. Kwakernaak, A. Rantzer, J.N. Tsitsiklis

Editors De-Shuang Huang

George William Irwin Queen’s University Belfast, UK E-mail: [email protected]

Institute of Intelligent Machines Chinese Academy of Sciences Hefei, Anhui, China E-mail: [email protected]

Kang Li Queen’s University Belfast, UK E-mail: [email protected]

Library of Congress Control Number: 2006930913 ISSN print edition: 0170-8643 ISSN electronic edition: 1610-7411 ISBN-10 3-540-37255-5 Springer Berlin Heidelberg New York ISBN-13 978-3-540-37255-4 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2006
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready by author, data conversion by Scientific Publishing Services, Chennai, India Cover design: design & production GmbH, Heidelberg Printed on acid-free paper

SPIN: 11816492

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Preface

The International Conference on Intelligent Computing (ICIC) was formed to provide an annual forum dedicated to the emerging and challenging topics in artificial intelligence, machine learning, bioinformatics, and computational biology, etc. It aims to bring together researchers and practitioners from both academia and industry to share ideas, problems and solutions related to the multifaceted aspects of intelligent computing. ICIC 2006 held in Kunming, Yunnan, China, August 16-19, 2006, was the second International Conference on Intelligent Computing, built upon the success of ICIC 2005 held in Hefei, China, 2005. This year, the conference concentrated mainly on the theories and methodologies as well as the emerging applications of intelligent computing. It intended to unify the contemporary intelligent computing techniques within an integral framework that highlights the trends in advanced computational intelligence and bridges theoretical research with applications. In particular, bio-inspired computing emerged as having a key role in pursuing for novel technology in recent years. The resulting techniques vitalize life science engineering and daily life applications. In light of this trend, the theme for this conference was “Emerging Intelligent Computing Technology and Applications”. Papers related to this theme were especially solicited, including theories, methodologies, and applications in science and technology. ICIC 2006 received over 3000 submissions from 36 countries and regions. All papers went through a rigorous peer review procedure and each paper received at least three review reports. Based on the review reports, the Program Committee finally selected 703 high-quality papers for presentation at ICIC 2006. These papers cover 29 topics and 16 special sessions, and are included in five volumes of proceedings published by Springer, including one volume of Lecture Notes in Computer Science (LNCS), one volume of Lecture Notes in Artificial Intelligence (LNAI), one volume of Lecture Notes in Bioinformatics (LNBI), and two volumes of Lecture Notes in Control and Information Sciences (LNCIS). This volume of Lecture Notes in Control and Information Sciences (LNCIS) includes 142 papers covering 4 relevant topics and 1 special session topics. The organizers of ICIC 2006, including Yunan University, the Institute of Intelligent Machines of the Chinese Academy of Science, and Queen’s University Belfast, have made enormous effort to ensure the success of ICIC 2006. We hereby would like to thank the members of the ICIC 2006 Advisory Committee for their guidance and advice, the members of the Program Committee and the referees for their collective effort in reviewing and soliciting the papers, and the members of the Publication Committee for their significant editorial work. We would like to thank Alfred Hofmann, executive editor from Springer, for his frank and helpful advice and guidance throughout and for his support in publishing the proceedings in the Lecture Notes series. In particular, we would like to thank all the authors for contributing their

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Preface

papers. Without the high-quality submissions from the authors, the success of the conference would not have been possible. Finally, we are especially grateful to the IEEE Computational Intelligence Society, The International Neural Network Society and the National Science Foundation of China for the their sponsorship. June 2006

De-Shuang Huang Institute of Intelligent Machines Chinese Academy of Sciences, China Kang Li Queen’s University Belfast, UK George William Irwin Queen’s University Belfast, UK

ICIC 2006 Organization

General Chairs:

De-Shuang Huang, China Song Wu, China George W. Irwin, UK

International Advisory Committee Aike Guo, China Alfred Hofmann, Germany DeLiang Wang, USA Erke Mao, China Fuchu He, China George W. Irwin, UK Guangjun Yang, China Guanrong Chen, Hong Kong Guoliang Chen, China Harold Szu, USA John L. Casti, USA Marios M. Polycarpou, USA

Mengchu Zhou, USA Michael R. Lyu, Hong Kong MuDer Jeng, Taiwan Nanning Zheng, China Okyay Knynak, Turkey Paul Werbos, USA Qingshi Zhu, China Ruwei Dai, China Sam Shuzhi GE, Singapore Sheng Zhang, China Shoujue Wang, China Songde Ma, China

Stephen Thompson, UK Tom Heskes, Netherlands Xiangfan He, China Xingui He, China Xueren Wang, China Yanda Li, China Yixin Zhong, China Youshou Wu, China Yuanyan Tang, Hong Kong Yunyu Shi, China Zheng Bao, China

Program Committee Chairs:

Kang Li, UK Prashan Premaratne, Australia

Steering Committee Chairs:

Sheng Chen, UK Xiaoyi Jiang, Germany Xiao-Ping Zhang, Canada

Organizing Committee Chairs:

Yongkun Li, China Hanchun Yang, China Guanghua Hu, China

Special Session Chair:

Wen Yu, Mexico

Tutorial Chair:

Sudharman K. Jayaweera, USA

Publication Chair:

Xiaoou Li, Mexico

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Organization

International Liasion Chair:

C. De Silva, Liyanage, New Zealand

Publicity Chairs:

Simon X.Yang, Canada Jun Zhang, China

Exhibition Chair:

Cheng Peng, China

Program Committee Aili Han, China Arit Thammano, Thailand Baogang Hu, China Bin Luo, China Bin Zhu, China Bing Wang, China Bo Yan, USA Byoung-Tak Zhang, Korea Caoan Wang, Canada Chao Hai Zhang, Japan Chao-Xue Wang, China Cheng-Xiang Wang, UK Cheol-Hong Moon, Korea Chi-Cheng Cheng, Taiwan Clement Leung, Australia Daniel Coca, UK Daqi Zhu, China David Stirling, Australia Dechang Chen, USA Derong Liu, USA Dewen Hu, China Dianhui Wang, Australia Dimitri Androutsos, Canada Donald C. Wunsch, USA Dong Chun Lee, Korea Du-Wu Cui, China Fengling Han, Australia Fuchun Sun, China Girijesh Prasad, UK Guang-Bin Huang, Singapore Guangrong Ji, China Hairong Qi, USA Hong Qiao, China

Hong Wang, China Hongtao Lu, China Hongyong Zhao, China Huaguang Zhang, China Hui Wang, China Vitoantonio Bevilacqua, Italy Jiangtao Xi, Australia Jianguo Zhu, Australia Jianhua Xu, China Jiankun Hu, Australia Jian-Xun Peng, UK Jiatao Song, China Jie Tian, China Jie Yang, China Jin Li, UK Jin Wu, UK Jinde Cao, China Jinwen Ma, China Jochen Till, Germany John Q. Gan, UK Ju Liu, China K. R. McMenemy, UK Key-Sun Choi, Korea Liangmin Li, UK Luigi Piroddi, Italy Maolin Tang, Australia Marko Hoþevar, Slovenia Mehdi Shafiei, Canada Mei-Ching Chen, Taiwan Mian Muhammad Awais, Pakistan Michael Granitzer, Austria Michael J.Watts, New Zealand

Michiharu Maeda, Japan Minrui Fei, China Muhammad Jamil Anwas, Pakistan Muhammad Khurram Khan, China Naiqin Feng, China Nuanwan Soonthornphisaj, Thailand Paolo Lino, Italy Peihua Li, China Ping Guo, China Qianchuan Zhao, China Qiangfu Zhao, Japan Qing Zhao, Canada Roberto Tagliaferri, Italy Rong-Chang Chen, Taiwan RuiXiang Sun, China Saeed Hashemi, Canada Sanjay Sharma, UK Seán McLoone, Ireland Seong G. Kong, USA Shaoning Pang, New Zealand Shaoyuan Li, China Shuang-Hua Yang, UK Shunren Xia, China Stefanie Lindstaedt, Austria Sylvia Encheva, Norway Tai-hoon Kim, Korea Tai-Wen Yue, Taiwan Takashi Kuremoto, Japan Tarık Veli Mumcu, Turkey

Organization

Tian Xiang Mei, UK Tim. B. Littler, UK Tommy W. S. Chow, Hong Kong Uwe Kruger, UK Wei Dong Chen, China Wenming Cao, China Wensheng Chen, China Willi Richert, Germany Worapoj Kreesuradej, Thailand

Xiao Zhi Gao, Finland Xiaoguang Zhao, China Xiaojun Wu, China Xiaolong Shi, China Xiaoou Li, Mexico Xinge You, Hong Kong Xiwen Zhang, China Xiyuan Chen, China Xun Wang, UK Yanhong Zhou, China Yi Shen, China

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Yong Dong Wu, Singapore Yuhua Peng, China Zengguang Hou, China Zhao-Hui Jiang, Japan Zhen Liu, Japan Zhi Wang, China Zhi-Cheng Chen, China Zhi-Cheng Ji, China Zhigang Zeng, China Ziping Chiang, Taiwa

Reviewers Xiaodan Wang, Lei Wang, Arjun Chandra, Angelo Ciaramella, Adam Kalam, Arun Sathish, Ali Gunes, Jin Tang, Aiguo He, Arpad Kelemen, Andreas Koschan, Anis Koubaa, Alan Gupta, Alice Wang, Ali Ozen, Hong Fang, Muhammad Amir Yousuf, An-Min Zou, Andre Döring, Andreas Juffinger, Angel Sappa, Angelica Li, Anhua Wan, Bing Wang, Rong Fei, Antonio Pedone, Zhengqiang Liang , Qiusheng An, Alon Shalev Housfater, Siu-Yeung Cho, Atif Gulzar, Armin Ulbrich, Awhan Patnaik, Muhammad Babar, Costin Badica, Peng Bai, Banu Diri, Bin Cao, Riccardo Attimonelli, Baohua Wang, Guangguo Bi, Bin Zhu, Brendon Woodford, Haoran Feng, Bo Ma, Bojian Liang, Boris Bacic, Brane Sirok, Binrong Jin, Bin Tian, Christian Sonntag, Galip Cansever, Chun-Chi Lo, ErKui Chen, Chengguo Lv, Changwon Kim, Chaojin Fu, Anping Chen, Chen Chun , C.C. Cheng, Qiming Cheng, Guobin Chen, Chengxiang Wang, Hao Chen, Qiushuang Chen, Tianding Chen, Tierui Chen, Ying Chen, Mo-Yuen Chow, Christian Ritz, Chunmei Liu, Zhongyi Chu, Feipeng Da, Cigdem Turhan, Cihan Karakuzu, Chandana Jayasooriya, Nini Rao, Chuan-Min Zhai, Ching-Nung Yang, Quang Anh Nguyen, Roberto Cordone, Changqing Xu, Christian Schindler, Qijun Zhao, Wei Lu, Zhihua Cui, Changwen Zheng, David Antory, Dirk Lieftucht, Dedy Loebis, Kouichi Sakamoto, Lu Chuanfeng, Jun-Heng Yeh, Dacheng Tao, Shiang-Chun Liou, Ju Dai , Dan Yu, Jianwu Dang, Dayeh Tan, Yang Xiao, Dondong Cao, Denis Stajnko, Liya De Silva, Damien Coyle, Dian-Hui Wang, Dahai Zhang, Di Huang, Dikai Liu, D. Kumar, Dipak Lal Shrestha, Dan Lin, DongMyung Shin, Ning Ding, DongFeng Wang, Li Dong, Dou Wanchun, Dongqing Feng, Dingsheng Wan, Yongwen Du, Weiwei Du, Wei Deng, Dun-wei Gong, DaYong Xu, Dar-Ying Jan, Zhen Duan, Daniela Zaharie, ZhongQiang Wu, Esther Koller-Meier, Anding Zhu, Feng Pan, Neil Eklund, Kezhi Mao, HaiYan Zhang, Sim-Heng Ong, Antonio Eleuteri, Bang Wang, Vincent Emanuele, Michael Emmerich, Hong Fu, Eduardo Hruschka, Erika Lino, Estevam Rafael Hruschka Jr, D.W. Cui, Fang Liu, Alessandro Farinelli, Fausto Acernese, Bin Fang, Chen Feng, Huimin Guo, Qing Hua, Fei Zhang, Fei Ge, Arnon Rungsawang, Feng Jing, Min Feng, Feiyi Wang, Fengfeng Zhou, Fuhai Li, Filippo Menolascina, Fengli Ren, Mei Guo, Andrés Ferreyra, Francesco Pappalardo, Chuleerat Charasskulchai, Siyao Fu, Wenpeng Ding, Fuzhen Huang, Amal Punchihewa,

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Organization

Geoffrey Macintyre, Xue Feng He, Gang Leng, Lijuan Gao, Ray Gao, Andrey Gaynulin, Gabriella Dellino, D.W. Ggenetic, Geoffrey Wang, YuRong Ge, Guohui He, Gwang Hyun Kim, Gianluca Cena, Giancarlo Raiconi, Ashutosh Goyal, Guan Luo, Guido Maione, Guido Maione, Grigorios Dimitriadis, Haijing Wang, Kayhan Gulez, Tiantai Guo, Chun-Hung Hsieh, Xuan Guo, Yuantao Gu, Huanhuan Chen, Hongwei Zhang, Jurgen Hahn, Qing Han, Aili Han, Dianfei Han, Fei Hao, Qing-Hua Ling, Hang-kon Kim, Han-Lin He, Yunjun Han, Li Zhang, Hathai Tanta-ngai, HangBong Kang, Hsin-Chang Yang, Hongtao Du, Hazem Elbakry, Hao Mei, Zhao L, Yang Yun, Michael Hild, Heajo Kang, Hongjie Xing, Hailli Wang, Hoh In, Peng Bai, Hong-Ming Wang, Hongxing Bai, Hongyu Liu, Weiyan Hou, Huaping Liu, H.Q. Wang, Hyungsuck Cho, Hsun-Li Chang, Hua Zhang, Xia Huang, Hui Chen, Huiqing Liu, Heeun Park, Hong-Wei Ji, Haixian Wang, Hoyeal Kwon, H.Y. Shen, Jonghyuk Park, Turgay Ibrikci, Mary Martin, Pei-Chann Chang, Shouyi Yang, Xiaomin Mu, Melanie Ashley, Ismail Altas, Muhammad Usman Ilyas, Indrani Kar, Jinghui Zhong, Ian Mack, Il-Young Moon, J.X. Peng , Jochen Till, Jian Wang, Quan Xue, James Govindhasamy, José Andrés Moreno Pérez, Jorge Tavares, S. K. Jayaweera, Su Jay, Jeanne Chen, Jim Harkin, Yongji Jia, Li Jia, Zhao-Hui Jiang, Gangyi Jiang, Zhenran Jiang, Jianjun Ran, Jiankun Hu, Qing-Shan Jia, Hong Guo, Jin Liu, Jinling Liang, Jin Wu, Jing Jie, Jinkyung Ryeu, Jing Liu, Jiming Chen, Jiann-Ming Wu, James Niblock, Jianguo Zhu, Joel Pitt, Joe Zhu, John Thompson, Mingguang Shi, Joaquin Peralta, Si Bao Chen, Tinglong Pan, Juan Ramón González González, JingRu Zhang, Jianliang Tang, Joaquin Torres, Junaid Akhtar, Ratthachat Chatpatanasiri, Junpeng Yuan, Jun Zhang, Jianyong Sun, Junying Gan, Jyh-Tyng Yau, Junying Zhang, Jiayin Zhou, Karen Rosemary McMenemy, Kai Yu, Akimoto Kamiya, Xin Kang, Ya-Li Ji, GuoShiang Lin, Muhammad Khurram, Kevin Curran, Karl Neuhold, Kyongnam Jeon, Kunikazu Kobayashi, Nagahisa Kogawa, Fanwei Kong, Kyu-Sik Park, Lily D. Li, Lara Giordano, Laxmidhar Behera, Luca Cernuzzi, Luis Almeida, Agostino Lecci, Yan Zuo, Lei Li, Alberto Leva, Feng Liang, Bin Li, Jinmei Liao, Liang Tang, Bo Lee, Chuandong Li, Lidija Janezic, Jian Li, Jiang-Hai Li, Jianxun Li, Limei Song, Ping Li, Jie Liu, Fei Liu, Jianfeng Liu, Jianwei Liu, Jihong Liu, Lin Liu, Manxi Liu, Yi Liu, Xiaoou Li, Zhu Li, Kun-hong Liu, Li Min Cui, Lidan Miao, Long Cheng , Huaizhong Zhang, Marco Lovera, Liam Maguire, Liping Liu, Liping Zhang, Feng Lu, Luo Xiaobin, Xin-ping Xie, Wanlong Li, Liwei Yang, Xinrui Liu, Xiao Wei Li, Ying Li, Yongquan Liang, Yang Bai, Margherita Bresco, Mingxing Hu, Ming Li, Runnian Ma, Meta-Montero Manrique, Zheng Gao, Mingyi Mao, Mario Vigliar, Marios Savvides, Masahiro Takatsuka, Matevz Dular, Mathias Lux, Mutlu Avci, Zhifeng Hao, Zhifeng Hao, Ming-Bin Li, Tao Mei, Carlo Meloni, Gennaro Miele, Mike Watts, Ming Yang, Jia Ma, Myong K. Jeong, Michael Watts, Markus Koch, Markus Koch, Mario Koeppen, Mark Kröll, Hui Wang, Haigeng Luo, Malrey Lee, Tiedong Ma, Mingqiang Yang, Yang Ming, Rick Chang, Nihat Adar, Natalie Schellenberg, Naveed Iqbal, Nur Bekiroglu, Jinsong Hu, Nesan Aluha, Nesan K Aluha, Natascha Esau, Yanhong Luo, N.H. Siddique, Rui Nian, Kai Nickel, Nihat Adar, Ben Niu, Yifeng Niu, Nizar Tayem, Nanlin Jin, Hong-Wei Ji, Dongjun Yu, Norton Abrew, Ronghua Yao, Marco Moreno-Armendariz, Osman Kaan Erol, Oh Kyu Kwon, Ahmet Onat, Pawel Herman, Peter Hung, Ping Sun, Parag Kulkarni, Patrick Connally, Paul Gillard, Yehu Shen,

Organization

XI

Paul Conilione, Pi-Chung Wang, Panfeng Huang, Peter Hung, Massimo Pica Ciamarra, Ping Fang, Pingkang Li, Peiming Bao, Pedro Melo-Pinto, Maria Prandini, Serguei Primak, Peter Scheir, Shaoning Pang, Qian Chen, Qinghao Rong, QingXiang Wu, Quanbing Zhang, Qifu Fan, Qian Liu, Qinglai Wei, Shiqun Yin, Jianlong Qiu, Qingshan Liu, Quang Ha, SangWoon Lee , Huaijing Qu, Quanxiong Zhou , Qingxian Gong, Qingyuan He, M.K.M. Rahman, Fengyuan Ren, Guang Ren, Qingsheng Ren, Wei Zhang, Rasoul Milasi, Rasoul Milasi, Roberto Amato, Roberto Marmo, P. Chen, Roderick Bloem, Hai-Jun Rong, Ron Von Schyndel, Robin Ferguson, Runhe Huang, Rui Zhang, Robin Ferguson, Simon Johnston, Sina Rezvani, Siang Yew Chong, Cristiano Cucco, Dar-Ying Jan, Sonya Coleman, Samuel Rodman, Sancho SalcedoSanz, Sangyiel Baik, Sangmin Lee, Savitri Bevinakoppa, Chengyi Sun, Hua Li, Seamus McLoone, Sean McLoone, Shafayat Abrar, Aamir Shahzad, Shangmin Luan, Xiaowei Shao, Shen Yanxia, Zhen Shen, Seung Ho Hong, Hayaru Shouno, Shujuan Li, Si Eng Ling, Anonymous, Shiliang Guo, Guiyu Feng, Serafin Martinez Jaramillo, Sangwoo Moon, Xuefeng Liu, Yinglei Song, Songul Albayrak, Shwu-Ping Guo, Chunyan Zhang, Sheng Chen, Qiankun Song, Seok-soo Kim, Antonino Staiano, Steven Su, Sitao Wu, Lei Huang, Feng Su, Jie Su, Sukree Sinthupinyo, Sulan Zhai, Jin Sun, Limin Sun, Zengshun Zhao, Tao Sun, Wenhong Sun, Yonghui Sun, Supakpong Jinarat, Srinivas Rao Vadali, Sven Meyer zu Eissen, Xiaohong Su, Xinghua Sun, Zongying Shi, Tony Abou-Assaleh, Youngsu Park, Tai Yang, Yeongtak Jo, Chunming Tang, Jiufei Tang, Taizhe Tan, Tao Xu, Liang Tao, Xiaofeng Tao, Weidong Xu, Yueh-Tsun Chang, Fang Wang, Timo Lindemann, Tina Yu, Ting Hu, Tung-Kuan Liu, Tianming Liu, Tin Lay Nwe, Thomas Neidhart, Tony Chan, Toon Calders, Yi Wang, Thao Tran, Kyungjin Hong, Tariq Qureshi, Tung-Shou Chen, Tsz Kin Tsui, Tiantian Sun, Guoyu Tu, Tulay Yildirim, Dandan Zhang, Xuqing Tang, Yuangang Tang, Uday Chakraborty, Luciana Cariello, Vasily Aristarkhov, Jose-Luis Verdegay, Vijanth Sagayan Asirvadam, Vincent Lee, Markus Vincze, Duo Chen, Viktoria Pammer, Vedran Sabol, Wajeeha Akram, Cao Wang , Xutao Wang, Winlen Wang, Zhuang Znuang, Feng Wang, Haifeng Wang, Le Wang, Wang Linkun, Meng Wang, Rongbo Wang, Xin Wang, Xue Wang, Yan-Feng Wang, Yong Wang, Yongcai Wang, Yongquan Wang, Xu-Qin Li, Wenbin Liu, Wudai Liao, Weidong Zhou, Wei Li, Wei Zhang, Wei Liang, Weiwei Zhang, Wen Xu, Wenbing Yao, Xiaojun Ban, Fengge Wu, Weihua Mao, Shaoming Li, Qing Wu, Jie Wang, Wei Jiang, W Jiang, Wolfgang Kienreich, Linshan Wang, Wasif Naeem, Worasait Suwannik, Wolfgang Slany, Shijun Wang , Wooyoung Soh, Teng Wang, Takashi Kuremoto, Hanguang Wu, Licheng Wu, Xugang Wang, Xiaopei Wu, ZhengDao Zhang, Wei Yen, Yan-Guo Wang, Daoud Ait-Kadi, Xiaolin Hu, Xiaoli Li, Xun Wang, Xingqi Wang, Yong Feng, Xiucui Guan, Xiao-Dong Li, Xingfa Shen, Xuemin Hong, Xiaodi Huang, Xi Yang, Li Xia, Zhiyu Xiang, Xiaodong Li, Xiaoguang Zhao, Xiaoling Wang, Min Xiao, Xiaonan Wu, Xiaosi Zhan, Lei Xie, Guangming Xie, Xiuqing Wang, Xiwen Zhang, XueJun Li, Xiaojun Zong, Xie Linbo, Xiaolin Li, Xin Ma, Xiangqian Wu, Xiangrong Liu, Fei Xing, Xu Shuzheng, Xudong Xie, Bindang Xue, Xuelong Li, Zhanao Xue, Xun Kruger, Xunxian Wang, Xusheng Wei, Yi Xu, Xiaowei Yang, Xiaoying Wang, Xiaoyan Sun, YingLiang Ma, Yong Xu, Jongpil Yang, Lei Yang, Yang Tian, Zhi Yang, Yao Qian, Chao-bo Yan, Shiren Ye,

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Organization

Yong Fang, Yanfei Wang, Young-Gun Jang, Yuehui Chen, Yuh-Jyh Hu, Yingsong Hu, Zuoyou Yin, Yipan Deng, Yugang Jiang, Jianwei Yang, Yujie Zheng, Ykung Chen, Yan-Kwang Chen, Ye Mei, Yongki Min, Yongqing Yang, Yong Wu, Yongzheng Zhang, Yiping Cheng, Yongpan Liu, Yanqiu Bi, Shengbao Yao, Yongsheng Ding, Haodi Yuan, Liang Yuan, Qingyuan He, Mei Yu, Yunchu Zhang, Yu Shi, Wenwu Yu, Yu Wen, Younghwan Lee, Ming Kong, Yingyue Xu, Xin Yuan, Xing Yang, Yan Zhou, Yizhong Wang, Zanchao Zhang, Ji Zhicheng, Zheng Du, Hai Ying Zhang, An Zhang, Qiang Zhang, Shanwen Zhang, Shanwen Zhang, Zhang Tao, Yue Zhao, R.J. Zhao, Li Zhao, Ming Zhao, Yan Zhao, Bojin Zheng, Haiyong Zheng, Hong Zheng, Zhengyou Wang, Zhongjie Zhu, Shangping Zhong, Xiaobo Zhou, Lijian Zhou, Lei Zhu, Lin Zhu, Weihua Zhu, Wumei Zhu, Zhihong Yao, Yumin Zhang, Ziyuan Huang, Chengqing Li, Z. Liu, Zaiqing Nie, Jiebin Zong, Zunshui Cheng, Zhongsheng Wang, Yin Zhixiang, Zhenyu He, Yisheng Zhong, Tso-Chung Lee, Takashi Kuremoto Tao Jianhua, Liu Wenjue, Pan Cunhong, Li Shi, Xing Hongjie, Yang Shuanghong, Wang Yong, Zhang Hua, Ma Jianchun, Li Xiaocui, Peng Changping, Qi Rui, Guozheng Li, Hui Liu, Yongsheng Ding, Xiaojun Liu, Qinhua Huang

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Table of Contents

Blind Source Separation A Unified Framework of Morphological Associative Memories Naiqin Feng, Yuhui Qiu, Fang Wang, Yuqiang Sun . . . . . . . . . . . . . . . . .

1

A New Speech Denoising Method Based on WPD-ICA Feature Extraction Qinghua Huang, Jie Yang, Yue Zhou . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

An Efficient Algorithm for Blind Separation of Binary Symmetrical Signals Wenbo Xia, Beihai Tan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

21

A New Blind Source Separation Algorithm Based on Second-Order Statistics for TITO ZhenLi Wang, XiongWei Zhang, TieYong Cao . . . . . . . . . . . . . . . . . . . .

29

A New Step-Adaptive Natural Gradient Algorithm for Blind Source Separation Huan Tao, Jian-yun Zhang, Lin Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

An Efficient Blind SIMO Channel Identification Algorithm Via Eigenvalue Decomposition Min Shi, Qingming Yi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

41

An Improved Independent Component Analysis Algorithm and Its Application in Preprocessing of Bearing Sounds Guangrui Wen, Liangsheng Qu, Xining Zhang . . . . . . . . . . . . . . . . . . . . .

48

Array Signal MP Decomposition and Its Preliminary Applications to DOA Estimation Jianying Wang, Lei Chen, Zhongke Yin . . . . . . . . . . . . . . . . . . . . . . . . . .

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Mixture Matrix Identification of Underdetermined Blind Source Separation Based on Plane Clustering Algorithm Beihai Tan, Yuli Fu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60

Non-linear Blind Source Separation Using Constrained Genetic Algorithm Zuyuan Yang, Yongle Wan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Intelligent Sensor Networks A Distributed Wavelet-Based Image Coding for Wireless Sensor Networks Hui Dong, Jiangang Lu, Youxian Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

Development of Secure Event Service for Ubiquitous Computing Younglok Lee, Seungyong Lee, Hyunghyo Lee . . . . . . . . . . . . . . . . . . . . . .

83

Energy Efficient Connectivity Maintenance in Wireless Sensor Networks Yanxiang He, Yuanyuan Zeng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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The Critical Speeds and Radii for Coverage in Sensor Networks Chuanzhi Zang, Wei Liang, Haibin Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 A Distributed QoS Control Schema for Wireless Sensor Networks Jin Wu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 A Framework of In-Situ Sensor Data Processing System for Context Awareness Young Jin Jung, Yang Koo Lee, Dong Gyu Lee, Mi Park, Keun Ho Ryu, Hak Cheol Kim, Kyung Ok Kim . . . . . . . . . . . . . . . . . . . . 124 A Mathematical Model for Energy-Efficient Coverage and Detection in Wireless Sensor Networks Xiaodong Wang, Huaping Dai, Zhi Wang, Youxian Sun . . . . . . . . . . . . . 130 A Method of Controlling Packet Transmission Rate with Fuzzy Logic for Ad Hoc Networks Kyung-Bae Chang, Tae-Hwan Son, Gwi-Tae Park . . . . . . . . . . . . . . . . . . 138 A Novel Algorithm for Doppler Frequency Rate Estimation of Spaceborne Synthetic Aperture Radar Shiqi Huang, Daizhi Liu, Liang Chen, Yunfeng Liu . . . . . . . . . . . . . . . . . 144 A Novel Genetic Algorithm to Optimize QoS Multicast Routing Guangbin Bao, Zhanting Yuan, Qiuyu Zhang, Xuhui Chen . . . . . . . . . . 150 A Probe for the Performance of Low-Rate Wireless Personal Area Networks Shuqin Ren, Khin Mi Mi Aung, Jong Sou Park . . . . . . . . . . . . . . . . . . . . 158 AG-NC: An Automatic Generation Technique of Network Components for Dynamic Network Management Eun Hee Kim, Myung Jin Lee, Keun Ho Ryu . . . . . . . . . . . . . . . . . . . . . . 165

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Clustering Algorithm in Wireless Sensor Networks Using Transmit Power Control and Soft Computing Kyung-Bae Chang, Young-Bae Kong, Gwi-Tae Park . . . . . . . . . . . . . . . . 171 Discriminating Fire Detection Via Support Vector Machines Heshou Wang, Shuibo Zheng, Chi Chen, Wenbin Yang, Lei Wu, Xin Cheng, Minrui Fei, Chuanping Hu . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 Dynamic Deployment Optimization in Wireless Sensor Networks Xue Wang, Sheng Wang, Junjie Ma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 Energy-Efficient Aggregation Control for Mobile Sensor Networks Liang Yuan, Weidong Chen, Yugeng Xi . . . . . . . . . . . . . . . . . . . . . . . . . . 188 Intelligent MAC Protocol for Efficient Support of Multiple SOPs in UWB-Based Sensor Networks Peng Gong, Peng Xue, Duk Kyung Kim . . . . . . . . . . . . . . . . . . . . . . . . . . 194 Topology Control in Wireless Sensor Networks with Interference Consideration Yanxiang He, Yuanyuan Zeng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

Intelligent Control and Automation Adaptive Depth Control for Autonomous Underwater Vehicles Based on Feedforward Neural Networks Yang Shi, Weiqi Qian, Weisheng Yan, Jun Li . . . . . . . . . . . . . . . . . . . . . 207 Adaptive Fuzzy Sliding-Mode Control for Non-minimum Phase Overload System of Missile Yongping Bao, Wenchao Du, Daquan Tang, Xiuzhen Yang, Jinyong Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 An Improved Genetic & Ant Colony Optimization Algorithm and Its Applications Tiaoping Fu, Yushu Liu, Jiguo Zeng, Jianhua Chen . . . . . . . . . . . . . . . . 229 Application of Adaptive Disturbance Canceling to Attitude Control of Flexible Satellite Ya-qiu Liu, Jun Cao, Wen-long Song . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Application of Resource Allocating Network and Particle Swarm Optimization to ALS Jih-Gau Juang, Bo-Shian Lin, Feng-Chu Lin . . . . . . . . . . . . . . . . . . . . . . 252

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Case-Based Modeling of the Laminar Cooling Process in a Hot Rolling Mill Minghao Tan, Shujiang Li, Jinxiang Pian, Tianyou Chai . . . . . . . . . . . 264 Fast Mesh Simplification Algorithm Based on Edge Collapse Shixiang Jia, Xinting Tang, Hui Pan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Hierarchical Multiple Models Adaptive Feedforward Decoupling Controller Applied to Wind Tunnel System Xin Wang, Hui Yang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Intelligent Backstepping Control for Chaotic Systems Using Self-Growing Fuzzy Neural Network Chih-Min Lin, Chun-Fei Hsu, I-Fang Chung . . . . . . . . . . . . . . . . . . . . . . 299 Modeling of Rainfall-Runoff Relationship at the Semi-arid Small Catchments Using Artificial Neural Networks Mustafa Tombul, Ersin O˘gul . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 A Novel Multi-agent Based Complex Process Control System and Its Application Yi-Nan Guo, Jian Cheng, Dun-wei Gong, Jian-hua Zhang . . . . . . . . . . 319 Neural Network Based Soft Switching Control of a Single Phase AC Voltage Restorer Kayhan Gulez, Tarık Veli Mumcu, Ibrahim Aliskan . . . . . . . . . . . . . . . . . 331 Neural Network Training Using PSO Algorithm in ATM Traffic Control Yuan-wei Jing, Tao Ren, Yu-cheng Zhou . . . . . . . . . . . . . . . . . . . . . . . . . . 341 Parameter Identification of Dynamical Systems Based on Improved Particle Swarm Optimization Meiying Ye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 Petri Net Modeling Method to Scheduling Problem of Holonic Manufacturing System (HMS) and Its Solution with a Hybrid PSO Algorithm Fuqing Zhao, Qiuyu Zhang, Yahong Yang . . . . . . . . . . . . . . . . . . . . . . . . . 361 Real-Time Motion Planning by Sampling Points on Obstacles’ Surfaces Towards HRI Hong Liu, Xuezhi Deng, Hongbin Zha, Keming Chen . . . . . . . . . . . . . . . 373 Sliding Mode Control Based on Fuzzy Neural Network for Missile Electro-hydraulic Servo Mechanism Chunlai Yu, Hualong Xu, Yunfeng Liu, Shiqi Huang . . . . . . . . . . . . . . . . 385

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Stability Analysis of Network Data Flow Control for Dynamic Link Capacity Case Yuequan Yang, Yaqin Li, Min Tan, Jianqiang Yi, John T. Wen, Xuewu Guo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395 Matrix Measure Stability Criteria for a Class of Switched Linear Systems Hongbo Zou, Hongye Su, Jian Chu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 Study on FOG-SINS/GPS Integrated Attitude Determination System Using Adaptive Kalman Filter Xiyuan Chen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 Supervisory Control for Rotary Kiln Temperature Based on Reinforcement Learning Xiaojie Zhou, Heng Yue, Tianyou Chai, Binhao Fang . . . . . . . . . . . . . . 428 A Data Reorganization Algorithm to Improve Transmission Efficiency in CAN Networks Jung-Ki Choi, Sungyun Jung, Kwang-Ryul Baek . . . . . . . . . . . . . . . . . . . 438 A Neural Network Approach to QoS Management in Networked Control Systems over Ethernet Wenhong Zhao, Feng Xia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 A Novel Micro-positioning Controller for Piezoelectric Actuators Van-Tsai Liu, Chun-Liang Lin, Hsiang-Chan Huang, Zi-Jie Jian . . . . 450 A Study on the Robust Control of an Inverted Pendulum Using Discrete Sliding-Mode Control J.Y. Yang, H.J. Lee, J.H. Hwang, N.K. Lee, H.W. Lee, G.A. Lee, S.M. Bae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456 A VRC Algorithm Based on Fuzzy Immune PID-Smith Ling He, Yu-cheng Zhou, Yuan-wei Jing, Hai-yu Zhu . . . . . . . . . . . . . . . 463 Absolute Stability of State Feedback Time-Delay Systems Hanlin He, Zhongsheng Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 Adaptive Fuzzy Control of Nonlinear Systems Based on Terminal Sliding Mode Shuanghe Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 Simulation of Air Fuel Ratio Control Using Radius Basis Function Neural Network Zhixiang Hou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

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An Experimental Study on Multi-mode Control Methods of Flexible Structure Using PZT Actuator and Modified IMSC Algorithm W.S. Lee, H.J. Lee, J.H. Hwang, N.K. Lee, H.W. Lee, G.A. Lee, S.M. Bae, D.M. Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 Applications of Computational Verbs to Image Processing of RoboCup Small-Size Robots Wanmi Chen, Yanqin Wei, Minrui Fei, Huosheng Hu . . . . . . . . . . . . . . 494 Auto-Disturbance-Rejection Controller Design Based on RBF Neural Networks Yongli Shi, Chaozhen Hou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500 CASTmiddleware : Security Middleware of Context-Awareness Simulation Toolkit for Ubiquitous Computing Research Environment InSu Kim, YoungLok Lee, HyungHyo Lee . . . . . . . . . . . . . . . . . . . . . . . . . 506 Cybernation Process of Lidar System Detecting the Atmospheric Carbon Dioxide Yue-Feng Zhao, Yin-Chao Zhang, Pei-Tao Zhao, Jia Su, Xin Fang, Jun Xie, Kai-feng Qv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 Design of a Robust Output Feedback Controller for Robot Manipulators Using Visual Feedback Min Seok Jie, Chin Su Kim, Kang Woong Lee . . . . . . . . . . . . . . . . . . . . . 520 Fuzzy Sliding Mode Controller with RBF Neural Network for Robotic Manipulator Trajectory Tracking Ayca Gokhan Ak, Galip Cansever . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527 Hybrid Fuzzy Neural Network Control for Complex Industrial Process Qingyu Yang, Lincang Ju, Sibo Ge, Ren Shi, Yuanli Cai . . . . . . . . . . . . 533 Intelligent Vehicle Control by Optimal Selection of Image Data M. Junaid Khan, Danya Yao, Juan Zhao, Shuning Wang, Yu Cai . . . . 539 Rule-Based Expert System for Selecting Scene Matching Area Guozhong Zhang, Lincheng Shen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 Multi-channel Measurement of Transmissivity of Smoke Tao Shen, Jian-she Song . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554 Multi-Model Predictive Control Based on a New Clustering Modeling Method Luwen zhou, Lifang zhou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 559

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Neural Network-Based an Adaptive Discrete-Time Global Sliding Mode Control Scheme Zhenyan Wang, Jinggang Zhang, Zhimei Chen, Yanzhao He . . . . . . . . . 565 Real Coded Genetic Algorithm for Optimizing Fuzzy Logic Control of Greenhouse Microclimate Fang Xu, Jiaoliao Chen, Libin Zhang, Hongwu Zhan . . . . . . . . . . . . . . . 571 Research and Implementation on the Mobile Intelligent Controller for Home Automation Service Jonghwa Choi, Dongkyoo Shin, Dongil Shin . . . . . . . . . . . . . . . . . . . . . . . 578 Sampled-Data Systems with Quantization and Slowly Varying Inputs Ge Guo, Huipu Xu, Yuan Tian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584 Set-Stabilization with Occasional Feedback Ge Guo, Jigong Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590 Spatial Reasoning for Collision Detection and Hardware Implementation Chirag Nepal, Seung Woo Nam, Dohyung Kim, Kyungsook Han . . . . . . 596 Stability Criteria for Switched Linear Systems Hongbo Zou, Hongye Su, Jian Chu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602 Suppressing of Chaotic State Based on Delay Feedback Wenli Zhao, Linze Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 608 Vector Controlled PMSM Drive Based on Adaptive Neuro-fuzzy Speed Controller Xianqing Cao, Liping Fan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 616

Data Fusion, Knowledge Discovery and Data Mining “Intelligent Yardstick”, an Approach of Ranking to Filter Non-promising Attributes from Schema in Data Mining Process Mohammad M. Hassan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623 A Local Computing-Based Hierarchical Clustering Algorithm Building Density Trees Wei-di Dai, Jie-Liu, Da-yi Zhao, Zhen-hua Liu, Jun-xian Zhang, Pi-lian He . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633 Support Vector Clustering and Type-Entropy Based Joint De-interleaving/recognition System of Radar Pulse Sequence Qiang Guo, Zheng Li, Xingzhou Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . 642

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Classification Rule Mining Based on Ant Colony Optimization Algorithm Peng Jin, Yunlong Zhu, Kunyuan Hu, Sufen Li . . . . . . . . . . . . . . . . . . . . 654 Dynamic Feature Selection in Text Classification Son Doan, Susumu Horiguchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664 Knowledge Verification of Active Rule-Based Systems Lorena Chavarr´ıa-B´ aez, Xiaoou Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 676 Lattice-Based Classification with Mixed Numeric and Nominal Data Wei Hu, Huanye Sheng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 688 Learning to Semantically Classify Email Messages Eric Jiang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700 Optimizing the Hyper-parameters for SVM by Combining Evolution Strategies with a Grid Search Ruiming Liu, Erqi Liu, Jie Yang, Ming Li, Fanglin Wang . . . . . . . . . . . 712 Prediction of Sinter Burn-Through Point Based on Support Vector Machines Xiaofeng Wu, Minrui Fei, Heshou Wang, Shuibo Zheng . . . . . . . . . . . . . 722 Under-Sampling Approaches for Improving Prediction of the Minority Class in an Imbalanced Dataset Show-Jane Yen, Yue-Shi Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 Utilizing a Hierarchical Method to Deal with Uncertainty in Context-Aware Systems Donghai Guan, Weiwei Yuan, Mohammad A.U. Khan, Youngkoo Lee, Sungy-oung Lee, Sangman Han . . . . . . . . . . . . . . . . . . . . . 741 A Multi-focus Image Fusion Method Based on Image Information Features and the Artificial Neural Networks Lijian Zhou, Guangrong Ji, Changjiang Shi, Chen Feng, Rui Nian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747 A Multilayer Topic-Map-Based Model Used for Document Resources Organization Jiangning Wu, Haiyan Tian, Guangfei Yang . . . . . . . . . . . . . . . . . . . . . . 753 A New Clustering Algorithm for Time Series Analysis Jianping Zeng, Donghui Guo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759

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A New IHS-WT Image Fusion Method Based on Weighted Regional Features Jin Wu, Bingkun Yin, Jian Liu, Jinwen Tian . . . . . . . . . . . . . . . . . . . . . 765 A Novel Algorithm of Mining Multidimensional Association Rules WanXin Xu, RuJing Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771 A Novel Discretizer for Knowledge Discovery Based on Multiknowledge Approaches QingXiang Wu, Girijesh Prasad, TM McGinnity, David Bell, ShaoChun Zhong, Jiwen Guan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778 A Novel Neural Network for Sensor Fusion Applied to Wood Growth Ring Moisture Measurement Mingbao Li, Shiqiang Zheng, Jun Hua . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784 A Novel Reduction Algorithm Based Decomposition and Merging Strategy Feng Hu, Xinghua Fan, Simon.X Yang, Chaohai Tao . . . . . . . . . . . . . . . 790 A Pattern Distance-Based Evolutionary Approach to Time Series Segmentation Jingwen Yu, Jian Yin, Duanning Zhou, Jun Zhang . . . . . . . . . . . . . . . . . 797 A Quality Prediction Method of Injection Molding Processes Using Sub-stage PCA-SI XiaoPing Guo, FuLi Wang, MingXing Jia . . . . . . . . . . . . . . . . . . . . . . . . 803 A Robust Algorithm for Watermark Numeric Relational Databases Xinchun Cui, Xiaolin Qin, Gang Sheng, Jiping Zheng . . . . . . . . . . . . . . 810 A Study on the RAP Approach and Its Application Jian Cao, Gengui Zhou, Feng Tang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816 An Analytical Model for Web Prefetching Lei Shi, Lin Wei, Zhimin Gu, Yingjie Han, Yun Shi . . . . . . . . . . . . . . . 822 An Optimal Interval for Computing Course and Ship Speed in Marine Gravity Survey Based on Approximate Reasoning Lihua Zhang, Chong Fang, Xiaosan Ge, Yilong Li . . . . . . . . . . . . . . . . . 828 Application of Association Rules in Education Sylvia Encheva, Sharil Tumin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834

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Associative Neighborhood According to Representative Attribute for Performing Collaborative Filtering Kyung-Yong Jung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 839 Benchmarking a Recurrent Linear GP Model on Prediction and Control Problems Xiao Luo, Malcolm Heywood, A. Nur Zincir-Heywood . . . . . . . . . . . . . . 845 Cognitive Computing in Intelligent Medical Pattern Recognition Systems Lidia Ogiela, Ryszard Tadeusiewicz, Marek R. Ogiela . . . . . . . . . . . . . . . 851 Data Mining-Based Analysis on Relationship Between Academic Achievement and Learning Methods During Vacation Hea-Suk Kim, Yang-Sae Moon, Jinho Kim, Woong-Kee Loh . . . . . . . . . 857 Database and Comparative Identification of Prophages K.V. Srividhya, Geeta V Rao, Raghavenderan L, Preeti Mehta, Jaime Prilusky, Sankarnarayanan Manicka, Joel L. Sussman, S Krishnaswamy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 863 Dynamic Multidimensional Assignment Algorithm for Multisensor Information Fusion System Yi Xiao, Guan Xin, He You . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869 Future Location Prediction of Moving Objects Based on Movement Rules Vu Thi Hong Nhan, Keun Ho Ryu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875 Fuzzy Information Fusion for Hypergame Outcome Preference Perception Yexin Song, Zhijun Li, Yongqiang Chen . . . . . . . . . . . . . . . . . . . . . . . . . . 882 Image Identification System Using MPEG-7 Descriptors Wonil Kim, Sanggil Kang, Juyoung Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . 888 Improved Text Mining Methods to Answer Chinese E-mails Automatically Yingjie Lv, Qiang Ye, Yijun Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894 Improvement on ARC-BC Algorithm in Text Classification Method Yu Zhao, Weitong Huang, Yuchang Lu . . . . . . . . . . . . . . . . . . . . . . . . . . . 903 Improving Structure Damage Identification by Using ICA-ANN Based Sensitivity Analysis Bo Han, Lishan Kang, Yuping Chen, Huazhu Song . . . . . . . . . . . . . . . . . 909

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Inferring Certification Metrics of Package Software Using Bayesian Belief Network Chongwon Lee, Byungjeong Lee, Jaewon Oh, Chisu Wu . . . . . . . . . . . . . 915 Influence Analysis in Linear Mixed Models Yu Fei, Jianxin Pan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921 Knowledge Reduction in Set-Valued Decision Information Systems Hong Wang, Wen-Xiu Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927 Modeling and Fusion Estimation of Dynamic Multiscale System Based on M-Band Wavelet and State Space Projection Peiling Cui, Guizeng Wang, Quan Pan . . . . . . . . . . . . . . . . . . . . . . . . . . . 933 Multiscale Feature Extraction for Time Series Classification with Hybrid Feature Selection Hui Zhang, Mao-Song Lin, Wei Huang, Saori Kawasaki, Tu Bao Ho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 939 Network Traffic Classification Using Rough Set Theory and Genetic Algorithm Ning Li, Zilong Chen, Gang Zhou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945 Optimization Feature Compression and FNN Realization Shifei Ding, Yuncheng Wang, Zhongzhi Shi, Fengxiang Jin . . . . . . . . . . 951 Paleolithic Stone Relic Analysis Using ARD Bum Ju Lee, Heon Gyu Lee, Keun Ho Ryu, Moon Haeng Huh, Jong Yun Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957 Pei-Radman Fusion Estimation Algorithm for Multisensor System Applied in State Monitoring Xue-bo Jin, You-xian Sun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 963 Privacy Preserving Association Rules Mining Based on Secure Two-Party Computation Weimin Ouyang, Qinhua Huang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 969 QuickBird Panchromatic and Multi-Spectral Image Fusion Using Wavelet Packet Transform Wenjuan Zhang, Jiayin Kang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 976 Satisfaction-Based Selection of XML Documents Sergio Andreozzi, Paolo Ciancarini, Danilo Montesi, Rocco Moretti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 982

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Special Session on Smart and Intelligent Home Technology An Adaptive Error Detection-Recovery QOS for Intelligent Context-Awareness: AEDRQ Eung Nam Ko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 990 An Efficient Method to Find a Shortest Path for a Car-Like Robot Gyusang Cho, Jinkyung Ryeu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1000 An Intelligent QOS Model for Adaptive Concurrency Control Running on Ubiquitous Computing Environments Eung Nam Ko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1012 Analysis and Extension of S/Key-Based Authentication Schemes for Digital Home Networks Ilsun You . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1022 Anonymous Voting Scheme on Multicast Dong-Myung Shin, Hee-Un Park, Woo-Jae Won, Jae-Il Lee . . . . . . . . . 1034 CAST: Design and Implementation of Secure Context-Awareness Simulation Toolkit for Ubiquitous Computing Research Environment InSu Kim, YoungLok Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1040 Support Vector Machine for String Vectors Malrey Lee, Taeho Jo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1056 RHDP-Scheme for RFID’s Efficiency Improvement on the Ubiquitous Computing Bok Yong Choi, Deok Gyu Lee, Jong Hyuk Park, Kwang Nam Choi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1068 A Study on the Improvement of Soldiers Training System for Using Ubiquitous Sensor Network Seoksoo Kim, Soongohn Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1078 Definition of Security Requirement Items and Its Process to Security and Progress Management Eun Ser Lee, Sun-myoung Hwang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1084 Design and Implementation of Web Security Access Control System for Semantic Web Ontology Eun-ser Lee, Sun-myoung Hwang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1090

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Designing of Patient-Focused Mobile Agent in the Ubiquitous Medical Examination System Jaekoo Song, Seoksoo Kim, Soongohn Kim . . . . . . . . . . . . . . . . . . . . . . . . 1096 Mobile Robot Path Planning by Circular Scan Code and Circular Distance Transform Method Gyusang Cho, Jinkyung Ryeu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1102 Ultrasonic Intruder Detection System for Home Security Yue-Peng Li, Jun Yang, Xiao-Dong Li, Jing Tian . . . . . . . . . . . . . . . . . 1108 Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1117

A Unified Framework of Morphological Associative Memories Naiqin Feng1,2, Yuhui Qiu2, Fang Wang2, and Yuqiang Sun1 1

College of Computer & Information Technology, Henan Normal University, Xinxiang 453007 2 Faculty of Computer & information Science, South West-China University, Chongqing 400715 [email protected]

Abstract. The morphological neural network models, including morphological associative memories (MAM), fuzzy morphological associative memories (FMAM), enhanced morphological associative memories (EFMAM), etc., are extremely new artificial neural networks. They have many attractive advantages such as unlimited storage capacity, one-short recall speed and good noisetolerance to erosive or dilative noise. Although MAM, FMAM and EFMAM are different and easily distinguishable from each other, they have the same morphological theory base. Therefore in this paper a unified theoretical framework of them is presented. The significance of the framework consists in: (1) It can help us find some new methods, definitions and theorems for morphological neural networks; (2) We have a deeper understanding of MAM, FMAM and EFMAM while having the unified theoretical framework.

1 Introduction The theory of artificial neural networks has been successful applied to a wide variety of pattern recognition problems [3,4]. In this theory, the first step in computing the next state of a neuron or in performing the next layer neural-network computation involves the linear operation of multiplying neural values by their synaptic strengths and adding the results. A nonlinear activation function usually follows the linear operation in order to provide for non-linearity of the network and set the next state of the neuron. In recent years, a number of different morphological neural network models and applications have emerged [1,5,8,12,15,16]. First attempts in formulating useful morphological neural networks appeared in [10]. Since then, only a few papers involving morphological neural networks have appeared. Suarez-Araujo applied morphological neural networks to compute homothetic auditory and visual invariants [2]. Davidson employed morphological neural networks in order to solve template identification and target classification problems [9], [11]. All of these researchers devised multi-layer morphological neural networks for very specialized applications. A more comprehensive and rigorous basis for computing with morphological neural networks appeared in [6] where it was shown that morphological neural networks are capable of solving any conventional computational problem. In 1998, Ritter et al. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1 – 11, 2006. © Springer-Verlag Berlin Heidelberg 2006

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proposed the concept of morphological associative memories (MAM) and the concept of morphological auto-associative memories (auto-MAM) [7], which constitute a class of networks not previously discussed in detail. MAM is based on the algebraic lattice structure ( R, ∧, ∨ , + ) or morphological operations. MAM behaves more like human associative memories than the traditional semilinear models such as the Hopfield net. Once a pattern has been memorized, recall is instantaneous when the MAM is presented with the pattern. In the absence of noise, an auto-MAM will always provide perfect recall for any number of patterns programmed into its memory. The auto-MAM MXX is extremely robust in recalling patterns that are distorted due to dilative changes, while auto-MAM WXX is extremely robust in recalling patterns that are distorted due to erosive changes. In 2003, Wang and Chen presented the model of fuzzy morphological associative memories (FMAM). Originated from the basic ideas of MAM, the FMAM uses two basic morphological operations (∧, ⋅) , (∨ , ⋅) instead of fuzzy operation (∧, ∨ ) in fuzzy associative memory [13]. FMAM solves fuzzy rules memory problem of the MAM. Under certain conditions, FMAM can be viewed as a new encoding way of fuzzy associative memory such that it can embody fuzzy operators and the concepts of fuzzy membership value and fuzzy rules. Both auto-FMAM and auto-MAM have the same attractive advantages, such as unlimited storage capacity, one-shot recall speed and good noise-tolerance to either erosive or dilative noise. However, they suffer from the extreme vulnerability to noise of mixing erosion and dilation, resulting in great degradation on recall performance. To overcome this shortcoming, in 2005, Wang and Chen further presented an enhanced FMAM (EFMAM) based on the empirical kernel map [14]. Although MAM, FMAM and EFMAM are different and easily distinguishable from each other, we think that they have the same theoretical base, i.e. the same morphological base, therefore they can be unified together. This paper tries to establish a unified theoretical framework of MAM, FMAM and EFMAM. The more the thing is abstracted, the deeper the thing is understood. Consequently it is possible that some new methods and theorems are obtained. This is the reason why we research and propose the unified theoretical framework of MAM, FMAM and EFMAM

2 Unified Computational Base of MAM, FMAM and EFMAM Traditional artificial neural network models are specified by the network topology, node characteristics, and training or learning rules. The underlying algebraic system used in these models is the set of real numbers R together with the operations of addition and multiplication and the laws governing these operations. This algebraic system, known as a ring, is commonly denoted by ( R, +, ×) . The basic computations occurring in the morphological network proposed by Ritter et al. are based on the algebraic lattice structure ( R, ∧, ∨ , + ) , where the symbols ∧ and ∨ denote the binary operations of minimum and maximum, respectively, while the basic computations used in FMAM and EFMAM are based on the algebraic lattice structure ( R + , ∧ , ∨ , ⋅) ( R + = (0, ∞ )) .

A Unified Framework of Morphological Associative Memories

3

In unified morphological associative memories (UMAM), the basic computations are based on the algebraic lattice structure (U , ∧ , ∨ , O ) , where U=R, or U = R+; O=

㧙

+, , ⋅ , or /. If U=R and O=+, then (U , ∧ , ∨ , O ) = ( R , ∧ , ∨ , + ) , which is the computational base of MAM; If U=R+ and O= ⋅ , then (U , ∧ , ∨ , O ) = ( R + , ∧ , ∨ , ⋅ ) , which is the computational base of FMAM and EFMAM. Of course, the symbol O or /. also can be other appreciated operators, for example,

㧙

3 Unified Morphological-Norm Operators 3.1 Operators in MAM, FMAM and EFMAM As that described in the preceding section, morphological associative memories are based on the lattice algebra structure ( R, ∧, ∨ , + ) . Suppose we are given a vector pair

Щ

Щ

x=(x1,…, xn)ƍ Rn, , and y=(y1,…,ym) Rm. An associative morphological memory that will recall the vector y when presented the vector x is given by

§ y 1 − x1 щ(-x)ƍ= ¨ # W=yƑ ¨ ¨y −x © m 1

" % "

y1 − x n ·

¸ ¸ y m − x n ¸¹ #

(1)

щx = y as can be verified by the simple computation since W satisfies the equation WƑ § ∨ in= 1 y 1 − x i + x i · ¸ =y # ¨ ¸ n ¨ ∨ i =1 y m − x i + x i ¸ © ¹

Wщ Ƒ x =¨

(2)

W is called the max product of y and x. We also can denote the min product of y and x using operator ш Ƒ like (1) and (2). Similarly, let (x1, y1),…,(xk, yk) be k vector pairs with ȟ ȟ ȟ ȟ xȟ=(x1 ,…, xn )ƍ Rn and yȟ=(y1 ,…, ym )ƍ Rm for ȟ=1,…, k. For a given set of pattern ȟ ȟ associations {(x , y ): ȟ=1,…, k} we define a pair of associated pattern matrices (X,Y), j where X = (x1,", x k ) , Y = (y1 , ", y k ) . Thus, X is of dimension n×k with i, jth entry xi

Щ

Щ

j

and Y is of dimension m×k with i, jth entry yi . With each pair of matrices (X,Y), two natural morphological m×n memories WXY and MXY are defined by k Ƒ ( −x ȟ ) '] and M XY = ∨ k [ y ȟ щ Ƒ ( −x ȟ ) '] . WXY = ∧ ξ =1[ y ȟ ш ξ =1

(3)

Ƒ (-xȟ)ƍ= yȟщ Ƒ (-xȟ)ƍ. It therefore follows from this definition that Obviously, yȟш

WXY”yȟш Ƒ (-xȟ)ƍ=yȟщ Ƒ (-xȟ)ƍ”MXY, ∀ ȟ=1,…, k.

(4)

In view of equations (2) and (3), this last set of inequalities implies that WXYщ Ƒ xȟ”[yȟш Ƒ (-xȟ)ƍ] щ Ƒ xȟ=yȟ= [yȟщ Ƒ (-xȟ)ƍ] ш Ƒ xȟ”MXYш Ƒ xȟ

(5)

∀ ȟ=1,…, k or, equivalently, that

WXY щ Ƒ X ”Y ”MXY ш Ƒ X.

(6)

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Ƒ X =Y, then WXY is called a щ Ƒ -perfect memory for (X, Y); if MXYш Ƒ X= Y, If WXYщ then MXY is called a ш Ƒ -perfect memory for (X, Y). The basic computations used in FMAM and EFMAM are based on the algebraic l l l lattice structure ( R + , ∧, ∨ , ⋅) ( R + = (0, ∞ )) . If the input vector x = ( x1 , " , xn ) ' is

defined in R + , and the output vector y = ( y1 , " , ym ) ' is defined in R + , by using some transformation, for example, exp (x) and exp (y) (acting on each component of n m x, y), the input vectors and output vectors can be transformed into R + and R + , respectively. Set X = (x1,", x k ) , Y = (y1 ,", y k ) , with each pair of matrices (X, Y), two new morphological m × n memories AXY and BXY are as follows: l

n

l

l

m

l −1

l −1

A XY = (∧ lk=1 ( y l ٤ (x ) ) , B XY = (∨ lk=1 ( y l ٤ (x ) ) §1 1 · (x ) = ¨ l , " , l ¸ xn ¹ © x1 l −1

(7)

'

xil > 0, ∀i = 1, " , n

§ ¨ ¨ l − 1 l − 1 y l ٤ (x ) = y l ٤ (x ) = ¨ ¨ ¨ ¨ ©

l

y1 l

x1 #

l

y1

"

l

xn

%

#

l

ym l

x1

l

ym

"

l

xn

(8)

· ¸ ¸ ¸ ¸ ¸ ¸ ¹

(9)

where ш ż and щ ż denote fuzzy composite operation (∧, ⋅) and (∨ , ⋅) often used in fuzzy set theory, respectively. In FMAM and EFMAM, the recall is given by AXYщ ż xl=(

ш y шż(x ) )щżx and B k l=1

l

l -1

l

ш

l XY ż x =(

щ y щż(x ) )шżx k l=1

l

l -1

l

(10)

With analyzing for MAM, FMAM and EFMAM, we can easily see that there exist reversible operators in memory and recall. For MAM, the reversible operators in memory and recall are – and +, respectively; for FMAM and EFMAM, they are / and ×, respectively. We unify them with the following definitions.

3.2 Unified Morphological-Norm Operators Definition 1. For an m×p matrix A and a p×n matrix B with entries from U, the o matrix product C =A щ B, also called the morphological max product norm of A and B, is defined by

cij = ∨ k =1aik Ο bkj = (ai1Οb1 j ) ∨ (ai 2 Οb2 j ) ∨ " ∨ (aip Ο bpj ) . p

o

(11) +

-

Φ

Where, щ is a unified morphological operator, which represents one of the щ , щ , щ , /

and щ . The symbol Ɉ represents a reversible operation, such as +,

㧙, ×, or /.

Definition 2. For an m×p matrix A and a p×n matrix B with entries from U, the o matrix product C =A ш B, also called the morphological min product norm of A and B, is defined by

A Unified Framework of Morphological Associative Memories

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cij = ∧ k =1aik Ο bkj = (ai1Οb1 j ) ∧ (ai 2 Οb2 j ) ∧ " ∧ (aip Ο bpj ) . p

(12)

o

+

Φ

-

Where, ш is a unified morphological operator, which represents one of the ш , ш , ш , /

and ш . The symbol Ɉ represents a reversible operation, such as +,

㧙, ×, or /.

Definition 3. For an m×p matrix A and a p×n matrix B with entries from U and the + + max product C =A щ B, the morphological operator щ is defined by:

cij = ∨ k =1aik + bkj = (ai1 + b1 j ) ∨ (ai 2 + b2 j ) ∨ " ∨ (aip + bpj ) . p

Similarly, we can define the morphological operators

(13)

щ- , Φщ , and щ/ .

Definition 4. For an m×p matrix A and a p×n matrix B with entries from U and the + + min product C =A ш B, the morphological operator ш is defined by:

cij = ∧ k =1aik + bkj = (ai1 + b1 j ) ∧ (ai 2 + b2 j ) ∧ " ∧ ( aip + bpj ) . p

Similarly, we can define the morphological operators

(14)

ш- , Φш , or ш/ .

ȟ

Щ

Definition 5. Let (x1, y1),…,(xk, yk) be k vector pairs with xȟ=(x1 ,…, xn )ƍ Rn and ȟ ȟ yȟ=(y1 ,…, ym )ƍ Rm for ȟ=1,…, k. For a given set of pattern associations {(xȟ, yȟ): ȟ=1,…, k} and a pair of associated pattern matrices (X,Y), where X = (x1,", x k ) , Y = (y1 , ", y k ) , the morphological min-product memory WXY is defined by ȟ

Щ

§ y1ȟ o x1ȟ " y1ȟ o xnȟ · ¨ ¸ WXY = Y ш X ' = ∧ ξ =1[ y ш ( x ȟ ) '] = ∧ξ =1¨ ȟ # ȟ % ȟ # ȟ ¸ ¨y ox " y ox ¸ m n¹ © m 1 o

k

ȟ o

k

(15)

And the morphological max-product memory MXY is defined by M XY = Y щ X ' = ∨ k [ y ȟ щ ξ =1 o

o

o

§ y1ȟ o x1ȟ " y1ȟ o xnȟ · ¸ ( x ȟ ) '] = ∨ξk =1¨¨ # % # ¸ ¨ yȟ o xȟ " yȟ o xȟ ¸ m n¹ © m 1

(16)

o

Since y ȟ ш ( x ȟ ) ' = y ȟ щ ( x ȟ ) ' , WXY and MXY follow from this definition that WXY ” y ȟ ш ( x ȟ ) ' = y ȟ щ ( x ȟ ) ' ” MXY ∀ξ = 1, " , k o

o

(17)

Let ш represents the reverse of ш , and щ represents the reverse of щ , that is, Ɉ and Ĭ are reversible each other. If Ɉ=+ or ×, then Ĭ= or ÷; on the contrary, if Ɉ= or ÷, then Ĭ=+ or ×. Then, WXY and MXY satisfy that Ĭ

o

Ĭ

㧙

o

㧙

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N. Feng et al.

WXY щ x ξ ≤ [ y ξ ш Ĭ

Ɉ

щ

(18)

Ĭ

(19)

(xξ ) '] щĬ xξ = y ξ = [yξ o (xξ ) '] шĬ xξ ≤ MXYшĬ xξ

∀ξ = 1, " , k or equivalently, that Ĭ

WXY щ X ≤ Y ≤ MXY ш X o

Definition 6. A matrix A=(aij)m×n is said to be a щ -perfect memory for (X,Y) if and o o only if Aщ X =Y. The matrix A=(aij)m×n is said to be a ш -perfect memory for (X,Y) if o

and only if Aш X = Y. In fact, in the existing MAM there are only two memories WXY and MXY defined by using operators ш and щ , respectively. In the existing FMAM and EFMAM, it is also the same, i.e. there are only two memories WXY and MXY defined by using / / operators ш and щ , respectively. But according to the definitions 1 to 6, there will be four memories in MAM, FMAM or EFMAM, respectively. The two additional + + Φ Φ memories defined by using operators ш and ш (for MAM), and by using ш and щ (for FMAM or EFMAM), respectively. That is to say, there are more methods in the unified framework than there are in MAM, FMAM and EFMAM.

4 Unified Morphological Theorems Ritter gave 7 theorems with respect to MAM in [7]. Wang et al. also proved 6 theorems with respect to FMAM in [13] and 4 theorems with respect to EFMAM in [14]. Our research result shows that these theorems can be unified. We give two of them and their proofs as two examples. Theorem 1: If A is щ -perfect memory for (X, Y) and B is ш -perfect memory for (X, Y), then o

o

A”WXY”MXY”B and WXY

щo X = Y =M шo X. XY

Proof of Theorem 1: If A is щ -perfect memory for (X, Y), then (A щ xȟ )i =y i for all ȟ = 1,…, k and all i=1,…, m. Equivalently o

∨

n j =1

( a ij Ο x ξj ) = y iξ

o

∀ ξ = 1, " , k

and

ȟ

∀ i = 1, " , m .

For MAM, U=R, Ɉ=±, Ĭ= B , it follows that for an arbitrary index j ∈ {1, " , n} we have

a ij Ο x ξj ≤ y iξ

∀ ξ = 1, " , k

⇔ a ij ≤ y iξ Θ x ξj ⇔ a ij ≤

For FMAM and EFMAM, U=R+, Ɉ=× or also can be derived.

∧ξ

k =1

∀ ξ = 1, " , k

( y iξ Θ x ξj ) = w ij

(20)

㧛, Ĭ=㧛 or ×, the set of inequalities (20)

A Unified Framework of Morphological Associative Memories

7

This shows that A”WXY. In view of (19), we now have Y=A щ X”WXY щ X”Y, o

o

and therefore, WXY щ X=Y. A similar argument shows that if B is ш -perfect memory o

o

for (X, Y), then MXY”B and MXY ш X=Y. Consequently we have A”WXY”MXY”B o

̱

and WXY щ X = Y =MXY ш X. o

o

o

Theorem 2: WXY is щ -perfect memory for (X, Y) if and only if for each ȟ = 1,…, k, o

Ĭ

each row of the matrix [yȟ щ (xȟ)ƍ]- WXY contains a zero entry. Similarly, MXY is ш perfect memory for (X, Y) if and only if for each ȟ = 1,…, k, each row of the matrix Ĭ MXY -[yȟ щ (xȟ)ƍ] contains a zero entry.

Proof of Theorem 2: We only prove the theorem in one domain for either the memory WXY or the memory MXY. The result of proof for the other memory can be derived in an analogous fashion. o WXY is щ -perfect memory for (X, Y) ⇔ ( WXY щ x ξ ) i = y iξ ∀ȟ =1,…,k and ∀i =1,…,m o

⇔ y iξ − ( WXY щ x ξ ) i = 0 ∀ȟ =1,…,k and ∀i =1,…,m o

∨

⇔ y iξ −

∧ ⇔ ∧ ⇔ ∧ ⇔

n j =1 n j =1 n

n j =1

( wij Ο x ξj ) = 0 ∀ȟ =1,…,k and ∀i =1,…,m

( y iξ − ( wij Ο x ξj )) = 0 ∀ȟ =1,…,k and ∀i =1,…,m ( y iξ Θ x ξj − wij ) = 0 ∀ȟ =1,…,k and ∀i =1,…,m Ĭ

([ y ξ щ ( x ξ ) '] − WXY ) ij = 0 ∀ȟ =1,…,k and ∀i =1,…,m

j =1

This last set of equations is true if and only if for each ȟ=1,…,k and each integer i Ĭ =1,…,m, each column entry of the ith row of [yȟ щ (xȟ)ƍ]- WXY contains at least one zero entry.

̱

We need to note that the conditions the equation set given above holds are different for MAM and for FMAM or EFMAM. For MAM, it holds in U=R; for FMAM or EFMAM, it holds in U=R+.

5 Discussions What are the advantages of the unified framework of morphological associative memories? We think that there are at least three benefits in it: Firstly, the unified theoretical framework is beneficial to understanding the MAM, FMAM and EFMAM. This paper analyzes the common properties of MAM, FMAM and EFMAM, and establishes the theoretical framework of unified morphological associative memory (UMAM) by extracting these common properties. The more the thing is abstracted, the deeper the thing is understood. Therefore the UMAM is of great benefit to us in research and applications with respect to MAM, FMAM and EFMAM. Secondly, the UMAM can help us find some new methods. In fact, the method of defining the morphological memory WXY or MXY in MAM, FMAM or EFMAM is

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N. Feng et al.

not unique. For example, according to (15) and (16), the WXY and MXY also can be defined by: WXY= ∧ ξK=1 ( y ξ

1

And MXY= ∨ ξK=1 ( y ξ

1

+ ξ ξ 2 K ξ Φ ш ( x ) ') or WXY= ∧ ξ =1 ( y ш ( x ) ')

+ ξ ξ 2 K ξ Φ щ (x ) ') or MXY= ∨ ξ =1 ( y щ (x ) ')

(21)

(22)

Consequently, there are more methods defining the memories WXY and MXY in the UMAM. Finally, the methods in the UMAM are complementary rather than competitive. For this reason, it is frequently advantageous to use these methods in combination rather than exclusively.

6 Experiments A number of experiments are conducted to demonstrate the advantages of the methods in UMAM. Three typical of experiments are as follows: Experiment 1. Let §0· §0· § 0 · § −1 · § 0 · § 0 · 1 2 2 3 3 ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ x = 0 , y = 1 ; x = −2 , y = −1 ; x = −3 , y = ¨ −2 ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨0¸ ¨0¸ ¨ −4 ¸ ¨ 0 ¸ ¨ 0 ¸ ¨ 0 ¸ © ¹ © ¹ © ¹ © ¹ © ¹ © ¹ 1

Then both 1

WXY=

ш

3 ȟ=1

§ 0 0 0 · § -1 1 3 · § 0 (yȟ ш (xȟ)ƍ)= ¨ 1 1 1 ¸ ∧ ¨ -1 1 3 ¸ ∧ ¨ -2 ¨¨ ¸¸ ¨¨ ¸¸ ¨¨ ©0 0 0¹ © 0 2 4¹ © 0

· ¸ 1 -2 ¸¸ 3 0 ¹ 30

=

§ -1 0 0 · ¨ -2 1 -2 ¸ ¨¨ ¸¸ ©0 0 0¹

and

щ (y щ (x )ƍ)= §¨¨

§ -1 1 3 · § 0 3 0 · § 0 3 3 · ¸ ¨ ¸ ¨ ¸ ¨ ¸ 1 1 1 ∨ -1 1 3 ∨ -2 1 -2 = 1 1 3 ¨ ¸¸ ¨¨ ¸¸ ¨¨ ¸¸ ¨¨ ¸¸ ©0 0 0¹ © 0 2 4¹ © 0 3 0 ¹ ©0 3 4¹ are perfect recall memories, because they satisfy the definition 6, respectively. But both § 0 0 0 · § -1 -3 -5 · § 0 -3 0 · § -1 -3 -5 · 3 + 2 WXY= ȟ=1(yȟ ш (xȟ)ƍ)= ¨ 1 1 1 ¸ ∧ ¨ -1 -3 -5 ¸ ∧ ¨ -2 -5 -2 ¸ = ¨ -2 -5 -5 ¸ ¨¨ ¸¸ ¨¨ ¸¸ ¨¨ ¸¸ ¨¨ ¸¸ © 0 0 0 ¹ © 0 -2 -4 ¹ © 0 -3 0 ¹ © 0 -3 -4 ¹ and § 0 0 0 · § -1 -3 -5 · § 0 -3 0 · § 0 0 0 · 3 + 2 MXY= ȟ=1(yȟ щ (xȟ)ƍ)= ¨ 1 1 1 ¸ ∨ ¨ -1 -3 -5 ¸ ∨ ¨ -2 -5 -2 ¸ = ¨ 1 1 1 ¸ ¨¨ ¸¸ ¨¨ ¸¸ ¨¨ ¸¸ ¨¨ ¸¸ © 0 0 0 ¹ © 0 -2 -4 ¹ © 0 -3 0 ¹ © 0 0 0 ¹ are not. 1

MXY=

ш

щ

3 ȟ=1

ȟ

-

ȟ

0 0 0·

A Unified Framework of Morphological Associative Memories

Experiment 2. Set x = 1

§1· §1· §2· § 0 · §3· §0· ¨ 2 ¸ , y1 = ¨ 0 ¸ ; x 2 = ¨ 3 ¸ , y 2 = ¨ −1¸ ; x3 = ¨ 4 ¸ , y 3 = ¨ 1 ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ ¨3¸ ¨0¸ ¨4¸ ¨ −1¸ ¨1¸ ¨0¸ © ¹ © ¹ © ¹ © ¹ © ¹ © ¹

If the Ritter’s method is used, then both 1

WXY=

ш

3 ȟ=1

§ 0 -1 -2 · § -2 -3 -4 · § -3 -4 -1 · (yȟ ш (xȟ)ƍ)= ¨ -1 -2 -3 ¸ ∧ ¨ -3 -4 -5 ¸ ∧ ¨ -2 -3 0 ¸ ¨¨ ¸¸ ¨¨ ¸¸ ¨¨ ¸¸ © -1 -2 -3 ¹ © -3 -4 -5 ¹ © -3 -4 -1 ¹

=

§ -3 -4 -4 · ¨ -3 -4 -5 ¸ ¨¨ ¸¸ © -3 -4 -5 ¹

=

§ 0 -1 -1 · ¨ -1 -2 0 ¸ ¨¨ ¸¸ © -1 -2 -1 ¹

and 1

MXY=

щ (y щ (x )ƍ)= §¨¨ 3 ȟ=1

ȟ -

· § -2 -3 -4 · § -3 -4 -1 · ¸ ¨ ¸ ¨ ¸ -1 -2 -3 ∨ -3 -4 -5 ∨ -2 -3 0 ¸¸ ¨¨ ¸¸ ¨¨ ¸¸ ¨ © -1 -2 -3 ¹ © -3 -4 -5 ¹ © -3 -4 -1 ¹

ȟ

0 -1 -2

are not perfect recall memories. But if the method in UMAM is used, then both 2

WXY=

ш

3 ȟ=1

§ 2 3 4· § 2 3 4· § 3 4 1· + (yȟ ш (xȟ)ƍ)= ¨ 1 2 3 ¸ ∧ ¨ 1 2 3 ¸ ∧ ¨ 4 5 2 ¸ ¨¨ ¸¸ ¨¨ ¸¸ ¨¨ ¸¸ ©1 2 3¹ ©1 2 3 ¹ © 3 4 1¹

=

§ 2 3 1· ¨1 2 2¸ ¨¨ ¸¸ ©1 2 1¹

=

§3 4 4· ¨ 4 5 3¸ ¨¨ ¸¸ ©3 4 3¹

and 2

MXY=

щ (y щ (x )ƍ)= §¨¨ 3 ȟ=1

ȟ +

§ 2 3 4· § 3 4 1· ¸ ¨ ¸ ¨ ¸ 123 ∨ 123 ∨ 452 ¸ ¨ ¸ ¨ ¸¸ ¨ ¸ ¨ ¸ ¨ ©1 2 3¹ ©1 2 3 ¹ © 3 4 1¹

ȟ

2 3 4·

are perfect recall memories. Experiment 3. Let §1 X=¨4 ¨ ¨4 ©

2·

§1 ¸ ¨ 2 , Y= 2 ¸ ¨ ¸ ¨1 4¹ ©

2 2 2

2 2 1

1·

¸. ¸ ¸ 1¹ 2

If the Ritter’s method in MAM is used, then 1

1

§1 1 1· § -1 -3 -3 · + WXY = Y ш X ' = ¨ 0 -2 -2 ¸ , 1WXY щ X= ¨ 2 2 2 ¸ Y; ¨ ¸ ¨ ¸ ¨1 1 1¸ ¨ −1 −3 −3¸ © ¹ © ¹ §0 M XY = Y щ X ' = ¨ 1 ¨¨ ©0

0 0 −1

§ 1 2 2· · 1 + ¸ , M X = XY ш ¨ 2 2 2 ¸ Y. 0 ¨ ¸ ¸¸ ¨1 1 1¸ −1 ¹ © ¹ 0

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N. Feng et al.

If the method in FMAM or EFMAM is used, then 2

2

§0.5 0.25 0.25· / Φ §1 WXY = Y ш X ' = ¨ 1 0.5 0.5 ¸ , 2WXY щ X= ¨ 2 ¨ ¸ ¨ ¨0.5 0.25 0.25¸ ¨1 © ¹ © §

/

M XY = Y щ X ' = ¨ ¨¨ ©

1

1

2

1

1

0 .5

1 2

1· 2¸

Y;

¸ ¸ 1 1¹

· 2 Φ § 1 2 2 · Y. , MXY ш X= ¨ ¸ 1 2 2 2¸ ¨ ¸ ¸¸ ¨ ¸ 0 .5 ¹ ©1 1 1¹ 1

They make not perfect memory for (X, Y). But if the method in UMAM is used, then 3

+ WXY = Y ш X ' = §¨ 2

3

3

+

4

5

5·

6

6

3

-

§1 2 1· = Y; 2 2 2¸ ¨ ¸ ¨1 1 1¸ © ¹

, 3WXY щ X= ¨

§4

5

§1 2 1· 3 ¸ , MXY ш X= ¨ 2 2 2 ¸ =Y. ¨ ¸ ¸¸ ¨1 1 1¸ 5¹ © ¹

§1

2

4·

¨ ¨1 ©

2

WXY = Y ш X ' = ¨ 2

Φ

¸ 4 ¸ ¸ 3¹

4

M XY = Y щ X ' = ¨ 4

Φ

4·

¨ ¨2 ©

¨¨ ©3

4

3

§4

M XY = Y щ X ' = ¨ 4 ¨¨ ©2

4

4 8 4

/

§1 2 1·

¸ , WXY щ X= ¨ 2 2 2 ¸ =Y; 4 ¨ ¸ ¸ ¨1 1 1¸ ¸ 2¹ © ¹ 4

§1 2 1· / , 4MXY ш X= ¨ = Y. ¸ 8 2 2 2¸ ¨ ¸ ¸¸ ¨1 1 1¸ 4¹ © ¹ 4·

The three experiments given above show that the methods in UMAM are complementary, and therefore the UMAM can solve more associative memory problems, especially to hetero-MAM, hetero-FMAM and hetero-EFMAM.

7 Conclusions This paper introduces a new unified theoretical framework of neural-network computing based on lattice algebra. The main emphasis of this paper was on the unification of morphological associative memories, fuzzy morphological associative memories, and enhanced fuzzy morphological associative memories. Our research and experiments showed that the MAM, FMAM and EFMAM could be unified in the same theoretical framework. The significance of the unified framework consisted in: on the one hand we got a better and deeper understanding of the MAM, FMAM and EFMAM from the unified framework UMAM; on the other hand we obtained some new methods from it. Therefore the UMAM can solve more problems of the associative memories than the MAM, FMAM, and EFMAM do. The lattice algebraic approach to neural-network theory is new and a multitude of open questions await exploration. For example, new methods of morphological associative memory need further investigation; the application base of the unified framework needs expanding, etc. It is our hope that these problems will be better solved in the future.

A Unified Framework of Morphological Associative Memories

11

Acknowledgments This research is supported by the Science Fund of Henan Province, China (0511012300) and key project of Information and Industry Department of Chongqing City, China (200311014).

References 1. Raducanu,B., Grana, M., Albizuri, F. X.: Morphological Scale Spaces and Associative Memories: Results on Robustness and Practical Applications, J. Math. Image. Vis., vol. 19, no. 2 (2003), 113-131. 2. Suarez-Araujo, C. P.: Novel Neural Network Models for Computing Homothetic in Variances: An Image Algebra Notation,” J. Math. Imaging and Vision, vol. 7, no. 1 (1997), 69-83. 3. Huang, D.S., Systematic Theory of Neural Networks for Pattern Recognition (in Chinese), Publishing House of Electronic Industry of China, May (1996) 4. Huang, D.S.,“On the Modular Associative Neural Network Classifiers, The 5th National United conf on Computer and Application, Beijing, Vol.3 Dec. (1999).7.285-7.290. 5. Ritter, G. X., Urcid, G.: Lattice Algebra Approach to Single-neuron Computation, IEEE Transactions on Neural Networks, Vol. 14, No. 2, (2003), 282-295. 6. Ritter, G. X., Sussner, P.: An Introduction to Morphological Neural Networks, in Proc. 13th Int. Conf. Pattern Recognition, Vienna, Austria, (1996), 709-717. 7. Ritter, G. X., Sussner, P., Diaz-de-Leon, J. L.: Morphological Associative Memories. IEEE Transactions on Neural Networks, Vol. 9, No. 2, (1998) 281-293. 8. Ritter, G. X., Recent Developments in Image Algebra, in Advances in Electronics and Electron Physics, P. Hawkes, Ed. New York: Academic, vol. 80, (1991) 243-380. 9. Davidson, J. L., Hummer,F.: Morphology Neural Networks: An Introduction with Applications, IEEE System Signal Processing, vol. 12, no. 2, (1993) 177-210. 10. Davidson, J. L., Ritter, G. X., A Theory of Morphological Neural Networks, in Digital Optical Computing , vol. 1215 of Proc. SPIE, July (1990) 378-388. 11. Davidson, J. L., Strivastava, R.: Fuzzy Image Algebra Neural Network for Template Identification, in 2nd Annu. Midwest Electrotechnol. Conf., Ames, IA, Apr. (1993) 68-71. 12. Pessoa,L. F. C., Maragos, P.: Neural Networks with Hybrid Morphological/rank/linear nodes: A Unifying Framework with Applications to Handwritten Character Recognition, Pattern Recognition, vol. 33, Jun. (2000) pp. 945-960. 13. Wang, M., Wang, S. T., Wu, X. J., Initial Results on Fuzzy Morphological Associative Memories, ACTA ELECTRONICA SINICA (in Chinese), vol. 31, May (2003) 690-693. 14. Wang, M., Chen, S. C., Enhanced FMAM Based on Empirical Kernel Map, IEEE Transactions on Neural Networks, vol. 16, no. 3, (2005) pp. 557-564, 15. Gader, P. D., Khabou, M. A., Koldobsky, A.: Morphological Regularization Neural Network s, Pattern Recognition, vol. 33, Jun. (2000) 935-944. 16. Sussner, P.: Generalizing Operations of Binary Morphological Associative Memories Using Fuzzy Set Theory, J. Math. Image. Vis., vol. 19, no. 2, (2003) 81-93.

A New Speech Denoising Method Based on WPD-ICA Feature Extraction Qinghua Huang, Jie Yang, and Yue Zhou Institute of Image Processing & Pattern Recognition, Shanghai Jiaotong University, Shanghai, China, 200240 {qinghua, jieyang, zhouyue}@sjtu.edu.cn

Abstract. Independent Component Analysis (ICA) feature extraction is an efficient sparse coding method for noise suppression. However, single channel signal can not be directly applied in ICA feature extraction. In this paper, we propose a new method using wavelet packet decomposition (WPD) as preprocessing for single channel data. Wavelet packet coefficients (WPCs) provide multi-channel data as input data to learn ICA basis vectors. Furthermore we project input data onto the basis vectors to get sparser and independent coefficients. Appropriate nonlinear shrinkage function is used onto the components of sparse coefficients so as to reduce noise. The proposed approach is very efficient with respect to signal recovery from noisy data because not only the projection coefficients are sparser based on WPCs but both the features and the shrinkage function are directly estimated from the observed data. The experimental results have shown that it has excellent performance on signal to noise ratio (SNR) enhancement compared with other filtering methods.

1 Introduction Data decomposition and representation are widely used in signal processing. One of the simplest methods is to use linear transformation of the observed data. Given observation (often called sensor or data) matrix X ∈ * m× N , perform the linear transformation X = AS + η .

(1)

where A ∈ * m× n represents basis data matrix or mixing data matrix (dependent on application), S ∈ * n× N contains the corresponding hidden components that give the contribution of each basis vector, η ∈ * m× N is error or noise, n is the number of hidden sources, m is the number of observations and N is the number of samples. The row of S should be as sparse as possible for sparse component or independent as possible for ICA[1]. The row of S is sparse when only a small number of the components are significantly non-zero at the same time. Sparse coding has many applications such as redundancy reduction and denoising. For supergaussian signal D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 12 – 20, 2006. © Springer-Verlag Berlin Heidelberg 2006

A New Speech Denoising Method Based on WPD-ICA Feature Extraction

13

independence and sparsity are consistent since sparsity is equivalent to supergaussian or leptokurtosis. The coefficients of ICA basis vectors usually have a sparse distribution then resulting in statistically efficient codes. Therefore ICA as a feature extraction method has been widely used in extracting efficient speech features and reducing noise[2,3]. However ICA requires signal from at least two separate sensors. For single channel data many ICA feature extraction methods directly segment the data into data matrix[4,5] and learn ICA feature basis using noise-free training signal as a prior knowledge[6]. Direct segmentation is based on the assumption that signal is stationary within a short time. But the assumption is approximate and not strict. Noise-free signal isn’t obtained in many practical applications. To overcome these limitations, we propose to use WPD to pre-process the observed data from a single sensor and then use the WPCs at different frequencies as input to learn ICA basis vectors. Furthermore we apply the sparsity of projection coefficients to reduce noise. Our method has advantages over other filtering methods in that both speech features and the nonlinear shrinkage function are estimated directly from the signals. Based on the sparsity of WPCs, the projection coefficients of ICA basis vectors are sparser. Experimental results have shown that the presented method is more efficient to reduce the additive Gaussian noise compared with other denoising methods. The paper is organized as follows. In section 2, the WPD as preprocessor and ICA feature extraction are described. In section 3 detailed speech denoising is introduced. Experiments and conclusions are presented in section 4 and section 5 respectively.

2 WPD-ICA Feature Extraction 2.1 Wavelet Packet Decomposition Standard ICA requires signal at least as many as sources. In many applications, single sensor signal is often obtained. We develop a new method to decompose the data

S(0,0)

A(1,0)

AA(2,0)

D(1,1)

AD(2,1)

DA(2,2)

Fig. 1. Wavelet Packet Decomposition

DD(2,3)

14

Q. Huang, J. Yang, and Y. Zhou

from a single sensor and then use the coefficients at different frequencies as input matrix to ICA. Projection of signal onto wavelet packet basis function is called wavelet packet decomposition. WPD has strong frequency resolution power and high time resolution power. It is a full binary tree decomposition [7,8,9] (Fig.1). WPD is used as a preprocessor to decompose the signal into a set of narrow band signals at first. If signal X is analyzed by n level full binary tree decomposition, we can get wavelet packet coefficient matrix (WPCM) X p using the following transformation

X p = Wp ⋅ X .

(2)

" C (0, N1 ) º " C (1, N1 ) »» , C(i,j) is the jth WPC of the ith node " " » » " C (m, N1 ) ¼ in n level decomposition, m = 0,1" 2n − 1 is the node index of n level of decomposition and N1 = N n (N is the number of samples) is the length of each node ª C (0,1) C (0, 2) « C (1,1) C (1, 2) where X p = « « " " « ¬C (m,1) C (m, 2)

coefficients. We use matrix X p to extract ICA feature. WPD is applied to decompose signal with noise. One of the primary properties of WPD is sparsity. That is, small WPCs are dominated by noise, while coefficients with a large absolute value carry more signal information than noise. The ICA feature vectors are learned from the WPCs, so the projection coefficients with a large absolute value also have more signal information than noise. Therefore the choice of wavelet and the level of decomposition play a critical role in this section and the following analysis. Concrete choice depends on the problem at hand. 2.2 ICA Feature Extraction

ICA as a feature extraction method can be detailed in the following n

X = AS = ¦ ai si .

(3)

i =1

where ai (each column of A) is a basis vector, all columns of A span a feature space which ensures that all projection coefficients s1 , s2 , " , sn satisfy mutually independent property. The idea of WPD-ICA is based on the following proposition [2]. Proposition 1: A (component-wise) linear operator T leaves the property of linear independence unaffected. Therefore we can use the ICA algorithm on the wavelet packet coefficient space to extract feature.

A New Speech Denoising Method Based on WPD-ICA Feature Extraction

15

We apply WPD as defined in Eq. (2) onto the two sides of Eq. (1) to get ­ X p = Wp ⋅ X ° °S p = Wp ⋅ S ® °η p = W p ⋅η ° X = AS + η = A( S + η ) = AS p p p p p ¯ p

(4)

where X p , S p , η p are WPCM of signal, projection coefficients and noise respectively and Sp = S p + ηp , ηp = A−1η p . The covariance matrix of the noise in the wavelet packet domain equals Cη p = E[η pη Tp ] = E[Wpηη T W pT ] = Wp E[ηη T ]W pT . If

Wp is orthogonal and Cη = σ 2 I , then we get that Cη p = σ 2 I . In the same way if A is orthogonal, Cηp = σ 2 I . This means that orthogonal transformations leave the Gaussian noise structure intact, which makes the problem more simply tractable. The sparsity of X p means that the distribution of X p is highly peaky and heavy-tail than the Gaussian distribution. The property gives us the advantage to use ICA feature extraction. It enforces super-Gaussian distributions on the coefficients of ICA basis Sp in terms of the central limit theorem. We can be sure that the basis coefficients will be described by even more highly peaked distributions since the inputs of ICA are described by highly peaked ones. So we can learn better basis representation for the signal. ICA feature extraction algorithm is performed to obtain the estimation of projection coefficient matrix Sp and the basis matrix A by unmixing matrix W in the following equation

Yp = WX p .

(5)

where Yp is the estimation of Sp . ICA basis matrix can be calculated by the relation A = W −1 . By maximizing the log likelihood of projection coefficients, both the independent coefficients and basis matrix can be inferred at the same time. The learning rule is represented as ∆W ∝

∂ log p ( Y p ) ∂W

T T W W = η [ I − ϕ (Y p ) Y p ]W

(6)

.

here the updating algorithm is natural gradient method which speeds the convergence considerably[2]. The ϕ ( y ) is score function which is defined as

ϕ ( y) = −

p′( y ) ∂ log p( y ) . In this paper, we use the generalized gaussian =− p( y ) ∂y q

distribution to estimate the p.d.f of y, that is p( y ) ∝ exp(− y ) where q can be

16

Q. Huang, J. Yang, and Y. Zhou

learned from the data[10]. Combing with the learning rule in Eq. (6), the unmixing matrix is iterated until convergence is achieved. The basis function matrix is then obtained.

3 Speech Denoising Speech feature basis and sparse projection coefficients onto these basis vectors are acquired in section 2.2. In the noisy environment, Yp denotes the noisy coefficients. S p is the original noise-free coefficients. ηp is the projection coefficients of Gaussian noise. The relation between them can be described as Yp = S p + ηp .

(7)

We want to estimate S p from the noisy coefficients Yp . We can use the Maximum Likelihood (ML) estimation method. The ML estimation gives the relation Sˆ p = h(Yp ) where the nonlinear function h(⋅) is called as shrinkage function and its inverse is given by h −1 ( S p ) = S p + σ 2ϕ ( S p ) ( σ is the standard derivation of Gaussian

noise)[6,11]. In general, a model for elimination of noise or other undesirable components for single sensor data is depicted in the following steps and Fig.2. š

X

Xp WPD

ICA (W)

Yp

Sp

Denoising

š

IICA (A)

X

Xp

IWPD

Fig. 2. Basic model for removing noise from single-sensor data

㧔1㧕Choose appropriate wavelet function and the best level of WPD. Use the WPCM

of observed noisy signal to learn ICA basis vectors and sparse projection coefficients. Apply the nonlinear shrinkage function on noisy coefficients to get the estimated noise-free coefficients. Inverse the ICA and WPD to obtain the recovered signal from the noisy signal.

㧔2㧕 㧔3㧕

4 Experiments In our experiments, male and female speech signals with added Gaussian noise are used to test the performance of the proposed method. The sampling frequency is 8kHz and 40000 samples of each signal are used. Signal added with white Gaussian noise is represented as X = X s + nw

nw ~ Ν (0, σ 2 ) .

(8)

A New Speech Denoising Method Based on WPD-ICA Feature Extraction

17

Noisy signal with a colored Gaussian noise is described as

X = X s + nc .

(9)

where nc is colored Gaussian noise and is modeled by an autoregressive process AR(2):

nc (t ) = 1.32nc (t − 1) − 0.89nc (t − 2) + nw (t ) .

(10)

Firstly the Daubechies function of order 8 has been chosen as the wavelet function and speech signal is analyzed by WPD through six level of decomposition. Wavelet packet coefficients are represented as " C (0, 625) º " C (1, 625) »» » " " » " C (m, 625) ¼

ª C (0,1) C (0, 2) « C (1,1) C (1, 2) Xp = « « " " « C C (63,1) (63, 2) ¬

The unmixing matrix W is initialized by 64×64 identity matrix and the learning rate is gradually decreased during iterations. W is learned by the algorithm in Eq. (6) and it is used as the filter to get sparse coefficients. Estimated noise-free coefficients are obtained by denoising the sparse coefficients. Enhanced signal is reconstructed from the estimated noise-free coefficients. To judge the performance of noise suppression, the signal to noise ratio is used

¦ signal (t ) SNR = 10 log ¦ noise (t ) 2

t

2

.

(11)

t

As a measure of the signal approximation the root mean squared error (RMSE) defined as RMSE =

N

¦ (S

ideal i

− Sireconstructed ) / N .

(12)

i =1

can be used. The RMSE is only an overall measure of the performance. In the first experiment of male speech signal, the noisy male speech signal corrupted by four different intensity of additive white Gaussian noise are used to test the method. The SNR of the input noisy signals are 0.1175, -6.2592, -9.1718 and 13.6174dB respectively. We can get high SNR and satisfied reconstructed signal. The output SNR results of the recovered male speech signal are 4.8094, 3.1309, 0.0918, 0.8782dB and RMSE results are 0.0398, 0.0433, 0.0504, 0.0529 respectively. It can be seen that the SNR have much improvement. Fig.3 shows the denoising results of the noisy male speech with the input SNR of -13.6174dB and it was compared to the filtering results from the median filter and the wavelet filter method. Table 1 denotes the SNR and RMSE of denoised signal under the condition of additive white Gaussian noise.

18

Q. Huang, J. Yang, and Y. Zhou

Fig. 3. The denoising results of noisy male speech when the input SNR is -13.6174dB (a) denotes the clean male speech signal (b) denotes the noisy signal with additive white Gaussian noise (c) denotes the denoising result of our method (d) denotes the denoising result of wavelet filter (e) denotes the denoising result of median filter with n=5 Table 1. Denoising results of male speech with white Gaussian noise

Input signal SNR(dB)

WPD-ICA denoised signal SNR(dB) RMSE

Wavelet denoised signal SNR(dB) RMSE

Median value filtered signal SNR(dB) RMSE

-13.6174 -9.1718 -6.2592 0.1175

-0.8782 0.0918 3.1309 4.8094

-2.2804 -1.7821 1.2803 1.4406

-8.0949 -6.0853 -4.8516 -1.8285

0.0529 0.0504 0.0433 0.0398

0.0568 0.0554 0.0475 0.0471

0.0759 0.0687 0.0646 0.0555

Female speech signal with four different intensity of additive colored Gaussian noise are used in another experiment. The SNR of the input noisy signals are 4.8004, 0.4854, -5.0242 and -12.6541dB respectively. Fig.4 denotes the results of three methods which suppress the additive colored Gaussian noise. The SNR and RMSE of denoised female speech can be seen from Table 2.

A New Speech Denoising Method Based on WPD-ICA Feature Extraction

19

Fig. 4. the denoising results of noisy female speech when the input SNR is -3.2423 dB (a) denotes the clean female speech signal (b) denotes the noisy signal with additive colored Gaussian noise (c) denotes the denoising result of our method (d) denotes the denoising result of wavelet filter (e) denotes the denoising result of median filter with n=5 Table 2. Denoising results of female speech corrupted by colored Gaussian noise

Input signal SNR(dB)

WPD-ICA denoised signal SNR(dB) RMSE

Wavelet denoised signal SNR(dB) RMSE

Median value filtered signal SNR(dB) RMSE

-17.1052

-8.1328

0.0797

-12.9301

0.1013

-13.0024

0.1016

-11.3516 -3.2423

-1.3560 2.1785

0.0568 0.0476

-3.7092 1.3112

0.0639 0.0497

-9.3792 -5.8208

0.0848 0.0710

2.5113

6.4278

0.0347

2.7661

0.0486

-4.2815

0.0657

5 Conclusions How to extract basis vectors directly from the single channel speech signal is the key problem in noisy speech denoising. Therefore in this paper we present a new approach to combine ICA feature extraction with WPD so as to extract basis function

20

Q. Huang, J. Yang, and Y. Zhou

directly from single channel data. WPD-ICA learns basis vectors using the high order statistics of the data. Projection coefficients onto the learned basis vectors are sparser and more suitable for reducing noise. Shrinkage function can also be obtained from data. Experiments on real speech signal with added Gaussian noise have shown that the proposed method can efficiently suppress noise and enhance signals.

References 1. Commo, P.: Independent Component Analysis, A New Concept? Signal Processing, Vol.36 (1994) 287-314 2. Hyvärinen, A., Karhunen, J., Oja, E.: Independent Component Analysis. Wiley, New York (2001) 3. Roberts, S., Everson, R.: Independent Component Analysis: Principles and Practice. Cambridge University Press, Cambridge (2001) 4. Lee, T.-W., Jang, G.-J.: The Statistical Structures of Male and Female Speech Signals. Proc. ICASSP, Salt Lack City, Utah, May (2001) 105-108 5. Lee, J.-H., Jung H.-Y., Lee, T.-W., Lee, S.-Y.: Speech Feature Extraction Using Independent Component Analysis. Proc. ICASSP, Istanbul, Turkey, Vol. 3, June (2000) 1631-1634 6. Hyvärinen, A.: Sparse Code Shrinkage: Denoising of Nongaussian Data by Maximum Likelihood Estimation. Technical Report A51, Helsinki University of Technology, Laboratory of Computer and Information Science (1998) 7. Mallet, S.: A Wavelet Tour of Signal Processing. Academic Press, second edition (1999) 8. Ravier, P., Amblard, P.O.: Wavelet Packets and De-noising Based on Higher-orderStatistics for Transient Detection. Signal Processing, Vol.81 (2001) 1909-1926 9. Donoho, D.L., Johnstone, I.: Adapting to Known Smoothness Via Wavelet Shrinkage. J. Amer. Stat. Assoc. Vol.90, Dec (1995) 1200-1224 10. Lee, T.-W., Lewicki, M.-S.: The Generalized Gaussian Mixture Model Using ICA. International workshop on Independent Component Analysis (ICA’00), Helsinki, Finland, June (2000) 239-244 11. Donoho, D.L.: De-noising by Soft Thresholding. IEEE Trans. Inf. Theory, Vol.41, No.3 (1995) 613-627

An Efficient Algorithm for Blind Separation of Binary Symmetrical Signals* Wenbo Xia and Beihai Tan School of Electronic and Communication Engineering, South China University of Technology 510640, China {WBX, northsea80}@163.com

Abstract. An efficient algorithm for blind separation of binary symmetrical signals is proposed, which don’t depend on the statistical characteristics of source signals. The mixture matrix is estimated accurately by using the relations of sensor signals in case of no noise and it is also proved in this paper, and the estimated mixture matrix is a primary column transformation of the original mixture matrix by the algorithm, through which the source signals are recovered by permutations and sign changes of their rows. In practice, they can be corrected by introducing headers in the bit-streams and differently encoding them. The algorithm is shown simple and efficient in last simulations.

1 Introduction Blind separation problem has been one hot topic in the recent years, which has gained much attention, see, e.g., [1],[2],[3],[4],[5],[6],[13],[15] etc. Blind source separation (BSS) is to recover the source signals without any information of both the source signals and the channels. In many previous researches, because one recovering independent components of sources by the sensor signals, so this kind of BSS problem is also called independent component analysis (ICA). There have existed a lot of algorithms and applications of BSS up to now. Specially, in paper [10], Xie’s conjecture corrected the famous Stone’s conjecture. BSS algorithms based on Xie’s conjecture should be without suspicion in basic theory. From now on, researches have a reliable basis to study BSS both in theory and algorithm design. In the same time, the applications of BSS cover many areas, such as: array processing, multi-user communication and biomedicine etc. For digital signals blind separation, there also were many algorithms, such as: AlleJan’ analysis method [7], K.Anand’s two-step clustering method [8], Li Yuanqing’s underdetermined algorithm [9] and others [11],[12],[14],etc. But these algorithms are *

The work is supported by the National Natural Science Foundation of China for Excellent Youth (Grant 60325310), the Guangdong Province Science Foundation for Program of Research Team (grant 04205783), the National Natural Science Foundation of China (Grant 60505005), the Natural Science Fund of Guangdong Province, China (Grant 05103553) and (Grant 05006508), the Specialized Prophasic Basic Research Projects of Ministry of Science and Technology, China (Grant 2005CCA04100).

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 21 – 28, 2006. © Springer-Verlag Berlin Heidelberg 2006

22

W. Xia and B. Tan

complicated in computations and impreciseness for restoration completely. This paper proposes a novelty blind separation algorithm of binary symmetrical signals, which only use the relations of sensor signals to estimate the mixture matrix and recover source signals, and its good performance is also testified by the last simulations. For the sake of simplicity, we suppose that the binary symmetrical signals are BPSK signals in this paper for discussion.

2 Model of Blind Separation of BPSK Signals In digital signals blind separation, Let m narrowband BPSK signals from m different users, arrive at an array of d antennas [8]. The measured baseband signal at the p th element is given by: ∞

m

x p (t ) =

¦

qi a pi

i =1

¦ b ( j )s(t − jT − τ ) + w i

i

p (t ) ,

(1)

j =1

where T is baud period, q i is the amplitude of the i th user’s signal, a pi is response of the p th sensor to the i th user signal, bi (∗) = ±1 bit-stream transmitted by the i th user, s (*) is signal waveform of unit energy, τ i is time delay of the i th signal to the array and w p (*) is additive white noise at the p th sensor. We assume that the time

taken for electromagnetic waves to traverse the array is small compared to τ i and that the maximum multi-path delay is small compared to T . Here, we absorb the multipath effect into the coefficients a pi , and hence, a pi are not explicitly parameterized in terms of the directions-of-arrival (DOA’s). The a pi are unknown coefficients to be estimated as we estimate the bit-streams of the users. If the τ i are all equal (which is a simplifying assumption that is not necessarily true in practice and deserves more study), one can perform matched filtering over a symbol period T to obtain [8] m

x p ( n) =

¦q a i

pi bi ( n) + w p ( n)

,

(2)

i =1

where w p (n) is a white noise with 0 mean and variance is σ 2 , and it can be denoted as vector: x(n) = As (n) + w(n) ,

(3)

where s (n) = [b1 (n) bm (n)]T , x(n) = [ x1 (n)  xd (n)]T , w(n) = [ w1 (n)  wd (n)]T , A = [q1a1 q2 a 2  qm am ] , a r = [a1r a 2 r  a dr ]T . If we have N snapshots and (3) can be denote as matrix X ( N ) = AS ( N ) + W ( N ) ,

(4)

where X ( N ) = [ x(1)  x( N )] , S ( N ) = [ s (1), s (2)  s ( N )] , and W ( N ) = [ w(1)  w( N )] .

An Efficient Algorithm for Blind Separation of Binary Symmetrical Signals

23

Next, we suppose that there exits no noise, mixture matrix A is nonsingular and d = m , that is to say the number of the sensor signals are equal to the number of source signals. To combine (3) and (4), we have x(n) = As (n) , (5) X ( N ) = AS ( N ) .

(6)

3 An Efficient Algorithm for BPSK Signals Blind Separation In this paper, in order to separate digital signals, we must estimate mixture matrix first. When N is enough great, column vector s (n) in (3) has 2 m distinct vectors denoted as V = {s1 , s 2  s 2m } , that is to say all column vectors of matrix S (N ) in (4) come from one of the set V . Similarly, we also get 2 m distinct vectors of sensor signals through (5) denoted as U = {x1, x2  x2 m } , and obviously all column vectors of matrix X (N ) come from one of the set U , namely xi = Asi

(i = 1,2, 2 m ) .

(7)

It is also denoted as x1i = a11 s1i +  a1m s mi x 2i = a21 s1i +  a 2 m s mi 

(i = 1,2, 2 m ) ,

(8)

x mi = a m1 s1i +  a mm s mi where x i = [ x1i  x mi ]T , s i = [ s1i  s mi ]T . Because s ij ∈ {+1,−1}, i = 1 m; j = 1 2 m , so x i + x j = A( s i + s j ) (i ≠ j , i = 1,2,  2m , j = 1,2,  2m ) .

(9)

It can be denoted like (8) as x1i + x1 j = a11 ( s1i + s1 j ) +  a1m ( s mi + s mj )

x 2i + x 2 j = a 21 ( s1i + s1 j ) +  a 2 m ( s mi + s mj )  x mi + x mj = a m1 ( s1i + s1 j ) +  a mm ( s mi + s mj )

(10)

From (10), we can know if ( s1i + s1 j ) = +2 or ( s1i + s1 j ) = −2 , but ( s ki + s kj ) = 0, k ≠ 1, k ∈ {1,2,  m} we can have xi + x j = (+2)a1 or xi + x j = (−2)a1 , that is to say the sum of the i th vector and the j th vector in the set U is (+2) times of the first column a1 of mixture matrix A or (−2) times of it. Similarly, when ( s qi + s qj ) = +2 or ( s qi + s qj ) = −2 , but ( s ki + s kj ) = 0, k ≠ q, k ∈ {1,2,  m} , then xi + x j = (+2)aq or xi + x j = (−2)aq , that means the sum of the i th vector and the j th vector in the set U is (+2) times of the column a q of mixture matrix A or (−2) times of it. Next, in

24

W. Xia and B. Tan

order to look for all column vectors in mixture matrix A , we will take any two vectors of the set U to add up, y l = x i + x j , l = 1C22m (i ≠ j , i = 1,2,  2 m , j = 1,2,  2 m ) .

(11)

Finally, let set Y = { yl , l = 1C22m } . Definition 1: In the set Y = { yl , l = 1C22m } , if y a = y b or ya = (−1) yb , a ≠ b , we will look on them as same cluster Gr , and r is the footnote of the cluster. Again, we define a set S = {sl , l = 1C22m } , s l = s i + s j , l = 1C22m (i ≠ j , i = 1,2,  2m , j = 1,2,  2m ) ,

(12)

y l = As l , l = 1C22m .

so

(13)

At the same time, according to definition 1, we also can cluster in the set S . When y a = y b or y a = (−1) y b , a ≠ b , we let their corresponding s a and s b into the same cluster H r . From definition 1 and combining equations (10), we can know that all column vectors of A must come from m clusters of Gr , and they are only different from the corresponding column vectors of m clusters of Gr by (+2) or (−2) times. Theorem 1: According to definition 1, when we classify Y = { yl , l = 1C22m } into different clusters, among all the clusters the m clusters which contain the column vectors of the mixture matrix A or the cluster whose element is zero vector, then the number of elements of them is most, and they are 2 m−1 respectively, but the number of elements of the other clusters is less than 2 m−1 . Proof: Let s l = s i + s j

γ

㧧 l = 1C 㧘 (i ≠ j, i = 1,2,  2 2 2m

m

, j = 1,2,  2m ) ;

< >; When sl = 0 , si can be taken 2 m distinct vectors. For every si , there exists a vector s j to make s i + s j = 0 , but because of symmetry, the number of appearance

2m = 2 m −1 . 2 < >; When sl = e1r , where e1r denotes a m × 1 vector whose r th element is (+2)

of sl = 0 is

δ

or (−2) , the other elements are all 0, and r is arbitrary. when e1r denotes the vector whose r th element is (+2) , the other elements are all 0, according to < >, the numsl = e1r

m −2

γ

e1r

is 2 . Similarly, when denotes the vector whose ber of appearance of r th element is (−2) , the other elements are all 0, the number of appearance of sl = e1r is 2 m −2 . So we can arrive a conclusion that the number of appearance of sl = e1r is 2 m −2 + 2 m− 2 = 2 m −1 , where e1r denotes a m × 1 vector whose r th element is (+2) or (−2) , the other elements are all 0.

An Efficient Algorithm for Blind Separation of Binary Symmetrical Signals

25

ε

2 2 < >; When sl = erk , where erk denotes a m × 1 vector whose r th element is (+2) and k th element is (−2) , the other elements are all 0; or whose r th element is (−2) and k th element is (+2) , the other elements are all 0, and r, k are arbitrary. 2 denotes the vector whose r th element is (+2) and k th element is (−2) , When erk

according to
, the number of appearance of s = e l

2 rk

is 2 m−3 , Similarly, when

2 erk denotes the vector whose r th element is (−2) and k th element is (+2) , the num2 is 2 m−3 . So we can arrive a conclusion that the number ber of appearance of sl = erk 2 is 2 m −3 + 2 m −3 = 2 m−2 . of appearance of sl = erk 2 2 , where erk denotes a m × 1 vector whose r th element Similarly, if when sl = erk is (+2) and k th element is (+2) , the other elements are all 0; or whose r th element is (−2) and k th element is (−2) , the other elements are all 0, and r, k are arbitrary, 2 is also 2 m −3 + 2 m −3 = 2 m−2 . the number of appearance of sl = erk Obviously, we know when the nonzero elements of the vector sl increase, the number of appearance of s l will decrease. Because sl is corresponding to yl , so when sl is zero vector or it has only a nonzero element, then the number of appear-

ance of sl is most, 2 m−1 , and the number of appearance of yl which come from the

̱

same cluster is most, and is 2 m−1 .

So when yl is nonzero vector and its appearance number is 2 m−1 , it must be a column vector of mixture matrix A . From theorem 1, in order to restore A , we should find m clusters in which elements are nonzero and the number of elements are most. We denote the m clusters as a new set Gˆ = {Gˆ , Gˆ  Gˆ } . We take a column vector from every Gˆ and make 1

2

m

i

them divided by 2 then denoted as aˆ , (i = 1,2  m) . A new matrix Aˆ is composed of aˆ , (i = 1,2  m) , and It is obvious that Aˆ is only a primary column transformation of i

mixture matrix A . So Aˆ = AP , where P is a primary matrix. Substituting (14) for (6) X ( N ) = Aˆ P −1 S ( N ) .

(14) (15)

Let Sˆ ( N ) = P −1 S ( N ) , we have X ( N ) = Aˆ Sˆ ( N ) .

(16)

−1

Because P is a primary matrix, so P is also a primary matrix and Sˆ ( N ) is only a primary row transformation of S ( N ) . From (16), Sˆ ( N ) = Aˆ −1 X ( N ) ,

(17)

so the source signals can be restored through Sˆ ( N ) by permutations or sign changes.

26

W. Xia and B. Tan

Algorithm summary, 1. Find 2 m distinct sensor signal vectors denoted as U = {x1 , x2  x2m } from N

sensor signals. Get the set Y = { yl , l = 1C22m } through equation (11) and cluster them by us-

Ձ

ing definition 1. Find m nonzero clusters whose elements’ number are all 2 m−1 in above clusters, and denoted as a set of them Gˆ = {Gˆ 1 , Gˆ 2  Gˆ m } . Take a column vector from every cluster Gˆ , (i = 1,2  m) and divide it by 2, then denoted as aˆ , (i = 1,2  m) .

Ղ

i

Form a new matrix Aˆ by aˆ , (i = 1,2  m) . 4. Restore source signals by (17).

4 Simulation Results In the experience, we suppose there are three BPSK source signals in the following fig.1, and take N = 1000 in case of no noise. Here, a 3 × 3 random mixture matrix ª 0.8304 0.0490 -1.8211º A = ««- 0.0938-1.3631 1.4675»» «¬- 0.4591- 0.2131 - 0.4641 »¼

is brought. The mixture signals are gotten by equation (6) and

the three mixtures are shown by the following fig.2. Then, a new mixture matrix ª- 0.0490-1.8211 0.8304º Aˆ = «« 1.3631 1.4675- 0.0938»» «¬ 0.2131- 0.4641- 0.4591»¼

is obtained by the above algorithm accurately and source sig-

nals are restored by equation (17) and shown by the fig.3.

Fig. 1. Three source signals

An Efficient Algorithm for Blind Separation of Binary Symmetrical Signals

27

Fig. 2. Three mixture signals

Fig. 3. Three restored source signals

We find that the estimated mixture matrix Aˆ is a primary column transformation of the original mixture matrix A through the algorithm, so the restored source signals are only different from the original source signals by permutations and signs, and source signals are restored successfully. Similarly, the algorithm can be applied to general binary symmetrical signals for blind separation through the example of BPSK signals.

28

W. Xia and B. Tan

5 Conclusions This paper gives a novel algorithm for blind separation of binary symmetrical signals and it doesn’t depend on the characteristics of statistical independence of source signals. According to the characteristics of binary symmetrical signals, we can estimate the nonsingular mixture matrix and proved in the paper. The simulations show the estimated matrix accurate and the algorithm simple with a little computation. Therefore, it has good performance and precision for blind separation of binary symmetrical signals.

References 1. Xie, S.L., Zhang, J.L.: Blind Separation of Minimal Information Based on Rotating Transform. Acta Electronica Sinica, v 30, n5, May(2002) 628-631 2. Li, Y., Wang, J., Zurada, J.M.: Blind Extraction of Singularly Mixed Source Signals. Neural Networks, IEEE Transactions on Volume 11,Issue 6, (2000) 1413 – 1422 3. Yang, H.H., Amari, S., Cichocki, A.: Information-theoretic Approach to Blind Separation of Sources in Nonlinear Mixture. Signal Processing, vol.64, (1998) 291-300 4. Zhang, J.L., Xie, S.L., He, Z.S.: Separability Theory for Blind Signal Separation. Zidonghua Xuebao/Acta Automatica Sinica, v30, n 3, May (2004) 337-344 5. Bofill, P., Zibulevsky, M.: Underdetermined Source Separation Using Sparse Representation.Signal processing, 81 (2001) 2353-2362 6. Xiao, M., Xie, S.L., Fu, Y.L.: A Novel Approach for Underdetermined Blind Sources Separation in Frequency Domain. Advances in Neural Networks-ISNN 2005, LNCS 3497 (2005) 484-489 7. Van der veen, A.J.: Analytical Method for Blind Binary Signal Separation, IEEE Trans. Signal Process, 45 (1997) 1078-1082 8. Anand, K., Mathew, G., Reddy, V.U.: Blind Separation of Multiple Co-channel BPSK Signals Arriving at an Antenna Array, IEEE Signal Process. Lett. 2 (1995) 176-178 9. Li, Y., Cichocki, A., Zhang, L.: Blind Separation and Extraction of Binary Sources. Communication and Computer Sciences, 86 (2003) 580-590 10. Xie, S.L., He, Z.S., Fu, Y.L.: A Note on Stone’s Conjecture of Blind Separation. Neural Computation, 16(2004) 245-319 11. Li, Y., Cichocki, A., Zhang, L.: Blind Deconvolution of FIR Channels with Binary Sources: A Grouping Decision Approach. Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03). 2003 IEEE International Conference on Volume 4 (2003) 289-292 12. Talwar, S., Viberg, M., Paulraj, A.: Blind Estimation of Synchronous Co-channel Digital Signals Using an Antenna Array. Part I: algorithms. IEEE Trans. Signal Process. 44 (1996) 1184-1197 13. Zhang, J.L., Xie, S.L.: Multi-input Signal-output Neural Network Blind Separation Algorithm Based on Penalty Function. Intelligent and Complex Systems, 2(2003) 353-362 14. Lee, C.C., Lee, J.H.: An effient method for blind digital signal separation of array data. Signal Processing 77 (1999) 229-234 15. Xie, S.L., He, Z.S., Gao, Y.: Adaptive Theory of Signal Processing. 1st ed. Chinese Science Press, Beijing (2006) 130-223

A New Blind Source Separation Algorithm Based on Second-Order Statistics for TITO ZhenLi Wang, XiongWei Zhang, and TieYong Cao Nanjing Institute of Communications Engineering P.O. Box 7, Nanjing, Jiangsu, 210007 China [email protected], [email protected]

Abstract. In this paper, we investigate a new blind source separation algorithm for TITO (two-input and two-output) channel system. Considering the case of the noisy instantaneous linear mixture of source signals, we form the matrix pair with the two 2×2 dimension symmetric, positive definite matrices via two covariance matrices. We apply a set of transforms such as the Cholesky factorization and SVD (singular value decomposition) to this formed matrix pair. And a unitary matrix is then obtained, which is an accurate diagonalizer of each matrix of this pair. Compared with the JADE algorithm and the SOBI algorithm, some numerical results show the better performance of the new algorithm.

1 Introduction Blind source separation (BSS), aiming at recovering unobserved signals or “sources” from observed mixtures, has recently received a lot of attention. This is due to the many potential application areas, such as communication [1], [2], biomedical measurements [3], [4], etc. It is often called “blind” because it exploits only on the assumption of mutual independence between the sources without relying on any α priori knowledge about mixing matrix. In our work, we concerned only with the separation of noisy linear combinations of the two source signals obtained from TITO channel system. In its form, one observes two sequences S1 (n) , S2 (n) recorded from two sensors, each observation X i ( n) being a noisy linear combination of two sources. Thus

㧘 X (n) = AS (n) + d (n) ,

where vector S(n) =[s1(n) s2 (n)]T , vector

X (n) = [x1(n) x2 (n)]T , vector d (n) denotes additive perturbed noise and A = (ai , j ) is fixed unknown invertible matrix. Sources can be recovered blindly by either estimating the mixing matrix A or its pseudo-inverse M = A# corresponding to the demixing system. Several papers have introduced blind identification algorithms based on joint diagonalization (see [5], [6], [7]). For instance, the SOBI algorithm presented in [5], [6] relies on stationary second-order statistics which are based on a joint diagonalization of a set of covariance matrices. Similarly, the joint diagonalization of the JADE algorithm [7] is performed by some fourth-cumulant matrices. However, it costs unnecessary computation amount for the joint diagonalization of many matrices in these previous techniques. Moreover, the approximate diagonalization degrades the separation performance of sources. In this paper, we D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 29 – 34, 2006. © Springer-Verlag Berlin Heidelberg 2006

30

Z. Wang, X. Zhang, and T. Cao

propose a new blind source separation algorithm based on accurate diagonalization second-order statistics for TITO channel system. The remainder of this paper is organized as follows: Section 2 presents a new blind separation algorithm based on accurate diagonalization second-order statistics. Some numerical results are given in Section 3 to illustrate the validity of this algorithm. Finally, the conclusion is presented in Section 4.

2 The New Blind Source Separation Algorithm We consider exploiting second-order statistics information of the whitened observation signal X w (n) . For independent sources, the sample autocorrelation covariance matrices and its delayed counterpart are defined as the follows Rˆ (0) = X (n) X T (n) = ARˆ (0) AT + σ 2 I w

w

s

Rˆ ( k ) = X w ( n + k ) X wT ( n) , k ≥ 1 & k ∈ Z

(1) (2)

Where T denote the transpose of a vector or a matrix. Under the white noise assumption, the JADE algorithm and the SOBI algorithm both obtain an estimation σˆ 2 of the noise variance, which is the average of the m − n smallest eigenvalues of Rˆ (0) . Where m and n denote the numbers of the sample covariance matrices and the sources, respectively. For TITO channel system, this variance estimation can’t be performed since m = n . In this paper, the presented algorithm reduces the influence of disturbing noise via a series of transforms. It is introduced by the following steps: Step 1. Form the matrix pair ( P, Q ) with the two 2×2 dimension symmetric positive definite matrices as the follows

P = Rˆ (1) Rˆ T (1)

(3)

(4) Q = Rˆ (2) Rˆ T (2) Step 2. Compute the Cholesky factorization of matrix P and matrix Q , respectively.

P = RPT RP

(5)

Q = RQT RQ

(6)

By using upper-triangle matrices RP and RQ , a new matrix F is then defined as the following equation:

F = RP ⋅ RQ −1

(7)

Step 3. Compute SVD (singular value decomposition) of matrix F .

Σ = U F T FVF Where Σ = diag(σ 1 , σ 2 ) , σ 1 ≥ σ 2 > 0 .

(8)

A New BSS Algorithm Based on Second-Order Statistics for TITO

31

Step 4. Form a unitary matrix U according to equation (9), which is an accuracy diagonalizer of each matrix of the pair ( P, Q ) . Namely, matrix U satisfies with the form U T PU = D1 and U QU = D2 , where D1 and D2 are both diagonal matrices. T

U = RQ −1 ⋅ VF

(9)

Proof Applying (5) and (9) to the matrix product of PU , we shall get

PU = RPT RP ⋅ RQ −1VF = RPT ⋅ ( RP RQ −1 ) ⋅ VF

(10)

(7) and (8) are then applied to (10)

PU = RPT ⋅ F ⋅ VF = RPT ⋅ U F ΣVF T ⋅ VF = RPT ⋅ U F Σ VF TVF = I ,

= RQT ⋅ ( RP RQ −1 )T ⋅U F Σ = RQT ⋅ F T ⋅U F Σ = RQT ⋅ VF ΣTU F T ⋅ U F Σ , U F T U F = I = RQT ⋅VF ΣT Σ = RQT VF ⋅ Σ 2 = ( RQ −1VF ) −T Σ 2 = U −T Σ 2

(11)

We can find the expression U PU = Σ from (11). Similarly, (6) and (9) are applied to the matrix product of QU T

2

QU = RQT RQ ⋅ RQ −1VF = RQT ⋅ VF

= ( RQ −1VF ) −T = U −T

(12)

The other expression U T QU = I are got from (12). Now we can easily know that D1 = Σ 2 , D2 = I . Clearly, the global minimum of the nonnegative function

C (U ) = off(U T PU + U T QU )

(13)

is achieved when matrix U simultaneously and accurately diagonalize the pair ( P, Q) , And this minimum value equals to zero. In equation (13), the “off” is defined as off( H ) = ¦ | H ij |2 . The proof of the uniqueness of matrix U can be seen in i ≤i ≠ j ≤ n

appendix B of index [6]. Step 5. The source signals are estimated as Sˆ ( n) = U T X w (n) , and the demixing matrix is estimated as M = UTW , where W denotes the whitening matrix.

32

Z. Wang, X. Zhang, and T. Cao

3 Simulation Results The experiment in this Section is intended to illustrate the superiority of our algorithm compared to the JADE algorithm and the SOBI algorithm. In this test, the JADE algorithm and the SOBI algorithm use 3 fourth-order cumulant matrices and 150 covariance matrices for joint diagonalization, respectively. In order to evaluate the performance of three algorithms, we calculate the error measure proposed by Amari etc [9]. N

N

| gij |

i =1

j =1

max k | g ik |

E = ¦ (¦

N

N

| gij |

j =1

i =1

max k | g kj |

− 1) + ¦ (¦

− 1)

(14)

gij is the (i, j ) -element of the global system matrix G = MA and maxj gij represents the maximum value among the elements in the i th row vector of G , maxj g ji denotes the maximum value among the elements in the i th column vector of where

G . The data X (n) = [ x1 (n) x2 (n)]T are synthesized by mixing two independent sources s5, s6 [8] through the matrix A , which is randomly generated in the interval [0,1]. The synthesized X (n) is then corrupted with white noise. In the situation of noise level ranging from -50 dB to 0 dB, Fig.1 shows that three curves are obtained by averaging ten times runs, which correspond to the JADE algorithm, the SOBI algorithm and the proposed algorithm, respectively. The main conclusion can be drawn from this figure is that the new algorithm performs better than the other two algorithms when noise power is less than -20 dB. Again, the performance of the new algorithm is still superior to that of the JADE algorithm when noise power increases from -20 dB to 0 dB.

Fig. 1. Noise power versus error measure for three algorithms: the JADE algorithm (dashed line with diamond), the SOBI algorithm (the dotted line with triangle-right) and the proposed algorithm (the dash-dot line with circle)

A New BSS Algorithm Based on Second-Order Statistics for TITO

33

Fig.2 shows a set of speech spectrograms in the case of noise power equaling to -

ª0.8349 0.6305º » . From this picture we can know ¬0.2258 0.7041¼

25 dB and the mixing matrix A = «

that, compared to the previous algorithms, the proposed algorithm has comparative performance by only using little second-order statistics information, which reduces the computation amount of the new algorithm.

Fig. 2. Speech spectrograms . (a), (b): The two source signals. (c), (d): The two mixing signals corrupted with white noise. (e), (f): The two separated signals of the JADE algorithm. (g), (h): The two separated signals of the SOBI algorithm. (i), (j):The two separated signals of the proposed algorithm.

4 Conclusion A new algorithm, which is applicable to TITO channel system, has been introduced for blind sources separation. In the proposed algorithm, a series of transforms are used to the formed matrix pair exploiting second-order statistics information. And the proof of accurate diagonalization of this pair is also presented. The separation of the two noisy source signals is studied in simulation experiments. Results show that our algorithm performs better than the JADE algorithm and the SOBI algorithm at low noise power. Besides, our algorithm still keeps better performance compared with the JADE algorithm when disturbed noise power increases.

References 1. Anand, K., Mathew, G., Reddy, V.: Blind Separation of Multiple Co-channel BPSK Signals Arriving at an Antenna Array. IEEE Signal Processing Letters. 2 (1995) 176-178 2. Chaumette, E., Comon, P., Muller, D.: ICA-based Technique for Radiating Sources Estimation: Application to Airport Surveillance. IEE Proceedings-F. 140 (1993) 395-401 3. Karhunen, J., Hyvarinen, A., Vigario, R. (ed.): Applications of Neural Blind Separation to Signal and Image Processing. In Proc. ICASSP. 1 (1997) 131-134

34

Z. Wang, X. Zhang, and T. Cao

4. Makeig, S., Bell, A., Jung, T.P, Sejnowski, T.J.: Independent Component Analysis of Electroencephalographic Data. In Advances in Neural Information Processing Systems. 8 MIT Press (1995) 5. Belouchrani, A., Cichocki, J.F.: Robust Whitening Procedure in Blind Source Separation Context. Electronics Letters. 36 (2000) 2050-2053 6. Belouchrani, A., Abed, M.K., Cardoso, J.F.(ed.): A Blind Source Separation Technique Using Second-order Statistics. IEEE Trans.Signal Processing. 45 (1997) 434-444 7. Cardoso, J.F., Souloumiac, A.: Blind Beamforming for Non-Gaussian Signals. IEE Proc. F (Rader and Signal Processing), 140 (1993) 362-370 8. http://www.kecl.ntt.co.jp/icl/signal/mukai/demo/hscma2005 9. Amari, S.I., Cichocki, A., Yang, H.H.: A New Learning Algorithm for Blind Signal Separation. In D.S Touretzky, M.C.Mozer & M.E. Hasselmo (Eds), Advance in Neural Information Processing Systems, Cambridge, MA: MIT Press (1996) 757-763

A New Step-Adaptive Natural Gradient Algorithm for Blind Source Separation Huan Tao, Jian-yun Zhang, and Lin Yu Information Engineering Dept., Electronic Engineering Institute, 230037 HeFei, China [email protected]

Abstract. The main differences between the mixed signals and origin signals: Gaussian probability density function, statistical independence and temporal predictability. The proposed BSS algorithms mainly derived from the Gaussian probability density function and statistical independence. A new adaptive method is proposed in the paper. The method uses the temporal predictability as cost function which is not studied as much as other generic differences between the properties of signals and their mixtures. Step-adaptive nature gradient algorithm is proposed to separate signals, which is more robust and effective. Compared to fixed step natural gradient algorithm, Simulations show a good performance of the algorithm.

1 Introduction The goal of blind signal separation (BSS) is to recover mutually independent signals from their mixture. The problem has recently attracted a lot of interest because of its wide number of applications in diverse fields and some effective methods have been proposed such as in [2],[5],[6]. BSS can be very computationally demanding if the number of source signals is large. Application call for a BSS method which is computationally affordable, fast convergent, stable and reasonable accurate. BSS can be decomposed into two-steps: the observations are first pre-whitened by a whitening matrix, and then an orthogonal matrix can be separately calculated by constraining the source separation with different cost function. There are three main differences between the mixed signals and origin signals: Gaussian probability density function, statistical independence and temporal predictability. The proposed BSS algorithms mainly derived from the Gaussian probability density function and statistical independence. A new cost function based on temporal predictability is proposed by Reference [1] and proved to be effective which found a new way for blind signal separation. But it has limitations. The added calculation of temporal predictability makes the separate algorithm based on nature gradient time-consuming and instable. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 35 – 40, 2006. © Springer-Verlag Berlin Heidelberg 2006

36

H. Tao, J.-y. Zhang, and L. Yu

In this paper, a new BSS method based on maximizing temporal predictability of signal mixtures has been introduced which has better separation performance.

2 Preliminaries 2.1 BSS Model As a general model for BSS let L observed signals be related to N independent source signals si (t )(t = 1,", N ) by L × N unknown channel matrix A:

x(t )  As (t ) n(t ) . Where

(1)

s (t ) = [ s1 (t ), s 2 (t ),", s N (t )]T and A is full-column rank matrix.

n(t )  (n1 (t ), n2 (t ), ", nm (t ))T is the vector of additive noise. Without loss of generality we assume in the derivation that signal are real-valued, L = N and no noise. The BSS can operate into two steps. The first step is to pre-whiten the observations according to a whitening matrix B which results in a set of uncorrelated and normalized signals. Pre-whitening can be carried out in any of known methods and it is not dealt with here. After pre-whitened, an appropriate cost function based on high-order statistics can separate the sources by forcing their independence. 2.2 Temporal Predictability In Reference [1], the definition of signal predictability F is: n

F (Wi, x)  log

V (Wi , x) V  log i  log U (Wi , x) Ui



œ( y  y ) i

i1 n

~

œ( y  y ) i

2

i

.

(2)

2

i

i1

Where

yi  Wi xi is the value of signal y at time i . The term U i reflects the extent ~

yi is predict by a short-term ‘moving average’ y i of values in y . In contrast, the term Vi is a measure of the overall variability of in y . As measured by

to which



the extend to which

yi is predicted by a long term ‘moving average’ y i of values in ~



y . The predicted value y i and y i of yi are both exponentially weighted sums of signal values measured up to time i 1 ,such that recent values have a larger weighting than those in the distant past:

A New Step-Adaptive Natural Gradient Algorithm for Blind Source Separation ~

~

y i  MS y i1 (1 MS ) yi1 0 b MS b 1 

37



.

(3)

y i  ML y i1 (1 ML ) yi1 0 b ML b 1 The half-life

hL of ML is much longer than the corresponding half-life hS of MS .

The relation between a half-life

h and parameter M is defined as M  21/ h .

3 Step-Adaptive Nature Gradient Algorithm Equation (2) can be rewritten as: 

F  log

Wi C Wi t ~

.

(4)

Wi C Wi t 

~

Where C is long-term covariance between signal mixtures, and C is short-term covariance, which can be expressed as: Reference [3] proved gradient ascent on F with respect to Wi could be used to maximize F .

∇F = Iteratively updating

2Wi − 2Wi ~ C− C. Vi Vi

(5)

Wi until a maximum of F is located: Wi +1 = Wi + µ∇F .

(6)

Commonly, the convergence time and stability is based upon the properly selection of step µ . Reference [4] has analyzed the stability conditions of nature gradient algorithm. A step-adaptive algorithm is desirable. Here we proposed a new step-adaptive algorithm. Intuitively, we can use the distance between the separation matrix and optimal separation matrix to adjust the step adaptively. But the optimal separation matrix is unknown before the signals separated. An alternation we use

∆W (k ) = Wi +1 − Wi

2 F

.

(7)

∆W (k ) , E (∆W (k )) is used to perform step-adaptive adjustment. In the process of adaptation, the increasing of E ( ∆W ( k )) means the To smooth the

fluctuation of algorithm, so a smaller step is desirable; on the contrary, the decreasing

38

H. Tao, J.-y. Zhang, and L. Yu

of E ( ∆W ( k )) means a larger step is wanted to accelerate the convergence of algorithm. The updating expression of step is:

µ (k + 1) = α (k ) µ (k ) .

α

(8)

can be expressed as follows:

­1+ γE(∆W(k)),E(∆W(k)) < E(∆W(k −1)) 1 °° , E(∆W(k)) > E(∆W(k −1) α(k) = ® 1 + E ( ∆ W ( k )) β ° °¯ 1, else



(9)

Where 0 < β < 1,0 < γ < 1  γ is in charge of the convergence speed and controls the steady error when convergence. E (∆W (k )) can be get form:

E(∆W(k +1)) =

k 1 E(∆W(k)) + ∆W(k +1) . k +1 k +1

β

(10)

4 Simulation and Performance Compared to fixed step nature gradient algorithm, the performance of the stepadaptive nature gradient algorithm is evaluated through simulations. Here we use three source signals with the sample of 5000 points. The mixing matrix A is generated randomly. The simulation parameters are as follows: λ L = 0.9, λ S = 0.004, µ 0 = 0.001, β = 0.5, γ = 0.06 . After separation, the

1 º ª0.02 0.04 « 1 0.1 »» . separated result is: 0.06 « «¬ 1 0.008 0.003»¼ To evaluate the separation performance and the convergence speed of different algorithms, we use the correlation coefficiency between the original signals and recovered signals. The definition of correlation coefficiency is defined by (11).

ρ ij =

cov(s i , s j ) cov(s i , si ) cov(s j , s j )

.

(11)

A comparison between fixed step nature-gradient algorithm with different steps and step-adaptive nature-gradient algorithm is done based on correlation coefficiency. The result is depicted in Fig. 1.

A New Step-Adaptive Natural Gradient Algorithm for Blind Source Separation

39

0 step=0.0005 step=0.002 step=0.01 adaptive step

-10

ρ(k) [dB]

-20

-30

-40

-50

-60

-70

0

0.5

1

1.5 2 number of iterations k

2.5

3 4

x 10

Fig. 1. Comparison of step-adaptation with fixed steps of 0.0005,0.002 and 0.01

From Fig.1, we can clearly see the step-adaptive nature-gradient algorithm is superior to fixed step nature-gradient algorithm in convergence speed.

5 Conclusion A new adaptive separation algorithm is proposed based on maximizing temporal predictability of signal which is not studied as much as other generic differences between the properties of signals and their mixtures. The algorithm is stepadaptive. So it is more robust compare to fixed step natural gradient. Simulations show that it is effective and can get good separation precision. The step-adaptive nature gradient algorithm can also be used to other BSS method based on different cost function.

References 1. James, V. Stone.: Blind Source Separation Using Temporal Predictability, Neural computation(in press) (2001) 1196-1199 2. Belouchrani, A., Abed-Meraim, K., Cardoso, J.F.: A Blind Source Separation Using Second Order Statistics. IEEE Trans. On signal processing,Feb. Vol.45 (1997)434-444 3. Amari, S I.:Natural Gradient Works Efficiently in Learning. Neural Computation(1998) 251-276

40

H. Tao, J.-y. Zhang, and L. Yu

4. Amari, S. I., Chen, T. P.,Cichocki, A.: Stability Analysis of Adaptive Blind Source Separation, Neural Networks(1997) 1345-1351. 5. Sergio, A., Cruces-Alvarez, Andrzej Cichocki, Shun-Ichi Amari.: On A New Blind Signal Extraction Algorithm: Different Criteria and Stability Analysis.. IEEE SIGNAL PROCESSING LETTERS, VOL.9,NO.8,AUGUST (2002) 6. Yan, Li, Peng Wen, David Powers.: Methods for The Blind Signal Separation Problem. IEEE Int. Conf. Neural Networks&Signal Processing. December (2002)

An Efficient Blind SIMO Channel Identification Algorithm Via Eigenvalue Decomposition* Min Shi and Qingming Yi Department of Electronic Engineering, Jinan University, Guangzhou, 510632, PR China [email protected]

Abstract. An effective blind multichannel identification algorithm is proposed in this paper. Different from the Prediction Error Method, the new algorithm does not require the input signal to be independent and identical distribution, and even the input signal can be non-stationary. Compared with Least-Square Approach, the new algorithm is more robust to the overestimation of channel order. Finally, the experiments demonstrate the good performance of the proposed algorithm.

1 Introduction Blind identification of Single-Input Multiple-Output (SIMO) systems has many applications, or potential applications in wireless communications, equalization, seismic data deconvolution, speech coding, image deblurring, echo cancellation[1-8], etc. For the FIR SIMO system, as long as the FIR channels do not share the common zeros and all channels are fully activated, the SIMO system can be identified by just second-order statistics of the output [1], which further makes the blind identification of SIMO systems so important. So many researchers paid much attention on this problem. Because of the predominant advantage in computation cost and the weak requirement in data samples of the receiving signals, the second-order statistics (SOS)-based methods are very attractive and obtain much attention. Among them, the least-square approach (LSA) [1], the linear prediction methods (LP) [2] and the subspace methods (SS) [3]and are the three main classes. When the channel order is known, the channels can be very precisely estimated by SS-based approaches and LSA-methods, however, which are very sensitive to the estimation error of channel order. Contrastively, LP methods are not so accurate as the former two methods, but robust to the channel order overestimation. LP methods usually require the input signal is independent and identically distribution (i.i.d) while the other two methods is not limited by this requirement. Relatively, the LS approaches are a little simpler than SS ones. *

This work was supported by the National Natural Science Foundation of China(Grant 60505005), the Guangdong Provincial Natural Science Foundation(Grant 05103553), and Guangdong Province Science and Technology Project (Grant 2005B10101013).

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 41 – 47, 2006. © Springer-Verlag Berlin Heidelberg 2006

42

M. Shi and Q. Yi

In this paper, we present a new blind identification algorithm for SIMO FIR system by improving the LS approaches. The proposed algorithm is simply based on generalized eigenvalue decomposition. The new algorithm can be easy implemented and is robust to the channel order overestimation than SS and LS approaches.

2 Problem Statement The single-input m -output channel can be formulated as: L

x ( t ) = ¦ h (τ ) s ( t − τ ) + n ( t ) , t = 1, 2," , T

(1)

τ =0

where x ( t ) = ( x1 ( t ) ," , xm ( t ) ) ∈ R m×1 is the observed signa1 vector, s ( t ) is the input T

signal, h (τ ) = ( h1 (τ ) ," , hm (τ ) ) , (τ = 0," , L ) denotes the FIR channel impulse response. The order of the convolution is L . The additive noise is denoted as a vector T n ( t ) = ( n1 ( t ) ," , nm ( t ) ) ∈ R m×1 . The blind identification problem can be stated as T

follows: Given the receiving signals determine

{hˆ ( < )} i

m

i =1

the

channels

{h ( < )}

m

i

i =1

{ x ( t ) i = 1,", m; t = 1,", T }

up

i

to

a

nonzero

, we aim to

scaling

factor,

i.e.

= c {hi ( < )}i =1 , ( c ≠ 0 ) , then we can further recover the input signal s ( < ) . m

Xu, Tong, et al point out that if the channel order is known in advance, the necessary and sufficient identifiability condition of SIMO system (1) is that the FIR channels have no common zero [1]. So we assume that the FIR channels of system (1) do not share the common zeros.

3 Identification Equations According to reference [1], we have the following equations: xi ( t ) = hi ( t ) : s ( t ) ,

x j (t ) = h j (t ) : s (t ) ,

(2)

where : stands for convolution operation. Thus h j ( t ) : xi ( t ) = h j ( t ) : ¬ª hi ( t ) : s ( t ) ¼º = hi ( t ) : ª¬ h j ( t ) : s ( t ) º¼ = hi ( t ) : x j ( t ) , i.e., h j ( t ) : xi ( t ) = hi ( t ) : x j ( t ) , ( i ≠ j, i, j = 1," , m )

(3)

From equation (3), we have ªhj º ª¬ X i ( L ) : − X j ( L ) º¼ « » = 0 ¬ hi ¼

(4)

An Efficient Blind SIMO Channel Identification Algorithm

43

where hk = ( hk ( L ) ," , hk ( 0 ) ) and T

ª xk ( L ) « x ( L + 1) X k ( L) = « k «# « «¬ xk (T − L )

xk ( L + 1) xk ( L + 2 ) # xk (T − L + 1)

" xk ( 2 L ) º » " xk ( 2 L + 1) » » % # » " xk (T ) »¼

(5)

where k = 1," , m . T

Denote h  ª h1T ," , hmT º , and we construct the following matrices: ¬ ¼ ª º½ « 0 " 0 X i +1 ( L ) − X i ( L ) 0 0 »° « » °° X i ( L) = « # 0 0 » ¾ m − i blocks # % «0 " 0 X ( L) 0 " − X i ( L )» ° m « N   

»° i −1 blocks m − i +1 blocks ¬ ¼ ¿°

(6)

where i = 1," , m .In equations (6), each block, e.g., 0 or { X k ( L ) , k = 1,", m} , has the size (T − L + 1) × ( L + 1) . In the noise free case, from SIMO system (1) we derive the following equations: X ( L) ⋅ h = 0

where matrix X ( L ) is

(7)

{(T − L + 1) ª¬m ( m − 1) 2º¼} × ª¬m ( L + 1)º¼ , and it is given by

ª º½ « X 1 ( L) »° « » °° m ( m + 1) X ( L) = « blocks # »¾ 2 « X m−1 ( L ) » ° «  

»° ¬ m blocks ¼ °¿

(8)

Now the blind identification problem (1) boils down to solving equations (7).

4 Blind Identification Algorithm The solution of equation (7) is not unique. To find the practical solution, we usually add some appropriate constraints, e.g., h = 1 or c H h = 1 for a constant vector c . 2 The LS approaches identify the channels of system (1) by solving the following optimization problem with constraints: ­ min J ( h ) = min X ( L ) ⋅ h 2 , 1 ° 2 h ® °¯ st : h 2 = 1.

(9)

44

M. Shi and Q. Yi

Xu, Tong et al [1] use the singular value decomposition (SVD) or fast subspace decomposition (FSD) to solve optimization problem (9). Of course, we can replace the constraint h = 1 by constraint c H h = 1 .Since the accurate channel order of 2

system (1) is unknown and estimating it is a challenging work in practice. Usually what we can do is overestimating the order. Without the loss of generality, we overestimate the channels order of system (1) as Lh ( Lh ≥ L ) . As mentioned in section 1, LSA algorithm is not robust to overestimation of channel order. To overcome this drawback, we attempt to improve the LSA algorithm, which intend to not only keep advantage of LSA algorithm, but also be robust to overestimation of channels order. Denote the ª¬ m ( Lh + 1) º¼ ×1 vector hˆ to be the estimation of h . Considering Lh ≥ L , if hˆ satisfies hk (τ ) = 0, (τ = L + 1,", Lh ; k = 1,"m ) , the overestimation of channel order will have not any influence on the channel identification of system (1). Hence the desirable estimation hˆ of h should be ­hˆ = ª hˆT ," , hˆT ºT , m¼ ¬ 1 ° ° T h −L § L ·  ® T °hˆk = c ¨ 0," , 0, hk ¸ = c ( 0," , 0, hk ( L ) ," , hk ( 0 ) ) , k = 1," , m,  

¨ ¸ ° Lh +1 © ¹ ¯

where

c is a nonzero constant. We construct the following

(10)

ª¬ m ( Lh + 1) º¼ × 1 vector:

­ ȝ = ª ȝT ," , ȝT º T ∈ R m( Lh +1) , m¼ ¬ 1 ° ® T Lh ° ȝk = µ ," , µ ,1 , k = 1," , m;0 < µ < 1. ¯

(

(11)

)

To make hˆ be robust to overestimation of channel order and satisfy expression (10) as possible as it can, we solve the following optimization problem with constraints:

()

­ ª X ( L ) ⋅ hˆ 2 + hˆ T diag ( ȝ ) l hˆ º , ˆ ( ) »¼ h ° min J h = min 2 hˆ « ¬ ® ° st : hˆ = 1, ¯ 2

(12)

where l is a positive integer. Because 0 < µ < 1 , it is easy to know that 1 > µ > " > µ Lh and 1 > µ l > " > µ lLh . So under the constraints hˆ = 1 and 2

l X ( Lh ) hˆ = 0 , minimizing hˆT ª¬ diag ( ȝ ) º¼ hˆ will force hˆ to approximately satisfy expression (10) in some degree. The constraint hˆ = 1 means hˆT hˆ = 1 . Thus the optimization problem (12) can be 2

formulated into the following one without constraint:

An Efficient Blind SIMO Channel Identification Algorithm

45

ª X ( L ) ⋅ hˆ 2 + hˆ T diag ( ȝ ) l hˆ º ( ) ¼» h 2 ˆ = min ¬« h min e hˆ hˆ hˆ T hˆ

()

l hˆ T ª X T ( Lh ) X ( Lh ) + ( diag ( ȝ ) ) º hˆ ¬ ¼ = min hˆ hˆ T hˆ

(13)

From expression (13), we have

()

l e hˆ ⋅ hˆT hˆ = hˆT ª X T ( Lh ) X ( Lh ) + ( diag ( ȝ ) ) º hˆ ¬ ¼

(14)

For equation (14), calculating the derivative of the two sides with respect to hˆ , we get

( ) ⋅ hˆ hˆ + 2 e hˆ hˆ = 2 ª X () ¬

∂ e hˆ

T

∂hˆ

Let

T

( Lh ) X ( Lh ) + ( diag ( ȝ ) ) º¼ hˆ l

(15)

( ) = 0 , from equation (15), we have

∂ e hˆ ∂hˆ

( ) ⋅ hˆ hˆ = 2

∂ e hˆ ∂hˆ

T

{ª¬ X

T

( Lh ) X ( Lh ) + ( diag ( ȝ ) ) º¼ − e ( hˆ ) ⋅ I l

} hˆ = 0

(16)

Equation (16) means that one can estimate hˆ by doing the eigenvalue decomposition with respect to matrix ª X T ( Lh ) X ( Lh ) + ( diag ( ȝ ) )l º , and the ¬ ¼ eigenvector corresponding smallest value is just the estimation of hˆ . So we obtain the proposed algorithm as follows:

XP Input the received signalsG x ( t ) = ( x1 ( t ) ,", xm ( t ) )T , t = 1,", T UG Set µ SG integerG l Gand the channel orderG Lh UG YP Construct the matrix X ( Lh ) Gand ȝ UG ZP Compute the eigenvalues and corresponding eigenvectors of matrixUG 4) The eigenvector corresponding smallest value is just the estimationG hˆ ofG h U

5 Numerical Experiments and Result Analysis Root-mean-square-error (RMSE) is employed as a performance measure of channel estimation. Usually, when RMSE1.0, the estimation of channels is not reliable. The input signal is supposed to be independent and identical distribution in the experiment. Computer simulations were conducted to evaluate the performance of the proposed algorithm in comparison with Least-Squares Approach (LSA) and Prediction Error Method (PEM). In the

46

M. Shi and Q. Yi

following two experiments, the related parameters of the proposed algorithm are set as: T = 1000 , µ = 0.99 and l = 2 experientially. All input signals are i.i.d Gaussian signals generated by Matlab command randn ( < ) . The channel coefficients are listed below.

h1 ( z ) = -0.4326+0.1253z −1 -1.1465z −2 , h2 ( z ) = -1.6656+0.2877z −1 +1.1909z −2 .

Table 1. The overestimation of channel order and corresponding RMSE for i.i.d input signal

Lh

2

3

4

5

6

7

8

9

LSA PEM Our

9.0984e-016 0.0424 9.3014e-006

0.99 0.08 0.03

0.97 0.26 0.14

1.04 0.27 0.14

0.10 0.31 0.14

1.03 0.31 0.14

1.08 0.32 0.14

1.10 0.32 0.14

(a) Noise free

(b) The received signals are added white Gaussian noise and the SNR is 40dB

Fig. 1. Performance comparison between LSA, PEM and the proposed algorithm

From Table 1 and Fig.1(a), when the order of channel is accurately given, LSA can obtain the precise estimation of channels. But for overestimation case without noise, we can see that both PEM algorithm and the proposed algorithm well identify the channels, but LSA does not do this. Additionally, Fig.1(b) shows the comparison result in the same simulation environment except adding white Gaussian noise to the receiving signals. All SNRs are 40dB. In this situation, we can see that only the proposed algorithm get the relatively satisfactory estimation (Fig.1(b)).

6 Conclusion Based on matrix eigenvalue decompostion, an effective blind multichannel identification algorithm is proposed in this paper. Different from the Prediction Error Method, the new algorithm does not require the input signal to be independent and

An Efficient Blind SIMO Channel Identification Algorithm

47

identical distribution, and even the input signal can be non-stationary. Compared with Least-Square Approach, the new algorithm is more robust to the overestimation of channel order and much faster.

References 1. Xu, G. H., Liu, H., Tong, L., Kailath T.: A Least-squares Approach to Blind Channel Identification. IEEE Trans on Signal processing, Vol.43 (1995) 2982-2993 2. Abed-Meraim K., Moulines E., Loubaton P.: Prediction Error Methods for Second-order Blind Identification. IEEE Trans on Signal processing, Vol. 45 (1997)694–705 3. Moulines E., Duhamel P., Cardoso J. F., Mayrargue S.: Subspace Methods for the Blind Identification of Multichannel FIR Filters. IEEE Trans on Signal Processing, Vol. 43 (1995) 516–525 4. Xie, S. L., He, Z. S., Fu, Y. L.: A Note on Stone's Conjecture of Blind Signal Separation. Neural Computation, vol. 17 (2005)321-330 5. He, Z. S., Xie, S. L., Fu, Y. L.: A Novel Framework of Multiphonic Acoustic Echo Cancellation. Progress in Natural Science (2005) 6. He, Z. S., Xie, S. L., Fu, Y. L.: A New Blind Deconvolution Algorithm for SIMO Channel Based on Neural Network. In: Machine Learning and Cybernetics, 2005. Proceedings of 2005 International Conference on, Vol. 6 (2005) 3602- 3616 7. Gazzah H. Regalia P. A., Delmas J. P., Abed-Meraim K.: A Blind Multichannel Identifaction Algorithm Robust to Order Overestimation. IEEE Transactions on Signal Processing, Vol. 50 (2002)1449-1458 8. Gazzah H. Regalia P. A., Delmas J. P.: Asymptotic Eigenvalue Distribution of Block Toeplitz Matrices Application to Blind SIMO Channel Identification. IEEE Transactions on Information Theory, Vol. 47 (2001) 1243 - 1251

An Improved Independent Component Analysis Algorithm and Its Application in Preprocessing of Bearing Sounds Guangrui Wen, Liangsheng Qu, and Xining Zhang College of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China {grwen, lsqu, zhangxining}@mail.xjtu.edu.cn

Abstract. Independent Component Analysis (ICA) is known as an efficient technique to separate individual signals from various sources without knowing their prior characteristics. Firstly, the basic principle of ICA is reviewed in Sec 2, and then an improved ICA algorithm based on coordinate rotation (CR-ICA) is proposed. Secondly, two advantages of the CR-ICA algorithm are discussed; the one is that the separation can be carried out without iteration, and the other is that less computation is needed to achieve the same effect. Finally, the experiment in recognition of mixed sound and practical application in preprocessing of bearing sounds proved that the CR-ICA algorithm is better than traditional ICA algorithm in separation precision and computation speed. Moreover, the advantages of the method and the potential for further applications are discussed in the conclusion.

1 Introduction The data collecting method of multi-measurement points and multi-sensors has been adopted widely in the mechanical equipment online monitoring and fault diagnosis system. The signals collected were sometimes mixed up by the signals coming from different sources. Separating some special signals from these mixed signals may help figure out the essentials of machine faults and enhance the quality of diagnosis information. Blind Source Separation (BSS) is introduced for the signals of unknown of source signal and mixture type. Independent Component Analysis (ICA) is a new technique of statistical signal processing accompanying with the development of BSS problems. ICA deals with the mixed signals derived from the linear and nonlinear combination of independent statistic signals with each other and aims at separating each independent component from the mixed signals. In 1994, Comon expatiated on the concept of ICA systemically and constructed a cost function directly based on high order statistic variables [1]. Bell and Sejnowski explained the BSS problem from the information theory point of view, and presented the maximum entropy ICA algorithm (Infomax-ICA) [2], i.e. the maximum difference entropy of outputs of neural networks predict the mutual information maximum between inputs and outputs in neural networks. Based on it, they presented stochastic D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 48 – 53, 2006. © Springer-Verlag Berlin Heidelberg 2006

An Improved ICA Algorithm and Its Application in Preprocessing of Bearing Sounds

49

gradient declined algorithm to complete maximum difference entropy simultaneously. Hereafter, many people including T.W.Lee etc. expanded the work of Bell and Sejnowski, and developed an improved expanding ICA algorithm.[3] The algorithm was useful for the signals displayed in super-gaussian and sub-gaussian condition. However, these ideas and algorithms were lack of computability or consistency essentially. I.e. the computation carried out with iteration and needed long computation time. In addition, the mixed signal seldom satisfied ideal symmetry distribution in practice, and they present skewness distribution generally [4]. This paper is a first attempt to apply the ICA in engineering diagnosis area. Case studies in this paper reveal its advantages. The potential application is also discussed.

2 Basic ICA Principle and Improved Algorithm 2.1 Basic ICA Principle ICA was originally developed to deal with the problems that are closely related to the cocktail-party problem [5,6]. Since the recent progress in ICA, it has become clear that this method will find widespread applications as well.

X = WS

(1)

where X is the observed vector, W is the mixed factor matrix, S is the source vector. Obviously, if we can get the inverse matrix of W , indicated by W T , we may easily obtain the source signal matrix S from the observed signal matrix X , the former S will be written as:

S =WT X

(2)

ICA can be used to estimate the source signals from the mixtures based on the information of their independence. As we know, independence of two random variables means that the joint probability distribution function (PDF) is equal to the product of individuals as Equation 4.

p(x1 , x 2 ) = p1 ( x1 ) p 2 (x 2 )

(3)

Basically speaking, ICA is an optimization problem; its objective is to optimize the coefficient matrix W so as to obtain the components S , the components of which are statistically as independent to each other as possible. Based on traditional ICA algorithms, this paper presents a new improved ICA algorithm, and applies it in engineering diagnostics area. 2.2 An Improved ICA Algorithm Based on Coordinate Rotation (CR-ICA) 2.2.1 Preprocessing for CR-ICA In the preceding section, we discussed the principle of the ICA algorithm. Practical detail algorithms based on these principles will be discussed in the next section. However, before applying an ICA algorithm on the data, it is usually very useful to do

50

G. Wen, L. Qu, and X. Zhang

some preprocessing. In this section, we discuss some preprocessing techniques that make the problem of ICA estimation simpler and better conditioned. a Centering The most basic and necessary preprocessing is to center X, i.e. subtract its mean vector M=E{X} so as to make X a zero-mean variable. This implies that S is zero-mean as well, as can be seen by taking expectations on both sides of Equation (1). This preprocessing is made solely to simplify the ICA algorithms. b Whitening Another useful preprocessing method is to whiten the observed variables. This means that before the application of the ICA algorithm (and after centering), we transform ~ the observed vector X linearly so that we obtain a new vector X which is white, i.e. its components are uncorrelated and their variances equal unity. With the original signal whitened, the correlation between the mix signals can be eliminated, and the independent component extraction algorithm can be simplified and its performance will be improved. Sometimes only whitening process may recover the waveform of source signals. In the rest of this paper, we assume that the data has been preprocessed by centering and whitening. 2.2.2 Algorithm Flow of CR-ICA ~ After mixed signals X are preprocessed, X becomes a unit covariance vector X , and ~ the components of X is perpendicular with each other. Then a new improved Inde~ pendent Component Analysis Algorithm is proposed to process this vector X . The algorithm is based on the coordinate rotation theory and can be used to search the optimum rotational angle with the help of the optimum algorithm. The detail steps of the algorithm are shown as follows: Step 1: Select rotation matrix R. By rotating transforms, matrix S will be obtained.

R =[

cos α sin α

~ − sin α ] S = R* X cos α

(4)

In order to obtain the optimum rotation angle, object function Q is built. Q = ¦ (cos α ⋅ xi − sin α ⋅ yi )3 i

(5)

~ ~ where xi , yi are two column elements of matrix X 2× n which is equal to X and n is ~ column number of matrix X . Step 2: Obtain object function Q’s derivative Q '

Q ' = 3* ¦ [(cos α ⋅ xi − sin α ⋅ yi )2 *(sin α ⋅ xi + cos α ⋅ yi )] i

(6)

Step 3: In order to obtain extremum of Q ' , Q ' is taken to zero. According to Equation (10)

An Improved ICA Algorithm and Its Application in Preprocessing of Bearing Sounds [sin α (cos α )2 ¦ xi3 − 2*cos α (sin α ) i

¦x y i

2 i

+ (cos α )

i

3

¦yx

2 i i

i

2

¦yx

2

i i

51

+ (sin α )3 ⋅

i

− 2sin α ⋅ (cos α ) 2 ¦ yi2 xi + cos α ⋅ (sin α )

2

i

¦y ]=0 3 i

(7)

i

Step 4: Suppose a = ¦ xi3 , b = ¦ yi xi2 , c = ¦ xi yi2 , d = ¦ yi3 , then formula (12) can i

i

i

i

be simplified as follow: c ⋅ tg 3α + (d − 2b)tg 2α + (a − 2c)tgα + b = 0

(8)

Step 5: Obtain the root value of Equation (12) using tgα as unknown. Step 6: Search an optimum angle from all angles obtained by step 5 to make object function obtain the minimum. Step 7: Use Equation (4) to do rotation transformation, then the independent component can be obtained.

3 Experiments In practical recongnition of signals, sound recongnition is one classical type [8]. Mixed sounds are made up of human voice and alarming whistel sound. The sounds are collected by two recorders and it is no doubtful that each sound collected by single sound recorder will receive another sound’s information. Fig.1(a) and (b).show the

(a)

(c)

(b)

(d)

Fig. 1. (a) (b) display the original mixed sound, and separated results are showed in Fig1.(c)(d)

52

G. Wen, L. Qu, and X. Zhang Table 1. The performance of two algorithms in recognition of mixed sounds

SNR/dB

Algorithm CR-ICA FastICA

y1

y2

103.81 110.39

102.87 107.43

Computation Time/S 0.806 1.560

mixed sounds. By whitening the mixed sounds and then applying the improved ICA algorithm, the independent signals can be obtained and shown in Fig.1(c) and (d). Table 1 displays the SNR results by using two algorithms. It is obviously that the proposed CR-ICA algorithm is better than traditional FastICA algorithm in separation precision and computation speed under the same conditions.

4 Applications The condition monitoring and fault diagnosis of rolling bearing have been investigated for a long time. Many efficient methods have been proposed, such as resonance demodulation and ferrography. Herein, we recognize the bearing faults by sampling bearing sound. In experiment, two Sound level Meters were mounted to pick up the machine sound. One aimed at the motor sound, the other aimed at the bearing sound. It is sure that each collected sound contains other part sound information. We use the CR-ICA method to preprocess the mixed sound. The original signals collected are shown in Fig.2(a,b). The preprocessing results are shown in Fig.2(c,d).

(a)

(c)

(b)

(d)

Fig. 2. The observed signals are shown in Fig. (a,b) and the preprocessing results are shown in Fig. (c,d)

An Improved ICA Algorithm and Its Application in Preprocessing of Bearing Sounds

53

As shown in Fig.2(c,d), the separated source like white noise is due to the motor, while the impulsive signal with periodic impacts was originated from the spall in the inner race of the tested bearing.

5 Conclusions This paper proposes an improved ICA algorithm (CR-ICA), and applies it to tackle the following problems in experiments and engineering diagnosis: recognition of mixed sound and preprocessing of bearing sound. The case studies show that the CRICA method performs better than the traditional ICA algorithms.

References 1. Comon P.: Independent component analysis, a new Concept, Signal Processing Vol.36 (1994) 287-314 2. Belland, A.J., Sejnowski, T.J.: An information-maximization approach to blind separation and blind separation and blind deconvolution, Neural Computation, Vol.7 (1995) 11291159 3. Lee, T.W., Girolami, M., Sejnowski, T.J.: Independent component analysis using an extended infmax algorithm for mixed sub-gaussian and super-gaussian sources, Neural Computation,11(2) (1999) 417-441 4. Li, X.F., Wen, G.R.: Analyzed method of skewness component in Blind Separation, Journal of Xi’an Jiaotong University, Vol.37 (2003) 703-707 5. Zhang, H., Qu, L.:Partially blind source separation of the diagnostic signals with prior knowledge. Proceedings of the 14th International Congress on Condition Monitoring and Diagnostic Engineering Management, Manchester, UK. Elsevier (2001) 177-184 6. Aapo Hyvarinen, Erkki Oja: Independent Component Analysis: Algorithms and Applications, Neural Networks, Vol 13 (2000) 411-430 7. Qu Liangsheng, He Zhengjia: Mechanical Fault Diagnostics, Shanghai Science & Technology press.(1986) 86-87 8. Aapo Hyvarinen, Erkki Oja: Independent Component Analysis by General Nonlinear Hebbian-Like Learning Rules, Signal Processing 64. (1998) 301-313 9. Xu Yonggang: Mechanical Dynamic Signal Processing, Doctor dissertation, Xi’an Jiaotong University (2003) 10. Liangsheng Qu, Guanghua Xu: The Fault Recognition Problem in Engineering Diagnostics, Insight, Vol 39, No 8 (1997) 569-574

Array Signal MP Decomposition and Its Preliminary Applications to DOA Estimation Jianying Wang, Lei Chen, and Zhongke Yin School of Information Sci. & Tech., Southwest Jiaotong University, Chengdu, 610031, China {jywang, chan, zkyin}@home.swjtu.edu.cn

Abstract. The idea of sparse decomposition is introduced into array signal processing, and a novel approach to DOA estimation is presented in this paper. The approach decomposes the array signal over an over-complete dictionary, the atoms of which are vectors established according to the array geometry. The sparse decomposition is implemented by matching pursuit (MP) in the proposed algorithm. High resolution of DOA estimation can be obtained according to the parameters of the atoms decomposed with MP. The DOA estimation resolution capabilities are shown to be much higher than MUSIC and ESPRIT, especially in the case of less array elements and lower SNR. Furthermore, the performance is not affected by the correlation of the signals to be resolved. Computer simulation confirms its validity.

1 Introduction Goals of sensor array signal processing is to estimate parameters such as directions of arrival (DOA) by fusing temporal and spatial information, captured via sampling a wavefield with a set of judiciously placed antenna sensors. Parameter estimation problems in theoretical as well as applied statistics have long been of great research interest. Two popular methods belonging to this class of techniques are the so called maximum likelihood method (MLM) which is based on the work of Capon [1] on frequency-wave-number analysis, and the maximum entropy method (MEM) based on the work of Burg [2]. Perhaps, the most important high resolution techniques currently being examined are the so called signal subspace techniques, such as MUSIC [3] and ESPRIT [4]. The key problem of eigen-subspace methods is the estimation of signal and noise subspace, and then the parameters can be achieved using the orthogonality of the signal and noise subspace. Besides, the algorithms based on higher order cumulant [5], neural network [6] and wavelet analysis [7] etc. have been proposed. At present, the algorithms most widely used in array signal processing, which are almost based on orthonormal decomposition of signals, project the array signal on an orthonormal and complete subspace. Because the signal is decomposed into weightedsum of each orthonormal basis function, the orthonormal decomposition has some disadvantages, such as orthogonality and completeness of the basis function system and, hence, inherent least resolution. So non-orthonormal decomposition provokes D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 54 – 59, 2006. © Springer-Verlag Berlin Heidelberg 2006

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more and more research interests in recent years [8-10]. This paper introduced nonorthonormal decomposition into the array signal processing area. By establishing over-complete family of basis functions and adjusting atom vector density of overcomplete dictionaries, the received array signal can be projected onto one basis vector which approximates very close to the desired signal. Based on sparse representations of the array signal, high-resolution spatial estimation was implemented. In this paper, using the idea of sparse decomposition, based on matching pursuit (MP) decomposition [8], a new method of high-resolution DOA estimation is firstly proposed. Computer simulations show that the new algorithm obtains higher resolution than the conventional DOA estimation algorithm in the case of definite density of atom vectors, and the new method has better performance especially at low SNR.

2 Array Signal Model Consider D far-field narrow-band sources which have known center frequency ω 0 impinging on the array (as shown in Fig. 1). In such array, the distance d between two elements causes the propagation delays τ . Then the complex output of the lth element at time t can be written as: D

xl (t ) = ¦ ali si (t − τ li (θi )) + ni (t )

l = 1,2,, M

(1)

i =1

Where a li is the corresponding sensor element complex response at frequency ω 0 and τ li is the propagation delay between a reference point and the lth sensor element for the ith wavefront impinging on the array from direction θ i , ni (t ) is the additive noise that is assumed to be a stationary zero-mean random process.

θ

Fig. 1. Array geometry

The received data vectors of the array can be written as: X( t ) = AS( t ) + N( t )

(2)

Where X (t ) is the M × 1 snapshot data matrix, the vector S( t ) is the D × 1 data vector of impinging signals. N( t ) is the M ×1 data matrix of additive noise.

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A is the array steering vector A = [ a1 a2  aD ] , For the ith signal, the vector a i

in the matrix A is given by a i = [exp(− jω 0τ 1i ), exp(− jω 0τ 2i ),, exp(− jω 0τ Mi )]T

i = 1,2,, D

(3)

Where τ li is the propagation delay between the reference point and the lth sensor for the ith wavefront impinging on the array from direction θ i . τ li is given by

τ li (θ i ) =

(l − 1)d sin θ i c

(4)

According to the array signal model described above, DOA estimation can be calculated though (4), as long as τ li is estimated by some method.

3 The DOA Estimation Based on MP Decomposition The conventional methods of array signal processing are almost based on orthonormal decomposition of signals, so there are many limits as mentioned above. In this paper, we introduce a new method of array signal processing with matching pursuit. Matching pursuit is a greedy algorithm that chooses at each step of decomposition process a waveform that approximates best a part of the signal. By using MP, the array signal can be decomposed over a family of functions chosen flexibly according to the characteristic of the signal itself. The characteristic of expansion coefficient can be utilized to get the interested information. According to the array signal model, in order to obtain The DOA estimation with equation (4), the atom vectors can be written as: 1 º ª » « exp(− jω d sin θ c ) 0 m » Gθ m (ai , t ) = S (t ) « » «  » « ¬exp(− jω0 ( M − 1)d sin θ m c )¼

m = 1,2,  , M

(5)

Where θ m is the DOA parameter which can be set according to the required searching precision. M is the total number of atoms in the dictionary. The parameters of vector atoms determined only by θ m . We can decompose the array signal over the dictionaries described above. According to the equation (5), we can establish an overcomplete vector family, and decompose the array signal over the family. By using MP, the array signal x can be decomposed into x = PG x + Rx

(6)

Where x is the signal received by array sensors, PG x is the signal’s projection on the atom vector which best matches the source, namely PG ( x ) = sup PG ( x ) , and Rx is θ m

the residual vector after approximating x with G .

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In the MP decomposition, we must select a vector atom that matches x almost at best. This selection must follow a restriction which given by vector projection theorem as follow: x − Gθ i = inf x − Gθ y y∈ m

(7)

Obviously, the atom vector that best matches the original array signal can be obtained by searching the value of θi . Therefore the estimation of DOA can be obtained by the atom parameter θi . On the contrary, the noise does not have the same characteristic as the array signal, so the projection of noise on the atom vector is approaching zero. So this method can achieve the de-noised signal.

4 Simulation Results In this section, we present some simulation results to compare the performance of the new DOA estimation algorithm with the conventional algorithms (ESPRIT, MUSIC). We use a uniform linear array with pair spacing λ 2 . The signal is narrow band of 256 samples that is built by adding white Gaussian noise. The source is located at 60o. All the results are averaged over 128 simulations run at each point. Fig. 2 shows the DOA estimation result with a 3-element array. The simulation displays that the new DOA estimation method based on array signal MP decomposition has better performance than the conventional methods in the case of less array elements, so the new algorithm is an efficient method in reducing the hardware costs. In order to improve the algorithm’s performance at low SNR, an array of 10 elements is used in the next simulation. Fig. 3 shows the DOA estimation STD versus the signal-to-noise (SNR) for 256 snapshots. The simulation results indicate that the

Fig. 2. DOA Estimation STD versus SNR

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Fig. 3. DOA Estimation STD versus SNR

new DOA estimation method has obviously higher resolution than the conventional methods such as ESPRIT and MUSIC, especially at low SNR. Another main advantage of the algorithm proposed in this paper is that, in the DOA estimation based on MP, the powers of the received signals are used instead of the signal subspaces; hence the system performance is robust to correlation between the inputs from different angles.

5 Conclusion A central problem in the array signals’ DOA estimation is how to exactly estimate the time delay. By decomposing the array signals over one over-complete dictionary, the time delay estimation has been clearly improved compared with decomposing over an orthonormal basis. As a result, higher resolution has been achieved with MP decomposition of the array signals. The new algorithm works well in the case of less array elements; therefore it can reduce the hardware costs. It performs well too at very low SNR circumstance, and can also be used when the signals are correlated. The newly proposed method in this paper should be beneficial to radar and sonar systems. On the other hand, the new method is just a preliminary probe into array signal sparse decomposition; whereas it was shown that the technique can achieve higher resolution in parameter estimation. From the analysis above, the method is quite promising, thus further research is needed on the algorithms and its performance.

References 1. Capon, J.: High-resolution Frequency-wave Number Spectrum Analysis. Proc. Of IEEE, Vol. 57(8) (1969) 1408-1418 2. BURG, J.P.: Maximum Entropy Spectral Analysis. PhD Thesis, Stanford University, Stanford, USA (1975)

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3. Schmidt, R.O.: Multiple Emitter Location and Signal Parameter Estimation. IEEE Trans. Antennas and propagation, Vol. 34(3) (1986) 276-280 4. Roy, R., Kailath, T.: ESPRIT--Estimation of Signal Parameters via Rotational Invariance Techniques. IEEE Trans. Acoustics, Speech, and Signal processing, Vol. 37(7) (1989) 984-995 5. Mendel, J.M.: Tutorial on Higher-order Statistics (spectra) in Signal Processing and System Theory: Theoretical Results and Some Applications. Proc. of IEEE, Vol. 79(3) (1979) 278-305 6. Southall Hugh, L., Simmers Jeffrey, A., Donnell Teresa H.O.: Direction Finding in Phased Arrays with a Neural Network Beamformer. IEEE Transactions Antennas and Propagation, Vol. 43(12) (1995) 1369-1374 7. Xu, W., Liu, T., Schmidt, H.: Beamforming Based on Spatial-wavelet Decomposition. Sensor Array and Multichannel Signal Processing Workshop Proceedings, Vol. 4(6) (2002) 480-484 8. Mallat, S., Zhang, Z.: Matching Pursuits with Time-frequency Dictionaries. IEEE Trans. Signal Processing, Vol. 41(12) (1993) 3397-3415 9. Eldar, Y.C., Oppenheim, A.V.: MMSE Whitening and Subspace Whitening. IEEE Trans. Information Theory, Vol. 49(7) (2003) 1846-1851 10. Arthur, P.L., Philipos, C.L.: Voiced/unvoiced Speech Discrimination in Noise Using Gabor Atomic Decomposition. Proc. Of IEEE ICASSP[C], Hong Kong Vol. I (2003) 820-828

Mixture Matrix Identification of Underdetermined Blind Source Separation Based on Plane Clustering Algorithm* Beihai Tan and Yuli Fu College of Electronic and Communication Engineering, South China University of Technology 510640, China [email protected], [email protected]

Abstract. Underdetermined blind source separation and sparse component analysis aim at to recover the unknown source signals under the assumption that the observations are less than the source signals and the source signals can be sparse expressed. Many methods to deal with this problem related to clustering. For underdetermined blind source separation model, this paper gives a new plane clustering algorithm to estimate the mixture matrix based on sparse sources information. Good performance of our method is shown by simulations.

1 Introduction Blind source separation (BSS) has been applied to many fields, such as, digital communication, image processing, array processing and biomedicine, and so on. Also, it has a lot of potential applications. Therefor, it has been a hot topic in signal processing and neural networks field [1-6]. Blind separation comes from cocktail problem [7], just to say, we only can restore source signals by gotten sensor signals, what’s more, mixture channel and source signals’ distributions are unknown. So the mathematics model of BSS is X (t ) = AS (t ) + N (t ) , t = 1 T .

(1)

where X (t ) = [ x1 (t ), x 2 (t )  x m (t )]T is sensor signals, A ∈ R m×n is mixture matrix,

and S (t ) = [ s1 (t ), s2 (t )  sn (t )]T is source signals, and N (t ) = [n1 (t ), n2 (t )nm (t )]T is noise. BSS aims at restoring source signals only by known sensor signals, generally, we suppose noise doesn’t exist. In general, if m is more than n , that is, the number of sensor signals is more than that of source signals [8], it is overdetermined BSS. We consider the case that m is less than n in this paper, namely, underdetermined BSS. Although it is difficult to restore source signals, we can use some other information, such as, sparseness of *

The work is supported by the National Natural Science Foundation of China for Excellent Youth (Grant 60325310), the Guangdong Province Science Foundation for Program of Research Team (grant 04205783), the Natural Science Fund of Guangdong Province, China (Grant 05006508), the Specialized Prophasic Basic Research Projects of Ministry of Science and Technology, China (Grant 2005CCA04100).

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 60 – 65, 2006. © Springer-Verlag Berlin Heidelberg 2006

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source signals, to restore source signals, and if some source signals aren’t sparse in time-domain, we can make them sparse through some transformation, such as, Fourier transformation or wavelet transformation, so BSS model is also written as x(t ) = a1 s1 (t ) + a 2 s 2 (t ) +  a n s n (t ), t = 1 T .

(2)

Where x(t ) = [ x1 (t ),  x m (t )]T , a i = [a1i ,  a mi ]T .

2 Sparse Representation of Underdetermined Blind Separation For underdetermined BSS, generally, some blind extraction algorithms [9], [10] are taken in past, but the algorithms can’t realize to restore all source signals. In order to restore all source signals in underdetermined BSS, researchers make use of some characteristics of signals, for example, sparse analysis is adopted to make signals sparse representation, so some underdetermined BSS algorithms are successfully. Among the good algorithms there are Belouchrani’s maximum likelihood algorithm [11] for discrete sources, Zibulevsky’s sparse decomposition algorithm [3], Lee [12] Lewicki [13] and Li’ overcomplete representation algorithms [5] and Bofill’ sparse representation in frequency domain [14]. Generally, sparse signal is that the one whose most sample points are zero or are near to zero, and a little sample points are far from zero. Here, we suppose that the source signal si (t ) is nonzero and the other source signals are zero or are near to zero at the time of t . So equation (2) can be written as (3) x(t ) = ai si (t ) . From above equation, we can known that ai and x(t ) are collinear so we can estimate mixture matrix A = [a1 , a2 , an ] by clustering x(t ) in all time. It is a very important algorithm for sparse component analysis solving underdetermined BSS, named by k-means clustering, and the algorithm includes two steps [5],[14], first, clustering centers are estimated by k-means clustering; second, source signals are estimated by known mixture matrix through linear programming. Because the above algorithms require that source signals are very sparse, so there is a lot of restriction for application. Recently, Pando Georgiev puts forward a new sparse component analysis method for underdetermined BSS based the next conditions [15]. A1) the mixture matrix A ∈ R m×n has the property that any square m × m submatrix of it is nonsingular. A2) each column of the source matrix S (t ) has at most m − 1 nonzero elements. A3) the sources are sufficiently rich represented in the following sense: for any index set of n − m + 1 elements I = {i1 , i2 in−m+1} ⊂ {1,2, n} there exist at least m column vectors of the matrix S such that each of them has zero elements in places with indexes in I and each m − 1 of them are linearly independent.

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For simplicity, we suppose m = 3, n = 4 to explain the paper’s algorithm for the problem. If m = 3, n = 4 , the equation (2) can be written as: x(t ) = a1 s1 (t ) + a 2 s 2 (t ) + a 3 s 3 (t ) + a 4 s 4 (t ), t = 1 T .

(4)

where x(t ) = [ x1 (t ), x2 (t ), x3 (t )]T and ai = [a1i , a2i , a3i ]T , according to A2), if the i th source signal and the j th source signal are nonzero at the time of t , then x(t ) = a i s i (t ) + a j s j (t ), t = 1 T .

(5)

From equation (5), we can know the sensor signal vector is in the same plane with vector ai and vector a j . Again, according to A1, every two columns in mixture matrix are independent, there are defined C 42 different planes by every two columns in mixture matrix. From equation (5), the mixture matrix A = [a1 , a2 , a3 , a4 ] can be estimated through plane clustering of sensor signals in no noise or little noise. Next, the plane clustering algorithm is given in detail and source signals are restored by it.

3 Mixture Matrix Identification Based on Plane Clustering Pando Georgiev has proved that the mixture matrix is identifiable when the conditions A1 ,A2 ,A3 are met. Because the mixture matrix is very important, but Pando Georgiev doesn’t give substantial algorithm for it, so this paper gives the substantial novel algorithm for estimating mixture matrix. For simplicity, we still suppose m = 3, n = 4 to explain the algorithm. To identify C 42 = 6 planes, we turn to identify their six normal lines , and if their normal lines are identified, then we identify their planes. In order to begin plane clustering, we initialize the sensor signals x(t ), t = 1T , which are normalized. If m = 3 , a sensor signal correspond to one point in the spherical surface, and the points of the below half spherical surface need to turn them to above half spherical surface symmetrically. Then, the new sensor signals are

­ ° ° ˆx(t ) = ® °− ° ¯

x(t ) x(t )

if x3 (t ) ≥ 0.

x (t ) x (t )

if x3 (t ) < 0.

, t = 1T .

(6)

Clustering xˆ (t ) is correspond to clustering x(t ) , and the points will locate in the above half spherical surface which are in the same planes with the planes by every two columns of the mixture matrix respectively. Similar to k-means cluster, normal lines clustering is to get their normal lines and modify them in clustering algorithm. For example, there are some initialized points y (t ) = [ y1 (t ), y 2 (t ), y3 (t )]T , t = 1,2, N 0 in a plane.To identify its plane, we suppose & its normal line is n 0 = [n 01 , n 02 , n 03 ]T , According to inner-product’ s definition, & & (7) (n0 , y (t )) = n01 ⋅ y1 (t ) + n02 ⋅ y2 (t ) + n03 ⋅ y3 (t ) = n0 ⋅ y (t ) × cos θ n&0 y (t ) ,

Mixture Matrix Identification of Underdetermined Blind Source Separation

63

& where θ n&0 y (t ) is the angle between the normal line n0 and the point y (t ) , so 0 ≤ θ n&0 y (t ) ≤ π , and −1 ≤ cos θ n&0 y (t ) ≤ 1 . From equation (7), if we need to identify the plane composed of the points y (t ) , & t = 1,2, N 0 , the normal line n0 = [n01 , n02 , n03 ]T must be found to let θ n&0 y (t ) tend to

π 2

& for any t ∈ {1,2, N 0 } , because n 0 = 1, y (t ) = 1 , so just to say

& n0 = arg min & n0

s.t.

N0

&

¦ (n , y(t )) 0

(8)

t =1

(n01 ) + (n02 ) + (n03 ) = 1. 2

2

2

Based on equation (8), the plane clustering algorithm is followed in detail. 1) 2) 3)

4)

Initialize the sensor signals x(t ), t = 1 T using equation (6) to get new sensor signals xˆ (t ), t = 1T . & & & & & & Bring six initialized normal lines randomly, n1 , n2 , n3 , n 4 , n5 , n6 . & Compute the inner-products of xˆ (t ), t = 1T and ni , i = 1 6 respectively, & & and take their absolute values, let X i = {xˆ (t ) | ( xˆ (t ), n i ) < ( xˆ (t ), n j ) , j ≠ i} . & Modify the initialized normal lines, let n = [sin θ cos ϕ , sin θ sin ϕ , cosθ ] , 0 ≤θ ≤

5)

π

㧘

0 ≤ ϕ ≤ π . For the sake of simplicity, the algorithm is shown by 2 the following Matlab programme. for i = 1 : 6 & & nˆ i = ni ; for θ = 0 : η1 : π / 2 for ϕ = 0 : η 2 : π & & if ( X i , n ) < ( X i , ni ) & & ni = n ; end end end end & & Where η1 ,η 2 denote step sizes respectively, ( X i , n ) , ( X i , ni ) respectively denote the sums of inner-product’s absolute value between all the elements of & & the set X i and normal lines n , and ni . & & If nˆi − ni < ε i i = 16 , the algorithm stops and ε i is a given little value,

㧘

otherwise, continue the step 3). Because each column vector ai in the mixture matrix compose a plane with other & & column a j ( j ≠ i ) , so ai must be orthogonal with three normal lines among n1 , n 2 , & & & & n3 , n 4 , n5 , n 6 and the three normal lines must be in the same plane. That is to say, if we find any three coplanar normal lines, the columns ai (i = 1, 4) will be estimated.

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4 Restoring Source Signals & Now, we suppose that the normal line is nk (k ∈ {1, 6}) of the plane composed of ai , a j (i ≠ j ) , and the set of the sensor signals is X l (l ∈ {1, 6}) which is coplanar with ai , a j (i ≠ j ) . For any x(t ) ∈ X l , so x(t ) = ai si (t ) + a j s j (t ) ,

(9)

x(t ) = Aij sij (t ) ,

(10)

or where Aij = [ai , a j ], sij (t ) = [ si (t ), s j (t )]T , so

sij (t ) = Aij # x(t ) .

(11)

Where Aij # denotes the generalized inverse matrix of Aij . So only the i th source signal and the j th source signal have nonzero values gotten by equation (11) at the time of t , but zero for the other source signals at the time of t .

5 Simulations Results In the experiment, a random 3 × 4 matrix brings for the simulation but meets the condition A1), and take N = 1000 , four source signals are denoted in fig 1, The iniª- 0.27574 0.18977- 0.67493 0.86583º « 0.59016 0.28866- 0.72862- 0.12535» , and the » « «¬ 0.75874- 0.93844 0.11652 0.48439»¼ ª 0.67479 0.86533- 0.27554- 0.19024º algorithm is « 0.7288 - 0.12444 0.59033- 0.28914» . » « «¬- 0.11622 0.48551 0.75867 0.93819»¼

tialized mixture matrix is

matrix by the above

Fig. 1. Four source signals

Fig. 2. Restored source signals

estimated mixture

Mixture Matrix Identification of Underdetermined Blind Source Separation

65

From the estimated mixture matrix and the above figures of restored source signals, the algorithm is successful except that the first and the fourth restored signals have sign difference from the third and the second source signals, which is allowed in BSS.

6 Conclusions This paper gives a novel and substantial algorithm for estimating the mixture matrix and restoring the sparse source signals in underdetermined BSS. The algorithm is feasible and its good performance is shown in the simulation results, and it also easy to expand the algorithm to high dimension underdetermined BSS by sparse component analysis.

References 1. Hyvarinen, A., Oja, E.: Independent Component Analysis: Algorithms and Applications. Neural Networks, 13 (2000) 411-430 2. Xie, S. L., Zhang, J. L.: Blind Separation Algorithm of Minimal Mutual Information Based on Rotating Transform. Acta Electronic Sinica, 30 (5) (2002) 628-631 3. Zibulevsky, M., Pearlmutter, B.A.: Blind Source Separation by Sparse Decomposition in a Signal Dictionary. Neural computation, 13 (4) (2001) 863-882 4. Xie, S. L., He, Z. S., Gao, Y.: Adaptive Theory of Signal Processing. 1st ed. Chinese Science Press, Beijing (2006) 130-223 5. Li, Y., Cichocki, A., Amari, S.: Analysis of Sparse Representation and Blind Source Separation. Neural Computation 16 (2004) 1193–1234 6. Zhang, J. L., Xie, S. L., He, Z.S.: Separability Theory for Blind Signal Separation. Zidonghua Xuebao/Acta Automatica Sinica, 30 (3) (2004) 337-344 7. Jutten, C., Herault, J.: Blind Separation of Sources, Part I: An Adaptive Algorithm Based on Neuromimetic. Signal Processing, 24 (1991) 1-10 8. Zhang, J. L., Xie, S. L.: Multi-input Signal-output Neural Network Blind Separation Algorithm Based on Penalty Function. Intelligent and Complex Systems, 2 (2003) 353-362 9. Li, Y., Wang, J., Zurada, J. M.: Blind Extraction of Singularly Mixed Source Signals. IEEE Trans on Neural Networks, 11 (2000) 1413-1422 10. Li, Y., Wang, J.:Sequential Blind Extraction of Instantaneously Mixed Sources. IEEE Trans. Signal Processing, 50 (5) (2002) 997-1006 11. Belouchrani, A., Cardoso, J. F.: Maximum Likelihood Source Separation for Discrete Sources. In Proc. EUSIPCO, Edinburgh, Scotland (1994) 768-771 12. Lee, T. W., Lewicki, M.S., Girolami, M., Sejnowski, T. J.: Blind Source Separation of More Sources Than Mixtures Using Overcomplete Representation. IEEE Signal Processing Letter, 6 (1999) 87-90 13. Lewicki, M. S., Sejnowski, T. J.: Learning Overcomplete Representations. Neural computation, 12 (2000) 337-365 14. Bofill, P., Zibulevsky, M.: Underdetermined Source Separation Using Sparse Representation. Signal processing, 81 (2001) 2353-2362 15. Georiev, P., Theis, F., Cichocki, A.: Sparse Component Analysis and Blind Separation of Underdetermined Mixtures. IEEE Transactions On Neural Networks, 16 (4) (2005) 992-996

Non-linear Blind Source Separation Using Constrained Genetic Algorithm Zuyuan Yang and Yongle Wan School of Electrics & Information Engineering, South China University of Technology, Guangzhou 510641, Guangdong, China [email protected], [email protected]

Abstract. In this paper, a novel adaptive algorithm based on constrained genetic algorithm (GA) is presented for solving non-linear blind source separation (BSS), which can both get out of the trap of local minima and restrict the stochastic decision of GA. The approach utilizes odd polynomials to approximate the inverse of non-linear mixing functions and encodes the separating matrix and the coefficients of the polynomials simultaneously. A novel objective function based on mutual information is used with the constraints to the separating matrix and the coefficients of the polynomials respectively. The experimental results demonstrate the feasibility, robustness and parallel superiority of the proposed method.

1 Introduction Since 1990, researchers have attached increasing importance to BSS which means recovering original sources without knowing source signals and transmitted channels. BSS is widely used in signal processing, and there have been several methods for solving linear mixing model [1], [3], [5] including the basic theory. In [12], Xie corrected Stone’s conjecture and the modified conjecture without suspicion supplied a reliable basis for researchers to study BSS both in theory and algorithm design. For nonlinear case, the highly non-unique characteristics of both linear separating matrix and non-linear demixing function make it almost impossible to recover sources completely without some extra constraints. At present, post-nonlinear model for nonlinear BSS is widely utilized. The approach in [2] was mainly for solving sparse signal and it was based on nonlinear PCA in [6]. In [7], [11], the algorithms based on neural network were developed by using the stochastic gradient descent method which was also used in [6]. This method may lead to fast learning convergence rate of weights, however, the result may converge to local minima of the contrast function. In order to get out of the trap of local minima, GA was used in [4], however it was only utilized to obtain the coefficients of the polynomials which approximated the nonlinear demixing functions and the separating matrix was still obtained by gradient method. Furthermore, GA is a stochastic selection algorithm, the convergence of which is not proved theoretically, so a proper constraint to the solution space will lead to a better result. However, it was seldom to see the constraint in [4]. The condition was used in [7], however, the algorithm was mainly utilized for blind signal extraction D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 66 – 71, 2006. © Springer-Verlag Berlin Heidelberg 2006

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in order. In [8], a constraint to the estimations was used, but this approach used a sigmoid function with only one parameter which may affect the approximation of the non-linear demixing functions. In [10], the assumptions to the coefficients of the polynomials simplified the contrast function. But the results violated the assumptions without the constraints corresponding to them in the algorithm. The post-nonlinear model is like following:

x(t ) = f ( A ⋅ s (t )) , y (t ) = W ⋅ g ( x(t )) .

(1)

Where x(t ) are mixtures of signals s (t ) , y (t ) are estimations of s (t ) . (see Fig. 1)

x1 s1

f1

sn

fn

g1

y1

gn

yn

xn

Fig. 1. Post-nonlinear mixing and demixing model

In this work, a novel objective function based on mutual information with the constraints to the separating matrix and the coefficients of the polynomials is used for post-nonlinear model. Instead of stochastic gradient descent method, GA is utilized to solve non-linear BSS. The parallel superiority of GA is used to get out of the trap of local minima for both separating matrix and coefficients of the polynomials, and the constraints are used to restrict the stochastic decision of GA. The paper is organized as follows: in Section 2, the algorithm to solve non-linear BSS is described in detail, including the construction of the fitness function. The experimental results are shown in Section 3. Finally, a conclusion is given in Section 4.

2 Blind Separation Using GA 2.1 Fitness Function

The selection of fitness function is based on information theoretic criterion, the y ," yn mutual information between 1 is defined as follows [11]: n

I ( y1 ," yn ) = − H ( y1 ," yn ) + ¦ H ( yi ) .

(2)

i =1

The function g is approximated as follows by Weierstrass approximation theorem: P

g j ( x j ) = ¦ g jk x 2j k −1 , j = 1," , n . k =1

where g jk are adjustable parameters. Therefore, the fitness function is used [10]:

(3)

68

Z. Yang and Y. Wan n n ­ ° L (W , g ) = − ln det W − ¦ E[log g ′j ( x j ) ] − ¦ H ( yi ) . ® j =1 i =1 °¯ H ( yi ) ≈ C − (k3i ) 2 12 − (k4i ) 2 48 + 3(k3i ) 2 k4i 8 + (k4i )3 16

(4)

where h jk = g jk h j1 for k ≥ 2 , and E[ yi2 ] = 1, E[ yi ] = 0 so as to WW T = I , C is a constant, k3i = E[ yi3 ], k4i = E[ yi4 ] − 3 . Suppose that g j1 = 1 , h jk  1(k ≥ 2) , from (4),

we can obtain the following non-linear programming problem with constraints: n

P

n

Max: f = ln det W + ¦¦ g jk E[(2k − 1) x 2j k − 2 ] + ¦ H ( yi ) .

(5)

s.t. h(W ) = WW T − I = 0, h ( g ) = g jk − ε ≤ 0, k ≥ 2 .

(6)

j =1 k = 2

i =1

where ε < 0.1 is a positive constant , H ( yi ) is estimated from (4). And (6) is equal to h j ( w) = 0, hi ( g ) ≤ 0, j = 1," , m1 , i = 1," , m2 .

(7)

Where m1 , m2 is from (9). Under the constraints, the feasible domain Q can be defined as follows [9]: Q = {( w, g ) h j ( w) = 0, hi ( g ) ≤ 0, j = 1, 2," , m1 , i = 1, 2," , m2 } .

(8)

㧘 m = (n

(9)

Definitions: w = [W11 , W12 ,"Wnn ]T

1

2

+ n) 2 , m2 = n ⋅ p − n .

­ H j ( w) = h j ( w) ∇h j ( w) , H max ( w) = max{H j ( w)} ° °° H i ( g ) = hi ( g ) ∇h j ( g ) , H max ( g ) = max{0, H i ( g )} . ® ° k1 = arg{ j H j ( w) = H max ( w)}, j = 1, 2," , m1 ° °¯ k2 = arg{i H i ( g ) = H max ( g )}, i = 1, 2," , m2

Def.1

Def. 2

DSFD ( w, g ) = H max ( g )∇hk2 ( g ) + sgn(hk1 ( w)) H max ( w)∇hk1 ( w) .

(10)

(11)

m1

d ( w, g ) = v0 ∇ w f − ¦ v j ∇h j ( w) .

Def. 3

(12)

j =1

where v j is weight of the gradient direction. In general, v0 = 0.5 , and

­°v∗j , if (hj (w) = 0) vj = ® . °¯sgn(hj (w)) ⋅ (Hmax (w) +δ ) (Hmax (w) +δ −λ ⋅ Hj (w)) else

δ

where

, λ

are

d ( w, g ) ⋅∇h j ( w) = 0 . T

positive

constants,

v∗j

are

multipliers

(13) satisfying

Non-linear Blind Source Separation Using Constrained Genetic Algorithm

69

Def. 4

FD = d ( w, g )T ⋅ (− DSFD ( w, g )) .

(14)

Def. 5

p °­ f ( w, g ) (1 + 1 FD ) , f ≥ 0 eval ( w, g ) = ® . p °¯ f ( w, g ) ∗ (1 + 1 FD) , f < 0

(15)

where p ≥ 1 , usually p = 2 . Then, the fitness function F ( w, g ) is given as ­e f ( w, g ) + e2 , ( w, g ) ∈ Q . F ( w, g ) = ® 1 ¯e1 ⋅ eval ( w, g ) + e2 , else

(16)

where e1 , e2 are positive real numbers such that F ( w, g ) ≥ 0 . 2.2 Operations Initial population: Select proper size N of the population, and encode the genes of the chromosome which corresponds to separating matrix W and coefficients of nonlinear function g with real number. Set proper parameters for the fitness function, crossover probability, mutation probability, maximum iteration number, and so on. Selection: Fitness-proportionate selection by roulette wheel is adopted, and the new generations come from combinational chromosomes with better fitness. Crossover: In the paper, the arithmetic combinatorial crossover operator is suggested:

­° wi( k +1) = α ⋅ wi( k ) + (1 − α ) w(j k ) , ® ( k +1) = α ⋅ w(j k ) + (1 − α ) wi( k ) °¯ w j

­° gi( k +1) = α ⋅ gi( k ) + (1 − α ) g (j k ) . ® ( k +1) = α ⋅ g (j k ) + (1 − α ) gi( k ) °¯ g j

(17)

Mutation: The weighted gradient direction from (12) is introduced for w :

w( k +1) = w( k ) + β ( k ) d ( w( k ) , g ( k ) ) and g ( k +1) = Mean( gi( k ) ), i = 1, 2," , m2 .

(18)

where β ( k ) is learning rate, and Mean( x) means the average of x . Stop rule: A maximum iteration number is determined to trigger the stop rule.

3 Experimental Results To provide an experimental demonstration of the validity of BSS with constrained GA, three sources will be used in post-nonlinear model. MSE and the residual crosstalk in decibels (Ct) [11] are used to evaluate accuracy of the algorithm. MSEi = E ( si (t ) − yi (t )) 2 , Cti = 10 log E[( yi − si ) 2 ] . where y, s are with unit variance.

(19)

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Z. Yang and Y. Wan

The linear mixing matrix and three nonlinear functions: ª 0.1870 A = «« 0.1624 ¬« 0.1286

0.6390 0.5200 º 0.9216 0.2316 »» , 0.1824 0.7413»¼

­ f1 = tanh( x ) ° ® f 2 = tanh(0.8 x) . ° f = tanh(0.5 x) ¯ 3

(20)

Polynomials of fifth order were used as the approximations for g = f −1 , according to the algorithm, we have obtained the results as follows: ­ g1 = x + 0.094569 x 3 + 0.039137 x5 ° 3 5 ® g 2 = x + 0.087650 x + 0.092012 x ° 3 5 ¯ g 3 = x + 0.098845 x + 0.045751x

ª 0.8188 -0.2598 -0.5230 º

, W = «« 0.3051 0.9686 -0.0589 »» . ¬«0.5074 -0.0840

(21)

0.8103 ¼»

Table 1. Crosstalk (Ct) and MSE corresponding to sources

Ct (dB) MSE

s1

s2

s3

-26.7264

-64.5408

-26.6678

0.0691

0.0016

0.0695

1 g1 h1

0 -1 -2

0

5

10

15

20

25

30

35

40

45

50

10

15

20

25

30

35

40

45

50

10

15

20

25

30

35

40

45

50

0 g2 h2

-0.5

-1

0

5

1 g3 h3

0

-1

0

5

Fig. 2. g i means the estimation of the non-linear demixing function according to the algorithm,

hi = f i −1 means the inverse of non-linear mixing function

Fig. 3. Original sources and the estimations

4 Conclusion In this paper, the post-nonlinear blind source separation model has been solved using constrained GA. The novelty of this approach is using reasonable constraints in the

Non-linear Blind Source Separation Using Constrained Genetic Algorithm

71

novel contrast function and a new fitness function is constructed. The experimental results show the validity of this method and the original sources are recovered acceptably up to scalings. It is proper to use constrained odd polynomials to approximate the inverse of non-linear distortion when it is under controlled. However, it may not work well under other conditions as it is a quite open question to estimate the inverse of a non-linear function, and there is still a long way for us to overcome it.

Acknowledgement This work is supported by the National Natural Science Foundation of China for Excellent Youth (60325310), the Guangdong Province Science Foundation for Program of Research Team (04205783), the Natural Science Fund of Guangdong Province, China (05103553), the Specialized Prophasic Basic Research Projects of Ministry of Science and Technology, China (2005CCA04100).

References 1. Li, Y., Andrzej, C., Amari, S.: Analysis of Sparse Representation and Blind Source Separation. Neural Computation, 16 (2004) 1193-1234 2. Gao, Y., Xie, S. L.: An Algorithm for Nonlinear Blind Source Separation Based on Signal Sparse Property and Kernel Function. Computer Engineering and Applications, 22 (2005) 33-35 3. Anthony, J. B., Terrence, J. S.: An Information-maximization Approach to Blind Separation and Blind Deconvolution. Neural Computation, 7(1995) 1129-1159 4. Tan Y., Wang, J.: Nonlinear Blind Source Separation Using Higher Order Statistics and A Genetic Algorithm. IEEE Trans on Evolutionary Computation, 5(2001) 600-612 5. Xie, S. L., He, Z. S., Gao, Y.: Adaptive Theory of Signal Processing. 1st ed. Chinese Science Press, Beijing (2006) 136-155 6. Gao, Y., Xie, S. L.: Two Algorithm of Blind Signal Separation Based on Nonlinear PCA Criterion. Computer Engineering and Applications, 22 (2005) 24-26 7. Zhang, J. L., He, Z. S., Xie, S. L.: Sequential Blind Signal Extraction in Order Based on Genetic Algorithm. Acta Electronica Sinica, 32 (2004) 616-619 8. Liu, H. L., Xie S. L.: Nonlinear Blind Separation Algorithm Based on Multiobjective Evolutionary Algorithm. Systems Engineering and Electronics, 27 (2005) 1576-1579 9. Richard, Y. K. F.,Tang, J. F., Wang, D.W.: Extension of A Hybrid Genetic Algorithm for Nonlinear Programming Problems with Equality and Inequality Constraints. Computers & Operations Research 29 (2002) 261-274 10. Martin-Clemente, R., Putonet, C. G., Rojas F.: Post-nonlinear Blind Source Separation Using Methaheuristics. Electronics Letters, 39 (2003) 1765-1766 11. Taleb, A., Jutten, C.: Source Separation in Post-nonlinear Mixtures. IEEE Trans on Signal Processing, 47 (1999) 2807-2820 12. Xie, S. L., He, Z. S., Fu, Y. L.: A Note on Stone's Conjecture of Blind Signal Separation. Neural Computation, 17 (2005) 321-330

A Distributed Wavelet-Based Image Coding for Wireless Sensor Networks Hui Dong, Jiangang Lu, and Youxian Sun National Laboratory of Industrial Control Technology Zhejiang University, Hangzhou 310027, China {dongh, jglu, yxsun}@iipc.zju.edu.cn

Abstract. The strict constrains of wireless sensor networks (WSN) on individual sensor node's resource brings great challenges to the information processing, especially in image capture sensor network. A Simple Wavelet Compression (SWC) processing of image coding is proposed to maximize compression and minimize energy cost in WSN. For low activity in WSN, we employ a Low-complexity Change Detection Algorithm (LCDA) to mark active blocks and we only encode these active regions to save energy. In particular, a position estimation and compensation method is presented to exploit the inherent correlations that exist between sensor readings based on distributed lifting scheme. The impact of this scheme on image signal quality is presented in the final. The simulation results showed that these approaches achieved significant energy savings without sacrificing the quality of the image reconstruction

1 Introduction Wireless sensor networks are being developed for a variety of applications such as environmental monitoring, habitat studies, marine biology and video-surveillance, just to mention a few. Such node is equipped with a sensing device that collects information from the environment (e.g., temperature, vibrations, audio, images) and transmits it through the networks to a central node, or sink, for processing or storage. Imaging sensors are able to provide intuitive visual information for recognition, monitoring, and surveillance. However, these sensors usually generate vast amount of data. For those battery-powered sensors, energy efficient transmission of the images collected and transmitted in the sensor network presents the most challenging problem [1]. In principle, image compression can reduce the amount of data to be transmitted by a considerable factor. On the other hand, it is well-known that most image coders exhibit a very high computational burden. This is not a matter of concern in desktop multimedia applications, but as for wireless sensor networks, where each of the sensors has limited power; current image coding schemes like JPEG standards can hardly reach such a threshold. Several energy efficient protocols of image compression, such as [2-5], are proposed for wireless applications. Magli E. [2] presents a low-complexity video compression with ultra low delay for real time wireless transmission based on change detection and JPEG-like compression of regions of interest. [3] propose an adaptive D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 72 – 82, 2006. © Springer-Verlag Berlin Heidelberg 2006

A Distributed Wavelet-Based Image Coding for Wireless Sensor Networks

73

and Energy Efficient Wavelet Image Compression algorithm (EEWIC) for lossy compression of still image, which consists of two techniques attempting to conserve energy by avoiding the computation and communication of high-pass coefficients: “HH elimination” and “H* elimination” technique. Another energy efficient power aware image compression [5] noted that maximum compression before transmission dose not always provide minimal energy consumption, and present a heuristic algorithm for it. The heuristic algorithm algorithm tries to minimize total energy dissipation with selecting the optimal image compression parameters under given the network conditions and image quality constraints. However, their approaches mainly focus on power efficient techniques for individual components and can not provide a favorable energy performance trade-off in the case of WSN. Fundamentally different from conventional image sensor, image sequences in WSN for environmental monitor are often characterized by low activity and high spatial correlation. These differences are calling for novel approaches for WSN and in particular in network data processing for saving energy consumption in transmission and computation. Based on fast lifting scheme, we propose an energy efficient distributed spatial-frequency wavelet transform algorithm for image compression, enabling significant reductions in computation as well as communication energy needed, with minimal degradation in image quality. Finally, the superior performance of this algorithm is demonstrated by comparing it with several other popular image compression techniques. The paper is organized as follows. Section 2 introduces the background and proposed algorithm. The Comparison of the scheme is addressed in Section 3. Section 4 presents some preliminary results. In Section 5 we present our conclusion and discuss future works.

2 Background and Proposed Algorithm We consider a wireless networks composed of a set of stationary, battery-powered sensor nodes, which is developed as part of the low power wireless sensor project at MIT (AMPS) [6]. Each of sensors is equipped with CLOCK, SENSOR, ADC, LED, RADIO and APPLICATION. The system set-up is shown in Figure 1. Sensor 1 Sensor 2

...

A/D

N hops

A/D Cluster head SWC

Centre node

... ...

A/D Sensor n

Fig. 1. The architecture of wireless system

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H. Dong, J. Lu, and Y. Sun

In order to reduce the communications cost, WSNs can be organized according to a cluster architecture. For the sake of simplicity, we assume that the area under observation is an 2D model plane where sensors are located. Data sampling by the sensors are collected at a source sensor node, clustered by a head node, which is either a central controller or gateway to the fixed network. The sensors and the central node were assumed to be placed as in Fig 1, where the “N” is number of hops on the shortest path between the sources and the sink and “n” is the number of sources, which capture the image signal from the environment. Fig. 2 shows the block diagram of the image coding with the proposed position estimation and compensation in the wavelet domain. In the proposed coding scheme, an input image signal is decomposed by the integer wavelet transform and transmits to the cluster head node. The position estimation finds a similarity block in the neighborhood sensor, which is matched with the current block, and then gets the position vector. The wavelet block consists of the wavelet coefficients which are only related to a local region of the image. According to position vector, we can shift the wavelet coefficients buffer and make it has strong correlation between coefficients of different sensors. In the final, we encode the similar coefficients block with proposed simple wavelet compression. The residual signal can be quantized and encoded by embedded zerotree wavelet (EZW) coder [7] or by set partitioning in hierarchical trees (SPIHT) coder [8]. Position

Position vectors

estimation sensor

Wavelet DWC coefficient

Change detection

...

...

Input sensor

Marked block

Change detection

Cluster head

Position compensation

Centre node

DWC Bit stream

Reference frame

DWC

Entropy coder

Fig. 2. Block diagram of proposed image coding scheme

2.1 Change Detection Unlike typical multimedia video, image sequences in WSN for environmental monitor are often characterized by low motion, when no object is expected to move within the scene but in case of anomalies. In this section we present a low-complexity algorithm to scans the image and mark those active regions within one frame, and we only encode these active regions to save energy consumption. Each input image signal data is divided into 8x8 blocks. In order to decrease complexity, these pixels in each block are hierarchically subdivided into the subsets number 1. 2, and 3 in order of importance [2]. The algorithm scans the value in the block according to the order of importance, computing the difference between each value and the one in the same position in the reference frame; then, it attempts to classify the difference as noise, shadow or illumination change, or object motion. Accordingly, Di, R, U is defined as follow:

A Distributed Wavelet-Based Image Coding for Wireless Sensor Networks

Di = xori (i ) − xref (i ) n

R = ¦ Di i =1

75

(1)

n

¦x

ori

(i )

(2)

i =1

U = Max ª¬ xori (i ) − xref (i ) º¼ ( i = 1...n )

(3)

Moreover, two values N and M are defined and used as a threshold to classify the signal. A sensitivity parameter S is defined as the maximum allowed number of “active” bits in an inactive block and P is defined as the number of pixels for which Di exceeds M. The simple code is presented in Algorithm 1. The reference frame is updated by copying the marked blocks of the marked frame onto the current reference frame. The threshold are automatically computed and updated during the analysis and encoding process[2]. Algorithm 1 For i=0 to n scan each pixel according to the order of importance if P>S then mark the block as activity encode this block proceeding with next block endif End For calculate R if RN and U>M then mark the block as activity encode this block proceeding with next block end if if RM then classify the block content as shadow or illumination. proceeding with next block end if update the reference frame compute the threshold and update it 2.2 The Wavelet Transforms Based on Lifting Scheme

The lifting scheme is an alternative method to compute wavelet transforms. It allows a faster implementation, along with a full in-place calculation of the coefficients [10, 11]. Lifting scheme contains three stages: split, prediction and update. The data is

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H. Dong, J. Lu, and Y. Sun

split into two disjoint sets, followed by a series of prediction and update steps to transform the coefficient data (Fig.3), where sn denotes the high-pass data and d n denotes the low-pass data after the transform is computed.

d j+1 sj

split

predict

update

+

s j+1

Fig. 3. Block diagram of the lifting process

The 5/3 filter structure is an ideal choice in low energy systems, which greatly relaxes computational requirements. It is given by: ­ ª s 0 (2 n ) + s 0 ( 2 n + 2) º ° d 1 ( n ) = s 0 ( 2 n + 1) − « » 2 ° ¬ ¼ ® ( d ( n − 1) + d ( n )) 1 ª º 1 1 ° s ( n ) = s (2 n ) + + » 0 « °¯ 1 4 2¼ ¬

(4)

The wavelet transforms based on lifting scheme has received widespread recognition in the field of image processing for its notable success in coding and obtained very good compression performance. The proposed wavelet transforms is just an extension of standard wavelet transforms. The entire process is carried out by executing standard wavelet transforms twice, one is executed inside sensor node (to reduce the temporal redundancy), and the other in cluster node (to reduce the spatial redundancy). 2.3 Position Estimation and Compensation

High spatial density of sensor networks induces a high level of network data redundancy, where spatially proximal sensor readings are highly correlated. The sensor nodes can compress their data based on the fact that there is another sensor measuring data that is correlated with it. In video coding, several types of interframe predictions have been used to reduce the interframe redundancy. Motion compensated prediction has been used as an efficient scheme for temporal prediction. Likely, a Position Estimation and Compensation method is proposed to fully exploit the spatial inherent correlations that exist between sensor readings. Different from the conventional motion estimation, the proposed position compensation is executed in wavelet domain, which can be overcome the shortcoming of shift-variant property [9]. In this section we present an algorithm on how to exploit the correlation between sensors using position estimation and compensation. The correlation degree between sensors is determined by the overlapping sensing area of correlated nodes. We consider a 2-D model for the sensing area of image sensors illustrated by Fig. 4a. Here S1, S2 is the location of the sensor node, R is the sensing, radius, V is the center line of sight of the camera's field of view which will be termed sensing direction, and Į is the offset angle of the field of view on both sides of V. Figure 4b is the experimental

A Distributed Wavelet-Based Image Coding for Wireless Sensor Networks

77

result of sensing, which illustrate the similarity of two sensor reading. We can examine every block therein and determine if it also falls in others’ sensing areas, and then use a block-matching algorithm (Position Estimation and Compensation) to reduce the spatial redundancy. Y

YĻ

object

V2

V1

bĻ

bĻ

b

b

b ß

a

ß

a

a

a

S1 S1

X'

S2

S2

X

b

a

Fig. 4. a. Sensing model of image sensors. b. Experimental image.

The image block matching schemes are based on mapping coordinate locations, in one image to corresponding locations in a second image. Assume that the distance between the location and the image plane for all sensors are the same and denoted by d, which can characterize the correlation between sensor readings. The (x1, y1), (x2, y2) is the location of the block b in S1, S2 respectively, and the b’ (x’,y’) is the virtual location of the block b(x2, y2) coordinate transformation. As 2-D model, coordinate transformation formula is: T

ª x2 º ªx 'º « y '» = « y » « 2» « » «¬1 »¼ ¬«1 »¼

T

§ 1 0 0 · § cos α ¨ ¸¨ ¨ 0 1 0 ¸ ¨ − sin α ¨ ¸¨ © a b 1¹© 0

sin α cos α 0

0· ¸ 0¸ 1 ¸¹

(5)

Where the (a, b) is the location of node S2 in S1 coordinate. Given the b and b’ loca)))* tion, we can get the position estimation vector bb ' . Fig. 4b illustrates the mapping. Following the same approach we can also determine the mapping relation between S1 and Sn. It is worth to be emphasized that the position estimation algorithm can be executed offline, so it is not a energy burden for wireless sensor network. Different from the position estimation, the position compensation is executed wavelet domain, which can be overcome the shortcoming of shift-variant property. Like motion compensation introducing in the MPEG standards, the block-based position compensation often produces discontinuities between the blocks because the neighboring motion vector are not coherent. These discontinuities lead to highfrequency components in the residual signals and generate large signals of the wavelet coefficients in the high-bands, so the coding efficiency can be degraded. The wavelet transform decomposes an image into four bands of LL, HL, LH, and HH, which are the low–low, the high–low, the low–high, and the high–high bands along the horizontal and the vertical directions, respectively. The so-called wavelet coefficient block (WCB) consists of those wavelet coefficients of an image that are

78

H. Dong, J. Lu, and Y. Sun

only related to a local region of the image (as shown in Fig. 5). We first makes posi)))* tion estimation in spatial domain and obtains position vectors ( bb ' ) for each prediction block. Then, with taking advantage of local spatial-frequency characteristic of )))* wavelet coefficients, we shift the WCB’s order in coefficients buffer according to bb ' to compensate the WCB of prediction block with that of reference block.

Fig. 5. a. Original image. b. Coefficient after the transform.

3 Comparison of the Scheme In order to fairly compare other distributed approach and the proposed algorithm, a cost function that takes into account both processing costs and transmission costs have to be defined. The total energy dissipated at each sensor will be split into three main components: E = E p + Et + Er

(6)

where E p is the energy consumption due to wavelet transform processing, Et , Er is energy dissipation for radio transmission and reception, which has also been developed to model by a sensor node when transmitting and receiving data [12]:

ET = Eelec k + ε amp kd 2

(7)

ER = Eelec k

(8)

Equation (7), (8) stand for the energy dissipated to transmit a k-bit packet over a distance d to receive the k-bit packet respectively, where Eelec is the energy dissipated to run transmit or receive electronics, and ε amp is the energy dissipated by the transmit power amplifier to achieve an acceptable E/N at the receiver. We assume that the energy used to transmit a bit is equivalent to the energy used to receive a bit over very short distances. For our radio, we use the parameters Eelec = 50nJ / b and ε amp = 100 pJ / b / m 2 . To determine the energy efficiency of each algorithm, we take a closer look at the computational complexity of the wavelet transform computed using lifting [10]. We analyze energy efficiency by determining the number of times certain basic operations are performed for a given input, which in turn determines the amount of switching activity, and hence the energy consumption. For standard wavelet algorithm, in the forward wavelet decomposition using the above filter (5/3 filter), 2 shift and 4 add

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79

operations are required to convert the sample image pixel into a low-pass coefficient. Similarly, high-pass decomposition requires 2 shift and 4 add. We model the energy consumption of the low/high-pass decomposition by counting the number of operations and denote this as the computational load. Thus, for a given input M x N bits image signal and wavelet decomposition applied through L transform levels, we can estimate the total computational load as follows: L

N DWC = MN (8 A + 4S )¦ l =1

1 4l −1

(9)

Besides various arithmetic operations, the transform step involves a large number of memory accesses. Since the energy consumed in external and internal data transfers can be significant, we estimate the data-access load by counting the total number of memory accesses during the wavelet transform. At a transform level, each pixel is read twice and written twice. Hence, with the same condition as the above estimation method, the total data-access load is given by the number of reads and writes operations: L

N R _ DWC = NW _ DWC = 2MN ¦ l =1

1 4l −1

(10)

The overall computation energy is computed as a weighted sum of the computational load and data-access load. A simple energy model can be used to model the active energy dissipation due to computation of the SA-1100 as a function of supply voltage [12]:

E p = NCVdd2

(11)

Where N is the number of clock cycles per task, which is determined by N SDWC , N R _ SDWC and NW _ SDWC . C is the average capacitance switched per cycle, and

Vdd is the supply voltage. For the StrongARM SA-1100, C is approximately 0.67 nF. Obviously, the cost of the proposed lifting algorithm for computing the wavelet transform is one half of the cost of standard algorithm asymptotically. For the HH elimination technique in EEWIC [3], the result is given as flow: CR _ HH = CW _ HH =

CHH =

E L 7 1 1 MN ¦ l −1 + 2 MM ¦ l −1 4 4 4 l =1 l = E +1

L MN (22 A + 19 S ) E 1 1 + MN (12 A + 10 S ) ¦ ¦ l −1 l −1 2 l =1 4 l = E +1 4

(12)

(13)

where E is applied to the first E transform levels out of the L total transform levels [3]. To get an idea of the impact on image data quality, we also measured the distortion that the wavelet algorithm brought. Reconstruction data quality is often measured

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H. Dong, J. Lu, and Y. Sun

using a metric know as Peak Signal to Noise Ratio (PSNR). This is defined as (in decibels):

PSNR = 20 log10

2b − 1 E x ( i, j ) − y ( i, j )

(14)

where x(i,j) is the pixel value of original image, y(i,j) is of the reconstructed image and b is the bit-depth (bpp) of the original image. We recognize the PSNR does not always accurately model perceptual image quality, but use it because it is a commonly used metric in the literature.

4 Simulation Results We performed a set of experiments in 2D model as proof of concept of our approach. In particular, the quality of image using the proposed method is studied. Peak Signal to Noise Ratio (PSNR) in dB between the original and reconstructed signal was calculated for objective quality assessment. In the experiments, all sensors have the same parameter setting. The size of image captured by a sensor is 176x 144 pixels. The sensing offset angle is π / 8 and the angle between sensing directions of the two sensors π / 4 . The Sampling frequency of image sensor is 1 frame/s .

Fig. 6. Different energy used between EEWIC and SWC without Change Detection Algorithm with respect to the number of sources (n) and the degree of correlation (d)

Fig.6 shows the different energy used in EEWIC and proposed SWC without Change Detection Algorithm, where nodes number N is 1000ҏ, sampling time T=4s and ҏwavelet decomposition layer k=3. The sources number (n) and the distance (d) is varied for 0 to 100 and 0 to 10 (m) respectively. Note that for the case of the number of sources n =10, energy expenditure of our algorithm is actually few change due to the propose algorithm concentrating on exploiting the correlation between sensors. On the other hand, we can find that the extent of correlation in the data from different sources can be expected to be a function of the distance (d) between them. The figure shows a steeply decreasing convex curve of energy difference that reaches saturation when the sensor distance (d) over 5m. Thus, under experimental condition, we

A Distributed Wavelet-Based Image Coding for Wireless Sensor Networks

81

defined the two sensors are so-called strongly correlated while the distance (d) between sensors is within [0m, 5m], otherwise they are weakly correlated. To get an idea of the impact on image quality, we present the comparisons of the proposed algorithm and EEWIC algorithm. Fig. 7 shows the PSNR value versus CR for case of specific data sensor reading while wavelet decomposition layer k=3. We can see in the figure, as the compression ratio increase, the quality of reconstruction data degrades. However, in doing so, by applying the SWC and WTIC techniques at same case, different result is obtained. For the compression ratio CR> Z beacon / Rate where Zbeacon and Rate represent for the packet size of beacon and the transmission rate of radio channel. The beacon density, ni(t), measures the probability of receiving a beacon for node i at time t. Then, it can be easily discovered that the resolution of a event takes place at point x, x ⊂ S , is

R f c ( x, t ) = n x (t ) ⋅ ∆t beacon ⋅ ( ) 2 + 1 r

(2)

where R and r are the range for sensing and transmission respectively. Defined the minimum threshold of fc(x,t) as f’, then the minimum threshold of beacon density nx(t) can be represented as

f '−1 r n' ( x ) = ( ) 2 ⋅ c R ∆t beacon

(3)

Based on the above analysis, it can be considered as when the incoming beacon probability is lower than n’(x), it means that the number of nodes that cover the point x are too small to provide certain degree of resolution, or vice versa. Therefore, the algorithm that controls the sleep interval can be given as follows.

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Twakei|0=0; Tsleepi|0=0; n=1; if ((tnow-last_update)>update_itvl) { if (((tnow-twakei|n-1)/ tbeacon)*x)>Maxth {tsleepi|n=tnow; twakei|n=tnow+Max_sleep; }; if (((((tnow-twakei|n-1)/ tbeacon)*x)<Maxth)&((((tnow-twakei|n-1)/ tbeacon)*x)>Minth)) {tsleepi|n=tnow; twakei|n=tnow+ Max_sleep*((((tnow-twakei|n-1)/ tbeacon)*x-Minth)/(Maxth-Minth)); }; if ((((tnow-twakei|n-1)/ tbeacon)*x) 0, there exists an integer p (the number of hidden neurons) and real constant optimal weight ∗ ∗ ∈ IRp×(n+1) and Who ∈ IRm×p such that matrices Wih ∗ ∗ Y(x) = Yn∗ (xa , Wih , Who ) + n (x),

(4)

where n (x) is the approximation error vector satisfying n (x) ≤ , ∀x ∈ D. The optimal approximator can be described as ∗ ∗ ∗ ∗ Yn∗ (xa , Wih , Who ) = Who σ(Wih xa ).

4

(5)

Adaptive Control Design for AUV Depth System

For the AUV’s depth control system modeled in (2), the control objective is to drive the AUV to track an expected depth trajectory yem . The tracking performance can always be characterized by the tracking error e := yem − ye . In order to increase the robustness of the controller to be designed, a sliding surface is introduced as: S = e˙ + λe, where λ is a small positive constant. Define    S η if |η| ≤ 1, S∆ = S − ε · sat , sat(η) = sgn(η) otherwise. ε If S ≤ ε, S∆ = S˙ ∆ = 0; and if S > ε, S∆ = S − ε and S˙ = S˙ ∆ . Then the derivative of S is

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S˙ = e¨ + λe˙ = y¨e + λe˙ = f (x) + g(x)δe + (−¨ yem + λe) ˙ ˙ + g(x)δe . = −ΛS + [ΛS + f (x) + (−¨ yem + λe)]

(6)

Define Y (x) := ΛS + f (x) + (−¨ yem + λe), ˙

(7)

which is uncertain, and can be on-line approximated by a feedforward NN described in Section 3. 4.1

Using NN as an Online Approximator

When the AUV cruises underwater, additional force and moment coefficients are added to account for the effective mass of the fluid that surrounds the vehicle and must be accelerated with the AUV. These coefficients are referred to as added (virtual) mass and include added moments of inertia and cross coupling terms such as force coefficients due to linear and angular accelerations. It would be difficult task to obtain the exact values of hydrodynamic coefficients, let alone those disturbances from currents and waves. The main idea of NN based control schemes is to apply NNs to online approximate the unknown nonlinear functions involved in the nonlinear systems to be controlled. On the basis of Theorem 1, we can see that there exists an op∗ ∗ , Who ) over a properly defined timal neural network approximator Yn∗ (xa , Wih ˆ ih , W ˆ ho ) to model the ˆ compact set, and we design a NN approximator Yn (xa , W ˆ ˆ unknown function Y (x), given the estimates Wih and Who . The NN approximation error Y˜n and the wight matrix estimation error are defined as follows, respectively ˆ ih , W ˆ ho ), Y˜n := Y (x) − Yˆn (¯ xa , W ∗ ˆ ih , ˜ ih := W − W W ih

˜ ho := W∗ − W ˆ ho . W ho According to Theorem 1, we can re-write the NN approximation error as ˆ ho σ(W ˆ ih xa ) Y˜n = W∗ σ(W∗ xa ) + n (x) − W ho

ih

˜ ho σ(W∗ xa ) + W ˆ ho σ(W∗ xa ) + n (x) − W ˆ ho σ(W ˆ ih xa ). =W ih ih Taking the Talor-series expansion on

(8)

∗ σ(Wih xa ),

we have   ∗ ˜ ih xa ), (9) ˆ ih xa ) + σ  (W ˆ ih xa ) W∗ xa − W ˆ ih xa + (W σ(Wih xa ) = σ(W ih   dσ1 (z) dσ1 (z) ˆ ih xa ) = diag dσ1 (z) | ˆ where σ  (W , | , · · · , | ˆ ˆ z=Wih1 xa z=Wih2 xa z=Wihp xa dz dz dz

∈ IRp×p , and (·) is the sum of the high-order terms of the argument in the Taylor-series expansion. Substituting (9) into (8), we can get   ˆ ih xa ) − σ  (W ˆ ho σ  (W ˜ ho σ(W ˆ ih xa )W ˆ ih xa +W ˆ ih xa )W ˜ ih xa +Ψ, (10) Y˜n = W ˜ ho σ  (W ˆ ih xa )W∗ xa + W ˜ ho (W ˜ ih xa ) + n (x). where Ψ = W ih

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Adaptive control and estimation laws to be designed will suppress the NN approximation error, and thus achieve satisfactory tracking performance. In order to facilitate the following design, we analyze the lumped term Ψ in the NN approximation error and explore its upper bound, following the approach used in [4]. Sigmoid function and its derivative are always bounded by certain constants, hence we assume c1 and c2 are some constants, and ∗ ˆ ih xa ) − σ(Wih ˆ ih xa ) ≤ c2 . σ(W xa ) ≤ c1 , σ  (W

Therefore, ∗ ˜ rmih xa ) = σ(W ˆ ih xa ) − σ(Wih ˆ ih xa )W ˜ ih xa  ˆ  (W (W xa ) − σ ˜ ih xa . ≤ c1 + c 2  W

(11)

According to Theorem 1, the norm of the optimal weight matrices of the trained ¯ ih NNs should be bounded by certain constants that are assumed to be W ¯ and Who , ∗ ∗ ¯ ih , Who ¯ ho , Wih F ≤ W F ≤ W  T  where  · F := tr (·) (·) with tr indicating the trace of a matrix, representing the Frobenius norm of a matrix. It is noted that the Frobenius norm of a vector is equivalent to the 2-norm of a vector. Then the norm on the residual term Ψ of the NN approximation error is ˆ ih xa )W∗ xa + W ˜ ho (W ˜ ih xa ) + n (x) ˜ ho σ  (W Ψ = W ih   ˜ ih F · xa  +  ˜ ho F · c2 · W ¯ ih · xa  + W ¯ ho c1 + c2 W ≤ W   ˆ ho F xa  ¯ ho +  + 2c2 W ¯ ih W ¯ ho xa  + c2 W ¯ ih W ≤ c1 W ¯ ho W ˆ ih F xa , +c2 W := bT w where

  ¯ ho +  2c2 W ¯ ih W ¯ ho c2 W ¯ ih c2 W ¯ ho T ∈ IR1×4 , b = c1 W   ˆ ho F xa  W ˆ ih F xa  ∈ IR4×1 . w = 1 xa  W

Then we have Ψ  ≤ bT w.

(12)

It is also noticed that g(x) is uncertain in that the involved coefficient k29 is unknown. Therefore, we need to adaptively estimate k29 . For the convenience of expression, define k := k29 , and the parameter estimation error k˜ =then the estimated g(x) can be expressed as:   gˆ(x) = kˆ −v 2 cos(θ − α) .

(13)

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Control and Parameter Estimation Laws

Once Yˆn and gˆ are employed as on-line approximators, we can design an adaptive AUV depth control system based on NNs: δe = gˆ−1 (−Yˆn + uc ),

(14)

where uc is the compensation control term and has the following form   S ˆT uc = −sat b w, ε

(15)

ˆ ∈ IR4×1 is an unknown vector to be estimated. where b The parameter estimation laws for the NN and associated unknown coefficients are designed as follows   T ˆ ih xa ) − σ  (W ˆ˙ ho = Γho σ(W ˆ ih xa )W ˆ ih xa S∆ , (16) W   T ˆ˙ = Γih xa S∆ W ˆ ih xa ) , ˆ ho σ  (W W ih

(17)

  ˙ kˆ = Γk S∆ −v 2 cos(θ − α) ,

(18)

ˆ˙ = Γw |S∆ |w. b

(19)

Figure 3 depicts the structure of the depth control system developed herein. In the implementation of the controller, the depth ye can be measured by a pressure meter, the pitch angle θ can be measured by an inclinometer while the pitch rate ωz1 requires a rate gyro or rate sensor. Parameter Estimation Laws

Expected Depth

+

+

•

-

•

NN Approximation

Yˆn

-

+ +

X

AUV System

AUV System Output

•

AUV System States

Compensation Control

Approximation

uc

gˆ −1

•

Adaptive NN Control

Fig. 3. Block diagram for the control scheme

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4.3

215

Stability Analysis

Theorem 2. (Stability) Consider the AUV depth control system described by (1) or (2) with the control given by (14) and parameter estimation laws provided by (16), (17), (18), and (19). Then the AUV depth tracking error will asymptotically converge to a neighborhood of zero, and all adjustable parameters will remain bounded. Proof. Choose a Lyapunov function V = V1 + V2 , where V1 =

1 2 S , 2 ∆

(20)

and V2 =

1 ˜ b ˜T. ˜ T ) + 1 tr(W ˜ T ) + 1 Γk k˜2 + 1 bw ˜ ho Γ −1 W ˜ ih Γ −1 W tr(W ho ih ho ih 2 2 2 2

(21)

In the following, the time derivative V˙ is to be evaluated for two cases: (1) |S| > ε, and (2) |S| ≤ ε. (1) Case 1: If |S| > ε, then S∆ = S − ε. Hence, the time derivative of V1 can be derived as follows: V˙1 = S∆ S˙ ∆ . Substituting (6), (14), and (15) into the above equation yields V˙ 1 = S∆ [−ΛS + Y (x) + g(x)δe ]       = S∆ −ΛS + Y˜n (x)+ Yˆn (x) +[˜ g (x) + gˆ(x)] gˆ−1 (x) −Yˆn (x) + uc   (22) = S∆ −ΛS + Y˜n (x) + g˜(x)δe + uc . Taking the NN approximation error Y˜n (x) (10) and the control law δe (14) into (22), we have   V˙ 1 = −S∆ ΛS∆ − S∆ ε + S∆ uc + S∆ k˜ −v 2 cos(θ − α) δe    ˆ ih xa )W ˆ ih xa ˜ ho σ(W ˆ ih xa ) − σ  (W +S∆ W  ˆ ih xa )W ˜ ih xa + Ψ ˆ ho σ  (W +W According to (12), we can further obtain    2 ˆ ih xa )W ˆ ih xa ˆ ih xa ) − σ  (W ˜ ho σ(W V˙ 1 ≤ −ΛS∆ + tr S∆ W     ˜ T w. ˆ ho σ  (W ˆ ih xa )W ˜ ih xa + k˜ −v 2 cos(θ−α) δe S∆ +|S∆ |b +tr S∆ W (23) On the other hand, the time derivative of V2 is T T ˜ ho Γ −1 W ˜ ih Γ −1 W ˆ˙ ) − tr(W ˆ˙ ) − Γ −1 k˜ kˆ˙ − b ˆ˙ ˜ T w−1 b. V˙ 2 = −tr(W ho ih ho ih k

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Substituing the parameter estimation laws (16), (17), (18), and (19), and the control law (14) into the above equation yields T T ˜ T w−1 b ˆ˙ ˆ˙ ) − tr(W ˆ˙ ) − Γ −1 k˜ kˆ˙ − b ˜ ho Γ −1 W ˜ ih Γ −1 W V˙ 2 = −tr(W ho ih ho ih k    ˆ ih xa ) − σ  (W ˜ ho σ(W ˆ ih xa )W ˆ ih xa = −tr S∆ W     ˆ ih xa )W ˜ ih xa − k˜ −v 2 cos(θ − α) δe S∆ −|S∆ |b ˜ T w. ˆ ho σ  (W −tr S∆ W

(24) Combining (23) and (24) leads to 2 V˙ ≤ −ΛS∆ .

(25)

(2) Case 2: If |S| ≤ ε, then S∆ = 0. Hence, V˙ = 0.

(26)

Considering the above two cases, (25) and (26) obviously imply that : (1) S∆ , ˜ ho , W ˜ ih , and w are all bounded; (2) S∆ ∈ L2 . According to the boundedness W of all the adjustable parameters, we can straightforwardly see that δe , uc , and ∞ S˙ ∆ are also bounded. Furthermore, limt→∞ 0 S∆ dt is bounded, and S∆ is uniformly continuous. Applying the Barbalat Lemma [12] yields lim S∆ = 0,

t→∞

(27)

which implies that the depth tracking error will asymptotically converge to a neighborhood of zero.

5

AUV Case Study

The simulation study is based on the model structure of certain AUV developed in [14]. Preset the expected cruising depth yem = 50m. Assume the following initial conditions: v = 30m/s, ye = 0; ωz1 (0) = 0. Then we employ a feedforward NN with the structure - 8 inputs, 10hidden neurons, and 1 output - to approximate the uncertain nonlinearity. The adaptive update gain matrices are set to be Γho = diag(5, · · · , 5) ∈ IR10×10 , Γih = diag(0.2, · · · , 0.2) ∈ IR8×8 , and Γk = 0.05, and all the initial weights are set to 0. For the sliding surface, we choose S = e˙ + 4e, and ε = 0.3. Figure 4 illustrates the depth response of the AUV (ye ), and Figure 5 shows the control input (δe ) - the stern plane deflection. A better performance may be obtained by further tuning the update gain and increasing the number of neurons in the hidden layer. A higher update gain gave a better tracking performance but, when the gain was too high, oscillatory behavior may happen.

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Fig. 4. Depth response of the AUV (ye )

Fig. 5. Control input - the stern plane deflection of the AUV (δe )

6

Conclusion

An adaptive NN controller for an AUV’s depth control system has been developed. The NN controller offers guaranteed tracking performance. Feedforward NN has been used to on-line approximate the uncertain nonlinear dynamics of the AUV. Without explicit prior knowledge of the vehicle dynamics, the proposed control technique could achieve satisfied tracking performance, and all the adjustable parameters involved are bounded during the course. Case studies show the effectiveness of the proposed method for AUV system. Whereas this work is only for the AUV’s depth channel, the next stage of the study is to apply the proposed NN based adaptive control scheme for AUV’s three-channel control system design.

References 1. Curtin, T. B., Bellingham, J. G., Catipovic, J., Webb, D. Autonomous Oceanographic Sampling Networks. Oceanography. 6 (1989) 86–94 2. DeBitetto, P. A.: Fuzzy Logic for Depth Control of Unmanned Undersea Vehicles. Proc. Symposium of Autonomous Underwater Vehicle Technology. (1994) 233–241

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3. Fossen, T.: Guidance and Control of Ocean Vehicles. Chichester: Wiley. (1994) 4. Fu, L.C., Chang, W.D., Yang, J.H., Kuo, T.S.: Adaptive Robust Bank-to-turn Missile Autopilot Design using Neural Networks. Journal of Guidance, Control, and Dynamics. 20 (1997) 346–354 5. Funahashi, K.I.: On the Approximate Realization of Continuous Mappings by Neural Networks. Neural Networks. 2. (1989) 183–192 6. Healey, A. J., Lienard, D.: Multivariable Sliding Mode Control for Autonomous Diving and Steering of Unmanned Underwater Vehicles. IEEE Journal of Oceanic Engineering. 18 (1993) 327–339 7. Hornik, K., Stinchcombe, M., White, H.: Multilayer Feedfroward Networks are Universal Approximators. Neural Networks. 2 (1989) 359–366 8. Ishii, K., Fujii, T., Ura, T.: Neural Network System for Online Controller Adaptation and its Application to Underwater Robot. Proc. IEEE International Conference on Robotics & Automation. (1998) 756–761 9. Kato, N.: Applications of Fuzzy Algorithm to Guidance and Control of Underwater Vehicles. Underwater Robotic Vehicles: Design and Control. J. Yuh (Ed.), TSI: Albuquerque. (1995) 10. Nakamura, Y.,Savant, S.: Nonlinear Tracking Control of Autonomous Underwater Vehicles. Proc. IEEE Int. Conf. on Robotics and Automation. 3. (1992) A4–A9 11. Nie, J., Yuh, J., Kardash, E., Fossen, T. I.: Onboard Sensor-based Adaptive Control of Small UUVs in the Very Shallow Water. Proc. IFAC-Control Applications in Marine Systems. Fukuoka, Japan. (1998) 201–206 12. Slotine, J.J. E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs. (1991) 13. Valavanis, K. P., Gracanin, D., Matijasevic, M., Kolluru, R.,: Demetriou, Control Architecture for Autonomous Underwater Vehicles. IEEE Contr. Syst.. (1997) 48– 64 14. Xu, D., Ren,., Yan, W.: Control Systems for Autonomous Underwater Vehicle. Xi’an: NPUP. (1990) 15. Xu, D., Yan, W., Shi, Y.: Nonlinear Variable Structure Double Mode Control of Autonomous Underwater Vehicles. Proc. IEEE International Symposium on Underwater Technology. Tokyo. (1990) 425–430 16. Yuh, J.: A Neural Net Controller for Underwater Robotic Vehicles. IEEE Journal Oceanic Engineering. 15 (1990) 161–166 17. Yuh, J.: Learning Control for Underwater Robotic Vehicles. IEEE Control System Magazine. 14 (1994) 39–46 18. Yuh, J.: An Adaptive and Learning Control System for Underwater Robots. Proc. 13th World Congress International Federation of Automatic Control. San Francisco, CA. A (1996) 145–150 19. Yuh, J.: Design and Control of Autonomous Underwater Robots: a Survey. Autonomous Robots. (2000) 7–24

Adaptive Fuzzy Sliding-Mode Control for Non-minimum Phase Overload System of Missile Yongping Bao1, Wenchao Du2,3, Daquan Tang4, Xiuzhen Yang5, and Jinyong Yu5 1

School of Mathematics and Information, Lu Dong University,Yantai,264001, P.R. China [email protected] 2 Graduate Students’ Brigade, Naval Aeronautical Engineering Institute, Yantai 264001, P.R. China 3 Special Missiles Representatives Office in Beijing of Military Representatives Bureau of NED in Tianjin, Beijing, 100076, P.R. China 4 School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics,Beijing 100083, P.R. China 5 Department of Automatic Control Engineering, Naval Aeronautical Engineering Institute, Yantai 264001, P.R. China

Abstract. An adaptive fuzzy logic system is incorporated with the Varibale Structure Control (VSC) system for the purpose of improving the performance of the control system. A sliding surface with an additional tunable parameter is defined as a new output based on the idea of output redefinition, as a result the overload system of missile with the characteristic of non-minimum phase can be transformed into minimum-phase system by tuning the parameters of the sliding surface, and a sliding-mode controller can be designed. For the existence of uncertainty of the parameters, a fuzzy logic system is used to approximate it, thus the chattering effects can be alleviated. Finally, the simulation results have been given to show the effectiveness of the proposed control scheme.

1 Introduction A system is a non-minimum phase one when it’s zero dynamics is unstable. To control non-minimum phase systems is more difficult than to control minimum phase systems, which can be shown by the process of I/O linearization, and the standard I/O linearization may cause the zero dynamics of the non-minimum phase system unstable, thus the ordinary control scheme can’t be applied. For the merits of I/O linearization, some researchers managed to extend the technique to non-minimum phase systems. A solution is to define a new output, thus the zero dynamics of new system can be stabilized. However building a meaningful relation between the original output and the new output is difficult. C. Kravaris and R.A. Wright [1] defined a new output by introducing the concept of static equivalence, which can guarantee that the compensated system is linear with respect to static I/O, but the dynamical process can not be guaranteed. H.Yang and H.Krishnan[2] applied the output redefinition technique to single-link flexible robots by coordinate transformation. Govert Monsees and Jacquelien Scherpen[3] pointed out that because the inversion of the non-minimum D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 219 – 228, 2006. © Springer-Verlag Berlin Heidelberg 2006

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phase system is not stable, the feedforward controller can not be used unless the desired input or the upper bound of the input is known. Conventional sliding-mode control can not be applied to the system with non-minimum phase, because its equivalent control term tends to infinity, such that Shkolnikov and Yuri B.Shtessel[4] designed dynamic sliding mode control for non-minimum phase systems. The acceleration system of tail-controlled missiles is a non-minimum phase system, namely the tail fins deflection first generates a small force on the fin opposed to the desired acceleration. In [5], the approximating lineariztion and feedback linearization is adopted, the dynamic model of missile is transformed into minimum phase parametric affine model. In [6] the model of missile with the acceleration as the output is simplified as a minimum phase system via partly linearization and singular perturbation-like technique, and I/O is exactly linearized. In [7], output redefinition and inversion is used to deal with the non-minimum phase characteristic of missile. In this paper, a new sliding surface with an additional tunable parameter is defined as a new output, thus output redefinition can be combined with Sliding-Mode Control(SMC) perfectly, and the non-minimum phase system of the missile overload can be controlled. Besides, fuzzy logic system is used to approximate the uncertain part of system, so that the control gain of SMC can be more fitting, and the chattering effect can be alleviated. This paper is organized as follows. In Section II, the original overload system of missile is transformed into a new one by refining a sliding surface as a new output. In Section III, a fuzzy sliding mode controller is designed and the stability is proved via Lyapunov stability theorem. In Section IV, a simulation example is provided to illustrate the performance of the proposed control scheme. Conclusion remarks are finally made in Section V.

2 Description of Missile Overload System Conventional acceleration model of the pitch channel of missiles [7] concludes three equations, but some researchers often treat the motor as a one order system, thus the control to design is not fin deflection but the control voltage, and the total equations are as follows

ω z = a24α + a22ω z + a25δ z

(1a)

α = ω z − a34α − a35δ z

(1b)

δz = − wδ z + wuδ

(1c)

ny = Where

ω z in(1a)

v v a34α + a35δ z g g

is angular acceleration ,

α

in (1b) is attack angle,

(1d)

n y in (1d) is

overload. (1a), (1b) and (1d) formulate the acceleration model of the pitch channel of missiles. (1d) is the mode of the motor. In Appendix a conclusion is given that the derivation of the overload is approximately proportional to the angular acceleration,

Adaptive Fuzzy Sliding-Mode Control

which can be expressed as

221

V n yb ≈ ω z . In the control scheme proposed in this paper, g

the derivation of the overload is only play the role of damping, so that the value of it precise or not is not a matter of cardinal significance. When the angular acceleration is used to replace the derivation of the overload, the sliding surface chosen as (2) becomes meaningful.

S = k1 (n y − n yd ) + k 2 (ω z − ω zd )

(2)

Where k1 is an additional tunable parameter which can not be seen in the traditional from of sliding surface. Take the sliding surface as new output , after some mathematical manipulations, it can obtain that

§ α · § m11 ¨ ¸ ¨ ¨ ω z ¸ = ¨ m21 ¨ S ¸ ¨ m © ¹ © 31

m12 m22 m32

m13 ·§ α · § 0 · § D1 · ¨ ¸ ¸¨ ¸ ¨ ¸ m23 ¸¨ ω z ¸ + ¨ 0 ¸uδ + ¨ D2 ¸ ¨D ¸ m33 ¸¹¨© S ¸¹ ¨© b ¸¹ © 3¹

(3)

Let S = 0 , then we can get the zero dynamics shown as

§ α · § m11 ¨¨ ¸¸ = ¨¨ © ω z ¹ © m21

m12 ·§ α · § D1 · ¸¨ ¸ + ¨ ¸ m22 ¸¹¨© ω z ¸¹ ¨© D2 ¸¹

(4)

To keep the zero dynamics stable, the polynomial shown in (5) must be a Hurwitz one, the aim can be obtained by choosing the values of k1 , k 2 .

§ m11 sI − ¨¨ © m21

m12 · ¸ = s 2 + h1 s + h2 m22 ¸¹

(5)

where

h1 = a34 − a 22 + k1

v a34 a35 + k 2 a 24 a35 + k 2 a 22 a 25 g

h2 = k2 a22a25a34 − a22a34 + k1k2

v v a22a25a34a35 − k1 a22a34a35 g g

+ k2 a22a24a25a35 − k2 a22a24a35 2

Besides, to guarantee the convergence of the sliding surface and the dynamical performance, the following relations should be satisfied

k1 k 2 > 0

(6)

B2 < k1 / k 2 < B1

(7)

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a34 − a 22 + k1

v a34 a35 + k 2 a 24 a35 + k 2 a 22 a 25 > 0 g

k 2 a22 a25 a34 − a22 a34 + k1k 2

v a22 a25 a34 a35 g

(8)

(9)

v 2 − k1 a22 a34 a35 + k 2 a22 a24 a25 a35 − k 2 a22 a24 a35 > 0 g

3 Adaptive Fuzzy Sliding Mode Controller Design Suppose the zero dynamics has already been stabilized by choosing

k1 , k 2 , and the

values of α , ω z and aerodynamic parameters can be measured or calculated, then it can obtain that

S = m 31 α + m 32 ω z + m 33 S + bu δ + D 3

(10)

Chose the candidate Lyapunov function as V1 =

1 S 2

2

(11)

If the control is chosen as

uδ = uc + u a where

(12)

1 1 u c = (−m31α − m32ω z − m33 S − D3 ) , u a = (− A1 S − A2 sign( S )) b b

Derivate (12), we have

V1 = SS = S(m31α + m32ωz + m33S + buδ + D3 ) = S(−A1S − A2sign(S))

(13)

= −A1S 2 − A2 S ≤0 thus the asymptotical stability of the system can be guaranteed. When there exists uncertainty, (3) can be changed into the following form

§ α · § m11 + ∆m11 ¨ ¸ ¨ ¨ω z ¸ = ¨ m21 + ∆m21 ¨ S ¸ ¨ m + ∆m 31 © ¹ © 31

m12 + ∆m12 m22 + ∆m22 m32 + ∆m32

§ D1 + ∆D1 · § 0 · ¸ ¸ ¨ ¨ + ¨ 0 ¸uδ + ¨ D2 + ∆D2 ¸ ¨ D + ∆D ¸ ¨ b + ∆b¸ 3¹ ¹ © 3 ©

m13 + ∆m13 ·§ α · ¸¨ ¸ m23 + ∆m23 ¸¨ωz ¸ m33 + ∆m33 ¸¹¨© S ¸¹

(14)

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and the zero dynamics will be

§ α · § m11 + ∆m11 ¨¨ ¸¸ = ¨¨ ©ω z ¹ © m21 + ∆m21

m12 + ∆m12 ·§ α · § D1 + ∆D1 · ¸¨ ¸ + ¨ ¸ m22 + ∆m22 ¸¹¨©ω z ¸¹ ¨© D2 + ∆D2 ¸¹

To keep the zero dynamics stable,the values of

§ m11 + ∆m11 sI − ¨¨ © m21 + ∆m21

(15)

k1 , k 2 must keep the polynomial

m12 + ∆m12 · ¸ a Hurwitz one. From (14),we have m22 + ∆m22 ¸¹

S = (m31 + ∆m31)α + (m32 + ∆m32)ωz + (m33 + ∆m33)S + (b + ∆b)uδ + D3 + ∆D3

(16)

Let

f = ( m 31 + ∆ m 31 )α + ( m 32 + ∆ m 32 )ω z + ( m 33 + ∆ m 33 ) S + D 3 + ∆ D 3

(17)

g = b + ∆b

(18)

S = f + gu δ

(19)

then (16) can be rewritten as

For the existence of uncertainty, fuzzy logic system is introduced to approximate it, which is not to tune the weights but the centers of the member function of the output. And the bell member functions are expressed in the form of (20)

µ ij (u j ) = 1 /(1 + where

u j − cij

2 bij

aij

)

(20)

cij presents the center of the member function, a ij determine the width of the

bell function and

bij characterize the slope. And the following rule sets are adoped

IF u1 is U1 AND um is Um THENF =ξi Rulei

i = 1,2,...R ,

(21)

Where u and F are input and output of the FLC , U i and ξ i are input and output linguistic variables. For FLS we chose product-operation rule of fuzzy implication and center of average deffuzifier as (22)

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m

i =1

j =1

R

m

FTOTAL = ¦ ξ i ∏ µ ij (u j ) / ¦∏ µ ij (u j ) i =1 j =1

R

(22)

= ¦ ξ iω ni = ξ T ω n i =1

where m

R

m

ω ni = ∏ µ ij (u j ) / ¦∏ µ ij (u j )

(23)

i =1 j =1

j =1

R, m are numbers of rules and inputs, ω ni is the ith element of the vector

ω n = (ω n1 , ω n 2 ,..., ω nR ) T ,for SISO FLC , m = 1 . Let

f = f + ∆f

(24)

g = g + ∆g

(25)

where f = m 31α + m 32 ω z + m 33 S + D 3 , ∆ f = ∆ m 31α + ∆ m 32ω z + ∆ m 33 S + ∆ D3 ,

g =b

㧘 ∆ g = ∆ b , then (16) can be rewritten as

S = f + ∆ f + ( g + ∆ g ) u δ

(26)

Fuzzy logic system is adopted to approximate ∆f , ∆g , that is T ∆fˆ = ξˆ f ω nf

(27)

T ∆gˆ = ξˆg ω ng

(28)

Firstly, define optimal parameters ξ f , *

ξ g * and minimal approximating error

me = (∆f − ∆f * ) − ~

Let ξ f

* = ξ f − ξˆ f

㧘 ξ~

(∆g − ∆g * ) uδ g + ∆gˆ

(29)

* = ξ g − ξˆg

g

And the following theorem can be got. Theorem 1: If control laws and adaptive laws are adopted as shown in(30)-(33)



ξˆ f = l1ω nf S 

ξˆg = −

1 l 2ω ng uδ S g + ∆gˆ

(30) (31)

Adaptive Fuzzy Sliding-Mode Control

uc = − ua =

Where

1 ( f + ∆ fˆ + A1 S ) g + ∆ gˆ 1 ( − A 2 sign ( S )) g + ∆ gˆ

225

(32)

(33)

l1 ,l 2 and A1 , A2 are positive real numbers, and A2 > me , then the system

(16) stable asymptotically. Proof Choose the candidate Lyapunov function as

V1 =

1 2 1 ~T~ 1 ~T~ ξg ξg S + ξf ξf + 2 2l1 2l2

(34)

derivate it, we will have

1 ~ T ~ 1 ~ T ~ V1 = SS + ξ f ξ f + ξ g ξ g l1 l2 = S{ f + ∆f + ( g + ∆g)[− −

1 ( f + ∆fˆ + A1S ) g + ∆gˆ

1 T~ T~ A2 sign(S )]} − Sωnf ξ f − Sωng ξ g uδ ˆ g + ∆g g + ∆g )uc − A1S − A2 sign(S ) = S{ f + ∆f − f − ∆fˆ + (1 − g + ∆gˆ

g + ∆g T~ T~ ) A2 sign(S )]} − Sωnf ξ f + Sωng ξ g uδ g + ∆gˆ ∆g~ + (∆g − ∆g * ) ~ uδ − A1S = S (∆f + (∆f − ∆f * ) − g + ∆gˆ T~ T~ − A2 sign(S )) − Sωnf ξ f + Sωng ξ g uδ

+ (1 −

~T = S (ξ f ωnf −

1 ~T 1 ~ ~ ξ g ωnguδ − ωnf Tξ f + ωngTξ g uδ g + ∆gˆ g + ∆gˆ

− A1S − A2 sign(S ) + (∆f − ∆f * ) −

(∆g − ∆g * ) uδ ) g + ∆gˆ

= S (− A1S − A2 sign(S ) + me ) ≤ − A1S 2 − ( A2 − me ) S ≤0 thus the asymptotical stability of the system can be guaranteed.

(35)

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4 Simulation

n

y

Į̬e

/g

Take the pitch channel overload model of some missile as an example, suppose the model of the motor is a one order system as − 17 (s + 17) , to verify the correctness and

t(s)

t(s) Fig. 1. Response curve of overload

α

Ȧ

z

u̬ V

(DŽ

Fig. 2. Response curve of

t(s) t(s)

ωz

Fig. 4. Curve of control voltage

n

y

S

/g

Fig. 3. Response curve of

t(s)

t(s) Fig. 5. Response curve of

S

Fig. 6. Response curves of verloadwith ± 20% parameter perturbation

Adaptive Fuzzy Sliding-Mode Control

227

effectiveness of the proposed control scheme, simulations are made for the nominal system and the system with parameter perturbation respectively when the reference input is square wave signal. The simulation results are shown as Figure1-6, where Figure1-5 are for the nominal system, the curve of overload is given in Figure 1,the curve of α is given in Figure 2, the curve of ω z is given in Figure 3, and the curve of control voltage is given in Figure 4, the curve of sliding surface is given in Figure 5. Curves of the overload with ± 20% parameter perturbation are shown in Figure 6(solid line for + 20% ,dashed line for − 20% ).

5 Conclusion In this paper, an adaptive fuzzy logic system is incorporated with the VSC system for the purpose of improving the performance of the control system. A sliding surface with an additional tunable parameter is defined as a new output based on the idea of output redefinition, as a result the overload system of missile with the characteristic of non-minimum phase can be transformed into minimum-phase system by tuning the parameters of the sliding surface, and a sliding-mode controller can be designed. For the existence of uncertainty of the parameters, a fuzzy logic system is used to approximate it, thus the chattering effects can be alleviated. Finally, the simulation results have been given to show the effectiveness of the proposed control scheme.

References 1. Kravaris, C., Wright, R.A.: Nonminimum-phase Compensation for Nonlinear Processes. AIChE. J. 38 (1992) 26-40 2. Yang, H., Hariharn, K., Marcelo, H.: Tip-trajectory Tracking Control of Single-link Flexible Robots via Output Redefinition. Proceedings of International Conference on Robotics and Automation Detroit, Michigan. (1999) 1102-1107 3. Zinober, A., Owens, D. (Eds.): Nonlinear and Adaptive Control. LNCIS 281, Springer-Verlag Berlin Heidelberg (2003) 239-248 4. Iiya, A.S., Yuri, B.S.: Aircraft Nonminimum Phase Control in Dynamic Sliding Manifolds. Journal of guidance ,control and dynamics, 24(3) (2001) 566-572 5. Chwa, D.K., Choi, J.Y.: New Parametric Affine Modeling and Control for Skid-toTurn Missiles. IEEE Transactions on Control Systems Technology, 9(2) (2001) 335-347 6. Lee, J.I., Ha, I.J.: Autopilot Design for Highly Maneuvering STT Missiles via Singular Perturbation-Like Technique. IEEE Transactions on Control System Technology, 7(5) (1999) 527-541 7. Ryu, J.H., Park, C.S., Tank, M.J.: Plant Inversion Control of Tail-Controlled Missiles. AIAA-97. 3766 (1997) 1691-1696

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Appendix To make the sliding surface S = k1 ( n y − n yd ) + k 2 (ω z − ω zd ) converge,

ω z

should be proportional to n y , which will be proved in the following conclusion. Conclusion 1: The acceleration of angular is approximately proportional to the derivation of overload of missile Proof Take the pitch channel model as an example, there exists the following relation

α = ω z − a34α − a35δ z

(A1)

V (a34α + a35δ z ) g

(A2)

n y =

substitute (A1) into (A2), it can obtain that

n y =

V (ω z − α ) g

(A3)

V (ω z − α) g

(A4)

derivate (A3) and we will have

n y =

Because α  is not easy to obtain and the value of which in small compared with the relation of (A5) can be got.

n y ≈

V ω z g

ω z , so (A5)

An Improved Genetic & Ant Colony Optimization Algorithm and Its Applications Tiaoping Fu1,2, Yushu Liu1, Jiguo Zeng1, and Jianhua Chen2 1

School of Computer Science and Technology, Beijing Institute of Technology, Beijing 100081, China [email protected] 2 Naval Arms Command Academy, Guangzhou 510430, China

Abstract. It is a crucial research to improve the efficiency of weapon-target assignment (WTA) of warship formation. However, the WTA problem is NP hard. Some heuristic intelligent algorithms usually result in local optimal. A novel genetic & ant colony optimization (GACO) algorithm is proposed which is based on the combination of genetic algorithm and ant colony algorithm. Genetic algorithm phase adopts crowding replacement and changeable mutation operator to create multiple populations. Due to the good initial pheromone distribution, ant colony optimization phase can avoid getting into local optimal. Then, a further study of how to use the algorithm on WTA is made. Some experiments are made. The results demonstrate that GACO has better efficiency than other classical algorithms. The bigger the WTA problem is concerned, the more advantage the algorithm makes. The proposed algorithm is viable for other NP-hard problems.

1 Introduction Following with the rapid progress of the modern technology, all kinds of anti-ship weapons gain fast development. The traditional anti-sea and anti-sub operations have largely changed into the scope of anti-air operations. Thus, a credible and efficient WTA algorithm is very necessary. However, the present firepower distribution researches of warship mainly focus on single warship operation, the achievement of warship formation cooperative firepower distribution is scarce. But, in the future seafight, facing for the complicated anti-air situation, warship formation must cooperatively control many kinds of missiles to attack the arriving targets. WTA problem is complicated optimization problem whose solutions numbers exponential increase with the numbers of weapons (M) and the numbers of targets (N). It is a multiple parameters and multiple constraints NP hard problem. Such resource allocation problems of combinatorial optimization have numerous local extrema [1], have the characters of nonlinear, discontinuous etc. The excellent performance of many heuristic intelligent algorithms has arose more and more research interests. Among these algorithms, genetic algorithm has the high-speed searching character, can solve the WTA problem well when combinated with other optimization algorithm. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 229 – 239, 2006. © Springer-Verlag Berlin Heidelberg 2006

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At the aspect of WTA problem, people bring forward many methods such as neural networks, genetic algorithms with greedy eugenics, expert system. However, these algorithm all have their advantage and shortage, cannot give attention to both speed and quality performances, so is hard to fit the real-time and precise firepower distribution demand of warship formation anti-air missiles attacking numerous targets. Facing for the urgent requirement, avoiding the shortage of present algorithm, an improved genetic & ant colony optimization (GACO) algorithm based on the combination of genetic algorithm and ant colony algorithm is proposed.

2 Air Defense WTA Problem for Warship Formation 2.1 Analyzation of WTA Problem Weapon-target assignment problem is an important research which make all weapons in a region cooperate action for protecting the own-force assets. Its mission is exerting multiple weapons colligating advantage as a whole, finding an optimal assignment of weapons to targets for a scenario with the objective of minimizing the expected threat of own warship formation. We have know the characters of assaulting target and anti-air missiles units and n ≥ m (when assaulting targets is more than anti-air missiles units or m > n , we can choose the n most dangerous assaulting targets based on the threat parameters and deal with other target in other groups). Aerial threat toward warship formation is very fearful. In the actual operation, the survival of formation is much more important than the cost of operation. In other words, we will not think over using the cheaper weapon resource but the safety of the warship formation can be confirmed. So, we proposed: we should stress on the protection of warship formation operation capability when assigning weapons to targets. Then, the considered WTA problems are to minimize the following colligation threat parameters function: m ª n x º min C = ¦ v j «∏ (1 − kij ) ij » j =1 ¬ i =1 ¼

(1)

Paying attention less to the cost of operation, but we take the threat parameter of every target into count during the WTA course. Thus, the direct results are reducing the dashing probability of the most dangerous targets and getting the basic intention of anti-air operation. On the other hand, the design will improve the algorithm efficiency greatly and meet the real-time requirement of decision-making. xij is decision variable. When weapon i attacks target j , xij = 1 , otherwise,

xij = 0 . v j is the threat parameter of target j . Threat parameter has relation with distance, bearing, speed of coming target and moving speed, direction of warship formation etc. kij is the damage probability of weapon i to target j . Also, we can get

kij by distance, bearing, speed of coming target and weapons capability of warship formation.

kij can be provided by C3I system of warship formation platform.

An Improved GACO Algorithm and Its Applications n

st.

¦x

ij

≤ g i , ( j = 1, 2, , m)

(2)

i =1

m

¦x

ij

≤ 1,

231

( i = 1,2,, n)

(3)

( i = 1,2,,n ; j = 1,2,,m)

(4)

j =1

xij ∈{0,1}

Formulation (2) replaces that the weapons assigned to target j can not exceed at some time. Formulation (3) represents that weapon some time.

i

gi

can only attack one target at

2.2 Computation of Target Threat Parameter The problem of threat judgment has relation with many factors, but these factors themselves are uncertain. However, fuzzy theory is a good tool to solve this kind of uncertain problem. Threat parameter has relation with distance, bearing, speed of coming target and moving speed, direction of warship formation etc which expressed by variable γ . Shown in Fig.1, we suppose warship formation lies on point W, target lies on point T. VT V ș VW

T

d

W Fig. 1. Sketch of the situation between the target and ship formation

We

suppose

there

are

target

Ti , their attribution parameters are

di , θ i , VRi (i=1,2,3…..n). When have n target, their attribution parameters are di ' , θ i ' , Vi ' after dealt without dimension. Thus, we can get the threat variable of each parameter γid , γiθ , γiV [2] , then, we can get the colligation threat value of target i toward warship formation. Then, we can put the threat value

vi got by ( F * γ ) 1/ 2

into the goal function of warship formation anti-air WTA optimization.

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3 The Improved Genetic & Ant Colony Optimization Algorithm for WTA Problem 3.1 Design of Improved Genetic Algorithm in GACO Algorithm Some researches have been done on the combination of genetic algorithm and ant colony optimization algorithm. But they mainly focus on the combination of simple genetic and ant colony optimization algorithm. However, they have some shortages. For example, the population variety of simple genetic algorithm is poor. It is easy to get into local optimal when the evolution generations are still very few. When ant colony optimization algorithm continues anaphase search based on the local Pareto optimum solutions, the entirely astringency of ant colony optimization is hard to ensure. If we increase the evolution generations of anaphase algorithm simply, the runtime of algorithm will increase greatly, the advantage of combination algorithm will disappear. It is a good way to maintain the variety of population by using crowding replacement. Crowding replacement can prevent the individual of high fitness from overpopulated by restricting that filial generation can only replace nearest parental generation. On the other hand, the property of individual that distance is farther has much more difference. Thus, the algorithm can get individuals that distance is farther and property has more difference when adopting crowding replacement. The implementation flow of genetic algorithm using crowding replacement in GACO is shown as: Step 1: Initialization Firstly, initial population and adaptive function is set in reason based on the character of the WTA problem. Real-number encoding can be closer to the problem, has strongpoint thereinafter: ameliorating the computing complexity and improving the computing efficiency of genetic algorithm; convenient for the hybrid with other classical optimization algorithm; good for designing genetic operator contraposing the problem; convenient for dealing with the complex constraint conditions. So, we adopted the real-number encoding in chromosome.

Ԙ

ԙ

Ԛ

ԛ

The chromosome string of the ith individual

xti of the tth generation is

aik11 aik22  ainkn . Thereinto n is the length of chromosome string, corresponding to the target number; gene bit

k

aij j replaces the serial number of weapon allocating to the

assaulting target in weapon units set:

k

a ij j

­0 ° ° =® °k j °¯

no target unit allocates to the i th w eapon the k j target unit allocates to the i th w eapon, k j ∈ {0,1, 2,  , m }

(5)

An Improved GACO Algorithm and Its Applications

233

Choose s individuals in the feasible region of solution space(s is the scale of colony, representing the s allocation plan), build up the initial colony X t {xti | i 12"V}. Step 2: Tournament option operators During the anaphase of genetic algorithm, the adaptability values of individuals in colony are equal approximately. Thus, if we choosing operators according to the adaptability values proportion simply, the choosing strength is poor. Tournament option operators has the function of automatically adjusting adaptability values proportion, choosing strength having nothing to do with the relative adaptability values among individuals, fitting for joining with crowding replacement especially. So, we adopt tournament option operators [3] choosing individuals to multiply. The tournament scale of tournament option is Size , the numeric area is [2, N]. The tournament scale has the relation formula with choosing strength and multiformity loss as SelIntTour (Size) = 2(log(Size) − log 4.14 log(Size) ) LossDivSize ( Size ) = Tour

1 − Size −1

− Tour

(6)

Size − Size −1

(7) ~

 xts based on their fitness δ ( X ) and Size individuals are chosen from xt1᧨xt2᧨ the individuals of highest fitness to multiply set are saved to form the multiply

 xt . set xt ᧨xt ᧨ Step 3: Crossover operators '1

'2

's

Choose two individuals

xt'i᧨xt'j ∈ xt'1᧨xt'2᧨  xt' s , deletes xt'i᧨xt'j from

xt'1 , xt'2 , xt's . Take

xt'i᧨xt'j as parents to disperse recombined, their offspring are xt'' k , xt''l . '' k

''l

'i

'j

''1

''2

'' s

Choose xt , xt or xt , xt to add into xt , xt ,, xt . Repeat the process s/2 times. Step 4: Time varying mutation operators If n bits of all chromosomes in whole colony get the same value, the searching space is only (1/ 2) n of the whole space when purely through crossover computing. This will decrease searching space greatly. Thus, we must adopt mutation operators to change the premature phenomena. Already having many experimental compare researches, the judgment of mutation is more important than crossover sometimes has been affirmed. Essentially, GA is a process of dynamic and adaptability. It will departure from the evolution spirit if adopting the way of fixing parameters. So, we hope modifying the value of strategy parameters during the GA computing course [4]. In our paper, we modify strategy parameters obeying the certain rule, changing the parameters based on genetic generations. Initial stages of algorithm, adopt larger mutation value, avoiding prematurity and maintaining the colony multiformity. Following the increasing of the genetic generations, mutation value drops continuously, making the computing converge to global optimization. The way is given by

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pm = 0.3 − 0.2×t / G

(8)

t is genetic generations, G is the total generations. ''1 ''2  xt''s to form next Based on mutation probability, mutation disturbs for xt ᧨xt ᧨ i  "V}. generation colony Xt 1 {xt 1 | i 12

where

Step 5: Individual crowding replacement As for xti+1 , 1 ≤ i ≤ S , suppose xt j , 1 ≤ j ≤ S is the nearest parent individual, also mean Euclid distance d ( xti+1 , xti ) is shortest. The d ( xti+1 , xti ) is given by d ( xti+1 , xti ) = (aik11 − a kj11 ) 2 + ( aik22 − a kj 22 ) 2  + (ainkn − a kjnn )

(9)

If δ ( xti+1 ) > δ ( xti ) , replacing xt by xt +1 , otherwise, reserving xt . Step 6: If currently generation t reaches the total iteration times tmax , then break and save the computing result. Otherwise, t++, turn to Step2. Step 7: Put finally colony into objective function, get the r Pareto optimum solutions, code these chromosomes of r Pareto optimum solutions, get r optimal assignments of weapon units to targets, keep the r assignments as the inputting of anaphase algorithm. i

i

i

3.2 Design and Link of Ant Colony Optimization Algorithm in GACO Algorithm Ant colony optimization was used to solve TSP problem [5] originally, searching the shortest route among all cities through ant colony randomly searching under the inspire of pheromone. In order that ACO can be used to WTA problem, in this paper, we express WTA problem into bipartite graph G=(V U E). V is the set of n points, representing n weapon units separately, corresponding n nodes of one side of bipartite graph. U is the set of m points, representing m targets separately, corresponding m nodes of the other side of bipartite graph. E is the border joining targets nodes with weapon units nodes E = {eij | i = 1,2,n; j = 1,2,m} . If some weapon unit i is

㧘㧘

assigned to target j, there is a border Otherwise, there isn’t border.

τ ij

between weapon unit i and target j,

eij linking weapon unit i with target j.

is the trace of border

eij . If there isn’t border

τ ij = 0 . The feasible route composed with many

borders in bipartite graph, is correspond with an assignment project between targets set and weapon units set. So, seeking the optimal solution on WTA problem is searching the optimal route in bipartite graph. The ant colony optimization in GACO is described as: Step 1: Initialization (1) encode r optimal assignments of former phase(GA), form the initial r routes of ant colony optimization. (2) the initial pheromone distribution between target set and weapon unit set is given by

An Improved GACO Algorithm and Its Applications

τ ij (t0 ) = τ 0 + ∆τ ij ; i = 1, 2, , n; j = 1, 2, , m. where τ ij (t0 ) represents the trace of border

235

(10)

eij at initial time( t0 = 0), τ 0 is

pheromone constant, being a small positive real number.

∆τ ij is given by

r

∆τ ij = ¦ ∆τ ijk

(11)

k =1

where ∆τ ij represents the trace of border k

eij of route k, r is the optimal assignments

of GA, corresponding the initial r routes. ­QSk ° ° ∆τijk = ® ° 0 °¯

has border between target j and weapon i in kth assignment project hasn't border between target j and

(12)

weapon i in kth assignment project

where Q is adjustment parameter, S k is the objective function value of the kth assignment project. (3) make every ant correspond with only one weapon node or target node and put the node into weapon Tabu Table or target Tabu Table. Step 2: Node choosing Any ant i (corresponding with weapon node i) chooses target node j basing on β °­arg max j∈allowi [τ ij (t )(ηij ) ] j=® J °¯

when q ≤ q0 otherwise

where q0 is the threshold value enacted in advance,

(13)

q0 =0.9, q is a random number

uniformly distributing in (0, 1), allowi is the set of all the targets which still now is not assigned to ant i, τ ij (t ) is the trace between weapon i and target j at time t. On WTA problem, the mathematical models of ηij are given based on different optimal rule. For example, we need decrease the threat value toward warship formation to maximum extent. The mathematical model should be the arithmetic product of damage probability kij and the threat value v j of target j.

ηij = kij × v j

(14)

J is the serial number of some weapon in allowi set, the value of J is decided by the way of roulette based on probability

Pis (t )

­ τ ij ( t )(η ij ) β °° β Pij ( t ) = ® ¦ τ ij ( t )(η ij ) j∈allowi ° 0 °¯

j ∈ allowi other

(15)

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Step 3: Local pheromone updating After every ant chooses its target node, use “local pheromone update” to update the trace of border eij .

τ ij (t + 1) = (1 −ψ )τ ij (t ) + ψ∆τ

(16)

where 0 < ψ ≤ 1 is a constant, representing the volatilization probability.

∆τ ij =

Q cbjk

(17)

k

where cbj is the total benefit of the current ant k from first node to now. One result of “local pheromone update” is that ants will not converge to a single route. Approved by experiment, the way is good for finding more latency optimal solutions and improves the quality of searching. Otherwise, all ants probably trap in an extraordinary small searching interspace. Step 4: Check of finishing node assignment (1) after all ants choose their target nodes and local update pheromone, set the Recorder Stack of ants. If the assigned weapons to the targets nodes have reached the maximum limitation, the target node will be set in the Recorder Stack of ant. Then ant moves to the next null weapon node which has not been assigned any target. Turn to Step 2. (2) if all weapon nodes have been traversed, then turn to Step 5. Step 5: Whole pheromone update After all ants having traversed all targets nodes, m solutions have been built up. These m solutions were taken into objective function and get the local optimal solutions. The best solution is preserved, using “whole pheromone update” to update the trace of borders of the best solution. The update rule of the “whole pheromone update” is given by

τ ij (t + 1) = (1 − ρ )τ ij (t ) + ρ∆τ ij (t )

(18)

where 0 < ρ ≤ 1 is the parameter which controls the attenuation process of pheromone. ­ 1 ° ∆τ ij (t ) = ® C elitist °¯ 0

if ij is one border of the best assignment otherwise

(19)

Step 6: Check of finishing evolution If currently generation t reaches the total iteration times Tmax, loop is terminated and the optimization resolution is got. Otherwise, turn to Step 2. 3.3 Flow of Warship Formation WTA Problem Based on GACO Algorithm In the first phase of computing, adopts genetic algorithm, making full use of the GA’s characters of rapidity, randomicity and global astringency. Its function is producing initial pheromone distribution of certain problem for next phase. In the second phase

An Improved GACO Algorithm and Its Applications

237

of algorithm, adopts ant colony optimization. Under the circumstances of having initial pheromone distribution, ant colony optimization converges on the optimal path through pheromone accumulation, renewal and the parallel processing, global searching ability of ACO. Its overall frame is given in the Fig.2. Warship formation air defense WTA Define object function based on decreasing threat to maximum extent Create a set of real-number encoding randomly

Calculate the probability; ant moves to next node based on the probability

Choose multiply set through tournament option operators

After ant chooses the target node, use “local update” to update border eij trace

Disperse recombine on crossover probability

After n ants traversed m target nodes, use “whole update” to update all borders trace

Mutate disturbance based on time varying operators

Reach genetic generations?

Initialize parameters; create initial pheromone distribution; put n ants on n weapon nodes

No

Yes Create some sets of optimal solution

Stop criterion satisfied?

No

Yes Optimal solutions output

Fig. 2. Flow of warship formation WTA based on GACO

4 Experimental Results and Analysis We make experiments aiming at air defense missile-target assignment problem of warship formation to test the performance of GACO. We suppose that the formation has eight missile weapon units, facing for eight targets at the same time. The threat values of these targets to formation and the damage probability of every missile to these targets are different. The damage probability kij can be calculated based on distance, bearing, speed of coming target and the missiles performance of warship formation.

kij is provided by

C 3 I system of warship formation. The genetic generations of GA in GACO are 20; crossover probability initial mutation probability

pcross =0.6;

pmutation =0.3. Initial pheromone of every routs of ACO is

60; trace update parameter ρ =0.2, ψ =0.2, iteration times are 30. As for 8 missiles assign to 8 targets problem, we adopt GACO and GAGE [1] algorithms which can meet the real-time demand in air defense missile-target assignment problem of warship

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fitness value

Fig. 3. The fitness curves of GACO and GAGE

formation. All experiments are performed on a 2.8GHz machine with 512 megabytes main memory. Programs are written in Windows/Visual C++ 6.0. The comparing results of the two algorithms are shown in the Fig.3. As a whole, the fitness value of GACO and GAGE drops following the generations continuously. The fitness curve descending extent of GA in GACO prophase is less than GAGE. The cause may lie in GAGE has been imported with Greedy Eugenics. The fitness value descending extent of GA anaphase in GACO becomes slow continuously. The cause may lie in GA is helpless for the using of feedback information in system. When computing to more generations, usually makes redundancy iteration and has low efficiency when searching precision solution. However, because GACO adopts the design of crowding replacement , time varying mutation operators and makes full use of the GA’s characters of randomicity and global astringency, it can maintain the variety of population well and produce good initial pheromone distribution for ACO. During ACO phase in GACO, the fitness value drop greatly, finally, the optimization value stabilizes at a number lower than GAGE’s. The cause lies that ACO has good initial pheromone distribution and makes use of the characters of parallel processing and positive feedback, realizing to find further precision solutions and avoid getting into local optimal. So, GACO has better optimization performance and speed performance than GAGE when solving the problem of air defense missile-target assignment. For testing the performance of GACO on cosmically assignment problem, we compare GACO with other intelligent optimization algorithms, for example: GA, GAGE, Simple Genetic & Ant Algorithm [6](GAAA), Niching Genetic and Ant Algorithm[7](NGAA). The results are shown in the Table.1. The strategy parameters of GA and ant colony algorithm are same as GACO for confirming the fairness. The number out of bracket is optimization value of objective function; the number in bracket is operation time of every algorithm. We can see from the Table.1, GACO has better effective and efficient performance than the other four algorithms obviously. The bigger the assignment problem is concerned, the more advantage the algorithm makes.

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Table 1. Comparison of optimization performance and speed performance among algorithms Algorithms GA GAGE GAAA

NGAA GACO

50weapons \ 50 targets 283.35 (42.76) 172.46 (28.37) 182.32 (12.38) 181.56 (6.13) 168.73 (5.85)

80weapons \ 80 targets 357.82 (54.75) 285.39 (31.57) 288.79 (18.96) 288.13 (9.94) 278.26 (7.68)

100weapons \ 80 targets 278.65 (51.98) 163.58 (21.06) 166.42 (10.35) 164.37 (9.67) 159.38 (6.02)

120weapons \ 80 targets 143.35 (36.78) 96.84 (9.32) 98.67 (7.53) 97.43 (6.41) 93.37 (5.27)

5 Conclusions The improved genetic & ant colony optimization adopts the advantages of genetic and ant colony optimization, overcoming their shortage and achieving a good result when using on WTA problem of warship formation. We make experiments on the algorithm and compare the experimental results with other algorithms. The results demonstrate: GACO has good searching efficiency and speed performance; GACO is a preferable optimization algorithm and can meet the real-time and precision demand in WTA problem. GACO is also viable for other NP-hard problems. Following the increasing of problem scale, the improvement is more greatly. Acknowledgments. This work was partially supported by the National Defense Science Foundation of China (Grant No. 10504033). We would like to thank Doctor. Yunfei Chen for his helpful and constructive comments.

References 1. Lee, Z. J.: Efficiently Solving General Weapon-Target Assignment Problem by Genetic Algorithms with Greedy Eugenics. IEEE Transactions on Systems, 33 (1) (2003) 113-121 2. Hu, S., Z, Y.: Determining the Threatening Degrees of Objects Using Fuzzy Operations. Acta Armarmentarii, 20 (1) (1999) 43-46 (in Chinese) 3. Georges, R. Harik.: Finding Multimodal Solutions Using Restricted Tournament Selection. In Larry. J. Eshelman, editor, Proceedings of the Sixth International Conference on Genetic Algorithms, Morgan Kaufmann, (1995) 24-31 4. Holland, J.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor, MI, MIT Press, Cambridge, MA (1992) 5. Dorigo, M.: Bonabeau E, Theraulaz G. Ant Algorithm and Stigmery. Future Generation Computer Systems, 16 (8) (2000) 851-871 6. Kumar, G. M, Haq, A. N.: Hybrid Genetic and Ant Colony Algorithms for Solving Aggregate Production Plan. Journal of Advanced Manufacturing Systems, 4 (1) (2005) 103-111 7. Chen, Y., Liu, Y, Fan, J., Zhao, J.: A Niching Genetic and Ant Algorithm for Generalized Assignment Problem. Transactions of Beijing Institute of Technology, 25 (6) (2005) 490494 (in Chinese)

Application of Adaptive Disturbance Canceling to Attitude Control of Flexible Satellite Ya-qiu Liu, Jun Cao, and Wen-long Song Northeast Forestry University, Harbin 150040, China [email protected], [email protected], [email protected]

Abstract. An adaptive inverse disturbance canceling method of an orbiting flexible satellite during normal pointing for “modal vibration disturbance”, which is difficult to cancel by the PID method since it’s modal frequency low and dense, and damping small, is proposed. Here, the adaptive inverse disturbance canceling, compared with the conventional feedback disturbance rejection method, performs in inner loop and is independent of dynamic response control loop. Since the adaptive inverse disturbance canceling performed is based on the PID control of dynamics response in this paper, the control structure is designed as following. Fist, the conventional PID method is designed for the dynamical control system of rigid satellite. Second, the modal vibration disturbance control is performed by adaptive inverse disturbance canceling method. The key of this approach is estimation of modal vibration disturbance, the difference is between disturbed output of the plant and disturbance-free output of the copy model, which is then input to the disturbance canceling filter which is a least squares inverse of rigid satellite model. Simulation results demonstrate the effectiveness of the controller design strategy for attitude control and modal vibration disturbance suppression.

1 Introduction The current trend of spacecraft is to use large, complex, and light weight space structures to achieve increased functionality at a reduced lunch cost. This results in these space structures being extremely flexible and having low fundamental vibration modes, and these modes are often excited during normal on-orbit operations, such as attitude maneuvers. When it is required to maneuver the attitude of the flexible spacecraft, the dynamic coupling between the solar panel vibration and the spacecraft attitude varies with the angle of attitude maneuver. Certain levels of vibration to the flexible solar arrays will be introduced. Therefore, vibration reduction is a critical problem related to maneuvering of flexible spacecraft. One basic method, which has been used in the past for disturbance canceling with linear plants, and three methods, which have been attempted in the past to cancel disturbances with nonlinear plants are presented in [1]. The first, based on a derivative plant model, suffers from high complexity; the second, based on the filtered-epsilon method, has been demonstrated to fail [2]; and the third [3], based on internal model control to be incorrect if on-line plant modeling is performed. These three approaches are abandoned here in favor of D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 240 – 251, 2006. © Springer-Verlag Berlin Heidelberg 2006

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extending the disturbance canceling method used for linear plants to encompass nonlinear plants as well. The adaptive inverse control has advantages in disturbance canceling [4]. Based on inverse thought the adaptive inverse disturbance canceling has performed in inner loop through a separate adaptive inverse filter, and it is independent of dynamics response control. By handing the problem in this way, we can improve as much as possible performance, a compromise is not required in the design process to obtain good dynamic response and good disturbance control [1,5]. Thus the adaptive inverse canceling method for normal pointing attitude control and vibration suppression of an orbiting spacecraft with flexible appendage is proposed by defining the correlative vibration as “modal vibration disturbance”. The key to this method is regard effect produced in modal vibration as a kind of correlated disturbance on the base of rigid controlling, and disturbance canceling has performed in inner loop separately. In this paper, the rigid spacecraft model and adaptive inverse disturbance canceller is modeled using NARX (Nonlinear AutoRegressive with eXogenous inputs model)[5,6,7], and improved RTRL-LMBP algorithm is designed for improve convergence speed and obtain better effect of disturbance canceling control.

2 Dynamics Description The slewing motion of a rigid hub with flexible appendage attached to the hub is graphically presented in Fig.1. The rotational motion only without any translation of the center of mass of the whole structure is considered in this paper. Define the OXY and oxy as the inertial frame and the frame fixed on the hub, respectively. The attitude angle denotes the relative motion between these two frames. Denote as the flexible deformation at point with respect to the oxy frame. It is assumed that the control torque is applied to the rigid hub only. Using Lagrangian method, the governing equations of motion for the spacecraft model are given by [8].

Iθ + ¦ Fn ⋅ qn (t ) = T , qn (t ) + 2ς pn q n (t ) + pn2 ⋅ qn (t ) + Fn ⋅ θ = 0

(1)

n

where Ih is the moment of inertia of the center body; T is the control torque; Fn is coupling coefficients; qn, ςn and pn is modal variable, damping ratio, constrained Modal frequency of the nth modal of flexible appendages respectively.

m

Y

x w(x,t)

¦Ñ, E y R

T

o

θ

O b

Ih

l X

Fig. 1. Spacecraft model with single-axis rotation

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Y.-q. Liu, J. Cao, and W.-l. Song

For the latter analysis, the model (1) can be transformed as the following form Is θ ( s ) − 2

¦

Fn s qn ( s ) = T ( s ), qn ( s ) =

− Fn s

2

n

2

s + 2ς pn s + pn 2

2

θ (s)

(2)

where s is the Laplace variable. The transfer function from control torque T to attitude angle ș can be written as: θ ( s) =

1 Is

2

⋅ (1 +

¦s n

Kn ⋅ s 2

2

+ 2ρn Λ n s + Λ n 2

)T ( s ) 1

(3)

where k n = Fn I , K n = k n (1 − k n ) , ρ n = ς (1 − k n ) 2 , Λ n = pn (1 − k n ) . The 2

2

2

block diagram of transfer function is then shown in Fig.2.

T ( s)

1 Is 2

+

¦s n

Kn ⋅ s 2 2 + 2ρn Λn s + Λ2n

θ ( s)

+

Fig. 2. Block diagram for flexible spacecraft with single-axis rotation

3 Dynamic Neural Networks A layered network is a feedforward structure that computes a static nonlinear function. Dynamics is introduced via the taped delay lines at the input to the network, resulting in a dynamic neural network, which is called NARX filter. It is general enough to approximate any nonlinear dynamical system, and either its structure or adaptive algorithm is more complicated than static network, but the ability to describe nonlinear dynamic system is strengthened greatly. 3.1 Adaptive Dynamic System Identification

NARX models have implicit feedback of delayed versions of their output to the input of the model. This feedback is assumed in all block diagrams in Fig. 3. The purpose of Fig. 3 is to show that this feedback, when training an adaptive plant model, may be connected to either the model output or the plant output. The first method is called a parallel connection for system identification, and the second method is called a seriesparallel connection for system identification. Networks configured in series-parallel may be trained using the standard backpropagation algorithm. Networks configured in parallel must be trained with either real-time recurrent learning (RTRL) or backpropagation through time (BPTT). The series-parallel configuration is simple, but is biased by disturbance. The parallel configuration is more complex to train, but is unbiased by disturbance. Therefore, in this work, nonlinear system identification is

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first performed using the series-parallel configuration to initialize weight values of the plant model. When the weight values converge, the plant model is reconfigured in the parallel configuration and training is allowed to continue. This procedure allows speedy training of the network, but is not compromised by disturbance. Zk

XN 3ODQW



P

yk

yk



6HULHV3DUDOOHO

 B

3DUDOOHO 0RGHO

ek

yˆ k

Pˆ

Fig. 3. Adaptive plant modeling

3.2 Adapting Dynamic Neural Networks

LM (Levenberg-Marquardt backpropagation) algorithm is the combination of the steepest decent algorithm with the Gauss-Newton algorithm. Compared with a conjugate gradient algorithm and a variable learning rate algorithm, the LevenbergMarquardt algorithm is much more efficient than either of them on the training steps and accuracy. With the aid of the approximate second derivative, the LM algorithm is more efficient than the gradient method. Therefore, it can be applied to online control. As the matrix is positive definite, the solution always exists, such that LM method is preferable to Gauss-Newton method. To improve training speed, the improved LMBP-RTRL algorithm based on the LM method is proposed. An NARX filter computes a function of the following form yk = f ( xk , xk −1 ,  , xk − n , yk −1 , yk − 2 ,  , yk −m , W ).

(4)

The familiar “sum of squared error” cost function is Vk = 1/ 2E (ek ek ). T

(5)

To Stochastic approximate Vk, we need to construct Vk ≈ (1/ 2)ek ek . T

(6)

For adapting NARX filters, it was fist done by RTRL algorithm, defining the Stochastic approximate function (6), where, ek=dk-yk. Then the Jacobians presentation is as follows. J (W )

dy k dW

=

∂y k ∂W

=

dek dW

n

+

¦ i =0

= −

∂y k dxk − i ∂xk − i dW

(7)

dy k dW m

+

¦ i =1

∂y k dy k − i ∂y k − i dW

(8) .

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Y.-q. Liu, J. Cao, and W.-l. Song

The first term ∂yk/∂W in (8) is the direct effect of a change in the weights on yk, which is denoted a Jacobians J0(W); The second term is zero; The final term can be broken up into two parts. The first, ∂yk/∂yk-i, can by obtained by BP algorithm. The second part, dyk-i/dW, is simply a previously calculated and stored value of dk/dW. When the system is “turn on,” dyi/dW are set zero for i=0,-1,-2,…, and the rest of the terms are calculated recursively from that point on. In the case of hiding time, a similar presentation follows,

e = {e1 , e2 ,  , eS } {e1 , e2 ,  , eN }

(9)

W = {w111 , w121 , , w1S R , b11 , bS1 , w112 ,  , bSM } {w1 , w2 ,  , wn }.

(10)

M

1

1

M

The J0(W) is of the following form:

§ ∂y1 (W ) ∂w1 ¨ ∂y (W ) ∂w ∂y 2 1 J 0 (W ) = =¨  ∂W ¨ ¨ © ∂y N (W ) ∂w1

∂y1 (W ) ∂w2



∂y2 (W ) ∂w2







∂y N (W ) ∂w2



∂y1 (W ) ∂wn ·

∂y2 (W ) ∂wn ¸

¸ ¸ ¸ ∂y N (W ) ∂wn ¹.

(11)



where, N = S M , n = S1 (R + 1) + S 2 (S1 + 1) + + S M (S M −1 +1) . The elements of J0(W) can be computed by improving algorithm of backpropagation. By defining new sensitivity m m si , h = ∂y h ∂ni , then

[ J 0 ]h , l =

∂yh

=

∂wl

[ J 0 ]h , l =

∂yh ∂wl

∂yh ∂wij

m

∂yh

=

∂yh ∂ni

m

=

∂bi

m

m m −1 = si , h a j .

∂ni ∂wij m

m

∂yh ∂ni

(12)

m

=

∂ni ∂bi m

m

m = si , h

(13)

And it is initialized at the final layer

siM, h =

∂yh ∂n

M i

­ f M ( niM )

i=h

¯0

i≠h

=®

(14)

It can also be shown that the sensitivities satisfy the following recurrence relation m m m m +1 T m +1 S = F (n )( W ) S

(15)

.

Continue, J0(W) may be calculated via (12) and (13). Let (d w y ) k

ª¬( dyk −1 dW )

T

( d x y ) k [( ∂yk ∂y k −1 )

( dy

k −2

( ∂y

k

dW )

T

∂yk − 2 )





J (W ) = − [ J 0 (W ) + ( d x y ) k ( d w

( dy

k −m

( ∂y y) ] k

.

k

dW )

T

º¼

T

∂yk − m )].

(16)

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Obtained the Jacobian matrix, the weights and offsets may be adjusted by LM method. The update becomes −1

∆W = − ª¬ J (W ) J (W ) + µ I º¼ J (W )e(W ). T

T

(17)

Where the parameter ȝ is multiplied by some factor ȕ whenever a step would result in an increased V(W). When a step reduces V(W), ȝ is divided by ȕ. Notice that when ȝ is large the algorithm becomes steepest descent, while for small ȝ the algorithm becomes Gauss-Newton. The LM algorithm can be considered a trust-region modification to Gauss-Newton. The algorithm is summarized as follow: 1) Let all inputs to the network and compute the corresponding network outputs and errors, and then compute value of the cost function. 2) Compute the Jacobian matrix. Networks configured in series-parallel may be trained using the standard backpropagation algorithm. A Networks configured in parallel must be trained with RTRL based on LMBP algorithm as (16). 3) Solve (17) to obtain ∆Wk; 4) Re-compute the cost function using Wk+∆Wk. If this new value is smaller than that computed in step 1, then reduce ȝ by ȕ, Let Wk+1=Wk+∆Wk, and go back to step 1. If the value is not reduced, then increase ȝ by ȕ and go back to step 3. 5) The algorithm is assumed to have converged when the norm of the gradient is less than predetermined value, or when value of the cost function has been reduced to some error goal.

4 Control Strategy During normal pointing attitude control of an orbiting flexible spacecraft, the modal vibration of flexible appendages is regarded as a kind of correlated disturbance defined as “modal vibration disturbance”, which is difficult canceling by the PID method since it’s modal frequency low and dense, damping small. An adaptive inverse control has advantage in disturbance canceling, which implemented only in the inner loop. Since the adaptive inverse disturbance canceling performed is based on the PID control of dynamics response in this paper, the control structure is designed as following. Fist, the conventional PID method is designed for the dynamical control system of rigid spacecraft. Second, the modal vibration disturbance control is performed by adaptive inverse disturbance canceling method. The PID controller design is not provided here, and in the following part only the disturbance canceller design is described. According disturbance canceling technology of adaptive inverse control [1,5], structure diagram illustrating the adaptive inverse “modal vibration disturbance” canceling for flexible satellite during normal pointing control mode as Fig.4. First, the dynamical system of the rigid spacecraft we wish to control is modeled using NARX neural network Pˆ . Second, a very close copy Pˆ of Pˆ , disturbance-free match to plant, is fed the same input as the plant NP, which is dynamics module based on reaction wheels of constrained mode of flexible spacecraft with single-axis rotation as Fig.2. The difference between the disturbed output of the plant and the disturbance-free output of the copy model is estimation of modal COPY

246

Y.-q. Liu, J. Cao, and W.-l. Song

vibration disturbance ηˆ , which is then input to a copy of disturbance canceller k

COPY −1 z Qˆ k ( z ) , and z Qˆ k ( z ) is a best least squares inverse of rigid spacecraft model PˆCOPY . −1

At the same time, the output of z Qˆ ( z ) is subtracted from the plant input to effect cancellation of the plant disturbance, such that the incentive element of modal vibration is cancelled in principle and the vibration can be effective reduced. The unit −1

COPY

k

delay z-1 of Qˆ ( z ) in recognition of the face that digital feedback links must have at least one unit of delay around each loop [1]. Thus, the current value of the plant disturbance ηˆ can be used only for the cancellation of future values of plant disturbance and cannot be used for instantaneous self-cancelation. The effects of these unit delays are small when the system is operated with a high sampling rate, however. COPY

k

k

z −1

Qˆ kCOPY ( z )

B

PˆCOPY _

0 _

Km Tm s + 1

PID

s

ηˆ k

 θ

Flexible Satellite Model

NP +

1 Tf s +1 The saved attitude angle information

Modeling input Offline identification

Desired response Low-pass filter process

Pˆ



Synthetic noise source

PˆCOPY

=

Qˆ k ( z ) error



n

 

Offline process for generating Qˆ k ( z )

Fig. 4. Adaptive inverse disturbance canceling for flexible satellite during normal pointing control mode

However, considering uncertainty of parameter of spacecraft in modeling or orbiting, the model Pˆ is required adaptively. At the same time, considering convergence speed, the model Pˆ is adapted using offline method, which performed as following: Fist, the modeling input is obtained by low-pass filtering saved signal of controller output and desired response is attitude angle of “quasi-rigid”, which obtains by filter “modal vibration disturbance” from attitude angle signal of flexible spacecraft, where the filter process based on 1-D DWT (Discrete Wavelet Transform). Second, real-time is to adjust the weight of Pˆ according to adaptive reference signal, which is the difference between the saved and filtered attitude angle signal of orbiting spacecraft and the output of model Pˆ . Finally, in order to improve convergence speed, the adaptive disturbance canceller ˆ Q ( z ) is generated by offline process, in which requires a synthetic noise source that has the same statistic characteristic with plant disturbance. In this application, the synthetic noise is superposed using sine signal, which should has any order modal k

Application of Adaptive Disturbance Canceling

247

vibration frequency (here considering only the first 5 order modal). Since the offline compute speed is much faster than real-time, to a specific Pˆ ( z ) , the optimal Qˆ ( z ) can be generated by offline process. In practice, in a sampling cycle of real system, offline compute the Qˆ ( z ) can be iterated hundreds or thousands times. In addition, considering dynamic describe performance of canceller Qˆ ( z ) , it is performed using NARX neural network. The whole process of scheme as shown in Fig.4 is performed as following: k

k

k

k

1) Data storage: The adaptive modeling signals of current Pˆ are provided by sample saved queue in the certain time, which has two components: the modeling input (output of controller) and attitude angle signal of flexible spacecraft. The queue is updated per certain time (for example 10 second), at the same time we have adapting once the Pˆ and updating the Pˆ , continue training Qˆ ( z ) and updating z Qˆ ( z ) . 2) Adaptation of model: Using the pairs of input-output, Pˆ is adapted, which are composed of both components of the queue processed through low-pass filter. Here the low-pass filter process is based on 1-D DWT, for example to obtain quasi-rigid attitude angle desired response a5, and we decompose disturbed output signal of the plant using the db10 wavelet into 5 levels. 3) Training of canceller: The Qˆ ( z ) is trained as soon as Pˆ was updated. Since the scheme in Fig.5 aim at rejection of “modal vibration disturbance”, so the synthetic noise is composed of superposed signal using sin waves with first 5 order modal frequency. Once z Qˆ ( z ) is updated, the disturbance canceling loop works on the new parameters, such the adaptive process is performed “real-time”. The above three processes go on continually, such can be performed well disturbance canceling control since Pˆ and z Qˆ ( z ) are adaptive. COPY

−1

k

COPY

k

k

−1

COPY

COPY

k

−1

COPY

COPY

k

5 Simulation Results In order to test the proposed control schemes, numerical simulations have been performed. The numerical model of the spacecraft is from the [9]. The low-frequency modes are generally dominant in a flexible system, in this paper, and the first five modes frequency and coupling coefficient are shown in table 1, a concerning modal truncation we can consult [10]. Fist, according to conventional method design the PID controller of rigid spacecraft with single-axis rotation as Fig.1. The parameter of PID is selected by Matlab toolbox rltool as KP=6, KI=0.05, and so the phase and amplitude margins of close loop system is 80°and 18dB respectively. In this simulation, the adaptive modeling signals of Pˆ ( z ) are provided by sample saved queue in 500s, the modeling input-output data is obtained through low-pass k

248

Y.-q. Liu, J. Cao, and W.-l. Song Table 1. Some Coefficients in Simulation Model Solved By Constrained Modes Order 1 2 3 4 5

Modal frequency ofconstrained Modes pn (rad/s) 2.6917 16.869 47.233 92.557 153.003

Coupling coefficients Fn (kg1/2 m) 2.6917 0.4301 0.1537 0.0785 0.0475




filter, which processes the queue by 1-D wavelet decompose using db10 into 5 levels, and an input of training Qˆ ( z ) is synthetic noise of 10000 samples. Both plant model [4,5] and N . and canceller are structured using NARX neural network N The parameter of training neural network is no longer provided. For comparative purposes, seven different cases of disturbance canceling control for normal pointing control are conducted: 1) only using the PI control, as showed in Fig.5; 2) applying the PI control with adaptive inverse disturbance canceller, as showed in Fig.6; 3) and 4) cases are the case of 2) with ±20% variance for modal k

( 2 , 2 ),10 ,1

(a) curve of attitude angle

(b) curve of attitude rate

Fig. 5. Response to PI case

(a) curve of attitude angle

(b) curve of attitude rate

Fig. 6. Response to PI with adaptive inverse disturbance canceller

( 5 ,5 ), 30 ,1

Application of Adaptive Disturbance Canceling

249

frequency, Pˆ and z Qˆ ( z ) without adaptively updated, plotted in Fig.7 and Fig.8; 5) and 6) cases are the case of 2) considering -20% variance for inertia, Pˆ and z Qˆ ( z ) without adaptively updated, which is showed in Fig.9 and Fig.10; 7) case 2) considering –50% variance for inertia, Pˆ and z Qˆ ( z ) (a) without and (b) with adaptively updated, which result showed in Fig.11. −1

COPY

k

COPY

COPY

−1

COPY

k

−1

COPY

(a) curve of attitude angle

COPY

k

(b) curve of attitude rate

Fig. 7. Response to PI with adaptive inverse disturbance canceller considering -20% variance −1 COPY and z Qˆ ( z ) without adaptively updated for modal frequency, Pˆ COPY

k

(a) curve of attitude angle

(b) curve of attitude rate

Fig. 8. Response to PI with adaptive inverse disturbance canceller considering +20% variance −1 COPY and z Qˆ ( z ) without adaptively updated for modal frequency, Pˆ COPY

k

The simulation results of PI control with disturbance canceller, considering ±20% and z Qˆ ( z ) without adaptively updated are shown in variance for inertia, Pˆ Fig.9 and Fig.10. Analysis of Fig.5~Fig.10 is shown that: (1) both effective rejection attitude dither (modal vibration) and great advance steady precision are performed using adaptive inverse disturbance canceling (Fig.5~Fig.6); (2) the adaptive inverse disturbance canceller has finite stability of scheme for uncertainty and variance of parameter (Fig.7~Fig.8). −1

COPY

COPY

k

250

Y.-q. Liu, J. Cao, and W.-l. Song

(a) curve of attitude angle

(b) curve of attitude rate

Fig. 9. Response to PI with adaptive inverse disturbance canceller considering -20% variance −1 COPY and z Qˆ ( z ) without adaptively updated for inertia, Pˆ COPY

k

(a) curve of attitude angle

(b) curve of attitude rate

Fig. 10. Response to PI with adaptive inverse disturbance canceller considering +20% variance −1 COPY and z Qˆ ( z ) without adaptively updated for inertia, Pˆ COPY

k

(a)

(b)

Fig. 11. The curve of attitude angle considering –50% variance for inertia (a) PˆCOPY and −1 COPY −1 COPY z Qˆ k ( z ) without adaptively updated (b) PˆCOPY and z Qˆ k ( z ) with adaptively updated

Application of Adaptive Disturbance Canceling

251

The above simulation results only demonstrate the action effect and stability of adaptive inverse disturbance canceller, and does not reflect that disturbance canceller requires disturbance control loop to adapt necessarily for work well. Therefore, to demonstrate adaptivity of Pˆ

COPY

and z Qˆ −1

COPY

k

( z ) is necessary.

and z Qˆ −1

Considering case (2) with –50% variance for inertia, (a) Pˆ

COPY

adaptively updated, as showed in Fig.11(a), and (b) Pˆ adaptively updated, which is showed in Fig.11(b).

COPY

COPY

k

and z Qˆ −1

( z ) without

COPY

k

( z ) with

6 Conclusions An adaptive inverse disturbance canceling method for “modal vibration disturbance”, which is difficult canceling by the PID method since it’s modal frequency low and dense, and damping small, is proposed. From the controlling effect, we can draw the conclusion that the modal vibration disturbance is rejected effectively and the precision of normal pointing attitude control is improved greatly; at the same time, the design of adaptive inverse disturbance canceller can ensure the parameter robustness. On the other hand, from design scheme, we can obtain that the control performance of disturbance rejection is improved, which does not affect system dynamic response since adaptive inverse disturbance canceling, compared with the conventional feedback disturbance rejection method, performs in inner loop and is independent of dynamic response control loop. Simulation results demonstrate that all above problems are solved by the research productions in this paper. The further work is to apply this method to the experimental study.

References 1. Widrow, B., Walach, E.: Adaptive Inverse Control, Prentice Hall P T R, Upper Saddle River, NJ (1996) 2. Carbonell Oliver, D.: Neural Networks Based Nonlinear Adaptive Inverse Control Algorithms. Thesis for the Engineer degree, Stanford University, Stanford, CA. (1996) 3. Bilello, M.: Nonlinear Adaptive Inverse Control. Ph.D. thesis, Stanford University, Stanford, CA. (1996) 4. Plett, G. L.: Adaptive Inverse Control of Plants with Disturbances. Ph.D. dissertation, Stanford Univ., Stanford, CA. (1998) 87-91 5. Plett, G. L.: Adaptive Inverse Control of Linear and Nonlinear Systems Using Dynamic Neural Networks. IEEE transactions on neural networks. 14 (2003) 360-376 6. Siegelmann, H.T., Horne, B.G.: Computational Capabilities of Recurrent NARX Neural Networks. IEEE Trans. on Systems, Man and Cybernetics - Part B: Cybernetic. 27 (1997) 208-215 7. Haykin, S.: Neural networks: A Comprehensive Foundation. Second Edition. Prentice Hall International (1999) 8. Junkins, J. L., Youdan K.: Introduction to Dynamics and Control of Flexible Structures. AIAA, (1993) 82-100 9. Jin Jun, S.: Study on CSVS Method for the Flexible Spacecraft, PhD thesis, Harbin Institute of Technology (2002) 10. Liu, D., Yang, D.M.: Modeling and Truncation of Satellite with Flexible Appendages. Journal of Astronautics. 4 (1989) 87-95

Application of Resource Allocating Network and Particle Swarm Optimization to ALS Jih-Gau Juang, Bo-Shian Lin, and Feng-Chu Lin Department of Communications and Guidance Engineering National Taiwan Ocean University, Keelung 20224, Taiwan, ROC [email protected] Abstract. This paper presents two intelligent aircraft automatic landing control schemes that use neural network controller and neural controller with particle swarm optimization to improve the performance of conventional automatic landing systems. Control signals of the aircraft are obtained by resource allocating neural networks. Control gains are selected by particle swarm optimization. Simulation results show that the proposed automatic landing controllers can successfully expand the safety envelope of an aircraft to include severe wind disturbance environments without using the conventional gain scheduling technique.

1 Introduction Conventional Automatic Landing Systems (ALS) can provide a smooth landing which is essential to the comfort of passengers. However, these systems work only within a specified operational safety envelope. When the conditions are beyond the envelope, such as turbulence or wind shear, they often cannot be used. Most conventional control laws generated by the ALS are based on the gain scheduling method [1]. Control parameters are preset for different flight conditions within a specified safety envelope which is relatively defined by Federal Aviation Administration (FAA) regulations. According to FAA regulations, environmental conditions considered in the determination of dispersion limits are: headwinds up to 25 knots; tailwinds up to 10 knots; crosswinds up to 15 knots; moderate turbulence, wind shear of 8 knots per 100 feet from 200 feet to touchdown [2]. If the flight conditions are beyond the preset envelope, the ALS is disabled and the pilot takes over. An inexperienced pilot may not be able to guide the aircraft to a safe landing at airport. According to Boeing's report [3], 67% of the accidents by primary cause are due to human factors and 5% are attributed to weather factors. By phase of flight, 47% accidents are during final approach or landing. It is therefore desirable to develop an intelligent ALS that expands the operational envelope to include safer responses under a wider range of conditions. The goal of this study is to prove that the proposed intelligent automatic landing controllers can relieve human operators and guide the aircraft to a safe landing in a wind disturbance environment. In this study, robustness of the proposed controller is obtained by choosing optimal control gain parameters that allow a wide range of disturbances to the controller. In 1995, Kennedy and Eberhart presented a new evolutionary computation algorithm the real-coded Particle Swarm Optimization (PSO) [4]. PSO is one of the latest D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCS 344, pp. 252 – 263, 2006. © Springer-Verlag Berlin Heidelberg 2006

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population-based optimization methods which dose not use filtering operation (such as crossover and mutation). Members of the entire population are maintained through the search procedure. This method was developed through the simulation of a social system, and it has been found to be robust in solving continuous nonlinear optimization problems [5]-[7]. The method is also suitable for determination of the control parameters which give aircraft better adaptive capability in severe environments. PSOs are best-suited for function optimization tasks. Their structure gives them some sort of a real time solution, while tuning some parameters, such as initial area, swarm size, and neighborhoods. There has also been proof of PSO being able to solve the Traveling Salesman Problem and doing multi-objective optimization tasks [8]. On the other hand, the ability to optimize functions makes PSO effective for adjusting neural network weights or some parameters to other evolutionary algorithms and techniques. Therefore, PSO is suitable for determining control parameters, which give aircraft better adaptive capability in severe environments. Recently, some researchers have applied intelligent concepts such as neural networks and fuzzy systems to intelligent landing control to increase the flight controller's adaptively to different environments [9]-[14]. Most of them do not consider the robustness of controller due to wind disturbances [9]-[12]. In [13], a PD-type fuzzy control system is developed for automatic landing control of both a linear and a nonlinear aircraft model. Adaptive control for a wide range of initial conditions has been demonstrated successfully. The drawback is that the authors only set up the wind disturbance at the initial condition. Persistent wind disturbance is not considered. In [14], wind disturbances are included but the neural controller is trained for a specific wind speed. Robustness for a wide range of wind speeds has not been considered. Juang [15]-[16] had presented a sequential learning technique that uses a conventional neural network with back-propagation through time algorithm in successful landing control. But the number of hidden units was determined by trial and error and the speed of convergence was slow. For sequential learning of Radial Basis Network, Platt [17] had developed an algorithm known as Resource Allocation Network (RAN). It starts with no hidden units and grows by allocating new hidden units based on the novelty in the observations that arrive sequentially. If an observation has no novelty, then the existing parameters of the network are adjusted by an LMS algorithm to fit that observation. RAN had been used for several applications varying from function approximation to nonlinear system identification. Its powerful approximation ability and fast convergence characteristic has been demonstrated. Here, we present two control schemes, RAN controller and RAN controller with PSO algorithm, to guide the aircraft to a safe landing and make the controller more robust and adaptive to the ever-changing environment.

2 System Description The pilot descends from cruising altitude to an altitude of approximately 1200ft above the ground. The pilot then positions the airplane so that the airplane is on a heading towards the runway centerline. When the aircraft approaches the outer airport marker, which is about 4 nautical miles from the runway, the glide path signal is intercepted (as shown in Fig. 1). As the airplane descends along the glide path, its pitch, attitude and speed must be controlled. The aircraft maintains a constant speed along the flight path. The descent rate is about 10ft/sec and the pitch angle is between -5 to +5 degrees.

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Finally, as the airplane descends 20 to 70 feet above the ground, the glide path control system is disengaged and a flare maneuver is executed. The vertical descent rate is decreased to 2ft/sec so that the landing gear may be able to dissipate the energy of the impact at landing. The pitch angle of the airplane is then adjusted, between 0 to 5 degrees for most aircraft, which allows a soft touchdown on the runway surface. Altitude 1200 ft Glide Path

| 50 ft

Flare Path

Runway Position

0 ft Touchdown

Fig. 1. Glide path and flare path

A simplified model of a commercial aircraft that moves only in a longitudinal and vertical plane is used in the simulations for implementation ease [14]. To make the ALS more intelligent, reliable wind profiles are necessary. Two spectral turbulence forms modeled by von Karman and Dryden are mostly used for aircraft response studies. In this study the Dryden form [14] was used for its demonstration ease. Fig. 2 shows a turbulence profile with a wind speed of 30 ft/sec at 510 ft altitude. Wind Gust velocity components: Longitudinal (Solid) & Vertical (Dashed) 20

10

ft/sec

0 -10 -20 -30

-40 0

5

10

15

20 25 30 Time (sec.)

35

40

45

50

Fig. 2. Turbulence profile

3 Landing Control In this study, the aircraft maintains a constant speed along the flight path. We assumed that the change in throttle command is zero. The aircraft is thus controlled solely by the

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pitch command. In this section, we present an intelligent neural network controller that uses the Resource Allocation Network to guide the aircraft to a safe landing in a wind disturbance environment. And then, Particle Swarm Optimization is used in the automatic landing system to improve the performance of the previous intelligent landing controller and make the controller more robust and adaptive to the ever-changing environment. 3.1 Resource Allocating Network Controller RAN is a modified neural network from Radial Basis Network. The output of the RAN algorithm has the following form: J

J

j =1

j =0

F (x ) = ¦ w j ϕ j (x ) + θ = ¦ w j ϕ j (x )

(1)

where ϕ j (x ) is the response of the jth hidden neuron to the input x and w j is the weight connecting the jth hidden unit to the output unit. θ = w0ϕ 0 is the bias term.

Here, J represents the number of hidden neurons in the network. ϕ j (x ) is a Gaussian function given by

(

§ x−m ¨ j ϕ j (x ) = exp¨ − 2 2σ j ¨ ©

2

)

· ¸ ¸ ¸ ¹

(2)

where m j = m j1 ,, m jp is the center, and σ j is the width of the Gaussian function.

The learning process of RAN involves allocation of new hidden units as well as adjusting network parameters. The network begins with no hidden units. As observations are received, the network grows by using some of them as new hidden units. The following two criteria must be met for an observation (x0 , y 0 ) to be used to add a new hidden unit to the network: xn − m j > εn

(3)

en = y n − F (x n ) > emin

(4)

where m j is the center (of the hidden unit) closest to x n . ε n and emin are thresholds to be selected appropriately. When a new hidden unit is added to the network, the parameters associated with the unit are w j +1 = e n m j +1 = x n

(5)

σ j +1 = κ x n − m j

κ is an overlap factor, which determines the overlap of the responses of the hidden units in the input space.

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When the observation (x0 , y 0 ) does not meet the criteria for adding a new hidden

[

T

]

T T

unit, the network parameters W = w0 , w1 , , w j , m1 , , m j

are updated using the

LMS as follows: W (n ) = W (n − 1) + ηe n a n

(6)

where Ș is the learning rate. a n is the gradient vector and has the following form:

[

T

]

T T

a n = 1, w1 , , w j , m1 , , m j

ª 2w j 2w T = «1, ϕ1 (x n ),  , ϕ j (x n ), ϕ1 (x n ) 21 (x n − m1 ) ,  , ϕ j (x n ) 2 x n − m j σ1 σj «¬

(

º

)» T

T

(7)

»¼

Therefore, the learning process is defined as: If x n − m j > ε n And en = y n − F (x n ) > emin

᧶

adding a new hidden unit, and parameters are chosen as w j +1 = e n m j +1 = x n

σ j +1 = κ x n − m j Else

W (n ) = W (n − 1) + ηe n a n

End In the scheme, the RAN algorithm is used to tune the neural controller and guide the aircraft to a safe landing in a wind disturbance environment. The RAN structure is shown in Fig. 3. Fig. 4 describes the control scheme in an intelligent automatic landing system, which consists of a PI controller, RAN controller, aircraft model, command, and a wind model. 3.2 Resource Allocating Network Controller with Particle Swarm Optimization

In the PSO algorithm, each member is called “particle,” and each particle flies around in the multi-dimensional search space with a velocity, which is constantly updated by the particle’s own experience - the experience of the particle’s neighbors or the experience of the whole swarm. PSO can be used to solve many of the same kinds of problems as the genetic algorithm (GA). This optimization technique does not suffer, however, from some of GA’s difficulties. Interaction in the group enhances, rather than detracts from, progress toward the solution. Further, a particle swarm system has memory, which the genetic algorithm does not have. Each particle keeps track of its coordinates in the problem space, which are associated with the best solution (fitness) it has achieved so far. This value is called pbest. Another value that is tracked by the global version of the particle swarm optimizer is the overall best value, and its location, obtained so far by any particle in the population. This location is called gbest. At each

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time step, the particle swarm optimization concept consists of velocity changes of each particle toward its pbest and gbest locations. Acceleration is weighted by a random term, with separate random numbers being generated for acceleration toward pbest and gbest locations. This is illustrated in Fig. 5, where

x k is the current position of a

x k +1 is its modified position, v k is its initial velocity, v k +1 is its modified velocity, v pbest is the velocity considering its pbest location, and v gbest is the velocity

particle,

considering its gbest location.

Fig. 3. Structure of RAN

Fig. 4. Aircraft automatic landing system with RAN controller

The operation of particle swarm optimization is shown in Fig. 6. The definition of the parameters is

vid(k ) : velocity of individual i at iteration k, Vdmin w : inertia weight factor,

≤ vid( k ) ≤ Vdmax

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c1 , c2 : acceleration constant, rand1, rand2 : uniform random number between 0 and 1,

xid(k ) : current position of individual i at iteration k , pbesti : pbest of individual i, gbest : gbest of the group.

k (v )

(v

k +1

x k +1 ) ( v gbest )

xk

( v pbest )

x k −1 Fig. 5. Movement of a PSO particle

In here, Initial conditions are: number of particles is 20, V min = −0.5 , V max = 0.5 , c1 = c 2 = 1.5 . The fitness function is defined as: For Turbulence strength=min : Į : max Do{ The Process of Landing } -3 ≤ h(T ) ft/sec ≤ 0, 200 ≤ x (T ) ft/sec ≤ 270, If -300 ≤ x(T ) ft ≤ 1000, -1 ≤ θ (T ) degree ≤ 5 Fitness =Turbulence strength Else Fitness = Turbulence strength - Į End End

­ ® ¯

4 Simulation Results In the simulations, successful touchdown landing conditions are defined as follows: -3 ≤ h(T ) ft/sec ≤ 0, 200 ≤ x (T ) ft/sec ≤ 270, -300 ≤ x(T ) ft ≤ 1000, -1 ≤ θ (T ) degree ≤ 5,

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where T is the time at touchdown. Initial flight conditions are: h(0)=500 ft, x (0) =235 ft/sec, x(0) =9240 ft, and γ o =-3 degrees. After using RAN, the controller can successfully guide the aircraft flying through wind speeds of 0 ft/sec to 70ft/sec. Table 1 shows the results from using different wind turbulence speeds with the original control gains that were used in [14] as shown in Fig. 7. Fig. 8 to Fig. 11 show the results of using RAN. The results indicate that the RAN controller can result in fast online adjusting, and it can implement a more robust network structure than [14]-[16] which can only overcome turbulence to 30 ft/sec, 50 ft/sec, and 65 ft/sec, respectively.

Initialize a population of particles with random positions and velocity

Calculate fitness function f(x)

Compare each particle’s fitness Generate initial pbest and gbest K=1

Vidnew

w u Vid  C1*rand()*(Pbest  Xid)  C 2 * rand () * (Gbest  Xid ) X idnew

X idold  Vidnew

Calculate fitness function F(new)

Yes

K+1

F(new)>Fp(old)

Pbest(n)=Xnew(n)

No Fp(new)>Fg(old)

No

Xold=Xnew Vold=Vnew

No Terminate condition

Yes Yes

Gbest=Pbest(n)

Optimal solution

Fig. 6. Operation of PSO

260

J.-G. Juang, B.-S. Lin, and F.-C. Lin Table 1. The Results From Using RAN Controller (k1=2.8; k2=2.8; k3=11.5; k4=6.0;)

Wind speed 0 20 40 45 50 55 60 65 70

horizontal velocity ( ft/sec ) 234.6779 234.6779 234.6779 234.6779 234.6779 234.6779 234.6779 234.6779 234.6779

᧤᧥

Landing point ft

᧤

᧥ ᧤

᧥

Aircraft vertical Pitch angle Speed ft/sec degree

750.0594 785.2610 808.7288 796.9949 527.1153 973.0034 855.6644 961.2695 867.3983

-2.7626 -2.1738 -2.0113 -2.0691 -2.2504 -1.3382 -1.6461 -1.5612 -1.3437

-1.4249 -0.5760 0.4015 0.4195 0.8709 1.1702 1.0376 0.9780 1.6158

Number of hidden units 20 52 93 117 119 125 132 140 140

Disturbance

θc

θe

δE

kθ

Aircraft Response

Rate loop Rate loop Position loop Position loop Flare: Typical value: Glide Slope: Typical value: Glide Slope: kθ = 2 .8 Flare:

k q = 2 .8

θ q

kq

kθ = 11 .5 k q = 6.0

Fig. 7. Pitch autopilot

Fig. 8. Aircraft pitch and pitch command

Fig. 9. Vertical velocity and command

Application of Resource Allocating Network and PSO to ALS

Fig. 10. Aircraft altitude and command

261

Fig. 11. Growth number of RAN hidden unit

Fig. 12. Aircraft pitch and pitch command Fig. 13. Vertical velocity and velocity command

Fig. 14. Aircraft altitude and command

Fig. 15. Growth number of RAN hidden units

In previous section, the control gains of the pitch autopilot in glide-slope phase and flare phase are fixed (as shown in Fig. 7). After using PSO, optimal control gains can be obtained. The controller can successfully overcome turbulence to 95 ft/sec. Table 2 shows the results from using different wind turbulence speeds. Fig. 12 to Fig. 15 show

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Table 2. The Results From Using RAN Controller with PSO (K1=2.3003; K2=2.3003; K3=11.6411; K4=20.913;)

Wind speed 30 35 40 45 50 55 60 65 70 75 80 85 90 95

horizontal Landing velocity point ft ( ft/sec ) 234.6779 796.9949 234.6779 785.2610 234.6779 576.8423 234.6779 820.4627 234.6779 808.7288 234.6779 820.4627 234.6779 698.9305 234.6779 867.3983 234.6779 902.5617 234.6779 543.5309 234.6779 750.0594 234.6779 761.7933 234.6779 785.2610 234.6779 620.9865

᧤᧥

Aircraft vertical Speed

Pitch angle

Number of hidden units

0.1305 0.3786 0.6208 0.8530 1.0986 1.3282 1.5423 1.7485 2.0277 1.8307 2.5887 2.8101 3.0111 3.5558

79 86 94 106 111 118 124 126 130 130 132 137 141 146

᧤ft/sec᧥ ᧤degree᧥

-2.0780 -1.9942 -1.8895 -1.9696 -1.6908 -1.5961 -1.4927 -1.3969 -1.3472 -1.2538 -1.2361 -1.1466 -1.0507 -1.0944

the results from using RAN with PSO. In comparison, while using RAN with the PSO algorithm, the controller is more adaptive to ever-changing environments.

5 Conclusion The purpose of this paper is to investigate the use of hybrid neural networks and evolutionary computation to aircraft automatic landing control and to make the automatic landing system more intelligent. Current flight control law is adopted in the intelligent controller design. Tracking performance and adaptive capability are demonstrated through software simulations. For the safe landing of an aircraft with a conventional controller, the wind speed limit of turbulence is 30 ft/sec. In this study, the RAN controller with original control gains can overcome turbulence to 70 ft/sec. The RAN controller with PSO algorithm can reach 95 ft/sec. These results are better than those without using the PSO algorithm. Especially, the PSO algorithm adopted in RAN has the advantage of using fewer hidden neurons. This is because the PSO method can be used to generate high quality solutions on complex parameter searches. From these simulations, the proposed intelligent controllers can successfully expand the controllable environment in severe wind disturbances. Acknowledgement. This work was supported by the National Science Council, Taiwan, ROC, under Grant NSC 92-2213-E-019 -005.

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References 1. Buschek, H., Calise, A.J.: “Uncertainty Modeling and Fixed-Order Controller Design for a Hypersonic Vehicle Model,” Journal of Guidance, Control, and Dynamics, vol. 20, no. 1, 42-48, (1997) 2. Federal Aviation Administration, “Automatic Landing Systems,” AC 20-57A, Jan. (1971) 3. Boeing Publication.: “Statistical Summary of commercial Jet Airplane Accidents”, Worldwide Operations (1959-1999) 4. Kennedy, J., Eberhart, R. C.: “ Particle Swarm Optimization,” Proceedings of IEEE International Conference on Neural Networks, Vol. IV, pp. 1942-1948, Perth, Australia, (1995) 5. Shi, Y., Eberhart, R. C.: “Empirical Study of Particle Swarm Optimization,” Proceedings of the 1999 Congress on Evolutionary Computation, 1945-1950, Piscataway, (1999) 6. Peter, J. A.: “Using Selection to Improve Particle Swarm Optimization,” Proceedings of IEEE International Conference on Evolutionary Computation, pp. 84-89, Anchorage, May (1998) 7. Zheng, Y. L., Ma, L., Zhang, L., Qian, J.: “On the Convergence Analysis and Parameter Selection in Particle Swarm Optimization,” Proceedings of the Second IEEE International Conference on Machine Learning and Cybernetics, November 2-5, (2003)1802-1807 8. Kennedy, J., Eberhart, R. C.: Swarm Intelligence, Morgan Kauffman publishers, San Francisco, CA, (2001) 9. Izadi, H., Pakmehr, M., Sadati, N.: “Optimal Neuro-Controller in Longitudinal Autolanding of a Commercial Jet Transport,” Proc. IEEE International Conference on Control Applications, CD-000202, 1-6, Istanbul, Turkey, June (2003) 10. Chaturvedi, D.K., Chauhan, R., Kalra, P.K.: “Application of generalized neural network for aircraft landing control system,” Soft Computing, vol. 6, 441-118, (2002) 11. Iiguni, Y., Akiyoshi, H., Adachi, N.: “An Intelligent Landing System Based on Human Skill Model,” IEEE Transactions on Aerospace and Electronic Systems, vol. 34, no. 3, 877-882, (1998) 12. S. Ionita and E. Sofron, “The Fuzzy Model for Aircraft Landing Control,” Proc. AFSS International Conference on Fuzzy Systems, pp. 47-54, Calcutta, India, February 2002. 13. Nho, K., Agarwal, R.K.: “Automatic Landing System Design Using Fuzzy Logic,” Journal of Guidance, Control, and Dynamics, vol. 23, no. 2, 298-304, (2000) 14. Jorgensen, C.C., Schley, C.: “A Neural Network Baseline Problem for Control of Aircraft Flare and Touchdown,” Neural Networks for Control, 403-425, (1991) 15. Juang, J.G., Chang, H.H., Cheng, K.C.: “Intelligent Landing Control Using Linearized Inverse Aircraft Model,” Proceedings of American Control Conference, vol. 4, 3269-3274, (2002) 16. Juang, J.G., Chang, H.H., Chang, W.B.: “Intelligent Automatic Landing System Using Time Delay Neural Network Controller,” Applied Artificial Intelligence, vol. 17, no. 7, 563-581, (2003) 17. Platt, J.: “A Resource Allocating Network for Function Interpolation,” Neural Computation, vol. 3, 213~225, (1991)

Case-Based Modeling of the Laminar Cooling Process in a Hot Rolling Mill Minghao Tan1, Shujiang Li1, Jinxiang Pian2, and Tianyou Chai2 1

School of Information Science and Engineering, Shenyang University of Technology, 110023 Shenyang, China [email protected] 2 Research Center of Automation, Northeastern University, 110004 Shenyang, China [email protected]

Abstract. Accurate mathematical modeling of the laminar cooling process is difficult due to its complex nature (e.g., highly nonlinear, time varying, and spatially varying). A case-based temperature prediction model is developed for the laminar cooling process using case-based reasoning (CBR) and the dynamical process model. The model parameters for the current operating condition are found by retrieving the most similar cases from the case base according to the current operating condition and reusing the solutions of the retrieved cases. The resulting model can predict the through-thickness temperature evolutions of the moving strip during the cooling process. Experimental studies based on industrial data from a steel company show the effectiveness of the proposed modeling approach.

1 Introduction In a hot rolling mill, the laminar cooling process is used to cool hot steel strips from the finishing temperature to the desired final cooling temperature. The intention of improving product quality as well as reducing production cost has led to higher demands on the laminar cooling control system. Good control performance of this process is vital to the desired mechanical properties and metallurgical structure of the steel product [1]. As a result the development of an accurate model capable of describing the heat transfer mechanism of the laminar cooling process with sufficient accuracy is essential [2]. In the literature many methods have been developed to model the laminar cooling process. Groch used statistical process models with simplified heat transfer descriptions [3]. Ditzhuijzen neglected the through-thickness heat conduction inside the strip and modeled the laminar cooling process as merely a first-order time delay [4]. However, because of the time varying and spatially varying nature of the laminar cooling process, it should instead be described by nonlinear partial differential equations with nonlinear boundary conditions. Empirical heat transfer equations were used by several authors to model the laminar cooling process [5], [6], [7]. A numerical model of the D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 264 – 274, 2006. © Springer-Verlag Berlin Heidelberg 2006

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laminar cooling process was developed in [8] which calculates the through-thickness temperatures at the strip center line during the cooling process. The heat transfer coefficients were determined by specific onsite experiments on the runout table cooling hardware. However, the heat transfer coefficients determined in this way can not reflect the changes in operating conditions and the model can only be used for offline development purposes. Accurate description of key process parameters during laminar cooling is essential to modeling the laminar cooling process. This paper takes a knowledge-based approach to modeling the laminar cooling process in which case-based reasoning (CBR) [9], [10] is integrated with the first principles dynamical model. The key process parameters are obtained using case-based reasoning [11] and physical analysis according to the operating conditions of the cooling process. Experimental studies with industrial data show superior accuracy of the proposed modeling approach.

2 Typical Laminar Cooling Process The schematic of a typical laminar cooling process is shown in Fig.1. After leaving the last finishing stand F7 the strip is cooled on the runout table by top and bottom water headers. At the entry to the cooling area the temperature and thickness of the strip is measured by the infrared pyrometer P1 and the X-ray gauge D1. At the end of the runout table the final cooling temperature of the strip is measured by P2 before it is wound at the downcoiler. The strip speed during the cooling process is tracked by speed tachometers. Nineteen banks of four headers are installed on the runout table, with each header having a constant flow rate. There are four spray patterns for the four headers in each water bank [2]. Speed

Top headers

F7 Bank 1

Bank 2

Bank 15

Bank 16

D1 P 1

Runout table 7.68 m 4.62m

Bank 19

Strip

Bottom headers

P2

Coilers 10.10 m

27.95 m

Water cooling area 100.8m

Fig. 1. Schematic of the laminar cooling process

The strip temperature is related to the operating conditions of the moving strip, such as the strip material, strip gauge, entry temperature, and the control signals such as the activated headers and the flow rate of cooling headers. The output of the laminar cooling process is the strip temperature. If the strip is divided into M through-thickness layers, the inputs of the laminar cooling process include the strip gauge d, the strip length L, the steel grade Gr,

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the entry temperature Te, the water temperature Tw, the environment temperature Ten, the strip speed v, the strip acceleration ac, the first activated top header Ht, the first activated bottom header Hb, the number of activated headers H, the header flow rate q, and the spray pattern π. The process outputs include the strip temperature on the top surface T0, the strip temperature on the bottom surface TM, and the temperatures of the through-thickness layers inside the strip T1…TM-1.

3 Physical Model of the Laminar Cooling Process [2] The temperature of the ith lengthwise strip segment is described by the following equation [2]

∂Ti ( y , t (i )) ∂ 2Ti ( y , t (i )) =a ∂t ( i ) ∂y 2

(1)

with the initial condition

Ti ( y , t (i )) = Ti 0 ( y )

(2)

and the boundary conditions

λ

t (i ) ∂Ti ( y, t (i )) d = α 0 [Tw 0 ( xk 0 + ³t v(t )dt, t ) − T ( i , t (i ))] d ∂y 2 y=

(3)

t (i ) ∂Ti ( y, t (i)) d = α M [TwM ( xi 0 + ³ v(t )dt, t ) − T (− i , t (i))] t d ∂y 2 y=−

(4)

i0

i

2

λ

i0

i

2

∂Ti ( y,t (i )) ∂y

=0

(5)

y =0

where a is the thermal diffusivity of the strip, Ti(y,t(i)) is the temperature of the ith strip segment at location y and instant t(i), λ is thermal conductivity of the strip, Tw0, TwM are the temperature of cooling water on the top and bottom surface of the strip, α0, αM are heat transfer coefficients on the top and bottom surface of the strip, di is the thickness of the ith strip segment, xi0 is the position of the ith strip segment at the initial time instant ti0.

4 Case Based Modeling Strategy of the Laminar Cooling Process The proposed case-based modeling strategy for the laminar cooling process is shown in Fig. 2. The dynamical model is established from physical analysis of the heat transfer process. The features of the current operating condition are extracted from the operating data and used to retrieve matching cases in the case base. The solution parameters of the current operating condition are determined by reusing the solutions

Case-Based Modeling of the Laminar Cooling Process in a Hot Rolling Mill

π Ht Hb H

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Laminar cooling process

Statistical analysis

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᧻

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Gr vh dh T h

Dynamical model of the

ac w L Tw T en

laminar cooling process

M odels of heat transfer coefficients and thermal conductivities

T0 T1 ,…TM

Fig. 2. Case-based modeling strategy for the laminar cooling process

of the retrieved cases. The obtained solutions are then tested by calculating the heat transfer coefficients, thermal conductivities, and thermal diffusivities and performing statistical analysis of the temperature predictions. 4.1 Dynamical Model of the Laminar Cooling Process

We can discretize (1)-(5) using finite difference as

(1+ a0

(1 − a0 a j ∆Γ

∆Γ ∆Γα0 ∆Γ + a0 )T0 (n +1) − a0 T1(n +1) = 2 (∆y) ∆yλ0 (∆y)2

a ∆Γα 0 a ∆Γα 0 ∆Γ ∆Γ − 0 )T0 ( n ) + a0 T1 ( n ) + 2 0 TW ∆ yλ 0 ( ∆y ) 2 ∆yλ0 ( ∆y ) 2 a j ∆Γ

a j ∆Γ

T j +1 ( n + 1) ( ∆y ) ( ∆y ) ( ∆y ) 2 (j=1,2, …, M-1) a j ∆Γ a j ∆Γ a j ∆Γ = T n + − T n + ( ) ( 2 2 ) ( ) ) T ( n ) j −1 j j +1 ( ∆y ) 2 ( ∆y ) 2 ( ∆y ) 2

(2 + 2

2

)T j ( n + 1) −

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(1 + aM aM

∆Γ α ∆Γ ∆Γ + aM M )TM (n + 1) − aM TM −1(n + 1) = 2 (∆y) (∆y)2 ∆yλM

∆ΓαM ∆ΓαM ∆Γ ∆Γ T (n) + (1 − aM )TM (n) + 2aM TW − aM 2 M −1 2 (∆y) (∆y) ∆yλM ∆yλM

(8)

where j is the jth through-thickness layer (j=0, 1, … M), T is the strip temperature, n is the nth time step, ∆Γ is time step size, aj is thermal diffusivity at layer j; λ0, λM is thermal conductivities at top and bottom surface; α0, αM is heat transfer coefficients at the top and bottom surface. Equations (6) and (8) describe the heat transfer on the surface of the moving strip and (7) describes the heat conduction between various layers within the strip. The determination of the heat transfer coefficients α0, αM, thermal conductivities λ0, λM and thermal diffusivities aj (j=0, M) is key to improving the model accuracy. When the header is activated, the heat transfer coefficients during water cooling are related to the spray intensity, the strip surface temperature and the strip speed, etc. Because the header flow rate is constant the heat transfer coefficients at the top and bottom surface are modeled as follows [2]

α0 = (2 − ((Hc − Ht ) /10.0+ 1)0.12)β1 (

v β2 d β3 T0 β4 ) ( ) ( ) 1.1vh dh Th

(9)

αM = (2 − ((Hc − Hb ) /10.0+1)0.12)β1 (

v β2 d β3 TΜ β4 ) ( ) ( ) Th 1.1vh dh

(10)

where Hc is the specified header, v is the strip speed at the specified header, d is the strip gauge at the specified header, Tj (j=0, M) is the strip temperature at the specified header, q is the cooling water flow rate at the specified header; vh is the speed of the strip head at the entry to the cooling section, dh is the thickness of the strip head measured at D1, Th is the temperature of the strip head measured at P1. β1 ,β2 ,β3 ,β4 are parameters to be determined. When the header is deactivated the heat transfer coefficients at the top and bottom surface are calculated by [2]

α0 = σ × ε ×

(T04 − Ten4 ) + 6.5 + 5.5 × v 0.8 T0 − Ten

α M = 0.8 × σ × ε ×

(T04 − Ten4 ) T0 − Ten

(11)

(12)

where σ is the Stefan-Boltzmann constant, ε= 0.82 is the emissivity. The thermal conductivities at the top and bottom surface λj (j=0, M) are found by [2]

λj = 56.43-(0.0363-c (v – 1.1⋅vh) )×Tj (j= 0, M)

(13)

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The thermal diffusivity at layer j is calculated by [2] ­8.65 − 0.0146 (T j − 400) °5.0 − 0.045 (T − 650) ° j aj =f(Tj)= ® T + 2 . 75 0 . 025 ( j − 700) ° °¯5.25 + 0.00225(T j − 800)

T j ∈ [400, 650) T j ∈ [650, 700) (j=0,…, M) T j ∈ [700, 800) T j ∈ [800, 1000]

(14)

Because the parameters β1 ,β2 ,β3 ,β4 and c vary with operating conditions, casebased reasoning is used to determine these parameters according to the changing operating conditions. 4.2 Case Representation and Retrieval

The case base stores knowledge of the laminar cooling process in the form of organized cases. Each case, consisting of two parts, case descriptors and case solutions, is a specific experience in modeling the laminar cooling process for a given operating condition. The case solutions include the parameters β1, β2, β3, β4 and c in (10), (11), and (14). They are mainly related to the key features of the process operating conditions, namely the steel grade, the strip gage, the strip speed, and the strip temperature, which are chosen as the case descriptors. The case structure is shown in Table 1. Table 1. Case Structure Case descriptors F f1 f2 f3 f4 Gr vh dh Th

Case solutions S s2 S3 s4

s1

β1

β2

β3

β4

s5 c

The current operating condition of the strip is defined as Cin, and the descriptors of Cin are F =(f1, f2, f3, f4). The solutions of Cin are defined as S=(s1, s2, s3, s4, s5). Assume there are m cases in the case base, C1, C2,…Cm. The descriptor vector of P P P P P Ck (k=1,…m) is defined as Fk = ( f k ,1 , f k , 2 , f k ,3 , f k , 4 ) , the solution vector of Ck is defined as

S kP = ( sk,P1 , sk,P2 , sk,P3 , sk,P4 , sk,P5 )

(15)

Due to the limited space the similarity functions between various descriptors are omitted in this paper. The reader is referred to chapter 2 of [2] for details. The similarity between the current operating condition Cin and the stored case Ck (k=1,…m) is 4

SIM ( C in , C k ) =

¦ω

l

× sim ( f l , f kP,l )

l =1

(16)

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SIM max = Max ( SIM (Cin , Ck )) k∈{1,m}

(17)

All cases with similarities greater than the threshold SIMth are retrieved from the case base. 4.3 Case Reuse

If no exact match for the current operating condition is found in the case base the solutions of the retrieved cases have to be adapted before they can be reused for the current operating condition. Suppose r cases have been retrieved from the case base {C1R , ..., C rR } , where the similarity between C kR (k=1,…r) and the current operating condition is SIMk. Assume SIM1 ≤ SIM2 ≤ ··· ≤ SIMr ≤ 1, then the solutions of the retrieved cases are

S kR = ( sk,R1 , sk,R2 , sk,R3 , sk,R4 , sk,R5 ) (k=1,…r)

(18)

The solution of the current operating condition is S=(s1, s2, s3, s4, s5), where r

¦w

k

sl =

× s k,Rl

k =1

(19)

r

¦w

k

k =1

(l=1,…5)

and wk (k=1,…r) is found as follows If Then

SIMr =1

­1 k = r ½ ¾ ¯0 k ≠ r ¿

wk= ®

Else wk =SIMk End If

(20)

(k=1,…r)

4.4 Case Revision and Case Retention

Case revision performs the evaluation test on the validity of the reused solutions that results from case reuse. The flowchart of case revision is shown in Fig. 3. The heat transfer coefficients, the thermal conductivities, and thermal diffusivities are calculated from the solutions of case reuse. Then the final cooling temperatures of the strip segments are calculated according to (6)-(8). The statistical evaluation signal ∆T is calculated by N

∆T = ¦ | T0 (i ) − Tcm (i ) | / N i =1

(21)

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271

where Tcm(i) is the final cooling temperature measurement (i=1,…N), N is the number of cooling temperature measurements, T0(i) is the final cooling temperature prediction by this model. In case ∆T < 10 , the case is retained into the case base. In case ∆T > 10 , case revision is performed to improve the accuracy of the solution from reuse. The revised case is tested of its redundancy before it is retained in the case base.

͠

͠

Given s1 ... s5 from case reuse

Calculate ∆T

∆ T > 10 ° C?

N

Y

Adjust β 1, i , so that the model predictions equal real measurements

β 1 = median ( β1,1, β1,2, ..., β 1,N )

Adjust ci in the same way as β 1 (i=1,...N)

c = median ( c1, c2,..., cN)

Adjust β 1, β 2, β 3, β 4, c

Calculate ∆T

N

∆ T ≤ 10 ° C?

Y

Case retention

Fig. 3. Flow chart of case revision

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5 Experimental Study In this experiment we use 61 data samples collected from a rolling mill and compare the model predictions with the results of [12]. The case descriptors for the experiment are shown in Table 2. Table 2. Case Descriptors Gr 316

dh 12

vh 2.9

Th 835

According to the descriptors in Table 2 one case was retrieved from the case base with SIMmax =0.62. Table 3 lists the case solutions calculated by the case-based reasoner for the specified operating condition. The model predictions of the proposed modeling method and ref [12] are plotted against the real cooling temperature measurements in Fig. 4. Table 3. Reasoning Results

β1

β2

β3

β4

4306

0.85

1.12

1.2

c 0.0052

Table 4. Model Accuracy Comparison SIM N 0.62 61

͠

Measurements ±10 This paper Ref [12] 61 39

Real measurements

This paper

Ref. [12]



Coiling temperature

       





                 

Seg. No.

Fig. 4. Comparison of final cooling temperature predictions

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Thirty-nine temperature predictions of the model in [12] are within 10°C of the temperature measurements, as can be seen from Table 4. Fig. 4 shows the model in [12] lost track of many of the cooling temperature measurements, esp. towards the final period. In sharp contrast, 100% (61/61) of the predictions of this paper are within 10°C of the measurements. It is evident that the proposed approach is very good at tracking the evolution of the strip temperature and capable of much better accuracy than the model in [12].

6 Conclusions The development of an accurate model is essential to better understanding and successful control of the laminar cooling process. This paper has introduced a novel hybrid approach to modeling the laminar cooling process that combines first principles modeling and case-based reasoning. Experiments based on data collected from the laminar cooling process of a hot mill have demonstrated the superior model accuracy of the hybrid modeling approach. The results in this paper can be generalized to a wide range of similar processes.

Acknowledgements This work was partly supported by the Ph.D. Funding Program of Shenyang University of Technology, the Program of Liaoning Department of Education under Grant No.2004D309, Shenyang Science and Technology Program under Grant No.10530842-05, the China National Key Basic Research and Development Program under Grant No.2002CB312201, and the Funds for Creative Research Groups of China under Grant No.60521003.

References 1. Chai, T.Y., Tan, M.H., et al Intelligent Optimization Control for Laminar Cooling. In: Camacho, B., Puente, D. (eds.): Proc. of the 15th IFAC World Congress. Elsevier, Amsterdam (2003) 691-696 2. Tan, M.H.: Intelligent Modeling of the Laminar Cooling Process. Tech. Rep. 18. Research Center of Automation, Northeastern University, Shenyang (2004) 3. Groch, A.G., Gubemat, R., Birstein, E.R.: Automatic Control of Laminar Flow Cooling in Continuous and Reversing Hot Strip Mills. Iron and Steel Engineer. 67(9) (1990) 16-20 4. Ditzhuijzen, V.G.: The Controlled Cooling of Hot Rolled Strip: A Combination of Physical Modeling, Control Problems and Practical Adaptation, IEEE Trans. Aut. Cont. 38(7) (1993) 1060-1065 5. Moffat, R.W.: Computer Control of Hot Strip Coiling Temperature with Variable Flow Laminar Spray. Iron and Steel Engineer. 62(11) (1985) 21-28 6. Leitholf, M.D., Dahm, J.R.: Model Reference Control of Runout Table Cooling at LTV. Iron and Steel Engineer. 66(8) (1989) 31-35

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7. Yahiro, K. J.: Development of coiling temperature control system on hot strip mill. Kawasaki Steel Mizushima Works Tech. Rep. 24. (1991) 8. Evans, J.F., Roebuck, I.D., Howard, R.W.: Numerical Modeling of Hot Strip Mill Runout Table Cooling. Iron and Steel Engineer. 70(1) (1993) 50-55 9. Kolodner, J.L.: Case-Based Reasoning. 1st edn. Morgan Kaufmann, New York (1993) 10. Watson, I., Marir, F.: Case-based reasoning: A review. Knowledge Engineering Review. 9(2) (1994) 355-381 11. A. Aamodt, and E. Plaza, "Case-based reasoning: Foundational issues, methodological variations, and system approaches," AI Communications, Vol. 7, pp. 39–59, 1994. 12. Shan, X.Y.: Transformation and Development of the Cooling Control System of the 2050mm Baosteel Hot Strip Mill. In: Ren, D. (eds.): Development of Science and Technology in Metallurgy. Metallurgical Industry Press, Hangzhou China (1999) 19-22

Fast Mesh Simplification Algorithm Based on Edge Collapse Shixiang Jia1, Xinting Tang2, and Hui Pan3 1

Department of Computer Science and Technology, Ludong University, 264025 Yantai, P.R. China [email protected] 2 Department of Computer Science and Technology, Ludong University, 264025 Yantai, P.R. China [email protected] 3 Department of Computer Science and Technology, Ludong University, 264025 Yantai, P.R. China [email protected]

Abstract. Firstly, we present a new mesh simplification algorithm. The algorithm is based on iterative half-edge contracting, and exploits a new method to measure the cost of collapse which takes the length of contracting edge and the dihedral angles between related triangles into account. The simplification does not introduce new vertex in original mesh, and enables the construction of nested hierarchies on unstructured mesh. In addition, the proposed algorithm adopts the Multiple-Choice approach to find the simplification sequence, which leads to a significant speedup with reduced memory overhead. Then we implement a mesh simplification system based on this algorithm, and demonstrate the effectiveness of our algorithm on various models.

1 Introduction Many high-resolution models are obtained by scanning systems or created by modeling systems. Unfortunately, these highly detailed models are hard to store and transmit, and will slow down the rendering speed, causing jerkiness of movement. In fact, such complex models are not always required. In order to get simpler versions of them, a simplification algorithm is needed. As for the algorithm, it takes a complex model and automatically generates an approximation using fewer triangles that looks reasonably similar to the original. We provide a new algorithm which tries to preserve the visually important parts of the model by using a new cost function to measure the approximation error. As the visual acuity of the human vision system is principally dependent upon three factors: size, orientation and contrast [1,2], our new cost function will focus on the edge length and the dihedral angles between related triangles. In order to speed up the algorithm, we use a probabilistic optimization strategy based on the Multiple-Choice Algorithm [3] to find the optimal decimation sequence. The Multiple-Choice technique does not require a global priority queue data structure which reduces the memory overhead and simplifies the algorithmic structure. We have developed a simplification D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 275 – 286, 2006. © Springer-Verlag Berlin Heidelberg 2006

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system based on the proposed algorithm, and applied our algorithm on many models with various size. The rest of the paper is organized as follows. We first review the related work in Section2. Section 3 describes our algorithm in detail. The implementation is discussed in Section 4. Section 5 presents a discussion of results and performance analysis. Section 6 concludes the paper.

2 Related Work The problem of surface simplification has been studied in both the computational geometry and computer graphics literature for several years. Some of the earlier work by Turk [4] and Schroeder [5] employed heuristics based on curvature to determine which parts of the surface to simplify to achieve a model with the desired polygon count. Vertex clustering algorithm described by Rossignac and Borrel [6] is capable of processing arbitrary polygonal input. A bounding box is placed around the original model and divided into a grid. Within each cell, the cell’s vertices are clustered together into a single new representative vertex. The method is very fast and effective, however, the quality of the approximation is not often satisfactory. This approach usually leads to a vertex distribution which does not adapt to the local curvature of the surface, and can not guarantee a proper manifold topology of the resulting approximation. Hoppe [7,8] posed the model simplification problem into a global optimization framework, minimizing the least squares error from a set of point-samples on the original surface. Later Hoppe extended this framework to handle other scalar attributes, explicitly recognizing the distinction between smooth gradients and sharp discontinuities. He also introduced the progressive mesh [8], which is essentially a stored sequence of simplification operation, allowing quick construction of any desired level of detail along the continuum of simplifications. However, the algorithm provides no guaranteed error bounds. There is considerable literature on surface simplification using error bounds. Cohen and Varsheny [9] have used envelopes to preserve the model topology and obtain tight error bounds for a simple simplification. An elegant solution to the polygon simplification problem has been presented in [10,11] where arbitrary polygonal meshed are first subdivided into patches with subdivision connectivity and then multiresolution wavelet analysis is used over each patch. These methods preserve global topology, give error bounds on the simplified object and provide a mapping between levels of detail. Garland [12] used iterative contractions of vertex pairs to simplify models and maintains surface error approximation of polygonal modes. This algorithm is efficient and can rapidly produce high quality approximation. Incremental decimation algorithms typically lead to superior model quality. These algorithms simply models by iteratively executing atomic decimation step such as edge collapse (see Fig. 1). An edge collapse takes the two endpoints of the target edge, moves them to the same position, links all the incident edges to one of the vertices, deletes the other vertex, and removes the faces that have degenerated into lines or points. Typically, this removes two triangular faces per edge contraction. To minimize the approximation error, a cost function measuring the quality of the approximation is proposed to guide the process of simplification [7,12].

Fast Mesh Simplification Algorithm Based on Edge Collapse

t2 t3 8

t2

t1 t4

277

t5

9

t3

9

t4

Fig. 1. Half-edge collapse. The (u, v) edge is contracted into point v. The t1 and t5 triangles become degenerate and are removed.

The particular sequence of edge collapse transformations must be chosen carefully, since it determines the quality of the approximating models. For those algorithms [7], the priority queue is a natural data structure to store the order of the edges to be simplified, which allows a variety of operations (inclusion, access and removal of the largest, etc.) to be efficiently performed. But it takes a long time to build the queue before starting the simplification process. Furthermore, each step of the decimation also consumes a significant amount of time to recompute the collapse cost of changed edges and to update their position in the priority queue. In order to accelerate this process, Wu and Kobbelt [3] have presented a technique called Multiple-Choice based on probabilistic optimization. It makes no use of a priority queue, but chooses the edge to be contracted from a small number of randomly selected edges. We provide a new algorithm which can preserve the visually important parts of the model by using a new cost function to measure the approximation error. In order to speed up the algorithm, we also use a probabilistic optimization strategy based on the Multiple-Choice Algorithm to find the optimal decimation sequence. Our system allows faster simplification than some quality method.

3 Simplification Algorithm 3.1 Atomic Decimation Operator Our algorithm is based on the half-edge collapse operation. Half-edge collapse is to choose an edge (u,v) and contract it to one of its endpoint v. After collapsing, all triangles adjacent to either u or v are connected to v, and triangles adjacent to both u and v are removed (see Fig. 1). We prefer half-edge collapse because of its simplicity. The methodology of halfedge collapse is in fact closely related to the vertex decimation approach. In each step of vertex decimation approach, a vertex is selected for removal. All the facets adjacent to that vertex are removed from the model and the resulting hole is triangulated. Instead of the vertex elimination and arising hole triangulation, half-edge contracting just merge one endpoint of the selected edge into the other endpoint. Half-edge contracting avoids the action of hole triangulation, and is generally more robust than vertex decimation. In this case, we do not need to worry about finding a plane onto which the neighborhood can be projected without overlap. In addition, half-edge contracting makes progressive transmission more efficient (no intermediate vertex coordinates) and enables the construction of nested hierarchies that can facilitate further applications.

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The change caused by edge collapse is quantified by collapse cost. The algorithm based on edge collapse has to solve two problems: one is how to calculate the collapse cost for every candidate; the other is how to find the simplification sequence. Then the algorithm can collapse the edge iteratively until the given criterion is satisfied. 3.2 Collapse Cost According to the characteristics of human vision system, observers are mainly sensitive with three attributes of the model: size, orientation and contrast [1,2]. According to the first attribute, the length of the edge should be considered when calculating its collapse cost. With the last two attributes, the dihedral angles between the related triangles are also important guidance. Our cost function will focus on the edge length and the sum of the dihedral angles.

t4 t5

D

t3 G t6 t7 t2 t1 t8

E

F

Fig. 2. The candidate for contracting

The principle of our algorithm is that the contracting edge should be at smooth areas (such as edge(a,b) in Fig. 2), so the dihedral angle between any two related triangles should be small. To calculate the collapse cost for edge(u,v) in Fig. 1, we need to do some work as follows: 1) Find out all the triangles adjacent to vertex u: t1, t2, t3, t4, and t5, and those adjacent to both vertex u and v: t1 and t5 2) Calculate the dihedral angle between t1 and t2, t3, t4, t5, and then those between t5 and t1, t2, t3, t4 3) Set the largest dihedral angle in step 2 as the final angle between the related triangles adjacent to edge(u,v). The final angle of edge(a,b) in Fig. 2 is very small(zero), so we can contract it. As a matter of fact, we can relax this condition to that when the edge is an exclusive edge we can also collapse it, such as edge(c,d) in Fig. 2. The collapse of edge(c,d) will have little influence to the appearance of the model. We can observe that the dihedral

t1

t2 t3

8

t4

t5

9

Fig. 3. The calculation of the triangles’ weight

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angle between t1 and t8 is very large while the one between t1 and t2 is very small. If we use the above algorithm for calculation, the collapse cost of edge(c,d) will be large, which is contrary to the fact, so we need to improve it. We give every triangle a weight when calculating the dihedral angle. For edge(u,v) in Fig. 3, when calculating the dihedral angle between t1 and the other triangles, we think the one between t1 and t2 is most important , so the weight of t2 to t1 should be largest, and the weights of t2, t3, t4 and t5 should decrease counterclockwise. While, when we calculate the dihedral angle between t5 and the other triangles, the weights of t4, t3,, t2 and t1 should decrease clockwise. We define that S is the set of triangles that are adjacent to vertex u, the number of the triangles in it is n and si (i=1, 2 , , ,n) indicates the ith triangle. B is the set of triangles that are adjacent to both u and v, the number of the triangles in it is m. We define the weight of si to bj as follows: W ( s i , b j ) = n /( n + D ( s i , b j )

(1)

where D(si, bj) in (1) denotes the number of triangles between si and bj. In Fig. 3, if bj is t1, D(si., t1) denotes the number of triangles which will be visited when traversing counterclockwise from t1 to si. For example, D(t2, t1)=1, D(t4, t1)=3. If bj is t5, D(si, t5) denotes the number of triangles which will be visited when traversing clockwise from t5 to si. Define fi (i=1, 2, , , n) indicates the unit normal vector of the ith triangle of S, and ej (j=1, 2, , , m) indicates the unit normal vector of the jth triangle of B. We define the collapse cost of edge (u, v) is: m

n

Cost (u , v ) =|| u − v || ×(¦¦ [(1 − (e j • f i )) × W ( si , b j )]) j =1 i =1

(2)

where ||u-v|| in (2) indicates the length of edge(u,v).

e j • f i =| e j | × | f i | × cosθ = cosθ

(3)

We use ej ⋅ fi to compare the value of the dihedral angleș, so we can avoid the calculation of arccosine. 3.3 Multiple-Choice Algorithm

Since the cost function has been defined, each possible atomic decimation operation (candidate) can be rated according to the function. So the remaining issue is to choose a candidate for each decimation step. In other words, we should find the optimal decimation sequence. Finding the optimal decimation sequence is a very complex problem [13] and consequently one has to find solutions with approximate optimality. Most of the algorithms adopt a greedy strategy to find a decimation sequence that is close to the optimal. For every decimation step, the algorithm will go through all possible candidates to find one with the lowest cost. An implementation of the greedy strategy usually requires a priority queue data structure for the candidates that has to be initialized and updated during the decimation. Our algorithm uses a different probabilistic optimization strategy based on Multiple-Choice algorithm to find the decimation sequence. The fundamental idea behind

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MCA is quite simple and intuitive and can be explained best by means of the wellestablished bins-and balls model [14,15]. In order to apply MCA to the model simplification problem we have to map balls, bins, and maximum load to the corresponding mesh entities [3]. Since the balls are enumerated in the outer loop (for each ball make a MC decision) they correspond to the decimation steps. The bins represent the possible choices in each step, hence they correspond to the possible candidates. The maximum load finally is the value that is to be optimized and consequently we associate it with the quality criterion that is used to rate the candidates. In this setup, the MCA approach to model simplification consists of testing a small set of d randomly selected candidates (edge collapses) in each step and performing that decimation operation among this small set that has the best quality value. Experiments show that using MCA approach our algorithm can produce approximations in almost the same quality as other algorithms based on greedy strategy when d = 6. Compared to the greedy optimization, the major benefit of the Multiple-Choice optimization is that the algorithmic structure is much simpler. For the Multiple-Choice optimization we do not need a priority queue and consequently we reduce the memory consumption and make the algorithm much easier to implement. 3.3 Algorithm Summary

Firstly, the importance of each vertex in a mesh should be evaluated. The most suitable edge for the contraction is searched in its neighborhood, and the one with the lowest cost is marked as the vertex’s importance. As for the most suitable edge for contraction we take the one that does not cause the mesh to fold over itself and preserves the original surface according to the criterion. Then we can decimate vertices one by one according their importance. Using the above idea of Multi-Choice techniques, the overall framework of our algorithm can be summarized as follows: 1. Determine the topology structure of the original mesh and calculate the unit normal of every triangle in the mesh. 2. For every vertex of the original model, calculate the cost of contracting the vertex to its neighborhood, which means to calculate the cost of all the edge adjacent to the vertex, picking the edge with the lowest cost as the vertex’s collapse edge. 3. Randomly choose d vertices from all candidates, and update the vertices needed to be recomputed among the d vertices. 4. Select the vertex with candidature edge of lowest cost from the d vertices, and contract its edge. After contracting, mark the related vertices needed to be updated. 5. Repeat step 3 and 4 until the given criterion is satisfied. Our algorithm does not need a global priority queue, so it is much easier to be implemented. In Table 1, we compare our algorithm with others.

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Table 1. Compared with others, our algorithm based on greedy strategy does not need a global priority queue

Algorithm step Initialize

Select candidate

Decimate

Our algorithm Others Initialize, Initialize, compute collapse cost for all compute collapse cost for all candidate, candidate perform global queue sorting Select d vertices randomly, update the vertex’s cost if Top of the queue necessary, pick the best out of d Perform operator Perform operator, locally recomputed cost, update global queue

4 Implementation Based on the above algorithm, we have developed a framework providing efficient simplification on models of various size. 9LHZ PRGHO

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Fig. 4. The structure of our simplification system. The system can read model file into internal data structure, simplify it interactively, and save the internal data back to model file.

The processing stage of the framework consists of the following steps (see Fig. 4): 1. 2. 3. 4. 5.

Read the input model file, and create internal data structure. Render the current model. Simplify the model according to the user’s aim. Render the simplified model. Repeat step 2-4 until the user is satisfied with the resulting model, then save it back to model file.

Step1 consists of reading the model file, triangulating the model, and storing all the points and triangles into the internal data structures. As our simplification algorithm can only deal with triangles as input, the models consisting of n-sided polygons need to be triangulated in the preprocessing phase.

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Class Vertex{ Vec3 location; // Vec3 is a vector class int index; set vertNeighbors; //vertices connected to this vertex set triNeighbors; //triangles of which this vertex is a part bool bActive; //false if vertex has been removed double cost; //cost of contracting the min cost edge int minCostNeighbor; // index of vertex at other end of the min cost edge } Class Face{ float weight; Vec3 direct; Vec3 normal;//normal of this triangle Vec3 point;// vertices of this triangle bool bActive; // active flag void getVerts(int& v1,int& v2,int& v3) } Class CShape { vector vertices; vector < Face > faces; Vertex& getvertex (int i); { return vertices( i ) }; Face& getface (int i ) { return faces( i );}; unsigned int vert_count( ) const; unsigned int face_count( ) const; unsigned int active_vert_count( ); unsigned int active_face_count( ); bool initialize( ); //find min cost edge for every vertex } Class CModel { vector shapes; void getshape (CShape& shape); bool initialize( ); //initialize every shape bool decimate(int percent); //control the process of simplification bool EdgeCollapse( int vertid )//contracting one edge }

As shown above, we define the basic internal data structure for model and simplification with the aid of Visual C++.

5 Results and Discussion In this section the efficiency of our algorithm is demonstrated. We have tried our implementation on various models of different sizes and varying shapes, and have

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achieved encouraging results. Table 2 summarizes the running time of our current implementation and compares it with Garland’s QEM algorithm [12] and Melax’s algorithm which is simple and fast [16]. All experiments are done on a commodity PC with Intel 2.4GMHz CPU and 1024M RAM. Table 2. Running time of different algorithms. All data reflects the time needed to simplify the model to 0 triangles

Model

Vertices

Triangles

telephone

34352

68575

lamp

5848

11672

bunny

34834

69451

Algorithm

Initialization time (secs.)

Simplification time (secs.)

Total (secs.)

QEM Melax Our QEM Melax Our QEM Melax Our

3.721 3.058 4.344 1.245 2.215 1.687 5.512 8.531 5.122

19.493 25.143 13.085 3.506 5.278 2.110 19.970 25.225 6.965

23.214 28.201 17.429 4.751 7.493 3.797 25.482 33.756 12.087

We also depict the absolute maximum geometric errors for the bunny and lamp model when decimating them to various levels of details (see Fig. 5 and Fig. 6). The approximation error is measured by the Hausdorff distance between the original model and the simplified result. The Hausdorff distance (sometimes called the L∞ norm difference) between two input meshes M1 and M2 is [17]:

K haus ( M 1 , M 2 ) = max(dev( M 1 , M 2 ), dev(( M 2 , M 1 )) 1

2

1

(4) 2

where dev(M , M ) in (4) measures the deviation of mesh M from mesh M . The Hausdorff distance provides a maximal geometric deviation between two meshes.

Fig. 5. Absolute maximum geometric error for bunny model. The size of bounding box is 15.6*15.4*12.1.

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Fig.7 demonstrates the visual quality of the approximations generated using our algorithm. In Fig.7 (i), the bunny model is drastically simplified (99%), but the major details of the original still remain. 

4(0 2XUDOJRULWKP 0HOD[

UR  UU  H  QR LW  DP  L[ RU  SS  D   



 WULDQJOHV





Fig. 6. Absolute maximum geometric error for lamp model. The size of bounding box is 15.6*15.6*22.6.

(a) telephone, 68575triangles

(d) lamp, 11672triangles

(b) 34287 triangles

(c) 1370 triangles

(e) 5836 triangles

(f) 232 triangles

Fig. 7. The visual quality of the approximations generated using our algorithm. The bunny model (i) is drastically simplified (99%), but the major details still remain.

Fast Mesh Simplification Algorithm Based on Edge Collapse

(g) bunny, 69451triangles

(h) 6945 triangles

285

(i) 694 triangles

Fig. 7. (continued)

6 Conclusion We have presented a surface simplification algorithm which is capable of rapidly producing high fidelity approximations of 3d meshes. Our algorithm can preserve the visually important features of the model. We also applied generic probabilistic optimization principle of Multiple-Choice algorithm to the problem of finding a simplification sequence. Experiments show that the MCA approach can reduce the memory overhead and lead to a simpler algorithmic structure. Based on the proposed algorithm, we have implemented a simplification system. We have processed many 3D meshes of different sizes on this system, and achieved encouraging results. This demonstrates the effectiveness of our algorithm.

References 1. Campbell, F. W., Robson, J. G.: Application of Fourier Analysis to the Visibility of Gratings. Journal of Physiology 197 (1968) 551-566 2. Blakemore, C., Campbell, F. W.: On the Existence of Neurons in the Human Visual System Selectively Sensitive to the Orientation and Size of Retinal Images. Journal of Physiology, 203 (1969) 237-260 3. Wu, J., Kobbelt, L.: Fast Mesh Decimation by Multiple–choice Techniques. In Vision, Modeling and Visualization. IOS Press (2002) 241–248 4. Turk, G.: Re-tilling Polygonal Surfaces. In Proceeding of ACM SIGGRAPH (1992) 55-64 5. Schoroeder, W.J., Zarge, J.A., Lorensen, W. E.: Decimation of Triangle Meshes. In Proc. Of ACM SIGGRAPH (1992) 65-70 6. Rossignac, J., Borrel, P.: Multi-resolution 3D Approximation for Rendering Complex Scenes. In Geometric Modeling in Computer Graphics Springer Verlag (1993) 455-465 7. Hoppe, H., DeRose, T., Duchamp, T., McDonald, J. A., Stuetzle, W.: Mesh optimization. Computer Graphics (SIG-GRAPH ’93 Proceedings) (1993) 19–26 8. Hoppe, H.: Progressive Meshes. In SIG-GRAPH 96 Conference Proceeding. ACM SIGGRAPH Addison Wesley August (1996) 99-108 9. Cohen, J., Varshney, A., Manocha, D., Turk, G.: Simplification Envelopes. In Proc. Of ACM SIGGRAPH ’96 (1996) 119-128

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10. Derose, T., Lounsbery, M., Warren, J.: Multiresolution Analysis for Surfaces of Arbitrary Topology Type. Technical Report TR 93-10-05 Department of Computer Science University of Washington (1993) 11. Eck, M., Derose, T., Duchamp, T., Hoppe, H., Lousbery, M., Stuetzle, W.: Multiresolution Analysis of Arbitrary Meshes. In Proceeding of ACM SIGGRAPH (1995) 173-182 12. Garland, M., Heckbert, P. S.: Surface Simplification Using Quadric Error Metric. In Proc. SIGGRAPH'97 (1997) 209-216 13. Agarwal, P., Suri, S.: Surface Approximation and Geometric Partitions. In Proceedings of 5th ACM-SIAM Symposium on Discrete Algorithms (1994) 24-33 14. Azar, Y., Broder, A., Karlin, A., Upfal, E.: Balanced Allocations. SIAM Journal on Computing, 29(1) (1999) 180-200 15. Kolchin, V., Sevastyanov, B., Chist-yakov, V.: Random Allocations. John Willey & Sons (1978) 16. Melax, S.: A Simple, Fast, and Effective Polygon Reduction Algorithm. Game Developer November (1998) 44-49 17. Southern, R., Blake, E., Marais, P.: Evaluation of Memoryless Simplification. Technical Report CS01-18-00, University of Cape Town (2001)

Hierarchical Multiple Models Adaptive Feedforward Decoupling Controller Applied to Wind Tunnel System∗ Xin Wang1,2 and Hui Yang2 1

Center of Electrical & Electronic Technology, Shanghai Jiao Tong University, Shanghai, P.R. China, 200240, 2 School of Electrical & Electronic Engineering, East China Jiaotong University, Jiangxi, P.R. China, 330013 [email protected]

Abstract. For the biggest wind tunnel in Asia, during the aerodynamic research on the scale models, it is difficult to keep the Mach number in the test section and the stagnation pressure constant strictly because the interaction is strong, the operation conditions change abruptly and the transient response’s requirements are high. To cope with these problems, a Hierarchical Multiple Models Adaptive Feedforward Decoupling Controller (HMMAFDC) is presented in this paper. The controller is composed of multiple fixed controller models and two adaptive controller models. Multiple models are used to improve the transient response of the wind tunnel. Hierarchical structure is presented to reduce the number of the fixed models greatly. To the optimal model selected by the switching index, the interactions of the system are viewed as measurable disturbance and eliminated using the feedforward strategy. It not only decouples the system dynamically but also places the poles of the closed loop system arbitrarily. The significance of the proposed method is that it is applicable to a MIMO system with a much small number of models. The global convergence is obtained. Finally, several simulation examples in a wind tunnel experiment are given to show both effectiveness and practicality.

1 Introduction A 2.4m x 2.4m injector driven transonic wind tunnel in China Aerodynamics Research and Development Center (CARDC) is the biggest wind tunnel in Asia [1]. It is used for aerodynamic research on scale models, which is very important for national defense and civil aviation. Aerodynamic research data of scale models are measured at a given Mach number with a constant stagnation pressure. It is required that in the initial stage, the response time should be no longer than 7.0 seconds; in the experiment stage, the steady state tracking errors are within 0.2% in 0.8 second and the overshoot should be avoided [2]. Recently several controllers are designed to satisfy the transient response’s requirement above. According to a 1.5m wind tunnel (FFA- T1500) in Sweden, several separate SISO models are used to control it [3]. For a 1.6m x 2m wind tunnel in ∗

This work is supported by National Natural Science Foundation (No. 60504010, 50474020) and Shanghai Jiao Tong University Research Foundation.

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 287 – 298, 2006. © Springer-Verlag Berlin Heidelberg 2006

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Netherlands, it is regarded as a second-order system and a PID controller is given [4]. Later a predictive controller is designed to control the Mach number in this wind tunnel with the angle of attack changing [5]. In USA, a system of self-organization neural networks are developed and tested to cluster, predict and control the Mach number of a 16-foot wind tunnel in NASA [6]. However, if the descriptions for the aerodynamics of a wind tunnel are different with the size of a wind tunnel, the controller should be also different. For the 2.4m x 2.4m transonic wind tunnel in CARDC, two SISO stable linear reduced order models are established and two PID controllers are designed to control the Mach number and the stagnation total pressure respectively [2]. But when the Mach number in the test section varies from 0.3 to 1.2, the interaction becomes stronger and a multivariable decoupling controller is needed [7]. In [1], two feedforward static decouplers with four fixed PI controllers are designed to solve this problem. But when the Mach number steps from 0.3 to 0.4, 0.5,…,1.2, the parameters of the wind tunnel will jump accordingly. The poor transient response cannot satisfy the high requirements of the wind tunnel above. So some special controller structure and algorithms are needed. To solve this problem, some multiple models adaptive controllers (MMAC) are designed to improve the transient response [8, 9]. One adaptive model, one reinitialized adaptive model and lots of fixed models are used to cover the region where the parameters change. For example, about 300 models are needed to cover the region where only one parameter changes [10]. The number of the models is so large that it increases the calculation time, which affects the selection of the sampling period. To reduce the huge number of models needed in MMAC, Localization, Moving Bank and other methods are presented [11, 12]. However, these methods can only reduce a small number of the models, which can’t solve this problem essentially. In our former work, a Hierarchical Multiple Models Adaptive Controller (HMMAC) was proposed to reduce the number of the fixed models [13, 14]. In [13], a decoupling controller using pole-zero cansellation method is proposed to deal with minimum phase system, while non-minimum pahse system is solved in [14]. Unfortunately, their structures are not suitable for the distributed control system (DCS) In this paper, a novel Hierarchical Multiple Models Adaptive Feedforward Decoupling Controller (HMMAFDC) is presented. Multiple models are used to improve the transient response of the wind tunnel. Hierarchical structure is presented to reduce the number of the fixed models greatly. To the optimal model selected by the switching index, the interactions of the system are viewed as measurable disturbance and eliminated using the feedforward strategy. It not only decouples the system dynamically but also places the poles of the closed loop system arbitrarily. Several simulation examples in the wind tunnel experiment illustrate the HMMADC.

2 Description of the System The 2.4m x 2.4m wind tunnel is an intermittent wind tunnel constructed for the aerodynamic research aim by CARDC. It is a closed-circuit interjector driven transonic tunnel and used for testing scale models, mostly of airplanes, in the speed region of 0.3 to 1.2 (see fig.1). The interjector is used to realize high Mach numbers with the limited amount of air storage while the Reynolds number can be increased in order to decrease

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the influence of model factors on the measurements. At the initial stage of the aerodynamic experiment, the main control hydraulic servo valve is opened and air is allowed to flow from storage bottle into the tunnel. Part of the air is let out through the main exhaust hydraulic servo valve; the other is injected into the tunnel by the injector. After the stable flowing field is established, the experiment proceeds. It has more than 40 operation cases. One of these cases is as follows [1]. At the initial stage of the experiment, the main control hydraulic servo valve is tuned to give the initial value of the Mach number in the test section with the main exhaust hydraulic servo valve and the choke finger at the preset position. After the stable flowing field is established, the exhaust hydraulic servo valve is tuned to keep the stagnation total pressure to be 1.5, and the choke finger makes the Mach number in the test section vary with ∆ M = 0.1 from 0.3 to 1.2, while the main control hydraulic servo valve is controlled to ensure the injector total pressure constant and compensates for the loss of the air storage pressure. When the Mach number in the test section is larger than 0.8, the choke finger is opened at its maximal position and the plenum exhaust valve is used to tune the Mach number in the test section correspondingly.

flow Main control hydraulic servo valve

Injector

Storge tank

Stagnation pressure control flow flow Test section

Choke finger

Stagnation

Main exhaust hydraulic servo valve

Mach number control

Fig. 1. The structure of the transonic wind tunnel

From these two particular models[7], the linear reduced-order model of the wind tunnel can be established according to each Mach number as follows

β1 −0.4 s ª e − « α y s ( ) ª 1 º 1s + 1 « = « y ( s)» ¬ 2 ¼ « − β 3 s + 1 e −0.4 s « (α s + 1) 2 3 ¬

−

β2

º e −0.4 s » ªu ( s) º »⋅« 1 » , β4 » u (s) e −0.4 s » ¬ 2 ¼ α4 s + 1 ¼

(α 2 s + 1)2

(1)

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where y1 ( s ) , y2 ( s ) , u1 ( s ) , u2 ( s ) are the Mach number in the test section, the stagnation total pressure, the choke finger opening and the main exhaust hydraulic servo valve respectively. αi , β i are parameters. and satisfy αi ∈ [αi min , αi max ] , βi ∈ [ βi min , β i max ] .

Select the sampling period as 0.1 second. Then the linear discrete time multivariable minimum phase system is described as

(I + A z 1

−1

+ A2 z −2 ) y(t ) = ( B0 + B1 z −1 ) u(t − 4) + d .

(2)

When the Mach number varies, the parameters of the system change accordingly. So the system can be viewed as a linear MIMO discrete-time system, which admits DARMA representation of the form A(t , z −1 ) y(t ) = B(t , z −1 )u(t − k ) + d (t ) ,

(3)

where u(t ) , y(t ) are the n × 1 input, output vectors respectively and d (t ) is a n × 1 vector denoting the steady state disturbance. A(t , z −1 ), B(t , z −1 ) are polynomial matrixes in the unit delay operator z −1 and B0 (t ) is nonsingular, for any t . Here

A(t , z −1 ) is assumed to be a diagonal polynomial matrix. The system satisfies the assumptions as follows: (1) The system parameters are time variant with infrequent large jumps. The period between two adjacent jumps is large enough to keep the jumping parameters constant. (2) Φ (t ) = [ − A1 (t ),; B0 (t ),; d (t )] is the system model, which changes, in a

compact set Σ . (3) The upper bounds of the orders of A(t , z −1 ) , B(t , z −1 ) and the time delay k are known a prior; (4) The system is minimum-phase. To decouple the system, the interaction caused by the input u j ( t ) to the output yi (t ) , ( j ≠ i ) is viewed as measurable disturbance. So the system (3) can rewritten

A(t , z −1 ) y(t ) = B(t , z −1 ) u(t − k ) + B(t , z −1 )u(t ) + d (t ) ,

(4)

where B(t , z −1 ) = B(t , z −1 ) + B(t , z −1 ) . B(t , z −1 ) = diag ª¬ Bii (t , z −1 ) º¼ is a diagonal polynomial matrix and B0 (t ) is nonsingular, ∀t . B(t , z −1 ) = ª¬ Bij (t , z −1 ) º¼ and

Bii (t , z −1 ) = 0 . From assumption (1), Ai ( t ) , B j (t ) , B j (t ) , d (t ) are piecewise constant (time variant system with infrequent large jumping parameters). During the period when no jumps happen, (4) can be rewritten as A( z −1 ) y(t ) = B( z −1 )u(t − k ) + B( z −1 ) u(t − k ) + d .

(5)

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3 HMMAFDC To reduce the number of fixed models, a hierarchical structure with l levels is adopted. Iupu t an d O utput D ata

1

Level 1

Level 2

1

ಹ

2

Level l

1

O p ti m a l F i x e d M o d e l

ಹ

2

᧧

ಹ ಹ

j2





ಹ ಹ

j1

ಹ

2



u, y

m

1

m

2



ಹ ಹ

jl

A d a p ti v e M o d e l

᧧

m

l

R e in iti a l iz e d A d a p ti v e M o d e l

O p ti m a l M o d e l

Fig. 2. Hierarchical principle of the HMMAFDC

(1) Utilizing the prior information, the set Σ , where the parameters of the system vary, is partitioned into m1 subsets Σ , ( s = 1, , m1 ) . In each subset, the center Φ and 1, s

1,s

its radius r are designed to satisfy that For any Φ ∈ Σ , Φ − Φ ≤ r . So the centers 1,s

1,s

1, s

1, s

Φ , s = 1, , m1 compose the level 1 fixed model set which covers the system 1,s

parameter set with their neighbors entirely. (2) According to the switching index, the best model in level 1 is selected as j1 . (3) Based on the best model j1 in level 1 and use the partition method presented above similarly, m2 centers are set up to compose the level 2 fixed model set on line dynamically, which covers the model j1 with their neighbors entirely. (4) According to the switching index, the best model in level 2 is selected as j2 . (5) Similarly, the best model in the last level i.e. level l is selected as jl , which is also the best model among all the fixed models. (6) At last, in level l + 1 , a free running adaptive model and a reinitialized adaptive model are added in. According to the switching index, the best model is selected among

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these three models above. The free running adaptive model is used to guarantee the stability of the wind tunnel while the reinitialized adaptive model’s initial value can be set to be that of the best model selected to improve the transient response of the wind tunnel. For the system (5), the cost function to be considered is of the form [15] 2

J c = P ( z −1 ) y(t + k ) − R( z −1 ) w(t ) +Q ( z −1 )u(t ) + S ( z −1 ) u(t ) + r ,

(6)

where w(t ) is the known reference signal. P ( z −1 ), Q ( z −1 ), R( z −1 ) are diagonal weighting polynomial matrices, S ( z −1 ) is a weighting polynomial matrix and r is the weighting vector respectively. Q ( z −1 ) is used to weight the control u(t ) and S ( z −1 ) is used to weight the interaction u(t ) , which is viewed as the measurable disturbance. Introduce the identity P ( z −1 ) = F ( z −1 ) A( z −1 ) + z − k G ( z −1 ) .

(7)

In order to get unique polynomial matrixes F ( z −1 ) , G ( z −1 ) , the orders of F ( z −1 ), G ( z −1 ) are chosen as n f = k − 1, ng = na − 1 .

(8)

Multiplying (5) by F ( z −1 ) and using (7), the optimal control law is as G ( z −1 ) y(t ) + H1 ( z −1 ) u(t ) + H 2 ( z −1 ) u(t ) + r = R( z −1 ) w(t ) ,

(9)

where H1 ( z −1 ) = F ( z −1 ) B( z −1 ) + Q ( z −1 ), H 2 ( z −1 ) = F ( z −1 ) B( z −1 ) + S ( z −1 ), r = Fd + r . From (9) and (5), the system equation can be derived as follows ª¬ P ( z −1 ) B( z −1 ) + Q ( z −1 ) A( z −1 ) º¼ y(t + k ) = B( z −1 ) R( z −1 ) w(t ) + ª¬Q ( z −1 )d − B( z −1 )r º¼ + ªQ ( z −1 ) B( z −1 ) − B( z −1 ) S ( z −1 ) º u(t ) . ¬ ¼

(10)

Note that (10) is not the closed loop system equation because there exists the input u(t ) , although it is viewed as the measurable disturbance. Equation (9) and (10) are just used to choose the polynomial matrixes to decouple the system. For the system, let Q ( z −1 ) = R1 B( z −1 )  S ( z −1 ) = R1 B( z −1 ) where R1 is a diagonal matrix. The system equation (10) can be rewritten as ª¬ P ( z −1 ) + R1 A( z −1 ) º¼ y(t + k ) = R( z −1 ) w(t ) + R1d − r .

(11)

From (11), considering P ( z −1 ), R( z −1 ), A( z −1 ) are diagonal matrices, it is concluded that by the choice of the weighting polynomial matrixes, the closed loop system can be decoupled dynamically. To eliminate the steady state error, the polynomial matrixes can be chosen as P ( z −1 ) + R1 A( z −1 ) = T ( z −1 ) , r = R1d .

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In the level l + 1 , the HMMADC is composed of three models. One is the fixed controller model Θ , i.e. the best model jl in level l , the others are a free-running l +1,1

adaptive controller model Θ and a re-initialized adaptive controller model Θ . l +1,2

l +1,3

To the adaptive controller models Θ , Θ , Multiplying (5) by F ( z −1 ) from the left l +1,2

l +1,3

and using (7), it follows that P ( z −1 ) y(t + k ) = G ( z −1 ) y(t ) + F ( z −1 ) B( z −1 )u(t ) + F (1)d .

(12)

Multiplying (5) by R1 from the left and using the chosen polynomial matrixes above, it follows that T ( z −1 ) y(t + k ) = P ( z −1 ) y(t + k ) + R1 A( z −1 ) y(t + k ) = G ( z −1 ) y(t ) + F ( z −1 ) B( z −1 )u(t ) + R1 B( z −1 ) u(t ) + F (1)d + R1d .

(13)

Using (7), (9) and the definitions of H ( z −1 ) , r , the recursive estimation algorithm of Θ and Θ is described as follows m +1

m+2

Ty(t + k ) = Gy(t ) + H1u(t ) + H 2 u(t ) + r ,

θˆi (t ) = θˆi (t − 1) + a (t )

X (t − k ) ⋅ ª y fi (t )T − X (t − k )T θˆi (t − 1) º¼ , 1 + X ( t − k )T X ( t − k ) ¬

y fi = Tii ( z −1 ) yi (t )

where

(14)

is

the

X (t ) = ª¬ y(t )T ,; u(t )T ,; u(t )T , ,1º¼ controller

T

auxiliary

system

(15) output,

is the data vector, Θ = [θ1 , , θ n ] is the

parameter

matrix

and

T

θi = ª¬ g , , g ; g ,, g ,; h ,, h ;º¼ , i = 1, 2, , n . The scalar a (t ) is set to 0 i1

0 in

1 i1

1 in

0 i1

0 in

avoid the singularity problem of the estimation Hˆ (0) [16]. To a HMMAFDC, the switching index is as follows 2

2

y f (t ) − y f ( t )

e f (t ) J=

i ,s

i,s

1 + X (t − k ) X (t − k ) T

=

(16)

i,s

1 + X (t − k ) X (t − k ) T

where y f (t ) = T ( z −1 ) y(t ) is the auxiliary output of system, e f (t ) is the auxiliary i ,s

output error between the real system and the model s in level i . For level 1 to l , let ji = arg min( J ) s = 1, , mi , i = 1, 2, , l correspond to the model whose auxiliary i,s

output error is minimum , then Θ is chosen to be the best controller in level i . But for j

the level l + 1 , there are only three models left. So let jl +1 = arg min( J ) s = 1, 2, 3 , l +1, s

then Θ is chosen to be the HMMADC and used to control the system. j +1

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(1) If jl +1 ≠ 3 , which means Θˆ (t ) is not the minimum output error controller, then l +1,3

re-initialize Θˆ (t ) as the optimal controller parameter to improve the transient l +1,3

response, i.e. Θˆ (t ) = Θ . Θˆ (t ) , Θˆ (t ) are estimated using (15) respectively and l +1,3

l +1, jl +1

l +1,2

l +1,3

the controller is set as Θ (t ) = Θ . l +1, jl +1

(2) If jl +1

= 3 , Θˆ (t ) , Θˆ (t ) are estimated using (15) respectively and the controller l +1,2

l +1,3

is set as Θˆ (t ) = Θˆ (t ) . l +1,3

The optimal control law can be obtained from

Gˆ ( z −1 ) y(t ) + ª¬ Hˆ 1 ( z −1 ) + Hˆ 2 ( z −1 ) º¼ u(t ) + rˆ = R( z −1 ) w(t ) .

(17)

4 Applications to the Wind Tunnel System The wind tunnel system (2) is of second order and the time delay equals to 4. Every 60 steps, the Mach number in the test section varies from 0.3 to 1.2 with ∆ M = 0.1 , which causes the parameters of the system jump simultaneously. Because the sampling period is selected as 0.1 second, 1 second in experiment means 10 steps in the simulation. The stagnation total pressure is required to be 1.5 all the time. Case 1: A conventional adaptive decoupling controller is designed to control the wind tunnel. Its initial value is chosen close to the real controller parameter model. The responses of the system are shown in Fig. 3 and 4. In the initial stage, after 7 seconds’ operation, the overshoots of the system are all less than 0.2%, which satisfies the requirement. But in the experiment stage, after 0.8 second’s operation, the overshoots of the system are much larger than 0.2%. The largest overshoot is 68.74%, which 340 times the requirement. In fact, during all experiment period, i.e. after the initial stage, the overshoots of the system are all much larger than 0.2%. So the adaptive controller cannot satisfy the requirement and be used to control the wind tunnel. Case 2: A multiple models adaptive decoupling controller is designed to control the wind tunnel. In this case, 30 fixed models are used to cover the region where jumping parameters vary. Note that the real system model is not among these fixed system models. Then 30 corresponding fixed controller models are set up using the transformation proposed above and two adaptive controller models are added to compose the multiple controller models. These two adaptive controller models’ initial values are same as those of the adaptive model in case 1. The responses of the system are shown in Fig. 5 and 6. Compared with that in case 1, the transient response of the wind tunnel is improved greatly when only 30 fixed models are added. In the initial stage, the overshoots of the system are all less than 0.2%, which satisfies the requirement. However, in the experiment stage, the overshoots of the system are all larger than 0.2%, especially the stagnation total pressure (see Fig.6).

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Case 3: A multiple models adaptive decoupling controller with 1000 fixed models is designed to control the wind tunnel. It is designed using the same algorithm as in case 2 but the number of the fixed models. As the number of the fixed models increases, the transient response becomes better. Both in the initial stage and in the experiment stage, the overshoots of the system are all less than 0.2%, which satisfies the requirement (see Fig.7 and 8). Case 4: A HMMADC is designed to control the wind tunnel. In this case, the same algorithm is used as in case 2 and 3 except a hierarchical structure with 3 levels and 10 models at each level adopted. Totally there are 30 fixed models added, the same number as in case 2, but the overshoots of the system are much better than those in case 2. They are similar to those in case 3, all less than 0.2%, which satisfies the requirement both in the initial stage and in the experiment stage. But the number is 33 times less than that in case 3 (see Fig.9 and 10). The results show that although the same algorithm is adopted in case 2, 3 and 4, the HMMADC can get better transient response with fewer models. 1.4

1.2

1

y1

0.8

0.6

0.4

0.2

0 0

50

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200 t/step

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Fig. 3. The Test-section-Mach-number using ADC 1.8 1.6 1.4 1.2

y2

1 0.8 0.6 0.4 0.2 0 0

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200 t/step

250

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Fig. 4. The Stagnation-total-pressure using ADC

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X. Wang and H. Yang 1.4

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0.6

0.4

0.2

0 0

50

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Fig. 5. The Test-section-Mach-number of MMADC using 30 models 1.8 1.6 1.4 1.2

y2

1 0.8 0.6 0.4 0.2 0 0

50

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200 t/step

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Fig. 6. The Stagnation-total-pressure of MMADC using 30 models 1.4

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0.8 y1

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0.6

0.4

0.2

0 0

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200 t/step

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Fig. 7. The Test-section-Mach-number of MMADC using 1000 models

HMMAFDC Applied to Wind Tunnel System 1.8 1.6 1.4 1.2

y2

1 0.8 0.6 0.4 0.2 0 0

50

100

150

200 t/step

250

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Fig. 8. The Stagnation-total-pressure of MMADC using 1000 models 1.4

1.2

1

y1

0.8

0.6

0.4

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0 0

50

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Fig. 9. The Test-section-Mach-number of HMMADC using 10,10,10 models 1.8 1.6 1.4 1.2

y2

1 0.8 0.6 0.4 0.2 0 0

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200 t/step

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Fig. 10. The Stagnation-total-pressure of HMMADC using 10,10,10 models

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5 Conclusions This paper presents a Hierarchical multiple models adaptive decoupling controller. Compared with the MMADC, the better transient response can be got with much fewer models, which reduce the number of the fixed models greatly.

References 1. Zhang, G.J., Chai T.Y., Shao C.: A Synthetic Approach for Control of Intermittent Wind Tunnel, Proceedings of the American Control Conference, (1997) 203–207 2. Yu W., Zhang G.J.: Modelling and Controller Design for 2.4 M Injector Powered Transonic Wind Tunnel, Proceedings of the American Control Conference, (1997) 1544–1545 3. Nelson D.M.: Wind Tunnel Computer Control System and Instrumentation, Instrument Society of America, (1989) 87–101 4. Pels A.F.: Closed-Loop Mach Number Control in A Transonic Wind Tunnel, Journal A, 30 (1989) 25–32 5. Soeterboek R.A.M., Pels A.F., et al.: A Predictive Controller for the Mach Number in A Transonic Wind Tunnel, IEEE Control Systems Magazine, 11 (1991) 63–72 6. Motter M.A., Principe J.C.: Neural Control of the NASA Langley 16-Foot Transonic Tunnel, Proceedings of the American Control Conference, (1997) 662–663 7. CARDC.: Measurement and Control System Design in High and Low Speed Wind Tunnel, National Defence Industry Press, Beijing (2002) (in Chinese) 8. Narendra K.S., Xiang C.: Adaptive Control of Discrete-Time Systems Using Multiple Models, IEEE Trans. on Automatic Control, 45 (2000) 1669–1686 9. Wang X., Li S.Y., et al.: Multiple Models Adaptive Decoupling Controller for A Nonminimum Phase System, 5th Asian Control Conference, (2002) 166–171 10. Narendra K.S., Balakrishnan J., Ciliz M.K.: Adaptation and Learning Using Multiple Models, Switching, and Tuning, IEEE Control Systems Magazine, 15 (1995) 37–51 11. Zhivoglyadov P.V., Middleton R.H., Fu M.Y.: Localization Based Switching Adaptive Control for Time-Varying Discrete-Time Systems, IEEE Trans. on Automatic Control, 45 (2000) 752–755 12. Maybeck P.S., Hentz K.P.: Inverstigation of Moving Bank Multiple Model Adaptive Algorithms, Journal of Guidance Control Dynamics, 10 (1987) 90–96 13. Wang X., Li S.Y., Yue H.: Multivariable Adaptive Decoupling Controller Using Hierarchical Multiple Models, ACTA Automatica Sinica, 31 (2005) 223–230 14. Wang X., Li S.Y., Yue H.: Hierarchical Multiple Models Decoupling Controller for Nonminimum Phase Systems, Control Theory and Application, 22 (2005) 201–206 15. Wang X., Li S.Y., et al: Multiple Models Direct Adaptive Controller Applied to the Wind Tunnel System, ISA Transactions, 44 (2005) 131–143 16. Goodwin G.C., Ramadge P.J., Caines P.E.: Discrete Time Multivariable Adaptive Control, IEEE Trans. on Automatic Control, 25 (1980) 449–456 17. Landau I.D., Lozano R.: Unification of Discrete Time Explicit Model Reference Adaptive Control Designs, Automatica, 17 (1981) 593–611

Intelligent Backstepping Control for Chaotic Systems Using Self-Growing Fuzzy Neural Network Chih-Min Lin1, Chun-Fei Hsu2, and I-Fang Chung3 1

Department of Electrical Engineering, Yuan-Ze University, Chung-Li, Tao-Yuan, 320, Taiwan, Republic of China [email protected] 2 Department of Electrical and Control Engineering, National Chiao-Tung University, Hsinchu, 300, Taiwan, Republic of China [email protected] 3 Institute of Bioinformatics, National Yang-Ming University, Taipei, 115, Taiwan, Republic of China [email protected]

Abstract. This paper proposes an intelligent backstepping control (IBC) for the chaotic systems. The IBC system is comprised of a neural backstepping controller and a robust compensation controller. The neural backstepping controller containing a self-growing fuzzy neural network (SGFNN) identifier is the principal controller, and the robust compensation controller is designed to dispel the effect of minimum approximation error introduced by the SGFNN identifier. Finally, simulation results verify that the IBC system can achieve favorable tracking performance.

1 Introduction In recent years, the fuzzy neural network (FNN) possesses the merits of the low-level learning and computational power of neural network, and the high-level human knowledge representation and thinking of fuzzy theory [1]. The fuzzy neural networks have been adopted widely for the control of complex dynamical systems owing to its fast learning property and good generalization capability. For the FNN approaches, the structure of the FNN should be determined by trial-and-error in advance for the reason that it is difficult to consider the balance between the rule number and the desired performance. To solve the problem of structure determination, much interest has been focused on the self-organizing neural network approach [2-4]. Without the need for preliminary knowledge, the self-organizing approach demonstrates the properties of generating the rules automatically. According to the way of the selforganizing approaches, the incremental rule construction has been widely used [2]. This paper proposes an intelligent backstepping control (IBC), which combines the advantages of neural network identification and adaptive backstepping control techniques, and it is applied to control a chaotic system to show its effectiveness. Finally, the effectiveness of the proposed SAFNC scheme is demonstrated by some simulations. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 299 – 308, 2006. © Springer-Verlag Berlin Heidelberg 2006

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2 Description of Chaotic Systems Chaotic systems have been known to exhibit complex dynamical behavior. The interest in chaotic systems lies mostly upon their complex, unpredictable behavior, and extreme sensitivity to initial conditions as well as parameter variations. Consider a second-order chaotic system such as well known Duffing’s equation describing a special nonlinear circuit or a pendulum moving in a viscous medium under control [5-8].

x = − px − p1 x − p 2 x 3 + q cos( wt ) + u = f + u

(1)

where p , p1 , p2 and q are real constants; t is the time variable; w is the fre-

x

x

quency; f = − px − p1 x − p 2 x 3 + q cos( wt ) is the chaotic dynamic function; and u is the control effort. Depending on the choice of these constants, it is known that the solutions of system (1) may exhibit periodic, almost periodic and chaotic behavior. For observing the chaotic unpredictable behavior, the open-loop system behavior with u = 0 was simulated with p = 0.4 , p1 = −1.1 , p 2 = 1.0 and w = 1.8 . The phase plane plots from an initial condition point (1,1) are shown in Figs. 1(a) and 1(b) for q = 1.8 and q = 7.0 , respectively. It is shown that the uncontrolled chaotic system has different trajectories for different q values.

q=1.8

q=7.0

x

x

(a)

(b)

Fig. 1. Phase plane of uncontrolled chaotic system

3 Design of Ideal Backstepping Controller The control objective is to find a control law so that the state trajectory x can track a reference xc closely. Assume that the parameters of the system (1) are well known, the design of ideal backstepping controller is described step-by-step as follows: Step 1. Define the tracking error e1 = x − xc

(2)

and the derivative of tracking error is defined as e1 = x − x c .

(3)

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The x can be viewed as a virtual control in the equation. Define the following stabilizing function α = x c − c1e1 (4) where c1 is a positive constant. Step 2. Define e2 = x − α

(5)

then the derivative of e2 is expressed as e2 = x − α = x − xc + c1e1 .

(6)

Step 3. The ideal backstepping controller can be designed as [9] u * = xc − f − c1e1 − c2 e2 − e1

(7)

where c2 is a positive constant. Substituting (7) into (6), it is obtained that e2 = −c2 e2 − e1 .

(8)

Step 4. Define a Lyapunov function as e12 e22 (9) + . 2 2 Differentiating (9) with respect to time and using (3)-(5) and (8), it is obtained that V = e e + e e V1 =

1

1 1

2 2

= e1 ( x − α − c1e1 ) + e2 (−c2 e2 − e1 ) = −c1e12 − c2 e22 ≤ 0 .

(10) Therefore, the ideal backstepping controller in (7) will asymptotically stabilize the system.

4 Design of Intelligent Backstepping Controller Since the chaotic dynamic function f may be unknown in practical application, the ideal backstepping controller (7) can not be precisely obtained. To solve this problem, the descriptions of the SGFNN identifier and the design steps of the IBC system are described as follows: 4.1 SGFNN Identifier

A four-layer fuzzy neural network, which comprises the input (the i layer), membership (the j layer), rule (the k layer), and output (the o layer) layers, is adopted to implement the proposed SGFNN. The signal propagation and the basic function in each layer are as follows: Layer 1 - Input layer: For every node i in this layer, the net input and the net output are represented as

neti1 = xi1

(11)

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y i1 = f i1 (net i1 ) = neti1 , i = 1,2 where

(12)

1 i

x represents the i-th input to the node of layer 1.

Layer 2 - Membership layer: In this layer, each node performs a membership function and acts as an element for membership degree calculation, where the Gaussian function is adopted as the membership function. For the j-th node, the reception and activation functions are written as

net y 2j = f j2 (net 2j

2 j

(x =−

2 i

− mij )

2

(σ ) ) = exp(net ) ,

(13)

2

ij 2 j

j = 1,2,..., m

(14)

where mij and σ ij are the mean and standard deviation of the Gaussian function in the j-th term of the i-th input linguistic variable xi2 , respectively; and m is the total number of the linguistic variables with respect to the input nodes. Layer 3 - Rule layer: Each node k in this layer is denoted by ∏ , which multiplies the incoming signals and outputs the result of the product. For the k-th rule node net k3 = ∏ x 3j

(15)

y k3 = f k3 (net k3 ) = net k3 , k = 1,2,..., n

(16)

j

where x 3j represents the j-th input to the node of layer 3. Layer 4 - Output layer: The single node o in this layer is labeled as Σ , which computes the overall output as the summation of all incoming signals net o4 = ¦ wk4 xk4

(17)

y o4 = f o4 (neto4 ) = neto4 , o = 1

(18)

k

where the link weight wk4 is the output action strength associated with the k-th rule; xk4 represents the k-th input to the node of layer 4; and y o4 is the output of the SGFNN. For ease of notation, define the vectors m and ı collecting all parameters of SGFNN as m = [m11 m21 m12  m2 m ]T

(19)

ı = [σ 11 σ 21 σ 12  σ 2 m ]

(20)

T

Then, the output of the SGFNN can be represented in a vector form fˆ = w T ĭ(m, ı )

(21)

where w = [w14 w24 ...wn4 ] and ĭ = [x14 x24 ...xn4 ] = [Φ 1 Φ 2 ... Φ n ]T . According to the T

T

universal approximation theorem, an optimal SGFNN approximator can be designed to approximate the chaotic system dynamics, such that [10] f = f * + ∆ = w *T ĭ * (m * , ı * ) + ∆

(22)

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where ∆ is the approximation error, w * and ĭ * are the optimal parameter vectors of w and ĭ , respectively, and m * and ı * are the optimal parameters of m and ı , respectively. Let the number of fuzzy rules be n * and the fuzzy rules be divided into two parts. The first part contains n neurons which are the activated part and the secondary part contains n * − n neurons which do not exist yet. Thus, the optimal weights w * , ĭ * , m * and ı * are classified in two parts such as ªw *a º ªĭ *a º ªm *a º ªı *a º w * = « * » , ĭ * = « * » , m * = « * » and ı * = « * » ¬w i ¼ ¬ĭ i ¼ ¬m i ¼ ¬ı i ¼

(23)

where w *a , ĭ *a , m *a and ı *a are activated parts, and w *i , ĭ *i , m *i and ı *i are inactivated parts, respectively. Since these optimal parameters are unobtainable, a SGFNN identifier is defined as ˆ (m ˆ a , ıˆ a ) ˆ Ta ĭ fˆ = w a

(24)

ˆ , m ˆ a and ıˆ a are the estimated values of w *a , ĭ *a , m *a and ı *a , reˆa, ĭ where w a

~

spectively. Define the estimated error f as ~ ˆ +∆ ˆ Ta ĭ f = f − fˆ = w *aT ĭ *a + w *i T ĭ *i − w a ~ ~ T ˆ T T ~ ~ ˆ ĭ +w ĭ +∆ =w ĭ +w a

a

a

a

a

(25)

a

~ ~ = w* − w ˆ . In the following, some adaptive laws will ˆ a and ĭ a = ĭ *a − ĭ where w a a a be proposed to on-line tune the mean and standard deviation of the Gaussian function of the SGFNN approximator to achieve favorable estimation of the dynamic function. To achieve this goal, the Taylor expansion linearization technique is employed to transform the nonlinear radial basis function into a partially linear form, i.e.

~ ~ + BT ı ~ +h ĭa = AT m a a

(26)

ª ∂Φ ª ∂Φ 1 ∂Φ n º ∂Φ n º  where A = « 1  » |m =mˆ a , B = « » |ı =ıˆ a , h is a vector of higher∂m a ¼ ∂ı a ¼ ¬ ∂m a ¬ ∂ı a ~ = m* − m ~ = ı * − ıˆ , and ∂Φ k and ∂Φ k are defined as ˆa, ı order terms, m a a a a a ∂m ∂ı a a

a

T

ª º ª ∂Φ k º ∂Φ k ∂Φ k 0 0 0» « » = «0( k −1)×2 ( m − k )×2 m m m ∂ ∂ ∂ 1k 2k ¬ ¼ ¬ a¼

(27)

T

ª º ª ∂Φ k º ∂Φ k ∂Φ k 0 0 0» « » = «0( k −1)× 2 ( m − k )× 2 ∂ı 1k ∂ı lk ¬ ¼ ¬ ∂ı a ¼ Substituting (26) into (25), it is obtained that ~ ~T ˆ ~ T Aw ~ T Bw ˆa +ı ˆ a +ε f = w a ĭa + m a a

(28)

(29)

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~ =m ~ T Aw ~ =ı ~ T Bw ˆ Ta A T m ˆ a and w ˆ Ta B T ı ˆ a are used since they are scalars; and where w a a a a ~ T T *T * ~ ˆ h + w ĭ + w ĭ + ∆ and assume it is bounded by the uncertain term ε ≡ w a

a

a

i

i

0 ≤ ε ≤ E , where E is a positive constant representing the approximation error bound. However, it is difficult to measure this bound in practical applications. Thus, a bound estimation mechanism is developed to observe the bound of the approximation error. Define the estimation error of the bound ~ (30) E = E − Eˆ where Eˆ is the estimated error bound. 4.2 Fuzzy Rule Generation In general, the selection of the number of fuzzy rules is a trade-off between desired performance and computation loading. If the number of fuzzy rules is chosen too large, the computation loading is heavy so that they are not suitable for practical applications. If the number of fuzzy rules is chosen too small, the learning performance may be not good enough to achieve desired performance. To tackle this problem, the proposed SGFNN identifier consists of structure and parameter learning phases. The first step of the structure learning phase is to determine whether or not to add a new node (membership function) in layer 2 and the associated fuzzy rule in layer 3, respectively. In the rule generating process, the mathematical description of the existing rules can be represented as the membership degree of the incoming data to the cluster. Since one cluster formed in the input space corresponds to one potential fuzzy logic rule, the firing strength of a rule for each incoming data xi1 can be represented as the degree that the incoming data belong to the cluster. The firing strength obtained from (16) is used as the degree measure

β k = y k3 , k = 1, 2, ..., n( N )

(31)

where n(N ) is the number of the existing rules at the time N. According to the degree measure, the criterion of generating a new fuzzy rule for new incoming data is described as follows. Find the maximum degree β max defined as

β max = 1≤max βk k ≤n ( N )

(32)

It can be observed that if the maximum degree β max is smaller as the incoming data is far away the existing fuzzy rules. If β max ≤ β th is satisfied, where β th ∈ (0,1) a pregiven threshold, then a new membership function is generated. The mean and the standard deviation of the new membership function and the output action strength are selected as follows:

minew = xi1 , σ inew = σ i , wnew = 0

(33)

where xi is the new incoming data and σ i is a pre-specified constant. The number

n( N ) is incremented n( N + 1) = n( N ) + 1 .

(34)

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4.3 IBC Design The proposed intelligent backstepping control (IBC) system is shown in Fig. 2, which encompasses a neural backstepping controller unb and an robust compensation controller u rc . The design of IBC for the chaotic dynamic system is described step-bystep as follows: Step 1. Define the tracking error e1 as (2), a stabilizing function α as (4) and e2 as (5). Step 2. The control law of the IBC is developed in the following equation uic = u nb + u rc

(35)

where

u nb = xc − fˆ − c1e1 − c2 e2 − e1

(36)

u rc = − Eˆ sgn(e2 )

(37)

and sgn(.) is a sign function and fˆ is the output of SGFNN. Substituting (35) into (6), it can be obtained that

e2 = f − fˆ − c2 e2 − e1 + u rc . By substituting (29) into (38), equation (38) becomes ~ T Aw ~ Tĭ ~ T Bw ˆ +m ˆa +ı ˆ a + ε − c2 e2 − e1 + u rc e2 = w a a a a

(38)

(39)

Step 3. Define the Lyapunov function as ~ ~ Tm ~ ~Tw ~ ~T ı ~ m ı e2 e2 w E2 V2 = 1 + 2 + a a + a a + a a + (40) 2 2 2η1 2η 2 2η 3 2η 4 ~ where E = E − Eˆ ; and η1 , η 2 , η 3 and η 4 are positive constants. Differentiating (40) with respect to time and using (39), it is obtained that

~ ~ ~ Tm ~ ~Tw ~ ~T ı ~ w m ı EE V2 = e1e1 + e2 e2 + a a + a a + a a +

η1

η2

η3

η4

~ T Aw ~ Tĭ ~ T Bw ˆ +m ˆa +ı ˆ a + ε − c2 e2 − e1 + u rc ) + = e1 (e2 − c1e1 ) + e2 (w a a a a ~ ~  ~ Tm ~ ~Tw ~ ~T ı ~ w m ı EE a a + a a+ a a +

η1

η2

η3

~ T (e ĭ ˆ + = −c1e12 − c2 e12 + w a a 2 ~ T ( e Bw ˆa+ ı 2 a

~ ı

a

η3

η4

~ w a

η1

~ m ~ T (e Aw ˆ a + a )+ )+m a 2

) + e2 (ε + u rc ) +

η2

~ ~ EE

η4

(41)

If the adaptive laws of the SGFNN identifier and the approximation error bound are chosen as

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~ = η e ĭ ˆ = −w ˆ w a a 1 2 a

(42)

~ = η e Aw ˆ a = −m ˆa m a 2 2

(43)

~ = η e Bw ˆa ıˆ a = −ı a 3 2

(44)

~  Eˆ = − Ǽ = η 4 e 2

(45)

then (41) can be rewritten as ~ ~ EE 2 2  ˆ V2 = −c1e1 − c2 e1 + ε e2 − E e2 +

η4

= − c e − c e + ε e2 − E e2 2 1 1

2 2 1

≤ −c1e12 − c2 e12 − ( E − ε ) e2 ≤ −c1e12 − c2 e12 ≤ 0 .

(46) ~ ~ ~ ~ Similar to the discussion of (10), it can be concluded that w a , m a , ı a and E are bounded and e1 and e2 converge to zero as t → ∞ .

adaptive laws (42), (43), (44)

β th

ˆ , ıˆ ˆ , m w a a a

SGFNN identifier (24)

xc

neural backstepping u nb + controller (36)

+ c1

d/dt

α − + d/dt

uic +

robust compensation u rc controller (37)

−

+

rule generation (31), (32), (33)

fˆ

e1

−

n(N )

 Eˆ

e2

bound estimation algorithm (45)

intelligent backstepping control

Fig. 2. IBC for chaotic system

Chaotic system (1)

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5 Simulation Results The IBC system has been tested on the abovementioned chaotic system to track a desired periodic orbit. The control parameters are selected as c1 = c2 = 1 ,

η1 = η 2 = η 3 = 20 , η 4 = 0.1 , σ i = 1.0 , and β th = 0.5 . These parameters are chosen to achieve favorable transient control performance considering the requirement of asymptotic stability and the possible operating conditions. The simulation results of the IBC for q = 1.8 and q = 7.0 are shown in Figs. 3 and 4, respectively. These results show that the proposed IBC design method can achieve favorable tracking performance. The simulation results not only the perfect tracking responses can be achieved but also the concise fuzzy rule’s size can be obtained since the proposed selforganizing mechanism and the online learning algorithms are applied. The simulation results show that by using the self organizing mechanism and the online learning algorithm, a perfect tracking response can be achieved as well as reduced fuzzy rule base size can be obtained.

control effort, u

state, x

xc

x

time (sec) (c)

time (sec) (a) control effort, u

state, x

x

xc

time (sec) (c)

time (sec) (a)

rule number

state, x

x

xc

time (sec) (d)

time (sec) (b)

rule number

state, x

xc

x

time (sec) (b)

Fig. 3. Simulation results of IBC for q=1.8

time (sec) (d)

Fig. 4. Simulation results of IBC for q=7.0

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6 Conclusions In this paper, an intelligent backstepping control (IBC) system has been proposed for the chaotic system. The developed IBC system utilized a self-growing fuzzy neural network identifier to online estimate the chaotic dynamic function. The control law of the IBC system is synthesized using the Lyapunov function, so that the asymptotic stability of the control system can be guaranteed. Finally, simulation results verified that the proposed IBC system can achieve favorable tracking performance of the nonlinear chaotic systems.

Acknowledgment The authors appreciate the partial financial support from the National Science Council of Republic of China under grant NSC-90-2213-E-155-016.

References 1. Lin, C.T., Lee, C.S.G.: Neural Fuzzy Systems: A Neuro-Fuzzy Synergism to Intelligent Systems, Englewood Cliffs, NJ: Pretice-Hall (1996) 2. Juang, C.F., Lin, C.T.: An On-line Self-constructing Neural Fuzzy Inference Network and its Applications. IEEE Trans. Fuzzy Syst., (1998) 12-32 3. Li, C., Lee, C.Y., Cheng, K.H.: Pseudo-error-based Self-organizing Neuro-fuzzy System. IEEE. Trans. Fuzzy Syst., (2004) 812-819 4. Lin, C.T., Cheng, W.C., Liang, S.F.: An on-line ICA-mixture-model-based Selfconstructing Fuzzy Neural Network. IEEE Trans. Circuits Syst., (2005) 207-221 5. Jiang, Z.P.: Advanced Feedback Control of the Chaotic Duffing Equation. IEEE Trans. Circuits Syst., (2002) 244-249 6. Yassen, M.T.: Chaos Control of Chen Chaotic Dynamical System. Chaos, Solitons & Fractals, (2003) 271-283 7. Wang, J., Qiao, G.D., Deng, B.: H ∞ Variable Universe Adaptive Fuzzy Control for Chaotic System. Chaos, Solitons & Fractals, (2005) 1075-1086 8. Ji, J.C., Hansen, C.H.: Stability and Dynamics of a Controlled Van Der Pol-Duffing Oscillator. Chaos, Solitons & Fractals, (2006) 555-570 9. Slotine, J.E., Li, W.: Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, New Jersey (1991) 10. Wang. L.X.: Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Englewood Cliffs, NJ: Prentice-Hall (1994)

Modeling of Rainfall-Runoff Relationship at the Semi-arid Small Catchments Using Artificial Neural Networks Mustafa Tombul1 and Ersin O÷ul2 1

Anadolu University Engineering Faculty of Civil Engineering Department, Eskiúehir/Turkey 2 III.Regional Directorate of State Hydraulic Work, Eskiúehir /Turkey [email protected], [email protected]

Abstract. The artificial neural networks (ANNs) have been applied to various hydrologic problems in recently. In this paper, the artificial neural network (ANN) model is employed in the application of rainfall-runoff process on a semi-arid catchment, namely the Kurukavak catchment. The Kurukavak catchment, a sub-basin of the Sakarya basin in NW Turkey, has a drainage area of 4.25 km2. The performance of the developed neural network based model was compared with multiple linear regression based model using the same observed data. It was found that the neural network model consistently gives good predictions. The conclusion is drawn that the ANN model can be used for prediction of flow for small semi-arid catchments.

1 Introduction Modeling of a rainfall-runoff process of a watershed is important in water resources management and design activities such as flood control and management, and design of various hydraulic structures in a watershed, etc. Traditional hydrologic models that are based on mathematical representation of watershed processes have been applied to stream flow predictions. These models typically require a significant effort of data collection including rainfall, stream-flow, and watershed characteristics. Additional efforts are needed for assessing model parameters, and performing model calibration and verification. Hydrologic models devoted to stream-flow predictions range from hourly to daily forecast of stream/flood flows [1, 2 3] The ANN models have been used increasingly in various aspects of science and engineering because of its ability to model both linear and nonlinear systems without the need to make any assumptions as are implicit in most traditional statistical approaches. In some of the hydrologic problems, ANNs have already been successfully used for river flow prediction [4], for rainfall-runoff process [5, 6]. Current research on ANN-hydrologic applications ranges from the predictions of peak discharge and time to peak from a single rainfall event, to the forecast of hourly or daily river stages or discharges [7, 8, 9, 10, 11, 12, 13, 14]. In the hydrological forecasting studies many experiments reported that ANNs may offer a promising D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 309 – 318, 2006. © Springer-Verlag Berlin Heidelberg 2006

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alternative for rainfall–runoff modeling [5, 2, 15, 16, 17, 18, 19, 20, 21, 10, 22, 23, 24, 25, 26]. The ANN models are powerful prediction tools for the relation between rainfall and runoff parameters. The results will support decision making in the area of water resources planning and management. In these hydrological applications, a feedforward back propagation algorithm is used [27]. The aim of this paper is to model the rainfall-runoff relationship in the semiarid small catchment (Kurukavak) located in Turkey using a black box type model based on ANN methodology.

2 The Study Catchment The Kurukavak catchment, a sub-basin of the Sakarya basin in north-west Turkey, has a drainage area of 4.25 km2 and ranges in altitude from 830 m to1070 m. The basin is equipped with three rain gauges (R1, R2 and R3) and one runoff recording station (H1) (Fig. 1). The Rainfall and Runoff daily data at the average of (R1, R2 and R3) stations were used for model investigation. The data contains information for a period of four years (1988 to 1991). The entire database is represented by 1460 daily values of rainfall and runoff pairs. The ANN model was trained using the resulting runoff and rainfall daily data. The database was collected by the Services of Rural Investigation Instute.

Fig. 1. Location of Kurukavak catchment in Turkey

3 The Structure of the ANN Artificial neural networks employ mathematical simulation of biological nervous systems in order to process acquired information and derive predictive outputs after the network has been properly trained for pattern recognition. The main theme of ANN research focuses on modeling of the brain as a parallel computational device for various computational tasks that were performed poorly by traditional serial computers.

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The neural network structure in this study possessed a three-layer learning network consisting of an input layer, a hidden layer and an output layer consisting of output variable(s) (Fig. 2). The input nodes pass on the input signal values to the nodes in the hidden layer unprocessed. The values are distributed to all the nodes in the hidden layer depending on the connection weights Wij and Wjk [28-29] between the input node and the hidden nodes. Connection weights are the interconnecting links between the neurons in successive layers. Each neuron in a certain layer is connected to every single neuron in the next layer by links having an appropriate and an adjustable connection weight.

Fig. 2. Architecture of the neural network model used in this study

In this study, the FFBP were trained using Levenberg–Marquardt optimization technique. This optimization technique is more powerful than the conventional gradient descent techniques [30]. The study [31] showed that the Marquardt algorithm is very efficient when training networks which have up to a few hundred weights. Although the computational requirements are much higher each iteration of the Marquardt algorithm, this is more than made up for by the increased efficiency. This is especially true when high precision is required. The Feed Forward Back Propagation (FFBP) distinguishes itself by the presence of one or more hidden layers, whose computation nodes are correspondingly called hidden neurons of hidden units. The function of hidden neurons is to intervene between the external input and the network output in some useful manner.

4 Method Application of ANN in Rainfall-Runoff Modeling The runoff at watershed outlet is related not only to the current rainfall rate, but also to the past rainfall and runoff situations because of its certain storage capacity. For a discrete lumped hydrological system, the rainfall-runoff relationship can be generally expressed as [32, 5]

[

Q(t ) = F R(t ), R(t − ∆t ),..., R(t − n x ∆t ), Q(t − ∆t ),...Q(t − n y ∆t )

]

(1)

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where R represents rainfall, Q represents runoff at the outlet of the watershed, F is any kind of model structure (linear or nonlinear), ∆t is the data sampling interval, and nx and ny are positive integers numbers reflecting the memory length of the watershed. In this study the Simplex search method is used to find a set of optimum values for those weights used in the ANN, which are denoted by w

by w

opt jk

opt ij

, 0 ≤ i ≤ n , 1 ≤ j ≤ l and

, 0 ≤ j ≤ l , 1 ≤ k ≤ l , 0 ≤ j ≤ l , 1 ≤ k ≤ m . The estimated runoffs, denoted by

Qˆ (t ) , are determined as a function of those optimum weights of the ANN, which is expressed as

[

Q(t ) = F R(t), R(t − ∆t),...,R(t − n x ∆t), Q(t − ∆t ),...Q(t − n y ∆t) woptij ,wopt kj

]

(2)

When the ANN is implemented to approximate the above relationship between the watershed average rainfall and runoff, there will be a number of n =n x +n y +1

nodes in the input layer, n =n x +n y +1 , while there is only one node in the output, i.e. m=1. The database collected represents four years daily sets of rainfall-runoff values for the Kurukavak basin. In this paper, we used the data for the last year (1991) for model testing, while the other remaining data (1988 to 1990) was used for model training/calibration. The training phase of ANN model was terminated when the mean squared error (RMSE) on the testing databases was minimal. The flow estimation simulations were carried out in two steps. First, only rainfall data was employed for the input layer. Then previous daily flow value was also incorporated into the input data group. They [17], indicated that a noticeable improvement in estimation performance was obtained with the incorporation of flow value into the input layer. In this present, then the flow at the precedent day (Q ) was also added to t-1 the input layer in order to increase the estimation performance.

5 Evaluation Measures the Model Performance The results of the network model (FFBP) applied in the study were evaluated for their performance by estimating the following standard global statistical measures. The statistical criteria consist of root mean squared of error (RMSE), coefficient of determination (R2) and the index of volumetric fit (IVF). They RMSE and (R2) is knowledge very well everybody. Also the index of volumetric fit (IVF)are defined as N ¦ Q sim,i i IVF = =1 N ¦ Qobs,i i =1

(3)

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where

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Q obs ,i and Q sim,i are respectively, the actual and predicted value of flow

(normalized between 0 and 1). The coefficient of determination (R2) statistic measures the linear correlation between the actual and predicted flows values. The coefficient of determination is often used to measure the performance of a hydrological model. The value is in the range of [-∞, 1]. The zero value means the model performs equal to a naive prediction, that is, a prediction using an average observed value. The value less than zero means the model performs worse than the average observed value. A value between 0.6-0.8 is moderate to good. A value more than 0.8 is a good fit. A value of one is a perfect fit. The RMSE was used to measure the agreement between the observed and simulated water balance. The closer the RMSE value is to zero, the better the performance of the model. The another index emplyoed to assess the model performance is the simple index of volumetrik fit (IVF), which is expressed as the ratio of simulated run off volume to the correspondind observed one. A value of for IVF one is a perfect fit.

6 Results and Discussions The goal of the training process is to reach an optimal solution based on some performance measurements such as RMSE, coefficient of determination known as Rsquare value (R2), and the IVF. Therefore, required ANN model was developed in two phases: training (calibration) phase, and testing (generalization or validation) phase. In the training phase, a larger part for database (three years) was used to train the network and the remaining part of the database (one year) is used in the testing phase. Testing sets are usually used to select the best performing network model. In this research, the ANN was optimal at 50 iterations with 4 hidden nodes. The corresponding accuracy measures of this network model on testing and training data are given in the following table (Table 1). Generally, accuracy measures on training data are better than those on testing data. Table 1. Statistical parameter and accuracy measures of this network model at training and testing phases

Training Phases Testing Phases

RMSE 0.021 0.072

R2 0.75 0.726

IVF 1.02 1.03

The comparison between the predicted and actual flow values at training and testing phases show good agreement with the R2 are respectively 0,75 and 0,726 (Figure 3a, 4a). As regards to the volumetric fit, the value of the IVF is 1.02 in the calibration period and 1.03 in the verification period. From these results, there is no

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doubt the ANN model is very successful in simulating the non-linear rainfall-runoff relationship on the Kurukavak catchment. Root mean square error (RMSE) value for the training and testing period was considered for performance evaluation and all testing stage estimates were plotted in the form of hydrograph (Figure 3b, 4b).

Training phase

3

Actual flow (m /s)

0.4 0.3 0.2 0.1

R2 = 0.75

0.0 0.0 0.1 0.1 0.2 0.2 0.3 0.3 0.4 0.4 0.5 3

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Fig. 3a. Comparision between the actual and ANN predicted flow values for traning phase

Flow (m3/s)

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0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0

100

200

300

400

500

600

700

800

900 1000 1100 1200

Time (day)

Fig. 3b. Comparision between the actual and ANN Predicted flow values for traning phase

Also the statistical parameters of the predicted and actual values of flow for the entire database are practically identical (Table 2). In order to evaluate the performance of the ANN, the multiple linear regression (MLR) technique was applied with the same data sets used in the ANN model. Figure 5 shows the comparative results obtained by MLR technique. The R2 values for MLR and ANN models are presented in Table 3. Apparently, the ANN approach gives much better prediction than the traditional method (MLR).

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Actual flow (m3/s)

Testing phase 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0

R2 = 0.7263 0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

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Fig. 4a. Comparision between the actual and ANN predicted flow values for testing phase

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Daily mean flow (m3 /s)

1.6

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1.4 1.2 1 0.8 0.6 0.4 0.2 0 0

100

200

300

400

Time (day)

Fig. 4b. Comparision between the actual and ANN predicted flow values for testing phase Table 2. Statistical parameter of the predictetd and actual flow at training and testing phases Training phases

Testing phases

Minimum

Actual Flow(m3/s) 0

Predicted Flow(m3/s) 0

Actual Flow(m3/s) 1E-5

Predicted Flow(m3/s) 0

Maximum

0.42157

0.4099

1.4817

1.3880

Mean Standart of Deviation Coefficient of Variation

0.0152 0.0419 2.75

0.0157 0.0371 2.36

0.0267 0.1379 5.07

0.0273 0.1200 4.44

Statistical parameter

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0.75 0.72

0.66 0.60

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1,6

1,6

1,4

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1,2 1 0,8 0,6 0,4

1,2 1 0,8 0,6 0,4 0,2

0,2

2

R = 0.6598 0 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Predicted flow (m3/s) (a)

R2 = 0,6028

0 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6

Predicted flow (m3/s) (b)

Fig. 5. Comparisionof correlation coefficients between actual and predicted flow ANN and MLR models.(a) Training phase (b) Testing phase

7 Conclusion In this study, the results obtained show clearly that the artificial neural networks are capable of model rainfall-runoff relationship in the small semi-arid catchments in which the rainfall and runoff are very irregular, thus, confirming the general enhancement achieved by using neural networks in many other hydrological fields. The results and comparative study indicate that the artificial neural network method is more suitable to prediction of for runoff flow small semi-arid catchments than classical regression model. The ANN approach could provide a very useful and accurate tool to solve problems in water resources studies and management.

References 1. Bertoni, J. C., Tucci, C. E., Clarke, R. T.: Rainfall-based Real-time Flood Forecasting. J. Hydrol., 131 (1992) 313–339 2. Shamseldin, A. Y.: Application of Neural Network Technique to Rainfall-runoff Modeling. J. Hydrol. 199 (1997) 272-294

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3. Rajurkar, M. P., Chaube, U. C.: 2002: Artificial Neural Networks for Daily Rainfall-runoff 4. Modeling. Hydrol. Sci. J., 478 (6)(2002) 865–877 5. Riad, S. J., Mania, L., Bouchaou, Y. Najjar.: Predicting Catchment Flow in Semi Arid Region via Artificial Neural Network Technique. Hydrological Process, 18 (2004) 2387-2393 6. Hsu, K. L., Gupta, H. V., Sorooshian, S.: Artificial Neural Network Modeling of the Rainfallrain of Process. Water Resour. Res, 31 (10) (1995)2517–2530 7. Chang, F. J., Suen, J. P.: A Study of the Artificial Neural Network for Rainfall-runoff process. Journal of Chinese Agricultural Engineering (In Chinese), 43 (1) (1997) 9-25 8. Smith, J., Eli, R. N.: Neural-network Models of Rainfallrunoff Process. J. Water Resour. Plan. Manage, 121 (6)(1995) 499–508 9. Thirumalaiah, K., Deo, M. C.: River Stage Forecasting Using Artificial Neural Networks. J. Hydrologic Eng, 3 (1) (1998) 26-31 10. Thirumalaiah, K., Deo, M. C.: Hydrological Forecasting Using Artificial Neural Networks. Hydrologic Eng, 5 (2) (2000) 180-189 11. Campolo, M., Andreussi, P., Soldati, A.: A River Flood Forecasting with a Neural Network Model. Water Resour. Res, 35 (4) (1999) 1191–1197 12. Imrie, C. E., Durucan, S., Korre, A.: River Flow Prediction Using Artificial Neural Networks: Generalization Beyond the Calibration Range. J. Hydrol, 233 (2000) 138-153 13. Liong, S. Y., Lim, W., Paudyal, G. N.: River Stage Forecasting in Bangladesh: Neural Network Approach. J. Comput. Civ. Eng, 14 (1) (2000) 1-18 14. 13.Tokar, A. S., Markus, M.: Precipitation-runoff Modeling Using Artificial Neuralnetworks and Conceptual Models. J. Hydrologic Eng, 5 (2) (2000) 156–161 15. Kim, G. S., Borros, A. P.: Quantitative Flood Forecasting Using Multisensor Data and Neural Networks. J. Hydrol., 246 (2001) 45–62 16. Sajikumar, N., Thandaveswara, B. S.: ANon-linear Rainfall–runoff Model Using an Artificial Neural Network. J. Hydrol., 216 (1999)32–55 17. Tokar, A. S., Johnson, P. A.: Rainfall–runoff Modeling Using Artificial Neural Networks. J.Hydrol. Eng., ASCE, 4(3)(1999)232–239 18. Cigizoglu, H. K, Alp, M.: Rainfall-Runoff Modeling Using Three Neural Network Methods. Artificial Intelligence and Soft Computing- ICAISC 2004, Lecture Notes in Artificial Intelligence, 3070 (2004) 166-171 19. Anctil, F., Perrin, C., Andreassian, V.: Impact of the Length of Observed Records on the Performance of ANN and of Conceptual Parsimonious Rainfall-runoff Forecasting Models. Environ.Modell.Software, 19 (2004) 357-368 20. Freiwan, M., Cigizoglu, H. K.: Prediction of Total Monthly Rainfall in Jordan using Feed Forward Backpropagation Method. Fresenius Environmental Bulletin, 14 (2) (2005) 142-151 21. Thirumalaiah, K., D., M. C.: Real-time Flood Forecasting Using Neural Networks. Computer-Aided Civil Infrastruct. Engng, 13 (2) (1998)101–111 22. Zealand, C. M., Burn, D. H., Simonovic, S. P.: Short term Streamflow Forecasting Using Artificial Neural Networks. J. Hydrol., 214 (1999) 32–48 23. Salas, J. D., Markus, M., Tokar, A. S.: Streamflow Forecasting Based on Artificial Neural Networks. In: Artificial Neural Networks in Hydrology, Govindaraju, R. S. and Rao, A. R. (eds.), Kluwer Academic Publishers, (2000) 24. Sivakumar, B., Jayawardena, A. W., Fernando, T. M. K. G.: River Flow Forecasting: use of Phase Space Recostruction and Artificial Neural Networks Approaches. J.of Hydrology, 265 (2002) 225-245

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25. Cigizoglu, H. K.: Estimation, Forecasting and Extrapolation of Flow Data by Artificial Neural Networks. Hydrological Sciences Journal, 48 (3) (2003) 349-361 26. Cigizoglu, H. K.: Corporation of ARMA Models into Flow Forecasting by Artificial Neural Networks. Environmetrics, 14 (4) (2003) 417-427 27. Kisi, O.: River Flow Modeling Using Artificial Neural Networks. ASCE J. of Hydrologic Engineering, 9 (1) (2004) 60-63 28. Lippmann, R. P.: An Introduction to Computing With Neural Nets. IEEE ASSP Magazine, (1987)4-22 29. Najjar, Y., Ali, H.: On the Use of BPNN in Liquefaction Potential Assessment Tasks. In Artificial Intelligence and Mathematical Methods in Pavement and Geomechanical Systems, (Edited by Attoh-Okine), (1998) 55-63 30. Najjar, Y., Zhang, X.: Characterizing the 3D Stress-strain Behavior of Sandy Soils: A Neuro-mechanistic Approach. In ASCE Geotechnical Special Publication Number 96, (Edited by G. Filz and D. Griffiths), (2000) 43-57 31. Cigizoglu, H. K., Kiúi, O.: Flow Prediction by Two Back Propagation Techniques Using k-fold Partitioning of Neural Network Training Data, Nordic Hydrology, (in press), (2005) 32. Hagan, M. T., Menhaj, M. B.: Training feedforward techniques with the Marquardt algorithm. IEEE Transactions on Neural Networks, 5 (6)(1994) 989-993 33. Chow, V. T., Maidment, D. R., Mays, L. W.: Applied Hydrology. McGraw-Hill, Inc., NY, (19

A Novel Multi-agent Based Complex Process Control System and Its Application Yi-Nan Guo, Jian Cheng, Dun-wei Gong, and Jian-hua Zhang College of Information and Electronic Engineering, China University of Mining and Technology, Xuzhou, 221008 Jiangsu,China [email protected]

Abstract. ComplH[ process control systems need a hybrid control mode, which combines hierarchical structure with decentralized control units. Autonomy of agents and cooperation capability between agents in multi-agent system provide basis for realization of the hybrid control mode. A novel multi-agent based complex process control system is proposed. Semantic representation of a control-agent is presented utilizing agent-oriented programming. A novel temporal logic analysis of a control-agent is proposed using Petri nets. Collaboration relationships among control-agents are analyzed based on extended contract net protocol aiming at the lack of reference[1].Taken pressure control of recycled gas with complicated disturbances as an application, five kinds of control-agents are derived from control-agent. Reachable marking tree and different transition of each derived control-agent are analyzed in detail. Actual running effect indicates multi-agent based hybrid control mode is rationality and flexible. Temporal logic analysis based on Petri nets ensures the reachability of the systems. Extended contract net protocol provides a reasonable realization for collaboration relationships.

1 Introduction Industry processes increasingly become larger and more complex. It is difficult to control them only by single controller based on traditional control theories. And complex process control systems require more flexibility, opening and reconfiguration. Aiming at solving above problems, new theories are urgently needed. Multi-agent systems (MAS) show strong adaptability in analyzing and designing complex process control systems because of their autonomy and opening [2]. So it has important meanings to apply MAS to design of complex process control systems. Up to now, many control architectures have been presented aiming at complex processes. They are generally divided into three kinds including centralized control, hierarchical control and decentralized control. Centralized control is unreliable and inflexible because information about all of controllers is supervised by one supervision unit[3]. And when a control problem is decomposed, connective relationships among controllers are more complicated as the number of partial controllers is more. In order to solve above difficulties, hierarchical control was proposed in which the functions of supervision are divided vertically. It has applied to D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 319 – 330, 2006. © Springer-Verlag Berlin Heidelberg 2006

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analyze complex processes widely. But horizontal division of bottom control functions was not included. Although decentralized control is horizontally distributed, it lacks cooperation between control units which always leads to sub-optimum [4]. It is obvious that the architecture, which combines hierarchical structure with decentralized control units, is reasonable. But there is a lake of appropriate control theories for analysis of above control mode. Multi-agent system consists of multiple autonomous agents by some cooperation mechanism. Each agent can implement tasks independently. Through cooperation and interaction among agents, MAS can accomplish complex tasks and their optimization. It is obvious that MAS provides the foundation for realizing above control mode. Up to now, MAS have been adopted to analysis of complex process control systems by many researchers. Hybrid control systems based on multiple agents were proposed [5]-[6]. Breemen utilized decompose-conquer strategy of MAS to decompose a complex problem to many sub-problems. Each sub-problem was solved by an agent. And the whole task was accomplished by cooperation among agents [7]-[10]. It provides design foundation and common framework for complex process control systems. But there is lake of semantic representation of agents and temporal logic analysis and implementation of their collaboration relationships based on agentoriented programming. Thereby a novel multi-agent based complex process control system is put forward in the paper. It makes the best of autonomy of agent and cooperation capability among agents to realize complex processes control which makes systems flexible and opening. In the rest of the paper, the kernel of control-agents and the collaboration strategies between them are proposed in Section2.To validate rationality of the systems, they are applied to pressure control system of recycled gas in Section3.At last, future work planned to extend the cooperation strategies is included.

2 Multi-agent Based Complex Process Control Systems Multi-agent based complex process control systems adopt a hybrid control mode, which combines hierarchical structure with decentralized control units. How to decompose control functions, realize each control unit and cooperate among control units are key problems. Aiming at above problems, decompose-conquer strategy, agent-oriented programming, Petri Nets (PNs) and contract net protocol are introduced. Decompose-conquer strategy is adopted to simplify the design of complex process control systems. In the strategy, division and integration are two key problems. Division is how to separate a complex process control problem into a group of control sub-problems according to the requirement of control. Each control sub-problem is solved by an agent, called control-agent. Integration is how to synthesize the solutions of sub-problems effectively. A division method has presented by Breemen[1]. In this paper, we emphasize particularly on semantic representation of control-agents adopting agent-oriented programming and temporal logic analysis of their cooperation relationships utilizing contract net protocol.

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2.1 Structure of Control-Agent All of control-agents have same structure and basic functions. So the normal kernel of control-agents, which is called base class of control-agents, is abstracted and described using agent-oriented programming as follows [11]. ::=< function FD> ::=<structure description SD> <environment description ED> ::=<symbol > ::=<waiting> <ED>::= ::= ::=<waiting> <Sa>::=<waiting> <SD>::=<parameters P> ::=<state control SCF> ::=< local controller F> <SCF>::=<state transfer function A> <parameter preservation function PIF> <parameter activation function PAF> ::=<message management><state supervision> Aiming at different control sub-problems, different instances of control-agent are derived from CControlagent. Output variables are sent to actuators as control signal. Communication variables are provided for other control-agents as interaction data. They are computed by controller according to input variables from sensors, formulized by [OUT CD ]T = F(IN, t ) . Different control-agents maybe have different F. Control-agents have three kinds of inner states which can be switched each other. OUT and COM of a control-agent are valid only when its inner state is activation. If AD is waiting, it indicates control-agent waits to be activated and has activation intention. Transfer of such inner states are controlled by SCF, which includes three kinds of A = {activation → inactivation, inactivation → waiting, waiting → activation} .Different control-agents have different transfer condition of SCF. To facilitate the analysis of above inner states and transfer relationships, PNs is utilized, which have been widely used to model, analyze and synthesize control laws for DES and MAS. A PN is a four-tuple N = ( P, T , F , m0 ) , where P is a finite set of places, T is a finite set of transitions, F (P × T ) (T × P) is a set of transition arcs, m0 : P Z is the initial marking with Z as the set of nonnegative integers[12]-[13]. In the paper, a PN denotes a control-agent where T={A,ICF,OCF} and P={AD,Ca,Sa}. Ca is input collaboration signal offered by other control-agents. Sa is output collaboration signal sent to other control-agents. The PN of a control-agent is illustrated in Fig.1. P1 , P2 and P3 denote AD,Ca and Sa respectively. Each place have

㸢

㼁

㺥

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three states corresponding to three kinds of states of AD, Ca or Sa, such as P1 , P1' , P1'' denote inactivation, waiting, activation respectively. Assuming inactivation=0, waiting=1, activation =2. The initial state of PN is m0 = [0 0 0] .

Fig. 1. State transfer of an agent described by PNs

From Fig.1, we can see a control-agent can control activation intention autonomously, but whether it is activated is determined by Ca. That is, a control-agent is activated only when activation intention and collaboration relationship are satisfied. And whether Sa is activated is controlled by inner states. Only when AD=activation, output collaboration signal to other control-agents is activated. 2.2 Collaboration Relationships Among Control-Agents Based on Contract Net Protocol Collaboration relationships among control-agents reflect coupling relationships among sub-problems with the restriction of execution time and compute resources. According to the characteristics of complex processes and share relationships of resources, coupling relationships among sub-problems can be divided into three kinds: independence, sequence and competition. Corresponding collaboration relationships among control-agents consist of parallel, sequence and prior-based competition [9]. But temporal logic analysis and implement method of above relationships were not given in [9]. So contract net protocol is utilized to analyze distributed control and autonomous cooperation among control-agents in the paper. Contract net protocol is a distributed negotiation mechanism based on a marketlike protocol [13]. In it, there are two types of roles: manager and bidder. A manager provides a task to be accomplished. A bidder implements a task according to the contract between it and the manager. In multi-agent based complex process control system, a control-agent can act as a manager or a bidder in different circumstances which is determined by above collaboration relationships. To facilitate the analysis and check the feasibility of such protocol, PNs is adopted. Suppose a PN denotes a control-agent. So above collaboration relationships can be mapped into relationships between PNs, as shown in Fig.2. PRIi is the prior of i th control-agent. It is obvious that there is no interaction about information between two control-agents in parallel. In other circumstances, Ca of PN2 is related to Sa of PN1 . In Fig.2(b), Ca of PN2 is activated after Sa of PN1 is activated. It indicates controlagents are executed orderly. However, only when Sa of PN1 is inactivated, Ca of PN2

A Novel Multi-agent Based Complex Process Control System and Its Application

(a)parallel

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(b)sequence

(c)prior-based competition( PRI1> PRI 2 ) Fig. 2. Collaboration relationships described by PNs

can be activated in Fig.2(c). It shows control-agents can not possess the same resources at the same time. Based on above collaboration relationships, contract net protocol is extended, as shown in Fig.3. Assuming a set of PNs is NS = {N1 , N 2 , N K } where K is size of NS.

(a) phase1

(b) phase2 Fig. 3. Extended contract net protocol

Extended contract net protocol includes two phase. Each phase contain a traditional establishment of a contract, including four steps: (1)Notification for bidding sent by managers: the manager announces a task to all bidders. (2)Decision-making by bidders: bidders determine whether they can perform the task. (3)Selection of contractor by managers: the manager chooses cooperative bidder. (4)Establishment of contract[3],[13]. Phase1: A task for a control sub-problem is announced to all control-agents. Assuming control− agent1 establishes a contract and perform its control strategies, as shown in Fig.3(a). Here, control− agent1 acts as a bidder.

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Phase2: When production circumstances vary, control− agent1 acts as a manager to establish a new contract. For example, control− agent2 establishes a new contract with control− agent1 ,as shown in Fig.3(b).In this phase, contracts reflect collaboration relationships between control-agents. And in different steps of establishment of a contract, states of Ca and Sa in each PN is different. Taken N1 , N 2 in Fig.3(b) as an example, temporal logic is discussed. We know collaboration relationship between them is sequence. Letting mij denotes the marking of N j in i th step. Assuming inactivation=0, waiting=1, activation =2. m11 = [2 2 1] ∩ m12 = [0 1 0] when N1 sends a task. If N 2 is capable of performing the task, m22 = [1 1 0] . After N1 selects N 2 as

a contractor, m31 = [1 1 1] . At last, while a contract is established, m42 = [1 1 1] . Through two phases, control-agents compose of a hierarchical structure which includes two layers: control-agents which act as managers make up the high layer and the low layer contains control-agents which act as bidders. It is obvious that this structure is dynamic. In extended contract net protocol, as some control-agents which act as bidders are added or deleted, other control-agents in the systems still work normally. This avoids the difficulty in centralized control mode. In conclusion, multi-agent based complex process control systems work with an opening and distributed collaboration mode. It makes the best of autonomy of agent and cooperation capability among agents to integrate hierarchical control and decentralized control which makes systems flexible.

3 Multi-agent Based Pressure Control System of Recycled Gas Recycled gas is the main fuel to provide energy for production of coke in coke plant. The stability of pressure of recycled gas directly influences the stability of inner temperature of coke oven, which affects the quality of coke and the quantity of gas. So pressure control of recycled gas is vital. The pressure of recycled gas is influenced by many disturbances. And pressure control system emphasizes particularly on different control performance in different circumstances. So it is difficult to satisfy all performances only using single controller. Therefore multi-agent based pressure control system of recycled gas is put forward based on above hybrid control mode. 3.1. Analysis of Disturbances

There are four kinds of disturbances which mainly influence the pressure of recycled gas[14]. Disturbances1: Periodical disturbance is caused by switching processes in current coke oven. The period of disturbance Tc=20min and each disturbance stays 45s. Recycled gas is provided to coke oven in two directions periodically so as to sufficient combustion and exhaust waste gas. Two directions include machine-side and coke-side. They are switched automatically every 20 minute, as shown in Fig.4. Because valve for recycled gas is closed for a short time in a switch process, pressure

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Fig. 4. Switching process

of recycled gas varies to maximum and stays during the switching process. And the fluctuation of pressure ǻp [1500,4500] Pa. This causes large ǻp as a switching process finishes. Disturbances2: Periodical disturbance is caused by switching processes in adjacent coke ovens. | ǻp | [200,800] Pa and period Ta=20min.Recycled gas is transmitted to different coke oven by gas pipes. Because gas pipes are connected in parallel, periodical switching processes in adjacent coke ovens result in coupling disturbance. Note Disturbances1 and Disturbances2 do not happen at the same time. Disturbances3: Random disturbance is caused by the change of quantity of gas for export and heating boiler. And | ǻp | [20,200] Pa. Disturbances4: Random fluctuation of pressure is caused by the hydrocharacteristic of gas. And | ǻp | [0,20] Pa. In a word, the fluctuation of pressure caused by different disturbances are different. And Disturbances1 leads to the largest ǻp , so it is the main disturbance.

㺃

㺃

㺃

㺃

3.2 Decomposition of Pressure Control System and Analysis of Control Strategies Based on Control-Agents

Control objectives of pressure control system of recycled gas are different in different circumstances. First, the fluctuation of pressure caused by periodical switching processes must be restrained as soon as possible. Second, control precision of pressure control system is restrained from +10Pa to -10Pa. Considering above disturbances and control objectives, pressure control of recycled gas is divided into periodical control sub-problems and regulation control sub-problems. Periodical control sub-problems restrain periodical disturbance as soon as possible. According to the source of periodical disturbances, periodical control of current coke oven and periodical control of adjacent coke oven are included. Regulation control sub-problems realize accurate control of pressure. According to the range of pressure fluctuation, large fluctuation control for Disturbances3 and small fluctuation control for Disturbances4 are obtained. In addition, because reference pressure of recycled gas is varied along with the production of different quality of coke, reference-setting sub-problem is used to set reference pressure. And four control sub-problems essentially make pressure changing with reference pressure in time.

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Each sub-problem is realized by an instance of control-agent. Based on above decomposition, RPagent for reference-setting sub-problem and PCCagent, PCAagent, LFRagent and SFRagent for four control sub-problems are derived from CControlagent. Different derived control-agents have different control strategies and transfer conditions for inner states. But reachable marking tree of PN RMT(PN) is same, as shown in Fig.5.

Fig. 5. Reachable marking tree of PN of control-agent

PCCagent. It restrains pressure fluctuation caused by periodical switching processes in current coke oven. Assuming p is pressure of recycled gas. t is the current time.Letting tcb = {t | t + K • Tc , K N +} and tca = {t | tcb + 45}denote the initiative time and the end time of a switching process in current coke oven respectively. Letting pcb = p |t =tcb and pcb = p |t =tca .In a switching process, pcb = pca and p = pmax |t㺃(tcb ,tca ) are satisfied.

㺃

To avoid overshoot caused by excess regulation, FPCC := [out= 0] is adopted. During a switching process, PCCagent is activated. So when transition t1 := [t = tcb ] in PN of PCCagent is satisfied, the marking changes from m0 = [0 0 0] to m1 = [1 0 0] . When transition t3 := [t = tca ] is satisfied, the marking changes from m5 = [2 0 0] to m10 = [0 0 0] . PCAagent. Control objective of PCAagent is to restrain large pressure fluctuation caused by periodical switching processes in adjacent coke ovens and other disturbances as soon as possible where | ǻp | [200,800] Pa. Letting tab = {t | t + K • Ta } and taa = {t | tab + 45} denote the initiative time and the end time of a switching process in adjacent coke ovens respectively. Assuming e is the error between reference pressure and actual pressure. PD control is adopted so as to restrain error and its increasing tendency quickly, formalized by FPCA := [out = KPPCA[e(k) - e(k -1)] + KDPCA[e(k) - e(k -1) + e(k - 2)]]. Letting epl and eph denote the minimum and maximum of absolute value of error ep =| e | . When transition t1 := [(t = tab ) (ep (eplPCA, ephPCA])]is satisfied, PCAagent has activation intention. The marking changes from m5 = [2 0 0] to m10 = [0 0 0] when transition t3 := [(t = taa ) (ep eplPCA) (ep > ephPCA])] is satisfied. LFRagent. It restrains frequent pressure fluctuation with high control precision and short transition time. Therefore PID control is adopted, described by

㺃

㺥 㺃

㺥 İ 㺥

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FLFR := [out = K PLFR [e (k ) - e (k - 1)] + K ILFR e (k ) + K DLFR [e (k ) - 2e (k - 1) + e (k - 2 )]]

㺃

LFR l

t1 := [ep (ep

LFR h

, ep

LFR h

] | ep

. When transition ep ] is satisfied, the marking changes from m0 = [0 0 0]

İ

PCA l

to m1 = [1 0 0] . SFRagent. Considering the sensitivity and life-span of actuators, the aim of SFRagent is to stabilize pressure within the range satisfied control precision and simultaneously decreasing the running times of actuators. So FSFR := [out = 0] is adopted. SFRagent has activation intention when transition t1 := [ep [eplSFR , ephSFR ] | ephSFR eplLFR ] is satisfied.

㺃

İ

3.3 Analysis of Collaboration Relationships Based on Contract Net Protocol

Because control sub-problems regulate pressure of recycled gas according to reference pressure given by RPagent, collaboration relationship between RPagent and other control-agents is sequence. Outputs of four control sub-problems share one actuator. So among PCCagent, PCAagent, LFRagent and SFRagent, only one can be activated in a control period. Collaboration relationship among them is competition. Because periodical disturbances have larger influences on pressure of recycled gas than hydro-characteristics of gas, PCCagent and PCAagent have larger priority than LFRagent and SFRagent. According to collaboration relationship among control-agents, detail steps of extended contract net protocol in pressure control system is shown as follows. Step1: A task for controlling pressure of recycled gas is announced to all controlagents. In this phase, all of control-agents are bidders. Step2: RPagent which has largest priority establishes a contract. But it does not have control functions. So RPagent acts as a manager to establish a new contract to realize tracking control along with reference pressure. This is reflected by the marking of PNRPagent, which is transferred from m4 to m6 instead of m5 . Step3: Control-agent, in which transition t1 is satisfied, establishes a contract with RPagent. In this phase, control-agents except RPagent are bidders. 3.4 Actual Running Effect

Multi-agent based pressure control system of recycled gas has been utilized in Yanzhou coking plant. The system is developed by Fix 6.5 configurable software for real-time supervising platform and Visual Basic 6.0 for realization of each derived control-agent. Real-time supervising data from sensors and control signal to actuators are transmitted between supervising platform and control-agents through DDE. An electromotive valve is adopted as an actuator in which degree is 0°-60°. In the plant, two kinds of coke are produced, which is export coke and metallurgy coke. Different kind of coke needs different quantity of gas. So reference pressure is different. And reference pressure varies from 500Pa to 1100Pa. In addition, there are three coke ovens in this plant. Three gas pipes for corresponding coke ovens are connected in parallel which lead to coupling disturbance. Control objective of system is to make the pressure fluctuation of recycled gas limited from -10Pa to +10Pa.

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On condition that reference pressure of recycled gas p v is 800Pa and the maximum pressure is 4500Pa. Metallurgy coke is produced. The pressure control system is running with parameters as shown in Tab.1. Table 1. Parameters in pressure control system

parameters K

value

PCA P

K DPCA

K

LFR P

K

LFR I

K

LFR D

SFR l

10

ep

200

ephSFR

value 0Pa 10Pa

ep

LFR l

10 Pa

ep

LFR h

230 Pa

100

ep

PCA l

230 Pa

800Pa

ephPCA

20 2

pv

parameters

1200 Pa

The measured curves of actual pressure before and after pressure control system proposed in the paper is adopted are shown in Fig.6(a) and (b) respectively. Four curves express reference pressure and actual pressure of recycled gas to three coke ovens respectively.

1#coke oven

2#coke oven

3#coke oven

(a) before the system is adopted

2#coke oven

3#coke oven

1#coke oven

(b) after the system is adopted Fig. 6. The measured curves of actual pressure

It is obvious that in all switching processes in current coke oven, pressure of recycled gas reach the maximum. And the influence of the switching process in 3# coke oven on other coke ovens is less than the influence of the switching process in 1# or 2# coke oven on other coke ovens. The reason of the phenomena is the length of

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gas pipes between 1# and 2# coke oven is shorter than them between 3# and other coke ovens. Before the pressure control system is adopted, pressure fluctuate caused by periodical disturbances vary within the large range for a long time and pressure fluctuate caused by other disturbances is also large. Through analysis of ash content, sulphur content, anti-crash intensity and wearable intensity of coke, it indicates large pressure fluctuate leads to the instability of quality of coke. After the pressure control system is adopted, there is no reverse overshoot when each switching process ends. The large pressure fluctuation of recycled gas caused by switching processes in adjacent coke ovens are controlled effectively. And pressure fluctuation is stabilized in ±10 Pa during no switching processes.

4 Conclusions Complex process control systems need a hybrid control mode, which combines hierarchical structure with decentralized control units. Autonomy of agents and cooperation capability between agents in multi-agent system provide basis for realization of the hybrid control mode. A novel multi-agent based complex process control system is proposed. Detailed semantic representation of control-agents is presented using agent-oriented programming. A novel temporal logic analysis of control-agents is proposed utilizing Petri nets. Collaboration relationships among control-agents are analyzed based on extended contract net protocol. Taken pressure control of recycled gas with complicated disturbance as an application, multi-agent based pressure control system of recycled gas is analyzed in detail. Five kinds of control-agents are derived from control-agent. Reachable marking tree and different transition of each derived control-agent are analyzed in detail. Actual running effect indicates the hybrid control mode is effective and flexible. Temporal logic analysis ensures the reachability of the systems. It also simplifies the temporal analysis. Extended contract net protocol provides a reasonable realization for collaboration relationships. The problem to be further studied is to apply the method to design of control system based on network for utilizing immigration characteristics of agent better in the heterogeneous operating platform.

Acknowledgements This work is supported by the Postdoctoral Science Foundation of China (2005037225), the Postdoctoral Science Foundation of Jiangsu Province ([2004]300) and the SR Foundation of CUMT (OC4465).

References 1. Breemen, V., Vries, T.J.A.:Design and Implementation of A Room Thermostat Using An Agent-based Approach.Control Engineering Practice Vol.9 (2001)233-248 2. Wooldridge, M.,Jennings, N.R.:Intelligent Agents:Theory and Practice.The Knowledge Engineering Review Vol.10.(1995)115-152

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3. Zhou, B.,Wang, D., Xi, L. et al: Agent-Based Hybrid Control System for Manufacturing Cells. Computer Integ rated Manufacturing Systems Vol.10 (2004) 292-297 4. Hu, G., Sun, Y.: Advances and Application of Multiple Model Control Method. Information and Control Vol.33 (2004)73-74 5. Kohu, W., Nerode, A. :Multiple Agent Autonomous Hybrid Control Systems.Proc.of the IEEE Conference on Decision and control (1992)16-18 6. Chen, L., Din, J.: Complex Process Control System Based on the Theory of Multi-Agent. Mechatronics,Vol.1 (2004)28-31 7. Wei, Z., Lu, Q.: Model of Distributed Computer Control System Based on the Multi-agent system.Journal of Hefei University of Technology Vol.27(2004)1570-1573 8. Fischer, K., Jacobi, S., Diehl, C., et al.: Multiagent Technologies for Steel Production and Control. Proc. International Conference on Intelligent Agent Technology Vol.2 Beijing (2004)555-558 9. Albert, J.N., Breemen, V.: Agent-Based Multi-Controller Systems. Ph.D. thesis. Netherlands. Twente University (2001) 10. Voos, H.:Intelligent Agents for Supervision and Control:A Perspective.Proc. International Symposium on Intelligent Control Greece (2000)339-344 11. Guo, Y., Gong, D., Zhou, Y.: Multi-Agent System Based Cooperative Interactive Evolutionary Computation model.Journal of System Simulation Vol.17(2005)1548-1552 12. Chang-jun, J.: Behavior Theory and Applications of Petri Net.Higher Education Press. Beijing (2003) 13. Hsieh, F.: Modeling and Control of Holonic Manufacturing Systems Based on Extended Contract Net Protocol.Proc. of the American Control Conference, Anchorage (2002) 50375042 14. Guo, Y.,Wang, S., Hao, R. et al.: Multi-layer Control Applied to Pressure Control of The Recycled Coal Gas in Coke Oven.Metallurgical Industry Automation (2002)13-15

Neural Network Based Soft Switching Control of a Single Phase AC Voltage Restorer Kayhan Gulez, Tarık Veli Mumcu, and Ibrahim Aliskan Yıldız Technical University, Electrical Engineering Department, 34349 Besiktas / ISTANBUL Fax.: +90212 2594869 {gulez, tmumcu, ialiskan}@yildiz.edu.tr

Abstract. A neural network based pwm type AC voltage restorer simulation is proposed in this paper. The objective is to apply the neural network switching control technique to the AC voltage restorer to decrease time delays during the switching conditions, to reduce switching losses. Thus, the proposed AC voltage restorer has some advantageous such as quick switching response, simpler and intelligent structure, better output waveform. With unknown and/or variable nonlinear loads, the semi-conductor’s triggering and extinction angles depend on the load parameters in a highly nonlinear fashion. The Artificial Neural Network techniques have proven suitable for parameter identification and control of such nonlinear systems. The transient condition of the AC voltage restorer is improved via neural network based control technique. The simulation of the switching conditions is shown, and MATLAB is used to simulate and test its performance. Simulation results were performed to verify the effectiveness of the proposed control strategies.

1 Introduction Power quality issues are of vital concern in most industries today. The power quality is an index to the quality of current and voltage available to industrial, commercial and household consumers of electricity. The quality of the voltage waveform at the entry point of a consumer’s premises depends upon the types of load within those premises. These loads may be linear or nonlinear (harmonic producing) in nature. For linear loads, any distortion in the voltage waveform should be the responsibility of the supply authority. Contrary to this, for nonlinear loads, any deviation from no load to full load voltage waveform is the responsibility of the consumer [1]. Therefore, the quality of the current depends entirely upon the quality of the voltage with the non-harmonic producing loads. For harmonic producing loads, the quality of current depends upon amount of load, resulting in a maximum distortion in current at light loads and the highest magnitude of the harmonics current at full load. The most common power quality problems faced by industries are: switching transients, swells, sags, surges, extended under-voltages, outages (black and brown), harmonics, and impulses with varying magnitude of the voltage at the point of common coupling (to PCC) [2], [3]. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 331 – 340, 2006. © Springer-Verlag Berlin Heidelberg 2006

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Switching Transients: Switching transients take place when there is a rapid voltage peak of up to 20,000 volts with a duration time of 10 micro seconds to 100 micro seconds. They are commonly caused by arcing faults and static discharge. In addition, major power system switching disturbances, initiated by the utilities to correct line problems, may happen several times a day. When an electric clothes dryer is started, the lights may dim for an instant and then return to normal. In an industrial plant, starting a large motor produces similar results. In both cases the line voltage momentarily decreases due to the inrush of current drawn by the heavy starting load. When a large load is removed from a circuit, the voltage may increase slightly and lights may get brighter for an instant. These events are referred to as sags and swells respectively. Swells: An increase from nominal voltage lasting one or more line cycles. Sags are also known as brownouts, sags are short term decreases in voltage levels. At times of extremely high power consumption, an electric utility may have to reduce the supply voltage for energy conservation purposes. This condition is called a “brownout.” or sags. Surge: A short term increase in voltage, typically lasting at least 1/120 of a second. Surges in an electrical power system can be caused by lightning, utility switching operations and system faults. Surge protection is generally provided by surge arresters located either in the utility system or within the customer’s power distribution system. The neural network based control technique helps the AC voltage restorer to regulate the switching conditions of the semiconductor elements. A detailed design of the neural network methodology is given in Section 4.

2 Fundamentals of the AC Voltage Restorer 2.1 AC/AC Boost Converters AC/AC Converters were built out of electromechanical components such as motorgenerator sets or rotary converters. With the advent of solid state electronics, it has become possible to build completely electronic frequency changers. These devices usually consist of a rectifier stage (producing direct current) which is then inverted to produce AC of the desired frequency. The inverter may use Mosfet, IGBT, thyristor. If voltage conversion is desired, a transformer will usually be included in either the AC input or output circuitry and this transformer may also provide galvanic isolation between the input and output AC circuits. A battery may also be added to the DC circuitry to improve the converter's ride-through of brief outages in the input power. Fig.1 shows the schematic diagram of a single-phase AC-AC boost converter. The AC-AC boost converter is connected on the secondary side of the step-up injection transformer. Under the sags in the voltage at the PCC vS, the boost converter injects a required voltage in series vinj to regulate the load voltage vL at a desired value. The boost converter has four active switches (IGBT with an anti-parallel diode constitutes a switch). The switches SC1 and SC2 form one pair and are turned on/off simultaneously. Similarly, switches SC3 and SC4 form another, pair and are turned on/off simultaneously [1].

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Fig. 1. General view to the single phase AC/AC converter

2.2 AC/AC Buck-Boost Converters AC/AC buck converters are used for controlling the supply voltage of sensitive loads. Otherwise, voltage swellings of supply voltage can cause your sensitive devices to break down. Another reason for using these converters is that some electrical/ electronic devices need to lower level voltage source than local AC network to

Fig. 2a. Source circuit of sags/swells of supply voltage

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run properly. However in this study, we proposed using the buck converter to regulate the voltage swells of the supply voltage of the load. Voltage sags and/or swells of supply voltage may occur on the same line in the real world. Only one AC source supplies more than one load and some of these loads may include source components of voltage sags/swells. In Fig. 2.a shows one of these circuit types and curve shape of load voltage for same time sags/swells can be seen here Fig. 2.b.[6][7]

Fig. 2b. Output signals of circuit which was showed in figure 2.a. (from top to bottom: - output of thrystor bridge, - AC voltage source, - Supply voltage of RLC load )

Therefore, we used an injection transformers; secondary winding which were used for the operation of buck-boost conversion. In this way, we could control to the sags and swells of the supply voltage of the load. Thus, the supply voltage of the load can be controlled in an appropriate voltage horizon (band). Fig. 3 shows the proposed AC-AC voltage restorer and additional circuit elements. A small modification (adding a centre tap), in the injection transformer secondary winding and the AC-AC buck-boost converter connection to this winding, makes it capable of taking care of voltage sags as well as swells [2]. On detection of voltage sags in the supply system, the contactors SW1 and SW2 are closed to contact position C1. For voltage swells, SW1 and SW2 are closed to contact position C2. The switches

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Fig. 3. A Single phase AC voltage restorer compensates for transients

SC1 and SC2 form one pair and are turned on/off simultaneously. Similarly, switches SC3 and SC4 form another, pair and are turned on/off simultaneously [1]. The value of Np/Ns is equal to 1/6. In Fig. 3, RS and LS are source resistance and inductance, respectively. The components, RW and LW are resistive and inductive components, respectively, of impedance between the injection transformer and the PCC. The parameters L and C are the LC filter’s components to eliminate the high frequency components contained in the voltage across points A and B. The SSVR’s devices (SC1– SC4) are switched to a high frequency (25 kHz), so, the LC filter is tuned to provide a voltage across C that matches with the wave shape of the PCC voltage. This SSVR topology, shown in Fig. 3, use another LC filter with components LF and CF [3]. This filter absorbs EMI noise emanating from the AC-AC converter due to the high frequency switching of devices SC1–SC4. For this converter, isolated gate drives synchronize the switching operations of rectifying switching elements with the line voltage. Fig. 4 shows the timing diagrams of the operation of switching and the switching frequency range of semi-conductor elements used in the simulation.

Fig. 4. Switching frequency range of the semi-conductor elements used in the simulation (mosfet and IGBT), and timing diagrams of the proposed AC/AC converter

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3 AC Voltage Restorer The proposed topology of the voltage restorer shown in Fig. 3 is capable of compensating voltage sags/swells. This topology exhibits a buck-boost control circuit to compensate the sag/swell in the supply voltage. Mosfets were used in this research and high frequency values could be reached for catching and controlling short term voltage sags/swells. Other power electronic devices can not be triggered at high frequency values where Mosfets can. In consideration of all these reasons, buck-boost AC voltage restorer circuit, which can be seen in Fig. 5 was developed.

Fig. 5. Proposed buck-boost AC voltage restorer circuit (Matlab function block includes neural network controller software)

4 Switching Conditions and Neural Network Controller Performance 4.1 Switching Conditions and Design of Neural Network Controller The network receives the load voltage error signals through the use of the buckboost voltage restorer. The network tries to keep supply voltage of the load in voltage horizon (band). The upper and lower bound values of the control horizon are ±03% of the voltage source. Table 1 is given to illustrate buck boost converter activation areas.

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Table 1. Buck-boost voltage restorer running conditions for voltage horizon of ±03% of AC voltage source

Inputs AC Source Value (V) >0

”0

Outputs

AC Source-Load Voltage Value • 4.7 V -4.7 V gbest then Pg = Xi . step 3. Updating: Calculate particle position and velocity according to (3) and (4). step 4. End condition: If the adaptive threshold of fitness value is satisfied or the number of iteration reaches to the set value, then update the weights of the neural network; otherwise go to step 2. 3.3 MCR Guarantees and Fairness According to the fairness definition, no set of ABR connections should be arbitrarily discriminated against and no set of connections should be arbitrarily favored. In the

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previous sections, we have explicitly assumed that all the active ABR connections have zero MCR, so the same feedback rate is sent to all active VC’s. However, if ABR connections have different nonzero MCR requirements, we have to consider other fairness criteria, one of which is called ”MCR plus equal share,” defined as follows for VCi : ERi j = MCRi + R

(10)

When MCRi = 0 (i = 1, 2, · · · , N), then ERi j = R; when MCRi > 0, (10) can guarantee all MCR’s. So the common rate in steady state will converge to: N

Rs =

Cabr − ∑ MCRi

(11)

i=0

N where Cabr

is the ABR bandwidth of the link consideration. That is to say, after meeting the requirements of the VC’s with MCR>0, the remaining ABR capacity is shared equally among all the VBR users.

4 Performance Evaluation Via Simulations In this section, we study the transient performance of the neural network controller under a variety of networking conditions and loads. We choose the similar simulation scenarios proposed by Kolaro [4]. It has two switches with 1680 cell buffers each, two groups of ABR sources with each group consisting of five persistent sources and one group of VBR source consisting of four VBR sources (Fig. 3). The desired queue length r=50 cells. All links have a capacity of 365 cells/ms (155 Mb/s). Obviously the link between the two switches is the bottleneck link. A Gr o u p 5 A B R S o u rc e s

A R e c e iv in g T e rm in a ls

B o t t le n e c k Lin k

100 o r 1000km ...

...

...

...

...

B Gr o u p 5 A B R S o u rc e s

...

S w it c h 1 C Gr o u p 4 VB R S o u r c e s

S w it c h 2

B R e c e iv in g T e rm in a ls

C R e c e iv in g T e rm in a ls

Fig. 3. Single bottleneck link simulation model

4.1 Simulation in LAN The distance from the sources A and B to the switch1 is 100 km and the round-trip propagation is 1 ms. The source parameters are chosen as follows: PCR=365 cells/ms, ICR=MCR=4 cells/ms. Sources in group A start transmission at time t = 1 ms, while sources in group B start at time t = 300 ms. Fig. 4 shows the rate for each source, when the sources in group A start transmission, the rates converge to stable value 73 cells/ms (365/5). When group B sources start transmission, all source rates stabilize around a new equilibrium of 36.5 cells/ms (365/10).

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350 300

Rate (cells/s)

250 The Rate of Souces A 200 The Rate of Souces A And B 150 100 50 0 0

0.1

0.2

0.3 0.4 Time (s)

0.5

0.6

0.7

Fig. 4. ABR rate in LAN 60

Queue Level (cells)

50

40 Source B Start

30

20

10

0 0

0.1

0.2

0.3 0.4 Time (s)

0.5

0.6

0.7

Fig. 5. Queue level of the buffer in LAN

From Fig. 5, the queue length converges to 50 cells which is the buffer set point after 175 ms and there is no overshoot. When group B sources start at time t =300 ms, the queue is stable after 100 ms with very small overshoot (1.8 cells). So it is easy to get the conclusion that the neural network controller can respond to the changes of network load on time. It has good robustness. 4.2 Simulation in WAN Here, we set the distance from the sources A and B to the switch1 to be 1000km and the round-trip propagation to be 10ms correspondingly. Other conditions are same as in simulation 4.1. Fig.6 depicts the compare of ABR source rate with 10 ms and 15 ms time delay respectively. The two curves are similar to each other with only a slight degradation for the curve which has 15 ms time delay. So it is easy to get the conclusion that the controller can well adapt to the variety of time delay. Next, we add four video MPEG sources at switch1. The MPEG sources have service priority over ABR sources and start transmission at time t = 1 ms. The ABR sources are persistent (with infinite backlog). As is shown in Fig.7, the aggregate rate of four MPEG sources is about 73 cells/ms. After t = 1 ms and t = 300 ms, the rate of ABR sources

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Rate (cells/s)

250 The Rate of Souces A 200 The Rate of Souces A And B

150 100 50 0 0

0.1

0.2

0.3 Time (s)

0.4

0.5

0.6

Fig. 6. ABR rate with different time delay in WAN 350 300

Rate (cells/s)

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The Rate of Souces A The Rate of Sources A And B

200

The Rate of MPEG 150 100 50 0 0

0.1

0.2

0.3 0.4 Time (s)

0.5

0.6

0.7

Fig. 7. ABR rate with VBR existing in WAN

stabilize around 58cells/ms and 29cells/ms respectively. Although the bandwidth of ABR varies at all times, the rates of all ABR sources converge to stable value quickly, with little oscillations. The simulation indicates that the neural network controller can overcome the bad effect caused by VBR in WAN effectively. 4.3 Simulation with Different MCR in WAN The simulations above have been done with the same MCR of all the ABR sources. Now we show that the scheme proposed achieves fairness and supports minimum rate guarantees (MCR>0). The ER can be computed by (10): ERi j = MCRi + R. The following MCR values are assigned to ten ABR sources. 1) Sources A(1), A(2), and A(3) (group S1) have MCR =49 cells/ms; 2) Sources A(4), A(5), and B(1) (group S2) have MCR =38 cells/ms; 3) Sources B(2), B(3), B(4) and B(5) (group S3) have MCR=26 cells/ms. Sources in group A start transmission at time t = 1 ms. From Fig. 8, we observe that the remaining bandwidth after the MCR guarantees are satisfied, namely 365-105-48=212 cells/ms, is equally shared amongst the five sources of group A. In other words, sources in group S1 get 35+212/10=56 cells/ms each,

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300

Rate (cells/s)

250

200 The Rate of S1 150 The Rate of S2 100

The Rate of S3

50

0 0

0.1

0.2

0.3 0.4 Time (s)

0.5

0.6

0.7

Fig. 8. ABR source rate with different MCR

whereas sources in group S2 [A(4) and A(5)] get 24+212/10=45 cells/ms. When sources from group B become active at time t =300 ms, the sum of all MCR’s becomes 225 cells/ms and the remaining bandwidth 365-225=140 cells/ms is equally shared amongst the ten sources, so that each source gets an additional bandwidth of 14 cells/ms on the top of its MCR. Indeed, from Fig. 8 we observe that: 1) Sources in group S1 get 49 cells/ms each; 2) Sources in group S2 get 38 cells/ms each; 3) Sources in group S3 get 26 cells/ms each.

5 Conclusion In this paper, we have presented a control-theoretic approach to design a closed-loop rate-based flow controller in high-speed networks. The neural network controller trained by PSO algorithm can be easily implemented in practice and overcome the adverse effect caused by the time delay and the uncertainties of network. Thus the source rates can respond to the changes of network rapidly and avoid the congestion effectively. Further, the algorithm can guarantee the MCR and achieve fairness. Simulation results show that in various environments (in LAN, in WAN or with VBR existing), the scheme has good adaptability and robustness.

Acknowledgement This work is supported by the National Key Spark Project and by the Detection Technology of Forest Products Volatile Foundation.

References 1. The ATM Forum Traffic Management Specifications, 4.0 ed. ATM Forum, (1996). 2. Bonomi F., Mitra D.,Seery J.B.: Adaptive Algorithms for Feedback-Based Flow Control in High-Speed, Wide-Area ATM Networks. IEEE Journal on Selected Areas in Communications (JSAC), vol. 13 (7). (1995) 1267-1283.

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3. Benmohamed L., Meerkov S. M.: Feedback Control of Congestion in Packet Switching Networks: The Case of A Single Congested Node. IEEE/ACM Trans. on Networking, vol. 1. (1993) 693-707. 4. Kolarov A., Ramamurthy G.: A Control-Theoretic Approach to The Design of An Explicit Rate Controller for ABR Service. IEEE/ACM Trans. on Networking, vol. 7. (1999) 741-753. 5. Quet P. F., Atalar B., Iftar A.: Rate-based Flow Controllers for Communication Networks in the Presence of Uncertain Time-varying Multiple Time-delays. Automatica, vol. 38. (2002) 917-928. 6. Sichitiu, Mihail L., Bauer, Peter H.: Asymptotic Stability of Congestion Control Systems with Multiple Sources. IEEE Trans. on Automatic Control, vol 51. (2006) 292-298. 7. Luigi Alfredo Grieco, Mascolo S.: Smith’s Predictor and Feedforward Disturbance Compensation for ATM Congestion Control. Proc. of the 41st IEEE CDC, Las Vegas(2002) 987-992. 8. Habib I., Tarraf A., Saadawi T.: A Neural Network Controller for Congest Control in ATM Multiplexers. Computer Networks and ISDN Systems, vol. 29. (1997) 325-334. 9. Rose Qingyang Hu , David W. Petr.: A Predictive Self-Tuning Fuzzy-Logic Feedback Rate Controller. IEEE/ACM Trans. on Networking, vol. 8. (2000) 697-709. 10. Eberhart R., Shi, Y.: Particle Swarm Optimization: Development, Applications and Resources. Proc. of congress on evolutionary computation, Piscataway, NJ: IEEE Press, (2001) 81-86.

Parameter Identification of Dynamical Systems Based on Improved Particle Swarm Optimization Meiying Ye College of Mathematics and Physics, Zhejiang Normal University, Jinhua 321004, P.R. China [email protected]

Abstract. Improved Particle Swarm Optimization (IPSO), which is a new robust stochastic evolutionary computation algorithm based on the movement and intelligence of swarms, is proposed to estimate parameters of nonlinear dynamical systems. The effectiveness of the IPSO algorithms is compared with Genetic Algorithms (GAs) and standard Particle Swarm Optimization (PSO). Simulation results of two kinds of nonlinear dynamical systems will be illustrated to show that the more accurate estimations can be achieved by using the IPSO method.

1 Introduction A fundamental part of control engineering is the identification of the systems being controlled. According to a known mathematical or an estimated model for systems, a controller will then be designed by a lot of different control techniques such that the certain output response of system can be satisfied. In system identification, considerable efforts have been devoted to develop methods for identification of system models and their parameters. Currently, a wide range of analytical techniques exists for linear systems. However, for nonlinear systems, limited progress has been made with analytical approaches. Instead, some success has been achieved with various traditional optimization methods such as least squares and local search. However, a fundamental problem of traditional optimization techniques is their dependence on unrealistic assumptions such as unimodal performance landscapes and differentiability of the performance function. Consequently, nonlinear problems are often oversimplified to fulfill such assumptions, which makes the found solutions hard to transfer back to the original problem. In recent years, parameter estimation techniques in nonlinear systems identification based on artificial intelligence have been successively proposed [1-3], such as using genetic algorithms (GAs) [4], and other stochastic search techniques. They seem to be a promising alternative to traditional techniques. First, GAs do not rely on any assumptions such as differentiability, continuity, or unimodality. Second, they are capable of handling problems with nonlinear constraints, multiple objectives, and time-varying components. Although GAs have been applied to parameter estimation, recent research has identified some deficiencies in GA performance [5]. This degradation in efficiency is D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 351 – 360, 2006. © Springer-Verlag Berlin Heidelberg 2006

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apparent in applications with highly epistatic objective functions, i.e., where the parameters being optimized are highly correlated (the crossover and mutation operations cannot ensure better fitness of offspring because chromosomes in the population have similar structures and their average fitness is high toward the end of the evolutionary process). Moreover, the premature convergence of GAs degrades its performance and reduces its search capability. Recently, a new evolutionary technique, the Particle Swarm Optimization (PSO), is proposed [6,7] as an alternative to GAs. Its development was based on observations of the social behavior of animals such as bird flocking, fish schooling, and swarm theory. PSO is initialized with a population of random solutions. Each individual is assigned with a randomized velocity according to its own and its companions’ flying experiences, and the individuals, called particles, are then flown through hyperspace. Compared with GAs, PSO has some attractive characteristics. It has memory, so knowledge of good solutions is retained by all particles; whereas in GAs, previous knowledge of the problem is destroyed once the population changes. It has constructive cooperation between particles, particles in the swarm share information between them. Due to the simple concept, easy implementation and quick convergence, nowadays PSO has gained much attention and wide applications in different fields [8]. In this paper, we demonstrate how to employ the Improved Particle Swarm Optimization (IPSO) method to obtain the optimal parameters of nonlinear systems. The results are compared to those obtained by GAs. It has been demonstrated that the IPSO has better performance than the GAs in solving the parameter estimation problem of nonlinear systems.

2 Problem Formulation This paper considers a class of nonlinear systems, which are described by the statespace model of the discrete form as

x(k + 1) = f (k , x(k ), u (k ), P1 ), y (k ) = h(k , x(k ), u (k ), P2 ),

(1)

where u ∈ R is the input of the system, x ∈ R n are the internal states, y ∈ R is the output, P1 and P2 are the vectors of system parameters, in which may contain the term of the delay time, to be determined. For simplification, let Θ = [θ1 , θ 2 ,  , θ m ] , where m is the total number of system parameters, be a new vector of parameters that collect all of parameters in P1 and P2 . In order to successfully estimate Θ , the following assumptions on the nonlinear system of equation (1) are requested.

(1) The output y must be measurable in each step and be also finite during the given sampling steps. (2) Each system parameter in Θ must be required in connection with the output y , i.e., the parameter Θ can be estimated from the measurement of the output y .

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Before proceeding with the optimization operations, a performance criterion or an objective function should be first defined, because the value of an objective function will deeply influence on how to perform the evolutionary type on Θ . In general, the IPSO only needs to evaluate the objective function to guide its search and no requirement for derivatives about the system. In this study, the total summation of square error ( SSE ) is taken as an objective function, which is given by q

q

k =1

k =1

SSE = ¦ [ y (k ) − yˆ (k )] 2 = ¦ e 2 (k ) ,

(2)

where q is the number of given sampling steps, yˆ is the evaluated output from IPSO, and e is the error between y and yˆ . Our objective is to determine the parameters Θ based on using the proposed IPSO in such a way that the value of SSE is minimized, approaching zero as much as possible.

3 Particle Swarm Optimization (PSO) The PSO simulates the behavior of swarm as a simplified social system. Like fish schooling and bird flocking, the social behavior of such organisms can be treated as an optimization procedure. In the PSO system, each particle tries to search the best position (state) with time in a multidimensional space. During flight or swim, each particle adjusts its position in light of its own experience and the experiences of neighbors, including the current velocity and position and the best previous position experienced by itself and its neighbors. This characteristic manifests two basic models of PSO. For more information, we refer reader to Kennedy et al. [7], a standard textbook on PSO, treating both the social and computational paradigms. The PSO differs from traditional optimization methods in that a population of potential solutions is used in the search. The direct fitness information, instead of function derivatives or related knowledge, is used to guide the search. As mentioned above, it is promising to solve the parameter estimation problem of nonlinear systems by adopting PSO. The PSO is initialized with a group of random particles (solutions) and then searches for optima by updating generations. Particles profit from the discoveries and previous experience of other particles during the exploration and search for higher objective function values. Let i indicate a particle’s index in the swarm. Each of m particles fly through the n -dimensional search space R n with a velocity vi , which is dynamically adjusted according to its own previous best solution si and the previous best solution sˆ of the entire swarm. The velocity updates are calculated as a linear combination of position and velocity vectors. The particles interact and move according to the following equations vi ( j + 1) = wvi ( j ) + c1r1 ( j )( si ( j ) − pi ( j )) + c2 r2 ( j )(sˆi ( j ) − pi ( j )) ,

(3)

pi ( j + 1) = vi ( j + 1) + pi ( j ) ,

(4)

where r1 ( j ) and r2 ( j ) are random numbers between zero and one. c1 ( j ) and c2 ( j ) are learning factors, usually about c1 = c2 = 2 . And w is an inertia weight, which is commonly taken as a decreasing linear function in index j from 0.9 to 0.6. It is

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possible to clamp the velocity vectors by specifying upper and lower bounds on vi , to avoid too rapid movement of particles in the search space. Then we can use the standard procedure to find the optimum. The searching is a repeat process, and the stop criteria are that the maximum iteration number is reached or the minimum error condition is satisfied. The standard procedure is described as below: Data: nonlinear system of equation (1), number of sampling steps q in equation (2), learning factors c1

㧘 c , inertia weigh w and maximal particle velocity v 2

max

in

equation (3), parameters θ1min , θ1max , θ 2 min , θ 2 max ,  , θ m min and θ m max in search space, swarm size N , and iteration number G (or the summation of square error SSE ). (1) Set the iteration number j to zero. Initialize randomly the swarm S of N particles (population number) such that the position xi (0) of each particle to meet the prescribed conditions. (2) Evaluate the fitness of each particle F ( xi ( j )) . (3) Compare the personal best of each particle to its current fitness, and set si ( j ) to the better performance, i.e.

­si ( j − 1) if F ( xi ( j )) ≤ F ( xi ( j − 1), si ( j ) = ® ¯ xi ( j ) if F ( xi ( j )) > F ( xi ( j − 1), (4) Set the global best sˆ( j ) to the position of the particle with the best fitness within the swarm, i.e.

sˆ( j ) ∈ {s1 ( j ), s2 ( j ),, sm ( j )} F ( sˆ( j )) = max{F ( s1 ( j )), F ( s2 ( j )),, F ( sm ( j )),} . (5) (6) (7) (8)

Change the velocity vector for each particle according to equation (3). Move each particle to its new position, according to equation (4). Let j = j + 1 . Go to step (2), and repeat until meets the stop criteria.

It can be easily seen that there are two key steps when applying PSO to optimization problems: the representation of the solution and the fitness function. One of the desirable merits of PSO is that PSO takes real numbers as particles. It is not like GAs, where transformation of binary encoding and special genetic operators are needed. The complete application of PSO, as well as the method to do parameter estimation of nonlinear systems, is discussed in the following section.

4 Improved Particle Swarm Optimization (IPSO) The PSO performance has been investigated in several papers since its presentation [9], [10]. The work presented in [11] describes the complex task of parameter selection in the PSO model. Comparisons between PSO and the standard GA formulation have been carried out in [12], where the author points out that the PSO performs well in the early iterations, but it presents problems reaching a near-optimal solution.

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The behavior of the PSO in the model presents some important aspects related with the velocity update. If a particle’s current position coincides with the global best position, the particle will only move away from this point if its inertia weigh and previous velocity are different from zero. If their previous velocities are very close to zero, then all the particles will stop moving once they catch up with the global best particle, which may lead a to premature convergence of the algorithm. In fact, this does not even guarantee that the algorithm has converged on a local minimum—it merely means that all the particles have converged to the best position discovered so far by the swarm. This phenomenon is known as stagnation [13]. The solution presented in [14] is based on adding a new parameter and additional equations. Another solution is presented in [15] by introducing a breeding and subpopulation. To solve the problem above, this paper proposes a new model called IPSO, by incorporating the mutation process often used in GA into PSO. This process allows the search to escape from local optima and search in different zones of the search space. This process starts with the random choice of a particle in the swarm and moves to different positions inside the search area. In this paper, the mutation process is employed by the following equation: x(k ) = − x(k ) + δ

where x(k ) is the random choice particle from the swarm, and δ is randomly obtained within the range [0, 0.2 × ( xmax − xmin )] , representing 0.1 times the length of the search apace. This pseudocode for the IPSO algorithm is given by begin Create and initialise While (stop condition is false) begin evaluation update velocity and position mutation end end

The IPSO algorithm was tested on benchmark problems. The results shown that the IPSO has better behavior than the GAs and PSO.

5 Simulation Experiments To verify the proposed IPSO algorithm in parameters estimation of nonlinear systems, several experiments were used as evaluation of the estimating power of the IPSO algorithm. MATLAB Simulation is processed in Intel Pentium4 1.2G processor with 512M RAM, under Windows XP. The fitness function f is a reciprocal of the objective function SSE as in equation (2). It implies the smaller SSE the value of particle, the higher its fitness value f =

1 . SSE

(5)

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Example 1. The Hénon map with unknown parameters is an example of twodimensional discrete-time chaotic system whose equations is described by x(k + 1) = 1 − Ax 2 (k ) + y (k ) , y (k + 1) = Bx(k )

(6)

where A and B are the two bifurcation parameters, and their actual values are assumed to be fixed at 1.4 and 0.3, respectively, in this simulation. We consider initial condition x(0) = 0.1 , y (0) = 0.1 , maximal particle velocity vmax = 2 , and the time step size q = 10 in this discrete-time system. Let Θ = [θ1 , θ 2 ] = [ A, B] be a vector of estimated parameters. Hence, the objective in parameter estimation is to determine Θ as accurately as possible. Other variables used in PSO or IPSO operations are givenby

θ1min = 0, θ1max = 2, θ 2 min = 0, θ 2 max = 2, N = 40, c1 = 2, c2 = 2, G = 300. The inertia weight w( j ) is taken as a decreasing linear function in iteration index j from 0.9 to 0.4. The optimization process is repeated 10 times and the averages of these results are provided. Table 1 lists the final estimated results after running 300 generations and makes comparisons with the GA method, whose variables are given by

θ1min = 0, θ1max = 2, θ 2 min = 0, θ 2 max = 2 N = 40, pc = 0.8, pm = 0.1, G = 300. where pc is the crossover probability and pm is the mutation probability. Table 1. Comparisons of estimated parameters with the proposed method and the GA and PSO method for the Hénon map

A Actual parameters

1.4000

B

SSE

0.30000

——

Elapsed time(s) ——

IPSO algorithm

1.4000

0.30000

1.0962 × 10

−15

PSO algorithm

1.3997

0.30003

2.0962 ×10

−12

Genetic algorithm

1.3933

0.33319

1.2783 × 10 −2

43.268 40.047 72.652

The convergence curves of SSE values produced by the IPSO algorithm with respect to numbers of iteration are plotted in Fig. 1. Also, Fig. 2 shows the tuning trajectories of two estimated parameters, i.e., A and B , with respect to numbers of iteration by means of our proposed method.

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0.6

Optimal SSE

0.5 0.4 0.3 0.2 0.1 0.0

0

50

100 150 200 Iteration index j

250

300

Fig. 1. Convergence curves of SSE for the Hénon map

Estimated parameters A,B

2.0 1.6 1.2

A B

0.8 0.4 0.0 -0.4

0

50

100

150

200

250

300

Iteration index j

Fig. 2. Trajectories of A and B using the IPSO method for the Hénon map

Example 2. The proposed IPSO is also applied to an example of three-dimensional continuous-time chaotic system. Let us consider the Lorenz chaotic system whose dynamic equations are in the following x = σ ( y − x), y = ρ x − xz − y, (7) z = xy − β z. It has been proved that the Lorenz system presents chaos when σ = 10 , ρ = 28 and β = 8 / 3 ≈ 2.6667 . In this simulation, the true value of unknown parameters is assumed to be Θ = [θ1 , θ 2 , θ 3 ] = [σ , ρ , β ] = [10, 28, 2.6667] . The initial state of system are taken as x(0) = 0.1 , y (0) = 0.1 , z (0) = 0 , maximal particle velocity vmax = 2 , and the time step size q = 100 , respectively. The data of the system states are generated via the Euler's method with a fixed time step of 0.01. Other variables used in PSO or IPSO operations are chosen as follows:

θ1min = 0, θ1max = 30, θ 2 min = 0, θ 2 max = 30, θ 3 min = 0, θ 3 max = 30, N = 40, c1 = 2, c2 = 2, G = 300. Here other IPSO parameters are the same as that in the Example 1.

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For this example, Table 2 lists the final estimated results after running 300 iterations and makes comparisons with the GA method, whose variables are givenby

θ1min = 0, θ1max = 30, θ 2 min = 0, θ 2 max = 30, θ 3 min = 0, θ 3 max = 30, N = 40, pc = 0.8, pm = 0.1, G = 300. In Fig. 3, the convergence curves of SSE values produced by the IPSO algorithm with respect to numbers of iteration are plotted. Fig. 4 shows the tuning trajectories of three estimated parameters, σ , ρ and β , with respect to numbers of iteration by means of our proposed method. Table 2. Comparisons of estimated parameters with the proposed method and the GA and PSO method for the Lorenz system

σ

ρ

β

SSE

Actual parameters

10.000

28.000

2.6667

——

IPSO algorithm

10.000

28.000

2.6667

1.3229 × 10

−15

31.797

PSO algorithm

10.002

28.003

2.6666

0.7311× 10 −13

29.043

Genetic algorithm

10.085

27.911

2.7029

6.1101

85.750

Time(s) ——

From the above two examples, the results presented show that a good optimal performance can be achieved by the proposed method for Hénon map and Lorenz system. To compare the performance of IPSO and PSO and GAs, the final estimation results using two different optimal algorithms are listed in Tables 1 and 2. There is obviously difference between the different parameter estimation methods in the SSE values. It is obvious that more accurate parameter estimation can be implemented using the IPSO for both nonlinear dynamical systems. The computational requirement of using the IPSO method is far less than that required by the GA method proposed. Again, the simulation results are shown in Figs. 1–4. From the Figs. 1 and 3, one can see the error SSE converges to zero as generation number j goes to infinity. Fig. 2 and Fig .4 show that the trajectories of the estimated parameters asymptotically converge to their actual values. 3.0

Optimal SSE

2.5 2.0 1.5 1.0 0.5 0.0

0

50

100 150 200 Iteration index j

250

300

Fig. 3. Convergence curves of SSE for the Lorenz system

Estimated parameters σ, ρ, β

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30 25

σ ρ β

20 15 10 5 0 0

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Iteration index j

Fig. 4. Trajectories of σ , ρ and β using the IPSO method for the Lorenz system

6 Conclusions This paper has presented a new technique of using the IPSO method for making parameter estimation of nonlinear dynamical systems. It is clear from the results that the proposed method can avoid the shortcoming of premature convergence of GA method and can obtain higher quality solution with better computation efficiency. The simulation results show that IPSO has much better potential in the field of dynamical system parameter estimation. Furthermore, this method provides a detailed design process for parameter estimation of uncertain chaotic systems and has wide practical applications in many other complex dynamical systems with all the unknown parameters.

Acknowledgements The Project Supported by Zhejiang Provincial Natural Science Foundation of China (Y105281).

References 1. Ursem, R.K., Vadstrup, P.: Parameter Identification of Induction Motors using Stochastic Optimization Algorithms. Applied Soft Computing. 4 (2004) 49–64 2. Kristinsson, K., Dumont, G.A.: System Identification and Control using Genetic Algorithms. IEEE Trans on Systems, Man, and Cybernetics. 22 (1992) 1033–1046 3. Chang, W.-D.: An Improved Real-coded Genetic Algorithm for Parameters Estimation of Nonlinear Systems. Mechanical Systems and Signal Processing. 20 (2006) 236–246 4. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. MA: Addison Wesley. (1989) 5. Gaing, Z.L.: A Particle Swarm Optimization Approach for Optimum Design of PID Controller in AVR System. IEEE Trans on Energy Conversion. 19 (2004) 384–391 6. Kennedy, J., Eberhart, R.C.: Particle Swarm Optimization. Proc IEEE Conf on Neural Networks. (1995) 1942–1948

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7. Kennedy, J., Eberhart, R.C., Shi, Y.: Swarm Intelligence. San Francisco: Morgan Kaufmann Publishers. (2001) 8. Eberhart, R.C., Shi, Y.: Particle Swarm Optimization: Developments, Applications and Resources. Proc Congr on Evolutionary Computation. (2001) 81–86 9. Kennedy, J.: Small Worlds and Mega-minds: Effects of Neighborhood Topology on Particle Swarm Performance. Proc Congr on Evolutionary Computation. (1999) 1931–1938 10. Suganthan, P.N.: Particle Swarm Optimizer with Neighborhood Operator. Proc Congr on Evolutionary Computation.. (1999) 1958–1962 11. Shi, Y., Eberhart, R.: Parameter Selection in Particle Swarm Optimization. Proc Annu Conf on Evolutionary Programming. (1998) 591–600 12. Angeline, P.: Evolutionary Optimization versus Particle Swarm Optimization Philosophy and Performance Differences. Proc Annu Conf on Evolutionary Programming. (1998) 601–610 13. Eberhart, R.C., Shi, Y.: Comparison between Genetic Algorithms and Particle Swarm Optimization. Lecture Notes in Computer Science. 1447 (1998) 611–616 14. Bergh, F.V.D., Engelbrecht, A.P.: A New Locally Convergent Particle Swarm Optimizer. Proc. IEEE Proc Conf Systems, Man, and Cybernetics. (2002) 96–101 15. Løvbjerg, M., Rasmussen, T.K., Krink, T.: Hybrid Particle Swarm Optimizer with Breeding and Subpopulations. Proc Conf on Evolutionary Programming. (2001) 469–476

Petri Net Modeling Method to Scheduling Problem of Holonic Manufacturing System (HMS) and Its Solution with a Hybrid PSO Algorithm Fuqing Zhao1, Qiuyu Zhang1, and Yahong Yang2 1

School of Computer and Communication, Lanzhou University of Technology, 730050 Lanzhou, P.R. China {zhaofq, zhangqy}@mail2.lut.cn 2 College of Civil Engineering, Lanzhou University of Techchnology, 730050 Lanzhou, P.R. China [email protected]

Abstract. Holonic manufacturing is a highly distributed control paradigm based on a kind of autonomous and cooperative entity called “holon”. It can both guarantee performance stability, predictability and global optimization of hierarchical control, and provide flexibility and adaptability of heterarchical control. In this paper, A new class of Time Petri Nets(TPN), Buffer-nets, for defining a Scheduling Holon is proposed, A TPN represents a set of established contracts among the agents in HMS to fulfill an order. To complete processing of orders, liveness of TPNs must be maintained. As different orders may compete for limited resources, conflicts must be resolved by coordination among TPNs. A liveness condition for a set of TPNs is provided to facilitate feasibility test of commitments.which enhances the modeling techniques for manufacturing systems with features that are considered difficult to model. A scheduling architecture, which integrates TPN models and AI techniques is proposed. By introducing dynamic individuals into the reproducing pool randomly according to their fitness, a variable population-size genetic algorithm is presented to enhance the convergence speed of GA. Based on the Novel GA and the particle swarm optimization (PSO) algorithms, a Hybrid PSO-GA algorithm (HPGA) is also proposed in this paper. Simulation results show that the proposed method are effective for the optimization problems.

1 Introduction Modern manufacturing systems have to cope with dynamic changes and uncertainties such as machine break down, hot orders and other kinds of disturbances. Holonic manufacturing systems (HMS)[1],[2],[3],[4] provide a flexible and decentralized manufacturing environment to accommodate changes dynamically. HMS is based on the notion of holon[5], an autonomous, co-operative and intelligent entity able to collaborate with other holon to complete the tasks. HMS requires a robust coordination and collaboration mechanism to allocate available resources to achieve the production goal. Multi-agent systems (MAS) [6],[7] provides desirable characteristics D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 361 – 372, 2006. © Springer-Verlag Berlin Heidelberg 2006

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to proactively handle uncertainties. HMS is usually modeled as a cooperative MAS. To optimize performance, contract net protocol[8] is applied to effectively and robustly allocate resource for HMS. As contract net protocol does not model the internal process of agents, direct application of contract net protocol to HMS may not yield satisfactory results. For example, undesirable states such as deadlocks, which cripple systems and degrade the performance, may occur. Although there are a lot of research works on HMS[9],[10],[11], however, deadlock issue has not been addressed[3],[12],[13]. So, the application of Petri net theory to HMS requires further study as HMS are different from centralized systems. How to combine the modeling and analysis capability of Petri nets with MAS to distribute tasks is an interesting problem. This paper presents a framework to model and control HMS based on Petri net and MAS theory. The remainder of this paper is organized as follows. Section 2 proposes a new class of Time Petri Nets(TPN), Buffer-nets, for defining a Scheduling Holon. In section 3, scheduling operation of a Scheduling Holon using Petri-nets is presented. Section 4 proposes a hybrid PSO-GA(HPGA) based evolutionary algorithm. A scheduling holon architecture, which integrates TPN models and HPGA techniques is given in Section 5. Section 6 concludes this paper.

2 Timed Petri-Net (TPN) Based Scheduling Holon 2.1 Buffer Nets Definition

1.

A

timed-PN

is called a Buffer net (B-net) if where the set of places R represents the resources

( P = R ∪ Q) ∧ ( R ∩ Q = Φ ) and the set of places Q represents the buffers, and the following three conditions are also satisfied:

I (r , t ) = O(r , t ) ∀t ∈ T , ∀r ∈ R (2) ∀t ∈ T , there exists a single p ∈ Q : I ( p, t ) = 1 and a single p '∈ Q : O ( P ' , t ) = 1, for p ≠ p ' ; (3) The subnet G ' = (Q, T , I ' , O ' , M ' ,τ ) ; where I ' and O ' are the restrictions of I to (Q × T ) and O to (T × Q ) , respectively, and M ' is the restriction of M to Q , is an acyclic graph without isolated places. (1)

Condition (1) assures that all the resources used by a transition are released after the firing of the transition. Condition (2) indicates that only one input (output) buffer is allowed for each transition. Condition (3) assures that no cycles are introduced. Definition 2. Initial and final states of a B-net (1) For a B-net, BI ⊂ Q is called a set of input buffer places if

∀p ∈ BI and t ∈ T , I ( p, t ) = 1 and O ( p, t ) = 0 , i.e. BI = { p ∈ Q | (!∃) t ∈ T O( p, t ) > 0} .

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(2) Bo ⊂ Q is called a set of output buffer places if

∀p ∈ Bo and t ∈ T , I ( p, t ) = 0 and O ( p, t ) = 1 , i.e. Bo = { p ∈ Q | (!∃) t ∈ T I ( p, t ) > 0} . (3) A state Mo is called an initial state (marking) for a B-net if {M ( p) = 0 ∀p ∉ ( BI ∪ R)} ∧ {M ( p) ≥ 1 (∀p ∈ R) ∨ (∀p ∈ BI )} . (4) A state M F is called an final (goal) state for a B-net if {M ( p ) = 0 ∀p ∉ ( Bo ∪ R )} ∧ {M ( p ) ≥ 1 (∀p ∈ R ) ∨ (∀p ∈ Bo)} . It is noted that final states.

BI ∩ Bo = 0 and the number of initial states equal the number of

2.2 B-Nets Based Scheduling Holon of HMS Three interesting properties can be observed in B-nets. A B-net is live (in the sense that M ≠ M F ), bounded (in the sense that the initial marking is bounded) and consistent (in the sense that BI and Bo merge to one place). Given an HMS formulation the following basic top–down procedure can be used to build the corresponding TPN. Each resource type is modeled as a place. A job J i is

Pi sub-nets that represent the Pi plans (Fig. 1(a)). The sub-nets are connected to two places. The first place pi _ start , called the input buffer, repre-

initially modeled as

sents the unprocessed parts that are ready to enter the system. A final place output buffer )represents parts that have been completed. A plan Pij is initially modeled (Fig.1(b)) as a sequence of (

Pi − end (the

qi j + 1 places

pij 0 , pij1 , pij 2 …) representing infinite buffers interconnected by PN subsystems,

each modeling a task. Places

pij 0 and pijqij are merged with the places pi _ start ,

Pi − end , respectively. In Fig. 1(c), a task

Tijk of the plan Pij that can be achieved by Cijk alternative op-

erations is modeled as

Cijk sub-PNs that share the input and output places ( Pijk −1 ,

Pijk , respectively) of the task. In Fig. 1(d), each operation source

Oi jkl is modeled as a single transition tijkl . If a re-

R ∈ [ R1 , R2 ,..., Rm ] modeled by place r ∈ [r1 , r2 ,..., rm ] is included in Sijkl

(i.e.

Oi jkl uses resource r ), then r is an input and an output place of the transition

and

τ (tijkl ) = hijkl , where τ

is the firing time of the transition tijkl .

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The initial (final) marking Mo( M f ) of the TPN is obtained by placing as many tokens in pi _ start ( p j _ end ) as parts of job

J i to be processed. Any place r repre-

senting a resource is initialized with as many tokens as the resources of this type that exist in the system. A TPN is said to be live if, no matter what marking has been reached, it is possible to ultimately fire any transition of the net by progressing through some further firing sequence. A B-net is live since for all M ≠ M F there exists at least one enabled transition. A TPN is said to be bounded if the number of tokens in each place does not exceed a given value for any marking reachable from Mo . From the B-net definition we can conclude that for any

t ∈ T , ¦ I ( p, t ) = ¦ O( p, t ) ∀p ∈ P . Hence a B-

net is bounded if Mo is bounded. We use B-nets to model scheduling holon of HMS. The kernel or primitives of the model are formed by: (1) the TPN modeling of the alternate operations in which each task can be achieved; (2) the model of the resources in the system. Resources are represented by resource-places in our TPN model. A token in a place means that the resource is idle and that it can be assigned to an operation. When starting the operation, a token will be removed from the place (the resource is busy) and after the operation is completed a token will be put back in the place (resource is available again). A resource can be shared by various processes.

pi_end

pi1 pi2 ... piN

pi_start Tij1 pi_end

O iN (c)

pi_end

(b) r1 Resource

pijk-1

Tijm

pij2 ...

(a)

O k1 O i2 ...

Tij2

pij1

. . .

rm pijk

pijk-1 Tijkl Oijkl pijk Sijkl (d)

Fig. 1. B-net modeling of job i in Scheduling Holon

3 Formulating the Scheduling Operation of a Scheduling Holon Using Petri-Nets In a Scheduling Holon, there are n (where n > 1) products to be produced using m (where m > 1) processing units. For each product, the sequence by which the processing units will be visited is pre-specified and is referred to as the product (or job)

Petri Net Modeling Method to Scheduling Problem

routing or processing recipes. Normally, the processing time

τ ij

365

for a product (or job)

i (i = 1,2,, n) in unit j ( j = 1,2,, m) is given. In a TPN, places can be used to model activities or resources, and time constants associated with places represent the processing duration of activities. A token residing in a place means either the availability of a resource, or an intermediate product being processed. Transitions can be used to model the discrete events of the involved activities, such as opening a valve, starting an operation, finishing a reaction, etc. Let Oij represent the operation (or processing activity) of product i at unit j . Operation Oij can be represented by two transitions t sij and t fij for the start and the termination of this operation, respectively, and one place pij with time duration

τ ij

for the processing activity (see Fig. 2a). For product i , suppose that Oij is the upward activity of operation

Oik (see Fig. 2b). All the activities of the same product can

be linked by additional intermediate places (see Fig. 2c). In a Scheduling Holon, different products may be processed in the same unit. This kind of resource sharing can be modeled by introducing a resource place p j ( j = 1,2,, m) for each processing unit. Suppose that operations

Oij ( j = 1,2,, m) share the same unit j , then place p j is both the input of the starting events and the output of the terminating events for all these activities. All operations in a Scheduling Holon can then be formulated by the following procedures: Step1: For product i , each processing activity is represented by two transitions

t sij and t fij , and one place pij . When there is no intermediate storage between activities, the final point of one place will correspond to the starting point of the following place; Step2: For product i , the i th initially marked place psi to represent the beginning of the job (e.g., the raw materials are ready), and the i th final place p fi to represent the finishing of the i th job are introduced; Step3: For processing unit

j , resource place p j is introduced to represent its

availability; Step4: In terms of job routing or product recipe, all the activities involved in product i are linked, and modeled as a TPN sub-model; Step5: All activities that share the same resource places p j

( j = 1,2,, m) are

interconnected, and the complete TPN for the scheduling Holon is created. Fig. 2d shows the TPN for a multi-product batch plant consisting of three products (p1–p3) and two processing units (u1-u5), where the processing times are given in Table 1.

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4 Hybrid PSO-GA Based Evolutionary Algorithm (HPGA) 4.1 A Novel GA Evolutionary computing (EC) is an exciting development in computer science. It amounts to building, applying and studying algorithms based on Darwinian principles of natural selection [14],[15]. Genetic algorithms (GA) are a family of computational models developed by Holland [16],[17]. GA operate on a population of potential solutions by applying the principle of the survival of the fittest to produce successively superior approximations to a solution. Recently, more attention has been paid to the population size adjustment. By introducing the age and maximum lifetime properties for individuals, Arabas eliminated the population size as an explicit parameter and developed the Genetic Algorithm with Variable Population Size (GAVaPS) [18]. The maximum lifetime depends on the fitness of the corresponding individual, while the age is incremented at each generation by one. Individuals are removed from the population when their ages reach the value of their predefined maximal lifetime. Further, Bäck et al. proposed a variant of GAVaPS, namely the Adaptive Population size GA (APGA) by remaining the best individual unchanged when individuals grow older [19]. Differently, Eiben gave a new population resizing mechanism based on the improvements of the best fitness in the population and therefore proposed the Population Resizing on Fitness Improvement GA (PRoFIGA) [20].

ts

ts

ij

tf

p si(0)

ij

p ij (tij)

p ij(tij )

ts

t f (ts ) ij

ij

(a)

ik

tf

ts22

ts31

p 22 (2)

p 2 (0)

tf11( ts13)

tf (ts ) i1

p 12 (2) tf13( ts14)

(b) tf

p s3 (0)

p 1 (0)

tf22( ts23)

p 31 (2)

tf31(t s33)

i2

p i2 (ti2 )

ik

p s2 (0)

ts11 p 11 (3)

p i1 (ti1 )

p ik (t ik )

p s1 (0)

i1

p 23 (4)

p 3 (0)

tf23( ts24)

p 33 (5)

tf33(t s35)

i2

p 4 (0) p fi(0) (c)

p 13 (3)

p 24 (4)

p 35(1)

tf14

tf24

tf35

p f1 (0)

p s2 (0)

p 35 (5)

p f3 (0) (d)

Fig. 2. Modeling a Scheduling Holon via TPN Table 1. Processing times (h) of products

Units U1 U2 U3 U4 U5

Products P1 3.0 2.0 3.0 0.0 0.0

P2 0.0 2.0 4.0 4.0 0.0

P3 2.0 0.0 5.0 0.0 5.0

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By introducing the “dying probability” for the individuals and the “war/disease process” for the population, the authors propose a novel approach in this paper to determine the population size and the alternation between generations. The symbols for our algorithm as follows: POP_INITIAL --- the initial population size, POP_MAX ---the max size of the population, SELECTION_POP--- the number of individuals selected into the reproducing pool in each iteration, sizeof_population--- the size of the current population, DIE_PROBABILITY[k] ----the pre-defined dying probability to those individuals lived for k generations, die probability ---the dying probability of the current individual, VALMAX ---the designated max fitness to determine whether the algorithm should be stopped, value_max--- the max fitness of the current population, value_min--- the least fitness of the current population. The step of the algorithm is summarized as follows: (1) Generate initial population: sizeof_population=POP_INITIAL; create randomly population[sizeof_population], die_probability[sizeof _population]= DIE_PROBABILITY[0]. (2) Evaluate the individual to obtain the max fitness and the least fitness of the population: value_max and value_min. (3) Memorize the best solution and stop if value_max > VALMAX or gap > GAP. (4) Select SELECTION_POP individuals into the reproducing pool randomly according to their fitness. (5) Divide individuals in the reproduction pool into couples randomly. All the couples perform the crossover and mutation operations. If the fitness of one child is larger than value_min, then put it into the population, else determine whether it should be put into the population according to the predefined probability; sizeof_population++. (6) Perform die process. For each individual, according to its die probability determine whether it will die. If the individual should die then sizeof_population- -; else if die_probability =DIE_PROBABILITY[k] then die_probability = DIE_PROBABILITY[k++]. (7) Perform the war/disease process: if sizeof _population > POP_MAX then select POP_INITIAL individuals randomly into the new population according to their fitness. Go to step 2. 4.2 PSO-GA Based Hybrid Algorithm Particle Swarm Optimization (PSO) also is an evolutionary computational model which is based on swarm intelligence. PSO is developed by Kennedy and Elberhart [21] who have been inspired by the research of the artificial livings. Similar to GAs, PSO is also an optimizer based on population. The system is initialized firstly in a set

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of randomly generated potential solutions, and then performs the search for the optimum one iteratively. Whereas the PSO does not possess the crossover and mutation processes used in GAs, it finds the optimum solution by swarms following the best particle. Compared to GAs, the PSO has much more profound intelligent background and could be performed more easily. Based on its advantages, the PSO is not only suitable for science research, but also engineering applications, in the fields of evolutionary computing, optimization and many others [22],[23]. This paper proposes a novel hybrid approach through crossing over the PSO and GA, called hybrid PSO-GA based algorithm (HPGA). The proposed algorithm executes the two systems simultaneously and selects P individuals from each system for exchanging after the designated N iterations. The individual with larger fitness has more opportunities of being selected. Simulations for a series of benchmark test functions show that the proposed HPGA method possesses better ability of finding the global optimum compared to the GA and PSO algorithms. This paper proposes a novel hybrid PSO-GA based algorithm (HPGA). The performance of the algorithm is described as follows: (1) Initialize GA and PSO sub-systems, respectively. (2) Execute GA and PSO simultaneously. (3) Memorize the best solution as the final solution and stop if the best individual in one of the two sub-systems satisfies the termination criterion. (4) Perform hybrid process if generations could be divided exactly by the designated iterative times N . Select P individuals from both sub-systems randomly according to their fitness and exchange. Go to step 2. In this section, the novel GA described in section 4.1 is employed in the hybrid algorithm HPGA. Therefore, the number of individuals should satisfy that P 0 ° + r (t ) + η ] [ g 0 − β (t )] , sgn( s ) = ® 0, s = 0 ° −1, s < 0 ¯

(8)

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From the analysis above, we get ss ≤ −η s < 0 , where η > 0 is constant. So under the control law (8), the sliding surface exists and is reachable. Since λ 2 + c2 λ + c1 is Hurwitz polynomial, the sliding surface is stable.

3 Design of SMC Based on FNN From (8) it can be seen that the undesirable control input chattering in the conventional SMC is caused by the discontinuous sign term sgn( s) . The switching control law uN which guarantees the reachability and existence of the sliding mode is in proportion to the uncertainty bound including α i (t ) xi , β (t ) uequ and r (t ) . However, the bound of parameter variations and the external disturbance are difficult to know in advance for practical applications. Therefore, usually a conservative control law with large control gain K is selected. However, it will yield unnecessary deviations from the switching surface, causing a large amount of chattering. online learning algorithm

δd

×

e1

s

X

d dt

s s

FNN

SMC

∆u N

uequ

× z −1

uN +

+

×

electro-hydraulic servo mechanism

δ

Fig. 2. Missile electro-hydraulic servo mechanism with SMC based on FNN

Therefore, a FNN is adopted in this study to facilitate adaptive switching control law adjustment. The control block diagram of the SMC based on FNN is shown in Fig.2. The inputs of the FNN are s and its derivative s , and the output of the FNN is the substituted sliding switch control ∆u N . The adjustment of ∆u N is stop when the output error between the position command and the actual plant is zero. If the output error e → 0 as t → ∞ implies s and s → ∞ as t → ∞ . If the uncertainties are absent, once the switching surface is reached initially, a very small value of u N would be sufficient to keep the trajectory on the switching surface, and the amplitude of chattering is small. However, when the uncertainties are present, deviations from the switching surface will require a continuous updating of u N produced by the FNN to steer the system trajectory quickly back into the switching surface. Though the true value of the lumped uncertainty cannot be obtained by the FNN, a less conservative control is resulted to achieve minimum control effort according to s and its derivative s [10].

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The structure of FNN can be seen in [11]. The signal propagation and the basic function in each layer are introduced below. Layer 1 is the input layer. The net input and the net output are represented as fi (1) = xi(0) = xi , xi(1) = fi (1) ( i = 1, 2 )

.

(9)

where x1 = s , x2 = s . In order to guarantee tracking precision, s and s should be changed into the uniformed form. The net input is initialized in the range [ −1,1] . Layer 2 is the linguistic variable layer. The term set of each fuzzy variable is{ NB , NS , ZE , PS , PB }. In this layer each node performs a membership function. The Gaussian function is adopted as the members function.

f

(2) ij

=−

( xi(1) − cij ) 2

σ

2 ij

, xij(2) = µi j = e

f ij( 2 )

(i = 1, 2; j = 1, ,5) .

(10)

Layer 3 is the fuzzy logic rule layer. (2) (3) f j(3) = x1(2) = a j = f j(3) (i1 , i2 = 1, ,5; j = 1,  , 25) . i1 x2 i2 , x j

(11)

Layer 4 is a uniformed layer. Each node is the uniformed form as following

f j(4) = x (3) j

25

= aj

¦x

(3) i

i =1

25

¦a

(3) i

, x (4) = a j = f j(4) ( j = 1, 2, , 25) . j

(12)

i =1

Layer 5 is the output layer. 25

25

j =1

j =1

f (5) = ¦ w j x (4) = ¦ w j a j , x (5) = ∆uN = f (5) j

.

(13)

BP is used in the learning algorithm for FNN. There are two phases including an off-line training one and on-line training one. They are described below respectively. 1) Off-line training phase. The training sample data are produced by fuzzy control [6]. For training the FNN, the cost function is defined as follows: J = 0.5 × (∆u*N − ∆uN )2 .

(14)

where ∆u*N is the desired output and ∆u N is the FNN’s output. Then the weight w j and the parameters ( cij , σ ij ) of membership function can be modified as follows w j (t + 1) = w j (t ) − β

cij (t + 1) = cij (t ) − β

∂J ∂w j

( j = 1, 2,, 25 ).

∂J ∂J , σ ij (t + 1) = σ ij (t ) − β ( i = 1, 2; j = 1,,5 ) ∂cij ∂σ ij

(15)

(16)

where β is the learning rate. ∂J ∂w j , ∂J ∂cij and ∂J ∂σ ij can be derived as follows such that the cost function defined in (14) is minimized by using the BP algorithm.

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2( xi − cij ) 2 2( xi − cij ) ∂J ∂J ∂J ( 2) = −(∆u*N − ∆u N )a j , = − , δ . = −δ ij(2) ij ∂w j ∂cij σ ij3 ∂σ ij σ ij2 1

where δ (5) = ∆u*N − ∆u N , δ (4) = δ (5) w j , δ (3) = j j

25

(¦ ai )2

25

25

i =1

k =1

(17)

(4) (δ (4) j ¦ ai − ¦ δ k ak ) i≠ j

k≠ j

i =1

n ­∂f k(3) i µ jj if xij(2) is the input of rule k = ° ∏ (2) (2) (3) δ ij = ¦ δ k Sij e , Sij = ® ∂xij j =1, j ≠ i k =1 ° 0 otherwise ¯ 2) On-line training phase. The pre-training FNN is implemented to enhance the control performance. Considering Computation effort and real-time character, the adjusted parameter is only w j . For training FNN, the cost function is defined as 25

−

( xi − cij )2

σ ij2

J c = 0.5 × ( y − xd )2 .

(18)

Thus the weight parameters w j can be modified as follows w j (t + 1) = w j (t ) + r ⋅ ( y − xd )a j (∂y ∂∆uN ) .

(19)

where r is the learning rate. Considering Computation effort , ∂y ∂∆u N is replaced by its sign function sgn(∂y ∂∆uN ) [11].

4 Simulation Results and Discussion For a missile electro-hydraulic servo mechanism (1), the nominal value [1] of some parameters are assumed as kui = 5mA / V , K Q = 12cm3 /( s ⋅ mA) , A = 10cm 2 ,

R = 17cm . Substituting the values into (2), we get a10 = 0 , a20 = 8873.64 , a30 = 37.68 , g 0 = 179425 , d = 0.86M + 9.73M , where M = M f 0 Sgnδ + M d , M f 0 is frictional torque amplitude, M d is position torque. Desired trajectory δ d (t ) = sin 2π t . The sampling period t = 1ms . Assume ∆ai = 0.5sin(2π t )ai 0 , so ∆ai ≤ α i (t ) = 0.5 × ai 0 , ∆g = 0.2sin(2π t ) g 0 , so

∆g ≤ β (t ) = 0.2 × g 0 , M f 0 = 3000 + 1000 sin 2π t , M d = 500 + 100sin 2π t . Choose the poles of the system as described by (6) at −80, −80 , we can obtain c1 = 6400 , c2 = 160 . The initial values of system state variables X (0) = [1 0 0]T . The initial values of u N is zero. All the parameters of the membership functions and connective weights are randomly initialized in the range [0,1] . Design parameter r = 0.15 , β = 0.25 , η = 1 . We do simulation research and compare results with that of conventional SMC under the same condition of parameter variations and external disturbances. Simulation results are indicated in Fig. 3 Fig. 8. Fig. 3 and Fig. 4 show the tracking

ˉ

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response of the system. Fig. 5 and Fig. 6 show the tracking error. Fig. 7 and Fig. 8 show the control input where the controller is taken as variable universe adaptive FSMC or the conventional SMC.

Fig. 3. Tracking response of system

Fig. 4. Magnifying figure of tracking response

Fig. 5. Tracking error of system

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Fig. 6. Magnifying figure of tracking error

Fig. 7. Control input with SMC based on FNN

Fig. 8. Control input with conventional SMC

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Simulation analysis: From the simulation results, we can conclude that: 1) if the controller is the conventional SMC, the tracking error is small and there are serious high frequency chattering in the control signal due to the sign function in the switching control; 2) if the controller is the SMC based on FNN, chattering phenomena is attenuated, the control input is smooth and the strength of the control signal can also be significantly reduced. The transient deviation of tracking error and control input, which are depicted in Fig.5 and Fig.7, respectively, are induced owing to the parameters initialization of the membership functions and connective weights especially under the occurrence of uncertainties. The tracking error is small because the adjusted parameter in the online training of the FNN can deal with the uncertainty of the system effectively.

5 Conclusions In this study, a design method of SMC based on FNN is proposed to control the position of missile electro-hydraulic servo mechanism. A FNN is introduced in conventional SMC, which uses the dynamical BP algorithm to ensure the existing condition of SMC. The high frequency chattering brought by sliding mode switch control can be effectively minimized, without sacrificing the robustness of sliding mode control. Simulation results indicate that the control approach can cope with uncertainties to obtain an excellent tracking result without the occurrence of chattering control input.

References 1. Zhu, Z. H.: Thrust Vector Control Servo System. Beijing, Astronautics press (1995) 2. Wang, Z. L.: Control on Modern Electrical and Hydraulic Servo. Beijing, Beijing University of Aeronautics and Astronautics press (2004) 3. Hung, J. Y., Gao, W. B., Hung, J. C.: Variable Structure Control: A Survey. IEEE Trans. Ind. Electron., Vol. 40, No.2 (1993) 2-22 4. A. G. Mohamed: Variable Structure Control for Electro-hydraulic Position Servo System. The 27th Annual Conference of the IEEE Industrial Electronics Society (2001)2195-2198 5. Liu, Y. F., Dong, D.: Research on Variable Structure Robust Control for Electro-hydraulic Servo System. Journal of Second Artillery Engineering Institute, Vol. 19, No.4(2005) 12-14 6. Duan, S. L., An, G. C.: Adaptive Sliding Mode Control for Electro-hydraulic Servo Force Control Systems. Chinese Journal of Mechanical Engineering, Vol.38. No.5 (2002) 109-113 7. Ha, Q. P., Nguyen, Q. H.: Fuzzy Sliding Mode Controllers with Applications. IEEE Transactions on industrial electronics, Vol.48. No.1 (2001) 38-46

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8. Mihajlov, M., Nikolic, V., Antic, D.: Position Control of an Electro-hydraulic Servo System Using Mode Control Enhanced by Fuzzy PI Controller. Mechanical Engineering, Vol.1. No.9 (2002) 1217-1230 9. Liu, Y. F., Miao, D.: 1553B BUS and Its Application in Electro-hydraulic Servo System. Machine Tool & Hydraulics, Vol.38. No.9 (2004) 106-108 10. Karakasoglu, A., Sundareshan, M. K.: A Recurrent Neural Network-based Adaptive Variable Structure Model Following Control of Robotic Manipulators. Automatica, Vol. 31. No.5 (1995) 1495-1507 11. Wang, Y. N.: Intelligent Control Engineering for Robots, Beijing, Science Press (2004)

Stability Analysis of Network Data Flow Control for Dynamic Link Capacity Case Yuequan Yang1, Yaqin Li1, Min Tan2, Jianqiang Yi2, John T. Wen3, and Xuewu Guo4 1

College of Information Engineering, Yangzhou University, Yangzhou 225009, China 2 Key Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China 3 Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA 4 Shanxi Jinyao Coking Co. Ltd, Shanxi 030001, China [email protected], [email protected]

Abstract. Much attention has been paid upon network data flow control in recent years. The main problem in this field is how to design good algorithm or control law for flow rate of network data flow sources and for updated price of communication links. Base on Lyapunov stability theory, this paper makes a deep analysis of stability of such network data flow control systems with the consideration of dynamic link capacity case. Simulations show that the stability analysis of dynamic link capacity of network data flow control system provided in the paper is enlightening and meaningful to further understand and design good control strategy of network data flow control problem.

1 Introduction In recent years congestion control has attracted much interest in the field of control theory research. Many good regulation methods and control schemes have been proposed. In the Internet environment, network flow is governed by the interconnection between information sources and communication links [1-9]. With this view, the central problem is to seek good regulation law for each source rate and update law of price for communication links. F. Kelly, A. Maulloo, and D. Tan (1988, [1]) and S. H. Low and D. E. Lapsley (1999, [2]) provided a common approach to flow control, that is, to decompose the problem into a static optimization problem and a dynamic stabilization problem. For the optimization the main task is to design algorithms to approximate to equilibrium of the closed loop system with some constraints of available queue length or available link rates based on gradient projection optimization techniques. In [2], the synchronous algorithm and asynchronous update algorithm are proposed. S. H. Low, F. Paganini, and J. C. Doyle (2002, [3]) pointed out that congestion control mechanisms in today’s Internet already represent one of the largest deployed artificial feedback systems. In [3], comprehensive D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 395 – 406, 2006. © Springer-Verlag Berlin Heidelberg 2006

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description and analysis were given with optimization-based framework. Considering the presence of communication delays, R. Johari and D. K. H. Tan (2001, [4]) gave stability condition of network rate control for both a single resource and a large network with constant round-trip delay. Especially, J. T. Wen (2004, [5]) developed a unifying framework for stabilizing source and link control laws, which encompass many existing algorithms in [1,6] and many special cases. Based on passivity theory, J. T. Wen proposed a comprehensive equilibrium stability analysis and dynamic control law design by constructing different passive system or strictly passive systems instead. The greatest advantage of this novel strategy is the combination of equilibrium stability and dynamic control law design for network flow control. Though, because the complexity and variety of network environment, capacity of links to be allocated is not static, but often dynamic according to its available bit rate for some networks such as ATM network environment in reality. Contraposing to this problem, this paper mainly aims at giving deep stability analysis of the optimum equilibrium manifolds of the primal optimal problem and its dual problem based on some mild conditions. This paper is organized as follows. In section 2, we provide some preliminary knowledge including some critical concepts, such as positive projection, strictly passivity and other critical results to be used in next sections. The main problem under consideration is described in detail in section 3. The deep L p stability analysis of the two kinds of systems based on rate control for information sources and link price update price law models is given based on Lyapunov stability theory in section 4. The simulation experiments are done in section 5. Finally, conclusion is made in section 6.

2 Preliminary Knowledge In this section, some preliminary knowledge about passivity theory and some critical results are given as follows. Definition 2.1. [5] Positive projection

( f (x)) +x

with some function

f (x ) is

defined as follows

­ f ( x ) ᧨ if x > 0, or x = 0 and f ( x ) ≥ 0 ( f ( x )) +x = ® ¯0 ᧨ if x = 0 and f ( x ) < 0

(1)

Now, assume there exist a system H , in which system state is vector

x ∈ R N , input

u ∈ R M and output y ∈ R M . According to passivity theory[10], some definitions are given as follows. Definition 2.2. The system H above is called passivity, if there exists a continuously differentiable energy function some

W ( x) ≥ 0 .

V ( x ) ≥ 0 satisfying V ( x ) ≤ −W ( x ) + u T y for

Stability Analysis of Network Data Flow Control for Dynamic Link Capacity Case

397

From the above definition, some system is passive if the system itself doesn’t generate energy, but possibly dissipates the energy injected into the system. Definition 2.3. The system H above is called strictly passivity, if there exists a V ( x) ≥ 0 satisfying continuously differentiable energy function

V ( x ) ≤ −W ( x ) + u T y for some W ( x ) > 0 . Lp stable, if Lp -norm of the state vector, and output vector of the controlled system exist simultaneously for p > 1 , or p = ∞ if input vector variable is L p .

Definition 2.4. The system is

Lemma 2.1[11] . Suppose that

W : [0, ∞) → −αW (t ) + β (t ) satisfies

D +W (t ) ≤ −αW (t ) + β (t )

(2)

D + denotes the upper Dini derivative, α is a positive constant, and β ∈ L p , p ∈ [1, ∞) , then

where

W where

−

Lp

1 p

1 q

≤ (αp ) W (0) + (αq) β

(3) Lp

p, q satisfies 1 1 + =1 p q

(4)

and when p = ∞ , the following estimate holds

W ≤ e −αt W (0) + α −1 β

L∞

(5)

3 Problem Formulation As we know, status of network environment is often changing along with time. Not only the number of network data flow source but also link rate capacity/bandwidth is variable. In fact, some network links in certain routing path might fail in work. In this note, we don’t plan to make consideration of this problem. Now we focus upon such an occasion that link rate capacities for sources are not constant, but dynamic changing along with time, denoted as c (t ) with respect to time variable t . Firstly, we assume network is constructed by N information resource and L communication links where N and L are some known integer number. Now we define a routing matrix

R = ( rij ) L× N with ­1 , if the source j passes through the link i rij = ® ¯0 , other

(6)

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s(l ) and l (s ) respectively, i = 1,  , L } . that is, s( l ) = { j | rlj = 1᧨j = 1,  , N } and l ( s ) = {i | ris = 1᧨ From the routine matrix, it is easily to define two sets

y ∈ R L and aggregate price of sources

Then the aggregate rate vector of links

q ∈ R N can be defined respectively as y = Rx, and q = R T p

(7)

where x ∈ R is called source rate vector and p ∈ R link price vector. In [1], the information flow control problem is described a static optimization prime problem and its dual problem as follows N

L

max x ≥0

where

¦

U i ( xi )

s. t.

Rx ≤ c(t )

i =1,, N

(8)

U i ( xi ) is utilization function with the strictly concave property and

c(t ) ∈ R L is link rate capacity vector with component cl (t ) representing the rate capacity of the link l . Its dual problem is easily obtained as follows min max p ≥0

x ≥0

¦ U (x ) − ¦ i

i

i =1,, N

pl ( yl − cl (t )) .

l =1,, L

(9)

After simple transformation, the above can be converted to be

min max p ≥0

If

x ≥0

¦{ U ( x ) − q x } + ¦ i

i

i

i =1,, N

i

l =1,, L

p l cl ( t )

(10)

U (x ) is differentiable, the first order condition for the maximization problem is U i' ( xi ) = qi

(11)

­= 0 , if y l < cl (t ) pl ® ¯≥ 0, if y l = cl (t )

(12)

and

where U i' ( xi ) = ∂U i ∂xi . From appendix I in [5], we know that if U i ( xi ) is strictly concave and routing matrix R is full row rank the (11) and (12) are sufficient to determine unique equilibrium for the constant link capacity. But what will happen when link capacity becomes dynamic changing along with time? The objective of flow rates and link update laws is to drive the actual source rate and link prices to their respective equilibrium dynamic. To realize this destination, there are several real constraints exist, such as decentralization network topology, no routing information, that is, routing matrix is unknown to network data flow source, no coordination and the link capacity is time varying.

Stability Analysis of Network Data Flow Control for Dynamic Link Capacity Case

399

In [1], the source update law is given by

x = K (U ' ( x ) − q(t )) where

+ x

(13)

K = diag{k } K = diag{ki }, ki > 0 , U ' ( x) ∈ R N with ith component

U i' ( xi ) . And the link price generation function is given by p = h( y ) where

(14)

h ( y ) ∈ R L , with l th component is hl ( yl ) which may be considered as a

penalty function enforcing the link capacity constraints,

yl ≤cl (t) . The function h( y )

is monotonically nondecreasing and nonnegative which is defined in [1] as

hl ( y ) =

( yl − cl + ε ) +

. Here, considering the dynamic capacity case, introducing a

ε2 buffering factor δ and dynamic adjusted factor γ (t ) , link price generated function is defined as follows

㇢

0, y l ≤ (1 − δ )cl (t ) ­ hl ( y l ) = ® 2 (1 − δ )cl (t ) < y l ¯γ (t )( y l − (1 − δ )cl (t )) ,

㇢

(15)

where

­δ , δ =® 1 ¯δ 2 ,

cl (t ) ≥ 0 cl (t ) < 0

,0 < δ 1 < δ 2 < 1 

(16)

The main motivation to define such a link price generation function above is to reduce the risk of link congestion under consideration of dynamic link capacity case. The buffering factor and dynamic adjusted factor become smaller while available link capacity becomes increasing which aims to widen the buffer size. But in this case under consideration, from (11) and (12), we can find that equilibrium is shifted and timely variant because link capacity c (t ) is not constant now. Therefore, equilibrium manifold can be obtained as

q * = U ' ( x * (t )) and p * = h( y * (t ))

(17)

It is remarkable to note that much attention should be paid to link capacity’s changing property such as rate changing velocity, changing shape and so on. The detailed analysis of the influence of dynamic link capacity upon equilibrium manifold and control performance will be done in next research step. In this note, network data flow control shown at Fig. 1 considering the differences between real-time data flow and equilibriums as follows Proposition 3.1. Assume that: (1) link capacity c l (t ) is dynamic changing with time;

(2) If U : R → R satisfies U ( x ) < − δ I N , δ > 0 , and I N is N × N unit matrix. (3). Routing matrix R is of full row rank, then optimality condition given by (11) and (12) has a unique equilibrium manifold (17). N

N

''

400

Y. Yang et al. * − ( p − p* ) − (q− q )

RT

-

y − y*

x− x*

x = K(U' (x) − q*)+x

R

p − p*

h Fig. 1. Diagram of network data flow control in error means

For simplicity some interpretation of the above proposition is given. When the variable t is frozen and denoted as t , it is apparent to see now the situation is same

c(t ) , there are unique equilibrium p ( t ) , q ( t ) , x ( t ) , y (t ) . So, when link capacity c l (t ) is

with the Appendix I in [5]. That is to say, for every *

*

*

*

*

*

*

*

dynamic changing with time, p ( t ) , q ( t ) , x ( t ) , y (t ) forms a dynamic equilibrium manifold each. Here we focus on the equilibrium manifold over the dynamic link capacity case. And the next task is to realize stability analysis of network flow control for the primal optimal control system and the dual optimal control system.

4 Stability Analysis Firstly, according to the passivity-based flow control structure shown in Fig. 1, we observe the system with source rate controller and link update law as follows

­ x = K (U ' ( x ) − q) +x ° ° p = h( y ) °y = ( ¦ x i (t )) l = Rx ® i∈s ( l ) ° °q = ( ¦ pl ) i = R T p ° l∈l ( i ) ¯

(18)

and we have the following results. Theorem 4.1. Considering the closed-loop system (18) shown in Fig. 1, with the

assumption that U ( x ) < −δI N , for some ''

δ >0,

and the link penalty function

h ( y ) satisfies

0 ≤ h ' ( y ) ≤ η , for all y ≥ 0 and all links

(19)

where η is a positive constant. Then the two following inequalities hold

x − x*

Lp

≤ kmax (δkmin p)−1/ p ( x(0) − x* (0)T K( x(0) − x* (0) + 2 kmax (δkminq)−1/ q 1 / 2kmax / kmin x * (t )

(20) Lp

Stability Analysis of Network Data Flow Control for Dynamic Link Capacity Case

p − p*

Lp

≤ η R x − x*

Lp

.

401

(21)

*

That is, if x (t ) is L p , then the system (18) is L p stable. Proof: We take the Lyapunov function as follows

V1 ( x − x * (t )) =

( xi − xi* (t )) 2 1 . ¦ ki 2 i =1,, N

(22)

Its derivative along the solution is

V1 =

¦(x

i

− xi* (t ))( x i − x i* (t )) / k i

i =1,, N

=

¦ (x

i

− x i* ( t ))( U i' ( x i ) − q i ) +x − ( x i − x i* ( t )) / k i x i* ( t )

(23)

i = 1 , , N

According to the definition of positive projection, it yields

( x i − x i* (t ))(U i' ( x i ) − qi ) +x ≤ ( x i − x i* ( t ))(U i' ( x i ) − qi )

(24)

With the above inequality, (23) can turn into

V1 ≤

¦(x

i

− xi* (t ))(U i' ( xi ) − qi ) − ( xi − xi* (t )) / ki xi* (t )

i =1,, N

=

¦( x − x (t ))(U ( x ) − q * i

i

' i

* i

i

+ qi* − qi ) − ( xi − xi* (t )) / ki xi* (t )

i =1,, N

=

¦( x − x (t ))(U ( x ) − U ( x (t )) + q i

* i

' i

i

' i

* i

* i

− qi ) − ( xi − xi* (t )) / ki xi* (t )

i =1,,N

= ( x − x * (t )) T (U ' ( x ) − U ' ( x * )) − ( x − x * (t )) T ( R T ( p ) − R T ( p * )) − ( x − x * (t )) T K −1 x * (t ) Considering the utilization function is strictly concave, then 2 V1 ≤ −δ ∆x − ∆x T kx * (t ) − ( y − y * (t )) T ( p − p * )

(25)

2

= −δ ∆x − ∆x T kx * (t ) − ( x − x * ( t )) T R T ( h ( Rx ) − h( Rx * )) And with the property of the function vector satisfies (19), further we have 2 V1 ≤ −δ ∆x + k ∆x x * (t ) − ( x − x * (t )T R T h ' (ξ ) R( x − x * ) 2

≤ −δ ∆x + k ∆x x * ( t )

≤ −2δk minV1 + 2k max / k min x * (t ) V1

(26)

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where

k = k max , k min = min{k i , i = 1, , N } , k max = min{ki , i = 1, , N } ,

∆x = x − x * and ξ ∈ [ Rx, Rx * ] which follows from the mean value theorem. We take

W = V1 and obtain D +W = −δk minW + 1 / 2k max / k min x * (t )

(27)

According Lemma 2.1, we get

W

Lp

≤ (δkmin p)−1/ p W (0) + (δkminq)−1 / q 1 / 2kmax / kmin x* (t )

Lp

and

W (t ) ≤ e −δkmint W (0) + (δk min ) −1 1 / 2k max / k min x * (t )

L∞

.

Therefore, following from the above, it is easy to obtain (20) and (21). Furthermore, * the system is L p stable if x (t ) is L p .

Remark 4.1. From (25), it is not difficulty to find that the forward system in Fig.1 is strictly passive when the following

∆x >

k

δ

x * (t )

(28)

holds. Further, it shows that for the case of dynamic link capacity the forward system strictly passivity partly depends not only on the approximate difference of information source rate x (t ) to the equilibrium dynamic x * (t ) but also on its changing degree. It is not always true that the faster the source flow rate approaches, the better performance of the system. Remark 4.2. According to theorem 4.1, we know that that the system under *

consideration is Lp stable depends upon the property of x (t ) , which in fact upon the property of dynamic link capacity c (t ) . Next, we consider the dual problem shown as Fig. 2. * − ( p − p* ) −(q− q ) x− x* ' − 1 x = (U ) (q) R RT



p − p*

y − y*

p = Γ( y − c(t))+p

Fig. 2. Diagram of the dual problem in error means

Stability Analysis of Network Data Flow Control for Dynamic Link Capacity Case

403

and we define it as follows

­ x = (U ' ) −1 ( q) ° + ° p = Γ( y − c(t )) p ° ® y = ( ¦ xi (t ) ) l = Rx i∈s ( l ) ° °q = ( pl ) i = R T p ¦ ° l∈l ( i ) ¯ Γ = diag{λl > 0, l = 1,, L} and λmin = min{λl , l = 1,, L}. where

(29)

and denote λmax

= max{λl , l = 1,, L}

Theorem 4.2. For the system (29) shown as Fig.2, assume that

− δ 1 I N ≤ U '' ( x ) ≤ −δ 2 I N

(30)

and for certain positive constant c 2 , the following condition

p (t ) ≤ c2

(31)

where c 2 is a positive constant, then the system (29) is L p stable. And furthermore, there exist

p− p*

Lp

≤ λmax(αp)−1/ p ( p(0) − x* (0)T Γ−1(x(0) − x* (0) + 2 λmax(αq)−1/ q β L

(32)

p

x − x * (t ) ≤ 1 / η 2 R p − p * (t )

Lp

(33)

where 2 α = δ 1−1λmin σ min (R)

(34)

β = 1 / 2λmax / λmin p * (t )

(35)

Proof: First, define the Lyapunov function as V2 ( p − p * ) =

( p l − p l* (t )) 2 1 ¦ 2 l =1,,L λl

Along with the (29), the difference of the above can be obtained

V2 =

¦( p

l

− p l* (t ))( p l − p l* (t )) / λl

l =1,, L

= ( p − p * ) T ( y − c ) +p − ( p − p * ) T Γ −1 p *

(36)

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≤ ( p − p * ) T ( y − y * ) − ( p − p * ) T Γ −1 p *

(37)

= ( p − p * ) T R ((U ' ) −1 ( R T p ) − (U ' ) −1 ( R T p * )) − ( p − p * ) Γ −1 p * = ( p − p * ) T R(U '' ) −1 (ξ ) R T ( p − p * ) − ( p − p * ) Γ −1 p * * The above follows from the mean value theorem, where ξ ∈ [ p, p ] and with the assumption (30), the above turns into 2 V2 ≤ −δ 1−1 R T ( p − p * (t )) + 1 / λmin p − p * p * 2 ≤ −2δ 1−1λminσ min ( R )V2 + 2 λmax / λmin p * V2

(38)

Further using W = V 2 , we have 2 D +W = −δ 1−1λminσ min ( R )W + 1 / 2λmax / λmin p * (t ) .

(39)

From Lemma 2.1, it is easy to get (32), and because of

x = (U ' ) −1 ( q) = (U ' ) −1 ( Rp ) and mean value theorem, the (33) is not difficult to be obtained . Remark 4.3. From (37), only when the following

p * = Λ ( p − p* ) , for Λ = diag{τ l > 0, l = 1,  , L} ,

(40)

then return subsystem is strictly passive. Remark 4.4. Through the deep analysis above, the condition stability of the system under consideration is comparatively tough. For dynamic link capacity case, the property of p * which is determined by dynamic link capacity, plays very important

role of the network data flow control system.

5 Simulations First, we assume simulation test is made based on the topological graph of network data flows shown in Fig.3, S1 S 2 1

5 3

2 S3

4 S 4 S5

Fig. 3. Topological graph of network data flows

Stability Analysis of Network Data Flow Control for Dynamic Link Capacity Case

and the routing matrix

405

R is given as follows ª1 «0 « R = «1 « «1 ¬«0

1 0

0 0 0º 1 1 0» » 1 1 1 0» » 0 1 1 1» 1 0 0 1 »¼

(41)

The buffering factor ϑ1 = 1 / 8,ϑ2 = 1 / 6 , and dynamic adjusted factor follows

γ (t ) is chosen as

㇢ c ( t ) < 0 ㇢ c ( t ) = 0 ㇢ c ( t ) > 0

­3, °

γ (t ) = ® 2 , °1, ¯

(42)

Here, two cases are considered in the simulation tests. Firstly, network link capacities available to be occupied for feedback based are constant, with 10, 8, 24, 15 and 16 Mb/sec from link 1 to link 5 respectively. The flow rate of each data flow is shown in Fig.4. Secondly, considering the dynamic link capacity case, that is, the dynamic capacity of link 3 and link 4 given by (43), the simulation test is shown is Fig.5. ­ 20 , ° c 3 ( t ) = ® 20 + 3 t , ° 15 , ¯

0 ≤ t ≤ 10 10 ≤ t ≤ 15 15 ≤ t

 c ( t ) = ­ 30 − t , ® 4 ¯ 20 ,

12

0 ≤ t ≤ 15 15 ≤ t

(43)

14 flow 1 flow 2 flow 3 flow 4 flow 5

10

flow 1 flow 2 flow 3 flow 4 flow 5

12

10

flow rate

flow rate

8

6

8

6

4 4 2

0

2

0

2

4

6

8

10

time

Fig. 4. Flow rate for constant capacity case

0

0

10

20

30

40

50

time

Fig. 5. Flow rate for dynamic capacity case

6 Conclusion In this paper L p stability analysis of network data flow control system with dynamic link capacity case from the Lyapunov stability point of view, is first done for both its prime flow control system and its dual control system. Moreover, the corresponding comparison with passive or strictly passive property of flow control system is made. The conclusion is that stability performance of network data flow control system under consideration depends on property of dynamic link capacities. The simulations

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illustrate the stability analysis in this paper is good and enlightening. Therefore, research about transient and statistical property of dynamic link capacity needs to be made in the fields of control and computer areas.

Acknowledgments This work is partly supported by the National Natural Science Foundation of China under Grant No. 60334020 and No. 60440420130.

References 1. Kelly, F., Maulloo, A., Tan, D.: Rate Control In Communication Networks: Shadow Prices, Proportional Fairness And Stability. J. Oper. Res. Soc. 49 (1998) 237-252 2. Low, S.H., Lapsley, D.E.: Optimization Flow Control—I: Basic Algorithm And Convergence. IEEE/ACM Trans. Networking. 7 (1999) 861-874 3. Low, S.H., Paganini, F., Doyle J.C.: Internet Congestion Control. IEEE Control System Magazine. 22 (2002) 28-43 4. Johari, R., Tan, D.K.H.: End-to-End Congestion Control for the Internet: Delays and Stability. IEEE/ACM Trans. Networking. 9 (2001) 818-832 5. Wen, J.T., Arcak, M.: A Unity Passivity Framework for Network Flow Control. IEEE Trans. Automatic Control. 49 (2004) 162-174 6. Paganini, F.: A Global Stability Result In Network Flow Control. System Control Letters. 46 (2002) 165-172 7. Ioannou, P., Tao, G.: Frequency Domain Conditions for Strictly Positive Real Functions. IEEE Trans. Automatic Control. 32 (1987) 53-54 8. Wen, J.T.: Time Domain and Frequency Domain Conditions for Strict Positive Realness. IEEE Trans. Automatic Control. 33 (1988) 988-992 9. Paganini, F., Doyle, J.C., Low, S.H.: Scalable Laws for Stable Network Congestion Control. In Proc. of Conference on Decision Control, Orlando, FL. (2001) 185-190 10. Arjan van der Schaft: L2-Gain and Passivity Techniques in Nonlinear Control. SpringerVerlag London Limited (2000) 11. Khalil, H.: Nonlinear Systems. 2nd ed. England Cliffs, NJ: Prentice Hall (1996)

Matrix Measure Stability Criteria for a Class of Switched Linear Systems Hongbo Zou, Hongye Su, and Jian Chu National Laboratory of Industrial Control Technology, Institute of Advanced Process Control, Zhejiang University, Hangzhou, 310027, P.R. China {hbzou, hysu, chuj}@iipc.zju.edu.cn

Abstract. The problem of stability analysis for a class of switched linear systems is studied in this paper based on the properties of matrix measure. The matrix measures of all subsystems are used to determine the stability of the switched linear systems. Based on this, sufficient conditions are reached, which can be used to determine the stability or instability of switched linear systems under arbitrary switching law. If a switching sequence satisfies some conditions, a theorem in this paper can be used to verify if it can stabilize the systems. The obtained conditions are simpler than the reported methods such as multi-Lyapunov functions and hence are easier to check. Numerical examples are used to demonstrate these conditions.

1 Introduction A hybrid system is a dynamic system which be composed of discrete and continuous dynamical systems. Those systems arise as models for phenomena which cannot be described by exclusively continuous or exclusively discrete processes. The continuous processes generally have the form of differential equations and the discrete processes usually are logical or decision-making processes. The standard model for such systems is given in [1]. When a system can only be described by a nonlinear arithmetical model such as a nonlinear differential equation, it is difficult to get its exact arithmetical model in practice and the control law is also difficult to design. So in this instance, more then one simple models can be applied to describe this system approximately. When the system state vector arrives in a special space, one of these simple models is used to replace the system’s nonlinear mathematical model. All of these simple models are called subsystems and thus this system is a hybrid system. The systems like this are also called switched systems for its mathematical models switching between these subsystems. So we can say that a switched system is a special type of hybrid systems and the system state is continuous during the switching instances. For the sake of simplicity, subsystems usually are the linear models such as linear differential equations. Systems whose subsystems are all linear models are called switched linear systems. Examples include the control of manufacturing systems [2,3], communication networks, traffic control [4,5,6], chemical processing [7] and automotive engine control and aircraft control [8]. It is pointed out in [13] that there are three basic problems in stability analysis and design of switched systems: D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 407–416, 2006. c Springer-Verlag Berlin Heidelberg 2006


408

H. Zou, H. Su, and J. Chu

1. Find conditions that guarantee that the switched system (1) is asymptotically stable for any switching signal(under arbitrary switching sequence). 2. Identify those classes of switching sequence for which the switched system (1) is asymptotically stable. 3. Construct a switching sequence that makes the switched system (1) asymptotically stable. In the last two decades, there has been increasing interest in stability analysis and controller design for switched systems, see, e.g., [9,10,11,12,13,14,15,16] and the references therein. Up to now, the most efficient methods used to analysis the stability of switched systems are the multiple Lyapunov functional (see [11,12,17,18,19] ) and the common Lyapunov functional (see [9,10,14,20,21] ). A number of other different methods have been discussed in [13]. The work of [9] has been focused on the synthesis of a stable switching sequence on unstable switched linear systems. In that, assuming that there exists a Hurwitz linear convex combination of all of its subsystem matrices, they proposed a stable dependent switching sequence to stabilize the system. Their rule and proof of stability relay on common Lyapunov functional. In [10] the stability of a class of switched linear systems with input delay was studied. Applying common lyapunov functional they gave the method of construction of switching regions and a stable switching rule when time delay is very small. In [15], the stability of the switched linear systems whose subsystems have their eigenvalues real, negative and non-repeating has been discussed. If this condition is satisfied, the system will be globally asymptotically stable. The jumping systems were also discussed in this paper and sufficient conditions were given to verify if a jumping system is stable under arbitrary switching sequence. Ref. [16] discussed some necessary conditions for stability of switched linear systems. Ref. [22] dealt with the systems whose subsystems are fully controllable. With state feedback of all subsystems, the considered systems will be globally asymptotically stable under arbitrary switching sequence. But the design methods and criterions were not given. The practical stability and stabilization problems for hybrid and switched linear systems are studied in [23]. They focused their attention on the hybrid systems and switched systems which no common equilibrium point exists for all subsystems. They also discussed the practical stabilizability of switched systems with time-varying subsystems. In this paper, the attention is focused on the stability analysis of switched linear systems whose subsystems are linear time-variant systems. Applying the properties of matrix measure, sufficient conditions have been reached which can be applied directly to analyze the stability of switched linear systems under arbitrary switching sequence. At the same time, on the base of these conditions, a stable switching sequence can be verified if a system is asymptotically stable under this switching sequence when the system is unstable under some switching sequences. It is not required tedious arithmetic to apply these theorems and thus is easy to implement practically. Notations: In this paper, only switched linear systems are considered. A switched system is a hybrid system without state jump at switching instants (see [23]).

Matrix Measure Stability Criteria for a Class of Switched Linear Systems

409

2 Problem Formulation and Definitions In this paper, we consider a class of switched linear systems of the following form, x˙(t) where x(t)

Aq (t)x(t)


n is the system state, Aq (t), (q

(1)

1
2





N) are continuous in
n n .

Definition 1. (matrix induced norm)[24] Let  be a given norm on n , Then for each matrix A n n , the quantity i defined by

Ai

sup Ax


x


1

sup Ax
x


x
1

n

(2)

is called the induced norm of A corresponding to the vector norm  . Definition 2. (matrix measure)[24] Let i be an induced matrix norm on n n . Then the corresponding matrix measure is the function  : n n 
defined by 

[A(t)]

lim 0

I
A(t)  1

(3)



Remark 1. Given vector norm  on n , it is general a very difficult task to obtain an explicit expression for the corresponding induced norm. Therefore it is difficult to obtain an explicit expression for the corresponding matrix measure.

3 Main Results Lemma 1 ([24]). The matrix measures corresponding to the norms  , 1 and 2 , respectively, are 

 [A(t)]

max Re[aii (t)]


[A(t)]

max Re[a j j (t)]


1

2

i

j

[A(t)]

max


ji


i j

 ai j (t) 

 ai j (t) 

[AH (t)
A(t)]2



(4) 

(5)

(6)

where Re[ai j (t)] means the real part of ai j (t), max means the maximum eigenvalue of a matrix and AH (t) is Hermition adjoint of A(t). Proof. Eq. (4) and (5) can be obtained from Definition 1 and Definition 2 easily. The H 1
2 following is the proof of (6). Let A(t
) I
A(t). A(t)i2 max [A (t)A(t)] . According to definition 2, we have

410

H. Zou, H. Su, and J. Chu i2
1)( A(t
) i2
1) ( A(t
) i2
1) A(t
) 2i2
1 lim 0 ( A(t
) i2
1) max [AH (t
)A(t
)]
1 1 lim lim 0 A(t
) i2
1 0 

2 [A(t)]

lim

( A(t
)

0

1 lim 2 0

max I
2 AH (t)A(t)
[AH (t)
A(t)] 

1
max A (t)A(t)
[AH (t)
A(t)] 1 lim 2 0  max [AH (t)
A(t)]2 H









(7)


1


1

Lemma 2 ([24]). Whenever  i is an induced norm on n
n , the corresponding matrix measure () has the following property
 i




Re[A(t)]

[
A(t)]

 i

[A(t)]



(8)

holds. Lemma 3 ([24]). Consider the differential equation A(t)x(t) 

x˙(t) 


n

(9)

n n

and A(t) is piecewise-continuous. Let  be a norm on where x(t)   ,A(t)  and let  i and [A(t)] denote, respectively, the corresponding induced norm and matrix measure on n
n . Then whenever t
t0
0 , we have

n ,

x0 (t) exp

 t 






[
A(t)]dt

x(t)

x0 (t) exp



 t

t0



[A(t)]dt 

(10)

t0

holds. Remark 2. From Lemma 2 and Lemma 3, it is clear that if [A(t)]  0 , then the system (9) is asymptotically stable. And if [
A(t)]  0, then the system (9) is unstable. Theorem 1. Consider the switched linear system (1). Let () be a matrix measure on n
n . This system is asymptotically stable under arbitrary switching sequence if 1
2
  
N. q (t)  [Aq (t)]  0, q Proof. Let





DS  (t0
i0 )
(t1
i1 )
  
(tk
ik )
   

(11)

denote the switching sequence of the system (1). In DS, (tk
ik ) means subsystem ik is running in [tk
tk1 ). Define  (12) max  max q (t)  0  q
t

and let the initial state of system (1) is x0 x(t)



 x(t0 )  0. According to (10),

 t

x0 exp

t0

i0 ()d




t  [t0
t1 ) 

(13)

Matrix Measure Stability Criteria for a Class of Switched Linear Systems

411

holds. Then we have
t 1

x(t1 )

i0 (
)d


x0 exp


t 1



i0 (
)d


x0 exp

t0





(14)

t0

When t
[t1  t2 ), being the same with (13) and (14), the following can also be reached,
t

x(t)

i1 (
)d


x1 exp


t



x0 exp

t1

t1

i1 (
)d




t 1

i0 (
)d






(15)

t0

Repeating this and we finally obtain the following, 
t

x(t)

x0 exp tk

ik (
)d



k 1
tm1 

 im (
)d


(16)

tm

m 0

Considering (12), we can botain 
t

x(t)

x0 exp t0





max d




x0 exp (t  t0 )

max

 t  t0 

(17)

Then we have 0



lim x0 exp (t  t0 )

lim x(t)

t


holds and thus lim x(t) t


t


max

0

(18)

0. This completes the proof.

Theorem 2. Consider the switched linear system(1). Let () be a matrix measure on This system is unstable under arbitrary switching sequence if [Aq (t)]  0, q 1 2     N.

nn .

 Proof. The proof resemble that of Theorem (1). Suppose min

and x(t0 )  0, consider the left side of (10), then we have 
t

x0 exp t0

Thus we have lim x(t) t




 min d




  x0 exp (t  t0 ) min


min [ qt

(Aq (t))]  0

x(t) 

(19)


. So system (1) is unstable.

Theorem 3. Consider the switched linear system (1). Let (11) is a switching sequence of the system. Let
ik ,
i k denotes the time in which ik (t)
[Aik (t)]  0 and ik (t)




[Aik (t)] 0 ,respectively, in (ik  tk ). And let T 
i k , T
i k respectively. If there exists a switching sequence such as (11) which make lim

t


T T




 

hold, then this system is asymptotically stable under this switching sequence.

(20)

412

H. Zou, H. Su, and J. Chu

Proof. Suppose a switching sequence DS as (11). Let q (t) (Aq (t)). In (ik
tk ), let  (t)  0 and (t)  0. Because (t) is continuous in [tk
tk1 ), thus ik ik ik ik ik we can denote i k max max i k (t) and ik max max ik (t). Under DS, (16) is t
[tk tk1 )

t
[tk tk1 )

available. And we can get the inequality as follows, x(t)






t

x0 exp tk

ik d


m 0



x0 exp (t
tk ) max 0
tk

0 im k 1

x(t)




im ()d

tm ik ()

t

where i
m is the time in which (im
tm ). And let max max 



k 1
tm1 






k 1  

i
m

i
m
max


i

m




 



(21)

i
m
max

m 0

i
m (t)

 0 and i

m is the time in which i
m (t)  0 in
 0, max max  i

m
max   0, we get

i
m
max 

0 im k

x0 exp(T

max


T





max )



(22)

Since (20) holds, for any M  0, there exists a T M  0 and when t  T M , we have
T max  (M
1) T

max



T

max


T





max


0 
MT
max

(23)


) 
 holds. Thus the following inequality can be hold. So lim (T max
T
max t
 reached
) 0 0
lim x(t)
lim x0 exp(T max
T
max (24) t


t


This completes the proof. Remark 3. For a switched linear system whose subsystems are all fully controllable is unstable under arbitrary switching sequence, we can make it stable by applying the feedback to make it satisfy theorem (1). Remark 4. Theorem 3 implies that making those subsystems whose matrix measures are negative run longer is a necessary condition for a stable switched linear system.

4 Numerical Examples To demonstrate Theorem 1 and 2 directly by numerical examples is somewhat difficult. Alternatively, we can take other ways indirectly to demonstrate Theorem 1 and 2. Example 1 ([11]). According to Theorem 1, if the switched system (1) is unstable under some switching sequences, then at least one of its subsystems has its matrix measure nonnegative. 2, x Consider the switched system (1) with the following parameters, n N [x1 (t)
x2 (t)]T ,  
1
100
1 10 A1
A2 
100
1 10
1

Matrix Measure Stability Criteria for a Class of Switched Linear Systems

413

Both of the subsystems are asymptotically stable. If select



1 if q(t  )

2 if q(t  )

q(t )

2 and x2 (t) 1 and x2 (t)

A1



½ (A1 )

1

(A2 )

2




(25)

 0, this system is unstable. The matrix

as the switching sequence, then, for any x(0) measure of A1 and A2 are as follows, 1

5x1 (t) 0
2x1 (t)



(A1 )

½ (A2 )

99  0

(A2 )

88  0


2




(26)

Neither of them is negative. Example 2 ([11]). According to Theorem 2, if the switched system (1) is stable under some switching sequences, then at least one of ( Aq ), q 1 2


N is positive. Consider the switched system (1) with the following parameters, n N 2, x [x1 (t) x2 (t)]T ,     0 10 1
5 2 A1 A2
0 0 2 0
5 Both subsystems are unstable. If we select



1 if q(t  )

2 if q(t  )

q(t )

2 and x2 (t) 1 and x2 (t)

0
25x1 (t) 0
4x1 (t)

as the switching sequence, then this system is asymptotically stable. We have 1

( A1 )



½ ( A1 )

1

( A2 )

( A1 )

10

½ ( A2 ) 2 ( A 2 )

3
5 1


2 




(27)

All of them are positive. Example 3. Consider the switched linear system (1) with the following parameters, n N 2, x [x1 (t) x2 (t)]T ,



A1



0
4 1 A2 0 0
4





0
4 0 1 0
4




we have i1 (A1 ) i½ (A1 ) i1 (A2 ) i½ (A2 ) 0
6  0, i2 (A1 ) i2 (A2 ) 0
1  0, i1 ( A1 ) i½ ( A1 ) i1 ( A2 ) i½ ( A2 ) 1
4  0 and i2 ( A1 ) i2 ( A2 ) 0
9  0. So we can not apply Theorem 1 and Theorem 2 to this example. Let we design the switching sequence as follows, q(t )



1

2

kx1 1 k x1

x2  0 x2  0




(28)

Actually, if let k 0
4, then this system is unstable and Fig1 show the trajectory of system with x0 [ 1 1]T . Let k 0
25, then this system is asymptotically stable. Fig 2 show the trajectory of the system whit x0 [ 1 1]T .

414

H. Zou, H. Su, and J. Chu 700 system trajectory switching line 1 switching line 2 600

500

400 x2 300

200

100

mInitial point -100

0

100

200

300

400

500

600

700

x

1

Fig. 1. Unstable State Trajectory with k

04

system trajectory switching line 1 switching line 2

mInitial point 1

0.8

0.6 x2

0.4

0.2

0

-1

-0.8

-0.6

-0.4

-0.2 x1

0

Fig. 2. Stable State Trajectory with k

0.2

0 25

0.4

0.6

Matrix Measure Stability Criteria for a Class of Switched Linear Systems

415

5 Conclusion In this paper, we study the problem of stability analysis for a class of switched linear systems. When the matrix measure of all subsystems for a switched linear system are negative, we show that the system is asymptotically stable under arbitrary switching sequence. A sufficient condition is shown under which the system is unstable under any switching sequence. When a switched linear system do not satisfy any condition above, we show the sufficient condition can be used to verify if the system is stable under a special switching sequence.

Acknowledgment This work is supported by the National Creative Research Groups Science Foundation of China under grant 60421002, the National Science Foundations of P. R. China (60503027) and the National Tenth Five-Year Science and Technology Research Program of China under grant 2004BA204B08.

References 1. Branicky, M., Borkar, V., and Mitter, S.: A Unified Framework for Hybrid Control: Model and Optimal Control Theory. IEEE transactions on Automatic Control, Vol.88 (1998) 31–45 2. Pepyne, D., and Cassandaras, C.: Optimal Control of Hybrid Systems in Manufacturing. Proc. IEEE, Vol.88 (2000) 1008–1122 3. Song, M., Tran, T., and Xi, N.: Integration of Task Scheduling, Action Planning, and Control in Robotic Manufacturing Systems. Proc. IEEE, Vol.88 (2000) 1097–1107 4. Horowitz, R., Varaiya, P.: Control Design of An Automated Highway System. Proc. IEEE, Vol.88 (2000) 913–925 5. Livadas, C., Lygeros, J., Lynch, N.A.: High-level Modeling and Analysis of the Trafficalert and Collision Avoidance System (TCAS). Proc. IEEE, Vol.88 (2000) 926–948 6. Varajya, P.: Smart Cars on Smart Roads: Problems of Control. IEEE Transactions on Automatic Control, Vol.38 (1993) 195–207 7. Engell, S., Kowalewski, S., Schulz, C., Strusberg, O.: Continuous-discrete Interactions in Chemical Processing Plants. Proc. IEEE, Vol.88 (2000) 1050–1068 8. Antsaklis, P.: Special Issue on Hybrid Systems: Theory and Applications - A Brief Introduction to the Theory and Applications of Hybrid Systems. Proc. IEEE, Vol.88 (2000) 887–897 9. Wicks, M., Peleties, P., DeCarlo, D.: Switched Controller Synthesis for the Quadratic Stabilization of A Pair of Unstable Linear systems. European Journal of Control, Vol.4 (1998) 140–147 10. Kim, S., Campbell, S.A., Liu, X.: Stability of a Class of Linear Switching Systems width Time Delay. IEEE Transactions on Circuits and Systems I, Vol.53 (2006) 384–393 11. Decarlo, R.A., Branicky, M.S., Petterson, S., Lennartson, B.: Perspectives and Results on the Stability and Stabilizability of Hybrid Systems. Proceedings of the IEEE, Vol.88 (2000) 1069–1082 12. Branicky, M.S.: Multiple Lyapunov Functions and Other Analysis Tools for Switched and Hybrid Systems. IEEE Transactions on Automatic Control, Vol.43 (1998) 475–482 13. Liberzon, D., Morse, A.S.: Basic Problems in Stability and Design of Switched Systems. IEEE Control Systems Magazine, Vol.19 (1999) 59–70

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14. Liberzon, D., Hespanha, J.P., Morse, A.S.: Stability of Switched Systems: A Lie-Algebraic Condition. Systems & Control Letters, Vol.37 (1999) 117–122 15. Mitra, R., Tarn, T.J., Dai, L.: Stability Results for Switched Linear Systems. in Proceedings of the American Control Conference, Arlington, USA (2001) 1884–1889 16. Sun, Z.: Stabilizability and Insensitivity of Switched Linear Systems. IEEE Transactions on Automatic Control, Vol.49 (2004) 1133–1137 17. Johansson, M., Rantzer, A.: Computation of Piecewise Quadratic Lyapunov Functions for Hybrid Systems. IEEE Transactions on Automatic Control, Vol.43 (1998) 555–559 18. Ye, H., Michel, A.N., Hou, L.: Stability Theory for Hybrid Dynamical Systems. IEEE Transactions on Automatic Control, Vol.43 (1998) 461–474 19. Xie, L., Shishkin, S., Fu, M.: Piecewise Lyapunov Functions for Robust Stability of Linear Time-Varying Systems. Systems & Control Letters, Vol.31 (1997) 165–171 20. Liberzon, D., Tempo, R.: Common Lyapunov Functions and Gradient Algorithms. IEEETransactions on Automatic Control, Vol.49 (2004) 990–994 21. Ishii, H., Basar, T., Tempo, R.: Randomized Algorithms for Synthesis of Switching Rule for Multimodal Systems. IEEE Transactions on Automatic Control, Vol.50 (2005) 754–767 22. Chen, D., Guo, L., Lin, Y., Wang, Y.: Stabilization of Switched Linear Systems. IEEE Transactions on Automatic Control, Vol.50 (2005) 661–666 23. Xu, X., Zhai, G.: Practical Stability and Stabilization of Hybrid and Switched Systems. IEEE Transactions on Automatic Control, Vol.50 (2005) 1897–1903 24. Vidyasagar, M.: Nonlinear Systems Analysis Prentice-Hall, Englewood Cliffs, New Jersey (1978) 64–90

Study on FOG-SINS/GPS Integrated Attitude Determination System Using Adaptive Kalman Filter Xiyuan Chen Department of Instrument Science and Engineering Southeast University, Nanjing City, 210096, P.R. China [email protected]

Abstract. A novel adaptive filter based on the model of marine FOGSINS/GPS (fiber optical gyroscope – strapdown inertial navigation/global positioning system) integrated attitude determination system is studied in this paper. Considering the actual situation of ship operation, the simulation experiment is made. The results show that the performance stability of this kind of adaptive filter is better than the conventional Kalman filter, and can calculate adaptively the matrix of system noise variance Q and measurement noise matrix R , so the estimation precision of the parameters such as attitudes etc. can be improved effectively for marine FOG-SINS/GPS integrated attitude determination system. Statistical performance after filtering for this integrated system is better than the GPS attitude determination system.

1 Introduction Positioning and attitude determination is an important component in navigation, guidance and control systems used for a wide range of moving platforms such as spacecraft, airplanes, robotics, land vehicles, and vessels. Traditionally, positioning and attitude information has been provided by inertial navigation systems (INS). The INS is self-contained and independent of any external signals. However, one of the main drawbacks of INS when operated in a stand-alone mode is the time dependent growth of systematic errors. This drawback is more obvious for marine inertial navigation systems operating over long time intervals. In contrast to the INS short-term accuracy, satellite-based kinematical positioning techniques can offer consistent accuracy during the period of positioning. Different systems have been developed based on whether the GPS measurements are used alone, or in combination with INS measurements. By mounting three or more GPS receiver antennas on the platform, a GPS-based attitude determination system can be constructed [1,2]. On the other hand, precise satellite measurements are ideally suited for the calibration of INS systematic errors. A calibrated INS system can then provide high-rate precise positioning and attitude information. Presently, the inertial navigation system (INS) and global positioning system (GPS) are widely used for marine navigation applications around the world. In this paper, GPS providing accurate vessel heading and pitch as well as position and velocity is D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 417 – 427, 2006. © Springer-Verlag Berlin Heidelberg 2006

418

X. Chen

employed to be integrated with FOG-SINS to constitute an outstanding marine integrated system, which requires higher accuracy both in position and attitude. The Kalman filter is usually used in the integrated navigation system, which is capable of estimating SINS errors online based on the measured errors between SINS and GPS. The accuracy of Kalman filters depends on a priori knowledge of system models and noise statistics. As long as the sensors and noise distributions do not change, the Kalman filter will give the optimal estimation [3]. In the practical applications for integrated inertial navigation system, the inertial measurement unit (IMU) integrated by inertial sensors such as three FOGs and three accelerometers is directly located under the gun base or beside the radar base for the strapdown inertial attitude system without any slider. It is easy for the sensor signal to be disturbed because of high dynamic environment such as vibration, impulse, etc. The attitude accuracy of the GPS attitude determining system is closely related to the calculation of distance between two antennae [4], so the attitude outputs of GPS are prone to be disturbed by the temporally changing signal noise than the position output, which will lead to significant performance degradation of the Kalman filter. A number of approaches can be taken for GPS/INS integrated system in order to improve the practicability and robustness of the Kalman filter. The CKF (Centralized Kalman Filter) and the FKF (Federated Kalman Filter) have been studied more for integrated navigation system in recent years [5]. The CKF can be applied to a system with multi-measurement sets to determine an optimal estimation of global system states. Another architecture that has received considerable attention as a practical means of decentralization is the FKF (Federated Kalman Filter). FKF differs from the conventional Kalman filter because each measurement such as SINS and GPS is processed in local filters, and the results are combined in a master filter. The primary disadvantage is that the FKF does not give performance equal to that of the CKF, even when local filters are based on true models of the system [6, 7]. Similar to the conventional Kalman filter, the accuracy of the CKF and the FKF depends on the correct priori models of the system. The purpose of an adaptive filter is to reduce or bound the gaps by modifying or adapting the Kalman filter. Since the basic source of uncertainty is due to unknown priori statistics of noise, one can estimate them online from the observed data. Another approach is to estimate the optimal Kalman gain directly without estimating the covariance of the process and measurement noise [8]. In the past few years, adaptive Kalman filtering based on innovation based adaptive estimation (IAE) has become one of the major approaches under study. Bian. et al. [9] summarized and analyzed these methods for GPS/INS integrated system, then proposed a novel IAE-AKF based on the maximum likelihood criterion for the proper computation of the filter innovation covariance and hence of the filter gain. The IAE-FLC (fuzzy logic control) methods decrease the computation time of the algorithm remarkably without increasing the system state dimension. Simulations verified their good robustness and accuracy. However, the key point, which is how to establish the fuzzy inference rules and select the membership function, is not provided with a convincing solution. Bian. et al. [9] theoretically deduced the proposed IAE-AKF algorithm in detail; the

Study on FOG-SINS/GPS Integrated Attitude Determination System

419

approach was tested in the developed INS/GPS integrated marine navigation system. The approach is direct without having to establish fuzzy inference rules compared with the IAE-FLC methods, but this method is necessary to test for the GPS/SINS integrated system in high dynamic environment. Based on the conventional Kalman filter, a real-time adaptive estimation Kalman filter is presented in this paper to improve the system’s overall performance when GPS and SINS measurement noise change abruptly in dynamic environment. A novel adaptive filter based on the model of marine FOG-SINS/GPS (fiber optical gyroscope – strapdown inertial navigation/global positioning system) integrated attitude determination system is studied in this paper. Considering the actual situation of ship operation, the simulation experiment was designed. This kind of adaptive filter can calculate adaptively the matrix of system noise variance Q and measurement noise matrix R , so the estimation precision of the parameters such as attitudes etc. can be improved effectively for marine FOG-SINS/GPS integrated attitude determination system. The organization of this paper is as follows: In Section 1, the research backgrounds are provided. Section 2 introduces the mathematical model of FOG-SINS/GPS integrated navigation system. A novel innovation adaptive filtering method based on system model and simulation experiments are presented in section 3, and finally, conclusions are given in section 4.

2 FOG-SINS/GPS Integrated Navigation System Model 2.1 State Equation for Integrated System Considering the characteristics of ship operation, assume the attitude error of GPS is expressed as the first-order Markov process equation; SINS navigation coordinate system is in the East-North-Up (ENU) frame. According to the SINS errors characteristics and GPS performance, the state equation of the integrated system can be written as follows: •

X = FX + W .

(1)

Where state variable of integrated system

X =[δL δλ δVE δVN φE φN φU ∇be ∇bn εbe εbn εbu δϕG δθG δγG]T .

(2)

δ L and δλ represent SINS latitude error and longitude error respectively; δVE and δ VN are east and north velocity errors respectively; φ E , φN , φU are east, north and azimuth misalignment angles respectively; ∇be and ∇ bn are the east and north accelerator biases respectively;

ε be , ε bn , ε bu represent

the constant drift rates of east, north

and azimuth gyros, respectively; δϕG , δθG , δγ G are GPS heading error and GPS pitch error, GPS roll error ,respectively. F is a 15 × 15 matrix, see equation (3) [10].

420

X. Chen

ª « 0 « « F21 « « F31 « F41 « « 0 « « « « F61 « « « F71 F=« « 0 « « 0 « 0 « « 0 « 0 « « « 0 « « « 0 « « « 0 «¬

0

0

1 RN

0

0

0

0

0

0

0

0

0

0

0 0 0

F23 F33 F43

0 F34 0

0 0 fU

0 − fU 0

0 fN − fE

0 c11 c12

0 c21 c22

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0

0

1 RN

0

F56

F57

0

0

c11

c21

c31

0

0

0

1 RE

0

F65

0

VN RN

0

0

c12

c22

c32

0

0

0

tgL RE

0

F75

VN RN

0

0

0

c13

c23

c33

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0 0 0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0 1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

−

−

−

0

τ ϕG −

1

τθG 0

º 0 » » 0 » » 0 » 0 » » 0 » » » » 0 » » » 0 » » 0 » » 0 » 0 » » 0 » 0 »» » 0 » » » 0 ». » 1 » » − τ γ G »¼

(3)

Where cij is an element of Cnb , which represents attitude matrix expressed as the relation between the ship coordinate system and geographic coordinate system. ª c11 c12 C = «c21 c22 « ¬«c31 c32

c 13 º c23 » » c33 ¼»

b n

Where F21 =

ϕ ,θ , γ

F56 = ω ie sin L +

F23 =

VE tgL; RE

VE tgL; RE

F71 = ωie cos L +

(4)

represent ship’s heading, pitch and roll, respectively.

VE sec LtgL; RE

F34 = 2ω ie sin L +

ªsinϕsinθ sinγ +cosϕcosγ cosϕsinθ sinγ −sinϕcosγ −cosθ sinγ º =« sinϕcosθ cosϕcosθ sinθ » . « » ¬«cosϕsinγ −sinϕsinθ cosγ −sinϕsinγ −cosϕsinθ cosγ cosθ cosγ ¼»

1 sec L; RE

F31 = 2ω ieVN cos L +

F41 = −2ω ieVE cos L − F57 = −ω ie cos L −

VE ; RE

VE VN sec 2 L; RE

VE 2 sec 2 L; RE

F61 = −ω ie sin L;

F33 =

VN tgL; RE

F43 = − 2ω ie sin L − 2

VE tgL ; RE

F65 = −ω ie sin L −

VE tgL; RE

(5)

VE V sec2 L; F75 = ωie cos L + E . RE RE

Where L is local latitude, ω ie is earth rotating angular rate, VE and V N are east and north velocities, respectively, and RE is the radius of the earth. The process noises

W are zero mean Gaussian processes with covariance Q . W = ª¬wδ L wδλ wδVE wδVN wφE wφN

T

wφU 0 0 0 0 0 wδϕG wδθG wδγG º¼ .

(6)

Study on FOG-SINS/GPS Integrated Attitude Determination System

421

τ ̓with different subscripts in equation (3) represents different time correlated constants corresponding to the GPS error states. In general they are selected from 100 seconds to 200 seconds. 2.2 Measurement Equation for Integrated System

Let LI = Lt + δL and λ I = λt + δλ represent SINS measurements of ship’s longitude

and

latitude,

respectively.

Let

LG = Lt − N N / R N

and

λG = λt − N E /( RE cos LG ) represent GPS measurements of ship’s longitude and latitude respectively, where Lt , λt are true values, N N and N E are north and east position errors of GPS receiver respectively. Let VIE = VE + δVIE , VIN = VN + δVIN be SINS measurements of ship’s east and north velocities respectively. Let VGE = VE − M E and VGN = V N − M N represent GPS measurements of ship’s east and north velocities respectively, where VE , V N are true values, M N and M E are north and east velocity errors of GPS receiver respectively. Let ϕI = ϕ + δϕ I , θ I = θ + δθ I and γ I = γ + δγ I represent SINS measurements of ship’s yaw, pitch and roll respectively. Let ϕG = ϕ + δϕG , θG = θ + δθ G and γ G = γ + δγ G represent GPS measurements of ship’s yaw, pitch and roll respectively. We assume that the measurement noise V is a zero-mean Gaussian process with covariance R independent with W . The measurement equation can be written as follows: ª ( LI − LG ) RN º ª RN δL + N N º «(λI − λG ) RE cos L» « RE cos Lδλ + N E » « » « » ªH p º ªV p º « » « » « » « »  « » « δVIE + M E » « » VIE − VGE « » . « » « » «Hv » «Vv » VIN − VGN Z=« » = « δVIN + M N » = « » X + « » = HX + V «  » « » « » « » H « » « δϕ − δϕ » « α» «Vα » ϕ I − ϕG I G « » « » « » « » ¬ ¼ θ I −θ G « » « δθ I − δθ G » ¬ ¼ « » « » γ I −γ G ¼ ¬ ¼ ¬ δγ I − δγ G

(7)

Where H p , H v , H α can be written as follows [11]: H p = [ diag[RN

RE cos L] 02×13 ] , Hv = [ 02×2  diag[1 1] 02×11 ]

ª c c « − 2 21 232 c21 + c22 « « c22 − H a = «03×4  2 « 1 − c23 « c12 c33 − c32 c13 « 2 « c132 + c33 ¬

−

c22 c23 2 2 + c22 c21 c21 2 1 − c23

c31c13 − c11c33 c132 + c332

1 0  03×5 0

º » » » .  − I 3×3 » » » » » ¼

(8)

422

X. Chen

3 Q , R Adaptive Kalman Filtering Algorithm and Simulation 3.1 Q , R Adaptive Filtering Algorithm [12]

It is well known that if the process can be approximated with a linear model plus white noise with known statistics, then an optimal (minimum mean squared error) Kalman gain P can be evaluated. The key to determining the performance of the Kalman filter, is only to depend on the priori known transmitted matrix φ , measurement matrix H, process noise covariance matrix R and measurement noise covariance matrix Q . When φ , H, R and Q are matched with the actual system, the optimal estimation condition will be satisfied; but for the disturbance and time variance system like the FOG-SINS/GPS integrated navigation system in the high dynamic environment, it’s so possible that the computation of P matrix is divergent and degradation of the performance of the filter will happen. For the robustness and the adjustability of P, in this section, the innovation-based Q , R adaptive estimation algorithm is presented. For time variance system, the innovation is to make use of the current real measurements to evaluate noise statistics characteristics and model parameters online. It is a significant approach to accomplish an adaptive Kalman filter by introducing the innovation sequence to adjust the calculation of the Kalman gain. The novel adaptive Kalman filter presented herein is normal to calculate adaptively Q matrix and R matrix. From the statistics covariance of the real-time residual online, but this adaptive filter is secondly optimal. Assume a discrete linear system is as follows X k = φk ,k −1 X k −1 + Γk −1Wk −1

Z k = H k X k + Vk

(9)

Where X k ( n dimension) is state vector which will be evaluated at k instant, Z k ( m dimension) is measurement vector at k instant, φ k ,k −1 is the first step system state transition matrix from k − 1 instant to k instant, matrix, H k ( m × n dimensions) is the measurement matrix at k instant, Γk ( n × r dimensions) is system noise matrix . Wk (r dimension) is the process noise vector and Vk (m dimension) is the measurement noise vector. Both Vk and Wk are assumed to be uncorrelated zero-mean Gaussian white noise sequences with covariance given by T E{Wk } = 0, E{WkW jT } = Qkδ kj , E{Vk } = 0, E{VkV j } = Rkδ kj , Qk and Rk are variance matrix

of system noise and measurement noise respectively, and δ kj is a Kronecker function defined as ­0 k ≠ j . ¯1 k = j

δ kj = ®

(10)

Let the initial state statistics characters be E{ X 0 } = m x 0 , Var{ X 0 } = C x 0 , X 0 is unrelated to the {Wk } and {Vk } .

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The recursive equations of an innovation-based conventional Kalman filter are as follows: X k / k −1 = φk , k −1 Xˆ k −1 , Pk / k −1 = φk ,k −1Pk −1φkT,k −1 + Γk −1Qk −1ΓTk −1 ,

K k = Pk / k −1 H k T ( H k Pk / k −1 H k T + Rk ) −1 , Xˆ k = Xˆ k / k −1 + Kk (Zk − H k Xˆ k / k −1 ) .

(11)

For stability of P matrix and eliminating calculation error, variance matrix innovation calculation formula deduced by Joseph is used Pk = ( I − K k H k ) Pk / k −1 ( I − K K H K )T + K K RK K K T .

(12)

For simplicity, assume filtering period is very short, Qk can be calculated as follows Qk = (Q + φ k +1,k Q φ kT+1,k )

T . 2

(13)

In equation (11), (12), system disturbance noise innovation variance matrix Qk and measurement noise innovation variance matrix Rˆ ( k ) can be calculated by innovation equation Q (k ) =

1 [( k − 1)Q ( k − 1) + K k ε ( k )ε T ( k ) K T k + Pk − Φ k , k −1 Pk −1Φ T k , k −1 ] k 1 Rˆ k = [( k − 1) Rˆ k −1 + ε ( k )ε T ( k ) − H k Pk , k −1 H T k ] . k

(14)

where ε k = Z k − H k X k , k −1 is an innovation sequence matrix. According to (11), (12),(14), adaptive filtering algorithm is obtained. The algorithm can evaluate noise characters and state vectors online. 3.2 Simulation Verification

To verify the better performance of the Q , R adaptive Kalman filter over the conventional Kalman filter for marine FOG-SINS/GPS integrated navigation system, assume the ship ideal angular movement equations are as follows ­ϕ = ϕ 0 + Aϕ sin(ωϕ t + φϕ ) ° . ®θ = Aθ sin(ωθ t + φθ ) °γ = A sin(ω t + φ ) γ γ γ ¯

(15)

Where Aϕ , Aθ and Aγ are swing angular amplitude of yaw, pitch and roll respectively;

φϕ , φθ and φγ

are initial swing phase of yaw, pitch and roll respectively.

The ship ideal velocities are as follows ­VE = V sin(ϕ ) ° . ®VN = V cos(ϕ ) °V = 0 ¯ U

(16)

Assume Aϕ = 14° , ωϕ = π / 3 ; Aθ = 9° , ωθ = π / 4 ; Aγ = 12° , ωγ = π / 5 ; initial heading ϕ0 = 45° , sailing velocity V = 15 m/s; initial phases of yaw, pitch and roll are zero. Assume FOG fix drifts are 0.1º/h, random drifts of FOG are 1º/h, accelerometer fix

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biases are 0.5×10-4g, random biases of accelerometers are 0.5×10-4 g, misalignment angles of east, north, up are each 1º. Quarter element attitude algorithm with one order is used in FOG-SINS, updating period of attitude is 10 millisecond. Assume GPS velocity measurement noise variance is 0.2m/s, GPS position measurement noise variances of east, north are each 15m, GPS three attitude measurement noise variances are each 0.4º, and initial values of adaptive Kalman filter parameters are as follows P0 = diag{(0.02$ )2 ,(0.02$ )2 ,(0.5m / s)2 ,(0.5m / s)2 ,(1$ )2 ,(1$ )2 ,(1$ )2 , (0.05mg )2 ,(0.05mg )2 ,(1$ / h)2 ,(1$ / h)2 ,(1$ / h)2 ,(0.4$ )2 ,(0.4$ )2 ,(0.4$ )2 ,} Q0 = diag{(0.02$ )2 ,(0.02$ )2 ,(0.5m / s) 2 ,(0.5m / s)2 ,(1$ )2 ,(1$ )2 ,(1$ )2 , (0.05mg )2 ,(0.05mg )2 ,(1$ / h)2 ,(1$ / h)2 ,(1$ / h)2 ,(0.4$ )2 ,(0.4$ )2 ,(0.4$ )2 ,} R0 = diag {(15 m ) 2 , (15 m ) 2 , (0.2 m / s ) 2 , (0.2 m / s ) 2 , (0.4 $ ) 2 , (0.4 $ ) 2 , (0.4 $ ) 2 }

For the convenience of analyses for the stability of filter and filtering process over long time, assume filtering period of adaptive filtering is 10 seconds, error correction with open loop for attitude is applied in integrated system [13]. Fig.1 represents the results simulated in static condition ((a), (b) vertical axes represent heading error and roll error respectively with unit in degrees). Fig.2 represents the results simulated in above description dynamic condition ((a), (b) vertical axes represent heading error and roll error respectively with unit in degrees). Due to limited space, Fig.3 (a), (b), (c) represent only roll error (unit: degree), latitude (unit: degree), north velocity (unit: m/s) of the adaptive filtering process of parameters evaluated, Fig.3 (d) shows the convergence process of the trace of matrix Q , the other parameters also converge with similar results.

Fig. 1. comparison between adaptive Kalman filtering and convention Kalman filtering correction error curve in static condition (solid line is adaptive filtering correction error, dash line is conventional filtering correction error)

From Fig.1 and Fig.2, we can conclude that Q , R adaptive Kalman filter has better performance than conventional filter, and it has fine precision in dynamic condition. In Fig.2, error evaluated by adaptive Kalman filter is consistent with the original error and show fine tracking performance. Fig.3 shows that the convergence performance of parameters is good although there exist very short fluctuation during initial 200

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(a) heading error

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(b) roll error

Fig. 2. comparison between error evaluated by adaptive Kalman filter and original error in dynamic condition (solid line is original error, dash line is error evaluated by adaptive filtering correction error)

T/10ms (a) roll error

T/10ms

(c) north velocity

T/10ms

(b) latitude error

T/10ms

(d) the trace of matrix Q

Fig. 3. convergence process of parameters evaluated during adaptive Kalman filter filtering process

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filtering periods. For the FOG-SINS/GPS integrated system, filtering period is longer, measurement errors are larger because of FOG-SINS error accumulation, and this case can be explained and shown in Fig.3. Main navigation parameters statistics data after filtering can be obtained. Output of integrated system using adaptive filter is stable and statistics results are shown in table 1. The results show that marine FOG-SINS/GPS integrated navigation system using Q , R adaptive Kalman filter can improve the precision of attitude and the other navigation parameters, and has better statistic performance than GPS attitude determination system. Table 1. Precision of output for FOG-SINS/GPS marine integrated system

parameters Mean error Standard error parameters Mean error Standard error

heading ϕ ( rad ) 3.11201959×10-4 2.409576×10-3

pitch θ ( rad ) -9.72846272×10-5 1.553160×10-3

East velocity

North velocity

Latitude

VE (m/s)

VN (m/s)

L ( rad )

2.278456×10-2 1.623810×10-1

-2.053372×10-2 1.666933×10-1

-1.462282×10-7 2.485179×10-6

roll γ ( rad ) 6.0350448×10-4 1.764169×10-3 Longitude

λ ( rad ) -1.234185×10-7 2.447358×10-6

4 Conclusions Considering the actual situation of ship operation, Q , R adaptive filter presented in the paper has fine filtering result that is reasonable for marine FOG-SINS/GPS integrated attitude determination system under the static and dynamic condition. The performance stability of this kind of adaptive filter is better than the conventional Kalman filter. Statistical performance after filtering for this integrated system is better than the GPS attitude determination system.

Acknowledgement The work was supported by the Southeast University Excellent Young Teacher Foundation ( 4022001002 ) and the National Defense Advanced Research Foundation (6922001019). The author would like to thank Dr. Song Ye and Prof. Dejun Wan of the Department of instrument science and engineering at Southeast University for helpful suggestions.

References 1. Van, G. F., Braasch, M.S.: GPS Interferometric Attitude and Heading Determination: Initial Flight Test Results. Navigation, Vol.38, No.4, (1991)297-316 2. Cohen, C.E.: Attitude Determination. In Global Positioning System Theory and Applications conf., American Institute of Astronautics, Washington D.C. Vol. 2, (1996) 519-538.

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3. Wang, B.: Study on Adaptive GPS/INS Integrated Navigation System. IEEE Proc. Intel. Transp. Syst. Vol. 2 (2003) 1016–21 4. Hide, C., Moore, T., Smith M.: Adaptive Kalman Filtering Algorithms For Integrating GPS and Low Cost INS.Position, Location and Navigation Symp, (2004) 227–33 5. Lee, T.G.: Centralized Kalman Filter with Adaptive Measurement Fusion: its Application to a GPS/SDINS Integration System with an Additional Sensor. International Journal of Control, Automation,and Systems. Vol. 1, No. 4,(2003) 6. Carlson, N.A.: Federated Filter for Computer Efficient, Near-optimal GPS Integration. IEEE Trans. on Aerospace and Electronic Systems, (1996) 306-314,. 7. Fried, K.: Avoinics Navigation Systems. A Wiley-Interscience Publication (1997) 8. Maybeck, P.S.: Stochastic Models. Estimation and Control volume 2, Academic Press, New York (1979) 9. Bian, H., Jin, Z., Tian, W.: Study on GPS Attitude Determination System Aided INS Using Adaptive Kalman Filter. Meas. Sci. Technol. Vol.16 ,(2005) 2072–2079 10. Ye, S.: Study on Data Processing and Fusion Technology in FOG Strapdown/GPS Integrated Attitude and Heading System [D]. Southeast University, Nanjing (2004) 11. Yang, Y., Bian, H., Tian, W., Jin, Z.: A Novel INS/GPS Integrated Navigation Technique. Journal of Chinese Inertial Technology, Vol.12, No.4, (2004) 23–26 12. Zhu, H., Mo, J.: Underwater Navigation Information Fusion Technology [M]. National Defense Press, Beijing (2002) 13. Yuan, X., Yu, J.-X.: Navigation System [M]. Beijing Aeronautics Industry Press, Beijing (1993)

Supervisory Control for Rotary Kiln Temperature Based on Reinforcement Learning Xiaojie Zhou, Heng Yue, Tianyou Chai, and Binhao Fang Research Center of Automation, Northeastern University, Shenyang, 110004, P.R. China [email protected]

Abstract. The burning zone temperature in rotary kiln process is a vitally important controlled variable, on which the sinter quality mainly relies. Boundary conditions such as components of raw material slurry often change during kiln operation, but related offline analysis data delay to reach or even are unknown to the human operator. This causes unsatisfactory performance of the burning zone temperature controller and subsequent unstable production quality. To deal with this problem, a Q-learning-based supervisory control approach for burning zone temperature is proposed, in which the signals of human intervention are regarded as the reinforcement learning signals, so that the set point of burning zone temperature can be duly adjusted to adapt the fluctuations of the boundary conditions. This supervisory control system has been developed in DCS and successfully applied in an alumina rotary kiln. Satisfactory results have shown that the adaptability and performances of the control system have been improved effectively, and remarkable benefit has been obtained.

1 Introduction Rotary kiln is a kind of large scale sintering device widely used in metallurgical, cement, refractory materials, chemical and environment protection industries. Its complicated working mechanism includes physical change and chemical reaction of material, procedure of combustion, thermal transmission among gaseous fluid, solid material fluid and the liner. The automation problem of such processes remains unsolved because of the following inherent complexities. It is a multivariable nonlinear system with strong coupling. The key controlled variable of burning zone temperature is difficult to measure. It has less manipulated variables than controlled variables. It has multiple control targets. Most of rotary kilns are still under manual control with human operator observing the burning status. As a result, the product quality is hard to be kept consistent and energy consumption remains high. Although several advanced control strategies including fuzzy control [1], intelligent control [2,3,4] and predictive control [5] have been introduced into process control of rotary kiln, all these researches focused on trying to achieve complete automatic control without human operators. As a matter of fact, the boundary conditions of a rotary kiln often change. For example, the material load, water content and components of the raw material slurry vary frequently and severely. Moreover, the offline analysis data of components of raw material slurry reach the operator with large time delay. Thus complete automatic control without D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 428 – 437, 2006. © Springer-Verlag Berlin Heidelberg 2006

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human operation for such a complex process is unpractical. To deal with the complexity of operation conditions, the authors have proposed an intelligent control system based on human-machine interaction for an alumina rotary kiln in [10], in which human intervention function was design so that, if the operation condition changed largely, the human operator observing burning status can intervene the control actions when the system is in the automatic control mode to enhance the adaptability of the control system. This paper develops a supervisory control approach for burning zone temperature based on Q-learning, in which the signals of human intervention are viewed as the reinforcement learning signals. Section 2 makes brief descriptions of process and control system architecture. Section 3 discusses the detailed methodology of Q-learning-based supervisory control approach. The implementation and industrial applications are shown in Section 4. Finally, Section 5 draws the conclusion.

2 Process Description and Control System Architecture The rotary kiln process is described as follows. Raw material slurry is sprayed into the rotary kiln from upper end (the kiln tail). At the lower end (the kiln head), the coal powders from the coal injector and the primary air from the air blower are mixed into bi-phase fuel flow, which is sprayed into the kiln head hood and combusts with the secondary air, which comes from the cooler. The heated gas was brought to the kiln tail by the induced draft fan, while the material moves to the kiln head via the rotation of the kiln and its self weight, in counter direction with the gas. After the material passes through the drying zone, pre-heating zone, decomposing zone and burning zone in sequence, soluble sodium aluminate is generated in the sinter, which is the final product of the kiln process. This process aims to reach high digesting rate of alumina and sodium oxide in the following sinter digestion procedure. How to keep the stability of temperature distribution along the above zones of the rotary kiln is the key problem during kiln operation. To reach this target, the operator or control system must keep all key controlled variables in technical required ranges. The burning zone temperature TBZ is indirectly measured by an infrared pyrometer located at kiln head hood, and the kiln tail temperature TBE is obtained through a thermocouple. In our previous study [10], a preliminary process control system for such a rotary kiln has been established, whose general structure is shown in Fig. 1. The related process control strategies include, 1) a hybrid intelligent temperature controller was designed, which coordinated the coal feeding u1, damper position of the induced draft fan u2, and primary air flow u3 to make TBZ, TBE, and the residual oxygen content in combustion gas OX satisfy technical requirements; 2) individual PI controllers were assigned to basic loops of primary air flow, primary air pressure and slurry flow of raw material; and 3) the function of human intervention was designed so that certain interventions to coal feeding control from experienced operator can be introduced in the mode of automatic control when the operating conditions changed significantly. This paper has constructed a supervisory control system consisting of a supervisory level and a process control level. The latter employs the aforementioned process control strategy, and the former adjusts the setpoints of TBZ, TBE, OX and the kiln rotary speed n according to the variances of such boundary conditions as production capacity in unit time per kiln,

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Human intervention uM TBZ_SP Setpoint of TBE Setpoint of OX

Hybrid intelligent temperature controller Primary air flow controller

Setpoint of air press. Setpoint of raw mat. flow Setpoint of n

Rotary kiln process

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Primary air pressure controller Raw material flow controller Kiln rotary motor speed controller

u1 u2 u3

Coal feeder Induced draft fan

Air blower

TBZ

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Feed pump

TBE OX

Kiln electromotor

Fig. 1. Structure of the original process control system for rotary kiln

components of raw material slurry. The final target of this supervisory control system is to keep the production quality index, i.e. the sinter unit weight, being acceptable even if the boundary conditions changed. From the viewpoint of technologists, TBZ_SP, i.e. the setpoint of TBZ is related with the sintering temperature Tsinter, which should be altered according to the changes of components of raw material slurry. The relationship between desired Tsinter and components of raw material slurry can be viewed as a unknown nonlinear function T sin ter = f ([ A / S ], [ N / R ],[C / S ], [ F / A]) .

(1)

where [A/S] is the alumina silica ratio of raw material slurry, [N/R] is the alkali ratio, [C/S] is the calcium silica ratio, [F/A] is the iron alumina ratio. Among them, the alumina silica ratio of raw material slurry has the strongest influence on Tsinter, the latter must be enhanced along with the enhancement of the former. As a matter of fact, the main problem we are facing is that the components of raw material slurry often change and the offline analysis data reach to the operator with large time delay so that the operator cannot directly adjust the setpoint of TBZ duly. As a result, a single hybrid intelligent temperature controller cannot maintain satisfactory performance. In such a case, a human operator usually rectifies the output of the temperature controller based on the experience of observing burning status through the human-machine interaction mechanism embedded in the control system. Such interventions can adapt the variation of operating conditions to a certain degree to sustain the sintering quality of the product. In the following section, a Q-learning strategy is employed to construct the self-adjusting knowledge about the setpoint of TBZ through learning from the human intervention signals.

3 Setpoint Adjustment Approach Based on Q-Learning 3.1 Bases of Q-Learning Reinforcement learning is learning with a critic instead of a teacher. The only feedback provided by the critic is a scalar signal r called reinforcement, which can be thought of

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as a reward or a punishment. Reinforcement learning performs an on-line search to find an optimal decision policy in multi-stage decision problems. Q-learning [9] is a reinforcement learning method where the learner builds incrementally a Q-function which attempts to estimate the discounted future rewards for taking actions from given states. The output of the Q-function for state x and action a is denoted by Q ( x, a ) . When action a has been chosen and applied, the environment moves to a new state, x′ , and a reinforcement signal, r , is received. Q ( x, a ) is updated by

˄

Q ( x, a ) ← 1 − α )Q( x, a ) + α {r + γ max Q ( x′, a′)} .

(2)

a′∈A ( x′ )

where A(x′) is the set of possible actions in state x′ , α is the learning rate and γ a discount factor. Learning system of burning zone temperature setpoint

Environment HMI

Critic

Human intervention

Reward r Qk+1(x,a) Actionvalue function look up table

TBZ

Learner Qk(x,a) Action Selector

TBZ_SP

Hybrid Intelligent Temperature Controller

u1 u2 u3

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G

State x State Perception

Fig. 2. The schematic diagram of setpoint adjustment approach for TBZ based on Q-learning

3.2 Principle of Setpoint Adjustment Approach Based on Q-Learning In this section, we may design an online self-learning system based on reinforcement learning to gradually establish the optimal policy of setpoint adjustment of TBZ. Although it cannot reach to the operator in time, the changes of components of raw material slurry may be indirectly reflected through certain state information about the rotary kiln process. The state information can be used to construct the environment state set of the learning system. Moreover, information of human interventions can be regarded as evaluations about whether the setpoint of TBZ is proper or not, for human interventions often occur when the performance is unsatisfactory. Thus this kind of information can be defined as reward signal from environment. The environment provides current states and reinforcement payoffs to the learning system. The learning system produces actions to perform in the environment. The learning system consists of a state perceptron, a critic, a learner and an action selector, as shown in Fig. 2. The state perceptron firstly samples and processes selected measurements to construct the original state space, and then maps the original

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continuous state space into a finite feature space based on a defined feature extraction function. The action selector employs a İ-greedy action selection rule to produce action and the learner updates value function of the state-action pair based on tabular Q-learning. The critic serves to calculate an internal practicable reward relying on some heuristic rules. 3.3 Construction of the State Perceptron In an MDP (Markov decision process), only the sequential nature of the decision process is relevant, not the amount of time that passes between decision stages. A generalization of this is the semi-Markov decision process (SMDP) in which the amount of time between one decision and the next is a random variable. For the setpoint adjustment learning process, we define τ s as state perception time span for the perceptron to get the state of the environment and τ r as reward calculation time span for the critic to calculate reward from the environment respectively. The shortest time span from one decision to the next is τ τ s τ r . If the operating condition of the rotary kiln is not kept in a relatively smooth status, the learning procedure should be postponed accordingly. First, based on human experience, some state variables are specified to buildup the state space S of the learning system. They are TBZ , averaged coal feeding u1 Ave t/h ,

˙ˇ

㧔 㧕

㧔 㧕

averaged flow rate of raw material slurry G Ave m3/h and temperature bias ∆TBZ , which are defined by J

u1 Ave = ¦ u1 ( j ) J .

(3)

j =1 J

G Ave = ¦ G ( j ) J .

(4)

∆TBZ = TBZ _ SP − TBZ .

(5)

j =1

where u1 ( j ) , G ( j ) are coal feeding, flow rate of raw material slurry on j th sampling respectively, J is the number of the samplings during τ s . Then we establish the state vector s = (TBZ , ∆TBZ , u1 Ave , GAve ) with s ∈ S . Since the state space S we consider in this paper is continuous, it is impossible to compute and store value functions for every possible state or state-action pair due to the curse of dimensionality. The issue is often addressed by generating a compact parametric representation, such as an artificial neural network [6], that approximates the value function and can guide future actions. In this paper, we practically choose to use a feature extraction method [8] to map the original continuous state space into a finite feature space, then we can employ tabular Q-learning to solve the problem. By identifying one partition per possible feature vector, the feature extraction mapping F defines a partitioning of the original state space. The burning zone temperature level feature f1 , the temperature setpoint bias level feature f 2 , the coal feeding level feature f3 , flow rate of raw material slurry level feature f 4 are defined respectively by

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­0, 1210 ≤ TBZ ( j ) < 1250 ° f1 = ®1, 1250 ≤ TBZ ( j ) < 1280 ∀j = 1,2,, J . °2, T ( j ) ≥ 1280 BZ ¯

(6)

­−2, ° °− 1, ° f 2 = ®0, °1, ° ¯°2,

∆TBZ ( j ) < −40 − 40 ≤ ∆TBZ ( j ) < −20 − 20 ≤ ∆TBZ ( j ) < 20

∀j = 1,2,, J

.

(7)

20 ≤ ∆TBZ ( j ) < 40 ∆TBZ ( j ) ≥ 40 ­0, 5 ≤ u1 Ave < 8 ° f 3 = ®1, 8 ≤ u1 Ave < 11 °2, 11 ≤ u < 14 1 Ave ¯

.

(8)

­0, 65 ≤ GAve < 75 ° f 4 = ®1, 75 ≤ GAve < 85 °2, G ≥ 85 Ave ¯

.

(9)

each one being a function from the state space S to a finite set Pm , m = 1,2,3,4 . Then we associate the feature vector F ( s ) = [ f1 (TBZ ),, f 4 (GAve )] to each state s ∈ S .The resulting set of all possible feature vectors, also defined as feature space X , is the Cartesian product of the sets Pm and its cardinality increases exponentially with the number of features. 3.4 Action Set The learning system aims to deduce the proper or best actions of setpoint adjustment of TBZ from specified environment state. The problem to be handled is how to choose the amendment of TBZ setpoint according to the changes of environment state. Thus the action set can be defined as A = {a1 , a 2 , a 3 , a 4 , a5 } = {−20,−10,0,10,20} . 3.5 Reward Signal For the learning system, the reward signal r is determined in table 1. where ∆TBZ (i) is the temperature bias on i th sampling respectively, I is the number of the samplings during τ r , n is the effective human intervention times during τ r . The Table 1. Determination of the reward signal

r ∆TBZ (i) ≥ 50 ∀i = 1,2,, I

n < 10 0

10 ≤ n < 20 −0.4

n ≥ 20 −1.0

30 ≤ ∆TBZ (i) < 50 ∀i = 1,2,, I

0 .2

0

−0.4

∆TBZ (i) < 30 ∀i = 1,2,, I

0 .4

0 .2

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“effective human intervention” indicates that it acts in opposite direction to the controller’s regulation while operator has made no amendment on the intervention action in a short following time. If the operator made a pseudo judgment, he should restore the coal feeding to the original level in a short following time. A positive reward is given if less human interventions occur and the error between setpoint and measured value of TBZ remains minor, and vice versa. 3.6 Algorithm Summary The whole learning algorithm is summarized as follows: 1) 2) 3) 4)

Initialize Q ( x, a ) by means of certain prior knowledge. Perceive a current state x during the current τ s by using (3)-(9). Select a setpoint adjustment action a by using İ-greedy policy [7] where İ=0.1. Take the selected action a and then obtain the reward r from table 1 calculated during the current τ r . 5) Perceive the next state x′ during the next τ s by using (3)-(9) and update the Q ( x, a ) by using (2), where α = 0.15 , γ = 0.90 . 6) Go to step 2 until the terminal condition is met, that is, all Q ( x, a ) almost no longer changes with time.

4 Industrial Application Shanxi Alumina Plant is the largest alumina plant in Asia with megaton production capacity. It has 6 oversize rotary kilns of ij4.5×110m. Its production employs the series parallel technology of Bayer and Sintering Processes. Such a production technology makes components of the raw material of rotary kilns often vary in large range. It is more difficult to keep a stable kiln operation than ordinary rotary kiln. A supervisory control system has been developed in the #4 rotary kiln of Shanxi Alumina Plant based on the proposed structure and the setpoint adjustment approach of burning zone temperature. It is implemented in the I/A Series 51 DCS of Foxboro. The Q-learning-based strategy has been realized in the configuration environment of Fox Draw and ICC of I/A Series 51 DCS. Related parameters are chosen as τ s 30min, τ r =120min. Fig. 3 shows a typical operating condition of mismatching of setpoint of TBZ and variations of components of raw material slurry. During observed 8 hours, the flow rate of raw material slurry has been kept about 80m3/h, remaining a normal level. From later offline analysis we knew that the components of raw material slurry were [N/R]=1.07, [C/S]=2.02, [A/S]=3.63, and [F/A]=0.07. According to the technical requirement, the desired sintering temperature should be about 1310 . The actual measured TBZ was around 1300 , remaining the rather high level. The coal feeding around 11t/h also remains in high level. But the actual setpoint of TBZ was kept at 1240 without reflecting the required sintering temperature. As a result, the temperature controller kept decreasing the coal feeding, while frequent human interventions of increasing coal feeding were often introduced by operator.

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Fig. 3. The trends when burning zone temperature sepoint mismatches components of raw material slurry

Fig. 4. The setpoint of burning zone temperature is properly adjusted after learning

Fig. 4 shows the condition that, after a period of learning, a set of relatively stable strategies of setpoint adjustment has been established so that the setpoint of the TBZ can be automatically adjusted according to the level of raw material slurry flow, the level of coal feeding, and trends of TBZ changing. The adaptability for variations of operating conditions has been significantly enhanced. During the shown 8 hours, the flaw rate of raw material slurry was kept around 83m3/h at normal level. At 13:00, the measured TBZ shifted from 1260 to 1295 . It was known, from later offline analysis, that the components of raw material slurry changed to be [N/R]=1.04, [C/S]=2.06, [A/S]= 3.50, and [F/A]=0.07. In such a condition, technical required sintering temperature should be about 1300 . While the current setpoint of TBZ remains 1255 , more and more human interventions were introduced gradually. At 13:30, based on the judgments to environment states that coal feeding during τ s remained high about 12t/h , and TBZ

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͠

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with regular flow rate of raw material slurry, the remained high above 1290 supervisory control system has amended the setpoint of TBZ to 1285 in order to satisfy the requirement of sintering temperature. The curves in following 5 hours shown that human interventions became less than before and coal feeding has been kept relatively stable.

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In the period of test run, the running rate of supervisory control system has been up to 90%. Negative influences on the heating and operating conditions from human factors have been avoided, rationalization and stability of sinter production has been kept, and operational life span of kiln liner has been prolonged remarkably. The qualification rate of sinter unit weight has been enhanced from 78.67% to 84.77%; production capacity in unit time per kiln has been increased from 52.95t/h to 55t/h with 3.9% increment. The kiln operating rate has been elevated up to 1.5%. Through the calculation based on average 10 reduction of kiln tail temperature and average 2% decrease of the residual oxygen content in combustion gas, it can be concluded that 1.5% energy consumption has been saved.

ć

5 Conclusion This paper develops a supervisory control approach for burning zone temperature based on Q-learning. The signals of human intervention are viewed as the reinforcement learning signals so that the learning procedure of the control system can be evaluated properly and a closed-loop online learning system is constructed. This control system has been successfully applied in an alumina rotary kiln in China, satisfactory results have been obtained and show that the adaptability and performances of the control system have been improved effectively, and the proposed strategy is an effective tool to improve the adaptability and performances of the kiln control system. Further research will focus on integration with supervised learning approach in rotary kiln control.

Acknowledgement The paper is supported by the National Fundamental Research Program (2002CB312201), by the State Key Program of National Natural Science (60534010), by the Funds for Creative Research Groups (60521003), and by Program for New Century Excellent Talents in University of China.

References 1. Holmblad, L. P., Østergaard, J. –J.: The FLS Application of Fuzzy Logic, Fuzzy Sets and Systems, 70 (1995) 135-146 2. Jarvensivu, M., Saari, K., Jamsa-Jounela, S. L.: Intelligent Control System of an Industrial Lime Kiln Process, Control Engineering Practice, 9(6) (2001) 589-606 3. Jarvensivua, M., Esko Juusob, Olli Ahavac: Intelligent Control of a Rotary Kiln Fired with Producer Gas Generated from Biomass, Engineering Applications of Artificial Intelligence, 14 (5) (2001) 4. Liu, Z. Q., Liu, Z. H., Li, X. L.: Status and Prospect of the Application of Municipal solid waste incineration in China, Applied Thermal Engineering, 26(11-12) (2006) 1193-1197 5. Rolando Zanovello, Hector Budman: Model Predictive Control with Soft Constraints with Application to Lime Kiln Control, Computers and Chemical Engineering, 23 (6) (1999) 791-806

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6. Sutton, R. S.: Generalization in Reinforcement Learning: Successful Examples using Sparse Coarse Coding, In: D. Touretzky, M. Mozer, M. Hasselmo, (eds.) Advances in Neural Information Processing Systems, NY: MIT Press (1996) 1038-1044 7. Sutton, R. S., Barto, A. G.: Reinforcement Learning: An Introduction, Cambridge, MA: MIT Press (1998) 8. Tsitsiklis, J. N., Van Roy, B.: Feature-based Methods for Large Scale Dynamic Programming, Machine Learning, 22(1-3) (1996) 59-94 9. Watkins, J. C. H., Dayan, P., Q-Learning, Machine Learning, 8(3-4) (1992)279-292 10. Zhou, X. J., Xu, D. B., Zhang, L., Chai, T. Y.: Integrated Automation System of a Rotary Kiln Process for Alumina Production, Journal of Jilin University (Engineering and Technology Edition), sup: 350-353 (in Chinese) (2004)

A Data Reorganization Algorithm to Improve Transmission Efficiency in CAN Networks Jung-Ki Choi, Sungyun Jung, and Kwang-Ryul Baek Department of Electronics Engineering, Pusan National University, Busan, Korea {choijk1979, syjung, krbaek}@pusan.ac.kr

Abstract. CAN network is multi-master/multi-slave communication protocol and also supports single-master/multi-slave. In single-master/multi-slave mode, CAN master transmits control messages to each slave. If many slaves need small data from CAN master, CAN network spends a lot of time transmitting CAN overhead bits. So the transmission efficiency in CAN network goes down. In this paper, we propose an algorithm that increases the transmission efficiency by reorganizing the data mathematically.

1 Introduction The CAN network is multi-master/multi-slave communication protocol and also supports single-master/multi-slave [1]. The configuration of single-master/multi-slave CAN network is shown in Fig. 1. One master and many slaves are connected to CAN network and master controls flow of data.

Fig. 1. The configuration of CAN network

As shown in Fig. 2, the frame of standard CAN has 47 bits of overhead. The overhead consists of SOF field, arbitration field, control field, data field CRC field ACK field and EOF field. To transmit data over CAN network, one stuff bit is added every 4 bits in the original frame. This because the CAN standard states that one stuff bit is added every 5 bits at the same level in the bit stream transmitted over the bus. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 438 – 443, 2006. © Springer-Verlag Berlin Heidelberg 2006

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Fig. 2. Format of the standard CAN frame

The time to transmit CAN message is: § ª 34 + 8S m º · Cm = ¨¨ « »¼ + 47 + 8S m ¸¸τ bit . 5 ©¬ ¹

(1)

where Cm is the longest time taken to transmit CAN message and Sm is the number of bytes in payload field of the message and IJbit is bit time of the CAN bus [2][3]. To transmit data over CAN network, many bits are added for making CAN message frame. Sometimes CAN network is inefficient because of the additional overhead bits. To reduce the overhead bits, CANopen uses the PDO mapping and PDO linking techniques [4]. But the techniques don’t provide mathematical calculation algorithm to reduce the overhead bits. In this paper, we propose an algorithm to improve transmission efficiency which is based on mathematical calculation of overhead bits and estimate how transmission efficiency is improved by using the proposed algorithm.

2 Transmitting CAN Message Using Sequential Algorithm Fig. 3 shows how CAN network transmits message frames using sequential algorithm. This algorithm is a normal method to transmit data over CAN network. To transmit n bytes of data to m slaves, CAN master transmits m messages one after one. And by using the ID in the CAN message frame, each slave detects the data what it needs.

Fig. 3. Transmitting CAN messages

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The time to transmit n bytes of data to m slaves is: · § ª 34 + 8 × n º Tmn = m × Cn = m × ¨¨ « + 47 + (8 × n) ¸¸τ bit . » 5 ¼ ¹ ©¬

(2)

According to the equation 2, as the number of slave increases and data increase, the transmission time increases.

3 A Data Reorganization Algorithm In section 3, data reorganization algorithm is proposed to increase transmission efficiency mathematically. At Fig. 4, m n bytes of data are reorganized into 8 bytes and transmitted with new ID. Fig. 5 shows the algorithm how slaves receive the reorganized data. All slaves save the data which are transmitted by CAN master. Each slave reads all frames, reassembles the whole combined messages and extracts its intended data.

μ

Fig. 4. Reorganization of data

Fig. 5. Transmitting reorganized message frames

The transmission time using the proposed algorithm is:

T ' mn = C 8 × floor ( m × n / 8 ) + C mod(

μ μ

μ

m × n ,8 )

.

μ

(3)

where floor(m n/8) is rounding down of the value m n/8 and mod(m n, 8) is the remainder of m n/8. Table 1 shows transmission efficiencies which are calculated by dividing the transmission time with sequential algorithm by the transmission time

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with the proposed algorithm. As the number of slave increases and data per each slave decreases, the transmission efficiency increases. By using the proposed algorithm, the transmission efficiency is improved up to 388% at CAN 2.0A, 250kbps. Table 1. Transmission efficiency (%) = Tmn / T’mn

The Number of slaves Data per slave 1 byte 2 byte 3 byte 4 byte 5 byte 6 byte 7 byte 8 byte

໬100 @ CAN 2.0A, 250Kbps

1

2

3

4

5

6

7

8

100 100 100 100 100 100 100 100

174 158 148 141 100 100 100 100

230 197 128 124 121 100 100 100

275 224 148 141 115 114 100 100

311 179 164 130 112 111 100 100

341 197 148 141 121 109 100 100

367 211 159 133 118 107 100 100

388 224 169 141 125 114 106 100

4 Modeling Using M/D/1 Queue The memory of CAN master can be modeled as an M/D/1 queue [3]. Fig. 6 shows M/D/1 queue in single-master/multi-slave system. To adopt M/D/1 queue model, we suppose that the data transmitted from master to slaves arrive according to Poisson process of rate Ȝ. And when master transmits data to slave, new arrived data wait in the master’s queue. And the service time is the time to transmit data from master to slaves over CAN network.

Fig. 6. CAN network of M/D/1 queue

In M/D/1 system, service time E[IJ] is constant according to the transmission data and Tmn is the service time using sequential algorithm and T’mn is the service time using the proposed algorithm and E[T] is mean total delay in the system [5]. § ª 34 + 8n º · E[τ ] = Tmn = m × ¨¨ « + 47 + (8 × n) ¸¸ × τ bit . » ©¬ 5 ¼ ¹

§ m×n · E[τ ] = T 'mn = C8 × floor ¨ ¸ + Cmod(m×n ,8) . © 8 ¹

E[T ] = E[τ ]

2− ρ . 2 − 2ρ

(4) (5) (6)

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where ȡ = arrival rate/service rate. By using the equation 6, we can get the graph of mean total delay at CAN 2.0A, 250kbps. Fig. 7 is the graph when transmission data per each slave is 1 byte. As the number of slave increases from 1 to 8 in sequential algorithm, the mean total delay increases 8 times. But the mean total delay using the proposed algorithm is decreased than sequential algorithm because CAN overhead bits are decreased by using the proposed algorithm. The mean total delay in Fig. 8 is not decreased as much as Fig. 7. And the mean total delay in Fig. 9 is not decreased because the overhead bits using the proposed algorithm are not decreased. E[T] (us) 10000

E[T] (us) 10000

Sequential algorithm

5000

Proposed algorithm

5000 8 slaves l slave

0

0

0.5 ȡ = arrival rate / service rate

1

0

0

8 slaves l slave

0.5 ȡ = arrival rate / service rate

1

Fig. 7. The mean total delay with 1 byte of the transmission data per slave E[T] (us) 10000

5000

E[T] (us) 10000

Sequential algorithm

5000

8 slaves

8 slaves

l slave 0

0

0.5 ȡ = arrival rate / service rate

Proposed algorithm

l slave 1

0

0

0.5 ȡ = arrival rate / service rate

1

Fig. 8. The mean total delay with 4 bytes of the transmission data per slave E[T] (us) 10000

E[T] (us) 10000

Sequential algorithm

8 slaves

5000

8 slaves

5000

l slave 0

0

0.5 ȡ = arrival rate / service rate

Proposed algorithm

l slave 1

0

0

0.5 ȡ = arrival rate / service rate

1

Fig. 9. The mean total delay with 8 bytes of the transmission data per slave

5 Conclusion When CAN master transmits small amount of data to many slaves using sequential algorithm, the transmission time is increased because of additional overhead bits. In this case, the transmission time is decreased by using the proposed data reorganization algorithm.

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To use the proposed algorithm, slave needs more memory to save received data. And the interrupt rate is raised from the CAN controller to the CPU. But the proposed algorithm can improve network performance. And it is useful in some embedded control network which have requirement of real time characteristic.

Acknowledgments This work was supported by the Regional Research Centers Program(Research Center for Logistics Information Technology), granted by the Korean Ministry of Education & Human Resources Development.

References 1. Bosch.: CAN Specification Version 2.0, Robert Bosch GmbH, Stuttgart (1991) 2. Tindell, K., Burns, A., Wellings, A.: Calculating Controller Area Network (CAN) Message Response Times. Proc. IFAC DCCS’94. Toledo, Spain (1994) 35-40 3. Lawrenz, W.: CAN System Engineering: From Theory to Practical Applications. Springer. Oct. (1997) 4. Farsi, M., Ratcliff, K., Barbosa, M.: An Introduction to CANopen. Computing & Control Engineering Journal, Vol. 10, Issue 4, Aug. (1999) 161-168 5. Leon-Garcia, A.: Probability and Random Processes for Electrical Engineering. Second Edition. Addison Wesley (1994)

A Neural Network Approach to QoS Management in Networked Control Systems over Ethernet Wenhong Zhao1 and Feng Xia2 1

Precision Engineering Laboratory, Zhejiang University of Technology, Hangzhou 310014, China [email protected] 2 National Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou 310027, China [email protected]

Abstract. The popularity of using Ethernet as an industrial communication network in networked control systems (NCSs) has significantly grown in recent years. Despite this, the quality of control (QoC) could be degraded by crosstraffic in Ethernet. To enable networked control over Ethernet, a proactive QoS (quality of service) management scheme that exploits the neural network technology is presented. Using the idea of QoS framework, the shared network resource is dynamically allocated among control loops with respect to crosstraffic fluctuations, which is predicted by a simple and computationally-fast neural network. Simulation results show that the proposed scheme is highly effective in improving the QoC of NCSs over Ethernet.

1 Introduction In the area of manufacturing automaton and process control, there is a trend in networked control systems (NCSs) to substitute conventional industrial networks with Ethernet [1-3]. In these systems, the same Ethernet may be shared by multiple sensing and actuation flows, periodic bulk data transfers, and other wide-area traffic such as FTP, HTTP, and TELNET flows [4]. It is well-known in the control community that in NCSs network-induced delays and packet losses could significantly deteriorate the quality of control (QoC), and in extreme cases cause instability [5]. Therefore, the QoC largely depends on the timeliness provided by the network, which is often tightly associated with the traffic condition. The presence of cross-traffic in Ethernet as well as the non-deterministic characteristic of the CSMA/CD (carrier-sense multiple access with collision detection) protocol that Ethernet uses makes it difficult to always guarantee required QoC in NCSs. Originally defined for multimedia and telecommunication systems, QoS (quality of service) is a promising framework for run-time management of certain resources that are shared by multiple applications. It has several advantages that make it interesting for use in NCSs. For instance, QoS enables graceful degradation, and QoS level adjustment is an attractive way to increase overall system utilization [6]. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 444 – 449, 2006. © Springer-Verlag Berlin Heidelberg 2006

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In this paper, we apply the idea of QoS framework to dynamically manage the bandwidth resource of NCSs. In the considered system, multiple control loops are closed over the same Ethernet, and have to compete for bandwidth resource with other non-control bursty cross-traffic. To attack the negative impact of varying traffic conditions on QoC, we present a proactive QoS management scheme based on neural networks (NNs), which enables networked control over Ethernet. The cross-traffic is predicted and then the network resources allocated to control loops are adjusted accordingly. In this way, the network QoS provided for each control loop is effectively managed during run time. It is argued by simulation results that our scheme could significantly improve the overall QoC of NCSs. The rest of this paper is organized as follows. Section 2 illustrates the features of NCSs over Ethernet. We present the neural network based QoS management scheme in Section 3. The performance of our method is evaluated in Section 4. This paper is concluded with Section 5.

2 NCS over Ethernet Although Ethernet was not created to guarantee the delivery of time-critical information and features non-deterministic nature of communication, it has become a prime candidate for control networks. The advantages of Ethernet (compared with fieldbuses such as ControlNET, CAN, WorldFIP, etc.) include low cost, widespread usage, flexibility, and high communication rate [1-3]. A typical structure of control applications over Ethernet is illustrated in Fig. 1. In a feedback control loop, the sensor and the controller send messages to the controller and the actuator respectively via the Ethernet. There are also other nodes generating cross-traffic, e.g. HTTP, FTP, or TELNET flows over the Ethernet. These cross-traffic may comes from, e.g. the plantlevel enterprise information management subsystem, computer integrated manufacturing system (CIMS), or Internet.

Controller 1

...

Controller N

CIMS

Other App.

Ethernet Sensor 1

Actuator 1 Plant 1

...

Sensor N

Actuator N Plant N

Fig. 1. Networked control over Ethernet

Existing experiments and applications have demonstrated that Ethernet can be successfully applied to real-time closed loop control systems [2,3]. Under low network loads, the Ethernet-induced delay is quite small (almost zero to be exact). Otanez et al [1] recommend that there is a linear relationship between utilization and collision rate for small payloads, and network utilization should not exceed 25% and 37% for 10 and 100Mbps Ethernet respectively.

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3 Neural Network Based QoS Management In this section, we present a proactive QoS management scheme to enable networked control over Ethernet. With response to network traffic fluctuations, bandwidth resources are dynamically allocated to control loops that share the same Ethernet channel with other non-control applications. Once a real-time control loop is closed over an Ethernet, the bursty nature of the cross-traffic will inevitably affect the QoC [4]. The stability of the system cannot always be guaranteed because Ethernet’s non-deterministic protocol makes it impossible to predict network delays. Therefore, it is critical to properly allocate the bandwidth among different flows so as to optimize the overall system performance. Fig. 2 shows the proposed QoS management scheme. It is assumed that the crosstraffic (here we refer to all non-control traffic) cannot be rescaled. Consequently, we attempt to adjust the bandwidth resources allocated to all control loops with the intent of minimizing network delays, especially for control traffic. Since time delays increase as the Ethernet collision rate increases, the network utilization will be kept at a specific level, Us, e.g. 25% for 10Mbps Ethernet, in order to avoid too frequent collisions. The objective of QoS management is to maximize the overall control performance in the presence of bursty cross-traffic. Similar to the methods in [7,8], the cross-traffic is predicted using a neural network. Based on the prediction results, the bandwidth allocated to each control loop is then dynamically adjusted. QoS Manager Dynamic Bandwidth Allocation

Control Loops

Non-Control Applications

Predicted Cross-Traffic Cross-Traffic

Neural Network

Ethernet

Fig. 2. NN based QoS management for NCSs over Ethernet

Predicting network traffic is a typical time series prediction problem, which can be successfully solved using NNs [9,10]. To achieve low overhead of QoS management, we here use a simple BP neural network to predict the next transmission rate of crosstraffic, rct, which has been normalized with respect to the whole data rate of the Ethernet, rE. We use the same structure of neural network as [10]. As shown in Fig. 3, it is a three-layer NN, with 5 inputs, 10 hidden neurons, and one output. Based on the predicted transmission rate of cross-traffic, the total transmission rate of all control flows will then be adjusted so that the overall network utilization will be Us. Following the idea of feedback scheduling [7], we change the sampling periods of all control loops as follows:

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N

hi ( k  1)

hˆi
∆rmin

(2)

where ǻrmin is a specified lower threshold for the absolute difference between the predicted value and current value of the transmission rate of cross-traffic.

4 Simulation In this section, we carry out simulations to evaluate the performance of the proposed approach using Matlab/Simulink and the TrueTime toolbox [11]. We consider a system composed of 10 independent control loops (i.e., N=10) and 5 disturbance nodes. In every control loop there is a sensor, a controller, and an actuator in addition to the controlled plant. All plants have the same transfer function G ( s ) = 1000 /( s 2 + s ) , and all controllers execute well-designed PID algorithms. The disturbance nodes generate cross-traffic. All nodes are connected via an Ethernet with a transmission rate of 10Mbps. Accordingly, the desired network utilization Us is chosen as 25%. The default sampling period of each control loop takes on a value of

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0.008, 0.009, or 0.01 s. The sizes of messages from sensor to controller and from controller to actuator are 100 bytes. Therefore, d = 200 bytes. The invocation interval of the QoS manager is set to 0.1s. To apply the proposed QoS management scheme, we need to train and test the utilized neural network. For this purpose, we first assemble a representative sample of cross-traffic transmission rates using the simulation setup. Then with a part of this sample we train the neural network using BP algorithm. The other part of this sample is used to verify the effectiveness of the obtained NN. Once satisfactory prediction performance is achieved by the NN, we implement the NN based QoS manager. Each plant experiences an input step change every 1s, and the whole simulation lasts 30s. The utilization of the Ethernet under our method (denoted NN-QoSM) is shown by the red solid line (without circles) in Fig. 4. For comparison, we also give results when no QoS management scheme is used (denoted Non-QoSM), see blue line with circles. It is clear that by using our method, the network utilization can be increased to optimize resource usage when the cross-traffic is light, and decreased to avoid frequent collisions when the cross-traffic is heavy. Our method yields a relatively stable utilization regardless of the fluctuations of the cross-traffic.

Fig. 4. Network utilization

Fig. 5. IAE values of control loops

To assess the QoC, we record IAE (the integral of absolute error) of each control loop, see Fig. 5. To take into account the stochastic nature of Ethernet’s CSMA/CD protocol, we here use the mean value of five simulation runs. Notice that the smaller the IAE, the better the QoC. Clearly, in comparison with the Non-QoSM case, our method can effectively improve the QoC.

5 Conclusions Since cross-traffic inevitably degrades control performance, QoS management is critically important for NCSs, especially when Ethernet is used as the communication network. In this paper, we present a proactive QoS management scheme using the neural network technology. It enables networked control over Ethernet where multiple control loops and non-control applications have to compete for the same bandwidth resources. With graceful degradation, the proposed method successfully minimizes

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the impact of cross-traffic on the QoC. We conduct simulation experiments to assess the performance of our method. Simulation results show that our method optimizes network resource usage when the cross-traffic is light and reduces collisions when the cross-traffic is heavy, both of which yields improved QoC.

Acknowledgement This work is partially supported by Zhejiang Provincial Natural Science Foundation of China under Grant No. M503059.

References 1. Otanez, P. G., Parrott, J. T., Moyne, J. R.,Tilbury, D. M.: The Implications of Ethernet as a Control Network. Proc. of Global Powertrain Conference, Ann Arbor, MI (2002) 2. Ji, K., Kim, W. J.: Real-Time Control of Networked Control Systems via Ethernet. Int. J. of Control, Automation, and Systems, Vol. 3, No. 4 (2005) 591-600 3. Tipsuwan, Y., Chow, M.-Y.: Neural Network Middleware for Model Predictive Path Tracking of Networked Mobile Robot over IP Network, Proc. 29th IEEE IECON’03, Vol. 2, Roanoke, VA (2003) 1419-1424 4. Robinson, B., Liberatore, V.: On the Impact of Bursty Cross-Traffic on Distributed RealTime Process Control. Proc. IEEE Int. Workshop on Factory Communication Systems, Vienna, Austria (2004) 147-152 5. Xia, F., Wang, Z., Sun, Y. X.: Integrated Computation, Communication and Control: Towards Next Revolution in Information Technology. Lecture Notes in Computer Science 3356 (2004) 117-125 6. Sanfridson, M.: Problem Formulations for QoS Management in Automatic Control. Technical Report TRITA-MMK 2000:3, ISSN 1400-1179, ISRN KTH/MMK-00/3-SE, Royal Institute of Technology (KTH), Sweden (2000) 7. Xia, F., Li, S. B., Sun, Y. X.: Neural Network Based Feedback Scheduler for Networked Control System with Flexible Workload. Lecture Notes in Computer Science 3611 (2005) 237-246 8. Moh, W. M., Chen, M. J., Chu, N. M., Liao, C. D.: Traffic Prediction and Dynamic Bandwidth Allocation over ATM: a Neural Network Approach, Computer Communications, Vol. 18, No. 8 (1995) 563-571 9. Frank, R.J., Davey, N., Hunt, S.P.: Time Series Prediction and Neural Networks, Journal of Intelligent and Robotic Systems 31 (2001) 91-103 10. Develekos, G., Michail, O., Douligeris, C.: A Neural Networks Approach to the Estimation of the Retransmission Timer (RTT). Proc. 9th Panhellenic Conf. in Informatics, Thessaloniki, Greece (2003) 11. Henriksson, D., Cervin, A., Årzén, K. E.: True Time: Simulation of Control Loops Under Shared Computer Resources. Proc. of the 15th IFAC World Congress on Automatic Control, Barcelona, Spain (2002)

A Novel Micro-positioning Controller for Piezoelectric Actuators Van-Tsai Liu1, Chun-Liang Lin2, Hsiang-Chan Huang1, and Zi-Jie Jian2 1

Department of Electrical Engineering, National Formosa University, Huwei, Taiwan 632, R.O.C. [email protected] 2 Department of Electrical Engineering, National Chung Hsing University, Taichung, Taiwan 402, R.O.C. [email protected]

Abstract. The main purpose of this study is to design a tracking controller for a dual-axes piezoelectric actuated platform. First, a Preisach model is used to numerically describe the hysteresis behavior of piezoelectric actuators. Next, on the basis of the Preisach model, a feed-forward controller is developed to compensate for the hysteresis nonlinearity. Then, a PID controller is introduced to further suppress the tracking error due to the modeling inaccuracy and hence to get precision tracking control. We utilize evolution algorithm to choose three optimality control gain for PID controller. The dual-axes motion control problem for the piezoelectric actuated platform is also investigated. A neural-net based decoupling control scheme is proposed to eliminate the contour error which is typical in dual-axes tracking control problem. The developed approaches are numerically and experimentally verified which demonstrate performance and applicability of the proposed designs under a variety of operating conditions.

1 Introduction Piezoelectric actuators have widely been used in many industrial applications such as noise-and-vibration control. However, the positioning precision can be significantly reduced due to nonlinear hysteresis effects when piezoelectric actuators are used in relatively long-range, positioning applications. Therefore, piezoelectric actuators are typically operated in the linear range to avoid positioning errors caused by nonlinear hysteresis effects. The compensation methods for the piezoelectric hysteresis have been widely proposed. Preisach model is the earliest model of hysteresis, Ge [1] set up hysteresis mathematic model by Preisach model. Ge and Choi generated the parameters of mathematic model using the tracking control [2] and feedforward controller to analyse the effects of different feedback circuit [3]. However, there are still some practical problems. First, the contour error which is typical in dual-axes tracking control problem is unsolved. To solve the coupling problem, a novel decoupling control scheme based on neural network is proposed in this paper. Many engineering applications of neural network have been found in the areas of signal processing, function approximation, etc [4]. Because of their high capacity and learning ability, neural networks are well suited to depict functions with local nonlinearities and fast D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 450 – 455, 2006. © Springer-Verlag Berlin Heidelberg 2006

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variations. Second, the Conventional PID controllers need to regulate three parameters which were usually chosen trial and error. This motivates intelligent control algorithms described in the follows. In this paper, we proposed evolutionary algorithms to choose three optimality control gains for PID controller [5]. A neural-net based decoupling control scheme is proposed to eliminate the contour error. Extensive simulations and experimental results are presented to confirm our proposed approach.

2 Preisach Model The Preisach model can be described as [1]

f (t ) = ³³ α ≥ β u (α , β )γ αβ [u (t )]dα d β .

(1)

where u(t ) is the input signal, f (t ) is the output response, u (α , β ) is the weighing function in Preisach model, α and β are, respectively, the upper bound and lower bound of input value, and γ αβ [u (t )] is the hysteresis operator which is set up between 0 and 1. The expressions of Preisach model can be defined as N −1

f ( t ) = ¦ ( fα ' β ' − f α ' β ' ) + f u ( t ) − f u ( t ) β ' . k =1

f (t ) =

N −1

¦ [ F (α

(2)

N −1

k

' k

, β k' − 1 ) − F (α k' , β k' )]

k =1

k

k −1

k

+ { F (α N' , β N' − 1 ) − F [α N' , u ( t )]} =

N −1

¦ ( fα k =1

' k

β k'

− fα ' β ' ) + fα ' k

k −1

N

u (t )

.

− fα '

N

(3)

β N' − 1

The actual displacement output of the piezoelectric actuator is measured when the experiment data f α i and i, j = 1, 2, , n have already known. The output f (t ) can use (2) and (3) to calculate output displacement of piezoelectric actuator. The experiment and simulation of hysteresis loops is shown in Fig.1.

Fig. 1. Experiment and simulation of hysteresis loops (x-axle)

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V.-T. Liu et al.

3 Design for Tracking Control Scheme In this paper, we propose a novel tracking control method including the feedforward controller and PID controller generated by evolutionary algorithms. The procedure is as follows. 1.

2.

Assign a reference signal and the control signal ud (0) to begin from 0. Take a sample displacement f d ( k ) using parameters of Preisach model (as (2)

and (3)), and compare the displacement to calculate the hysteresis output f r . The error is used to update the control signal, its formulation is as the expression. ud (k ) = udold ( k ) + ∆ud ( k ) .

3.

(4)

where ∆ud (k ) is the modified control voltage, ud ( k ) and udold (k ) are, respectively, the control voltage with and without modifying it. Input the next reference displacement signal and repeat the step 2, and let ud old ( k ) = ud ( k ) . To make the tracking error minimum, the fitness function is defined as

f ∝

1

( fd −

f act )

2

.

(5)

where f d is reference displacement input, and f act is actual displacement. We assume that there are w individuals in every generation, each individual is denoted by the vector v = ( k i , N ( 0, σ 2 ) ) , where k i denotes the vector of three PID control

parameters, N ( 0, σ 2 ) denotes the vector of the group zero average, σ is the standard

deviation for gauss function. The g-th mutation can defined as k ij( g +1) = k ij( g ) + N ( 0, σ 2 ) , i = 1, , w, j = 1, , l .

(6)

The three gain parameters of PID controller are produce in the way as follows: k i′ = k i + N ( 0, σ 2 ) .

(7)

σ ′ = σ ⋅ exp(ζ ) .

(8)

where ζ is determined to have zero average and normal distribution function between two generations variation ∆σ 2 . The rules for searching parameters can be determined (g) (g) by f max − f min < ε , where ε is the upper bound, f max = max fi and f min = min fi . i =1,, w

i =1,, w

4 Cross Coupling Control in Dual-Axes Systems The main purpose of this section is to use a decoupling controller based on neural network to reduce the contour error of dual-axes cross-coupling. The neural network is L layer of feedforward type neural network, it is defined as NN (v,W1 ,W2 , ,WL ) ,

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where Wi (i = 1, , L) ∈ ℜn ×n is the weighing matrix from (i − 1) layer to i layer. The input vector is ε (e x , e y ) . The structure of the neural network is i

i −1

Cc (ε ) = Ψ L [WL ⋅⋅⋅ Ψ 2 [W2 Ψ1[W1ε ]]] .

(9)

The activation function vector Ψi [⋅]: ℜ  ℜ is defined as ni

ni

Ψi [ z] ≡ [ψ 1 ( z1 )ψ ni ( zni )]T x + y = z .

(10)

The activation function ψ ( z ) of hidden layer is expressed as ­° ½° § 1− e−zβ · Fs ≡ ®ψ (⋅): R  R |ψ (z) = λ ¨ , β, λ > 0¾ . −z β ¸ + 1 e © ¹ ¯° ¿°

(11)

where β and λ are parameters of the activation function. The activation function of the output layer is linear type: Fl ≡ {ψ (⋅) : R  R | ψ ( z ) = λ z , λ > 0} .

(12)

To minimize track error, defined fitness function as f ∝

where

wi , i = 1, 2

1

.

w1 ( ex + e y 2 ) + w2 C xy 2

(13)

is the weighing factor; Cxy is the cross covariance, it is defined as C xy =

1 tf

³

tf

0

x(t ) y(t )dt −

1 t 2f

³

tf

x(t )dt

0

³

tf

y (t ) dt .

0

(14)

where t f is the operating time. The weighing parameter set of the neural network is shown as:

S = {k1 , k2 , , kw } , i = 1,..., w .

(15)

where

(

n n -1 ki = ª¬vecT ( wiin, j1 ) , vecT ( wi21,kj ) , L, vecT wi(,kj)( ) T bias , vecT ( wiout )º¼ , ,1k ) , vec ( wi

)

, j = 1,, L, J , k = 1, , K , n=2,, N ,

The mutations can be defined as

k (ijg +1) = k ij( g ) + N ( 0,σ 2 ) , i = 1,, w, j = 1,, l .

(16)

5 Experimental Verification 5.1 The Experiment and Simulation Results of the Single Axle Control

A piezoelectric actuated platform is introduced to confirm the feasibility. The position of the piezoelectric actuators ranges from 40 µm to 25 mm, the range of the control voltage is 0~5V. The precision specification of the sensor is 0.1µm. The evolutionary

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algorithm is first proposed to choose optimal parameters. The parents are w = 15 , the offsprings of mutation are λ = 7 ⋅ w , and the fitness function is defined as (5). After 50 generations, the fitness function of x-axle converges. The sinusoidal wave is used as the input signal where the amplitude is 30µm and frequency is 0.1Hz. When using the feedforward controller, the rms error of the x-axle is 2.0185 µm, the tracking error is 6.73 % and the maximum error is 3.344 µm, the rms error of the y-axle is 1.7688 µm, the tracking error is 5.9 % and the maximum error is 2.9833 µm. When using the feedforward controller with the PID feedback controller, the rms error of the x-axle is 0.9389 µm, the tracking error is 3.13 %, the maximum error is 4.87 µm, the rms error of the y-axle is 0.4189 µm, the tracking error is 1.4 %, the maximum error is 2.274 µm. Obviously, the PID controller with evolutionary algorithms improves the rms error and tracking error, and the positioning accuracy is quite satisfactory. 5.2 The Experiment and Simulation Result of the Dual-Axes Control

The cross-coupling controller based on neural network was used to eliminate the contour error. The structure of the neural network controller is described in (9), where the activation function is described as (10). In this paper, there are 24 hidden layers. The activation function of hidden layer is expressed as (11). The parents are w = 15 , the offsprings of mutation are λ = 7 ⋅ w , and the fitness is defined as (13). After 50 generations reproduction to derive the weighing value of the neural network. The cosine wave is used as dual-axes input signal where the amplitude is 20 µm and frequency is 1Hz. A round with 10 µm radius is plotted as shown in Fig.2.

Fig. 2. The cross-decoupling control and reference tracking

R.M.S. of the contour error without using cross-coupling control is 0.7923µm, the rms of the tracking error of the x-axle is 0.6770 µm, the rms of the tracking error of the y-axle is 0.6007 µm. When using cross-coupling control, the contour error is 0.5321µm, the tracking error of the x-axle is 0.4574 µm, the tracking error of the yaxle is 0.4737 µm. From the experimental results, the cross-coupling controller can improve the contour error and the tracking error rms of dual-axes.

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6 Conclusion In this paper, a feed-forward controller and a PID controller with evolutionary algorithms are proposed to compensate for the hysteresis nonlinearity. The tracking error is obviously suppressed by the PID controller. The contour error which is typical in dual-axes tracking control problem is eliminated by the neural-net based decoupling control scheme. From the experimental results, the developed approaches demonstrate the performance and applicability under a variety of operating conditions.

References 1. Ge, P., Jouaneh, M. : Modeling Hysteresis in Piezoceramic Actuators, Precision Engineering, vol. 17, no. 3 (1995) 211-221 2. Choi, G. S., Kim, H. S., Choi, G. H. :A Study on Position Control of Piezoelectric Actuators, IEEE International Symposium on Industrial Electronics (1997) 851-855 3. Ge, P., Jouaneh, M. : Generalized Preisach Model for Hysteresis Nonlinearity of Piezoceramic Actuators, Precision Engineering, vol. 20, no. 2 (1997) 99-111 4. Yamada, T., Yabuta, T. : Nonlinear Neural Network Controller for Dynamic System, in Proc. of 16th IEEE Annual Conference, vol. 2 (1990) 1244-1249 5. Lin, C. L., Jan, H. Y. : Multiobjective PID Control for a Linear Brushless DC Motor: an Evolutionary Approach, Proc. of IEE Electric Power Applications, vol. 149 (2002)

A Study on the Robust Control of an Inverted Pendulum Using Discrete Sliding-Mode Control J.Y. Yang1, H.J. Lee2,*, J.H. Hwang1, N.K. Lee2, H.W. Lee2, G.A. Lee2, and S.M. Bae3 1

Dept. of Aerospace and Mechanical Engineering, Hankuk Aviation University, 200-1, Hwajeon-dong, Deogyang-gu, Goyang-city, Geonggi-do, #412-791, Korea [email protected], [email protected] 2 Digital Production Processing & Forming Team, Korea Institute of Industrial Technology, 994-32, Dongchun-dong, Yeonsu-gu, Incheon Metropolitan City, #406-130, Korea {naltl, nklee, hwlee, galee}@kitech.re.kr 3 Industrial & Management Engineering, Hanbat National University, SAN 16-1, Duckmyoung-dong, Yusong-gu, Daejon Metropolitan City, #305-719, Korea [email protected]

Abstract. In this paper, discrete sliding mode controller (DSMC) with slidinglike condition is evaluated experimentally the robustness point of view. DSMC was modified to use a pseudo-sliding methodology and a variable sliding gain methodology. DSMC with a pseudo-sliding methodology and a variable sliding gain methodology perfectly eliminate a chattering problem and can control the system use a small control action. The usefulness of the designed DSMC in this paper is demonstrated by the control of an inverted pendulum system and the robustness of DSMC experimentally evaluated for model error. To provide a performance benchmark with respect to robustness, a direct comparison was made against linear quadratic control.

1 Introduction It is well known that the continuous sliding mode control (CSMC) has robustness for parameter uncertainties and external disturbances [1-5]. But discretization of CSMC reduces robustness. The sampling may cause undesirable system performances or unstable behavior. For that reason, many investigations were reported to solve this problem. However, most of all restricted to the local behavior around the sliding mode. But ‘Sliding-like Condition’ by Chen [6] is a global discrete sliding condition. It implies that the system does not sliding in the sliding mode, but moves in a layer with a finite thickness. Sliding mode control is considered a nonlinear controller, not because of a nonlinear structure or model but because of control action switching. Such a high frequency motion known as chattering is highly undesirable in practice and will result in unnecessary wear and tear on the actuator components. Then, in this paper chattering pre-vented DSMC was designed [7]. To mitigate high controller action and *

Corresponding author.

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 456 – 462, 2006. © Springer-Verlag Berlin Heidelberg 2006

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sensitivity to the assigned parameters of system, a variable sliding gain methodology was incorporated in the sliding laws [1]. The inverted pendulum is a classic nonlinear system which widely used to verify the usefulness of many control techniques. In this paper, discrete sliding mode controller (DSMC) with sliding-like condition is evaluated experimentally the robustness point of view. DSMC was modified to use a pseudo-sliding methodology and a variable sliding gain methodology. The usefulness of the designed DSMC in this paper is demonstrated by the control of an inverted pendulum system and the robustness of DSMC experimentally evaluated for model errors. To provide a performance benchmark with respect to robustness, a direct comparison was made against linear quadratic control. The designed DSMC which is a chattering free and low control action controller has a good robustness for pendulum length error on the order of ±50% as a compared to LQC in the same condition. Moreover, the designed DSMC can assure the stable actuator performance without chattering because it needs a very small control action to control the system.

2 Inverted Pendulum Systems The inverted pendulum system is described in Fig. 1. The DC motor translates the cart through a ball screw. Two rails on both sides of the ball screw support the cart. Two encoders measure the cart’s position and the pendulum angle. The system is modeled under the following assumptions. First, the pendulum angular displacement is very small. Second, the pendulum is restricted to the vertical. Third, the pendulum, the ball screw and the rail are rigid. Fourth, the friction and damping force are negligible at joint. The last, the friction is constant between the cart and the ball screw. M and m are the masses of the cart and the inverted pendulum, respectively; l is the pendulum length. The position of the cart is r and θ is the angular position of the inverted pendulum. The dynamic equations can be derived based on the Lagrangian equations. After linearization at θ ≅ 0, then

x (t ) = Ax(t ) + Bu (t ) + ζ (t ) where x = ª¬ r θ

(1)

T

r θ º¼ , ζ (t ) is the disturbance error, and

0 ª0 «0 0 « mg A = «0 − « M « ( M + m) g «0 «¬ Ml Fr = b + (

−

1 0 Fr

M Fr

Ml

2π 2 K m Kb ) r R

0º 1»

»

ª 0 º « 0 » « » « Fv » B=« » « M » « Fv » «¬ − Ml »¼

0»

,

,

Fv =

» » 0» »¼

2π K m r

R

(2)

(3)

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Parameters of inverted pendulum system are shown in Table 1, then 0 1 ª0 «0 0 0 A=« «0 −196.14 −24.965 «¬0 29.421 0.624

0º 1» » 0» 0 »¼

,

ª 0 º « 0 » » B=« « 81.467 » « » ¬« −2.037 ¼»

(4)

The system ( A, B) is controllable.

Fig. 1. The inverted pendulum system Table 1. Parameters of inverted pendulum system

Parameter Cart mass Pendulum mass Pendulum length Cart friction coefficient Displacement per ball screw one revolution Motor torque constant Motor reverse electromotive force constant Motor armature resistance

Symbol M m l b

Value 1.0kg 0.2kg 40cm 0.5kg/s

r

1.27cm

Km

4.94N·cm/A

Kb

0.0607V/rad/s

R

0.3Ω

3 Controller Design 3.1 Discrete Sliding Mode Controller

The inverted pendulum system is a single input system, it can be described a continuous time-invariant system. Define the error state as e(t ) = x - xd , then (1) becomes e (t ) = Ae(t ) + Bu (t ) + ζ (t ) (5)

A Study on the Robust Control of an Inverted Pendulum Using DSMC

where xd = [rd

459

0 0 0]T , u (t ) is the control input, ζ (t ) contains the disturbance

errors, and the pair ( A, B) is controllable. If the sampling time T is sufficiently fast so that (5) can be directly discretized as e k +1 = (I + TA )e k + TBuk + Td k

(6)

where e (t ) ≈ (e k +1 − e k ) / T , the input u (t ) is generated by a zero-order-hold as u (t ) = uk for kT ≤ t < (k + 1)T . The disturbance d k contains both the modeling and truncation errors, it is bounded as d k < δ for all k. Where δ is a positive constant, the input uk depends on ek −1 . The sliding function is [6] sk = cT ek

(7)

Let the control law uk depends on e k −1 as [6] uk = −(cT B) −1[cT Aek + w sgn( sk −1 )]

(8)

where sgn( sk −1 ) is the sign function of sk −1 and w = δ c . The following characteristic equation

det λ I − (I − B(cT B )−1 ) A = 0

(9)

which possess stable eigenvalues with Re(λ) < 0. And the characteristic equation of a discrete system is

det

( z − 1) I − (I − B(cT B) −1 ) A = 0 T

(10)

If λ is selected to satisfy z < 1 , the system is stable. Pseudo-Sliding and Variable Sliding Gain To prevent chattering, the sigmoid-like function replaces with the signum function of (9). The sigmoid-like function is

υδ (s)=

s ( s +δ )

(11)

where 0  G  1 (set as 0.005). To mitigate high controller action and sensitivity to the assigned parameters of system, a variable sliding gain was incorporated in the sliding laws [1].The variable sliding gain decreases the magnitude of the sliding action on approach to the sliding surface and can therefore prevent overshoot. The variable sliding gain is w=

ws n

¦x

i

i =1

+ε

(12)

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where w is the initial value for the sliding gain , w = δ c , (δ = 0.5) , and ε is a positive constant set at 0.1. Now the new control law is uk = −(cT B) −1[cT Ae k + wυδ ( sk −1 )]

(13)

3.2 Linear Quadratic Controller

The LQ control has a linear feedback law of the following form u = -Kx

(14)

where K is the feedback gain matrix. To optimize this gain matrix, weighting matrices Q and R for input and output, respectively, are designed to minimize a cost function J . ∞

J = ³ (x T Qx + u T Ru )dt

(15)

0

4 Experimental Results The inverted pendulum of the experiment is shown in Fig. 2. DSMC is implemented by a PC (DSP-board, CEMTOOL/SIMTOOL) with sampling time T =0.001 sec. DSMC was designed as eigenvalues of the feedback system (10) are {-20, -4.97±i0.89} and cT = [ −0.2553 −24.9111 −0.1123 −4.9828] . LQC was designed R = 1, Q = diag [1 0 1 0] , K = [-1.0 -525.6 -1.8 -105.6].

Fig. 2. Inverted pendulum apparatus

4.1 Robustness Test for Pendulum Length Error The pendulum length for the experiment is 40cm. Hence DSMC and LQC were designed as 20cm and 60cm pendulum length (±50% errors). And these controllers apply to the correct inverted pendulum system to experimentally evaluate robustness of the designed controller. This set of robustness tests would be the most realistic in an industrial environment and could be extended to other plants where the system

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parameters are time varying. Fig. 3, 4 show the robustness test results of DSMC and LQC, respectively. LQC has vibration of the response more than DSMC and the control input of LQC is twice as high as the control input of DSMC.

(⎯black):desired , (⎯ red):correct model, (⎯green):+50% error, (⎯blue):-50% error

Fig. 3. DSMC

Fig. 4. LQC

5 Conclusions In this paper, DSMC with a pseudo-sliding methodology and a variable sliding gain methodology was designed and experimentally evaluated robustness for model error. From the result of the robustness test performed on the inverted pendulum, it can be

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concluded that DSMC shows a high level of robustness in the presence of model error on the order of ±50%. As a compared to LQC, DSMC shows a higher level of robustness than LQC. All of the control input magnitude and frequency of DSMC are very low then LQC’s. It means that the designed DSMC can ensure the stable actuator performance for control.

Acknowledgements This work has been sponsored by MOCIE (Ministry of Commerce, Industry and Energy) of Korea.

References 1. Harry N. Iordanou , Brian W.Surgenor: Experimental Evaluation of the Robustness of Discrete Sliding Mode Control Versus Linear Quadratic Control. IEEE Transactions on Control Systems Technology, Vol. 5, No. 2, (1997) 254-260 2. Utkin VI: Variable Structure Systems with Sliding-modes. IEEE Trans Automatic Control (1977) 212-222 3. Vadim Utkin, Jürgen Guldner, Jingxin Shi: Sliding Mode Control in Electromechanical Systems. CRC press (1999) 4. Vadim I. Utkin: Variable Structure Systems with Sliding Modes. IEEE Transactions an Automatic Control, Vol. 22, No. 2, (1997) 212-222 5. Vadim I. Utkin: Sliding Modes in Control and Optimization. Springer-Verlag Berlin, Heidelberg (1992) 6. Yon-Ping Chen, Jeang-Lin Chang, Sheng-Renn Chu: PC-based Sliding-mode Control Applied to Parallel-type Double Inverted Pendulum System. Mechatronics, Vol. 9, (1999) 553-564 7. Christopher Edwards, Sarah K. Spurgeon: Sliding Mode Control ; Theory and Applications. Taylor & Francis (1998) 8. K. David Young, Vadim I. Utkin, Umit Ozguner: A Control Engineer’s Guide to Sliding Mode Control. IEEE Transactions on Control Systems Technology, Vol. 7, No. 3, (1999) 328-342 9. Weibing Gao, Yufu Wang, Abdollah Homaifa: Discrete-Time Variable Structure Control Sys-tems. IEEE Transactions on Industrial Electronics, Vol. 42, No. 2, (1995) 117-122 10. Sami Z. Sarpturk, Yorgo Istefanopulos, Okyay Kaynak: On the Stability of Discrete-Time Sliding Mode Control Systems. IEEE Transactions on Automatic Control, Vol. AC-32, No. 10, (1987) 930-932 11. Gene F.Franklin, J. David Powell, Michael Workman: Digital Control of Dynamic Systems. Addison Wesly Longman (1998)

A VRC Algorithm Based on Fuzzy Immune PID-Smith Ling He1, Yu-cheng Zhou2, Yuan-wei Jing1, and Hai-yu Zhu1 2

1 Northeastern University, Shenyang 110004, China Research Institute of Wood Industry, Chinese Academy of Forestry, Beijing 100091, China

Abstract. VRC algorithm is a new active queue management (AQM) arithmetic based on rate. The response rate of VRC algorithm is rapider than traditional AQM arithmetic. A new VRC algorithm based on the fuzzy immune adaptive PID control and Smith predictor is proposed. PID parameters’ online selfadapting was implemented by immune feedback mechanism. Moreover the Smith predictor was successfully introduced into feedback to compensate the time delay in network. Contrasted with traditional PID algorithm, fuzzy immune PID-Smith is validated by simulation results. It can adjust itself to new network conditions rapidly and stably, can converge to queue size-setting value, and can get better robustness.

1 Introduction Network congestion is the main reason to cause descent of network capability. One side, the source should adjust transmission speed of data on the state of network congestion to reduce network congestion; on the other side, the network should participate in management and control of resource, i.e. adopt active queue management (AQM) in the Router[1]. AQM can be divided into two types: 1) the rate-based congestion control. 2) the queue-based congestion control. Recent years, different AQM are proposed. The representative AQM algorithm are RED[2], REM[3], ECN[4] and so on. C.Hollot[5] and other researchers designed P and PI controller used as AQM algorithm by classical control theory. As the improving of PI algorithm, PID algorithm[6] introduced the integral to eliminate static error. But PID algorithm is lack of the adaptive mechanism to the dynamic network. Currently, many scholars take note of the effect to AQM control capability caused by time delay in network[7,8]. But it is lack of considering the improvement of self-adaptive ability to network circumstance. A virtual rate control arithmetic(VRC) is proposed in [9]. The algorithm is the congestion control algorithm based on rate. VRC algorithm is capable of response the flux change rapidly. The fuzzy immune PID control and Smith predictor is combined in this paper. So the non-linearity of system model and the uncertainty of time delay can be compensate by fuzzy controller. The system can realize real time online control rapidly. The Smith predictor can conquer the instability effect to system by time delay. The simulation indicates that the new arithmetic can get better steady and dynamic performance than traditional VRC algorithm. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 463 – 468, 2006. © Springer-Verlag Berlin Heidelberg 2006

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2 Analysis of Virtual Rate Control Algorithm In [10], the dynamic model of TCP network is proposed based fluid model: 1 W (t ) W (t − R(t )) W (t ) = − p(t − R(t )) R(t ) 2 R(t − R(t ))

q (t ) = r (t ) − C

(1)

(2)

W (t ) is the TCP window size. q(t ) is the queue length. R (t ) is the round road time delay (RTT). p (t ) is the mark/discard probability of packets. C is the link capability. r (t ) is the input rate. B is the buffer size. The VRC algorithm use Router queue length and input rate as the control variables. A proportion rate control mechanism is proposed in [9]. p(t ) = [α ( r (t ) − rt (t ))]+ , α > 0

(3)

rt (t ) is the goal rate, [⋅]+ = max(min(⋅,1), 0) . For making the queue length q(t ) approach the goal queue length Qref , the goal rate can be shown as (6):

rt (t ) = C + γ (Qref − q (t )), γ > 0

(4) *

But the input rate r * is always higher than goal rate rt at the balance point. For compensating the rate error, virtual goal rate is introduced. rt (t ) in (3) can be replaced by the virtual goal rate p(t ) = [α (r (t ) − rv (t ))]+

(5)

The update of virtual goal rate can minimize the difference between r (t ) and rt (t ) .

rv (t) = rt (t) −∆rv (t), t = nTs

(6)

∆rv (t + Ts ) = ∆rv (t ) + β Ts (r (t ) − rt (t )), β > 0

(7)

Then we can get the mark probability expression of VRC: t

p(t ) = [α (r (t ) − C ) + α ( β + γ )(q(t ) − Qref ) + αβγ ³ (q(τ ) − Qref )dτ ]+ 0

(8)

(10) can be express as (11) if the restrict of buffer size is neglect. t

p(t ) = K D e(t ) + K P e(t ) + K I ³ e(τ )dτ 0

(9)

(11) is a PID control fashion. K D = α , K P = α (β + γ ) , K I = αβγ , α , β and γ are constant coefficient. The system can guarantee local stabilization and get minimum error between the queue length and goal value if the K P , K I , K D satisfy some condition in [9]. But the AQM algorithm should adapt the infection of dynamic change and disturbing in the network. In the paper, the fuzzy immune control is introduced into the VRC

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algorithm. The fuzzy immune controller can correct the change of network parameter online. At the same time, the Smith predictor is introduced to eliminate the influence to system caused by time delay. The system can get better steady and dynamic performance.

3 Control Strategy The control model exist strong uncertainty, non-linearity and affixation yawp. So the controller parameters should respond the change of network condition under realistic network flux. There need an adaptive control mechanism to track the change of network condition. In this paper, we ameliorate two functions based on traditional VRC algorithm: one is introducing the fuzzy immune PID controller which can selfadaptive adjust PID parameter online; the other is introducing the Smith predictor to compensate the time delay of network. 3.1 Fuzzy Immune PID Control Algorithm

Classical linear PID controller is hard to ensure the robustness and the effectiveness while the model is uncertain. The discrete equation is given by k ª e(k ) − e(k − 1) º R(k ) = k p e(k ) + kiT ¦ e(j ) + kd « » T ¬ ¼ j =0

(10)

Based on immune-feedback principle, we introduce the control structure[11] If we treat the amount of the antigens as control error e(k ) between the set point and the output of a control system. We can get the feedback control law in [11]: R(k ) = K ª¬1 − Șf ( R(k ) ,ǻR(k ) ) º¼ e(k )

(11)

We now can derive the output of the immune-PID controller as follow:

ª e(k ) − 2e(k − 1) + e(k − 2) º R(k ) = R (k − 1) + k 'p [ e(k ) − e(k − 1)] + ki Te(k ) + kd « » T ¬ ¼

(12)

where k 'p = K ª¬1 − Șf ( R (k ), ∆R (k ) ) º¼ , K=k1 is used to control the response speed, k1 is a stimulation factor, k2 is a suppression factor, Ș = k2 k1 is used to control the stabilization effect. When we design the immune PID control law, we now propose to employ a fuzzy controller to implement the nonlinear function f (⋅) . Fuzzy controller are the applications of fuzzy set and fuzzy inference in control theory, here our operation is typically divided into the following three phases. 1) Fuzzification: It is a procedure to define fuzzy sets for R (k ) , ∆R (k ) and f (⋅) . Here for R (k ) and ∆R (k ) , we define two fuzzy sets respectively, they are “positive” (P) and “negative” (N); Three fuzzy sets are defined for f (⋅) . They are “positive” (P), “zero” (Z) and “negative” (N). The membership function are defined over ( −∞, + ∞ ) .

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We choose Z model function, S model function and Triple model function to describe the fuzzy set of input and output variables. 2) Inference: We apply the four fuzzy rules below: a. If R is P and ∆R is P then f ( R, ∆R ) is N b. If R is P and ∆R is N then f ( R, ∆R ) is Z

c. If R is N and ∆R is P then f ( R, ∆R ) is Z

d. If R is N and ∆R is N then f ( R, ∆R ) is P For these rules, we use Zadeh fuzzy-logic AND operator. 3) Defuzzifization: We apply center of gravity method to calculate the output of fuzzy controller. 3.2 The Designing of the Fuzzy Immune PID-Smith Controller

The combination of fuzzy immune PID and Smith predictor can solve the control problem of large time delay system effectively. As figure 1 shows, G P ( s ) is the estimative model of control object, τ is the estimative time delay. Smith predictor control is one of the main methods to conquer large delay. If the Smith predictor is introduced into delay system, and the estimate model is matching with the real model, the character equation will not exist e − R s . That is to say the Smith predict control can eliminate the effect of time delay. adaptive adjust parameter of PID

e(k )

Q ref

fuzzy aapproach of immune feedback function

fuzzy immune PID controller

_

p (t )

control object

e R s

 RC 2 2N º ª 2 N 2 «s  2 » R C¼ ¬

N 1º ª R «s  » R¼ ¬

window

queue

~ G (s)

q (t )

+ +

Fig. 1. Is the network system frame of fuzzy immune PID-Smith control. G ( s ) is the Smith predictor, G ( s ) = G P ( s )(1 − e −τ s ) .

4 The Simulation Analyze We make simulation of the system. We take C = 5Mb / s , the capability of buffer is 300 packets , the number of TCP connection N = 60 . the time delay R = 0.04 s, Qref = 150 packets . We take PID-VRC as the comparison. Firstly, we can get control curve of the two algorithms in LAN. R = 0.04 s A disturb is put into the system at 20s. The result is shown as Fig.2.

A VRC Algorithm Based on Fuzzy Immune PID-Smith 180

467

350

160

fuzzy immune PID-Smith PID-VRC

300

140

y(t)/packet

q(t)/packet

250 120 100 80 60 40

200 150 100 50

20

PID-VRC fuzzy immune PID-Smith-VRC

0

0 -20

0

10

20

30

40

50

-50

60

0

5

10

t/s

15

20

25

30

t/s

Fig. 2. The simulation curve in LAN

Fig. 3. The simulation curve in WAN

Secondly, we make simulation in WAN. We change the delay time into R = 0.6s . The control curve of the two control algorithmic are shown as Figure 3. 300

800 PID-VRC fuzzy immune PID-Smith

250

PID-VRC fuzzy immune PID-Smith 600

y(t)/packet

y(t)/packet

200 150 100 50

400

200

0

0 -200 -50 -100

0

10

20

30

40

50

60

t/s

Fig. 4. The result when the parameter changes

-400

0

10

20

30

40

50

60

t/s

Fig. 5. The result under the worst network condition

Then we change the parameter of control object, i.e. N = 80 , C = 4Mb / s . The control curve of the two control algorithmic are shown as Figure 4. At last, we get simulation under the worst network condition, i.e. N = 80 , C = 4Mb / s , R = 0.6s . The control curves are shown as Figure 5. We can see that the fuzzy immune PID-Smith arithmetic has better stability and robust than PID-VRC arithmetic.

5 Conclusion AQM is a technique hotspot of TCP congestion control. But the existing AQM arithmetic do not consider the influence of parameter change and large delay. A new VRC algorithm is produced in this paper. The new algorithm combines the fuzzy immune PID and Smith predictor. So it improve the self-adaptive ability of network, and realize the self-adaptive function of PID parameters online based on the status of network dynamic changes. At the same time, the algorithm compensates the delay of network. The analysis of simulation shows that the new algorithm has less packet discard probability, and can get to the goal queue length rapidly. The influence of the network change and time delay is self-adaptive conquered by the algorithm.

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Acknowledgement This work is supported by the National Key Spark Project and by the Detection Technology of Forest Products Volatile Foundation.

References 1. Braden B, Clark D, et al.: Recommendations on Queue Management and Congestion Avoidance in the Internet. RFC2309, Internet Engineering Task Force (1998) 2. Floyd S, Jacobson V.: Random Early Detection Gateways for Congestion Avoidance. IEEE / ACM Transactions on Networking (1993) 397–413 3. Floyd S, Gummadi R, et al.: Adaptive RED: An Algorithm for Increasing the Robustness of RED’s Active Queue Management [EB/OL]. http://www.icir.org/f loyd/ papers/adaptive Red. Pdf (2001) 4. Kunniyur S, Srikant R.: End-to-end Congestion Control: Utility Functions, Random Losses and ECN Marks. IEEE/ACM Trans on Networking, (2003) 689–702 5. Hollot C V, Misra V, et al.: On Designing Improved Controllers for AQM Routers Supporting TCP Flows. Proc of IEEE INFOCOM 2001 (2001) 1726–1734 6. Misra V, et al.: Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows with An Application to RED. ACM SIGCOMM 2000, Sweden (2000) 151–160 7. Ying L, et al.: Global Stability of Internet Congestion Control with Heterogeneous Delays. American Control Conference, New York (2004) 8. Ren F.Y., et al.: The Congestion Control Algorithm of Large Delay Network. Journal of software, 14 (2003) 503–511 9. Park E C, Lim H, Park K J, et al.: Analysis and Design of the Virtual Rate Control Algorithm for Stabilizing Queues in TCP Networks. Int. J. Computer Networks. 44 (2004) 17–41 10. Misra V, Gong W B, Towsley D.: Fluid-based Analysis of a Network of AQM Routers Supporting TCP Flows with an Application to RED [DB/OL]. http://www.net.cs.umass. edu/~misra/ (2001) 11. Wei W, Guo-hong Z.: Artificial Immune System and Its Application in The Control System. Control Theory and Application. 19 (2002) 158–160

Absolute Stability of State Feedback Time-Delay Systems Hanlin He1 and Zhongsheng Wang2 1

2

College of Sciences, Naval University of Engineering, Hubei, Wuhan, P.R. China, 430033 [email protected] Department of Electric Engineering, Zhong Yuan Institute of Technology, Henan, Zhengzhou, P.R. China, 450007

Abstract. Given a linear time-delay system and a corresponding algebraic Riccati equation, a method is proposed for synthesizing state feedback controllers for nonlinear Lurie’s control systems. Using Lyapunov functional analysis, the state feedback controllers of insuring absolute stability of closed systems is proposed, and the corresponding sector of absolute stability is also given. By using the comparison results of the algebraic Riccati equation, it is easy known that when the gain becomes larger, the sector of absolute stability becomes bigger.

1

Introduction

Many nonlinear physical systems can be represented as a feedback connection of a linear dynamical system and a nonlinear element. When the nonlinear elements satisfying some sector condition, the problem of showing that the origin is uniformly asymptotically stable for all nonlinearities in the sector, is called absolutely stability. The problem was originally formulated by Lurie and sometimes
called Lurie s problem [1-2]. In recent years, increasing attention has been devoted to the problems of stability of Lurie type control systems with time-delay. Various techniques of absolute stability have been proposed over the past years, including time-delay-dependent and time-delay-independent absolute stability criteria; see, e.g. [3-12]. This paper considers a linear time-delay system that is not stable, but via state feedback, we can show that the synthesized time-delay system is absolute stability with some sector. The result shows that when the gain becomes larger, the sector of absolute stability becomes bigger.

2

Preliminaries

Throughout this paper, the following notations are used. X ≥ Y (respectively X > Y ), where X and Y are symmetric matrices, means that the matrix X − Y is positive semi-definite (respectively, positive definite). λmin (P ) and λmax (P ) denote the minimal and maximal eigenvalues of matrix P . Cτ = C([−τ, 0], Rn ) D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 469–473, 2006. c Springer-Verlag Berlin Heidelberg 2006


470

H. He and Z. Wang

denotes the Banach space of continuous vector functions mapping the interval [−τ, 0] into Rn with the topology of uniform convergence φC = max−τ ≤θ≤0 φ(θ) for any φ ∈ Cτ . . refers to either the Euclidean vector norm or the induced matrix 2-norm. Definition 1 [1]: A memoryless function h : [0, ∞) × RP −→ RP is said to belong to sector 1)[0, ∞] if v T h(t, v) ≥ 0. 2)[K1 , ∞] with K1 = K1T if v T (h(t, v) − K1 v) ≥ 0. 3)[0, K2 ] with K2 = K2T if h(t, v)T (h(t, v) − K2 v) ≤ 0. 4)[K1 , K2 ] with K = K2 − K1 = K T if (h(t, v) − K1 v)T (h(t, v) − K2 v) ≤ 0.

3

Main Result

Consider the linear time-delay system described by x(t) ˙ = Ax(t) + Ad x(t − τ ) + Bu(t),

(1)

x(t0 + θ) = φ(θ), θ ∈ [−τ, 0)

(2)

with the initial condition (2), where x(t) ∈ R is the state, u(t) ∈ R is the control input, τ > 0 is the time-delay of the system, A, Ad , B, C are known real constant matrices of appropriate dimensions. Furthermore, pair (A, B) is assumed to be stabilizable. Suppose there is a symmetric positive matrix R such that 2BRB T > Ad ATd , then for a given symmetric positive matrix, the following Riccati equation has symmetric positive matrix solution P [13]. n

AT P + P A − P (2BRB T − Ad ATd )P + I + Q = 0,

m

(3)

where I is the identity matrix. Via the state feedback u = Kx + v,

(4)

where K = −RB P . The system (1) becomes T

x(t) ˙ = (A + BK)x(t) + Ad x(t − τ ) + Bv(t).

(5)

Consider the following time-delay Lurie control system x(t) ˙ = (A + BK)x(t) + Ad x(t − τ ) + Bv(t), y(t) = C T x(t), v(t) = f (y(t)), f ∈ [−L, L],

(6)

where 0 ≤ L = LT . Under the stated condition, we have the following result. Theorem 1: Suppose P, Q, K are given by (3) and (4), then when λmax (L)
0 , ∆ = ® x : sn −1 ≤ ¨¨ © β n −1 ¹ °¯

(7) qn −1

½ ° ¾ °¿

Proof. Taking the first order derivative of sn −1 , we can get

sn −1 = sn −2 + α n− 2 sn −2 + β n −2 Since si = si −1 + α i −1 si −1 + β i −1 siq−i1−1

pi −1

d qn −2 sn −2 dt

pn − 2

.

(8)

, and the l th order derivative of si is

si( l ) = si(−l 1+1) + α i −1 si(−l 1) + β i −1

d l qi −1 si −1 dt l

pi −1

.

(9)

476

Shuanghe Yu

Then it can be easily induced step by step till the following equation is achieved: n−2

n −2

k =0

k =0

sn −1 = f ( x ) + bu(t ) + ¦α k sk( n − k −1) + ¦ β k

d n − k −1 ( q k sk dt n − k −1

pk )

.

(10)

Substituting the control law (6) into (10) yields § f ( x) sn −1 = −α n −1 sn −1 − ¨¨ β n −1 − qn −1 pn −1 sn −1 ©

· qn−1 ¸¸ sn −1 ¹

If we choose the Lyapunov function candidate as V = § f ( x) V = −2α n −1V − 2γ ¨¨ β n −1 − qn−1 p n−1 sn −1 ©

where 0 < γ =

p n −1

.

(11)

1 2 sn −1 , its first derivative is 2

· γ ¸¸V = −2α n −1V − 2γ β n' −1V γ . ¹

(12)

pn −1 + qn −1 < 1 . It means that as long as the condition 2 pn −1

β n' −1 = β n −1 −

f ( x) s

qn −1 pn −1 n −1

≥ β n −1 −

f U ( x) s

qn −1 pn −1 n −1

>0.

(13)

which is equal to the outside of the region ∆ , is satisfied, the Lyapunov theorem always is satisfied. With the finite time stability defined in [6], we can conclude that the system will enter the region ∆ at least in the finite time (7). Q.E.D. Remark 1. If we choose β n −1 > f U ( x ) and pn −1 q n −1 > 1 , we can always make the neighborhood ∆ of the sliding manifold s n −1 small enough

4 FTSM Control Design with Fuzzy Approximator Firstly we make the following assumption: There exists a coefficient vector θ such *

*T

that the optimal fuzzy model f * ( x ) = θ ξ ( x ) approximates the unknown system function f (x ) with the minimum approximation error ε over a compact set U , that is, ∃θ such that f ( x ) − f * ( x ) = ε , ∀ x ∈ U . According to the assumption, the actual system function can be expressed as *

*T

f ( x) = θ ξ ( x) + ε .

(14)

If we use the fuzzy logic model (5) to estimate the unknown function f (x ) in T system (1) as fˆ ( x ) = θˆ ξ ( x ) , the estimation error can be given by T ~T *T e = f ( x ) − fˆ ( x ) = θ ξ ( x ) − θˆ ξ ( x ) + ε = θ ξ ( x ) + ε .

(15)

Adaptive Fuzzy Control of Nonlinear Systems Based on Terminal Sliding Mode

477

~T ~ * where θ = θ − θˆ , and define e1 = θ ξ ( x ) as the estimation error with respect to the optimal approximator. Theorem 2. The parameter vector θˆ = [θˆ1 θˆM ] of the fuzzy logic system (5) can be continuously updated as



θˆi = (α n e1 + β n e1qn

pn

)ξ i ( x ) .

(16)

in order to attain the optimal approximator to the unknown system (1), the following properties can be guaranteed: (a). The estimation error e1 will convergence to zero in a finite time. (b). The estimated parameters θˆ of the fuzzy model will remain bounded. i

1 2 e1 . For proving e1 = 0 2 will be reached in a finite time, we take the time derivative of V1 .

Proof. (a). Define the Lyapunov function candidate V1 =

 M ~ V1 = e1e1 = e1 ( ¦i =1θ iξi ( x )) M

= −e1 ( ¦ (α n e1 + β n e1qn

pn

j =1

)ξi2 ( x ) .

(17)

= −α nV1 − β nV1( p n + qn ) 2 pn Because of 0 < ( pn + qn ) 2 pn < 1 , the above formula is a FTSM. Therefore V1 = 0 , i.e. e1 = 0 will be reached in finite time. (b). Consider the Lyapunov function candidate: V2 =

1 2 1 M ~2 e1 + ¦θ i . 2 2 i =1

(18)

and take the first derivative, we have M

~ ( p +q ) 2 p V2 = −α nV1 − β nV1 n n n − ¦ θ i (α n e1 + β n e1( pn + qn ) i =1

pn

)ξ i ( x )

.

(19)

( pn + qn ) 2 p n n 1

= −2α nV1 − 2 β V

Thus, we have V2 ≤ 0 for all V1 ≥ 0 , V2 will be asymptotically convergent. Therefore, the estimated parameters θˆ i will remain bounded in the case of its bounded initial value. Remark 2. We can get the following indirect adaptive fuzzy global FTSM controller n −2 n−2 1 d n − k −1 u (t ) = − ( fˆ ( x ) + ¦ α k sk( n − k −1) + ¦ β k n − k −1 s k( qk b dt k =0 k =0

pk )

+ α n −1 sn −1 + β

n −1

snq−n −11

pn −1

) . (20)

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Shuanghe Yu

Because the estimate error satisfies f ( x ) − fˆ ( x ) ≤ f U ( x ) , the system states will

reach a reduced region in a faster finite time.

5 Simulations Given an unstable plant x (t ) =

1 − e − x (t ) + u (t ) . 1 + e − x(t )

(21)

The control objective is to force the system state to track the desired state trajectory xd = sin(t ) . We define six fuzzy sets over the intervals [-3,3] with labels N 3 , N 2 , N1 , P1 , P2 , P3 , and the membership functions are Gaussian form. Here the approximation error is ω = fˆ x θ − f ( x ) and the tracking error is e = x − x . With

( )

d

f

(a) Approximation

(c) Tracking

(b) Tracking error

(d) Control

Fig. 1. FTSM control of an unstable unknown nonlinear system

Adaptive Fuzzy Control of Nonlinear Systems Based on Terminal Sliding Mode

479

the adaptive laws and the control law designed in section 3 and 4, the simulation results are shown in Fig. 1, which demonstrates the convergences of the approximation error and tracking error are all assured in spite of the unknown nonlinear function, and the chattering of traditional sliding mode control is reduced.

References 1. Sala A., Guerra T. M., Babuska R.: Perspectives of Fuzzy Systems and Control. Fuzzy Sets and Systems. (2005) 432–444 2. Yu, S., Yu, X., Shirinzadeh B., Man Z.: Continuous Finite-Time Control for Robotic Manipulators with Terminal Sliding Mode. Automatica. (2005) 1957–1964 3. Yu, S., Yu, X., Man Z.: A Fuzzy Neural Network Approximator with Fast Terminal Sliding Mode and Its Applications. Fuzzy Sets and Systems. (2004) 469–486 4. Hong, Y., Huang, J., Xu, Y.: On An Output Finite-Time Stabilization Problem. IEEE Trans. on Automatic Control. (2001) 305-309 5. Rojko A., Jezernik K.: Sliding-Mode Motion Controller with Adaptive Fuzzy Disturbance Estimation. IEEE Trans on Industrial Electronics. (2004) 963-971

Simulation of Air Fuel Ratio Control Using Radius Basis Function Neural Network Zhixiang Hou College of Automobile and Mechanical Engineering, Changsha University of Science and Technology, 410076 Changsha, China [email protected]

Abstract. In order to decrease emission and fuel consumption of gasoline engine, we should accurately control air fuel ratio approach to the theoretical value. But its accurate control is very difficulty, especial under transient conditions. A composite air fuel ratio control strategy based on neural networks is advocated in this paper, where feedback control is achieved by means of regular PI controller to ensure the system stability and antidisturbance, and feedfoward control is achieved by virtue of neural networks controller to enhance response ability of control system. The simulation was finished using experiment data of HL495 gasoline engine, and the results show the effectiveness of this control method. Thus the system can effectively avoid the present defects elicited by enormous calibration to accurate control air fuel ratio with fair self-adaptability.

1 Introduction Air fuel ratio accurate control is a key index decreasing emission and fuel consumption of gasoline engine, and we should accurately control air fuel ratio approach to the theo-

retical value. The subtle fluctuation of the actual air fuel ratio would result in serious declining of the conversion efficient in three-way catalytic. Due to the intake manifold of gasoline engine having the characteristics of the fuel film speciality and the instability during the course of intake-air and the indeterminacy of fuel quality and operating conditions, the control accuracy about air fuel ratio under transient condition is much bad. So feedforward compensation is achieved by calibration under transient condition. But the control accuracy about air fuel ratio under transient condition is difficult to dominate, as the complicated calibration, the fussy table look-up, special for the poor self-adaptability based on calibration which is used to compensate the fuel consume when the gasoline engine aging and working environment changing. In recent years, intelligent control strategy based on neural networks has become the focus of the research on air fuel ratio accuracy control both internal and internet [1-5]. The thesis advances a new composite control method that is based on neural networks to modify the present defect with the poor self-adaptability, elicited by enormous calibration to control air fuel ratio under transient condition. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 480 – 485, 2006. © Springer-Verlag Berlin Heidelberg 2006

Simulation of Air Fuel Ratio Control Using Radius Basis Function Neural Network

481

2 Mean Value Model of Gasoline Engine As far as the model of gasoline engine is concerned, two important models are used widely. One is Mean Value Engine Model (MVEM), which is a model based-time and focuses on the overall dynamic character. Other is Cylinder-by-Cylinder Engine Model (CCEM), which uses different control methods to each cylinder by taking into account the formation of gas mixture among every cylinder and the diversities among intake and exhaust flow phase, compression phase and combustion work phase. Generally speaking, the model is more complex the control of engine is more difficult. We hope that the model of gasoline engine possibly has the fewer parameters and lower orders so that we could modify and adjust the parameters easily under each operating condition. MVEM could simulate the dynastic response processes of gasoline engine with high precision. Taking engine inter temperature as constant, MVEM can be simply expressed using the following formula (1) [6]. m fv = (1 − X ) m fc 1  ff = m ( − m ff + X m fc )

τf

(1)

m fi = m fv + m ff

Where m fv is the mass flow of fuel vapor, m fc being the mass flow of fuel, m ff being the mass flow of fuel file , m ff being the variable ratio of fuel file, m fi being the fuel mass flow at admission valve, τ f and X being respectively fuel file vapor constant and fuel injection partition coefficient, whose estimation value could be calculated according to formula (2). Xˆ = 9 . 6 × 10

τˆf = 1 . 67 ω

−5

ω + 0 . 7236

− 0 . 65

(2)

Where ω is engine rotation speed. MVEM seems a linear system apparently, but it is a nonlinear in fact because τ f and X are time-varying parameters. The total injection quantity is defined as formula (3): m fc = k f T

(3)

Where T is fuel injection time, k f being fuel injection coefficient. According to MVEM, gas flow m ao delivered through the intake pipe into the cylinder is expressed using formula (4) [7]: m ao = φη vol m a ω

(4)

Where ηvol is volumetric efficiency and φ is calculated by the following formulas (5) η vol = ( 24 . 5ω × 10 4 ) m a 2 + ( − 0 . 167 ω + 222 ) m a + ( 8 . 1 × 10 − 4 + 0 . 352 ) φ =

Ve 4π V m

(5)

Where Ve is engine emission, Vm being engine volume, ma being the flow ratio through the throttle, which could be tested by flow sensor directly. Air fuel ratio

482

Z. Hou

control is to adjust fuel injection time according to the entering-air amount to control the actual air fuel ratio near the theoretical one which is indicated as λdes .

3 Structure of Air Fuel Ratio Control Using Neural Networks Feedforward and feedback control are respectively achieved by means of neural networks controller and regular PI controller. Feedback control is to ensure the system stability and anti- interference, which is achieved by regular PI controller using oxygen sensor signals; Feedforward control is to enhance response ability of control system under transient conditions. The structure of air fuel ratio control is shown in figure 1. Neural Networks Controller uses the leaning algorithm based on teachers to calculate the output fuel injection time ( T 1 ), compares it with the total injection time T , and then rectify the weights of neural network. The purpose of study is to minimize the odds about fuel injection time between the actual and the outputted by neural networks. So radius basis function neural networks whose inputs are the engine rotation speed ω and the throttle degree α which are the two chief factors affecting engine admission volume is adopted.

Fig. 1. Structure of air fuel ratio control using neural network

4 Radius Basis Function Neural Networks Radius basis function neural network is a three layers feedforward network, whose mapping relation from the output to the input is nonlinear and the one from the hidden layer to the output is linear. The structure of RBF network is shown in figure 2. Supposed X = [ x1, x 2,… xn]T is the input vector of RBF neural network, and H = [h1, h 2, … hm ]T is radial basis vector, where hj is GES function as following formula (6).

᧨

᧨

h j = exp(

x − CJ 2bj

2

2

),

j = 1,2,…m

(6)

The central vector at node j is represented in terms of C = [ c j 1 , c j 2 , … , c jn ] T , and basis width vector is supposed in the form of B = [b1, b 2,… , bm ]T , where bj is the basis width degree parameter at node j, which is greater than zero. Taking following

Simulation of Air Fuel Ratio Control Using Radius Basis Function Neural Network

483

Fig. 2. Structure of RBF neural network

formula (7) as the weights vector, the overall output of the RBF neural network could be expressed as formula (8). W = [ w1, w2,…, wm]T

(7)

ym ( k ) = w1h1 + w2 h2 + … + wmhm

(8)

Taking formula (9) as performance index function, weights, central node and node basis width parameters were modified according to formula (10)-(14) based on gradient descent algorithm J=

(9)

1 [ y ( k ) − ym ( k )] 2 2

wj ( k ) = wj ( k −1) + η ( y ( k ) − Ym ( k ) )h + α (wj ( k −1) − wj ( k − 2 ) ) ∆bj = ( y ( k ) − Ym ( k ) ) wjhj

X − Cj bj

2

(11)

3

bj ( k ) = bj ( k −1) + η∆bj + α (bj ( k −1) − bj ( k − 2) ) ∆cji = ( y ( k ) − Y ( k ) m) wj

(10)

xj − cji bj 2

cji ( k ) = c( y ( k ) − Ym ( K ) ) + η∆cji + α (cji ( k −1) − cji ( k − 2) )

(12) (13) (14)

Where η is study ratio, α being the momentum factor.

5 Simulation of Air Fuel Ratio Control Using RBF Neural Network The electronic jet engine of HL495Q is used on trial, whose working-volumetric with single cylinder is 710cm3 , engine emission being 2.84L, calibration power and rotate speed being 73.5KW/3800r/min, compression ratio being ε = 7.8 . Experiment was achieved using the typical throttle signals that is used widely abroad showed in figure 3, where the throttle changes one time for every 5 seconds, and every time changes 5‫ޕ‬, and sample ratio is 0.01 second, and throttle bring on the fluctuation of velocity within 2 seconds. When throttle act as figure 3, engine rotation speed and air flow ratio are shown in figure 4 and figure 5 respectively. The topulogy structure of RBF

484

Z. Hou

neural networks is determined 2-5-1 by trail training, and the throttle degree and engine rotation speed are the input vector, fuel injection time (T1) is the output value, definition function e = ¦ T 0 is the error function of the neural networks. Presumed the initial value of fuel injection time is T 1 = 0ms, T 0 = 0.3ms, the value of subgrade reaction is kp, the integral coefficient is ki, the physical parameters and correlative control parameters are shown in table 1. 2

Fig. 3. Throttle degree

Fig. 4. Rotation speed

Fig. 5. Air flow ratio

Table 1. Simulation parameter

㧔CM 㧕 V (L)

Ve

710

3

m

2.8

Kf

Kp

Ki

η

α

¬

des

5.47 2.53 0.1 0.01 0.08 14.7

Simulation algorithm is displayed as followsing: Step1: initializing correlative parameters. Step2: calculating the air flow ( m fi ) based on the throttle degree and engine rotation speed according to formula (4).  fc according to formula (3), and then calculating Step3: calculating fuel injection m the fuel quantity according to formula (1). Step4: calculating the actual air fuel ratio according to formula λf = m ao (which is m fi

simulated by the computation model instead of oxygen sensor), then getting the error of air fuel ratio, then calculating fuel injection time T0 by PI controller Step 5: if T 0 ≥ 0.001ms, we should calculate the error of neural networks according to e = ¦ T 0 2 , and then adjust the weights, central vectors values and output fuel injection time T1, then calculate the total fuel injection time T ;if T 0 ≤ 0.001ms, we could consider the error is slight. So the weights are constant and the overall outputs are produced by neutral networks. Step 6: go to step 2 The simulation result is shown in figure 6 according to the above algorithm when throttle act as figure 3. Seen from figure 6, actual air fuel ratio was control near

Simulation of Air Fuel Ratio Control Using Radius Basis Function Neural Network

485

 Fig. 6. Simulation result of air fuel ratio control

theoretical one and its overshoot is less than 2%, and control system of air fuel ratio based on RBF neural network owes perfect respond ability and fair self-adaptability.

6 Conclusion The thesis advances a composite control method of air fuel ratio based on neural networks, which can effectively avoid the present defects elicited by enormous calibration to control air fuel ration with fair self-adaptability. The simulation results show the effectiveness of this control method.

References 1. Shiraishi, S.L., Cholpri, D.D.: CMAC Neural Network Controller for Fuel Injection System. IEEE Transaction on Control System Technolojy. (1995)32-38 2. Won, M., Choi, S.B.: Air Fuel Ratio Control Of Spark Ignition Engines Using Gaussian Network Sliding Control. IEEE Transaction on Control System Technolojy. (1998)678-687 3. Wendeker, M.: Hybrid Air Fuel Ratio Control Using The Adaptive And Neural Networks. SAE pape2000-01-1248. (2000)1477-1484 4. Shayler, P.J., Goodman, M.S.: Transient Air/Fuel Ratio Control Of An Engine Using Network. SAE paper 960326.(1996)410-419 5. Guoyou, L.: The Research On Self-adaptability Fuzzy Neural Mix Coupling Controller. Advanced Technology Communication. (2004)78-80 6. Hendricks, E.: Mean Value Modeling Of Spark Engines. SAE paper 9606 (1996)1359-1372 7. Manzie, C., Palaniswami, M., Watson, H.: Gaussian Networks For Fuel Inject Control. Proc instn Mech Engrs. (2001)1053-1068

An Experimental Study on Multi-mode Control Methods of Flexible Structure Using PZT Actuator and Modified IMSC Algorithm W.S. Lee1, H.J. Lee2,*, J.H. Hwang1, N.K. Lee2, H.W. Lee2, G.A. Lee2, S.M. Bae3, and D.M. Kim1 1

Dept. of Aerospace and Mechanical Engineering, Hankuk Aviation University, 200-1, Hwajeon-dong, Deogyang-gu, Goyang-city, Geonggi-do, #412-791, Korea [email protected], {jhhwang, dmkim}@hangkong.ac.kr 2 Digital Production Processing & Forming Team, Korea Institute of Industrial Technology, 994-32, Dongchun-dong, Yeonsu-gu, Incheon Metropolitan City, #406-130, Korea {naltl, nklee, hwlee, galee}@kitech.re.kr 3 Dept. of Industrial & Management Engineering, Hanbat National University, SAN 16-1, Duckmyoung-dong, Yusong-gu, Daejon , #305-719, Korea [email protected]

Abstract. In this paper, the modified independent modal space control (IMSC) algorithm, which is a method for reducing the number of actuators, is used for flexible structural vibration control. By comparing the experimental results obtained by the IMSC and modified IMSC algorithm, the performance of those is examined. The performance of the IMSC algorithm is more effective than modified IMSC algorithm in the responses of PZT sensors and the input voltages to PZT actuators. But the IMSC algorithm is limited for many applications since it is needed the number of actuators as many as controlled modes. For this reason, the modified IMSC algorithm is proposed in this paper. That of the modified IMSC algorithm is similar with the IMSC algorithm but there are discontinuous responses because of switching algorithm. Therefore, if the switching algorithm has gradually varying according to shape of control forces, its performance is more effective and applicable than the IMSC algorithm. This paper will provide an essential experimental basis material for that study.

1 Introduction Many researchers study about variable vibration control algorithms of flexible space structures. But the control algorithms using actual controllers are hard to apply. Because orders of system are high, the calculation quantity is a burden to proposed algorithm. Especially when controlling in real-time, it comes to be much more. To resolve these problems more effectively, Independent modal space control (IMSC) algorithm was proposed by Meirovitch and Joint researchers [1]. IMSC algorithm converts a modal matrix at transformation matrix and makes coupled equation of motion of a structure with uncoupled equation in modal coordinate system. And then

*

Corresponding author.

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 486 – 493, 2006. © Springer-Verlag Berlin Heidelberg 2006

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we can easily design a controller in modal space. In this case, the design of controller is simple without a number of systems DOF (Degree Of Freedom). Because it uses each mode state, control is accomplished independently. The namely calculation quantity becomes very little. Using this control method, it plans the control force of each mode first and it calculates a real control force by coordinate transformation. Also, if a number of controlled mode and actuators are same, controllability is always satisfied and a control spillover will be minimized. For a design of modal control force, if using a state estimator with a distributed sensor, estimating modal state can be excluded from an observation spillover. But in spite of many strong point, it is necessary for this vibration control algorithm to be equal a number of controlled mode with actuators. For these reasons, application field of IMSC is restricted [2-3]. In this paper, the modified independent modal space control (MIMSC) algorithm, which is a method for reducing the number of actuators, is used for a flexible structural vibration control. So we can control more the number of modes than actuators through the simulation and experimental approach. To examine the performance of IMSC and modified IMSC algorithm, we will compare the experimental results obtained by those two algorithms.

2 Basic of Controllers and Modeling with Piezoelectric Material Piezoelectric (PZT) material is one of the smart materials and describes the material of generating an electric field when the material is subjected to a mechanical stress (direct effect), or, conversely, generating a mechanical strain in response to an applied electric field. PZT ceramics are essentially small-stroke large-force solid-state actuators with very good high-frequency performance. So it has wide band applications particularly in NANO systems and Micro Electro-Mechanical Systems (MEMS) [4]. 2.1 Modeling Cantilever Beam with PZT The equations of sensor and actuator which considers mass effect as PZT materials attached to cantilever beam; are given by [6]

Vs (t ) =

2 Qb d ht x ∂ w( x, t ) = ν b ³x 2 dx, ν b = − E31 c 2 1 Cb ε 33 S11lc ∂x

(1)

Where Vs (t ) is a output voltage from PZT sensor and it is generated a charge Qb by PZT ceramic characteristics, Cb is a capacitance of PZT sensor, coefficient.

ν b is

a voltage

V ( x, t ) = [ H ( x − x1 ) − H ( x − x2 )] Va (t )

(2)

M Λ = ηb V ( x, t ), ηb = 1 d31 Ec b( tc + tb )

(3)

2

V ( x, t ) is a voltage distribution by input voltage Va (t ) to PZT actuator. M Λ is a bending moment of PZT actuator. According to the above derivations, we could derive the equation of motion of cantilever beam with PZT and estimate responses of a sensing and actuating.

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2.2 Locations of PZT Sensors and Actuators By using a modal position sensitivity function of cantilever beam, we attached PZT sensors and actuators to the beam that affects considering modes [6]. And then PZT sensors and actuators were placed with same location and opposite side of the beam. The reason is that a good influence point of sensing and actuating is a same place and then controller has a minimum phase differences. 2.3 Modal Parameter Estimation We estimated a modal parameter of cantilever beam with PZT by measuring the frequency response function (FRF). So we could minimize a mass effect of PZT. FRF was obtained by attached PZT sensors and actuators and resulted in following. Table 1. Results of modal test

Frequency (Hz) 4.023 25.623

1st mode 2nd mode

Damp. (%) 2.3 1.7

3 Theoretical Backgrounds of IMSC and MIMSC 3.1 IMSC IMSC control algorithm converts a modal matrix at transformation matrix and makes coupled equation of approximated motion of a structure with uncoupled equation in modal coordinate system. And then we can easily design a controller in modal space [1], [3]. The approximated equation of motion of cantilever beam in modal coordinate system is derived by

Iv( t ) + Λv (t ) = f (t )

(4)

Where I is an n unit matrix and Λ is diagonal matrix ( Λ = diag[ω  ω ] ), it consists of diagonal elements that are formed of natural frequency squares. f (t ) is a n-modal control force vector( f (t ) = [ f 1 (t ) f 2 (t )  f n (t )]T = P T u(t ) ). And then n is a number of controlled mode, v ( t ) is a modal displacement vector ( v (t ) = [v (t ) v (t )  v (t )] = P q (t ) ) that is used to model the controller. T

1

2

2

2

1

n

T

n

3.2 Modified IMSC The weak point of IMSC is that IMSC needs enough actuators to control the vibration modes. So Baz and Poh presented modified independent modal space control (MIMSC) to be able to be applied IMSC when a number of actuators was less than controlled modes. Procedure of MIMSC is composed of two-steps. First, we split a system into controlled mode or not in order. And then regularly moment, actuators are

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operated to the mode that has a biggest modal energy at same moment in controlled modes. So the important things are easiness and efficiency of designing control force in IMSC and reducibility of actuator number in MIMSC. This reasons of MIMSC algorithm affected active vibration control of flexible structures. 3.3 Design of Controller and Observer Multi-mode control algorithm will be able to compose each mode control forces only it knows the mode condition. So in this paper, for estimating mode state, we adopted Luenberger observer and utilized standard LQ regulator for getting control gains. In these experiments, we did not consist of residual mode for convenience manner [7].

Fig. 1. Schematics of a multi mode control

4 Preparation of Experiments For active vibration control, we attached PZT ceramics to cantilever beam according to modal position sensitivity function under certain pressure and temperature conditions [10-11].

Fig. 2. Bonding Process of PZT material to cantilever beam

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Then we used a charge amplifier to supplement a low output current of PZT sensor and a high voltage amplifier to improve an input to PZT actuators. And we utilized step-motor for a constant impulse external force to the cantilever beam. The schematic and photograph of the experimental system are shown in Fig.3. Specifications of flexible beam and PZT actuator are shown in Table 2 and 3.

(a) Schematic of experimental system

(b) Photograph of experimental system Fig. 3. Schematic and photograph of experimental system Table 2. Specification of flexible beam

Length (mm)

Width (mm)

Thickness (mm)

Young’s Modulus (GPa)

Density (kg/m3)

Poisson’s Ratio

450

15

1.0

69

2780

0.33

Table 3. Specification of PZT actuator

Actuator & Sensor (PZT C-63)

Piezoelectric Charge Constant

Length (mm)

Width (mm)

Thickness (mm)

Young’s Modulus (Gpa)

( d 3 1, 1 0 − 12 m / V )

30

15

0.3

67

-165

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5 Results of Experiments and Simulations Simulation control gains and observer gains were obtained. And those are equally applied to IMSC and MIMSC in our experiments. Using IMSC algorithm and uncontrolled results of simulation are as follows.

Fig. 4. Controlled responses using IMSC Simulations

We practiced each control algorithm using gains from simulation and some compensations system for errors like nonlinearities. We monitored a response of system and got feedback errors by PZT sensor attached to the free end of cantilever beam. We used two sensors in IMSC and MIMSC algorithm to observe feedback error. To apply IMSC algorithm to this system, system must have actuators of the same number as sensors. Therefore we used two actuators in IMSC. In MIMSC algorithm, we used a single actuator on the root position of cantilever beam because can reduce the number of actuators in this algorithm. The results are as shown in Fig.5.

Fig. 5. Comparison of responses in the time domain-Experiments

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In the experiments time domain, the result of IMSC algorithm was similar with MIMSC. As results of IMSC algorithm compared with MIMSC in the PSD (Power Spectrum Density) using above given time domain, the control effect of IMSC is better than MIMSC algorithm in second natural frequency. And there are discontinuous responses because of switching algorithm. But the differences are very small. These results in frequency domain are as shown in Fig.6. Therefore, if the switching algorithm has gradually varying according to shape of control forces, its performance is more effective and applicable than the IMSC algorithm. Because it can reduce the number of actuator, the MIMSC algorithm is more efficiency in controllability and control power than the IMSC.

Fig. 6. Comparison of responses in PSD

6 Conclusions In this paper, IMSC and MIMSC methods are applied to control a multi-mode vibration of flexible structure using PZT actuator and sensor. Our experiments’ results show that MIMSC method has advantages of easy controller and observer design from the experiment. The MIMSC method has high control efficiency because restricted modes are controlled. These restricted modes have large modal energy out of infinite modes. And the MIMSC method can control effectively using a few numbers of actuator. Therefore the MIMSC method could be applied to the control method of flexible system that has restricted numbers of actuator and space.

Acknowledgements This work has been sponsored by MOCIE (Ministry of Commerce, Industry and Energy) of Korea.

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References 1. Leonard Meirovitch: Dynamics and Control of Structures, John Wiley & Sons, (1990) 2. Baz, A. and Poh, S.: Performance of an Active Control System with Piezoelectric Actuators. J. Sound and Vibration, Vol. 126, No 2, (1988) 327-343 3. Hwang, J.H., Kim, J. S., Baek, S.H.: A Method for Reduction of Number of Actuators in Independent Modal Space Control. KSME International Journal, Vol. 13, No. 1, (1999) 42-49 4. Kenji Uchino: Piezoelectric Actuators and Ultrasonic Motors. Kluwer Academic Publishers (1997) 5. Inderjit Chopra: Smart Structures. Univ. of Maryland 6. Hwang Jin-Kwon: System Identification and Vibration Control of Flexible Structures Using Piezoelectric Materials, Seoul national Univ. (1997) 7. Leonard Meirovitch: Computational Methods in Structural Dynamics. Kluwer Academic Pub. (1980) 8. Daniel J. Inman: Engineering Vibration. Prentice Hall (1994) 9. Kenneth G. McConnell: Vibration Testing – Theory and Practice. John Wiley & Sons (1995) 10. Khulief Y. A.: Vibration Suppression in Rotating Beams Using Active Modal Control. J. Sound and Vibration, Vol. 242, No. 4, (2001) 681-699 11. Kermani M. R., Moallem M. and Patel R. V.: Optimizing the Performance of Piezoelectric Actuators for Active Vibration Control, IEEE International Conference on Robotics Washington, DC May (2002)

Applications of Computational Verbs to Image Processing of RoboCup Small-Size Robots Wanmi Chen1, Yanqin Wei1, Minrui Fei1, and Huosheng Hu2 1

Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronics Engineering & Automation, Shanghai University, 200072 Shanghai, China [email protected], [email protected], [email protected] 2 Department of Computer Science, University of Essex, Colchester CO4 3SQ, U.K. [email protected]

Abstract. Computational verbs have been applied to digital image processing recently in which the grey values of an image are treated as a dynamic evolving process in space [5]. The paper is to apply such a theory in the RoboCup domain. First, the computational verbs for our small-size soccer robots are developed based on the theory. Then, the modelling and matching are investigated and analyzed to obtain verb similarity. The developed system reduces the computation cost by using row-wise and column-wise compositions of spatial verbs, and makes the vision system have high accuracy and high process speed.

1 Introduction RoboCup is an international joint project that aims to foster AI and intelligent robotics research by providing a standard problem where wide range of technologies can be integrated and examined [1]. The ultimate goal of the RoboCup project is to develop a team of fully autonomous humanoid robots that can win against the human world champion team in soccer by 2050. It is anticipated that the project also promote many real-world applications of AI and robotics. In order for a robot team to actually perform a soccer game, various technologies must be incorporated, including design principles of autonomous agents, sensor integration, data fusion, strategy acquisition, real-time reasoning and multi-agent collaboration. In the RoboCup competition, there are different leagues such as simulation league, small-size robot league, middle-size robot league, legged robot league and, etc. In all these leagues, it is common for two teams of multiple fastmoving robots to operate under a dynamic environment, either a simulated or a real pitch. In the small-size robot league, the game is designed to imitate the real soccer match condition. It is a centralised system – a central computer sends the commands through decision-making programs. The system consists of four parts: an overhead vision system, a decision-making system, a wireless communication system and five mobile robots. Among these parts, the overhead vision system monitors the current status on D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 494 – 499, 2006. © Springer-Verlag Berlin Heidelberg 2006

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the pitch and sends robot position and moving directions to the central computer so that the control algorithm can decide how each robot should act. Since the small-size robot league of RoboCup is a highly dynamic system, it is very important that its vision system should have the real-time performance and highly accuracy. In [2], an efficient detection algorithm is developed to detect simple colour patches on top of individual mobile robots so that their positions can be calculated accurately. It starts by searching for the key patch, and then detecting and sorting the additional patches radically. After that, the rotational correspondence of the additional patches is matched with the geometric model of the pattern. But its accuracy needs to be improved. In this paper, computational verb theory is adopted in the image processing process of our robot system so that the position and moving direction of individual robots can be detected fast and accurately. The rest of the paper is organised as follows. Section 2 reviews the background of computational verb theory [3] and its application to image processing [5]. In Section 3, the colour marker on top of our small-size robot is described. Section 4 describes how to construct canonical spatial computational verbs for image processing of our robots. In Section 5, real-time matching of images and spatial computational verbs is explained. Section 6 presents some preliminary experimental results. Finally, a brief conclusion is given in Section 7.

2 Verb Image Processing – Background Computational verbs are a dynamic system, i.e. a dynamic process in time, space or state space [3][4]. By the mathematics principle, the dynamic system includes 4 parts: (i) time; (ii) state space (include all advisable status together); (iii) distance function for distinction of two different statuses; and (iv) the state evolving law - a time function. The theory treats the grey values of an image as a dynamic process along spatial coordinates, namely spatial verbs [5]. This paper investigates the application of these spatial verbs in the RoboCup domain since verb image processing is a promising way to reduce computation costs for image processing. As we know, the traditional image processing algorithms deal with an image as a static picture where lines and shapes are purely geometric items [5]. The complexity of an image operator is proportional to the product of the width and height of the image. This requires expensive computing power and makes real-time applications very demanding. On the other hands, verb image processing handles images in a different way in which the complexity of a verb image processing operator is proportional to the sum the width and height of the image. This will demand much less computing power and make real-time applications be economic. Basically, verb image processing is to find the relationship between an image and a template spatial verb. The evolving function of a spatial verb denotes the change of grey values along spatial coordination, which was decoupled into two functions, namely a brightness profile function and a shape outline function [5]. In other words, one function deals with the brightness information and the other handles the spatial configuration. Their canonical form is

E v (i , j ) =

Wd

wd

k =− wd

l =− wd

¦ ¦

f p ( k , l ) × f o (i − k , j − l )

(1)

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where Wd is the window size. fp(.) is the brightness profile function. fo(.) is the shape outline function. {i, j, k ,l} are the pixel index of 2D images. To simplify the computational complexity, the canonical form (1) can be constructed by chosen either row-wise or column-wise compositions: (i) the row-wise composition:

Ev (i, j ) =

wd

¦

f p (l ) × fo (i, j − l )

(2)

f p ( k ) × f o (i − k , j )

(3)

l =− wd

and the column-wise composition: E v (i , j ) =

wd

¦

k = − wd

By using either (2) or (3), the computational cost cab be reduced dramatically [5].

3 Colour Markers on Robots The RoboCup Small-Size robot competition is based on global vision systems that are installed at the top of the football pitch. The individual robots have no independent visual ability embedded. Each robot has colour makers on its top as shown in Fig. 1. The colour markers can be detected by the overhead cameras. Since the ball and two teams of robots are moving very fast, it is very important that the image processing algorithm can be implemented in real time, i.e. at least 25 frames per second so that the decision system can find the positions and moving directions of the ball and all the robots on the pitch in good accuracy.

(a)

(b)

(c)

Fig. 1. Colour marker on the top of the robot. (a) Robot’s marker.(b) Its grey image. (c) Colour edges.

The robot marker has different colours: (i) the red colour is the robot orientation; (ii) the yellow colour is the team marker, and (iii) the green colour is the marker of a team member. To implement verb image processing, the colour image will be converted into the grey image, as shown in Fig. 1(b). The 2-value shape of the robot marker is shown in Fig. 1(c), in which we have 9 pixels for the diameter of a team mark, 17 pixels for the diameter of the middle circle, and 25 pixels for the diameter of the outer circle. Suppose the grey value of all circles is uniform. The image size of the top-view of the robot is 31x31 pixels in our experimental setting.

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4 Constructing Spatial Computational Verbs To establish the evolve function of spatial verbs, we need to establish both the brightness profile function and shape outline function in this section. 4.1 Brightness Profile Function As the colour marker of the robot is converted into the grey value image with the spatial coordinates that are symmetric, we can resolve its brightness profile function as the row-wise and the column-wise compositions. The image evolves the difference with the matching of the moulding board to row-wise and column-wise compositions. If the image size is N* M, we are computing the sum N+ M instead of N* M. So, the computing speed is much improved. According to the colour mark arrangement in Fig.1(a) and the grey values in Fig.1 (b), we can get as follows the brightness profile function (row and column). 1 i ∈[−15, −12]  [12,15] ­ ° 2 i ∈[−12, −8]  [8,12] °1 − 144 − i 60 f p (i) = ® i ∈[−8, −4]  [4,8] ° 13 − 16 − i 2 2 ° 15 i ∈[−4,4] ¯

(4)

where the size of window is 31x31 pixels, and the origin is at the center of the mark.

(a)

(b)

Fig. 2. Function simulation. (a) Brightness profile function. (b) Shape outline function.

4.2 Shape Outline Function The ideal outline of the marking is shown in Fig.1(c). By using (2) and (3), we can obtain the row-wise and column-wise verb of the moulding board. Both the brightness profile function and the shape outline function are shown in Fig.2.

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5 Real-Time Matching of Image and Spatial Computational Verb The final step is target identification and matching, which is described in this section. 5.1 Computational Verb of an Image In the vision system, the computer receives the colour masks taken from the overhead camera. Its RGB information is converted to the grey value by using the following formula: Pi = 0.3*R + 0.59*G+ 0.11*B (5) After getting the grey value, we adopt the boundary measurement method [6] to convert the grey image into a 2-value boundary image. The shape outline function of the image verb is then obtained. As the boundary image may not be clear enough, we use Gauss filters and smoothness processing algorithms to remove all the low frequency noise interference. 5.2 The Matching of Image and Molding The process of the verb matching is a process of identification of the verb similarity degree [5], which is defined as follows: ­0 ¦ V 1( i, j ) + V 2 ( i, j ) = 0 ° ( i , j )∈Ω °° ¦ V 1( i, j ) − V 2 ( i, j ) ® °S (V1, V2) =1 − ( i , j )∈Ω other V 1( i, j ) + V 2 ( i, j ) ° ¦ °¯ ( i , j )∈Ω

(6)

ZKHUH S ∈ [0,1] and ȍ is the size of the matching window. Note that the higher the degree is, more likely an object is. Obviously, if two verbs are from the same image then the resemble degree is 1.

6 Experiments and Results Our vision system is connected to a desktop PC with 2.4GHz CPU and 256M EMS. The camera has a resolution of 640*480 pixels, with RGB output. The accurate timer counts the running time of the control program at a cycle time of 20ms. The position error is about 1 pixel (3mm). Table 1 shows the estimation of our vision system capacity before and after using computational verbs. Table 1. Comparison before and after using computational verbs

Guide line Time-consuming Error identification Orientation error Angle error

Before 2 pixels >20 o

After 0, 0 Density( p j , ε ), i ≠ j, pi ∈ C, p j ∈ C

}

(2)

Where C is a cluster. Actually, the cluster representative is the root node of the density tree. Definition 3(local computing coefficient). The local computing coefficient is the value of local computing radius of objects divided by input original radius. That is

ξ= Where

ξ ≥ 1 , ε range

εrange ε0

is the local computing radius of objects,

(3)

ε0

is the input original

radius. The local computing coefficient sets the same computing range for every object. Users can predefine ξ to reduce the cost time of computing distance matrix. 2.2 The Algorithm LOCHDET algorithm could be divided into five steps: Step 1: compute the distance array Dist(i,j) among all objects. Step 2: set the allowed maximum radius of the neighborhood ε max .

Step 3: create the density-tree until no point is added according to the local density fluctuation. Step 4: merge those “closer” clusters to improve clustering accuracy. Step 5: delete clusters containing one object or very few objects. In our algorithm, we create the same data structure for each object: the distance from its father node; the identifier of itself; radius of neighborhood of its father node; and point density of its father node. The details for the five steps in the following are based on this structure.

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2.2.1 Computing Dist(i ,j)

Generally, the computational complexity of calculating similarity matrix Dist(i,j) is O(n 2 ) .A local computing technology is used to reduce the cost time. The restricted

computing range is determined by input parameters

ε0

and ξ , not computing all of

the distances between any objects. As shown in Figure 1, the distance between object P and B at the X dimension is PB X , and PB X < ε range , the distance between P and B , PB , is calculated and stored into Dist(i,j) . However, the distance between object P and C at the X dimension is PC X , and PC between P and C ,

X

> ε range , the distance

PC , is abandoned, and set PC = +∞ .Obviously, this method

converts the overall computation into the local computation.

|PC|X P

|PB|X B C

ε range = ξ ⋅ ε 0 Fig. 1. Local computation

2.2.2 Setting the Allowed Maximum Radius of the Neighborhood This process is divided into two steps: first, the possible maximum radius of the

neighborhood

' ε max is

calculated by using the same method in CABDET algorithm.

However, unlike CABDET algorithm, the ε max value can’t be set as the allowed '

maximum radius of the neighborhood for making the best of the local computation. Then, the second step is to set the allowed maximum radius of the neighborhood by the following operation: ' ε max = min{ε max , ε range }

(4)

2.2.3 Generating Tree Structure The process of generating density-tree structure is the same as CABDET algorithm, which could be divided into two steps: sequentially find those unprocessed objects with the highest point density as the root node of each potential tree, then call the function “Searching_For_Sons” and iterate until no new object is added. The detail of this process is available in CABDET algorithm [6].

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2.2.4 Merging Those “Closer” Clusters Clusters by generating density-tree structure have the character of inner tightness. One cluster will be split into several segments which are tagged as different clusters under the unsuitable parameter settings. The aim of this process is to merge those closer clusters at the guideline of hierarchical clustering idea. Many methods are used to identify those closer clusters, such as minimum distance and representatives’ distance. In our experiment, two methods are respectively used to improve clustering accuracy. 2.2.5 Deleting “Noise” Clusters The LOCHDET algorithm marks all possible clusters, even clusters containing only one object. After merging, if some clusters containing few objects are isolated from others, the algorithm deletes them directly according to “noise” threshold predefined by users. 2.2.6 Computational Complexity Suppose n is the number of objects with d dimension L is the length of data space, and the local computing radius is ε range . If the data sets obey uniform distribution, the

computational complexity of Dist(i,j) is O(n ⋅ maximal radius of the neighborhood

d 2d ε range

⋅ n) . In computing the possible Ld , a typical sorting algorithm has the

' ε max

computational complexity of O(n ⋅ logn) when ranking objects according to point density. The computational complexity of merging clusters depends on using strategy. If users adopt the minimum distance, LOCHDET only index Dist(i,j) simply; if users adopt the representatives’ distance, its computational complexity is O(m 2 ) , where m is the number of cluster representatives. Therefore, the whole algorithm has the d 2d ε range complexity of O(n ⋅ ⋅ n) O(n ⋅ logn) O(m 2 ) . Generally speaking, d L m Max_uncovered_cases) Adjust Min_cases_per_rule with a certain step; for (p = 1; p < No_ant_populations; p++) j = 1; /* convergence test index */ Initialize all trails with the same amount of pheromone; for (i = 1; i < No_ant_in_each_populationsp, j < No_rules_converg; i++) Anti starts with an empty rule and incrementally constructs a classification rule Ri by adding one term at a time to the current rule until Min_cases_per_rule is not satisfied or each term is used; Prune rule Ri; Update the pheromone of all trails by increasing pheromone in the trail followed by Anti (proportional to the quality of Ri) and decreasing pheromone in the other trails (simulating pheromone evaporation); if (Ri is equal to Ri-1)/*update convergence test */ j++; else j = 1; Choose the best rule Rbest among all rules Ri constructed by all the ants in all the populations; Add rule Rbest to DiscoveredRuleList; TrainingSet = TrainingSet-{set of cases correctly covered by Rbest}; end end end At first, the Ant-Miner algorithm is introduced as follow. 3.1 General Description of Ant-Miner Each iteration of the outer loop, i.e. while loop, of Algorithm I discovers one classification rule, and this rule is added into the list of discovered rules. Then the cases that covered by this rule are removed for training set, until the number of uncovered cases is bigger than Max_uncovered_cases. Each iteration of the interior loop, i.e. for loop, of Algorithm I consists of three steps, including rule construction, rule pruning, and pheromone updating.

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1. Rule construction. An ant adds one term at a time into the rule, which it is constructing, according to the value of heuristic function and the amount of pheromone, until 1) any another term to be added into the rule would make that the number of cases covered by this rule is smaller than Min_cases_per_rule, or 2) all attributes have already been used by this ant. 2. Rule pruning. Rule Ri constructed by Anti is pruned in order to remove irrelevant terms. One term is removed at a time from the rule, and the change of the quality of this rule is computed. Then the term, which makes the greatest improvement of the quality of this rule, is removed. This process is repeated until there is only one term in this rule or there is no term whose removal will improve the quality of this rule. 3. Pheromone updating. The amount of pheromone in each trail is updated, increasing the pheromone in the trail followed by Anti according to the quality of rule Ri and decreasing the pheromone in the other trails to simulate the pheromone evaporation. Each of iteration of interior loop corresponds to the behavior of one ant. After one ant finished this process, another one starts, until all ants have finished or the current Anti constructed a rule that is exactly the same as the rule constructed by the previous No_rules_converg – 1 ants. When all the interior loops are completed, the best rule among the rules constructed by all ants is added into the list of discovered rules, and a new iteration of the outer loop starts with reinitializing the same amount of pheromone in all trails. 3.2 Pheromone Updating In the beginning of each of iteration of the outer loop, all trails are initialized with the same amount of pheromone. The initial amount of pheromone is defined as follow.

τ ij (t = 0 ) =

1 a

¦b

(1)

i

i =1

where a is the total number of attributes and bi is the number of possible values that can be taken on by attribute Ai. Pheromone updating is based on two basic ideas: 1) the amount of pheromone in each term occurring in the rule which discovered by current ant should be increased in proportion to the quality of the rule; 2) the amount of pheromone in each term that does not occur in current rule should be decreased to simulate pheromone evaporation. The quality of a rule is defined as Q=

TP TN ⋅ TP + FN FP + TN

(2)

where TP (true positives) is the number of cases that are covered and whose class is predicted correctly by the rule, FP (false positives) is the number of cases that are covered and whose class is predicted falsely by the rule, FN (false negatives) is the number of cases that are not covered but that have the class predicted by the rule, TN (true negatives) is the number of cases that are not covered and that do not have the class predicted by the rule.

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Then pheromone updating formula of termij occurring in the rule is presented as

τ ij (t + 1) = τ ij (t ) + τ ij (t ) ⋅ Q

(3)

where termij is j th value of attribute Ai. The pheromone evaporation is simulated by normalizing the value of each pheromone τ ij , i.e. dividing τ ij by the summation of all τ ij . This is proved as follow. The summation of increasing pheromone is equal to the summation of increasing pheromone of termij occurring in current rule Ri, i.e.

¦ ∆τ = ¦τ (t ) ⋅ Q

termij ∈ Ri

ij

i) If termij does not occur in Ri, the value of its pheromone

(4)

τ ij

does not change. Then

the difference between the normalizing value of this time and last time is

τ ij (t )

¦¦τ (t ) + ¦ ∆τ

−

ij

i

j

τ ij (t ) 0 = § · τ ij (t ) ⋅ ¨¨ ¦¦τ ij (t ) + ¦ ∆τ ¸¸ ¦¦ i j © i j ¹

(6)

i.e. the amount of pheromone in this term is increased; For enhancing predictive accuracy and simplicity of rules, ACO-Miner improves Ant-Miner algorithm with the following three aspects. 3.3 Multi-population Parallel Strategy Ant colony in ACO-Miner is divided into some populations. These populations are parallel and run separately. This strategy can avoid dependence on initial term due to the random choice of term at the beginning of interior loop. Each population has the same amount of ants, searches rules in current training set separately, and has its

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own list of amount of pheromone and list of discovered rules respectively. When the interior loop of each population is completed, all of the rules in every list are ordered by the quality of the rules. Then the best rule with the highest quality is added into the final list of discovered rules. The number of ant populations is greater, the dependence on initial term is smaller, but the cost of computing is bigger. The number of ant populations can be adjusted according to the number of cases in training set. 3.4 Adjusting Parameters Step by Step In ACO-Miner, the minimum number of cases covered per rule (Min_cases_per_rule) is a variable. It is set a bigger value at the early phase (e.g. 1/20 of the number of cases in training set), and is set a smaller value at the late phase (e.g. 1/50 of the number of cases in training set). During this process, it is decreased step by step. On one hand, setting a bigger value at the early phase can reduce the time of computing and enhance the running efficiency of the algorithm. On the other hand, decreasing the value of Min_cases_per_rule properly can discover new rules more effectively and make more cases in the training set covered. 3.5 Adopting the Cost-Based Discretization Method The cost-based discretization method, proposed in [16], is adopted in ACO-Miner algorithm to replace the C4.5-Disc discretization method used in Ant-Miner algorithm. In practical application, the essentiality of different attributes is discriminating. For example, in the analysis of customer loyalty, the duration of customer relationship keeping has higher essentiality than the time since recently buying. The cost of misclassification is diverse for different attributes. The method proposed in [16] introduces the concept of misclassification cost, puts appropriate weights to different attributes, and make the result of discretization more reasonable.

4 Experimental Results For evaluating the performance of ACO-Miner, we apply SIMiner, a selfdevelopment data mining software system based on swarm intelligence, to experiment on six data sets taken from UCI Repository on Machine Learning. The main characteristics of these data sets are summarized in Table 1. ACO-Miner has five user-defined parameters, namely: 1) the number of ant populations (No_ant_populations); 2) the number of ants in each population (No_ant_in_each_populationsp); 3) the maximum number of uncovered cases in the training set (Max_uncovered_cases); 4) the minimum number of cases per rule (Min_cases_per_rule); 5) the number of rules used to test convergence of the ants (No_rules_converg).

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Data Set Ljubljana breast cancer Wisconsin breast cancer Tic-tac-toe dermatology hepatitis Cleveland heart disease

#cases 282 683 958 366 155 303

#categ. attrib. 9 9 33 13 8

#contin. attrib. 9 1 6 5

#class 2 2 2 6 2 5

The values of these five parameters will be given according to different experiments. The ten-fold cross-validation method is taken in all the following experiments. All the following experiments are implemented with SIMiner, a data mining software system based on swarm intelligence developed by our own with Java. SIMiner consists of three main modules, i.e. data preprocessing module, classifying module, and clustering module. Some data mining methods based on swarm intelligence, including ACO-Miner and Ant-Miner, are implemented in classifying module and clustering module. These two modules are extensible by jointing other algorithm. The first two modules are used in our experiments. The data sets are preprocessed using this module, including filling the missing values, discretizing the continuous attributes, and generating the subsets for ten-fold cross-validation. Once the data sets are ready, the mining of classification rules with ACO-Miner can be implemented using classifying module. 4.1 Comparing ACO-Miner with Ant-Miner and CN2 We have evaluated the performance of ACO-Miner by comparing it with Ant-Miner and CN2. The five parameters are set as follows: 1) No_ant_populations = 3; 2) No_ant_in_each_populationsp = 3000; 3) Max_uncovered_cases = |TrainSet|/30; 4) Min_cases_per_rule = |TrainSet|/30; 5) No_rules_converg = 10. where |TrainSet| is the number of cases in initial train set but not current train set. The results comparing the predictive accuracy are reported in Table 2. Table 2. Predictive accuracy of ACO-Miner, Ant-Miner, and CN2

Data Set Ljubljana breast cancer Wisconsin breast cancer Tic-tac-toe dermatology hepatitis Cleveland heart disease

Predictive accuracy (%) ACO-Miner Ant-Miner 79.31±3.26 75.28±2.24 96.73±2.56 96.04±0.93 91.63±2.48 73.04±2.53 93.15±0.97 94.29±1.20 91.20±2.73 90.00±3.11 58.72±1.88 59.67±2.50

CN2 67.69±3.59 94.88±0.88 97.38±0.52 90.38±1.66 90.00±2.50 57.48±1.78

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From table 2, we can find that in three out of the six data sets the predictive accuracy of ACO-Miner is the highest. In the other three data sets it is the second one. These results indicated that ACO-Miner is competitive with Ant-Miner and CN2 with respect to predictive accuracy, even better than the other two algorithms in some domains. The results comparing the simplicity of the rules are reported in Table 3. Table 3. Simplicity of the rules of ACO-Miner, Ant-Miner, and CN2

Data Set Ljubljana breast cancer Wisconsin breast cancer Tic-tac-toe dermatology hepatitis Cleveland heart disease

Number of rules ACO-Miner Ant-Miner 6.63±0.46 7.10±0.31 4.58±0.21 6.20±0.25 8.23±0.53 8.50±0.62 6.57±0.34 7.30±0.15 3.20±0.23 3.40±0.16 8.79±0.78 9.50±0.92

CN2 55.40±2.07 18.60±0.45 39.7±2.52 18.50±0.47 7.20±0.25 42.40±0.71

As reported in table 3, the simplicity of the rules obtained by ACO-Miner is much better than CN2 in all six data sets, and is appreciably better than Ant-Miner, too. 4.2 Influence of Multi-population Parallel Strategy The influence of multi-population parallel strategy is analyzed by setting different value of No_ant_populations. ACO-Miner was run with three values of No_ant_populations, i.e. 3, 10, and 15. The other parameters are the same as before. The results running with different value of No_ant_populations are presented in Table 4. Table 4. Influence of multi-population parallel strategy on ACO-Miner

Data Set Ljubljana breast cancer Wisconsin breast cancer Tic-tac-toe dermatology hepatitis Cleveland heart disease

No_ant_populations =3 =10 79.31±3.26 79.56±2.78 96.73±2.56 96.78±2.33 91.63±2.48 92.47±3.25 93.15±0.97 93.15±1.06 91.20±2.73 92.39±2.91 58.72±1.88 59.03±2.47

=15 79.59±3.11 96.78±2.33 91.92±2.76 93.32±1.17 92.46±2.43 59.07±2.39

As we can observed in table 4, the predictive accuracy of ACO-Miner enhances as the value of No_ant_populations increases, but when the value of No_ant_populations has been big enough, the enhancement has become unobvious.

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5 Conclusion This paper has proposed an algorithm for classification rules discovery called ACOMiner. It is based on the ACO algorithm, a swarm intelligence algorithm, and the Ant-Miner algorithm, an algorithm for classification rules mining. In ACO-Miner algorithm, multi-population parallel strategy is proposed, the cost-based discretization method is adopted, and parameters in the algorithm are adjusted step by step. With these improvements, performance of the algorithm is advanced, and predictive accuracy is enhanced than Ant-Miner. SIMiner, a data mining software system based on swarm intelligence developed by our own with Java, is applied to evaluate the performance of the ACO-Miner algorithm. Six data sets taken from UCI Repository on Machine Learning have been used in our experiments. The results illuminate that the algorithm proposed in this paper has better performance in predictive accuracy and simplicity of rules. In the future research, SIMiner need be improved further, and more data mining algorithms should be integrated in. On the other hand, the performance of ACO-Miner should be enhanced by other kinds of heuristic function and pheromone updating strategy, and the applications of ACO-Miner in other domains should be researched.

Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant No. 70431003).

References 1. Han, J., Kamber, M.: Data Mining: Concepts and Techniques. Morgan Kaufmann Publishers, San Francisco (2000) 2. Kantardzic, M.: Data Mining: Concepts, Models, Methods, and Algorithms. IEEE Press, New Jersey (2003) 3. Bonabeau, E., Dorigo, M., Theraulaz, Guy.: Swarm Intelligence: from Natural to Artificial Intelligence. Oxford University Press, New York (1999) 4. Muata, K., Bryson, O.: Evaluation of Decision Trees: a Multi-Criteria Approach. Computers & Operations Research 31 (2004) 1933-1945 5. Carvalho, D. R., Freitas, A. A.: A Hybrid Decision Tree/Genetic Algorithm Method for Data mining. Information Sciences 163 (2004) 13-35 6. Li, R. P., Wang, Z. O.: Mining Classification Rules Using Rough Sets and Neural Networks. European Journal of Operational Research 157 (2004) 439-448 7. Dorigo, M., Maniezzo, V., Colorni, A.: Ant System: Optimization by A Colony of Cooperating Agents. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics 26 (1996) 29-41 8. Dorigo, M., Gambardella, L. M.: Ant Colonies for the Traveling Salesman Problem. Biosystems 43 (1997) 73-81 9. Dorigo, M., Di Caro, G.: Ant Colony Optimization: a New Meta-heuristic. In: Proceedings of the Congress on Evolutionary Computation, Washington DC, USA (1999) 1470-1477

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10. Dorigo, M., Di Caro, G., Gambardella, L. M.: Ant Algorithms for Discrete Optimization. Artificial Life 5 (1999) 137-172 11. Dorigo, M., Bonabeaub, E., Theraulaz, G.: Ant Algorithms and Stigmergy. Future Generation Computer Systems 16 (2000) 851-871 12. Parpinelli, R. S., Lopes, H. S., Freitas, A. A.: Data Mining with An Ant Colony Optimization Algorithm. IEEE Transactions on Evolutionary Computation 6 (2002) 321-332 13. Liu, B., Abbass, H. A., McKay, B.: Classification Rule Discovery with Ant Colony Optimization. In: Proceedings of the IEEE/WIC International Conference on Intelligent Agent Technology, Halifax, Canada (2003) 83-88 14. Shelokar, P. S., Jayaraman, V. K., Kulkarni, B. D.: An Ant Colony Classifier System: Application to Some Process Engineering Problems. Computers & Chemical Engineering 28 (2004) 1577-1584 15. Admane, L., Benatchba, K., KOUDIL, M., DRIAS, H., GHAROUT, S., HAMANI, N.: Using Ant Colonies to Solve Data-Mining Problems. In: IEEE International Conference on Systems, Man and Cybernetics, Hague, Netherlands (2004) 3151-3157 16. Janssens, D., Brijs, T., Vanhoof, K., Wets, G.: Evaluating the Performance of Cost-Based Discretization Versus Entropy- and Error-Based Discretization. Computers & Operations Research 33 (2006) 3107-3123 17. Kohavi, R., Sahami, M.: Error-Based and Entropy-Based Discretization of Continuous Features. In: Proceedings of the second international conference on knowledge & data mining. Portland, Oregon USA (1996) 114-119

Dynamic Feature Selection in Text Classification Son Doan and Susumu Horiguchi Graduate School of Information Science Tohoku University, 6-3-09 Aoba, Sendai 980-8579, Japan {s-doan, susumu}@ecei.tohoku.ac.jp

Abstract. We study the problem of feature selection in text classification. Previous researches use only a measurement such as information gain, mutual information, chi-square for selecting good features. In this paper we propose a new approach to feature selection - dynamic feature selection. A new algorithm for feature selection is proposed. In this algorithm, by combining different measurements for features and tuning parameters, several feature subsets are generated, the best feature set which achieves the best performance from a classifier is obtained from those. Experiments dealing with the real-world data set show that the proposed dynamic feature selection outperforms traditional feature selection methods.

1

Introduction

Text classification is the traditional problem in both machine learning and natural language processing communities. One of the most interesting issues recently in text categorization is feature selection problem. It plays a very important role in data mining in general and text classification in particular. Theoretically, feature selection is shown as the NP-hard problem [1] and many solutions based on search heuristics are proposed such as [3],[4],[5]. Feature selection problem for text data seems to be more difficult due to its non-structure. Text data can be found in the form of raw text or emails or Web pages. In addition, the number of terms in many text documents is large and this leads difficult to construct a classifier from features. There are two general models for feature selection in machine learning community: a wrapper model and a filter model [3],[4]. In the wrapper model, feature can be chosen so that they achieve the best performance of a classifier. The strategy for wrapper model is “try-and-test” the feature subsets. This model yields high performance, however it is hardly practical because it requires a lot of time for computations. Otherwise, the filter model does not require much time. It chooses the most “informative” features by filtering features through a measurement. The measurement can be determined by an existing measurement in information theory such as entropy, mutual information [7],[14] or statistics measurements such as chi-square, etc [9], [13]. In text categorization, almost researches use the filter model because of the large number of terms in text data. Some measurements have been proposed [7], [9]. However the drawback of D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 664–675, 2006. c Springer-Verlag Berlin Heidelberg 2006


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the filter model is that the feature subset is heuristically chosen. In addition, it ignores the role of the classifier in feature selection step. In this paper we propose a new feature selection approach - dynamic feature selection - in text classification. In our approach, by combining different measurements for features and tuning parameters, several feature subsets are generated, the best feature set which achieves the best performance from a classifier is obtained from those. Experiments dealing with the real-world data set and standard classifiers, Rocchio and naive Bayes, show that the proposed dynamic feature selection outperforms traditional feature selection methods. This paper is organized as follows. Section 2 briefly introduces related work. Section 3 introduce the proposed dynamic feature selection. Classifiers Rocchio and naive Bayes in text categorization are described in Section 4. Experimental results are shown in Section 5. Section 6 draws conclusions.

2

Related Work

Text classification consists of two main steps: pre-processing and classifier building. Feature selection is an important step in text classification. Pre-processing includes tasks such as feature extraction, feature selection and document representation. After pre-processing, a document will be represented as a vector of features in Vector Space Model [10] or a “bag-of-words” in probabilistic model; features are the components in a vector or a “word”. Therefore, feature selection plays a very important role in steps later and affects the performance of the whole system. Two most common approaches in feature selection are the filter and the wrapper [3],[4],[7]. In the wrapper approach, the subset of features is chosen based on the accuracy of classifiers. Technically, the wrapper method is relatively difficult to implement, especially with a large amount of data. Instead, the filtering approach is usually chosen because it is easily understood and for its independent classifiers. The filter approach, as its name implies, chooses a subset of features by filtering based on the scores which were assigned by a specific weighting method. In general, feature selection in text categorization are followings: [7],[11],[14]. 1. Using all terms in the vocabulary: This method uses all terms existing in documents as features (hereafter we refer a feature as a term in a document). It starts from the point of view that all terms in documents have information reflecting those contents. 2. Document frequency criterion: Features are selected by their frequencies in a document, with a threshold. 3. Class-based criterion: Select features based on their frequency in a class. 4. Information gain measure: Given a set of categories C = {ci }m i=1 , the information gain of term x is given by [11],[14]: IG(x) = −

m $ i=1

P (ci ) log P (ci ) +

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P (x)

m $

P (ci |x) log P (ci |x)

i=1 m $

+P (¯ x)

P (ci |¯ x) log P (ci |¯ x).

(1)

i=1

5. Mutual information measure: Mutual information of term t in class c is given by [11],[14]. P (x ∧ c) . (2) M I(x, c) = log P (x).P (c) for a set of categories C = {ci }m i=1 , mutual information of each term t can be calculated by, m $ P (x ∧ ci ) log . (3) M I(x, C) = P (x).P (ci ) i=1 There are also other measures for feature selection, for example, chi-square and odd-ratio . . . [7],[11],[14]. Among these measures, mutual information and information gain measure are mostly used [2],[11],[12],[14].

3

Dynamic Feature Selection in Text Classification

The feature selection problem in text classification can be stated as follows: Given a original set X consisting of n features x1 , x2 , . . . xn , choose the optimal subset S of X so that S achieves highest effectiveness of text classification. To solve this problem, we assume that each feature can be weighted by a specified measurement. Each measurement corresponds to a specified criterion. Our basic idea is to combine these measurements in order to choose the optimal subset. Mathematically, feature selection can be stated as follows. Choose a proper subset S of X, given a set of criteria τ1 , τ2 , . . . , τt , within which each criterion determines a ranking of X. Formally, we have: Criterion τ1 : xσ1 (1) θ1 . . . θ1 xσ1 (N ) ... ... Criterion τt : xσt (1) θt . . . θt xσt (N ) where σi is a permutation of the set {1, . . . , N }, and θi is the order relation based on criterion τi with a threshold value θi After ranking X according to a multiple criteria as above, for each criterion τi , we select a subset Si of X based on a threshold θi . The combined set is given by S=

% i=1

Si .

(4)

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Algorithm. DynamicFeatureSel(X - original feature set, S - optimal feature set, θ1 , . . . , θt - threshold values, σ - the classifier) for i =1 to t loop Si ← ø; Step 1. Rank all features based on criterion τi ; Step 2. Choose first features based on θi ; Step 3. Return Si ; end loop; S ← S1 ∪ S2 ∪ . . . ∪ St ; Return S Fig. 1. The algorithm DynamicFeatureSel for selecting optimal feature set

By tuning parameters θi , we can generate several subsets S and the optimal feature subset is the subset that achieves highest performance of the classifier. Thus we call the approach dynamic feature selection. Algorithmically, the process of the dynamic feature selection is depicted as in Figure 1. In order to investigate the advantages of this approach to traditional methods, we apply to two baseline models: Vector Space Model with the Rocchio algorithm and probabilistic model with naive Bayes algorithm.

4

Classifiers

Suppose we have a database D including m document d1 , d2 , . . . , dm , and a set of given k classes C = (c1 , c2 , . . . , ck ). Given a document d , our problem is to build a classifier σ that can assign the document d , that is σ(d ) to a class. We investigate briefly two algorithms Rocchio and naive Bayes as the followings. 4.1

Rocchio Algorithm

Rocchio algorithm (also called relevance feedback) is proposed by Rocchio [8] and is used as the common technique in information retrieval. It is also considered as the baseline algorithm for text classification [11], [13]. It deals with documents in Vector Space Model. One document is represented as a vector in a Vector Space Model. Each dimension corresponds to a term and the importance of terms can be assigned by some existing term weighting methods such as tf , idf , or tf idf , etc. The number of terms may increase several thousands, this leads the number of dimensions of Vector Space is very large. Thus, one of the requirement in Vector Space Model is to reduce the number of dimensions. It corresponds to the problem of feature selection under consideration. Suppose that we have n terms T = (t1 , t2 , . . . , tn ), therefore we have n dimensions. The training set can be divided into two parts: a positive set P S and a negative set N S. The Rocchio algorithm is used to construct a vector characterizing all documents in a class in a vector space depending on the positive and negative sets. c is given by:

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c=

$ di $ dj β α − . |P S| ||di || |N S| ||dj || di ∈P S

(5)

dj ∈N S

where |P S|, |N S| are the number of documents in the positive and negative sets and ||di ||, ||dj || are the Euclidean length of vectors di , dj . α and β are parameters reflecting the factor of positive and negative set, in this paper we set α and β to 1 as the original. Each class has a classifier vector, thus, we can construct k classifier vectors, (c1 , . . . , ck ). A document d in Vector Space Model is represented as a vector d
. Then, the similarity between the vector d
and class ci can be calculated by the cosine between them as follows, sim(ci , d
) = cosine(ci , d
) =

d
.ci . ||d
||.||ci ||

(6)

Then, the class of the document d is calculated by the following formula, σ(d ) = arg max sim(ci , d
).

(7)

i∈[1...k]

4.2

Naive Bayes Algorithm

The naive Bayes algorithm is based on probabilistic model, in which each document can be represented as a bag-of-word. Suppose that a document d consisting of terms t1 , t2 , . . . tn . The naive Bayes algorithm calculates the probability of a class belonging to each document with the assumption of independent variables (attributes). The formulation is based on the Bayes theorem is given by: P (ci |d ) ∝ P (d |ci )P (ci ) = P ((t1 , t2 , . . . , tn )|ci )P (ci ) =

k &

P (tj |ci )P (ci )

j=1

Thus, the class of document d is calculated by the following formula, σ(d ) = arg max P (ci |d ).

(8)

i∈[1...k]

5 5.1

Experiments Experimental Methodology

We apply both algorithms Rocchio and naive Bayes to text classification problem. In order to validate and further investigate the dynamic feature selection, we consider two cases of text classification: binary classification, the problem of assigning a document into only two classes, positive and negative classes, and multiple classification, the problem of assigning a document into more than two classes.

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Table 1. 20Newsgroup Dataset comp.graphics comp.windows.x comp.os.ms-windows.misc comp.sys.mac.hardware comp.sys.ibm.pc.hardware talk.politics.guns talk.politics.mideast talk.politics.misc talk.religion.misc soc.religion.christian

sci.electronics sci.crypt sci.space sci.med misc.forsale alt.atheism rec.sport.baseball rec.sport.hockey rec.autos rec.motorcycles

In binary classification, we compare dynamic feature selection to the method using all terms in vocabulary. Two criteria corresponding to document frequency and information gain measures are chosen. This is because these two measurements are often selected for binary classification [14]. The details of choosing parameters are indicated in Section 5.4. In multiple classification, we compare dynamic feature selection to the method using all terms in vocabulary and the method which uses only a measurement. In the experiments we choose mutual information measure because it is often selected for multiple classification [13]. The details are indicated in Section 5.4. 5.2

Real-World Database

The data set used in our experiments is 20Newsgroup. It is Usenet’s emails collected by Ken Lang and used as the benchmark data for text classification. It has 20 different groups, each group has 1000 documents in which there is no document belonging to more than 2 groups. The names of groups in 20Newsgroups is shown in Table 1. We used Rainbow package for text pre-processing [6]. Experiments are executed in SunOS 5.8 operating system, Perl, sed and awk programming languages. 5.3

Performance Measurement

Here we describe the performance of text classification in general, e.g, in case of multiple classes. Conventional performance measurement in text classification involves precision/recall, the F1 measure, and the break-even point (BEP ). For a binary classifier, precision and recall are defined as follows [14]: P =

Documents found and correct . Total documents found

(9)

R=

Documents found and correct . Total documents correct

(10)

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Human assign Human assign yes no Classifier predict yes a b Classifier predict no c d

Table 3. Global contingency for a set of classes Set of classes Human assign Human assign C = {c1 , c2 , . . . , c|C| } yes no |C| |C| $ $ Classifier predict yes A = ai B= bi i

Classifier predict no

C=

|C| $

i

ci

D=

|C| $

i

di

i

Mathematically, they are expressed through the contingency table for a category in Table 2. P = a/a + b. (11) R = a/a + c.

(12)

There is often a trade-off between precision and recall: precision P is often high and recall R low when data is limited but when data is greater, P decreases as R increases. The relationship between precision and recall is characterized by a graph called an precision/recall curve. F1 measurement combines precision and recall, characterizing the performance of classification and defined as follows, F1 = 2P R/(P + R).

(13)

The break-even point (BEP ) is that at which precision equals recall (P = R). The BEP , often used when comparing the accuracy of different methods, is calculated using interpolation in which the BEP is the average of precision and recall when they are closest to each other. For multiple classes, microaveraging of precision and recall is calculated based on the global contingency table in Table 3. 'k ai A = 'k i=1 . A+B i=1 (ai + bi )

(14)

'k ai A micro-R = = 'k i=1 . A+C i=1 (ai + ci )

(15)

micro-P =

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Table 4. F1 and BEP for comp.graphics and comp.windows.x with Rocchio algorithm parameters θ1 θ2 20 2 20 4 20 10 40 2 40 4 40 10 100 2 100 4 100 10 all terms

comp.graphics F1 BEP 71.25 70.31 71.55 69.66 71.21 69.86 72.63 72.05 72.00 70.03 70.53 68.88 74.22 72.99 72.72 71.65 70.96 69.03 70.99 69.47±0.04

comp.windows.x F1 BEP 71.08 69.15 68.79 65.51 67.11 62.57 67.35 70.63 69.11 66.88 68.12 65.12 71.20 69.39 69.48 66.65 68.55 65.50 67.35 63.04±0.03

Microaveraging F1 (micro-F1 ) measures system performance for multiple categories is calculated by micro-F1 =

2 · micro-P · micro-R . micro-P + micro-R

(16)

In this paper we use all micro of F 1, BEP , and precision/recall for evaluating performance of text classification for binary classes. For multiple classes we use microaveraging F 1 and BEP . 5.4

Experimental Results

Binary Classifier. We choose two groups comp.graphics and comp.windows.x for binary classification. Parameters in algorithm DynamicFeatureSel are selected as follows: τ1 is information gain, τ2 is document frequency. Two threshold values θ1 and θ2 are set as θ1 = 20, 40, 100 and θ2 = 2, 4, 10, respectively. the classifiers are Rocchio and naive Bayes. Parameters in Rocchio are set to 1. The total number of terms in vocabulary is 6740 and the number of terms after applying the algorithm are 303, 983 and 3327, respectively. The experiments are implemented 10-fold cross-validation. Table 4 shows the F1 and BEP of two groups comp.graphics and comp.windows.x for Rocchio algorithm and Table 5 for naive Bayes algorithm. The result shows that, in almost cases, dynamic feature selection methods outperformed the method using all terms in vocabulary. In case we choose appropriate parameters, we can achieve the highest performance, this case θ1 = 100 and θ2 = 2. In case of Rocchio algorithm, F 1 and BEP scores achieve the highest performance 74.22 and 72.99 for comp.graphics, and 71.20 and 69.39 for comp.windows.x In case of naive Bayes algorithm, F 1 and BEP scores achieve the highest performance 84.25 and 82.67 for comp.graphics, and 83.02 and 82.93 for comp.windows.x.

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Table 5. F1 and BEP for comp.graphics and comp.windows.x with naive Bayes algorithm parameters θ1 θ2 20 2 20 4 20 10 40 2 40 4 40 10 100 2 100 4 100 10 all terms

comp.graphics F1 BEP 81.38 79.74 81.38 80.11 81.48 79.84 81.93 79.12 81.87 80.07 80.39 78.67 84.25 82.67 82.74 81.45 80.11 79.40 81.71 80.34

comp.windows.x F1 BEP 79.74 78.20 79.74 80.11 79.89 79.85 79.58 79.16 80.44 80.05 78.96 78.67 83.02 82.93 81.67 81.47 79.53 79.41 80.43 80.26

Precision/recall curves are shown in Figure 2 and Figure 3. Figure 2 shows the results for Rocchio algorithm, and Figure 3 for naive Bayes algorithm. We can easily see that precision/recall curves of all methods using dynamic feature selection are above the method using all terms. comp.graphics

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Fig. 3. Precision/recall curves of category comp.graphics and comp.windows.x with θ1 = 40, θ2 = 2, 4, 10, (two figures above) and θ1 = 100, θ2 = 2, 4, 10 using naive Bayes classifier

We can also see that, compared with Rocchio algorithm, naive Bayes achieved better performance with the same number of features. Multiple Classifiers. We chose total 20 groups for multiple classification. Parameters in DynamicFeatureSel are chosen as follows: τ1 is mutual information and τ2 is document frequency. θ1 is set to 2500 and 10000, respectively and θ2 is set to 2, 4, 6, and 8. Then, the number of features with θ1 = 2500, θ2 = 2, 4, 6, 8 are 9751, 14676, 18912, and 22599, respectively. In case of θ2 = 10000, θ1 = 2, 4, 6, 8, the number of features are 14022, 17605, 21041 and 24207, respectively. The total number of all terms without feature selection is 114444. Three baseline methods for feature selection are chosen for comparisons: selection with mutual information measure and using all terms in vocabulary. We chose the number of features 2500 (denoted baseline 1) and 10000 (denoted baseline 2), the same as the parameters θ1 . The experimental results for Rocchio algorithm is shown in Table 6, and for naive Bayes in Table 7. In both tables we can find that all cases using both parameters θ1 and θ2 outperformed baseline 1 and baseline 2, and favorably comparable to the method using all terms in vocabulary. We note that, with the same parameters, we can achieve highest performance in both algorithms. In our case, with θ1 = 2500 and θ2 = 8 we achieve 80.8 and 82.3 for Rocchio and naive Bayes, respectively. Then, we have the optimal subset with only 22599 terms, using only 22599/114444 ≈ 20% all terms in vocabulary.

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S. Doan and S. Horiguchi Table 6. Micro F1 performance of 20Newsgroups, Rocchio algorithm Parameters θ1 θ2 2500 2 2500 4 2500 6 2500 8 10000 2 10000 4 10000 6 10000 8 baseline 1 baseline 2 all terms

1 82.0 80.4 80.6 80.7 80.1 81.0 81.2 80.2 74.9 79.6 81.6

2 79.4 79.2 81.5 81.6 81.5 80.2 81.1 81.3 75.3 80.1 80.9

3 80.0 81.4 81.0 81.9 79.1 80.1 81.8 80.1 76.3 80.3 80.6

4 80.8 80.7 80.3 81.4 79.5 81.3 80.3 81.3 77.2 81.0 81.1

Trials 5 6 7 79.6 80.5 79.1 79.7 81.0 79.5 80.6 81.0 80.8 80.4 80.2 80.7 80.6 80.2 80.3 82.0 81.8 81.3 80.4 79.1 80.1 79.7 79.9 81.5 76.8 75.8 75.4 78.8 79.9 80.5 77.8 81.8 79.9

8 79.9 80.0 79.9 80.4 80.7 80.8 79.7 83.4 77.0 79.5 81.5

9 79.6 79.6 80.1 80.3 79.7 80.3 81.6 81.4 75.2 79.9 82.1

10 80.8 81.0 81.3 80.3 81.4 81.1 81.2 80.0 76.7 76.7 81.6

ave. 80.2 80.3 80.7 80.8 80.9 81.0 80.6 80.1 76.1 80.0 80.8

Table 7. Micro F1 performance of 20Newsgroups, naive Bayes algorithm Parameters θ1 θ2 2500 2 2500 4 2500 6 2500 8 10000 2 10000 4 10000 6 10000 8 baseline 1 baseline 2 all terms

6

1 81.2 80.2 82.5 82.2 80.9 80.9 82.0 82.5 78.7 79.5 82.8

2 80.3 81.0 82.0 82.3 80.9 81.7 81.7 81.3 77.8 79.6 83.6

3 80.3 81.5 83.2 83.0 81.7 82.9 81.3 81.7 71.1 80.9 82.3

4 81.0 80.6 81.2 81.8 82.5 81.2 82.9 82.5 79.0 80.2 82.6

5 79.8 81.0 81.9 81.9 81.1 81.5 81.2 82.6 78.4 80.4 81.3

Trials 6 7 80.8 81.3 81.1 80.9 81.8 81.9 83.0 82.2 81.6 80.1 79.9 80.9 81.5 82.6 81.1 82.2 75.9 76.5 80.4 78.8 81.9 83.7

8 79.9 81.1 82.1 81.2 82.7 82.0 81.0 81.5 78.3 80.5 83.9

9 79.1 81.5 79.4 82.8 82.4 82.5 82.3 81.1 78.7 79.1 81.5

10 79.9 81.3 81.8 82.6 81.0 81.3 82.1 81.6 78.0 79.7 83.6

ave. 80.4 81.0 81.8 82.3 81.5 81.6 81.8 81.9 77.3 79.9 82.7

Conclusions

This paper proposed a new dynamic feature selection in text classification. We showed that, by tuning parameters in algorithm DynamicFeatureSel, the optimal feature subset can be obtained. The advantages of performance have been investigated in terms of F 1, BEP , and precision/recall curves.

References 1. Amaldi,E., Kann,V.:On the Approximation of Minimizing non Zero Variables or Unsatisfied Relations in Linear Systems, Theoretical Computer Science, 12(209)(1998)237–260 2. Baker,L., McCallum,A.:Distributional Clustering of Words for Text Classification, In Proc of SIGIR-98(1998) 96–103

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3. Blum,A., Langley, P.:Selection of Relevant Features and Examples in Machine Learning, Artificial Intelligence, 97(1-2)(1997)245–271 4. Kohavi ,R., John,G.: Wrappers for Feature Subset Selection, Artificial Intelligence, 97(1-2)(1997)273–324 5. Liu,H., Motoda,H.: Feature Selection for Knowledge Discovery and Data Mining, Kluwer Academic(1998) 6. McCallum,A., Bow: A Toolkit for Statistical Language Modeling, Text Retrieval, Classification and Clustering (1996) http://www.cs.cmu.edu/∼ mccallum/bow 7. Mladenic,D.: Feature Subset Selection in Text Learning, In Proc of European Conference on Machine Learning(ECML)(1998) 95–100 8. Rocchio,J.: Relevance Feedback in Information Retrieval, In G. Salton, editor, The SMART retrieval system: Experiments on Automatic Document Processing, chapter 14, Prentice Hall (1971)313–323 9. Rogati,M., Yang,Y.: High-performing Feature Selection for Text Classification, In International Conference on Information and Knowledge Management-CIKM2002, (2002) 659–661 10. Salton,G., WongA., Yang,C.: A Vector Space Model for Automatic Indexing, Communications of the ACM, 18(11)(1975)613–620 11. Sebastiani,F.: Machine Learning in Automated Text Categorization, ACM Computing Survey, 34(1)(2002)1–47 12. Yang,Y.: An Evaluation of Statistical Approaches to Text Categorization, Information Retrieval Journal (1999)69–90 13. Yang,Y., Liu,X.: A Re-examination of Text Categorization Methods, In Proc. of 22th SIGIR, ACM Intl. Conf. on Research and Development in Information Retrieval (1999)42–49 14. Yang,Y., Pedersen,J.: A Comparative Study on Feature Selection in Text Categorization, In Proceeding of the 14th International Conference on Machine Learning (ICML97) (1997)412–420

Knowledge Verification of Active Rule-Based Systems Lorena Chavarr´ıa-B´aez and Xiaoou Li Secci´ on de Computaci´ on Departamento de Ingenier´ıa El´ectrica CINVESTAV-IPN Av.IPN 2508, M´exico D.F., 07360, M´exico [email protected], [email protected]

Abstract. Active rules are a mechanism to provide a reactive behavior to software systems. They are not exempt to have errors, which can be introduced inadventently during their development phase. Determining if a rule set is free of errors, involves to verify its correcteness. In this work, we first extend the error definitions given for production rules, in order to consider all the elements of ECA rules. After, we propose a method, based on CCPN, to detect them. Unlike other works, our approach is able to detect errors independently of initial marking.

1

Introduction

Active rules are a mechanism by which some software systems, called active systems, can exhibit a reactive behavior due to they enable them to execute actions automatically when a relevant event happens and some conditions are met. Since active rules have three components: an event, a condition and an action, frequently they are called ECA (Event-Condition-Action) rules. In order to assure active rules in a software system will not cause undesired performance, it is necessary to verify that they are free of errors. Errors are introduced during the design of the system or knowledge adquisition. They can be originated by causes such as: 1) the lack of the system specification or lack of adherence; 2) semantics as well as syntactic errors introduced during system implementation [7]. Main structural (syntactic) errors identified are: inconsistency, incompleteness, redundancy and circularity. Verification process is useful to check if the rule base matching with the specifications (when they exist), as well as to check its consistency and completeness, which are affected by semantics and syntatic errors. Verification is related to building the system right. Several research works have been developed in order to verify the consistency and completeness of production rules. However, production rules are just a special case of active rules. As to active rule base analysis, only few related works exist [9] and they are mainly focused on analyze properties such as termination (circular rules) and confluence, rather than verifying structural errors. Earlier production rule-bases verification process involves the comparison of rule pairs [6], however, recent proposals [2], [3], [4], [5] uses graphical techniques D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 676–687, 2006. c Springer-Verlag Berlin Heidelberg 2006


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to do it. In this sense, a production rule base can be verified by means of Petri Nets (PN). In [5] a special PN type, called  − net, is proposed, and in [3] authors propose the use of a Colored PN. In both cases, authors use analysis tools (such as reachability and transition graphs) to determine if errors are present. Nevertheless, these tools can detect errors depending on the initial marking of the net. In [4], authors propose to performs a static analysis of the PN by using a Predicate/Transition net to model the knowledge base. With this model, they detect errors through a syntactic pattern recognition method. This method allows to authors to detect errors independently of initial marking of the net. But it is only designed to verify production rules bases. For ECA rules, there are works focused only on analyze specific characteristics [9], such as termination and confluence, but there is not any work focused on error detection. For this reason, in this paper, we firstly analyze active rule bases, and extend the structural errors in production rule-based systems to active rule bases. Then, a method based on a PN extension, called Conditional Colored PN (CCPN), is proposed to detect those errors, we use the incidence matrix of CCPN as analysis tool. Our work contributes to ECA rules base verification activities because we can detect errors into rule bases and we can identify some enhacement to the rules. The rest of the paper is organized as following: Section 2 reviews structural error definitions in production rules, active rules characteristics and CCPN model. Section 3 defines structural errors in active rule bases. Section 4 presents our methods to detection structural errors based on CCPN model, also shows some examples. Section 5 exposes the conclusion and future work.

2

Preliminar Definitions

In this section, we review main structural errors that can happen during the development of a production rule base. Then general knowledge model of active rules are introduced. Finally, how CCPN is used to model active rules is illustrated by an example. 2.1

Structural Errors in Production Rule Base

The most common structural errors in rule bases are: inconsistency, incompleteness, redundancy and circularity [2], [4], [7]. Inconsistency has a main characteristic conflicting rules. They occur when under the same premises, their conclusions are contradictory. For example, consider the following two rules: p → q and p → ¬q. Both rules have the clause p as premise but they reach contradictory conclusion. Incompleteness refers to the situation that when a rule base lacks necessary information to answer important questions, i.e., there are missing rules. Missing rules can happen due to factors, such as: 1) facts that are not used within the inference process; 2) conclusions not affected by any rules; and 3) a failure to cover all legal values of some input. Apart from missing rules, other rule types that characterize incompleteness are dead-end rules and unreachable rules. If the conclusion of a rule can neither match the premise of any other rules, nor the

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final conclusion, this conclusion is called dead end. On the other hand, if there is no reference path in rule base to reach the system target conclusion with any initial conditions, this conclusion is an unreachable goal. Redundancy includes subsumed and redundant rules. Two rules are redundant if they have the same premises (does not matter the order in which the atoms can be arranged) and reach identical conclusions. For example, consider the following rules: p ∧ q → r and q ∧ p → r. Does not matter the order of the atoms in the premises, both rules conclude the same. One rule is considered subsumed by another if it has more constraints in the premise, but they have the same conclusion. For example, consider the following two rules: p ∧ q ∧ r → s and p ∧ q → s. We can say that rule p ∧ q ∧ r → s is subsumed by rule p ∧ q → s because this last have less constraints and both conclude the same fact. Circularity. Occurs when a sequence of rules employs a circular reasoning, i.e., they cause a loop, so they are circular rules. We show some circular rules: p → q and q → p. When the first rule finds a match and fires, its conclusion will cause that the second rule fires too. But when this last fires, its conclusion will match the first rule again, which will generate an infinite loop. 2.2

ECA Rules Description

As we mentioned, an active (ECA) rule has three parts. The event part of a rule describes a happening to which the rule may be able respond. The condition examines the context in which the event has taken place. The action describes the task which will be carried out by the rule if the event has taken place and the condition is fulfilled. The general form of an ECA rule is the following: ON event IF condition THEN action When an event is detected, the rule is activated. When the rule is activated, it may be triggered or not depending on the evaluation result of the condition. During the action execution of a rule, other events can in turn be signaled that may produce a cascade rule firing. Due in this moment we only are interested in static analysis of ECA rules, we will omitt the execution model of ECA rules. For more details, see [1]. 2.3

CCPN for Modeling ECA Rules

Colored Petri Nets (CPN) is a high-level PN which integrates the strength of PNs with the strength of programming languages.Thus, CPN can manipulate data values. Due to this, Conditional Colored Petri Net (CCPN) was designed as an CPN extension. CCPN is a model for specification of ECA rules [8]. Due to space restrictions, we only show the modeling process for ECA rules by using CCPN. However, it is important to say that CCPN has a formal definition. For more details to CCPN, see reference [8].

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CCPN has a graphical and mathematical representation. The graphical elements used in CCPN are showed in Figure 1.

Fig. 1. List of CCPN elements

Mathematical representation of CCPN is given by incidence matrix which shows the relations between places and transitions. The rows of the matrix represent transitions and the columns represent places. The absolute value of an element Ai,j represents the weight of the arc that connects the transition i with the place j. If the value of Ai,j is zero it means that there is not connection between the transition i and the place j. An entry Ai,j with negative value means that place j is an input place for the transition i. An entry Ai,j with positive value means that place j is an output place for the transition i. Modeling ECA Rules with CCPN. In general, an ECA rule can be mapped to CCPN elements as following: condition part is mapped to a conditional transition, and event and action parts are mapped to input and output places of transitions, respectively. Matching between events and input places has the following characteristics: Primitive places, (Pprim ) , represent primitive events; Composite places, (Pcomp ) , represent composite events; Copy places, (Pcopy ) , are used when one event triggers two or more rules. An event can be shared by two or more rules, but in PN theory, one token need to be duplicated for share. A copy place takes the same information as its original one; Virtual places, (Pvirt ) , are used for accumulating different events that trigger the same rule. For example, when the event part of a rule is the composite event OR. Matching between conditions and transitions has the following characteristics: Rule transitions, (Trule ) , represent a rule; Composite transitions, (Tcomp ) , represent composite event generation; Copy transitions, (Tcopy ) , duplicate one event for each triggered rule.

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Fig. 2. Different structures for an ECA rule

Figure 2 shows different CCPN structures in which an ECA rule can be mapped. A whole ECA rule base is formed by connecting those common places that are both output and input of two different transitions, i.e., places that represent actions that a rule must carry out meanwhile these actions are events that activate other rules. The following example, in the context of active databases, will be used through the paper. Example 1. The rule base is based on the following relational database: Tables STUDENT (Name, Career, Speciality, IdTutor, IdS ) PROJECT ( IdP, Budget ) TEACHER (Name, IdT, Category, Salary, Status) NOTE (IdEst, Mark, IdSub) The following rules form the rule base. Rule 1 ON insert TEACHER IF TEACHER.Salary > 15000 THEN delete from TEACHER where TEACHER.IdT = new.TEACHER.IdT Rule 2 ON delete TEACHER IF TEACHER.Status != ”Tutor” THEN delete from STUDENT where STUDENT.IdS = TUTOR.IdS Rule 3 ON or(insert NOTE, update NOTE.Mark ) IF NOTE.Mark < 6 THEN delete from STUDENT where STUDENT.IdS = NOTE.IdS

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Rule 4 ON insert TEACHER IF TEACHER.Category < 3 THEN delete from TEACHER where TEACHER.IdT = new.TEACHER.IdT Rule 5 ON update NOTE.Mark IF NOTE.Mark < 6 then delete from STUDENT where STUDENT.IdS = new.STUDENT.IdS Rule 6 ON and(insert TEACHER, insert PROJECT) if PROJECT.Budget < 20000 then delete from PROJECT where PROJECT.IdP = new.PROJECT.IdP Rule 7 ON insert PROJECT IF PROJECT.Budget < 20000 then delete from PROJECT where PROJECT.IdP = new.PROJECT.IdP Rule 8 ON insertPROJECT IF PROJECT.Budget < 20000 THEN delete from PROJECT where PROJECT.IdP = new.PROJECT.IdP The rule base of Example 1 can be mapped into a CCPN as shown in Figure 3, by following CCPN modeling process. Also, Figure 3 shows the matching between rules and transitions of CCPN.

Fig. 3. CCPN of Example 1

3

Structural Errors in Active Rule Bases

In this section we present our extension of one of the main structural errors that can happen during the desing of the ECA rule base. 3.1

Subsumed Rules

Subsumed rules, as they are defined in production rule-based systems, are related with the fact that if a rule has less premises than another and both generate the

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same action, then the rule with less premises subsumes to the other due to, with less premises, it can reach the same results. In such systems the AND connector is used in order to join the restrictions of the premises. ECA rules not only have an AND operator but a more extensive range of operators [1]. In this section we are going to examine subsumed rules when operators AND and OR are employed. For both types of operators, it is possible that a rule is totally or partially subsumed into another. Subsumed rules - composite event AND Composite event with an AND operator forces that all elements that it involves must happen. If two rules execute the same action but one of them needs less restrictions than the other, we say that this one subsumes to the other. In general, we have two ways of subsumed rules: totally and partially subsumed. Totally subsumed rule is the case that both event and condition of a rule are subsumed into the event and condition of another and both rules generate the same action. Partially subsumed rules differs from totally subsumed rules in the sense that the conditions may be different in each rule, so that one rule subsumes to the other only if their conditions are both true. When we have an AND operator, we adopt the definition that in rule based systems is given for subsumed rules. Definition 1. Totally subsumed rules (composite event AND). Rule 2 is subsumed by Rule 1 if the following conditions are met: a) event and condition of Rule 1 are a subset of those of Rule 2, and b) both execute the same action or the action of Rule 2 is a subset that of Rule 1. Let us consider Rule 6 and Rule 7 of Example 1. We say that Rule 7 subsumes to Rule 6 totally because its event is a subset of that of Rule 6 and both verify the same condition and execute the same action. When both rules execute the same action and the event of one of them is subsumed by the event of the another, but they do not evaluate the same condition, then a rule subsumes to the other when both conditions are evaluated true. Let us suppose the condition of Rule 6 is changed to: IF TEACHER.Category < 5. Obviously Rule 6 and Rule 7 are no longer totally subsumed. Only when their conditions are met we can say than Rule 7 subsumes to Rule 6 because with less constraints it is possible to reach the same result. Subsumed rules - composite event OR Now let us consider OR type composite event. Unlike AND composite event, in which it is necessary that all constraints in the premise are met in order to reach the rule conclusion, composite event OR only needs that one of its constraints defined in the premise occurs. Similar to AND operator, we define totally and partially subsumed rules for OR type composite events. Definition 2. Totally subsumed rules (composite event OR). Rule 1 is subsumed by Rule 2 if: a) the event and condition of Rule 1 are a subset those of Rule 2; and b) the action of Rule 1 is the same (or a subset) of that of Rule 2.

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Consider Rule 3 and Rule 5 of Example 1. We say Rule 3 subsumes to Rule 5 because the first one contains more events that may cause its triggering, the actions are the same. There are cases in which a rule ”looks like” to be subsumed by another but they have different conditions. In this case, we have partially subsumed rules since if condition of any of them is not true, then rules will not be subsumed. For example, taking into account Rule 3 and Rule 5 of Example 1, if the condition of Rule 3 is changed to NOTE.Mark != 7, then those rules are no longer totally subsumed. A rule is subsumed to another only when both conditions are evaluated true.

4

Error Detection

As we have mentioned, several works have attempted to verify production rulebased systems [3], [5] based on PN’s. However, to detect errors they depend on the initial marking of the net. We propose to perform a static analysis in order to identify structural errors based on incidence matrix of the CCPN. Incidence matrix represents, in a simple manner, interactions among the rules. Before we can present our methods it is necessary to define some concepts. Definition 3. Initial place. An initial place in a CCPN, is a place that only has output arcs and no input arcs. For instance, in Figure 3, places E5 , E0 , E2 and E3 are examples of initial places. An initial place in incidence matrix only has a negative value in its column. Definition 4. End place. An end place is that only has input arcs and no output arcs. In Figure 3, places E12 and E9 are end-places. An end place in incidence matrix only has positive values in its column. Definition 5. Incident place. An incident place is a primitive place that has more than one input arc. In Figure 3, place E1 is an incident place. An incident place has more than one positive value in its column, of course, the colum must to correspond to a primitive place. Definition 6. Route (RU (pi , tj )). Given to an initial place pi and a rule typed transition tj in a CCPN, a route RU from pi to tj RU (pi , tj ) is a finite sequence of pairs of arcs that connect places and transitions and vice versa, as the following way: RU (pi , tj ) = (pi , tk ) → (tk , pn ) → . . . → (tm , ps ) → (ps , tj ) where: pi is an initial place; tj is a rule typed transition; pr is a place, r = n, . . . , s;

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td is a transition, d = k, . . . , m; (pr , td ) is an input arc; (td , pr ) is an output arc. For example, in Figure 3, a route from E0 to T5 is RU (E0 , T5 ) = (E0 , T4 ) → (T4 , CopyE0 ) → (CopyE0 , T7 ) → (T7 , E1 ) → (E1 , T5 ) Algorithm 1 describes the procedure for generating routes, based on incidence matrix. Algorithm 1. Detecting routes into incidence matrix Input: Incidence matrix Output: List of routes 1. for i = 0 to i < # rows 2. for j = 0 to j < # columns 3. if w (ti , pj ) < 0 4. Adds pi to Places set 5. ∀pi ∈ P laces 6. if pi is an initial place 7. The transitions and places ”visited” form a route 8. Return to step 5 9. else 10. for k = 0 to k < # rows 11. if w (tk , pj ) > 0 12. Adds tk to Transitions set 13. ∀t ∈ T ransitions 14. Go to step 2 In general terms, to generate a route from incidence matrix, we have to look for negative values in its rows and, for each one of them, to look for positive values in its columns. For each positive value, to look for negative values in its rows and continue until to find an initial place. As we mentioned earlier, during the construction of CCPN a matching between ECA rules and transitions must be registered. In order to obtain the information about the matching, we define the following procedures: Get transitions(e): Returns the transitions for which e is an output place. Get routes(t): Returns a list of all the routes of a transition t. Routes are obtained by means procedure described earlier. Get composite(r): Returns the composite events that are in a route, r. Get primitives(p): Returns the component places of a composite place, p. Type of(p): Returns the type (AND, OR) of a composite event p. Incidence matrix of CCPN of Figure 3 is given in Figure 4. After defining the described procedures, we can provide procedures for detect structural errors.

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Fig. 4. Incidence matrix of CCPN of Example 3

4.1

Procedures for Error Detection

In this section, we will describe procedures for detecting structural errors for ECA rules. Subsumed rules Algorithm 2 shows how to detect if a rule is subsumed by another. Algorithm 2. Detecting subsumed rules Input: Incidence matrix Output: Subsumed rules 1. ∀p ∈ Incidence list 2. T r = Get transitions( p ) 3. ∀t ∈ T r 4. Ru = Get routes( t ) 5. ∀r ∈ Rul 6. p = Get composite( r ) 7. if p != ∅ 8. pp = Get primitives( p ) 9. If any element of pp is in any route of Ru* 10. If Type of( p ) is AND 11. Then pp subsumes to p 12. If Type of( p ) is OR 13. Then p subsumes to pp * Omitting the routes in which composite event is.

A similar procedure is applied to verify conditions. The procedure identifies composite places along routes that executing the same action. If any of its component places is in another rule, then it subsumes to rule with composite event.

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Verification Example

To show our verification methods, we will use the rule base of Example 1. Subsumed rules Incidence places are the following: {E12 , E1 , E9 } . We will analyze places E9 and E12 because into routes for transitions for place E1 there is not composite places. Transitions for place E9 are T5 , T6 and T8 . We can see that in routes for transition T5 threre is not any composite place. So, we only check routes for transitions T6 and T8 . Routes for transition T6 and transition T8 , both are into Tr, are the following: RU (E2 , T6 ) = (E2 , T0 ) → (T0 , EC4 ) → (EC4 , T6 ) RU (E3 , T6 ) = (E3 , T1 ) → (T1 , EC4 ) → (EC4 , T6 ) RU (E3 , T8 ) = (E3 , T1 ) → (T1 , CopyE3 ) → (CopyE3 , T8 ) The only composite event is stored in place p = EC4 , its component places are pp = {E2 , E3 } . A subset of pp, E3 , is in the only route of T8 . Type of EC4 is OR, so that, rule represented by transition T6 subsumes to rule represented by transition T8 . On the other hand, for place E12 we have the following analysis. Transitions for E12 are T9 , T10 and T12 . Routes for each transitions are the following: RU (E5 , T9 ) = (E5 , T11 ) → (T11 , CopyE5 ) → (CopyE5 , T2 ) → (T2 , EC6 ) → (EC6 , T9 ) RU (E0 , T9 ) = (E0 , T4 ) → (T4 , CopyE0 ) → (CopyE0 , T2 ) → (T2 , EC6 ) → (EC6 , T9 ) RU (E5 , T12 ) = (E5 , T11 ) → (T11 , CopyE5 ) → (CopyE5 , T12 ) RU (E5 , T10 ) = (E5 , T11 ) → (T11 , CopyE5 ) → (CopyE5 , T10 ) The composite event is p = EC6 and its component events are E5 and E0 . Since the place E5 is a subset of composite place EC6 , E5 is into the route of T10 and the type of this place is AND, we can say that rule represented by transition T10 subsumes to rule represented by transition T9 . As rule represented by transition T12 is the same that rule represented by transition T10 , transition T12 also subsumes to transition T9 . Through CCPN is easy to detect the described errors because we have the rules interactions description into incidence matrix. Detection can be done on the ECA rules itself but is more difficult due to ECA rules is not ordered according to firing sequence.

5

Conclusion and Future Work

In this paper we propose the definitions of structural errors for ECA rules. Some of structural errors definitions have been considered to verify production rulebase systems, but never to verify active rule-based systems. Also, we expose a static approach in order to detect (to verify) errors in ECA rules bases. Error

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verificaction is an important issue due to increasing necessity to execute actions automatically and independently of the user. As well as to improve quality software systems and contribute to do easy the maintenance process. In our approach to verify ECA rules-based systems we consider the structural errors defined and CCPN for modeling them. Comparing with others works, our approach has the following advantages: 1) We use CCPN incidence matrix as analysis tool because it contains all the information related to interactions among rules, so, we can detect errors independently of the initial event set; 2) Our methods are based on route concept, which is easily obtained through information stored into incidence matrix, also, they are easy to implement. Due to restrictions of space, we do not show all the definition that we have, as well as all the methods to detect them based on CCPN model. This verification process can be done in any stage of rule base development in order to, whenever a new rule is added, to check if any errors can happen. As future work we propose to extend our definitions to consider complex events with time stamps. Also, to incorporate a dynamic analysis to determine more accurately the occurrence of errors. Of this way, since the maintenance issue is the main obstacle to actives systems become widely used we can contribute to simplify it.

References 1. Paton, N., D´ıaz,O.: Active Database system. ACM Computing Surveys, Vol. 31, No. 1 (1999) 63-103 2. Nazareth, D. L.: Investigating the Applicability of Petri Nets for Rule-Based Systems Verification. IEEE Transactions on Knowledge and Data Engineering, Vol. 4, No. 3 (1993) 402-415 3. Wu, Q. , Zhou, C., Wu, J.,Wang, C.: Study on Knowledge Base Verification Based on Petri Nets. International Conference on Control and Automation (ICCA2005), Budapest, Hungry (2005) 4. Zhang, D., Nguyen, D.: PREPARE: A Tool for Knowledge Base Verification. IEEE Transactions on Knowledge and Data Engineering, Vol. 6, No. 6 (1994)983-989 5. He, X., Chu, W., Yang, H.: A New Approach to Verify Rule-Based Systems Using Petri Nets. Information and Software Technology, Vol. 45, No.10 (2003) 663–670, 6. Gupta, U.: Validating and Veryfying Knowledge-Based Systems. Uma Gupta, Los Alamitos, California (1990) 7. Gonz´ alez J. A., Dankel D.: The Engineering of Knowledge-Based Systems. Prentice Hall (1993) 8. Li, X.O., Mar´ın, Joselito M., Chapa, Sergio, V.: Applying Petri Nets on Active Database Systems. IEEE Transactions on System, Man, and Cybernetics, Part C: Applications and Reviews, accepted for publication (2005) 9. Baralis, E., Ceri, S.,Paraboschi, S.: Compile-Time and Run-Time Analysis of Active Behaviors. IEEE Transactions on Knowledge and Data Engineering, Vol. 10, No. 3 (1998) 353-370

Lattice-Based Classification with Mixed Numeric and Nominal Data Wei Hu and Huanye Sheng Computer Science Dept. Shanghai Jiaotong Univ. 200030 Shanghai, China [email protected], [email protected]

Abstract. Traditional classification methods are often designed for certain types of data. They cannot be directly applied to dataset with mixed numeric and nominal data. Only after numeric data was discretized or nominal data was encoded, could algorithms work. As data should accommodate to algorithm, such learning scheme is approach oriented to some extend. This paper presents a new data mining scheme called lattice-based learning (LBL), whose central idea is formulating algorithms using basic operations on lattice structure. Since both numeric and nominal data can be easily embedded into lattices, LBL algorithms are applicable to any dataset with mixed data. We detail lattice-based classification (LBC) algorithm in this paper. The performance of LBC has been studied on different datasets. Results show that LBC is an effective method for classification with mixed data and LBL learning is a promising scheme for data mining.

1 Introduction Traditional algorithms often assume data are either numeric or nominal [2, 10, 12, 13], but in the real world one has to deal with dataset with mixed numeric and nominal data. Most solutions adopt data preprocessing techniques and fall into one of the following categories: (1) Discretize numeric data and apply algorithms for nominal data [12]. The discretization process often causes loss of important information especially the difference between two numeric values. (2) Encode nominal data as numeric data and apply algorithms for numeric data. Nominal data can be converted into binary representations, using 0 or 1 to represent either a nominal value absent or present [9]. These binary representations can then be handled as numeric data. To some extend, traditional learning scheme is approach oriented as data is accommodating to algorithm. In this paper, we present a new data mining scheme called lattice-based learning (LBL), whose central idea is formulating algorithms using basic operations on lattice structure. As long as dataset is embedded into a lattice, which is a no information losing process, any LBL algorithm will work. Some basic notions of lattice structure are introduced as follows. An element u of a partially ordered set (S, % ) is an upper bound of a subset A of S, if a % u for every a∈A; an element u is a least upper bound or sup of subset A, if u is an D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 688 – 699, 2006. © Springer-Verlag Berlin Heidelberg 2006

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upper bound of A and u % v for every upper bound v. Lower bounds and greatest lower bounds (inf) are defined similarly, everywhere reversing the inequalities. A lattice is a partially ordered set L in which any pair of elements a, b∈L has a sup a∧b and an inf a∨b. By induction, one shows that any finite set of elements of a lattice has a sup and an inf. We denote sup and inf of finite subset A by A and A respectively. If L1 and L2 are lattices, then L1×L2 is also a lattice, where (a1,a2) % (b1,b2) if and only if a1 % b1 and a2 % b2. Suppose a dataset has m attributes A1, A2, …, Am. We can embed the dataset with mixed data into a lattice L by the following two steps:

ġ

Ģ

(1) Embed Ai into lattice Li for all i from 1 to m. If Ai is a numeric attribute, define Li to be Ai and define a % b to mean a ≤ b. Then Li is a lattice, where a∧b = max{a,b} and a∨b = min{a,b}. If Ai is a nominal attribute, define Li to be Ai  {⊥,∅}and define a % b to mean a=⊥ or b=∅ or a=b. Then Li is a lattice, where a∧b is a if a=b otherwise is ⊥ and a∨b is a if a=b otherwise is ∅. (2) Compute Cartesian product of all lattices. Lattice L is just L1×L2× …×Lm. It is worth noting that the embedding method is not unique. For instance, let N be the union set of some nominal data and define LN to be the family of the subset of N, and a % b to mean a ⊆ b. Then LN is a lattice, where a∧b = a  b and a∨b = a  b. Data classification is an important form of data analysis that can be used to extract models describing important data classes. The rest of this paper will present a member of LBL family, lattice-based classification (LBC).

2 The LBC Algorithm The output of LBC algorithm is classification rule with hierarchically structured exceptions (RE) [3], which is a list of if-else rules connected by except-edges and if not-edges (Figure 1). Because each rule of RE may have at most one except-edge and one if not-edge, formal definition of RE can be recursively expressed as a triple , where R is an if-else rule, X and N are except-RE and if not-RE respectively. It is easy to transform RE into decision list and decision tree [11]. Compared with other representations of classification rules, RE is more effective and more similar with human cognitive results. When an instance is inputted, RE is performed in the following manner. Rules connected by if not edges behave like decision lists: only if a rule is not applicable to an input instance, the next rule is applied. As one rule’s except-RE contains information of exceptions to the rule, a rule may fire only if its except-RE does not classify the input instance. 2.1 Special Case Our discussion of LBC starts from a special case with no nominal data. Consider an artificial training data with two numeric attributes X and Y (Figure 2). There are 27 instances, of which 11 are positive and 16 are negative.

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R0 except if not R1

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R3 except if not

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antecedent R0 R1 R2 R3 R4

astigmatism=no AND tear=normal age=presbyopic AND spectacle=myope AND astigmatism=no AND tear=normal astigmatism=yes AND tear=normal spectacle=hypermetrope AND astigmatism=yes AND tear=normal

consequent lenses=none lenses=soft lenses=none lenses=hard lenses=none

Fig. 1. An example RE

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0.2 0.4 0.6 0.8 1.0 positive negative

Fig. 2. A scatter diagram of artificial dataset

Let’s examine how LBC induces RE for positive instances. (1) We first try to characterize a set of positive instances {e3, e5, e6, e9, e10, e14, e15, e16, e21, e22, e25} with one if-else rule R1 IF 0.05≤X≤0.82 AND 0.15≤Y≤0.75 THEN Class=positive. whose antecedent is obtained by computing maximum and minimum of instances’ X value and Y value and consequent is the class of instances. The rule corresponds to a minimum rectangle range covering all positive instances, which also covers some negative instances {e4, e7, e8, e11, e17, e18, e19, e20, e23}. To measure the validity of rule(s), we compute the ratio of exceptions to the whole negative instances, called exception rate. This measure indicates whether a description of instances is general or specific. If the rate is lesser than a predefined threshold (0.3 for instance), rule(s) will be adopted. Here, exception rate of R1 is 8/16 (>0.3) and the rule is unadopted as it is too general.

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(2) One method for specializing description is partition instance set, constructing rule for each part and then characterizing positive instances with all the rules. Suppose 16 positive instances are split into two parts {e3, e5, e6, e9, e10, e14, e15, e16} and {e21, e22, e25}. Rule R2 IF 0.05≤X≤0.42 AND 0.25≤Y≤0.75 THEN Class=positive and rule R3 IF 0.75≤X≤0.82 AND 0.15≤Y≤0.45 THEN Class=positive. are learned for two parts respectively. Exception to rule R2 is {e4, e7, e11} and R3 covers no negative instance. The exception rate of R2 and R3 (3/16) is lesser than threshold (0.3), so R2 and R3 connected by if not-edge if not R2

R3

are adopted to summarize of common characteristic of positive instances. (3) Then, how to handle with exception to R2? A natural idea is to reduce the original task to a new RE induction task, whose positive instance set is R2’s exception {e4, e7, e11} and negative instance set is {e3, e5, e6, e9, e10, e14, e15, e16} from which R2 is learned. Suppose RE RE2 has been induced for {e4, e7, e11}. RE for 16 positive instances can be constructed by connecting RE2 with R2 using an except-edge. if not R2 R3 except

RE2 (4) The method for dealing with exception is applied recursively until no exceptions occur. In binary classification problem, once description of one class is given, that of another class can be obtained under the closed world assumption. Here, we introduce a special rule, called default rule, R0 IF true THEN Class=negative whose antecedent is always true. And the following RE, connecting R0 by except-edge, is applicable to predict class of new instance and distinguish between positive and negative instances. R0 except if not R2

R3 except

RE2

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2.2 Lattice Extension Now we extend the approach proposed in former subsection to lattice structure. Consider (again!) the special case, whose basic operations are: (1) Constructing if-else rule. Rule in last subsection corresponds to a range whose bounds are maximum value and minimum value of finite number set. If a number is regarded as an element in lattice, whose binary relation % is relation less than or equal to ≤, computing maximum (minimum) of a set is just computing sup (inf) of the set in the lattice. (2) Testing weather an instance is covered by a rule. This operation in last subsection is implemented by comparing X (Y) values of the instance with the bounds. It is easily extended to a partially order set. Therefore, the approach for numeric data can be extended to lattice. The extended approach for classification rule induction is formulated by operations on lattice structure and is a member of LBL learning scheme. Suppose a dataset has m attributes A1, A2, …, Am and it is embedded into a lattice L using the method mentioned in section 1. A lattice-based approach to inducing RE for positive instances in binary classification problem is depicted as follows.

Input : Set of positive instances P Set of negative instances N Threshold θ Rule with exceptions RE Algorithm LBC: 1 if P = ∅ then 2 return 3 end if 4 {P1, P2, …, Pk} = Partition (P, N, θ) 5 for all i from 1 to k do Pi % (A1, A2, …, Am) % Pi 6 Ri = IF THEN Class = P.Class 7 end for 8 NR=RE 9 for all i from 1 to k do 10 NR.R = Ri 11 LBC (Ri(N), Pi, θ NR.X) 12 NR = NR.N 13 end for

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The formal parameter P is a positive instance set while N is a negative instance set. θ is a predefined threshold to control the size of exception. RE is a rule with exceptions to be induced, which is a recursive structure corresponding to triple mentioned before. Partition procedure first split the nonempty positive instance set into a number of subsets according to a validity measure (Line 4). The measure of a cluster of subsets {A1, A2, …, Al}is defined by exception rate of corresponding rules

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l

| Val ({A1, A2, …, Al}, N) =

 Ri ( N ) | i =1

|N|

.

where Ri is the if-else rule corresponding to subset Ai, N is negative instances and Ri(N) is negative instances covered by rule Ri. The Partition procedure returns {P1, P2, …, Pk} whose Val measure is lesser than threshold θ. We detail the Partition procedure in the next subsection. Next, if-else rule is constructed for each subset (Line 5 to 7). Here, Pi and Pi are sup and inf of subset Pi in lattice L. P.class represents the class of instances in set P, which is positive originally. Then the algorithm is called again to deal with exceptions to rule Ri (Line 11). Here, formal parameter P is Ri(N) which is subset of negative instances, and P.Class is negative. Finally, RE for exceptions is connected by except-edge (Line 11) and rules for different subsets are connected by if not-edge (Line 12). It is easy to extend the algorithm to induce RE for a certain class from dataset with multi classes of instances. And then, LBC is applicable to multi classification problem by adding a default rule

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2.3 Partition Procedure

The thing left to decide is how to split a given set into a proper number of subsets. Some notions of partition and partition sequence are introduced first. A partition π of a set S is a collection of disjoint nonempty subsets of S that have S as their union. In other words, the collection of subsets {Si | i∈I where I is an index set} forms a partition of S if and only if (1) Si ≠ ∅ for i∈I, (2) Si  Sj = ∅, when i≠j, and (3) S i = S .



 i∈I

Each subset is a block of the partition. Partition α is a refinement of another partition β if, for all block A of α, there exits a block B of β such that A ⊆ B.

π(1), π(2), …, π(n) is a partition sequence of a finite set S if and only if (1) π(1) = {S}, (2) π(i) is a refinement of π(i-1) for i from 2 to n, and (3) π(n) = {{s}| s∈S }. There are many methods for acquiring a partition sequence from a finite set. The simplest approach is hierarchically and randomly partitioning the set. One can also use clustering algorithms, some of which are applied to dataset with mixed numeric and nominal data [7, 8].

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The following theorem tell us if a partition sequence of training dataset is obtained, partition sequence of any subset can be computed easily. Theorem: Let α(1), α(2), …, α(n) be a partition sequence of finite set A and B ⊆ A. Then sequence β(1), β(2), …, β(n) , where

β(i) = {X  B | X is a block of α(i)} for all i from 1 to n, is a partition sequence of B. Proof (1) β (1)= {A  B}={B}. (2) For all block W of β(i), there exits a block X of α(i) such that W = X  B. For X of (i) α , there exits a block Y of α(i-1) such that X ⊆ Y. For Y of α(i-1), there exists a block Z= Y  B of β(i-1). Because X ⊆ Y, W = X  B ⊆ Y  B =Z. Therefore, β (i) is a refinement of β (i-1) for i from 2 to n. (3) β(n)= {{a}  B | a∈A}= {{b}| b∈B}. Ƒ Since any finite subset of training dataset has been associated with a partition sequence, partition problem is reduced to finding a partition in a given partition sequence according to the Val measure. Suppose that P and N are finite set, P  N = ∅ and π(1), π(2), …, π(n) is a partition sequence of P. The Val measure has two useful properties on the partition sequence. (1) Val decreases on partition sequence i.e., Val(π(i), N) ≥ Val(π(j), N) for all i≤j. (2) Val(π(n), N) = 0. Proof (1) We reduce property 1 to proposition: for all finite set A and B, RA(N)  RB(N) ⊆ RA∪B(N) where RA is rule learned from A, RB from B and RA∪B from A  B. First, suppose x∈RA(N)  RB(N). This implies that x∈RA(N) or x∈RB(N). Now suppose that x∈RA(N). A % x % A. Because A⊆A  B, A % A  B and It follows x∈N and A  B % A. Hence, A  B % A % x % A % A  B and x∈RA∪B(N). This shows that RA(N)  RB(N) ⊆ RA∪B(N). (2) Suppose A is block of π(n). It follows that A ={p} where p∈P. Because A= A= Ƒ p and P  N = ∅, RA(N)=∅. It follows that Val(π(n), N) = 0.

Ģ

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Property 2 assures that for all θ >0 there exists at least one partition whose Val value is lesser than θ. Property 1 tells us binary search is an effective method to find partition

π = arg max {Val(π(i), N)| Val(π(i), N)< θ }. π (1) ,π ( 2 ) ,...,π ( n )

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2.4 Comparison with Other Works

Most traditional RE induction algorithms are fall into the scheme proposed in the Counterfactuals algorithm [14]: (1) Find an interesting rule pertaining to instances. (2) Learn the exceptions recursively. (3) Learn the remaining instances recursively. Dimopoulos et al.’s method is parametric on a classical rule learning algorithm to find interesting rules [4]. The Induct algorithm seeks the rule with the most discriminatory power. It is a very fast and effective statistical approach to empirical induction [5]. Kivinen et al. presented an Occam algorithm for learning rules that are organized into up to k levels [6]. Compared with these methods, LBC does not need to learn the remaining instances recursively. This is because for all finite set A RA(A)=A, where RA is rule learned from A.

3 Experiments To perform empirical evaluation of our approach, we have performed two experiments on data classification. One is to analyze relation between threshold, clustering algorithm, numbers of rules and performance of lattice-based algorithm. And another is to compare the effect of using different classification methods Datasets: We have selected two databases from University of California Irvine Data Repository [1]. Of these, one dataset only numeric data (shuttle), another dataset mixed data (abalone). Learning system: A LBC learning system called VC04 has been implemented. It offers a platform to adjust learning parameters of LBC. Adjustable parameters include training and testing data, threshold value, lattice type, similarity between two instances, similarity between instance and set, similarity between two sets, clustering algorithm type and testing type. 3.1 Experiment 1: Analyze Relation Between Threshold, Clustering Algorithm, Numbers of Rules and Performance of LBC

We choose dataset abalone for our first experiment. The dataset has 7 numeric attributes and 1 nominal attribute. There are 4,177 examples each of 29 types: 1 to 29. We group classes 1-8, 9 and 10, and 11 on and treat the task as a 3-classificaiton problem. The learning parameters of experiment 1 are listed as follows. Threshold θ : range from 0.15 to 0.95. Clustering algorithm: Randomly partition, Simple K-means and ECCAS [8]. Lattice: Dataset is embedded into a lattice using the method discussed in section 1 and all attributes are used. Similarity between two instances: L1 measure. Similarity between instance and set: Average similarity. Testing Type: 8-fold stratification.

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#error 150 120 90 60 30 0 0.0 0.2 random

0.4 0.6 0.8 1.0 θ K-means ECCAS

Fig. 3. Relation between threshold, clustering algorithm and numbers of errors

#rule 1000 800 600 400 200 0 0.0 0.2 random

0.4 0.6 0.8 1.0 θ K-means ECCAS

Fig. 4. Relation between threshold, clustering algorithm and numbers of rules

The learning results are shown in Figure 3 and Figure 4. As can be seen in Figure 3, performance of LBC using Simple K-means is slightly worse than that of LBC using ECCAS, better than that of LBC using randomly partition. For each clustering algorithm, the error rate is high when θ is close to 0.15 or 0.95. This is because when θ is close to lower bound, the output rules are too specific, and when θ is close to upper bound, the output rules are too general. In Figure 4, output rules size of LBC using Simple K-means is slightly larger than that of LBC using ECCAS, less than that of LBC using randomly partition. For each clustering algorithm, the rules size is larger when θ is close to 0.15 or 0.95. When threshold θ is close to lower bound, few exceptions occur, which is not easy to be satisfied. Then subsets are split into many parts and bring many rules. On the other hand, big θ allows many exceptions. Then LBC will be called many times and output RE will have many levels.

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3.2 Experiment 2: Compare the Effect of Using Different Classification Methods

The dataset Shuttle has 58,000 examples, 43,500 for training and 14,500 for testing. There are 9 numeric attributes and 7 classes: Rad Flow, Fpv Close, Fpv Open, High, Bypass, Bpv Close and Bpv Open. The attributes concern the position of radiators in a NASA space shuttle, and the classes are the appropriate actions to be taken during a space shuttle flight. The learning parameters are listed as follows. Threshold θ : range from 0.3. Clustering algorithm: Simple K-means. Lattice: Dataset is embedded into a lattice using the method discussed in section 1 and all attributes are used. Similarity between two instances: L1 measure. Similarity between instance and set: Average similarity. Testing Type: Using testing set. Table 1. Comparison among different algorithms for Shuttle dataset

Algorithm NewId BayTree Cn2 Cal5 LBC (simple kmeans) Cart C4.5 Ac2 KNN LVQ

ErrorRate 0.01 0.02 0.03 0.03 0.08 0.08 0.10 0.32 0.44 0.44

Time Train 6180 240 11160 313 610 79 13742 2553 32531 2813

Test ? 17 ? 10 60 2 11 2271 10482 84

Table 1 shows a comparison among different algorithms. LBC outperforms C4.5, kNN, Ac3 and slightly worse than NewId and BayTree. The dataset abalone is used again in experiment. Now first 3133 instances are used for training and final 1044 are for testing. The learning parameters are listed as follows. Threshold θ : range from 0.3. Clustering algorithm: Simple K-means. Lattice: Dataset is embedded into a lattice using the method discussed in section 1 and all attributes are used. Similarity between two instances: L1 measure. Similarity between instance and set: Average similarity. Testing Type: Using testing set. The learning results for both 3-classificaiton task and 29-classificaiton task are given in table 2. As can be seen, the presented algorithm clearly outperforms Linear

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Algorithm

29-class es

3-class es

Backprop Dystal Cascade (no hidden nodes) Cascade (5 hidden nodes) C4.5 Linear Discriminate k Nearest Neighbor (k=5) LBC (simple kmeans, θ = 0.3)

? ? 24.86 26.25 21.50 0.00 3.57 19.45

64.00 55.00 61.40 65.61 59.20 32.57 62.46 63.82

Discriminate, Nearest Neighbor, and is slightly worse than Cascade and Backprop. Comparing with C4.5, it is worse than C4.5 in 29-classificaion task, but better in 3-classificaion task.

4 Conclusions In this paper, we have presented a new learning scheme called lattice-based learning (LBL), whose central idea is formulating algorithms using basic operations on lattice structure. As long as dataset is embedded into a lattice, which is a no information losing process, any LBL algorithm will work. Lattice-based classification (LBC) for dataset with mixed data, a member of LBL family, is discussed in detail. The performance of LBC has been studied on different datasets. Results show that LBC is an effective method for classification with mixed data and LBL learning is a promising scheme for data mining.

References 1. Blake, C., and Merz, C.: UCI Repository of Machine Learning Databases. (1998) 2. Breiman, L., Friedman, J. H., Olshen, R., A. and Stone, P.J.: Classification and Regression Trees. Wadsworth, Belmont. (1984) 3. Compton, P., Jansen, R..: Knowledge in Context: A Sstrategy for Expert System Maintenance. In Proceedings of AI'88: 2nd Australian Joint Artificial Intelligence Conference. (1988) 292–306 4. Dimopoulos, Y., Kakas, A. C.: Learning Non-monotonic Logic Programs: Learning Exceptions. In Proceedings of the 8th European Conference on Machine Learning. (1995) 5. Gaines, B.R., Compton, P.J.: Induction of Ripple Down Rules. In Fifth Australian Conference on Artificial Intelligence. (1992) 6. Kivinen, J., Mannila, H., and Ukkonen, E.: Learning Hierarchical Rule Sets. In Proc. of the 5th Annual ACM Workshop on Computational Learning Theory. Pittsburgh, Pennsylvania, July 27–29. (1992) 37–44

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7. Li, C., Biswas, G.: Unsupervised Learning with Mixed Numeric and Nominal Data. IEEE Transactions on Knowledge and Data Engineering. Vol. 14. No. 4. (2002) 8. Li, X.Y., Ye, Y.: A Supervised Clustering and Classification Algorithm for Mining Data with Mixed Variables. IEEE Transactions on Systems, Man, and Cybernetics. Part A: Systems and Humans. (2005) 9. Ralambondrainy, H.: A Conceptual Version of the K-means Algorithm. Pattern Recognit. Lett., Vol.16. No. 11. (1995) 1147–1157 10. Salzberg, S.: A Nearest Hyperrectangle Learning Method. Machine Learning 6(3). (1991) 251-276 11. Scheffer, T.: Algebraic Foundation and Improved Methods of Induction of Ripple Down Rules. In Proc. Pacific Knowledge Acquisition Workshop. (1996) 12. Quinlan, J.R.: C4.5 Programs for Machine Learning, Morgan Kaufmann, San Mateo, CA. (1993) 13. Quinlan, J.R.: Improved Use of Continuous Attributes in C4.5, Journal of Artificial Intelligence Research 4. (1996) 77–90 14. Vere, S.: A. Multilevel Counterfactuals for Generalization of Relational Concepts and Production. Artificial Intelligence, 14. (1980) 139–164

Learning to Semantically Classify Email Messages Eric Jiang University of San Diego, 5998 Alcala Park San Diego, California 92110, United States of America [email protected]

Abstract. As a semantic vector space model for information retrieval (IR), Latent Semantic Indexing (LSI) employs singular value decomposition (SVD) to transform individual documents into the statistically derived semantic vectors. In this paper a new junk email (spam) filtering model, 2LSI-SF, is proposed and it is based on the augmented category LSI spaces and classifies email messages by their content. The model utilizes the valuable discriminative information in the training data and incorporates several pertinent feature selection and message classification algorithms. The experiments of 2LSI-SF on a benchmark spam testing corpus (PU1) and a newly compiled Chinese spam corpus (ZH1) have been conducted. The results from the experiments and performance comparison with the popular Support Vector Machines (SVM) and naïve Bayes classifiers have shown that 2LSI-SF is capable of filtering spam effectively.

1 Introduction Over the years, various spam or unsolicited email message filtering technology and anti-spam software products have been developed and deployed. Some are designed to stop spam at the server level and may rely on DNS blacklists of domain names that are known to originate spam. This approach can be problematic and insufficient due to the lack of accuracy of the name lists. The other major type of spam filtering functions at the client level. Once an email message is downloaded, its header and/or content can examined to determine whether the message is spam or legitimate. Many machine learning algorithms in text categorization [11] have been successfully used in client-side spam detection and filtering applications. Among them, naïve Bayes [9], Racchio’s algorithm [8], decision tree with boosting [10], Support Vector Machines (SVM) [2] are the most popular. In this paper, a new spam filtering model (2LSI-SF), based on Latent Semantic Indexing (LSI), is proposed. In Section 2, LSI is briefly introduced and its original reference is provided. In Section 3, the 2LSI-SF model is described, and its experiments on some email corpora and a performance comparison with the SVM and naïve Bayes classifiers are presented in Section 4. Some concluding remarks are provided in Section 5. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 700 – 711, 2006. © Springer-Verlag Berlin Heidelberg 2006

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2 Latent Semantic Indexing As a popular vector space model for information retrieval (IR), LSI [3] employs a rank-reduced term-document space through the singular value decomposition (SVD) [5] and effectively, it transforms individual documents into their semantic content vectors to estimate the major associative patterns of terms and documents and to diminish the obscuring noise in term usage. Since the search in the space is based on the semantic content of documents, this approach is capable of retrieving relevant documents even when the query and such documents do not share any common terms. Several variations of the LSI model have been proposed recently. For instance, an enhanced LSI implementation, which updates LSI by performing nonlinear perturbations to the LSI space, has been developed in [6] and it represents a more accurate semantic model for effective information retrieval.

3 Spam Filtering Model LSI can be used as a learning algorithm for text categorization by replacing the notion of query-relevance with the notion of category-membership. In regard to spam filtering, it can be used to classify incoming messages into either legitimate or spam category. An experiment of this approach on the Ling-Spam corpus was reported in [4]. However, there is a need to fully justify the validity of this approach as a general spam filtering model and to investigate the practicability of the approach in incorporating further space dimensionality reduction and category discriminative information in the training data. First, as pointed out recently by the author of Ling-Spam [1], the performance of a learning based spam filter on Ling-Spam can be over-optimistic because all legitimate messages in this corpus are topic-specific, and hence it may not reflect the performance that can be achieved on the incoming messages of a real email user. Secondly, the SVD algorithm can be computationally expensive for large data sets, and the exploration of additional dimensionality reduction with LSI is particularly valuable in order to make it a viable spam filtering system. This can be accomplished by reducing both sizes of the feature set and the training data set. Thirdly, LSI itself is a completely unsupervised learning algorithm and when it is applied to the (supervised) spam filtering problem, the valuable existing email discrimination information on the training data should be utilized and be integrated in the model learning. Lastly, email classification is a cost sensitive learning process and it is always desired to develop email filters that minimize the misclassification errors of legitimate messages. The potential utilization of category semantic spaces in this aspect is worth investigating. In this section the model 2LSI-SF is described in terms of its structure and major components. 3.1 Feature Selection Two levels of feature selection have been used in 2LSI-SF for dimensionality reduction. In this paper, a term, or a feature is referred to as a word, a number, a symbol, or

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simply a punctuation mark. Dimensionality reduction aims to trim down the number of terms to be modeled while the content of individual messages is preserved. First, features are selected in an unsupervised setting. The process is carried out by removing the stop or common terms and applying a term stemming procedure. Then, the terms with low document frequencies or low global frequencies are eliminated from the training data, as these terms may not help much in differentiating messages for categories and instead they can add some obscuring noises in message classification. The selection process also removes the terms with very high global frequencies in the training data. The high frequent terms can mislead the classification process in 2LSI-SF due to the tf portion of the weighting scheme (see Section 3.2) and in addition, many of these terms seem distribute almost equally between spam and legitimate categories and are not valuable in characterizing messages in different categories. Next, features are selected by their frequency distributions between spam and legitimated messages in the training data. This supervised feature selection step intends to, through those classified samples in the training data, further identify the features that distribute most differently between categories. In 2LSI-SF, the Information Gain (IG) measure [14] is used in this selection process. IG quantifies the amount of information gained for category prediction by the knowledge of the presence or absence of a term in a document. More specifically, the Information Gain of a term T about a category C can be defined as

IG (T , C ) =

¦ ¦

P ( t , c ) log

c∈{ C , C ) t ∈ ( T ,T )

P (t , c ) P (t ) P (c )

(1)

where P(c) and P(t) denotes the probability that a document belongs to the category c and the probability of t occurs in a document, respectively, and P(t, c) is the joint probability of t and c. Through the process of feature selection, the feature dimensionality of the training data can be significantly reduced. For, instance, in the experiments with PU1 (see Section 4.2 for detail) the original feature size that is over 20,000 has been trimmed down to tens, hundreds, and thousands. 3.2 Message Vector and Term Weighting After feature selection, each message is encoded as a numerical vector whose elements are the values of the retained feature set. Each term value is associated with a local and global term weight, representing the relative importance of the term in the message and the overall importance of the term in the corpus, respectively. It is our belief that in the context of email messages, term frequencies can be more informative than the simple binary coding in classifying if a given message is spam. There are several choices to weight a term locally and globally based on its frequencies. Some preliminary experiments we performed on several weighting

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combinations have indicated that the traditional log(tf)-idf weighting scheme [6] produces very satisfactory performance and was used in our experiments. 3.3 Augmented Category LSI Spaces For a give document set, LSI builds a rank-reduced vector space that characterizes the principal correlations of terms and documents in the set. In regard to document classification, multiple LSI spaces can be constructed, one for each category, and each of the spaces is constructed from the only documents of one category. It is assumed that a pure category-based LSI space offers a more accurate content profile, and more representative term and document correlations for the category. In practice, however, this approach may not work very well because documents from different categories can be quite similar and difficult to be distinguished from each other. It is especially true in email filtering. Many spam messages are purposely written in a way to have legitimate looks and to mislead spam filters. In 2LSI-SF, assuming that the training data have been separated into the spam and legitimate sets, this problem is ameliorated by augmenting each of the category sets to include a small number of the training samples that are most close to the category but belong to the opposite category. Because of their closeness to a category set, the new incoming messages that are similar to those augmented samples are prone to be misclassified in the LSI spaces built from pure category sets but can be correctly classified in the LSI spaces built from our augmented category sets. The similar strategy has been used in data compression [12]. Each of the augmented category sets is then used to build the corresponding semantic space for message classification. In 2LSI-SF, the expansion of the category training sets is carried out by clustering both sets and finding their cluster centroids for sample comparison and selection. Given a group of messages and their vector representations, the centroids is a vector computed by averaging the term weights in the group. It is noted that email messages, though vary significantly in content, can likely be grouped by topics into a number of clusters where some underlying semantic term and document correlations are expectedly present. For instance, spam email might be grouped into classes such as get-rich ads, adult products, and online-shopping promotions. Since the clustering is performed after feature selection, the individual centroids are the encoded content vectors representing the most important retained features of the corresponding message classes and effectively, they provide a mechanism to summarize the topics of the related classes. Once the clusters for a category set are formed and their centroids are identified, all training samples from the other category set are compared against to the centroids, and the most similar ones are selected and added to the category set. The similarity between a sample d and a centroid c is measured by their vector cosine value

cos( d , c ) =

d ⋅c || d || × || c ||

(2)

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The cosine value above offers a comparison of sample d with all messages in the cluster where the centroids c is constructed. Mathematically, it measures an average similarity between the sample and these messages. A variant of the well-known k-means clustering algorithm was used in 2LSI-SF. The number of clusters and the sizes of augmented samples can vary depending on the corpus and the space dimensionality, and in our experiments presented in Section 4, an average size 50 of the augmented samples is used, and the fixed 11 clusters are constructed for both category sets. The fixed cluster size is determined empirically by a silhouette plot [7] on the training data. A preliminary analysis on 2LSI-SF has indicated that the size of the augmented samples to a category set has certain impact on the classification accuracy for the category. This characteristic can potentially be used further improve classification on legitimate messages. It should be pointed out that the proposed approach of using augmented categorybased semantic spaces is effective in terms of integrating the most valuable category discrimination information into the LSI model learning and characterizing the principal semantic content structure of each category. The two-space configuration of 2LSISF, which is embedded in our classification algorithms described in the next subsection, also helps improve the classification accuracy of incoming messages. 2LSI-SF requires the construction of two LSI spaces. However, the dimensionality of each space in this model is substantially reduced and this can be especially useful for dealing with large training sets. 3.4 Message Classification To classify incoming email messages, three classification algorithms are considered. Each of them treats incoming messages as individual queries and utilizes the embedded email discrimination information in the model. The first algorithm uses the most semantically similar message in the training data, which is determined by comparing all training sample messages in both augmented LSI spaces, to classify incoming messages. The algorithm is referred to as Single. It is simple, but can be less accurate as more spam messages are warily designed and written to have legitimate looks. The second algorithm classifies incoming messages by using a group of the top m most similar samples in the training data compared in the LSI spaces. The counts or sums of cosine similarity values, of spam and legitimate sample messages in the group make the classification decision. The algorithm uses the latter approach is referred to as Multiple. The third message classification algorithm is a hybrid approach that combines the ideas of Single and Multiple with the hope to mollify some problems associated with the algorithms. This algorithm is named as Hybrid. It has a few parameters that are set heuristically, and can be configured by the user, depending upon users’ tolerance level to spam and potential misclassification errors.

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4 Experiments In this section, the experiments of 2LSI-SF on the benchmark spam testing corpus PU1 and a new Chinese email collection ZH1 are presented. A comparison with the SVM and naïve Bayes methods is also provided. 4.1 Performance Evaluation The performance of a spam classifier can be evaluated by spam precision (S-prec) and recall (S-rec), legitimated precision (L-prec) and recall (L-rec). In brief, the precision is gauged by the percentage of messages classified to a category which actually are, whereas the recall is quantified by the percentage of messages from a category that are categorized by the classifier. These measurements, however, do not take an unbalanced misclassification cost into consideration. Spam filtering can be a cost sensitive learning process in the sense that misclassifying a legitimate message to spam is typically a more severe error than misclassifying a spam message to legitimate. In our experiments, a cost sensitive and unified weighted accuracy [1] is also used as a performance criterion and it can be defined as WAcc ( λ ) =

λ nL−>L + nS −>S

λ (nL−>L + nL−>S ) + (nS −>S + nS −>L )

(3)

where nL->L, nL->S, nS->S and nS->L denotes the count of the classification L->L (legitimate classified as legitimate), L->S (legitimate misclassified as spam), S->S (spam classified as spam), and S->L (spam misclassified as legitimate), respectively, and Ȝ is a cost parameter. The WAcc formula assumes that the error of L->S is Ȝ times more costly than the error of S->L. In our experiments, Ȝ = 1 (L->S and S>L have the same cost) and Ȝ = 9 (L->S has a higher cost than S->L) are used. The setting of Ȝ = 999 has also been proposed in literature. However, this setting can be inaccurate when the training data are not large enough. For this reason, the setting is not used here. For performance comparison, two well-known classification models: naïve Bayes and SVM that have been popular choices for email filtering applications are also considered in our experiments. The Weka [13] implementations of both models are used and the input data to both classifiers are the same as to 2LSI-SF, namely, the processed set of message vectors after feature selection and term weighting. 4.2 Experiments on PU1 PU1 is a benchmark spam testing corpus that was released recently [1]. It contains a total of 1099 real email messages, with 618 legitimate and 481 spam. The experiments on PU1 are performed using stratified 10-fold cross validation. More specifically, the PU1 corpus is partitioned into ten equally-sized subsets. Each experiment takes one subset for testing and the remaining for training, and the process repeats ten

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Table 1. Classification results on various small feature sets and message classification algorithms # features

50

150

S-prec S-rec L-prec L-rec

.861 .906 .927 .885

.944 .927 .945 .956

S-prec S-rec L-prec L-rec

.841 .900 .921 .867

.917 .910 .932 .935

S-prec S-rec L-prec L-rec

.857 .971 .975 .874

.926 .977 .982 .939

250 Hybrid .963 .958 .967 .971 Single .947 .942 .956 .958 Multiple .933 .973 .979 .945

350

450

550

650

.953 .940 .954 .963

.972 .935 .952 .979

.979 .935 .952 .984

.983 .929 .948 .987

.919 .925 .942 .935

.944 .927 .945 .956

.943 .927 .946 .955

.918 .940 .952 .934

.920 .985 .988 .932

.957 .981 .985 .964

.964 .971 .978 .971

.970 .969 .976 .976

times with each subset takes a turn for testing. The performance is then evaluated by averaging over the ten experiments. Table1 summarizes the classification results on three message classification algorithms and various small feature sets from 50 to 650 with an increment of 100. For both Hybrid and Multiple algorithms, its S-prec and L-rec measurements show an upward trend while its L-prec and S-rec measurements shift up and then down after the size 250 or 350 as the number of the retained features being increased. This phenomenon implies that feature expansions can especially be beneficial to profile legitimate messages more accurately and subsequently reduce the critical misclassifications of legitimate messages. It is also interesting to note that Multiple offers very high values of S-rec and L-prec and is expected to classify most of spam messages correctly. For the Single algorithm, its measurements are less predictable but all of Table 2. Classification results on various expanded feature sets and message classification algorithms # features

1650

2650

S-prec S-rec L-prec L-rec

.985 .923 .944 .989

.981 .921 .942 .985

S-prec S-rec L-prec L-rec

.928 .927 .945 .942

.921 .938 .952 .953

S-prec S-rec L-prec L-rec

.970 .963 .972 .976

.967 .950 .963 .974

3650 Hybrid .989 .921 .943 .992 Single .941 .938 .952 .953 Multiple .970 .944 .958 .977

4650

5650

6650

8000

.994 .915 .939 .995

.992 .910 .936 .994

.988 .915 .939 .990

.983 .910 .935 .987

.957 .933 .951 .966

.965 .935 .952 .973

.961 .938 .954 .969

.967 .923 .943 .974

.973 .944 .959 .979

.967 .935 .953 .974

.981 .917 .940 .985

.982 .904 .931 .987

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them peak at the size of 250. Overall, it seems that there should be a minimum requirement of feature set size (say around 250) on this corpus in order to achieve an acceptable classification performance. Clearly, the algorithm Single is less competitive than Multiple and Hybrid over these feature sets and while Multiple outperforms in S-rec and L-prec, Hybrid achieves a better performance when the unbalanced costs of misclassification errors are taken into consideration. The generally higher cost of L->S than S->L is reflected in the quantities of S-prec and L-rec. For text classifiers, the size of feature set can have an effect on their classification performance. Most of spam experiments have been reported in literature use relatively small feature sets. The performance of 2LSI-SF on expanded feature sets has also been experimented. Table 2 shows the results on feature sets ranging from 1650 to 6650 with an increment of 1000. The category of 8000 in the table refers to the feature sets retained without going through the supervised feature selection step. The numbers of the retained features are roughly around 8000. It can be seen in Table 2 that as the feature set gets larger, both S-rec and L-prec values seem to have a downward or flat trend for all algorithms while the values of Sprec and L-rec have an upward trend with the exception of Hybrid that its values peak at the size of 4650. The same observation applies when comparing the results of the expanded sets in Table 2 with those from the feature set of 650 (the last column in Table 1). A further study of message classification counts generated by the filter has shown that as more features are included for model learning, both L->L and S->L counts are likely (but just slightly) increased, whereas the L->S count is likely a bit decreased, and the S->S count seems unwavering. For 2LSI-SF, we may conclude that a richer feature set helps further characterize legitimate messages and classify them correctly, but it contributes less or nothing to improving classification accuracy for spam messages. In addition, the precisions and recalls for both categories are generally improved as feature sets get larger. However, when the size of feature set reaches to certain point (250 or 350 in our experiments, and see Table 1), further enlarging feature set may generate higher spam precision and legitimate recall but lower or same spam recall and legitimate precision. In order to compare the performance of 2LSI-SF on PU1 with the SVM and naïve Bayes (NB) classifiers and also take the unbalanced misclassification costs into consideration, the average weighted accuracies WAcc are computed for all feature sets that have been considered. Fig. 1 and Fig. 2 show a comparison of three 2LSISF algorithms with SVM and NB for the cost parameter Ȝ = 1 and Ȝ = 9, respectively. For Ȝ = 1, Single is clearly inferior to all other four approaches that have most of their accuracy values above 95%. Among these top four, Multiple is the best performer over the small feature sets whereas NB and SVM are the top-rated when large feature sets are considered. For Ȝ = 9, all algorithms except Single deliver good performance. And for most of the feature sets, Hybrid consistently achieves the highest accuracy that peaks at the size 4650 with 98.9%. It is interesting to note that NB does extremely well on PU1 and likely, its performance is boosted by our feature selection process.

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average weighted accuracy

1

0.95

Hybrid Single 0.9

Multiple SVM NN

0.85 50

150

250

350

450

550 650 1650 2650 number of retained features

3650

4650

5650

6650

8000*

6650

8000*

Fig. 1. Average weighted accuracy with Ȝ = 1 (PU1)

average weighted accuracy

1

0.95

Hybrid Single Multiple

0.9

SVM NN

0.85 50

150

250

350

450

550 650 1650 2650 number of retained features

3650

4650

5650

Fig. 2. Average weighted accuracy with Ȝ = 9 (PU1)

4.3 Experiments on ZH1 In this subsection, the experiments of 2LSI-SF on a newly complied Chinese spam corpus ZH1 [15] and a performance comparison with SVM and NB are presented. The experiments intend to demonstrate the capability of a model for classifying email written in a language with different linguistic structures. Chinese text does not

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1

0.98

0.96

average weighted accuracy

0.94

Hybrid

0.92

Single Multiple

0.9

SVM NB

0.88

0.86

0.84

0.82

0.8 50

150

250

350

450

550 650 1650 2650 3650 number of retained features

4650

5650

6650

7650

8650

Fig. 3. Average weighted accuracy with Ȝ = 1 (ZH1) 1

average weighted accuracy

0.95

0.9

0.85 Hybrid Single Multiple SVM

0.8

NB

0.75 50

150

250

350

450

550 650 1650 2650 3650 number of retained features

4650

5650

6650

7650

8650

Fig. 4. Average weighted accuracy with Ȝ = 9 (ZH1)

have explicit word boundaries like English and words in the text can be extracted by some specialized word segmentation software [15]. The construction of ZH1 is very similar to PU1, and ZH1 is made up of 1205 spam and 428 legitimate sample messages. The experiments on ZH1 are also performed using stratified 10-fold cross validation and the varied feature sets with the size up to 8650 are used. Fig. 3 and Fig. 4 show the average weighted accuracy values obtained by all five classifiers over the feature sets for Ȝ = 1 and Ȝ = 9, respectively. For the case with

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equal misclassification cost (Ȝ = 1), Fig. 3 indicates that SVM performs best, followed by the group of three 2LSI-SF algorithms, and NB evidently fails to be comparable. When a higher cost of misclassifying legitimate messages is considered (Ȝ = 9), a similar observation can be made, but this time, Hybrid from 2LSI-SF becomes more competitive to SVM. Both models deliver high classification performance on the corpus. The experiments on both PU1 and ZH1 corpora have demonstrated that the proposed 2LSI-SF model, in particular the Hybrid approach, is very effective for spam detection and filtering, and represents a very competitive alternative to the wellknown classifiers such as SVM and naïve Bayes.

5 Conclusions As a rank-reduced vector space model, LSI has been successfully used in information retrieval and other applications. In this paper, an LSI-based spam filtering model, 2LSI-SF, is proposed that classifies email messages by their semantic content. The model utilizes the valuable email discriminative information in the training data and incorporates several pertinent feature selection and message classification algorithms. The experiments of 2LSI-SF on some email testing corpora have shown that 2LSI-SF is very effective in learning to classify unwanted (spam) email messages. The competitive performance of 2LSI-SF is also demonstrated by comparing the model with two popular email classifiers: SVM and naïve Bayes. As future work, we plan to improve the accuracy and efficiency of the 2LSI-SF model by further exploring spam email structures such as number of images contained in email and to develop a commercial quality spam filtering system.

Acknowledgments The author would like to thank the anonymous reviewers for their valuable comments on the paper.

References 1. An Androutsopoulos, I., Paliouras, G., Michelakis, E.: Learning to Filter Unsolicited Commercial E-mail. Technical Report 2004/2, NCSR Demokritos (2004) 2. Christianini, B., Shawe-Taylor, J.: An Introduction to Support Vector Machines and other Kernel-Based Learning Methods. Cambridge University Press (2000) 3. Deerwester, S., Dumais, S., Furnas, G., Landauer, T., Harshman, R.: Indexing by Latent Semantic Analysis. Journal of the American Society for Information Science. (1990) 391-409 4. Gee., K.: Using Latent Semantic Indexing to Filter Spam, Proceedings of the 2003 ACM Symposium on Applied Computing (2003) 460-464 5. Golub, G., Vn Loan, C.: Matrix Computations. John-Hopkins, Baltimore, 3rd edition (1996)

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6. Jiang., E., Berry, M.: Solving Total Least-Squares Problems in Information Retrieval, Linear Algebra and its Applications (2000) 137-156 7. Kaufman, L., Rousseeuw, P.: Finding Groups in Data, Wiley (1990) 8. Rocchio, J.: Relevance Feedback Information Retrieval, The Smart Retrieval System Experiments in Automatic Document Processing (Salton, G. ed.), Prentice-hall (1971) 313-323 9. Sahami, M., Dumais, S., Heckerman, D., Horvitz, E.: A Bayesian Approach to Filtering Junk E-mail, Proceedings of AAAI workshop (1998) 55-62 10. Schapier, R., Singer, Y.: BoosTexter: A Boosting-based System for Text Categorization, Machine Learning (2000) 135-168 11. Sebastiani, F.: Machine Learning in Automated Text Categorization. ACM Computing Surveys (2002) 1-47 12. Schutze, H., Hall, D., Pedersen, J.: A Comparison of Classifiers and Document Representations for the Routing Problem, Proceedings of SIGIR (1995) 229-237 13. Weka -Data Mining Software in Java, http://www.cs.waikato.ac.nz/ml/weka/ 14. Yang, Y., Pedersen, J.: A Comparative Study on Feature Selection in Text Categorization, Proceedings of the 14th International Conference on Machine Learning (1997) 412-420 15. Zhang, L., Zhu, J., Yao, T.: An Evaluation of Statistical Spam Filtering Techniques, ACM Trans on Asian Language Information Processing (2004) 243-369

Optimizing the Hyper-parameters for SVM by Combining Evolution Strategies with a Grid Search Ruiming Liu1, Erqi Liu2, Jie Yang1, Ming Li1, and Fanglin Wang1 1

Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University 200240, Shanghai, P.R. China {liuruiming, jieyang, mingli, hardegg}@sjtu.edu.cn 2 Institute of the Second Academy, China Aerospace Science & Industry Corporation 100854, Beijing, P.R. China [email protected]

Abstract. In real-world applications, selecting the appropriate hyper-parameters for support vector machines (SVM) is a difficult and vital step which impacts the generalization capability and classification performance of classifier. In this paper, we analyze the distributing characteristic of hyper-parameters that the optimal hyper-parameters points form neighborhoods. For finding all the optimal points (on the grid points) in neighborhoods, based on this characteristic, we propose a hybrid method that combines evolution strategies (ES) with a grid search (GS), to carry out optimizing selection of these hyperparameters. We firstly use evolution strategies find the optimal points of hyperparameters and secondly execute a grid search in the neighborhood of these points. Our hybrid method takes advantage of the high computing efficiency of ES and the exhaustive searching merit of GS. Experiments show our hybrid method can successfully find the optimal hyper-parameters points in neighborhoods.

1 Introduction The statistical learning method of support vector machines (SVM) has been researched widely ever since it was proposed by Vapnik [1]. It has been successfully used to complete classification, regression and clustering tasks. However, in realworld problems, you have to give appropriate kernel functions for specific training dataset and the appropriate hyper-parameters for them. The nicer performance of SVM depends on the right selection of these parameters. In some papers, the hyperparameters also were called multiple parameters which comprise of a regularization parameter [3] (soft margin parameter [2], penalty parameter in [4]) and kernel parameters. There has been quite a bit of attention on the selection of hyper-parameters for SVM [3], [4], [5], [6], [7], [8], [9], [10], [13], [14]. In the beginning, the grid search was recommended [4] to find the best hyper-parameters. It’s a natural and exhaustive parameter searching approach which can obtain the global optimization parameters. At the same time, grid search has to try every possible point of parameters that makes computing times excessive. The computing times will increase exponentially as the D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 712 – 721, 2006. © Springer-Verlag Berlin Heidelberg 2006

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number of parameters increases. For reducing computing quantity, the gradient descend maybe is the most reasonable solving approach. Some researcher has used the gradient descent to choose the best hyper-parameters for SVM [5], [6], [7], [8]. Nevertheless, the gradient descent needs to meet a series of differentiable conditions. That is impossible in most practice. Its application therefor is restricted consumedly. Recently, evolution algorithms (EA) have been applied to select the optimization hyper-parameters in [3], [9], [10]. EA have greater computing efficiency than grid search and can optimize parameters of non-differentiable functions. Thus, it’s not a bad choice. Friedrichs and Igel [3] used the covariance matrix adaptation evolution strategy (CMA-ES, [11], [12]) to optimize the hyper-parameters of Gaussian kernel function (radial basis function, RBF). They have demonstrated on benchmark datasets that the CMA-ES can improve the results achieved by grid search. Liu et al. [9] gave a weighted support vector machine with GA-based parameter selection (GA-WSVM). The kernel function that they investigated was also Gaussian kernel function. Rojas et al. [10] have used a genetic algorithm (GA) to search the parameterization space of SVM kernels with multiple parameters for classification application and achieved a fine performance. In this paper, we will analyze the distributing characteristic of hyper-parameters for SVM. Based on this characteristic, we propose a hybrid method to carry out optimizing selection which can find all the optimal points (on the grid points) in respective neighborhoods. The cross-validation results are used as evaluation of hyper-parameters selection. In the following, we give a brief review and analysis of SVM in section 2. In section 3, we give analyses of the distributing character of hyper-parameters and thoroughly present how to find all the hyper-parameters in neighborhoods for SVM by our hybrid method, ES-GS. We show some experiment results in section 4 and draw a conclusion in section 5.

2 Support Vector Machines We mainly focus our attention on the SVM for classification. The basis principle of SVM classifier is to map the data into a higher dimension feature space and then find a linear separating hyper-plane with the maximal margin in that high dimension space, by which we can correctly separate the data. * * We consider the problem of binary classification. Let S = {( x1, y1 ),,( xm , ym )} be * n the training set where xi ∈ (i = 1, , m ) is an n-dimension input vector, * yi (i = 1, , m) is the corresponding label of xi and its range is {−1, +1} . The task of SVM is to learn an optimal separating hyper-plane, which can be represented as

* * < w, xi > + b = 0 .

(1)

When the datasets are linearly separable, the problem of seeking the optimal separating hyper-plane can be transformed into following optimization problem [15]:

* * minimisew,b < w ⋅ w > * * subject to yi (< w ⋅ xi > +b) ≥ 1,

(i = 1,, m)

(2)

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The linearly separable case is simple and easy to understand. However, the real-world datasets will in general be linearly non-separable in the feature space. In order to still find the separating hyper-plane, the slack variable ξi associated with misclassification is introduced. Then the optimization problem (3) changes into the following form: m * * minimisew ,b < w ⋅ w > + C ¦ ξi2

(3)

i =1

s.t.

* * y i ( < w ⋅ xi > + b ) ≥ 1 − ξ i ,

(i = 1, , m )

It is applied to give penalties to the misclassification. What we should pay more attention to is the regularization parameter C, one of hyper-parameters. We will have a detail discussion about it in section 3.1. In order to obtain the solution of equation (3), the dual representation is needed. The dual objective function and corresponding restrictive conditions is described as: m

¦ αi −

m axim ise

i =1 m

¦α

s .t .

i

1 2

m

¦

* * y i y jα iα j < x i ⋅ x j >

i , j =1

yi = 0 ;

(4)

0 ≤αi ≤ C

i =1

i , j = 1,  , m When

the

datasets

are

non-linearly

separable,

a

kernel

function

** * * K ( x, z ) =< Φ( x), Φ( z ) > is used so that separating the data precisely is realized by a hyper-plane. The function Φ can map the raw data to a feature space in which it is yet linearly separable. In this space, the SVM learns a separating hyper-plane by solving the following quadratic optimization problem: m

maximise

¦ αi − i =1 m

s.t .

¦α y i

i

1 m * * ¦ y i y jα i α j K < x i , x j > 2 i , j =1 = 0;

0 ≤ αi ≤ C

(5)

i =1

i , j = 1,  , m There are many various kernel functions [16]. However, as examples, we only investigate two popular kernel functions in this paper:

噝The polynomial kernel function:

K ( x, z ) =< x ⋅ z + 1 > d .

(6)

噝The Gaussian kernel function: 2

x−z K ( x, z ) = exp( − ). 2σ 2

(7)

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The exponent d of polynomial kernel function and the width σ of Gaussian kernel function are the so-called kernel parameters. More kernel functions and details about them can be found in [16].

3 Hyper-parameters Optimization Based on ES-GS 3.1 Hyper-parameters and Its Distributing Characteristic In section 2, we have reviewed the basis theory of SVM and given a simple introduction of a regularized parameter and kernel parameters. For the SVM with a fixed kernel function, its hyper-parameters are composed of a regularized parameter and kernel parameters, e.g. (C,σ ) being the hyper-parameters of SVM with Gaussian kernel function. The regularized parameter C can give a balance between minimizing the number of training errors and maximizing the margin width. Furthermore, as C decreases, the width of the margin increases. In the other hand, the kernel parameters dominate the mapping results of datasets. They play a leading role in separable degrees of dataset in feature space. Accordingly, the classification performance is greatly influenced by the selection of hyper-parameters. In practice, we found that the optimal points of hyper-parameters do not exist uniquely as an unattached point. In [16], author has also mentioned that the regularized parameter C may have more than one optimal value. Moreover, after a number of experiments, we discovered a more important phenomenon that there are usually other optimal hyper-parameters points in the neighborhood of one optimal hyper-parameters point. All of these optimal hyper-parameters points have the same value of evaluation function (fitness function), e.g., the cross-validation criterion [16], AUC [10] or the validation rate [9]. Namely, these optimal hyper-parameters points form a neighborhood in which the values of evaluation function are equal and optimal, which means the top of function surface is flat. Fig. 1 gives a function example to demonstrate this characteristic.

Fig. 1. An example showing hyper-parameters distribution characteristic

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In the previous works and papers, few authors have paid an enough attention to this significant distributing characteristic of optimal hyper-parameters. They settled for finding only one hyper-parameters point. Their selection results of hyper-parameters are some unattached optimal points of hyper-parameters, such as in [14] and [16]. Seeking a good method that can find more optimal hyper-parameters or give their ranges is necessary. That makes it be impossible to select more robust parameters in solving engineering problems. 3.2 Evolution Strategies and the Grid Search As one of the important classes of evolution algorithms (EA), evolution strategies (ES) are often used as optimization tools. Distinguished from genetic algorithms (GA), ES algorithm doesn’t need coding and encoding processes. Especially, it has self-adaptation search capacity which makes it quickly and nicely guide to optimal points. The ES algorithm has three basis operations: 1) Mutation: The main variations in evolution algorithms are mutations. The mechanism of ES mutation is implemented by making perturbations, namely adding random numbers which follow a Gaussian distribution to its variable vector (chromosome). Let ( x1 , , xn ) be the chromosome involving n variables. We represent a mutation operator by a formulation as follows:

xik +1 = xik + N (0, σ ik +1 ) .

σi the number of generation. The σ i

Where the strategy parameters

are actually step sizes of mutation and k is will also evolve in their own way.

σ ik +1 = σ ik exp(τ ⋅ N (0,1)) . Where

τ

(8)

(9)

is learning rate controlling the self-adaptation speed of σ i .

2) Recombination: Mutation performs a search step which is only based on the information of only one parent, while recombination can shares several parents’ information. It reproduces only one offspring from ρ parents. ES has two versions of recombination technique: discrete recombination and intermediate recombination. The discrete recombination selects every component randomly for the offspring from relevant components of ρ parent individuals. In contrast, the intermediate recombination gives an equal right to all ρ parents for reproduction. The offspring take the average of ρ parent vectors as its value. When the variables are discrete, we need to perform a rounding operation. 3) Selection: Selection operation is necessary to direct the search to the promising range of the object parameter space and give a result of optimization. The basic selection approaches of ES are comma selection ( µ , λ ) and plus selection ( µ + λ ) . For ( µ , λ ) selection, only the

λ

offspring individuals can be selected, while the parental individuals are

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not in the selected set. This selection technique will forget the information of parent generation. Thus we can avoid pre-converging on the local optimal points. However, the plus selection ( µ + λ ) gives a choice from the selection set which comprises the parents and offspring. It can ensure the best individuals survive and preserve them. Moreover, the fitness is also very important to ES. It is a criterion for evaluating searching result. There are several approaches that can evaluate the searching results of hyper-parameters for SVM, such as the k-fold cross-validation [14], the radius-margin [1] and the area under the curve of the classifier function [10], etc. The cross-validation usually is used as a tool of evaluation of statistical learning method. Due to avoiding the overfitting problem, it often is applied to train classifiers. In papers [4], [14], [16], the cross-validation becomes an evaluation criterion of the hyper-parameters. The authors of paper [3] have tested the several evaluation criteria and proved they generate qualitatively the same results. We consider the cross-validation is a direct and easy-tounderstand criterion. So, we use k-fold cross-validation technique to train and test SVM. Finally, we use the correct classification rate of k-fold cross-validation as the fitness of ES. The grid search is an exhaustive search method. It examines the search space entirely. Each dimension of a grid represents a variable to be optimized. The variables can be successive or discrete. The grid search requires specifying a range for each dimension, which defines the maximum and minimum values of the dimension. Moreover, we should give the number of divisions along each dimension that can regularize how fine the grids are. 3.3 The ES-GS Method for Hyper-parameter Optimization In the section 3.1, we have analyzed the distributing characteristic of hyperparameters. That is the optimal hyper-parameters usually form a neighborhood in which the evaluation function has an equal and optimal value. Because this distribution characteristic draws little attention previously, few people have given an appropriate method which can find all of the optimal hyper-parameters in each neighborhood. Indubitably, the grid search is an exhaustive search method which can find every optimal hyper-parameters points, but its efficiency of computing is too low. When the number of parameters is even a little large, the grid search will be computationally unfeasible. ES algorithm is efficient and has been successfully applied to optimize hyper-parameters. However, it will stop the searching process when the one optimal point is found. So it can only find single optimal point and can not find all the optimal points in neighborhoods. We propose a hybrid method to select the hyper-parameters based on the distributing characteristic of them, mentioned above. This method combines evolution strategies with a grid search to select the hyper-parameters, which is called ES-GS by us. The details of ES-GS are described as follows. We firstly find some optimal hyper-parameters points by ES. That takes full advantage of computing efficiency of ES. In the running process of ES, we make a

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timely record of evolution step size

σi

of every hyper-parameter. When the optimal

hyper-parameter points are found, we let its relevant step size be σ . After finding some optimal hyper-parameters points by ES, we start a grid search in the neighborhood of them. Each dimension (axis) of the grid relates to one of hyper*

parameters of SVM. The range of each dimension is twice the step size σ of ES and the *

centre of the grid is the optimal hyper-parameter points corresponding to σ which have been found by ES. The number of divisions, denoted by l, can be adjusted by a trade-off between the precision and computing quantity. For ensuring convergence, ES must have a precision control that means the search will stop when the present fitness is close enough with the previous fitness. Therefor, ES can not find all points in neighborhoods. This is why we carry out a grid search after ES. The grid search needs to be given a range for each dimension. We make use of the results of ES and let each range to be equal to twice its relevant step size. This range selection technique can not only make grid window most possibly lay over all optimal hyper-parameters points in the neighborhood, but also ensure the searching range not to be too large. The large range of grid search dimension results in much computing time. By the way, some authors firstly run a grid search and then execute ES [3] is in order to make ES have a more quickly searching. However, our scheme (ES-GS), running a grid search after ES, is order to find all the optimal points in neighborhoods. *

4 Experimental Results and Discussions 4.1 Datasets and Programs The goal of experiments in this section is to verify the validity of ES-GS, used to find the optimal hyper-parameters, which is proposed in this paper. For enhancing possibility of finding global optimal hyper-parameters, we select a ( µ , λ ) -ES and

set µ = 3 , λ = 3 and ρ = 3 . The recombination manner is intermediate recombination. For the number of divisions GS, l, is set to be 10. The IRIS dataset from the UCI repository [17] is selected as training data and testing data. For completing the experimental task, we only need to consider a binary classification problem. However, the IRIS dataset has three class labels. We modify the dataset as binary class datasets just like in [4], [9], [10]. The IRIS1v23 denote class 2 and class 3 are viewed as one class (class23) and we classify class1 and class23. Similarly, the IRIS2v13 and IRIS3v12 are the same as IRIS1v23. For fully proving that our method is in effect, we tested two SVMs with two different kernel functions, i.e., the polynomial kernel function SVM (P-SVM for short) and the Gaussian kernel function SVM (G-SVM). Their hyper-parameters respectively are (C , d ) and (C , σ ) . The program is written in matlab language and implemented on Matlab 7.0. We ran the experiments on a Pentium IV (2.4GHz) PC with 512MB RAM.

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4.2 Results and Discussions We train and test P-SVM and G-SVM by 10-fold cross-validation respectively on each modified IRIS dataset. Then the testing results were used as the fitness of ES. The table 1 shows the results of hyper-parameters optimization which is obtained by the ES. They are some unattached points. Table 1. The optimal hyper-parameters results of single ES P-SVM

SVM Dataset IRIS1v23

G-SVM

(C , d )

Fitness

(C , σ )

Fitness

(500, 5)

1.0000

(500, 10)

1.0000

IRIS2v13

(27, 7)

0.9200

(252, 6)

0.9533

IRIS3v12

(126, 2)

0.9533

(500, 11)

0.9600

The results of grid search, a group of hyper-parameters and its relevant fitness (correct classification rate), can build a database. For example, we selected one of results in table 1, P-SVM on IRIS2v13, to show its ES-GS optimization results in table 2. The values in brackets are (C , d , Fitness ) respectively. The points surrounded by dashed lines are optimal points of hyper-parameters of P-SVM. We can see they distribute in a neighborhood. From Table 2, we obtained sound confirmation of the distributing characteristics of hyper-parameters, which has been analyzed in section 3.1. Furthermore, this experiment also verified the ES-GS, proposed by us, can be competent for finding all the optimal hyper-parameters in a neighborhood. That is different from existed approaches which can find only some unattached optimization hyper-parameters points. Table 2. The optimal hyper-parameters results of ES-GS for P-SVM onIRIS2v13 Ă Ă Ă Ă Ă Ă Ă Ă Ă (15.7,3,90.7) (15.7,4,90.7) (15.7,5,91.3) (15.7,6,92.0) (15.7,7,92.0) (15.7,8,92.0) (15.7,9,92.0) (15.7,10,90.7) Ă Ă (18.2,3,90.0) (18.2,4,90.0) (18.2,5,92.0) (18.2,6,92.0) (18.2,7,92.0) (18.2,8,92.0) (18.2,9,91.3) (18.2,10,89.3) Ă Ă (20.7,3,90.0) (20.7,4,90.0) (20.7,5,92.0) (20.7,6,92.0) (20.7,7,92.0) (20.7,8,92.0) (20.7,9,90.7) (20.7,10,89.3) Ă Ă (23.2,3,89.3) (23.2,4,91.3) (23.2,5,92.0) (23.2,6,92.0) (23.2,7,92.0) (23.2,8,92.0) (23.2,9,89.3) (23.2,10,89.3) Ă Ă (25.7,3,90.0) (25.7,4,91.3) (25.7,5,92.0) (25.7,6,92.0) (25.7,7,92.0) (25.7,8,91.3) (25.7,9,89.3) (25.7,10,88.0) Ă Ă (28.3,3,90.0) (28.3,4,91.3) (28.3,5,92.0) (28.3,6,92.0) (28.3,7,92.0) (28.3,8,91.3) (28.3,9,89.3) (28.3,10,88.0) Ă Ă (30.8,3,90.7) (30.8,4,91.3) (30.8,5,92.0) (30.8,6,92.0) (30.8,7,92.0) (30.8,8,89.3) (30.8,9,89.3) (30.8,10,88.0) Ă Ă (33.3,3,90.7) (33.3,4,91.3) (33.3,5,92.0) (33.3,6,92.0) (33.3,7,92.0) (33.3,8,89.3) (33.3,9,88.7) (33.3,10,88.0) Ă Ă (35.8,3,90.7) (35.8,4,92.0) (35.8,5,92.0) (35.8,6,92.0) (35.8,7,91.3) (35.8,8,89.3) (35.8,9,88.0) (35.8,10,88.0) Ă Ă (38.3,3,90.7) (38.3,4,92.0) (38.3,5,92.0) (38.3,6,92.0) (38.3,7,91.3) (38.3,8,89.3) (38.3,9,88.0) (38.3,10,88.7) Ă Ă Ă Ă Ă Ă Ă Ă Ă

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5 Conclusions In this paper, we analyzed the distributing characteristic of hyper-parameters of SVM. The optimal hyper-parameters points of SVM are not unattached that means they form a neighborhood in which they have an equal criterion function value. Aiming at this characteristic, we proposed a hybrid method of combining evolution strategies with a grid search (ES-GS) and used this method to optimize the hyper-parameters for SVM. Our method is based on the following idea. The ES can only search some unattached points of hyper-parameters but has a high computing efficiency. Although GS can find allover the hyper-parameters, it will be computationally unfeasible when the variables are excessive or the variables have a large range. Our method presented in this work, ES-GS, can synthesize their advantages and escape from their drawbacks. The experiments have shown that ES-GS can quickly find all the optimal hyper-parameter points. Finally, we have to mention that the ES can not guarantee to find global optimization points of hyper-parameters. In theory, the global optimum is obtained when the number of generations goes to infinity. That is impossible in practice.

References 1. Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995) 2. Cortes, C., Vapnik, V.: Support Vector Network. Machine learning, 20 (1995) 273-297 3. Friedrichs, F., Igel, C.: Evolutionary Tuning of Multiple SVM Parameters. Neurocmputing, 64 (2005)107-177 4. Hsu, C., Chang, C., Lin, C.: A Practical Guide to Support Vector Classification, Department of Computer Science and Information Engineering, National Taiwai University (2003) 5. Chapelle, O., Vapnik, V., Bousquet, O., Mukherjee, S.: Choosing Multiple Parameters for Support Vector Machines. Machine Linearing, 46 (2002) 131-159 6. Chung, K.-M., Kao, W.-C., Sun, C.-L., Lin, C.-J.: Radius Margin Bounds for Support Vector Machines with RBF Kernel. Neurocmputing, 15 (2003) 2643-2681 7. Gold, C., Sollich, P.: Model Selection for Support Vector Machine Classification, Neurocomputing, 55 (2003) 221-249 8. Keerthi, S.-S.: Efficient Tuning of SVM Hyper-Parameters Using Radius/Margin Bound and Iterative Algorithms. IEEE Transactions on Neural Networks, 13 (2002) 1225-1229 9. Liu, S., Jia, C.-Y. Ma, H.: A New Weighted Support Vector Machine with GA-based Parameter Selection. Proc. the 4th Int’l Conf. on Machine Learning and Cybernetics(ICMLC’05), (Aug. 2005) 18-21 10. Sergio, A., Rojas, Delmiro, F.-R.: Adapting Multiple Kernel Parameters for Support Vector Machines Using Genetic Algorithms. Division of parasitology national institute for medical research London NW71AA, UK and department of computer science university college London 11. Hansen, N., Ostermeier, A.: Convergence Properties of Evolution Strategies with the Derandomized Covariance Matrix Adaptation: the (ȝ/ȝ,Ȝ)-CMA-ES. Proc. of the 5th European Congress on Intelligent Techniques and Soft Computing(EUFIT’97), (Sept. 1997), 650-654

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12. Hansen, N., Ostermeier, A.: Completely Deranomized Self-adaptation in Evolution Strategies. Evolutionary Computation, 9 (2001) 159-195 13. Cassabaum, M.-L., Waagen, D.-E., Rodriguez, J.-J., Schmitt, H.-A.: Unsupervised Optimization of Support Vector Machine Parameters, Automatic target recognition XIV, edited by Firooz A. Sadjadi, Proceedings of SPIE, 5426, 316-325 14. Imbault, F., Lebart, K.: A Stochastic Optimization Approach for Parameter Tuning of Support Vector Machine. Proc. the 17th Int’l conf. on Pattern Recognition (ICPR’04) 15. Nello, C., John S.-T.: An Introduction to Support Vector Machines and Other Kernelbased Learning Methods. Cambridge university Press.(2000) 16. Steve, R.-G.: Support Vector Machines for Classification and Regression, Faculty of engineering, science and mathematics school of electronics and computer science.(1998) 17. Blake, C.-L., Merz, C.-J.: UCI Repository of Machine Learning Databases. http://www.ics.uci.edu/~learn/MLRepository.html. (1998)

Prediction of Sinter Burn-Through Point Based on Support Vector Machines Xiaofeng Wu1,2, Minrui Fei1, Heshou Wang1,3, and Shuibo Zheng3 1

School of Mechatronical Engineering and Automation, Shanghai University, Shanghai 200072, China 2 Automation Department of Laiwu Steel Group, Laiwu 271104, China 3 Shanghai Fire Research Institute of Ministry of Public Security, Shanghai 200032, China [email protected]

Abstract. In order to overcome the long time delays and dynamic complexity in industrial sintering process, a modeling method of prediction of burn-through point (BTP) was proposed based on support vector machines (SVMs). The results indicate SVMs outperform the three-layer Backpropagation (BP) neural network in predicting burn-through point with better generalization performance, and are satisfactory. The model can be used as plant model for the burn-through point control of on-strand sinter machines.

1 Introduction The sintering process is a preprocess for blast-furnace materials. The quality of sinter is very important for smooth operation and high productivity of the blast furnace since it improves the permeability and reducibility of the burden material. The raw mix in the form of small pellets composed essentially of ore, coke and water, is loaded onto a moving strand and leveled to form a bed and also included in the raw mix are return fines: pieces of sinter which are returned for reprocessing because they are too small. The strand is constructed from metal and refractory links, allowing a large fan to suck air down through the bed to the wind boxes where the temperature of sucked air is measured, and the raw mix is fused to form a sinter. When the sinter reaches the end of the strand, it is crushed and products of acceptable size are brought to the blastfurnace, while the return fines are refed for reprocessing. For an optimal operation of the plant, the location along the stand where the sintering process is completed, the so-called burn-through point is important. It is characterized by the maximum of the exhaust gas temperature. The burn-through point is largely determined by the ignition temperature, the height of the bed and the strand speed [1]. Several successful attempts have been made to model the sintering process analytically [2, 3, 4]. The applicability of these models is limited by the fact that a large number of physical properties of the sinter material are

㧘

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 722 – 730, 2006. © Springer-Verlag Berlin Heidelberg 2006

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difficult to obtain. The existing mathematical models are, however, too complicated for control purposes. In this paper, the prediction model based on support vector machines for burnthrough point in the iron ore sintering process is built. The feasibility of applying SVMs to burn-through point modeling was investigated by comparing it with threelayer Backpropagation neural network.

2 Support Vector Regression Support vector machines [4] based on statistical learning theory (SLT), a new powerful learning machine, have up to date had a sound orientation towards realworld applications due to the industrial context. SVMs classifiers [4, 6, 7] became competitive with the best available systems for recognition tasks in a short period of time from initial work on OCR (optical character recognition). In regression [6, 8] and time series prediction applications [9], excellent performances were soon obtained. Given a data set {( x1 , y1 ), ( x2 , y2 )" ( xl , yl )}  & u \ , where Χ denotes the space of the input patterns and l is the total number of samples. A primal space is transformed into a high-dimensional feature space by a nonlinear map ĭ ( x ) = (φ1 ( x ), φ2 ( x ), , φn ( x ) ) . Approximating the data set with a nonlinear

function f ( x ) = ȦT ĭ ( x ) + b.

(1)

The coefficients Ȧ and b can be obtained by minimizing the regularized risk function

minmize

1 2

2

Ȧ + C Remp

Remp = The first term Ȧ

2

. 1 l L( yi , f ( xi )). ¦ l 1

(2)

is regularization term, i.e. confidence interval, which controls

the function capacity. The second term Remp is the empirical error measured by the loss function L( yi , f ( xi )) . The initial choice for loss function 4 is the ε -insensitive loss function

L( yi , xi ) = yi − f ( xi ) ε ,

(3)

Where ­° y − f ( xi ) − ε , yi − f ( xi ) ε = ® i °¯ 0,

yi − f ( xi ) ≥ ε otherwise.

.

(4)

Other loss functions include quadratic ε -insensitive loss, Huber’s loss and Laplacian loss. C is referred as the regularization constant. ε is called the tube size.

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Optimization problem (2) can be further transformed to the following primal objective function

Minimize

1 2

l

2

Ȧ + C ¦ (ξi + ξi* ) i =1

­ yi − ȦT ĭ( xi ) − b ≤ ε + ξi ° subject to ® ȦT ĭ( xi ) + b − yi ≤ ε + ξi* ° * ≥ 0, ¯ ξi , ξi

(5)

where ξ i , ξ i* are positive slack variables. C determines the trade-off between the flatness of f and the amount up to which deviations larger than ε are tolerated. A Lagrange function from the primal objective function and the corresponding constraints was constructed as follows:

L=

1 2

2

l

l

i =1

i =1

Ȧ + C ¦ (ξi + ξi* ) − ¦α i (ε + ξi − yi + ȦT ĭ( xi ) + b) l

l

i =1

i =1

.

(6)

− ¦ αi* (ε + ξi* + yi − ȦT ĭ( xi ) − b) − ¦ (ηiξi + ηi*ξi* ). This Lagrange function has a saddle point with respect to the primal and the dual variables at the optimal solution. The dual variables in Eq.(6) satisfy positive constraints, i.e. α i , α i* ,ηi ,ηi* ≥ 0 . By means of Karush-Kuhn-Tucker (KKT) conditions, we obtain

­ ∂L ° ∂Ȧ ° ° ∂L ° ° ∂b ® ° ∂L ° ∂ξi ° ° ∂L °¯ ∂ξi*

l

= Ȧ − ¦ (α i − α i* )ĭ( xi ) = 0 i =1

l

= ¦ (α i − α i* )

=0

= C − α i − ηi

=0

= C − α i* − ηi*

= 0.

i =1

.

(7)

Based on Mercer condition, we have a kernel function K such that K ( xi , x j ) = ĭ ( xi )T ĭ ( x j ) . Thus SVMs avoid computing explicitly the map ĭ( x) and exploit the kernel function instead. Any function which satisfiers Mercer condition can be used as kernel function. Utilizing Eq.(7) to eliminate the primal variables (Ȧ, b, ξi , ξi* ) in (6), we can obtain the Wolfe dual optimization problem:

Prediction of Sinter Burn-Through Point Based on Support Vector Machines

­ 1 l * * ° - 2 ¦ (α i − α i )(α j − α j ) K ( xi , x j ) ° i , j =1 Maximize ® l l ° − ε (α + α * ) + y (α − α * ) ¦ ¦ i i i i i °¯ . i =1 i =1 ­ ° subject to ® ° ¯

l

¦ (α

i

725

(8)

− α i* ) = 0

i =1

0 ≤ α i , α i* ≤ C.

By solving quadratic program (8), regression function (1) is rewritten as: l

f ( x ) = ¦ (α i − α i* ) K ( xi , x ) + b,

(9)

i =1

where α i , α i * satisfy α i × α i * = 0, α i ≥ 0, α i * ≥ 0 . Only a number of coefficients (α i − α i * ) are nonzero values, and the corresponding training data points have approximation errors equal to or larger than ε . They are called support vectors. Various kernels can be used as follows: (1) Linear Kernel: K ( x , xi ) = xT xi || x − xi ||2 ) 2σ 2 (3) Polynomial Kernel: K ( x , xi ) = ((γ xT xi ) + r )d , d = 1, 2, , N .

(2) RBF Kernel: K ( x, xi ) = exp(−

Here, σ , γ , r and d are kernel parameters.

3 Experimental Methodology 3.1 Data Processing

(1) Data Preprocessing The set of measured data used is from Lai Gang No.2 265 m2 Sinter plant with 27 wind boxes. The desired value of BTP is the location of the 25th wind box. BTP can not be directly measured in sintering process. It is estimated by the three measurement points ( x1 , T1 ), ( x2 , T2 ), ( x3 , T3 ) of the exhaust gas temperature towards the end of the strand. ( x2 , T2 ) is the highest exhaust gas temperature measurement point. The three points is applied to fit quadratic curve Tgas = Ax 2 + Bx + C . The maximum value x0 = − B / 2 A is used for the estimation of BTP. Scaling training data before applying SVMs is very important. The signals are likely to be measured in different physical units. These attributes in greater numeric ranges dominate those in smaller numeric ranges. Each attribute is recommended to linearly scale to the range [-1, 1] or [0, 1].

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Suppose to scale a certain attribute of training data set from ' min

[ ymin

ymax ] to

' max

ª¬ y y º¼ . y is the raw attribute value of training data or test data. The scaled value is obtained by ' y ' = ymin +

' ' ymax − ymin ( y − ymin ) . ymax − ymin

(10)

(2) Data Postprocessing Each output value yp of SVMs should be converted to its original unit by yraw_p = ymin +

ymax − ymin ' ( y p − ymin ). ' ' ymax − ymin

(11)

3.2 Performance Criteria

The learning and generalization prediction performance is evaluated using the following statistical metrics, namely, the learning mean squared error (LMSE) and generalized mean squared error (GMSE). MSE =

1 n ¦ ( yi − yˆi )2 . n i =1

(12)

n is the total sample number, y and yˆ i represent measured and estimated values respectively. LMSE is MSE on the training set and GMSE is the criteria on the test set. 3.3 Running Environment

SMO [10] for solving regression problem is implemented in this experiment and the program is developed using the VC++ language. The source files is compiled as Mexfile in Matlab. A three-layer BP neural network is used as a benchmark. There are three nodes in the input layer. The number of output node is equal to 1. The number of hidden nodes is determined based on the experimental results. Bayesian Regulation backpropagation [11] is used as network training function. The transfer function of the hidden layer is a tangent sigmoid function and a linear transfer function in the output layer is used. The BP software used directly from Matlab 6.1 neural network toolbox version 4.0.1.

4 Using SVMs and BP for BTP Prediction BTP prediction model has 3 inputs and 1 output. The three inputs are bed height h , ignition temperature T and strand velocity v . The output is BTP. The structure of BTP prediction model is shown in Fig. 1.

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h

T

v Fig. 1. The structure of BTP prediction model

The training set is 152 samples and 70 samples are used as the test set, which are shown in Fig. 2. Few training and test data can demonstrate better learning ability of SVMs. We choose RBF kernel with width σ =1.7, the loss function with ε =0.001 and regularization constant C =100 in SVMs. The number of hidden nodes in the BP network is 9. The number of support vector for training is 115. The results on the training and test are given in Table 1. The results of BP and SVMs model approximation to BTP

Fig. 2. Measurement points of three input quantity

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LMSE GMSE

SVMs 0.000108 0.000275

BP 0.000007 0.001506

(a) training set

(b) test set Fig. 3. BP prediction model approximation to BTP

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(a) training set

(b) test set Fig. 4. SVMs prediction model approximation to BTP

are shown in Fig. 3 and Fig. 4, respectively. Fig. 3 (b) and Fig. 4 (b) show theprediction abilities of the BP and SVMs using a set of measured data which had not been used during the training. It can be seen better generalization performance can

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be achieved via SVMs than the BP. This indicates SVMs has better generalization capability to prevent the overfitting problem. The SVMs prediction model is capable of predicting BTP with good accuracy.

5 Conclusion This paper presents a new prediction model of burn-through point in the sintering process based on support vector machines. SVMs require only small amount of training samples to obtain better generalization performance than the BP network. Support vector machines provide an effective prediction method for BTP with proper accuracy. The prediction model of BTP is to be further investigated as control model for the BTP control system in the sintering process.

Acknowledgement This work was supported by Doctoral Program Foundation of Science & Technology Special Project in University (20040280017), Key Project of Science & Technology Commission of Shanghai Municipality under grant 04JC14038, and Shanghai Leading Academic Disciplines (T0103).

References 1. Hu, J. Q., Rose, E.: Simulation of an Iiron Ore Sintering Plant. Research Report No.488. Department of Automatic Control and Systems Engineering, University of Sheffield, England (1993) 2. Young, R. W.: Dynamic Model of Sintering Process. Ironmaking and Steelmaking, 5 (1979) 25-31 3. Rose, E., Anderson, W. R. M., Orak, M.: Simulation of Sintering, IFAC World Congr., 10, (1993) 289-194 4. Augustin, M., Arbeithuber, C., JORGL, H. P.: Modeling and Simulation of an Iron Ore Sinter Strand. Proc. EUROSIM Congress '95, Sept. 11-15, Vienna, Austria (1995) 5. Vapnik, V. N.: The Nature of Statistical Leaning Theory. Springer-Verlag, New York (1995) 6. Vapnik, V. N.: Statistical Learning Theory. John Wiley & Sons, New York (1998) 7. Schölkopf, B.: Learning with Kernels. Ph. D. Thesis. Universität Tübingen, (1997) 8. Smola, A. J., Schölkopf, B.: A Tutorial on Support Vector Regression. NeuroCOLT2 Technical Report Series. UK: University of London, London (1998) 9. Müller, K. R., Smola, A. J., Rätsh, G.: Using Support Vector Machines for Time Series Prediction. Advances in Kernel Methods. Cambridge, MIT Press, MA (1998) 185–208 10. Platt, J. C.: Fast Training of SVMs Using Sequential Minimal Optimization. Schölkopf, B., Burges, C. J. C, Smola, A. J. Advances in Kernel Methods-Support Vector Learning. Cambridge, MIT Press, MA (1998) 185–208 11. Foresee, F. D., Hagan, M. T.: Gauss-Newton Approximation to Bayesian Regularization. Proceedings of the International Joint Conference on Neural Networks, Canada (1997)

Under-Sampling Approaches for Improving Prediction of the Minority Class in an Imbalanced Dataset Show-Jane Yen and Yue-Shi Lee Department of Computer Science and Information Engineering, Ming Chuan University 5 The-Ming Rd., Gwei Shan District, Taoyuan County 333, Taiwan {sjyen, leeys}@mcu.edu.tw

Abstract. The most important factor of classification for improving classification accuracy is the training data. However, the data in real-world applications often are imbalanced class distribution, that is, most of the data are in majority class and little data are in minority class. In this case, if all the data are used to be the training data, the classifier tends to predict that most of the incoming data belong to the majority class. Hence, it is important to select the suitable training data for classification in the imbalanced class distribution problem. In this paper, we propose cluster-based under-sampling approaches for selecting the representative data as training data to improve the classification accuracy for minority class in the imbalanced class distribution problem. The experimental results show that our cluster-based under-sampling approaches outperform the other under-sampling techniques in the previous studies.

1 Introduction Classification Analysis [5, 7] is a well-studied technique in data mining and machine learning domains. Due to the forecasting characteristic of classification, it has been used in a lot of real applications, such as flow-away customers and credit card fraud detections in finance corporations. Classification analysis can produce a class predicting system (or called a classifier) by analyzing the properties of a dataset having classes. The classifier can make class forecasts on new samples with unknown class labels. For example, a medical officer can use medical predicting system to predict if a patient have drug allergy or not. A dataset with given class can be used to be a training dataset, and a classifier must be trained by a training dataset to have the capability for class prediction. In brief, the process of classification analysis is included in the follow steps: 1. Sample collection. 2. Select samples and attributes for training. 3. Train a class predicting system using training samples. 4. Use the predicting system to forecast the class of incoming samples. The classification techniques usually assume that the training samples are uniformly-distributed between different classes. A classifier performs well when the classification technique is applied to a dataset evenly distributed among different D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 731 – 740, 2006. © Springer-Verlag Berlin Heidelberg 2006

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classes. However, many datasets in real applications involve imbalanced class distribution problem [9, 11]. The imbalanced class distribution problem occurs while there are much more samples in one class than the other class in a training dataset. In an imbalanced dataset, the majority class has a large percent of all the samples, while the samples in minority class just occupy a small part of all the samples. In this case, a classifier usually tends to predict that samples have the majority class and completely ignore the minority class. Many applications such as fraud detection, intrusion prevention, risk management, medical research often have the imbalanced class distribution problem. For example, a bank would like to construct a classifier to predict that whether the customers will have fiduciary loans in the future or not. The number of customers who have had fiduciary loans is only two percent of all customers. If a fiduciary loan classifier predicts that all the customers never have fiduciary loans, it will have a quite high accuracy as 98 percent. However, the classifier can not find the target people who will have fiduciary loans within all customers. Therefore, if a classifier can make correct prediction on the minority class efficiently, it will be useful to help corporations make a proper policy and save a lot of cost. In this paper, we study the effects of undersampling [1, 6, 10] on the backpropagation neural network technique and propose some new under-sampling approaches based on clustering, such that the influence of imbalanced class distribution can be decreased and the accuracy of predicting the minority class can be increased.

2 Related Work Since many real applications have the imbalanced class distribution problem, researchers have proposed several methods to solve this problem. As for re-sampling approach, it can be distinguished into over-sampling approach [4, 9] and undersampling approach [10, 11]. The over-sampling approach increases the number of minority class samples to reduce the degree of imbalanced distribution. One of the famous over-sampling approaches is SMOTE [2]. SMOTE produces synthetic minority class samples by selecting some of the nearest minority neighbors of a minority sample which is named S, and generates new minority class samples along the lines between S and each nearest minority neighbor. SMOTE beats the random oversampling approaches by its informed properties, and reduce the imbalanced class distribution without causing overfitting. However, SMOTE blindly generate synthetic minority class samples without considering majority class samples and may cause overgeneralization. On the other hand, since there are much more samples of one class than the other class in the imbalanced class distribution problem, under-sampling approach is supposed to reduce the number of samples which have the majority class. Assume in a training dataset, MA is the sample set which has the majority class, and MI is the other set which has the minority class. Hence, an under-sampling approach is to decrease the skewed distribution of MA and MI by lowering the size of MA. Generally, the performances of under-sampling approaches are worse than that of undersampling approaches.

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One simple method of under-sampling is to select a subset of MA randomly and then combine them with MI as a training set, which is called random under-sampling approach. Several advanced researches are proposed to make the selective samples more representative. The under-sampling approach based on distance [11] uses distinct modes: the nearest, the farthest, the average nearest, and the average farthest distances between MI and MA, as four standards to select the representative samples from MA. For every minority class sample in the dataset, the first method “nearest” calculates the distances between all majority class samples and the minority class samples, and selects k majority class samples which have the smallest distances to the minority class sample. If there are n minority class samples in the dataset, the “nearest” approach would finally select k× n majority class samples (k ≥ 1). However, some samples within the selected majority class samples might duplicate. Similar to the “nearest” approach, the ”farthest” approach selects the majority class samples which have the farthest distances to each minority class samples. For every majority class samples in the dataset, the third method “average nearest” calculates the average distance between one majority class sample and all minority class samples. This approach selects the majority class samples which have the smallest average distances. The last method “average farthest” is similar to the “average nearest” approach; it selects the majority class samples which have the farthest average distances with all the minority class samples. The above under-sampling approaches based on distance in [11] spend a lot of time selecting the majority class samples in the large dataset, and they are not efficient in real applications. In 2003, J. Zhang and I. Mani [10] presented the compared results within four informed under-sampling approaches and random under-sampling approach. The first method “NearMiss-1” selects the majority class samples which are close to some minority class samples. In this method, majority class samples are selected while their average distances to three closest minority class samples are the smallest. The second method “NearMiss-2” selects the majority class samples while their average distances to three farthest minority class samples are the smallest. The third method “NearMiss3” take out a given number of the closest majority class samples for each minority class sample. Finally, the fourth method “Most distant” selects the majority class samples whose average distances to the three closest minority class samples are the largest. The final experimental results in [10] showed that the NearMiss-2 approach and random under-sampling approach perform the best.

3 Our Approaches In this section, we present our approach SBC (under-Sampling Based on Clustering) which focuses on the under-sampling approach and uses clustering techniques to solve the imbalanced class distribution problem. Our approach first clusters all the training samples into some clusters. The main idea is that there are different clusters in a dataset, and each cluster seems to have distinct characteristics. If a cluster has more majority class samples and less minority class samples, it will behave like the majority class samples. On the opposite, if a cluster has more minority class samples and less majority class samples, it doesn’t hold the characteristics of the majority class samples and behaves more like the minority class samples. Therefore, our

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approach SBC selects a suitable number of majority class samples from each cluster by considering the ratio of the number of majority class samples to the number of minority class samples in the cluster. 3.1 Under-Sampling Based on Clustering Assume that the number of samples in the class-imbalanced dataset is N, which includes majority class samples (MA) and minority class samples (MI). The size of the dataset is the number of the samples in this dataset. The size of MA is represented as SizeMA, and SizeMI is the number of samples in MI. In the class-imbalanced dataset, SizeMA is far larger than SizeMI. For our under-sampling method SBC, we first cluster all samples in the dataset into K clusters. The number of majority class samples and i the number of minority class samples in the ith cluster (1ูiูK) are SizeMA and i SizeMI , respectively. Therefore, the ratio of the number of majority class samples to i i the number of minority class samples in the ith cluster is SizeMA / SizeMI . If the ratio of SizeMA to SizeMI in the training dataset is set to be m:1, the number of selected majority class samples in the ith cluster is shown in expression (1): i Size MA i SSize MA = (m × SizeMI ) ×

K

¦

i Size MI

i Size MA

i =1

(1)

i Size MI

In expression (1), m × SizeMI is the total number of selected majority class samples K

i

that we suppose to have in the final training dataset. ¦ SizeMA i =1

i SizeMI

is the total ratio of

the number of majority class samples to the number of minority class samples in all clusters. expression (1) determines that more majority class samples would be selected in the cluster which behaves more like the majority class samples. In other i is larger while the ith cluster has more majority class samples and words, SSizeMA less minority class samples. After determining the number of majority class samples

which are selected in the ith cluster, 1ูiูK, by using expression (1), we randomly choose majority class samples in the ith cluster. The total number of selected majority class samples is m× SizeMI after merging all the selected majority class samples in each cluster. At last, we combine the whole minority class samples with the selected majority class samples to construct a new training dataset. Table 1 shows the steps for our under-sampling approach. For example, assume that an imbalanced class distribution dataset has totally 1100 samples. The size of MA is 1000 and the size of MI is 100. In this example, we cluster this dataset into three clusters. Table 2 shows the number of majority class samples i i i Size MA , the number of minority class samples SizeMI , and the ratio of Size MA to i SizeMI for the ith cluster.

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Table 1. The structure of the under-sampling based on clustering approach SBC

Step1. Step2. Step3.

Step4.

Determine the ratio of SizeMA to SizeMI in the training dataset. Cluster all the samples in the dataset into some clusters. Determine the number of selected majority class samples in each cluster by using expression (1), and then randomly select the majority class samples in each cluster. Combine the selected majority class samples and all the minority class samples to obtain the training dataset. Table 2. Cluster descriptions

Cluster ID 1 2 3

Number of majority class samples 500 300 200

Number of minority class samples 10 50 40

i i SizeMA / SizeMI

500/10=50 300/50=6 200/40=5

Assume that the ratio of SizeMA to SizeMI in the training data is set to be 1:1, in other words, there are 100 selected majority class samples and the whole 100 minority class samples in this training dataset. The number of selected majority class samples in each cluster can be calculated by expression (1). Table 3 shows thenumber of selected majority class samples in each cluster. We finally select the majority samples randomly from each cluster and combine them with the minority samples to form the new dataset. Table 3. The number of selected majority class samples in each cluster

Cluster ID 1 2 3

The number of selected majority class samples 1×100× 50 / (50+6+5) =82 1×100× 6 / (50+6+5) = 10 1×100× 5 / (50+6+5)= 8

3.2 Under-Sampling Based on Clustering and Distances

In SBC method, all the samples are clustered into several clusters and the number of selected majority class samples is determined by expression (1). Finally, the majority class samples are randomly selected from each cluster. In this section, we propose other five under-sampling methods, which are based on SBC approach. The difference between the five proposed under-sampling methods and SBC method is the way to select the majority class samples from each cluster. For the five proposed methods, the majority class samples are selected according to the distances between the majority class samples and the minority class samples in each cluster. Hence, the distances

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between samples will be computed. For a continuous attribute, the values of all samples for this attribute need to be normalized in order to avoid the effect of different scales for different attributes. For example, suppose A is a continuous attribute. In order to normalize the values of attribute A for all the samples, we first find the maximum value MaxA and the minimum value MinA of A for all samples. To lie an attribute value ai in between 0 to 1, ai is normalized to

ai − MinA MaxA − MinA

. For a categorical

or discrete attribute, the distance between two attribute values x1 and x2 is 0 (i.e. x1x2=0) while x1 is not equal to x2, and the distance is 1 (i.e. x1-x2=1) while they are the same. Assume that there are N attributes in a dataset and Vi

X

represents the value of at-

tribute Ai in sample X, for 1ูiูN. The Euclidean distance between two samples X and Y is shown in expression (2). distance( X , Y ) =

N

¦ (Vi

i =1

X

− ViY ) 2

(2)

The five approaches we proposed in this section first cluster all samples into K (K • 1) clusters as well, and determine the number of selected majority class samples for each cluster by expression (1). For each cluster, the representative majority class samples are selected in different ways. The first method SBCNM-1 (Sampling Based on Clustering with NearMisss-1) selects the majority class samples whose average distances to M nearest minority class samples (M • 1) in the ith cluster (1ูiูK) are the smallest. In the second method SBCNM-2 (Sampling Based on Clustering with NearMisss-2), the majority class samples whose average distances to M farthest minority class samples in the ith cluster are the smallest will be selected. The third method SBCNM-3 (Sampling Based on Clustering with NearMisss-3) selects the majority class samples whose average distances to the closest minority class samples in the ith cluster are the smallest. In the forth method SBCMD (Sampling Based on Clustering with Most Distant), the majority class samples whose average distances to M closest minority class samples in the ith cluster are the farthest will be selected. For the above four approaches, we refer to [10] for selecting the representative samples in each cluster. The last proposed method, which is called SBCMF (Sampling Based on Clustering with Most Far), selects the majority class samples whose average distances to all minority class samples in the cluster are the farthest.

4 Experimental Results For our experiments, we use three criteria to evaluate the classification accuracy for minority class: the precision rate P, the recall rate R, and the F-measure for minority class. Generally, for a classifier, if the precision rate is high, then the recall rate will be low, that is, the two criteria are trade-off. We cannot use one of the two criteria

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to evaluate the performance of a classifier. Hence, the precision rate and recall rate are combined to form another criterion F-measure, which is shown in expression (3). MI’s F-measure =

2× P× R P+R

(3)

In the following, we use the three criteria discussed above to evaluate the performance of our approaches SBC, SBCNM-1, SBCNM-2, SBCNM-3, SBCMD, and SBCMF by comparing our methods with the other methods AT, RT, and NearMiss-2. The method AT uses all samples to train the classifiers and does not select samples. RT is the most common-used random under-sampling approach and it selects the majority class samples randomly. The last method NearMiss-2 is proposed by J. Zhang and I. Mani [10], which has been discussed in section 2. The two methods RT and NearMiss-2 have the better performance than the other proposed methods in [10]. In the following experiments, the classifiers are constructed by using the artificial neural network technique in IBM Intelligent Miner for Data V8.1. Table 4. The experimental results on Census-Income Database

Method

MI’s Precision

MI’s Recall

MI’s F-measure

MA’s Precision

MA’s Recall

MA’s F-measure

SBC RT AT NearMiss-2 SBCNM-1 SBCNM-2 SBCNM-3 SBCMD SBCMF

47.78 30.29 35.1 46.3 29.28 29.6 28.72 29.01 43.15

88.88 99.73 98.7 81.23 99.80 99.67 99.8 99.73 93.48

62.15 46.47 51.9 58.98 45.28 45.64 44.61 44.94 59.04

94.84 99.63 98.9 91.70 99.67 99.49 99.63 99.54 96.47

67.79 23.92 39.5 68.77 20.07 21.39 17.9 19.05 59.15

79.06 38.58 43.8 78.60 33.41 35.21 30.35 31.99 73.34

We compare our approaches with the other under-sampling approaches in two real datasets. One of the real datasets is named Census-Income Database, which is from UCI Knowledge Discovery in Databases Archive. Census-Income Database contains census data which are extracted from the 1994 and 1995 current population surveys managed by the U.S. Census Bureau. The binary classification problem in this dataset is to determine the income level for each person represented by the record. The total number of samples after cleaning the incomplete data is 30162, including 22654 majority class samples which the income level are less than 50K dollars and 7508 minority class samples which the income level are greater than or equal to 50K dollars. We use eighty percent of the samples to train the classifiers and twenty percent to evaluate the performances of the classifiers. The precision rate, recall rate, and F-measure for our approaches and the other approaches are shown in Table 4. Fig 1 shows

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N M -1 SB C N M -2 SB C N M -3 SB C M D SB C M F

SB C

iss -2

T A N ea

rM

RT

200 180 160 140 120 100 80 60 40 20 0 SB C

Execution time (min.)

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M ethods

Fig. 1. The execution time on Census-Income Database for each method

the execution time for each method, which includes selecting the training data and training the classifier. In Table 4, we can observe that our method SBC has the highest MI’s F-measure and MA’s F-measure while comparing with other methods. Besides, SBC only need to take a short execution time which is shown in Fig 1. The other real dataset in our experiment is conducted by a bank and is called Overdue Detection Database. The records in Overdue Detection Database contain the information of customers, the statuses of customers’ payment, the amount of money in customers’ bills, and so on. The purpose of this binary classification problem is to detect the bad customers. The bad customers are the minorities within all customers and they do not pay their bills before the deadline. We separate Overdue Detection Database into two subsets. The dataset extracted from November in 2004 are used for training the classifier and the dataset extracted from December in 2004 are used for testing task. The total number of samples in the training data of Overdue Detection Database is 62309, including 47707 majority class samples which represent the good customers and 14602 minority class samples which represent the bad customers. The total number of samples in the testing data of Overdue Detection Database is 63532, including 49931 majority class samples and 13601 minority class samples. Fig 2 shows the precision rate, the recall rate and the F-measure of minority class for each approach. From Fig 2, we can see that our approaches SBC and SBCMD have the best MI’s F-measure. Fig 3 shows the execution times for all the approaches in Overdue Detection Database. In the two real applications which involve the imbalanced class distribution problem, our approach SBC has the best performances on predicting the minority class samples. Moreover, SBC takes less time for selecting the training samples than the other approaches NearMiss-2, SBCNM-1, SBCNM-2, SBCNM-3, SBCMD, and SBCMF.

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F

D

M SB C

M SB C

N M -3

N M -2

SB C

SB C

N M -1

SB C

iss -2

T N ea

rM

A

RT

200 180 160 140 120 100 80 60 40 20 0 SB C

Execution time (min.)

Fig. 2. The Experimental Results on Overdue Detection Database

Methods

Fig. 3. Execution time on Overdue Detection Database for each method

5 Conclusion In a classification task, the effect of imbalanced class distribution problem is often ignored. Many studies [3, 7] focused on improving the classification accuracy but did not consider the imbalanced class distribution problem. Hence, the classifiers which are constructed by these studies lose the ability to correctly predict the correct deci-

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sion class for the minority class samples in the datasets which the number of majority class samples are much greater than the number of minority class samples. Many real applications, like rarely-seen disease investigation, credit card fraud detection, and internet intrusion detection always involve the imbalanced class distribution problem. It is hard to make right predictions on the customers or patients who that we are interested in. In this study, we propose cluster-based under-sampling approaches to solve the imbalanced class distribution problem by using backpropagation neural network. The other two under-sampling methods, Random selection and NearMiss-2, are used to be compared with our approaches in our performance studies. In the experiments, our approach SBC has better prediction accuracy and stability than other methods. SBC not only has high classification accuracy on predicting the minority class samples but also has fast execution time. However, SBCNM-1, SBCNM-2, SBCNM-3, and SBCMF do not have stable performances in our experiments. The four methods take more time than SBC on selecting the majority class samples as well.

References 1. Chawla, N. V.: C4.5 and Imbalanced Datasets: Investigating the Effect of Sampling Method, Probabilistic Estimate, and Decision Tree Structure. Proceedings of the ICML’03 Workshop on Class Imbalances, (2003) 2. Chawla, N. V., Bowyer, K.W., Hall, L. O., Kegelmeyer, W. P.: SMOTE: Synthetic Minority Over-Sampling Technique. Journal of Artificial Intelligence Research, 16 (2002) 321– 357 3. Caragea, D., Cook, D., Honavar, V.: Gaining Insights into Support Vector Machine Pattern Classifiers Using Projection-Based Tour Methods. Proceedings of the KDD Conference, San Francisco, CA (2001) 251-256 4. Chawla, N. V., Lazarevic, A., Hall, L. O., Bowyer, K. W.: Smoteboost: Improving Prediction of the Minority Class in Boosting. Proceedings of the Seventh European Conference on Principles and Practice of Knowledge Discovery in Databases, Dubrovnik, Croatia (2003) 107-119 5. Clark, P., Niblett, T.: The CN2 Induction Algorithm. Machine Learning, 3 (1989) 261-283 6. Drummond, C., Holte, R. C.: C4.5, Class Imbalance, and Cost Sensitivity: Why UnderSampling Beats Over-Sampling. Proceedings of the ICML’03 Workshop on Learning from Imbalanced Datasets, (2003) 7. Del-Hoyo, R., Buldain, D., Marco, A.: Supervised Classification with Associative SOM. Lecture Notes in Computer Science, 2686 (2003) 334-341 8. Japkowicz, N.: Concept-learning in the Presence of Between-class and Within-class Imbalances. Proceedings of the Fourteenth Conference of the Canadian Society for Computational Studies of Intelligence, (2001) 67-77 9. Zhang, J., Mani, I.: KNN Approach to Unbalanced Data Distributions: A Case Study Involving Information Extraction. Proceedings of the ICML’2003 Workshop on Learning from Imbalanced Datasets, (2003). 10. Chyi, Y. M.: Classification Analysis Techniques for Skewed Class Distribution Problems. Master Thesis, Department of Information Management, National Sun Yat-Sen University, (2003)

Utilizing a Hierarchical Method to Deal with Uncertainty in Context-Aware Systems Donghai Guan, Weiwei Yuan, Mohammad A.U. Khan, Youngkoo Lee*, Sungy-oung Lee, and Sangman Han Department of Computer Engineering Kyung Hee University, Korea {donghai, weiwei, khan, sylee, i30000}@oslab.khu.ac.kr, [email protected]

Abstract. In context-aware systems, one of the main challenges is how to model context uncertainty well, since perceived context always yields uncertainty and ambiguity with consequential effect on the performance of contextaware system. To handle uncertainty in context-aware systems, firstly, we should know from where uncertainty comes. In this paper, we argue that uncertainty comes from several sources for each context level in context-aware systems. Based on this argument, we propose a hierarchical method to deal with context uncertainty in different levels, with the aim of reducing uncertainty and, developing a pattern to better understand this uncertainty. This will, in turn, helps in improving the system’s reliability.

1 Introduction Context plays an important role in ubiquitous computing systems. A lot of work has been done in trying to develop applications in ubiquitous computing environments context aware [1] [2] [3] [4] [5] [6]. One of the main challenges in context-aware systems is how to tackle context uncertainty well, since perceived context always yields uncertainty and ambiguity with consequential effect on the performance of context-aware systems [7] [8]. To handle context uncertainty well, first, we need to get the knowledge about the origins of uncertainty. Fig. 1 shows typical information flow in a context-aware ubiquitous system. In this architecture, we argue that information flow from lower level to higher level will inevitably generate uncertainty so that we should analyze it in different phases: Phase 1: Raw sensor data to low-level context (S-LC) The main factor that promotes uncertainty in S-LC is the often inherent inaccuracy and unreliability of many types of low-level sensors, which may lead to contradicting or substantially different reasoning about low-level context. In this phase, we propose to apply Dempster-Shafer Evidence Theory to handle uncertainty. „

*

Prof. Youngkoo Lee is the corresponding author.

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 741 – 746, 2006. © Springer-Verlag Berlin Heidelberg 2006

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Phase 2: Low-level context to high-level context (LC-HC) This phase is always referred to “Context Aggregator” or “Context Synthesizer”. In this phase, reasoning is always in the uncertain conditions. In this regard, we propose to use Bayesian Networks to infer high-level context. „

Fig. 1. Information flow in context-aware systems

2 S-LC Uncertainty Sensor’s inherent uncertainty is the main source of this phase’s uncertainty. To handle this problem, sensor redundancy is usually applied. Sensor redundancy could improve system’s reliability, however, at the same time, it always generates sensor competition problem [9]. Sensor competition means the results of sensors representing the same measurement are competitive. Let us consider the following scenario: The sensors here are three RFIDs (A, B and C). The output of each RFID is a Boolean variable (true or false). True means a user (Bob) is in room, while, false means it isn’t. Suppose the three RFIDs’ outputs are different. Two RFIDs shows that Bob is room, while, another one shows Bob is not in room. This is a typical sensor competition problem. In the following part, we will describe how to solve it. 2.1 Dumpster-Shafer Theory The advantage of Dempster-Shafer theory is that it can work well even in the case of lack of knowledge of the complete probabilistic model required for other methods such as Bayesian inference. The Dempster-Shafer theory of evidence represents uncertainty in the form of belief functions. It is based on two ideas: the idea of obtaining degrees of belief for one question from subjective probabilities for a related question, and Dempster’s rule for combining such degrees of belief when they are based on independent items of evidence [10]. Dempster-Shafer theory starts by assuming a universe of discourse, also called a frame of discernment, which is a set of mutually exclusive alternatives (similar to a state space in probability), denoted by Ω . Any hypothesis A will refer to a subset of Ω for which observers can present evidence. The set of all possible subsets of Ω ,

Utilizing a Hierarchical Method to Deal with Uncertainty in Context-Aware Systems

including itself and the null set ∅ , is called a power set and designated as the power set consists of all possible hypothesis

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2Ω . Thus,

2Ω ={ A1 , Ω , An }.

We can assign hypothesis to any of the three types of values. Basic probability numbers are a mapping of each hypothesis A to a value m(A) between 0 and 1, such that z

the basic probability number of the null set ∅ is

z

the sum

m(∅) =0, and

m( A1 ) + … + m( An ) =1.

The second type of assignment is a belief function that maps each hypothesis B to a value bel(B), between 0 and 1, define as

bel ( B) =

¦

m( Aj )

j: A j ⊂ B

(1)

The belief function represents the weight of evidence supporting B’s provability. The third type of assignment is a plausibility function that maps each hypothesis B to a value pls(B) between 0 and 1, defined as

pls ( B) =

¦

m( A j )

j: A j ∩ B ≠∅

(2)

The plausibility function is the weight of evidence that doesn’t refute B, and belief and plausibility are related by

pls ( B ) = 1 − bel ( B )

(3)

Where B is the hypothesis “not B”. Shafer showed that a one-to-one correspondence exists between basic probability numbers, belief, and plausibility, meaning that any of the three functions is sufficient for deriving the other two. Dempster’s Rule for combination is a procedure for combining independent pieces of evidence. Suppose m1 ( A) and m2 ( A) are the basic probability numbers from two independent observers. Dempster’s rule for combination consists of the orthogonal sum

m( B) = m1 ( B) ⊕ m2 ( B) =

¦

m1 ( Ai )m2 ( Aj )

¦

m1 ( Ai )m2 ( Aj )

i , j : Ai ∩ A j = B

(4)

i , j: Ai ∩ A j =∅

We can combine more than two belief functions pairwise in any order. 2.2 Using Dempster-Shafer Theory in Our Scenario

Ω = {T , T } , where T means Bob is in room, and T is the compliment event meaning Bob is not in the room. For this Ω , the power set has three

In our scenario,

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elements: hypothesis H={T} that Bob is in room; hypothesis H={ T } that Bob is not; and hypothesis U= Ω that Bob is in room or not. Suppose the probability of RFID A being trustworthy is α . If RFID A claims that Bob is in room, then its basic probability assignment will be

m1 ( H ) = α m1 ( H ) = 0

m1 (U ) = 1 − α

(5)

If RFID A claims that Bob in not in room, its basic probability assignment will be

m1 ( H ) = 0 m1 ( H ) = α m1 (U ) = 1 − α

(6)

Likewise, given prior probabilities for the trustworthiness of RFID B and C, we would construct their basic probability assignments m2 and m3 similarly. Next, the combined belief of A, B, and C in H is

bel ( H ) = m( H ) = m1 ( H ) ⊕ m2 ( H ) ⊕ m3 ( H )

(7)

Following Dempster’s rule for combination (Equation 4), We can compute this by combining any pair of arguments and then combining the result with the remaining third argument. For example, let’s first combine m1 and m2 :

1 [m1 ( H ) m2 ( H ) + m1 ( H ) m2 (U ) + m1 (U )m2 ( H )] K 1 m1 ( H ) ⊕ m2 ( H ) = [m1 ( H )m2 ( H ) + m1 ( H )m2 (U ) + m1 (U )m2 ( H )] K 1 m1 (U ) ⊕ m2 (U ) = m1 (U )m2 (U ) K m1 ( H ) ⊕ m2 ( H ) =

(8)

Where

K = m1 ( H )m2 ( H ) + m1 ( H )m2 (U ) + m1 (U )m2 ( H ) + m1 ( H )m2 ( H ) + m1 ( H )m2 (U ) + m1 (U )m2 ( H ) + m1 (U )m2 (U )

(9)

We can similarly combine the result from Equation 8 with m3 . To use Dempster-Shafer theory, A, B and C’s reliability must be known. We calculate initial reliability of each sensor by keeping a malcount for each of them and then comparing the malcounts to a set of thresholds; a malcount exceeding higher thresholds lowers the sensor’s reliability rating.

3 LC-HC Uncertainty In our paper, we propose to use Bayesian networks. Bayesian networks are a powerful way of handling uncertainty in reasoning. A Bayesian network is a directed acyclic graph of nodes. Nodes represent variables and arcs representing dependence relations

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among variables. For example, if there is an arc from node A to another node B, then A is a parent of B. In Bayesian networks, for each node, the conditional probability on its parent-set is stored. These locally stored probabilities can be combined using the chain rule [11] to construct the overall joint probability distribution P. Two main merits of Bayesian networks drive us to adopt it. One is that Bayesian networks can handle incomplete data sets. This point is very important as context-aware system is always partially-observable. The other one is that using Bayesian networks, we can learn causal relationships between low-level context and high-level context. So if only one or two kinds of low-level are available, we can select the most important one by causal relationships so as to improve reasoning accuracy. Let’s see an example of Bayesian network. Considering the case in which the system needs to infer whether the user is having lunch or not. For inferring such an activity it is needed that we have some data about the location of the user, time of the day, and some data about his actions.. Through prior knowledge, we may construct a Bayesian network shown in Fig. 2. Then activity can be deduced from this network.

Fig. 2. Bayesian network for activity reasoning

4 Conclusions and Future Work In this paper, we propose a hierarchical method to deal with uncertainty in contextaware systems. Two different methods: Dempster-Shafer Theory and Bayesian Networks are applied in two different phases in our paper. We argue that this hierarchical method is feasible from the viewpoint of mathematical model. However, when using mathematical methods in real applications, many other aspects, such as hardware feasibility, time delay etc. should also be considered. The involve matter of these aspects in our current model is a topic of our future research. We are currently studying the application of different approaches on our test bed—CAMUS [12] and comparing their performance.

Acknowledgement The research was supported by the Driving Force Project for the Next Generation of Gyeonggi Provincial Government in Republic of Korea.

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References 1. Dey, A.nind K., Gregory D. A.: Towards a Better Understanding of Context and ContextAwareness. In Proc. of the 2000 Conference on Human Factors in Computing Systems, Netherlands (2000) 304-307 2. Anind, K. D., Daniel, S., Gregory, D. A.: A Conceptual Framework and a Toolkit for Supporting the Rapid Prototyping of Context-Aware Applications. In J. Human-Computer Interaction (HCI) Journal, London, UK (2001) 97-166 3. Jason, I. H., James, A. L.: An Infrastructure Approach to Context-Aware Computing. In J. Human-Computer Interaction (HCI), London, UK (2001) 287-303 4. Steven, A. S., Barry, B., Cadiz, JJ.: Interaction Issues in Context-Aware Interactive Environments. In J. Human-Computer Interaction (HCI), London, UK (2001) 363-378 5. Pascoe, J., et al.: Issues in Developing Context-Aware Computing. In Proc. of the International Symposium on Handheld and Ubiquitous Computing. Springer-Verlag, Heidelberg, Germany (1999) 208-221 6. Schilit, W. N.: A Context-Aware System Architecture for Mobile Distributed Computing. PhD Thesis. Columbia University (1995) 7. Satyanarayanan, M.: Pervasive Computing: Vision and Challenges. In IEEE Proc. of IEEE Personal Communications (2001) 10-17 8. Satyanarayanan, M.: Coping with Uncertainty. In J. of IEEE Pervasive Computing (2003) 2-3 9. Wilfried, E.: Sensor Fusion in Time-Triggered Systems. Ph. D. dissertation, Vienna University of Technology (2002) 10. Shafer, Glenn, Judea Pearl: Readings in Uncertain Reasoning. Morgan Kaufmann (1990) 11. Jensen, F.V.: Introduction to Bayesian Networks. University College London Press (1998) 12. Hung, N.Q., Shehzad, A., Kiani, S. L., Riaz, M., Lee, S.: A Unified Middleware Framework for Context Aware Ubiquitous Computing. In the 2004 IFIP International Conference on Embedded And Ubiquitous Computing, EUC2004, Japan (2004) 672-681

A Multi-focus Image Fusion Method Based on Image Information Features and the Artificial Neural Networks Lijian Zhou, Guangrong Ji, Changjiang Shi, Chen Feng, and Rui Nian College of Information Science and Engineering, Ocean University of China, Qingdao, 266003, China [email protected], [email protected], [email protected], [email protected], [email protected]

Abstract. An approach to multi-focus signal level image fusion is presented, which is based on image information features and the multiplayer feedforward neural networks (MLFN). Three feature parameters (spatial frequency, definition and information entropy) are chosen, which can reveal image visual information effectively. For assessing objectively fusion image quality, the root mean square error (RMSE) is taken as the assessment criterion. Experimental results show that the fusion method based on image visual features and the MLFN can effectively fuse the multi-focus image, and is superior to the wavelet and multiwavelets methods quantitatively.

1 Introduction With the availability of the multisensor data in many fields, such as remote sensing, medical imaging or machine vision, image fusion has emerged as a promising and important research area [1]. The goal of image fusion is to integrate complementary information from multisensor data such that the new images are more suitable for the purpose of human visual perception and computer-processing tasks such as segmentation, feature extraction, and object recognition. Depending on the representation format at which image information is processed, it is often divided into three categories, namely, signal level, feature level and decision level [2]. Higher feature level and decision level combine information in the form of feature descriptors and probabilistic variables extracted from the source images. In signal level fusion, the combination mechanism works directly on the pixels obtained at the sensor outputs. In this paper, we focus on signal level image fusion for multi-focus images. Multi-focus problem is that the objects of the image cannot be in focus at the same time due to the limited depth-of-focus of optical lenses in CCD devices. The aim of multi-focus images fusion is to achieve all objects “in focus” by combining a few of images of different focus, and to keep details as more possible as. In recent decades, the wavelets transform methods [1, 3-7] and the artificial neural networks methods [810] have become an attractive tool in image fusion field. In this paper, a novel approach to multi-focus image information features analysis and fusion method is proposed, which is based on the MLFN. The MLFN can preserve the image sub-block, which is in focus. The next sections are organized as follows. We analyze the feature parameters of the input images in section 2. In D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 747 – 752, 2006. © Springer-Verlag Berlin Heidelberg 2006

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section 3, we give the algorithm of fusing images base on the MLFN. Experiments will be presented in section 4 and the last section gives some conclusions.

2 Image Information Feature Parameters In signal-level image fusion, the most important aspects of this process are the truthful representation of the saliency of input image features and the ability to correctly transfer this visual information into the fusion image. Therefore the key problem in fusion is which features can present image details and make a reliable comparison of information from different inputs effectively. By analyzing and comparing several parameters appropriate to multi-focus image, we choose the following three parameters as feature parameters, which can reveal the detail information of the image effectively. 2.1 Spatial Frequency (SF) Spatial frequency is used to measure the overall activity level of an image [11], which is an important indication to measure the image details. The higher the spatial frequency, the more the image details are. For an M × N image F window block, the spatial frequency is defined as

SF = RF 2 + CF 2 where

(1)

RF and CF are the row and column frequencies, respectively. RF =

1 M −1 M −1 [F (i, j ) − F (i, j − 1)]2 ¦¦ MN i =0 j =1

(2)

CF =

1 M −1 M −1 ¦¦ [F (i , j ) − F (i − 1, j )]2 MN j =0 i =1

(3)

㧔Mean Gradient㧕

2.2 Definition

It represents mini-detail difference and texture character.

∇G = where ∆xf (i, respectively.

1 MN

M

N

¦¦

∆xF (i, j ) 2 + ∆yF (i, j ) 2

(4)

i =1 j =1

j ) , ∆yf (i, j ) are the difference of F (i, j ) along x and y direction,

2.3 Information Entropy The information entropy of the image can reflect the image quality. For a single image, we may take the gray value of the pixels as independent samples, the gray distribution of this image is

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p = {p(0), p(1),, p(i ),, p( L − 1)}

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(5)

where p (i ) is the ratio between the number of the pixels whose gray value equals i and the total pixels of the image, L is the total gray level. According to the information theory, the information entropy of the image is defined as follows. N

I = −¦ p( i ) log( p( i ))

(6)

i =0

where N is 0~255 in general.

3 The Multi-focus Images Fusion Based on the MLFN 3.1 The Fusion Algorithm First, we extract three feature parameters to get the feature vector map of the original image to get the feature vector. Second, combine the feature vector to constitute the input samples, and train the MLFN. Third, test the trained neural networks. At last, verify the fusion result. In detail, the algorithm consists of the following steps: (1) Extract three feature parameters. Decompose the source image Fi into M×N blocks. Denote the jth image block by Fij . From each image block, calculate three feature parameters. Denote the feature vector for

(

)

Fij by SFFij , MG Fij , IE Fij , which present spatial frequency, definition

and information entropy, respectively. And they are normalized to the range [0, 1]. (2) Train the MLFN. The input vector of the MLFN is the difference vector

(

The input vector = SFF1 j − SFF2 j , MGF1 j − MGF2 j , IEF1 j − IEF2 j

)

(7)

The expectation output is labeled according to

­1 The exp ectation outputij᧹® ¯0

if Fij is the clearer otherwise

(8)

The detail train process can refer to reference [12]. (3) Perform testing of the trained neural networks. The jth block Z j of the fused image is then constructed as

Z j᧹Fij if the output > 0.5

(9)

(4) Verify the fusion result. If the neural network decides that a particular block comes from Fij , but with the majority of its surrounding blocks from Fkj , this block switched to Fkj .

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3.2 The Design and Algorithm of the MLFN Many artificial neural network models have been proposed for tackling a diverse range of problems, including pattern classification, function approximation and regression. The fusion problem we examine here can be considered as a classification problem. In this paper, the traditional MLFN and the training algorithm of the networks [12] are used. For simplicity, we consider the processing of just two source images. Moreover, we assume that the source images have been registered. The number of the input nodes is the number of the extracted image information features. The output node is 1. In general, the number of hidden layer nodes is one bigger than the number of the input nodes. So the node number of the every layer is 3, 4 and 1. The initial values can be obtained by the function of Matlab function base.

4 Simulation Experiments and Results Figures 1(a) shows a 256-level image of size 256×256 with good focus everywhere. Figures 1(b) and (c) show a pair of test images, which are blurred by a Gaussian of radius 1.5 in the left part and the right part of the Figures 1(a), respectively. Only one man in either image is in focus. We trained the MLFN with the different size subblock samples (4×4, 8×8, 16×16) because it is also important how to choose the size of the image sub-block. According to the three information features of the couple image, twenty pair of samples is selected from two source images. After training the MLFN, we fuse the overall source images, the results are shown in figure2 (a), (b) and (c). For comparison, we fuse them using the scalar wavelet transform method and the multiwavelets transform method [1, 3-7] with the same fusion scheme, respectively. We use the Daubechies2 (db2) wavelet and the Chuilian (CL) multiwavelets in the experiments. The fusion results are shown in figure 2(d) and (e). From figure 2, the results are very similar visually. For assessing objectively fusion image quality, the root mean square error (RMSE) is taken as the assessment criterion. We calculate the RMSE between the fusion image and the original clarity image, as shown in Table 1. The smaller the RMSE is, the better the fusion effect is. Table 1 shows the fusion method in this paper is

(a)

(b)

(c)

Fig. 1. Original image and input source images (a) Original clarity image. (b) Input source image 1 (the left part is in focus). (c) Input source image 2 (the right part is in focus).

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(a)

(b)

(d)

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(c)

(e)

Fig. 2. Fusion results (a) Fusion result based on the MLFN (the size of the sub-block is 4×4). (b) Fusion result based on the MLFN (the size of the sub-block is 8×8). (c) Fusion result based on the MLFN (the size of the sub-block is 16×16). (d) Fusion result based on db2 wavelet. (e) Fusion result based on CL multiwavelets. Table 1. Objective performance of multi-focus image fusion approaches

RMSE

DWT DBSS (2.2) 0.76

DMWT CL 0.62

MLFN (4×4) 0.56

MLFN (8×8) 0.44

MLFN (16×16) 0.54

superior to the other two methods and the fusion results of the 8×8 sub-block is better than ones of the 4×4 sub-block and the 16×16 sub-block with the fusion method in this paper.

5 Conclusions This paper addressed two issues: 1) an analysis of image information features and 2) the image fusion method based on MLFN. By analyzing the information characteristic of multi-focus image, we found the spatial frequency, definition and information entropy of the image can reflect the image detail information very effectively. So we combine these feature parameters through the MLFN to fusion the source images. Experiments show that the fusion method proposed in this paper outperforms the scalar wavelet and multiwavelets transform method. In addition, we do some other experiments with other images using these method, the results is the same as the results of this paper.

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Acknowledgments The National Natural Science Foundation of China (60572064) fully supported this research.

References 1. Manjunnath, H. Li., Mitra, S. K.: Multisensor Image Fusion Using the Wavelet Transform. Graphical Models and Image Processing. Vol. 57, 3 (1995) 235–245 2. Klein, L.: Sensor and Data Fusion Concept and Applications. Bellingham, SPIE, 1999 3. Valdimir, S. P.: Gradient-Based Multiresolution Image Fusion. IEEE Transactions on Image processing. Vol.13, 2 (2004) 228–237 4. Youcef chibani, Amrane Houacine: Redundant versus Orthogonal Wavelet Decomposition for Multisensor Image Fusion. Pattern Recognition. 36 (2003) 879–887 5. Zhang Z., Blum, R.S.: A Categorization of Multiscale Decomposition-based Image Fusion schemes with a Performance Study for a Digital Camera Application. Proc. IEEE. Vol. 87, 8 (1999) 1315–1326 6. Wen, C.Y., Chen, J. K.: Multi-resolution Image Fusion Technique and its Application to Forensic Science. Forensic Science. Vol. 140, (2003) 217–232 7. Pajares G, Mauel J.C.: A Wavelet-based Image Fusion Tutorial. Pattern Recognition. 37 (2004) 1855–1872 8. Shutao Li, JamesT.Kwok, Yaonan Wang.: Multifocus Image Fusion using Artificial neural networks. Pattern Recognition. 23 (2002) 985–987 9. Liu Ningning, etc.: An information Integration Method of Texture and Gray Based Neural Network. Journal of Software. 6 (2002) 575–579 10. Zhaoli Zhang, Shenghe Sun.: Image Data Fusion Algorithm Based on the One-dimensional Self-organizing Neural Networks. ACTA elctronica SINCA. Issue 9, (2000) 74–77 11. Eskicioglu, A.M., Fisher, P.S.: Image Quality Measure and their Performance. IEEE Trans. Comm. 12 (1995) 2959–2965 12. Xingjun Yang, Junli zheng : Artificial Neural network and Blind Processing. TheTsinghua Publication House. (2003) 31–40

A Multilayer Topic-Map-Based Model Used for Document Resources Organization Jiangning Wu, Haiyan Tian, and Guangfei Yang Institute of Systems Engineering, Dalian University of Technology, Dalian, 116024, China [email protected], [email protected]

Abstract. Nowadays with the worldwide prevalence of Internet-connected computers, web resources ad hoc electronic document resources become flooded. How to organize an overwhelming amount of information and hence make an efficient retrieval from the Internet is always the hot topic in knowledge management as well as information retrieval. The Topic Map (TM) offers a framework for modeling and representing knowledge resources and plays a role as “GPS” in the information universe. It is hereby introduced into our study to organize document resources. By employing the concept of TM, a multilayer Topic-Map-based model is proposed in this paper. It organizes the concepts generalized from domain document contents in a hierarchical way and leads the searching process in a narrower topic space. The proposed model has been used to Chinese document organization, which makes knowledge navigating more efficiently.

1 Introduction With the massive amount of information on line and lack of automated co-ordination in its organization, extracting and making future use of this knowledge is becoming more and more problematic. The knowledge is usually available electronically in unstructured or semi-structured documents. Searching useful information from such documents is often inefficient and relies heavily upon their organizational types. In order to improve the efficiency of information retrieval, we need to organize the unstructured or semi-structured information in a good way. Topic Map (TM) is a new technology for knowledge organization, which provides an approach that marries the best of several technologies, including those of traditional indexing, library science etc., with advanced techniques of linking and addressing [1]. Dubbed “GPS of the information universe”, TM is destined to provide powerful new ways of navigating large and interconnected knowledge base. According to traits of TM in knowledge organization, we, in the research, try applying it to document organization, which is one of the important branches of knowledge organization, to realize effective organization and retrieval of electronic documents. This paper is organized as follows. In Section 2, we firstly introduce some basic concepts about Topic Map and then present a multilayer TM-based Document Organization Model (TMDOM) which is proposed based on the Topic Map’s richly cross-linked structure and capabilities of topics used to group together objects that D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 753 – 758, 2006. © Springer-Verlag Berlin Heidelberg 2006

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relate to a single abstract concept. In Sections 3 and 4, the creation process of TMDOM, including document representation, document clustering and TM creation, and the corresponding example are presented in detail. Finally, we conclude our research in Section 5.

2 A Multilayer TM-Based Document Organization Model 2.1 Topic Map: A New Technology for Knowledge Organization When designing the knowledge structure for a certain domain, TM is helpful as it creates the conceptual structure to navigate the large knowledge base. The essential idea behind TM is to organize the out-of-order information by domain ontologies in order to exhibit the semantic structure of resources definitely. It is a highly flexible and powerful standard for the organization and representation of knowledge and a tool for providing access to that knowledge. Main contents of TM can be summarized in the following three parts: a model, two spaces and three concepts. A model is the TM model. Two spaces are topic space and resource space, where the topic space is the knowledge map and the resource space is a collection of information resources. Three concepts are topic, association and occurrence. A topic is a subject in the domain of discourse. Associations are relations between topics, and occurrences, which may be external or internal to the topic map, are information resources relevant to topics. Topics and resources are connected by occurrences. Topics and associations can be grouped according to their individual types that are called topic types and association types. Topics, topic types and occurrences help us to organize information and design indexes; associations and association types help us to describe relations between topics. TM is actually a kind of knowledge network, in which each node can be seen as a topic and links between nodes are relations between topics. We can organize abstract knowledge as a knowledge map to create knowledge structure for flooded information. 2.2 A Proposed TMDOM Model Limitation of traditional methods for document organization lies in that they couldn’t incarnate relations between documents or topics clearly, whereas TM makes it possible to define arbitrarily complex knowledge structures by introducing “topics”, “associations”, and “occurrences”. So, in this paper, we propose a TM-based Document Organization Model named TMDOM for document resources organization. Topic space of TMDOM consists of n layers. On the n-layer, the topics are concerned with some broad research fields, where the associations show the relationships between two topics. From (n-1)-layer to 2-layer, topics on each layer are subtopics or small categories of topics corresponding to their upper layers. On the 1-layer, topics are names of documents related to their corresponding parent topics on the 2-layer. Associations between any two documents are their similar relationships. Occurrences are documents themselves or details that can be found in “resource” by links. From descriptions above, we can see that all concepts like topic, association and occurrence etc. in this model are simplified as several types. For example, there are

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only two kinds of topics: titles of documents and domain ontologies. All associations are grouped into three types: is sub-topic of, is super-topic of, and is related to. All occurrences are linked to locations of documents stored in the resource space. TMDOM model arranges all concepts extracted from the given domain document contents in different hierarchical levels, by which knowledge can be organized in the interconnected form and searching can then be performed in the narrower topic space than in the resource space. According to a series of related topics returned, we can easily find information we are looking for through the links between topics and their occurrences.

3 Creation of the Proposed TMDOM Model In view that the topic space of the proposed model is hierarchical, we need to identify which cluster each document belongs to and which layer the cluster should be on. In this study, we use hierarchical clustering algorithms to group documents at first and then define the topic for each cluster manually. The creation process can be summarized in the following three modules: document representation, document clustering and TM creation. 3.1 Document Representation In this module, we should fulfill two tasks: First, documents have to be transformed into adequate computer-readable representations to simplify search and comparison of documents; second, the most suitable features for representing the documents should be selected and weighed depending on their importance. Once appropriate features are selected to represent the documents, the documents are then transformed to the feature space with much reduced size which makes the further analysis, organization and clustering more efficiently. By using the weighting terms, document di can be represented as di= {(ti1, wi1), (ti2, wi2) … (tik, wik)…}, where tik denotes a feature term in di and wik is the weight of tik in di, M is the number of documents in the collection and N is the number of feature terms that we have selected. 3.2 Document Clustering The whole clustering process is multistage and it is described as follows. 1. The first clustering process: Compute the similarity between each pair of documents and select the two documents between which the similarity is maximal, then group them into one cluster and represent the cluster according to frequencies of feature terms in the two documents. Then go on with the agglomerate clustering process and repeat it until the maximal similarity is smaller than a predefined threshold. After the first clustering process, we should determine what documents each final cluster contains. At last we will get the results that could be represented as L2Cg={(tg1, wg1), (tg2, wg2) … (tgk, wgk) …} (g=1, 2, … G; k=1, 2, … N) and d1, d2, …di… Ÿ L2Cg, where L2Cg means one cluster on the 2-layer and G is the number of clusters on the 2-layer. L2Cg={(tg1, wg1), (tg2, wg2) … (tgk, wgk) …} means that cluster L2Cg could be represented in this form and d1, d2, … di … Ÿ L2Cg means cluster L2Cg includes seeds: d1, d2, …… di ……

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2. The second clustering process: It is almost the same as the first clustering process just mentioned. After the second clustering process, we will get results represented as L3Ch= {(th1, wh1), (th2, wh2) … (thk, whk)…} (h=1, 2, … H; k=1, 2, … N) and L2C1, L2C2 … L2Cg … Ÿ L3Ch, where L3Ch means one cluster on the 3-layer and meanings of other expressions are similar to those described above, H is the number of clusters on the 3-layer. Go on for the next clustering process again and again until the final clusters on the highest layer are what we initially expect. Then the whole clustering process is over. 3.3 TM Creation In this module we should determine associations between topics and create the TM. There are mainly two kinds of topics: one refers to the titles of documents and another refers to the clusters that we get from the clustering process. For these clusters, we only have to determine the topics according to keywords and their frequencies in the corresponding clusters with the help of domain experts. This process is similar to ontology building so we don’t give particular descriptions here. TM creation can be summarized in the following four steps. 1. Topics: Topics of 1-layer are titles of documents and we express them as L1Ti that means one topic on the 1-layer. Here each topic can be represented the same as its document. For example, L1Ti= di = {(ti1, wi1), (ti2, wi2) … (tik, wik)…} (i = 1, 2, … M; k = 1, 2, … N). From 2-layer to n-layer we have to determine topics for all clusters one by one manually. Meanwhile each topic can be represented the same as its cluster. For example, one topic on the 2-layer L2Tg= L2Cg = {(tg1, wg1), (tg2, wg2) … (tgk, wgk)…} (g=1, 2, … G; k=1, 2, … N). 2. Associations between topics on the same layer: Compute similarities between any two topics on the same layer, e.g., Sim (L1T8, L1T12), Sim (L2T3, L2T6), etc. 3. Associations between topics on adjacent two layers: For each topic on layers from 2 to n, find all its subtopics and compute similarities between the topic and its subtopics. Clusters and topics on each layer are one-one so seeds of each cluster are also subtopics of the current topic. For example, L3C8 includes seeds: L2C2, L2C6 so subtopics of L3T8 are: L2T2, L2T6. So we should compute similarities between L3T8 and L2T2, L2T6. 4. Occurrences: Link topics on the 1-layer, namely documents on the 1-layer, with their corresponding occurrences in resource space.

4 An Example for Creating a 3-Layer Topic Map In this paper, we select 200 documents related to topics “text clustering”, “text categorization”, “feature extraction”, “Chinese word segmentation” and “automatic abstracting” from China Journal Full-text Database (CJFD) for a simple experiment. We adopt extended Boolean model and define a new similarity calculation formula for document clustering. Suppose two documents be di= {(ti1, wi1) … (tik, wik)…} and dj = {(tj1, wj1) … (tjk, wjk)…} (i, j=1, 2, … 200; k=1, 2, … 421), then their similarities can be calculated by the following formula:

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N

¦(w

ik

− w jk ) 2

.

k =1 N

Sim ( d i , d j ) = 1 − (

¦

N

wik 2 ) × (

k =1

¦

w jk 2 )

(1)

k =1

where meanings of all variables are the same as described previously and here N=421. At last, we get 5 clusters on the 2-layer and 1 cluster on the 3-layer. By determining topics and their associations, the final Topic Map can be created as shown in Fig. 1. text mining

3-layer

2-layer

text clustering

text categorization

Chinese word segmentation

feature extraction

automatic abstracting

Topic Space 1-layer

Resource Space

Fig. 1. Structure of TMDOM based on the small-sized sample set

In Fig. 1, there are three layers of topics and topics on the 1-layer are titles of documents that we don’t indicate here because of space limitation and associations between them are also omitted. From the experimental results, we find that some documents are linked to topic “text mining” directly and some documents couldn’t be grouped into any cluster. This is because there may be some exceptions in the feature extraction process or their similarities with each topic may be too small. Anyhow, through TM in Fig. 1 we can see the conceptual structure of domain “text mining” clearly. With such a TM users could search for documents they need conveniently and this makes effective organization and retrieval of document resources come true.

5 Conclusion According to the concepts of TM that was firstly standardized by ISO in 2000, a multilayer TM-based document organization model is proposed in this paper in order to improve the efficiency of document organization and document retrieval. In addition, we introduce the creation process of TM that could be summarized in three modules: document representation, document clustering and TM creation. For clearly describing, an example for creating a 3-layer topic map is given in the last part of this paper.

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Due to the limitation of the space, we just present the key points in our proposed model and don’t list the experimental results here, which will be found in the following papers related to this research topic.

Acknowledgement This work is supported by Natural Science Foundation of China (NSFC) under grant 70431001 and many thanks to the viewers for their helpful comments.

References 1. What’s in a Topic Map? http://www.webreference.com/xml/column77/2.html 2. Nils Pharo: Topic Maps–Knowledge Organization Seen from the Perspective of Computer Scientists:http://www.elag2004.no/papers/Pharo.pdf 3. Jianxia Ma:A Study of Application of Topic Map in Knowledge Organization. New Technology of Library and Information Service, No. 7. (2004) 11–16 4. Steve Pepper: The TAO of Topic Maps–Finding the Way in the Age of Infoglut, http://www.ontopia.net/topicmaps/materials/tao.html 5. http://www.gca.org/papers/xmleurope2000/papers/s29-04.html 6. http://www.isgmlug.org/n3-4/n3-4-15. html 7. Feng Dai:Research of Knowledge Representation Technology Based on Topic Map, Journal of South-Central University for Nationalities, Vol. 23. No. 1. (2004) 84–87 8. http://www.gca. org/papers/xmleurope2000/papers/s22-02.html 9. Richard T. Freeman, Hujun Yin: Tree View Self-organization of Web Content, Neurocomputing, Vol. 63. (2005) 415–446 10. Zechun Han:The Theme Map-An Effective Method for Organizing and Revealing Knowledge. Journal of Xinzhou Teachers University, Vol. 21. No. 4. (2005) 122–124 11. Alexander Sigel:XML Topic Maps in Knowledge Organization. http://kpeer.wim.uni-koeln. de/~sigel/veroeff/TU-Eindhoven2004/FINAL/Eindhoven2004_Abstract.pdf

A New Clustering Algorithm for Time Series Analysis Jianping Zeng and Donghui Guo Department of Physics, Xiamen University, Fujian 361005, P. R. China [email protected], [email protected]

Abstract. Conventional model-based clustering algorithms for time series data are limited in improving the clustering performance and also their computation complexity is high. In order to tackle this problem, a new model-based clustering algorithm with a certainty factor is proposed to evaluate the certainty degree of time series data being in a cluster. The new algorithm can be used to show a reasonable result for time series data clustering and reduce the computation complexity greatly. Performance of the algorithm is verified by the experiments on both synthetic data and real data.

1 Introduction Model-based clustering algorithms for time series are the ones that attempt to learn an expressive model for the patterns from the series data and then perform clustering either in model space or in data space by applying distance or similaritybased clustering algorithms [1],[2]. Model-based clustering of time series appears to achieve better performance and it has been shown as a promising method for time series analysis [3]. HMM (Hidden Markov Model) has been introduced into the model-based clustering algorithm to fit the sequences in recent years[2],[3],[4]. Generally, HMM-based clustering can be classified into two categories, i.e., clustering with no model merging [2] and clustering with model merging [1],[3]. For convenience, we refer the two algorithms as (HMM-HC1) and (HMM-HC2) respectively. Although the first approach is simple, it is not suitable to distinguish between more similar time series. However, the second one can get better performance when the sequences are more similar to each other, but its computation complexity can be very high. A new algorithm, CBCFM (Clustering algorithm for time series analysis Based on Certainty Factor Model) based on the certainty factor model is proposed to deal with the problem of existing HMM-based clustering algorithm.

2 Clustering Algorithm Based on Certainty Factor Model The CBCFM algorithm, with SN sequences as input, is shown in table 1. And the algorithm is present in detail in the section. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 759 – 764, 2006. © Springer-Verlag Berlin Heidelberg 2006

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1. Create SN HMMs for each sequence 2. Compute SN similarity matrixes 3. Compute certainty factor matrix 4. Hierarchical agglomerative clustering and select the best result 2.1 Description of Certainty Factor Model Certainty factor was first proposed in MYCIN system to denote the certainty of inference rules [5]. Also computation of certainty factor of rules can be performed under different circumstances [6]. Here, we bring the concept of certainty factor to evaluate the certainty degree that sequences are grouped into one cluster. We denote E as the facts in inference, and H as the inference results. And the certainty factors of E,H, and the rule “if E then H” are CF(E), CF(H) and CF(H,E) respectively. Then the computation formulas of certainty factor for inference rule are as follows [6].

CF ( H ) = CF ( H , E ) × max{0, CF ( E )}

(1)

Especially, when E = E1 and E2 and … and En, then

CF ( E ) = min{CF ( E1 ), CF ( E2 ), , CF ( En )}

(2)

When E = E1 or E2 or … or En, then

CF ( E ) = max{CF ( E1 ), CF ( E2 ),  , CF ( En )}

(3)

When two inference rules have the same inference result but different certainty factor, for example, there are two rules: if E1 then H CF(H,E1), and if E1 then H CF(H,E2), then the final certainty factor can be calculated by the formula as follows,

CF12 ( H ) = CF1 (H ) + CF2 ( H ) − CF1 (H ) × CF2 (H )

(4)

2.2 Algorithm Description Let SX={X1,X2,…,XSN}denote a set of SN time series. First, SN HMMs λi (i=1…SN) are learnt from each of the SN sequences using Baum-Welch algorithm [7]. More detail description of HMM can be found in [7]. Compute Similarity Matrixes (1) Compute P(Xi|λx), i=1 to SN, the probability of the sequence Xi, given the model λx. This can be get through forward algorithm [7]. Then a vector, VP={vp1,vp2,…,vpSN}, here, vpi=logP(Xi|λx), describes how well the given model λx matches a given observation sequence Xi. (2) Transform the vector VP into the similarity matrix VM x = [vmij ] indicating the x

similarity between each sequence by the following formula.

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­ vp j / vpi , j > i ° ,j =i vm = ®1 °vp / vp , i > j j ¯ i x ij

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(5)

Where, 1 ≤ i, j ≤ SN . Then, by applying SN models to step (1) and (2), SN similarity matrixes VMx, x=1…SN, can be got. Compute the Certainty Factor Matrix First, we define the inference rules for a give pair sequences (Xk,Xl). Generally, there are three types of rules, see table 2 for reference. Table 2. Rules for building certainty factor matirx

RULE1 RULE2 RULE3

IF Sim(λk,Xk,Xl) THEN C(Xk,Xl) cf1 IF Sim(λl,Xk,Xl) THEN C(Xk,Xl) cf2 IF Sim(λi,Xk,Xl) THEN C(Xk,Xl) cf i3

SN

Where, cf1+cf2+

¦

cfi 3 =1 and i=1…SN, k=1…SN, l=1…SN, ki, li, and

i =1,i ≠ k ,i ≠ l

Sim(λi, Xk,Xl) means the similarity between Xk and Xl under the evaluation of λi. C(Xk,Xl) means Xk and Xl are in the same cluster. cf1, cf2 and cf i3 are the certainty factor of the rule. Next, we apply the formula (1) and (4) to these rules to compute the certainty factor matrix FM = [fmkl], 1”k,l”SN. That is, we combine the RULE1 and RULE2, and the certainty factor, denoted as cf12, is as follows, k

l

cf12 = vmkl × cf1 + vmlk × cf 2

− (vmklk × cf1 ) × (vmlkl × cf 2 )

(6)

Then, we combine RULE3 by recursively applying the following formula,

cf i ( i +1) = vmkli × cfi 3 + vmkli +1 × cf( i +1) 3 − (vmkli × cfi 3 ) × (vmkli +1 × cf( i +1) 3 )

(7)

where i =1…SN, and ik, il. Then, finally we can then get the final certainty degree fmkl for Xk and Xl. It is reasonable to suppose that cf1=cf2 and the value of all cfi3 (i=3…SN) are equal. Then we can set these parameters as follows,

cf1 = cf2 =cf and cfi3 = (1-2*cf) / (SN-1), (i=3…SN) Where, cf is a parameter that is related to the dataset. And it can be estimated by CF(H) with setting CF(E)=1 in formula (1). So, if the model λi is correctly learnt from Xi, then Xi and Xj can be considered in a same cluster with a high certainty factor. Then, cf should be related to the probability that the HMM can be correctly learnt from a sequence.

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Hierarchical Agglomerative Clustering and Select the Best Clusters. The process is done by the following four steps.

(1)

(2)

Perform a hierarchical agglomerative clustering. However, we compute the certainty factor for the nodes in the hierarchical tree. It is calculated by formula (1)-(4). And we denote the clustering result of each agglomeration as C={C1,C2,…Cm}, where m is the number of clusters. Compute the valid index for the cluster C, using the following certainty degree evaluation index, which is similar to Dunn's Index [8]: certIndex = max { max { 1≤i ≤ m 1≤ j ≤ m , j ≠ i

δ (C i , C j )

min {∆ (C )}

1≤ k ≤ m

where,

}}

(8)

k

∆ ( S ) = min { fmxy } is the certainty degree of the cluster S, and x , y∈S

δ ( S , T ) = max { fmxy } is the certainty degree for the separation of cluster S and T. x∈S , y∈T

(3) (4)

Repeat 1-2 until one cluster remains. Select the best clustering result

From (8), we can see that the smaller the certIndex is, the higher certainty degree in the cluster and less certainty degree between any two clusters. So, we can simply select the clustering result that makes the certIndex minimal.

3 Experiments The rate of correctness (RC) which is defined as the number of correctly clustered sequences divided by total sequences number, is usually used to evaluate the performance of clustering algorithm. Two kinds of experiment were done in the paper. One was based on synthetic data and the other one was done on real world data. On synthetic data, we carried out three experiments. Each experiment (Exp-1, Exp-2, Exp-3, Exp-4) was done with different number of sequences, length of sequence and distance between models. Here we use Kullback Leibler[7] as the distance measurement for two models. In Exp-1, 4 datasets were generated to evaluate the effect of model distance on the performance of clustering algorithm. Exp-2 checked the time complexity of the algorithms as total sequences number increases. Exp-3 checked the effect of sequence length on clustering. The original HMM used to generate the four datasets is with the number of hidden states 4 and the number of visible states 10 and the probability distribution matrix is randomly set. In EXP-4 testing on time series data from real word, we used an intrusion detection test dataset provided by Schonlau et al (http://www.schonlau.net). This dataset was collected from keyboard sequential commands on a UNIX platform issued by each of 70 users. Each user is represented by 15,000 commands, collected over time from a few days to a few months. We randomly selected 2,3,4,5,6 users and selected 24, 30, 39, 44 and 59 sequences in our clustering experiment respectively. To avoid the randomness, each of the tests were done ten times and the average results were achieved.

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The result of RC under different model distance and different sequence length are shown in table 3 and table 4. And we can see that as the model distance decreases, the RC of CBCFM is higher than that of the other two algorithms. When the length decreases, the RC also decreases, but CBCFM can get a good result than others. The result of EXP-4 is shown in table 5. Because the intrusion detection test dataset may not be fit by a HMM perfectly, and this may cause the performance to become worse than test result on synthetic data. However, the performance of CBCFM is still better than HMM-HC2. Table 3. Rate of Correctness and model distance

Model Distance 0.02 0.04 0.06 0.08 0.10

HMM-HC1 0.56 0.61 0.64 0.71 0.75

HMM-HC2 0.60 0.69 0.79 0.90 1.0

CBCFM 0.62 0.75 0.95 0.99 1.0

Table 4. Rate of Correctness and sequence length

Length of Sequences 40 60 80 100

HMM-HC1 0.55 0.61 0.65 0.72

HMM-HC2 0.68 0.72 0.78 0.95

CBCFM 0.86 0.90 0.92 1.0

EXP-2 was conducted on DELL PC with PIII, 512M RAM and Windows 2000 OS, the result is shown in table 6. It is clearly that as the number of sequence increases, the complexity of HMM-HC2 increases quickly, while the CBCFM and HMM-HC1 spend less time and shows lower time consumption. From these experiments, we can see that the clustering performance of CBCFM is the best in despite of the similarity in time series data increases. Furthermore, its computation complexity can be kept in a lower level. Table 5. Rate of correctness and the sequences number

Number of Clusters/Sequences 2/24 3/30 4/39 5/44 6/59

HMM-HC2

CBCFM

0.92 0.82 0.69 0.65 0.63

1.0 0.88 0.85 0.82 0.796

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Number of Sequences 15 30 45 60

HMM-HC1

HMM-HC2

CBCFM

5 8 12 23

77 171 398 569

13 25 38 50

4 Conclusion A new HMM-based clustering algorithm CBCFM incorporated with certainty factor model has been proposed in this paper. Experiments show that CBCFM can get better performance even if the model distance or the length of sequence becomes smaller. By avoiding merging models in the process of clustering, the CBCFM algorithm can greatly reduce the computation complexity.

References 1. Zhong S., Ghosh, J.: A Unified Framework for Model-based Clustering. Journal of Machine Learning Research, 4 (2003) 1001-1037 2. Bicego, M., Murino, V., Figueiredo, M. A. T.: Similarity-based Clustering of Sequences Using Hidden Markov Models. Machine Learning and Data Mining, 12 (2003) 86-95 3. Zhong S.: Probabilistic Model-based Clustering of Complex Data. The University of Texas at Austin. Ph.D. Thesis, USA (2003) 4. Tobias, S., Christian, D., Stefan, W.: Mining the Web with Active Hidden Markov Models. Proceedings of IEEE International Conference on Data Mining, (2001) 645-646 5. Buchanan, G., Shortliffe, E.: Rule-Based Expert Systems:The MYCIN Experiments of the Stanford Heuristic Programming Project. Addison-Wesley Publishing Co., New York (1984) 90-104 6. Shao, J. L., Zhang, J., Wang, C. H.: Fundament of Artificial Intelligence. Electrics industry press of China, Beijing (2003) 97-99 7. Rabiner, L. R.: A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of. IEEE. 77 (2) (1989) 257 – 286 8. Ujjwal, M., Sanghamitra, B.: Performance Evaluation of Some Clustering Algorithms and Validity Indices. IEEE Transaction on pattern analysis and machine intelligence, 12 (2002) 1650-1654

A New IHS-WT Image Fusion Method Based on Weighted Regional Features 2

Jin Wu1,2, Bingkun Yin1, Jian Liu , and Jinwen Tian 1

2

College of Information Science and Engineering, Wuhan University of Science and Technology,430081 Wuhan, P.R. China [email protected] 2 HuaZhong University of Science and Technology, Image Information and Intelligence Control Laboratory of the Ministry of Education 430074 Wuhan, P.R. China [email protected]

Abstract. The goal of image fusion is to create new images that are more suitable for the purposes of human visual perception, machine vision, object detection and target recognition. This paper preserves a new IHS-WT method based on weighted regional features for the fusion of a high-resolution panchromatic image and a low-resolution, multi-spectral image. Firstly, the multi-spectral image is transformed into IHS component. Secondly, the histogram-matched panchromatic (New PAN) image and intensity component (I) are decomposed into wavelet coefficients respectively. Thirdly, the new intensity component can be obtained by fused the wavelet coefficient data of New PAN and I through adaptive weights based on window region features. Finally, the new intensity, hue, and saturation components are transformed back to RGB. A comparative analysis is carried out against other existing strategies. The results show that the proposed method can achieve better performance in combing and preserving spectral-spatial information for the test images.

1 Introduction Image fusion combines different information from images of different sources into a composite image with more accurate description. It can be used to improve the reliability of the computational vision task or to provide a human observer with a deeper insight about the nature of observed data. The current definition of image fusion can take place at the pixel, local feature and decision level. In this paper, our task is merging a low-resolution, multi-spectral image with a high-resolution panchromatic image so as to achieve optimal resolution in the spatial and spectral domains. Many image fusion methods for the purpose have been proposed, however, most methods such as IHS [1], PCA [2], and HPF [3], distort the spectral characteristics of the multi-spectral image. Although the Wavelet Transform method (WT) can achieve better spectral and spatial quality than the IHS, PCA and HPF [4], but it may suffer from ringing because of giving up the low frequency component of the panchromatic image completely. Consequently, we proposed a new D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 765 – 770, 2006. © Springer-Verlag Berlin Heidelberg 2006

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image fusion algorithm based on IHS, WT and the regional features. The subjective visual effect and the objective statistical results indicate that this method is useful for image fusion.

2 IHS Transform and Wavelet Transform Fusion Method 2.1 IHS Transform Fusion Method The widespread use of the IHS transform to merge images is based on its ability to separate the spectral information of an RGB composition in its two components H and S, while isolating most of the spatial information in the I component [5]. Generally, the IHS transformation includes following steps: 1) Transformation of three multi-spectral bands from RGB to IHS space. 2) Substitution of the intensity image (I) by the Pan image. 3) Inverse transformation of the hue, saturation, and the replacement intensity to RGB space. 2.2 Classical Wavelet Fusion Method Wavelet transform is a global mathematical analysis. It is based on a multi-resolution analysis, and can easily detect local features in signal processing. As a result, wavelet is very suitable for data fusion. The classical wavelet-based image fusion can be performed in the following steps: 1) The two input images are decomposed separately into approximate coefficients and detailed coefficients. 2) The high detailed coefficients of the multi-spectral image are replaced with those of the panchromatic image. 3) The new wavelet coefficients of the multi-spectral image are transformed with the IWT to obtain the fused multi-spectral image. The fusion image may suffer from ringing because it discards low frequency component of the panchromatic image completely. Therefore, a new wavelet transform method should be applied. In this paper, we use the adaptive weights based on window region features such as variance and energy to reconstruct the new coefficients.

3 A New IHS-WT Fusion Method In the IHS-WT method, the multi-spectral image is first transformed from RGB into the IHS space. Making the hue and saturation components unchanged, we can merge the panchromatic image with the intensity component in order to obtain the fused intensity component I ' , and then inverse transforming back to RGB. By means of the steps presented above, the fused image, which providing a better merger between the multispectral and high-resolution images, is generated. However, the heart of the IHSWT method is how to acquire the fused intensity component I ' .

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Let A be the high resolution panchromatic image and B be the intensity from the IHS representation of the multi-spectral image. They are both transformed with pyramid wavelet transform. We can obtain approximate coefficients S A ( 2 J ; x, y ) ,

S B ( 2 J ; x, y ) and detailed coefficients WAK ( 2 j ; x, y ) , WBK ( 2 j ; x, y ) . Here, J denotes

decomposition level, K = 1, 2,3 denotes the three directions and j = 1, 2," J denotes different resolutions. The fused approximate coefficients are obtained with weighted average method. The fusion rule is:

S ( 2 j ; x, y ) = k1 < S A ( 2 j ; x, y ) + k2 < S B ( 2 j ; x, y ) .

(1)

Where k1 , k2 are the weighted coefficients and their relation satisfy the equation

k1 + k2 = 1 . For the detailed components, in order to preserve localized feature information as more as possible, we compare the coefficient of A with the correspond coefficient of B, and give a greater weight to the one that contains more detail information. It can be defined as: W K ( 2 j ; x, y ) = k1 <WAK ( 2 j ; x, y ) + k2 <WAK ( 2 j ; x, y ) .

(2)

We define the adaptive weighted coefficients k1 and k2 as Eq.(3) based on window region features [6]. In this way, we give the different coefficients different weights. This method can take full advantage of the localized feature information of the images. N

k1 = ∏ f An n =1

ª N n N nº «∏ f A + ∏ f B » , k2 = 1 − k1 . ¬ n =1 ¼ n =1

(3)

Where, f An is the nth local feature of A and f Bn is the nth local feature of B. N denotes the total number of local features. In this paper, we use variance and energy of the corresponding local regions of the source images (A and B). Then, we have: 2

k1 = ∏ f An n =1

2 ª 2 n º + f f Bn » , k2 = 1 − k1 , ∏ ∏ A « ¬ n =1 ¼ n =1

(4)

f A1 = DA (2 j ; x, y ), f B1 = DB (2 j ; x, y ) ,

(5)

f A2 = E A (2 j ; x, y ), f B2 = EB (2 j ; x, y ) .

(6)

Where, DAK ( 2 j ; x, y ) and DBK ( 2 j ; x, y ) are WAK ( 2 j ; x, y ) and WBK ( 2 j ; x, y ) ’s variance respectively in the range of n × n window whose center coordinate is ( x, y ) . E A (2 j ; x, y ) and EB (2 j ; x, y ) are the energy of the region, they are defined

by:

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E A (2 j ; x, y ) = ¦ c ( x ', y ') ª¬WAK (2 j ; x ', y ') º¼ ,

(7)

EB (2 j ; x, y ) = ¦ c ( x ', y ') ª¬WBK (2 j ; x ', y ') º¼ .

(8)

2

x ', y '

2

x ', y '

where x ', y ' are in the rang of n × n , the c ( x ', y ' ) is the corresponding weighted coefficient. The method based on IHS and weighted regional features of wavelet transformations can be performed in the following steps: 1) Transform the multi-spectral image into the IHS components. (Forward IHS transform). 2) Perform histogram match between panchromatic image and intensity component (I), and get new panchromatic image (New Pan). 3) Decompose the histogram-matched panchromatic image and intensity component (I) into wavelet coefficients respectively. 4) Use Eq.(1) and Eq.(2) to form the new intensity. 5) Transform the new intensity, the hue, and the saturation components back into RGB space (inverse IHS transform).

4 Experiments and Fusion Results Analysis In this paper, we merge the SPOT panchromatic image and landsat multi-spectral image to show the availability of the proposed algorithm. The tested methods include IHS fusion method, the combined IHS and classical wavelet method (IHS-WT), the combined IHS and local deviation of wavelet method (IHS-CWT) [7], and the new IHS-WT image fusion method based on weighted regional features. The fusion effect images are shown in Fig.1. Seen from the visual effect, the fused image with the new method not only preserves most of the spectral information of the multi-spectral image but also improves the spatial details distinctly. Compared with the IHS method, the method has obvious advancement in preserving the spectral information and some improvement in enhancing spatial details. Compared with the IHS-WT method, and the IHS-CWT method, the new algorithm’s performance in fusing spatial details is almost the same but it has an obvious advancement in preserving spectral information. So the new method is superior to the former. The statistical parameters, such as standard variance σˆ , entropy H , definition g , distortion degree D , deviation index Dindex , and the correlation coefficient ρ xy [8], are chosen to quantitatively analyze the different fusion results. In Table 1, the σˆ , H , and ρ xy of the fused image using the new algorithm are all bigger than those of the fused image using IHS method, they increase by 0.9273, 0.0071 and 0.2384 respectively; meanwhile, equivalent in g , the D reduces 16.9815, and the Dindex reduces 0.3481. It indicates that the new algorithm is superior to IHS method in the way that it preserves spectral information and enhances spatial details.

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(a)

(b)

(c)

(d)

(e)

(f)

Fig. 1. Original images and fused images with different methods. (a), (b) Original SPOT, Landsat images. (c) The IHS method. (d) The IHS-WT method. (e) The IHS-CWT method. (f)Fused Image with the IHS-WT based on weighted regional features. Table 1. The Quantization Measurement Results of The Four Methods

σˆ IHS 53.4678 IHS-WT 54.7212 IHS-CWT 54.8411 Proposed algorithm 54.3951 Different images

H

g

D

Dindex

5.2859 5.2965 5.2970

20.1161 28.4583 0.5387 20.4559 12.8560 0.2254 20.8017 12.7887 0.2151

5.2930

19.7409 11.4768 0.1906

ρ xy 0.7183 0.9477 0.9483 0.9567

Although, compared with the IHS-WT method, and the IHS-CWT method, the fused image using our new method is inferior in σˆ , H and g , but superior in D , Dindex and

ρ xy .

Compared with the former method, the D , Dindex and

ρ xy increase

by

1.3792, 0.0348 and 0.009 respectively. Compared with the latter method, the D , Dindex and ρ xy increase by 1.3119, 0.0245 and 0.0084 respectively. It indicates that the new method’s performance is equivalent to the two methods in reflecting the spatial details but is better than the latter in preserving the spectral information.

5 Conclusion Remote sensing image data fusion method based on IHS transform or wavelet transform is an important way to integrate every kind of image information. In this paper,

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for combing the advantages of the two methods to achieve a better fusion result, a remote sensing image fusion method with combining the IHS and based on weighted regional features wavelet is proposed. The new algorithm can preserve the spectral information in the fused image; meanwhile, it can merge the spatial details of the panchromatic image. So the new algorithm’s performances are improved well in preserving spectral information and enhancing spatial details. Both objective statistical parameters and subjective visual effect indicate that the new method can well improve spatial resolution of the remote sensing image as the IHS, the IHS-WT, and the IHSCWT method, especially; it is more effective on preserving spectral content of remote sensing image.

References 1. Carper, W. J., Lillian, T. M., Kiefer, W.: The Use of Intensity-hue-saturation Transformations for Merging SPOT Panchromatic and Multi-spectral Image Data. Photogrammetric Engineering & Remote Sensing, Vol.56 (1990) 459-467 2. Chavez, P. S. J., Kwarteng, Y.: Extracting Spectral Contrast in Landsat Thematic Mapper Image Data Using Selective Principal Component Analysis. Photogrammetric Engineering & Remote Sensing, Vol.55 (1989) 339-348 3. Chavez, P. S. J., sides, C., Anderson, A.: Comparison of Three Different Methods to Merge Multiresolution and Multispectral Data: Landsat TM and SPOT panchromatic. Photogrammetric Engineering & Remote Sensing, Vol.57 (1990) 295-303 4. Zhou, J., Civco, D. L., Silander, J.A.: A Wavelet Transform Method to Merge Landsat TM and SPOT Panchromatic Data. Int. J. Remote Sensing, Vol.19 (1998) 743-757 5. Pohl, C., Genderen, J. L. V.: Multisensor Image Fusion in Remote Sensing: Concepts, Methods and Applications. Int. J. Remote Sens., Vol.19 (1998) 823-854 6. Huang, J., Pan, Q., Pi, Y.N., Li, J.: An IHS Image Fusion Method Based On Weighted Regional Features. Computer Engineering and Applications, Vol.41 (2005) 39-41 7. Wu, J., Huang, H.L., Liu, J., Tian, J.W.: Remote Sensing Image Data Fusion Based on IHS and Local Deviation of Wavelet Transformation. IEEE ROBIO2004, (2004) 564-568 8. Li, B.C., Wei, J., Peng, T.Q.: Objective Analysis and Evaluation Of Remote Sensing Image Fusion Effect. Computer Engineering and Science, Vol.26 (2004) 42-46

A Novel Algorithm of Mining Multidimensional Association Rules WanXin Xu1,2 and RuJing Wang1 1

Hefei Institute of Intelligent Machines, Chinese Academy of Sciences, 230031 Hefei, Anhui, China [email protected] 2 Department of Automation, University of Science and Technology of China, 230027 Hefei, Anhui, China [email protected]

Abstract. In this paper, a novel algorithm of mining multidimensional association rules in relational database is proposed. First, design a particular structure including many indexes to save multidimensional itemsets, which makes time of finding itemsets decrease. Basing on statistic idea, the algorithm saves all frequent 1-itemsets and their support members at scanning the database for the first time. Frequent k-itemsets will be generated with no necessary to scan the database more times because of using these support members. Compared with some traditional algorithms of mining association rules, the algorithm presented in this paper has better executive efficiency and expansibility, which is proved in our experiments.

1 Introduction Data mining has been defined as “The nontrivial extraction of implicit, previously unknown, and potentially useful information from data” [1,2]. Association rule, which describes correlations of data items in large numbers of data, is a manner of expressing knowledge. It was first presented by R.Agrawal in 1993 [3]. Then, more and more scholars began to research on association rule and many methods are based on the algorithm Apriori proposed by R.Agrawal in 1994[4]. Association rule can be classified as single-dimensional association rule and multidimensional association rule by dimension appeared in rule. Multidimensional association rule can be classified as inter-dimension association rule and hybrid-dimension association rule. Inter-dimension is called when there are not repetitious predications appeared in the same rule, while hybrid-dimension is called when there are. What this paper discusses is mining multidimensional inter-dimension association rules directly in relational database. To mine association rules in relational database, some papers present a method which transforms relational database into transaction database and uses Apriori algorithm to mine rules. Because the performance of the former algorithm is not very good, frequently used methods [5,6] of mining multidimensional association rules from relational database are those which improve on classical algorithms [3,4,7] using SQL tools. These algorithms are fast and effective to a certain extent, so they are used in many applications. However, they often need to scan the target database many times and may also cost much time. To find a solution to this problem, D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 771 – 777, 2006. © Springer-Verlag Berlin Heidelberg 2006

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this paper introduces a new structure and presents an algorithm named MDIM (Multi_Dimensional_Indexing_Mining) basing on the structure.

2 Definitions 2.1 Association Rule Suppose I = {i1, i2, … , im} is a set of items. D is a database of transactions. Each transaction T is a set of items and has an identifier called TID. Transaction T satisfies T ⊆ I. Suppose A is a set of items. Transaction T includes A if and only if A ⊆ T. Definition 1. Association rule is an implication formula with a form “A ⇒ B”, where A and B are all itemsets and satisfy that A ⊂ I, B ⊂ I and A ∩ B= ∅ . Definition 2. Rule “A ⇒ B” is true in sets D of all transactions with a support (denoted by s) and a confidence (denoted by c), where A and B are all itemsets. Support s is a percentage of transactions including both A and B (A ∪ B) in transaction sets D. Confidence c is a percentage of transactions including both A and B (A ∪ B) in transactions only including A. That is: s = P( A ∪ B) , c =

P( A ∪ B) . P( A)

(1)

2.2 Apriori Algorithm and Apriori Property Apriori algorithm is one which mines single-dimensional and boolean type of association rule. First, the algorithm scans database once and generates all frequent 1-itemset. Secondly, let k=2. Every different two of all (k-1)-itemsets are linked into a candidate k-itemset, then the database is scanned again and all frequent k-itemsets are generated. Repeat this process until no new frequent itemsets is generated. In this algorithm, an important property which is called Apriori property is used. Property 1(Apriori property). All not empty subsets of frequent itemsets must be frequent [1,2]. 2.3 Itemsets in Multidimensional Data Sets Suppose RDB is relational database with m records and n dimensions. All dimensions, which are also called predications or fields, constitute a dimension combination with a formula (d1, d2, …, dn), in which dj represents j-th dimension. The i-th record can be expressed as value combination with a formula (vi1, vi2, …, vin), where vij represents j-th value in i-th record, 1 ” i ” m and 1 ” j ” n. Definition 3. A formula like (dj, vij) is called an “item” in relational database or other multidimensional data sets, which is denoted by Iij. That is: Iij = (dj, vij), where 1 ” i ” m and 1 ” j ” n.

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Definition 4. Suppose that A and B are items in the same relational database RDB. A equals B if and only if the dimension and the value of the item A are equal to the dimension and the value of the item B, which is denoted by A=B. If it is not true that A equals B, it is denoted by AB. Definition 5. A set constituted by some “item” defined in definition 3 is called “itemset”. The “itemset” which are constituted by all items in relational database is called “Full itemset”, and it is denoted by S. That is: S {Iij 1” i ” m, 1 ” j ” n}.

㧩 Ί

3 Structure, Strategy and Algorithm There are two courses in mining association rule. First, find all frequent itemsets in target database. Secondly, generate association rules from frequent itemsets. The first course is the core of the algorithm and has an important effect on mining efficiency, while the second course is simple relatively. So algorithm MDIM mainly improves the first course. Furthermore, there should be a series of operations of data pretreatment before mining. These operations include data cleaning, integration, transformation and reduction. After these operations, the database will become more appropriate for mining interesting rules [1,2,5]. 3.1 Structure and Strategy Structure. Algorithm MDIM defines four simple data structures named DimSizeNode, DimSetNode, ValueSetNode and SupMemNode, respectively. A 4-level link list structure, which is based on the four simple structures and used to reserve itemsets in database, is generated in algorithm MDIM. An example is given to show the structure in figure 1 and the data used in the example come from a relational table shown in table 1. Table 1. A relational table used by algorithm MDIM

ID 1 2 3 4 5 6 7 8

Field 1 Field 2 Field 3 Field 4 Field 5 1 1 1 1 1 2 2 1 2 1 2 2 2 2 1 1 1 2 1 1 2 3 2 1 2 1 1 1 1 1 2 3 2 1 2 2 2 1 2 1

From the structure displayed in the figure 1, it is easily to find that an itemset is divided into two parts, one of which is dimension combination and the other is value combination. Two parts of an item set are reserved in different places. The structure named DimSetNode stores the dimension combination and the structure named ValueSetNode stores the value combination.

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Fig. 1. 4-level link list structure used by MDIM (minimum support is 0.5)

For example, {(1, 2), (3, 1)} is a 2-itemset with two support records whose serial numbers are 2 and 8. In our structure, the 2-itemset will be stored under the node whose type is DimSizeNode and field named dimSetSize is 2. The dimension combination (1, 3) is reserved in a node whose type is DimSetNode and (1, 3) locates in a place which a field named dimPtr points to. The value combination (2, 1) is reserved in a node whose type is ValueSetNode and (2, 1) locates in a place which a field named valuePtr points to. 2 and 8 locate in a place which a field named memberHead points to and a field named memberNum is filled with 2 and a field named frequent can be got by comparing the memberNum with the appointed parameter. Strategy. As many indexes on dimension, dimension combination and value combination are created in the 4-level link list structure, itemsets and the number of their support members can be found easily and quickly, which makes the time consuming of matching and finding itemsets decrease. Furthermore, as the 4-level structure stores the support members of itemsets, support members set of newly generated candidate k-itemsets can be get by computing the intersection of support member sets of two frequent (k-1)-itemsets instead of scanning target database to get. So, the database will be scanned only once and all frequent itemsets can be generated. 3.2 Algorithm MDIM Input: RDB(a relational database), min_sup(minimum support). Output: indexHead(an access to all frequent itemsets). Multi_Dimension_Indexing_Mining(RDB, min_sup){ indexHead = Initialize_DimSizeNode(1);

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indexHead = Gen_Candidate_1_Itemsets(RDB); Gen_Frequent_ItemSets(indexHead, min_sup); lastIndex = indexHead; while (Lk-1 ∅ ){ curIndex = Gen_Candidate_k_ItemSets(lastIndex); Gen_Frequent_ItemSets(curIndex, min_sup); lastIndex → next = curIndex; lastIndex = curIndex; } return indexHead; } Gen_Candidate_k_ItemSets(lastIndex){//(k•2) curIndex=Initialize_DimSizeNode(lastIndex.dimSize+1); for each itemset l1 in lastIndex for each itemset l2 in lastIndex if(l1[1] = l2[1] l1[2] = l2[2] … l1[k-2]= l2[k-2] l1[k-1]  l2[k-1]) then //Create a candidate k-itemset c using l1 and l2. //Then, insert c into curIndex. The support members //of c are the intersection of support members of //l1 and those of l2. Combine_2ItemSets_To_1ItemSets(curIndex,l1,l2); return curIndex;

ш

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} Gen_Frequent_ItemSets(curIndex, min_sup){//(k•1) for each itemset=(dimSetPtr, valueSetPtr) in curIndex if valueSetPtr → memberNum • min_sup then valueSetPtr → frequent = true; else valueSetPtr → frequent = false; } 3.3 Theoretical Analysis Suppose that target relational database is RDB whose number of records is M and number of dimensions is N(N represent a decision system, where U = {u1, u2, …, ui, …, u|U| } is a finite non-empty set, called an instance space or universe, and where ui is called an instance in U. A = {a1, a2, a3, …, ai, …, a |A|}, also a finite non-empty set, is a set of attributes of the instances, where ai is an attribute of a given instance. D is a non-empty set of decision attributes, and A∩D = Ø. For every a ∈ A there is a domain, represented by Va, and there is a mapping a(u) : U → Va from U into the domain Va , where a(u) represents the value of attribute a of instance u and is a value in the set Va. Va = a(U) = {a(u) : u ∈ U } for a ∈ A.

(1)

For a decision system, the domain of decision attribute is represented by Vd = d(U) = {d(u) : u ∈ U } for d ∈ D.

(2)

2.2 Value Number Distribution In order to obtain a statistical table, a set of distribution numbers are defined as follows. Let N d k , ai ,vx represent the number of instances with decision value dk and attribute value

vx ∈ Vai .

N d k ,ai ,vx = | {u : d (u ) = d k and ai (u ) = vx for all u ∈ U } | . N ai ,vx =

¦

d x ∈Vd

N d x ,ai ,vx .

where N ai ,vx is the number of instances with attribute value vx ∈ Vai .

(3)

(4)

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3 Adaptive Discretizer 3.1 Definition of Dichotomic Entropy

Let vx ∈ Vai be a value of continuous attribute ai and the continuous attribute ai is split by border value vbd. In order to indicate instance number and homogeneous degree over the decision space within an attribute value interval, a decision distributional index is defined as follows.

Ed (vstart → vend ) =

¦ −N

d k ∈Vd

d k ,vstart →vend

log 2 (

N d k ,vstart →vend N ai ,vstart →vend

).

(5)

where N d k ,vstart →vend represents the number of instances with decision value dk and attribute value within vstart and vend, and N ai ,vstart →vend represents the number of instances attribute value within vstart and vend for all decision values. This decision distributional index indicates homogeneous degree for corresponding interval. Based on this index, two decision distributional indexes can be obtained when an interval is split. A dichotomic entropy for splitting point vbd is defined as

E (vbd ) =

1 1 Ed (vstart → vbd ) + Ed (vbd → vend ) . |U | |U |

(6)

where |U| is the total number of instances. According to machine learning theory [5-7, 10-11], the smaller the entropy is, the better the attribute discretization. Applying Equation (6), a border value vborder can be obtained by minimizing dichotomic entropy. vborder = arg min E (vbd ) vbd ∈Vai

§ 1 · 1 = arg min ¨ Ed (vstart → vbd ) + Ed (vbd → vend ) ¸ . |U | vbd ∈Vai © | U | ¹

(7)

3.2 Adaptive Rules

Applying Equation (7), a continuous attribute can be split into two intervals. Then an interval is selected to split further. In principle, an interval with an inhomogeneous value distribution and large number of instances should be split. In order to get a quantitative criterion, a distributional index for instance number distribution over the attribute values and the decision space within an interval, which is called a value distributional index, is defined as follows. Ev (vstart → vend ) =

¦

vstart ≤ vx < vend

¦ −N

d k ∈Vd

d k , ai , vx

log 2 (

N d k , ai ,vx N ai ,vx

).

(8)

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It is obvious that Ev (vstart → vend ) is small if the distribution varies with value vx at high frequency. Ev (vstart → vend ) is large if the distribution varies with value vx very slowly, in other words, the distribution over value vx is homogeneous. Mathematically, it is easy to prove that the maximal value of Ev (vstart → vend ) is equal to the decision distributional index Ed (vstart → vend ) for the same interval. Based on the difference of Ed (vstart → vend ) - Ev (vstart → vend ) , a compound distributional index is defined as follows. ∆E (vstart → vend ) =

Ed (vstart → vend ) − Ev (vstart → vend ) . |U |

(9)

where |U| is total number of instances in the instance information system. Dividing by |U| ensures that ∆E (vstart → vend ) is a real value within [0,1] and ∆E (vstart → vend ) decreases as the instance number of the interval decreases i.e. the interval becomes smaller. This compound distributional index can be applied as a criterion to determine whether an interval is to be split further. An interval with largest ∆E (vstart → vend ) is selected to split during a splitting operation in an adaptive discretizer. If ∆E (vstart → vend ) = 0 i.e. the value distribution is a homogeneous distribution with respect to vx, it is not necessary to split the interval further. In most cases, 5 intervals are enough for reaching a high decision accuracy in our experiments. Therefore, adaptive discretizer stops when the number of intervals reaches five or ∆E (vstart → vend ) is less than a threshold. These adaptive rules are thus very different from the approach in [6]. The value of ∆E (vstart → vend ) reflects the two distributional indexes (decision distributional index and value distributional index) and depends on the number of instances within the interval. The larger the decision distributional index is, the larger the value of ∆E (vstart → vend ) . The larger the value distributional index is, the smaller the value of ∆E (vstart → vend ) . The larger the number of instances within the interval is, the larger the value of ∆E (vstart → vend ) . Value ∆E (vstart → vend ) is thus a compound index to provide guidance to an interval that should be split.

4 Experimental Results A set of 13 benchmark data sets from the UCI Machine Learning Repository [9] was applied to test both multi-knowledge approaches with the discretizer and without the discretizer. The decision accuracies under the ten-fold cross validation standard are given in Table 1. Column ‘No-Discretizer’ lists decision accuracies for multiknowledge approach without the discretizer. Column ‘Adaptive Discretizer’ lists decision accuracies for multi-knowledge approach with the discretizer. In order to compare with an unsupervised discretizer, column ‘5-equal Discretizer’ lists decision accuracies for multi-knowledge approach with a 5-identical-interval discretizer. It can be seen that multi-knowledge approach with the adaptive discretizer improved

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decision accuracies for 13 data sets. The average accuracy over 13 data sets is better than multi-knowledge approaches without the adaptive discretizer and with a 5identical-interval discretizer. Column C-type Attributes gives the number of continuous attributes that contain in corresponding data set. The names with ‘♣’ indicate that some attribute values are missing in the data set. Table 2 shows that combination of new discretizer and the multi-knowledge approach can obtain higher decision accuracy than other conventional approaches. Table 1. Improvement results for applying the discretizer to multi-knowledge Attribute Number 60 27 34 13 15 13 13 44 6 4 6 38 39

Data Name Sonar Horse-colic ♣ Ionosphere Wine Crx_data♣ Heart Hungarian♣ SPECTF Bupa Iris_data Ecoli Anneal♣ Bands♣ Average

C-type Attributes 60 7 34 13 6 6 6 44 6 4 6 6 20

Instance number 208 300 351 178 690 270 294 80 345 150 336 798 540

NoDiscretizer

Adaptive Discretizer

77.8 80.0 90.6 98.9 85.1 83.3 85.4 73.8 65.5 96.7 71.5 99.4 77.8 83.5

97.1 86.3 93.7 99.4 86.5 86.3 85.4 98.8 70.2 96.7 75.3 99.7 79.6 88.8

5-equal Discretizer

91.4 80.3 92.6 97.8 85.0 85.1 84.0 92.5 67.0 93.3 75.0 99.7 76.5 86.2

Table 2. Comparison of different combination approaches Combination Approach Original-C4.5[12] Chi-C4.5[12] MChi-C4.5[12] MDLPC-C4.5[12] New discretizer-MK

Iris 95.33 94.0 94.7 94.0 96.7

Wine 92.7 88.8 93.2 87.7 99.4

Bupa 68.4 50.0 50.3 63.5 70.2

Heart 53.8 55.1 32.9 54.5 86.3

5 Conclusion Based on a value distribution, a compound index, which is composed of a decision distributional index and a value distributional index, was defined and applied to determine to the interval that should be split during discretization. Dichotomic entropy was defined and minimal dichotomic entropy was applied to determine the border value for splitting an interval. Using this approach, a continuous attribute can be split in two intervals at the border point with minimal dichotomic entropy; then the compound index is applied to select the new intervals to split further until the desired

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number of intervals is reached or the compound index is small enough. The adaptive discretizer was combined with the multi-knowledge approach to making decision. The experimental results on 13 benchmark data sets shows that the average accuracy has been improved. This adaptive discretizer can be combined with other machine learning approaches for further study.

References 1. Lin, T.Y., Cercone, N. (eds): Rough Set and Data Mining, Kluwer Academic Publishers, (1997) 2. Polkowski, L., Tsumoto, S., Lin, T.Y. (eds): Rough Set Methods and Applications, New Developments in Knowledge Discovery in Information Systems, Physica-Verlag, A Springer-Verlag Company, (2000) 3. Hu, X., Cecone, N., Ziarko, W.: Generation of Multiple Knowledge from Databases based on Rough Set Theory, in: Lin TY and Cercone N (eds) Rough Set and Data Mining, Kluwer Academic Publishers, (1997)109-121 4. Wu, Q.X., Bell, D.A., McGinnity, T.M.: Multi-knowledge for Decision Making, International Journal of Knowledge and Information Systems, Springer-Verlag, 7 (2) (2005)246 – 266 5. Dougherty, J., Kohavi, R., Sahami, M.: Supervised and Unsupervised Discretization of Continuous Features, Proc. Of International Conference on Machine Learning, (1995) 194202 6. Wu X.D.: A Bayesian Discretizer for Real-Valued Attributes. The Computer J., 39 (1996) 688-691 7. Lukasz A.K., Krzysztof J.C.: CAIM Discretization Algorithm, IEEE Transactions on Knowledge and Data Engineering, 16 (2) (2004) 145-153 8. Pawlak, Z.: Rough Sets: Theoretical Aspects Data Analysis, Kluwer Academic Publishers, Dordrecht (1991) 9. Blake, C.L., Merz, C.J.: UCI Repository of Machine Learning Databases, http://www.ics.uci.edu/~mlearn/MLRepository.html, UC Irvine, Dept. Information and Computer Science, (Download in 2003) 10. Quinlan, J.R.: Induction of Decision Trees, Machine Learning, 1 (1) (1986)81-106 11. Mitchell, M.T.: Machine Learning. McGraw Hill Co-published by the MIT Press Companies, Inc. (1997) 12. Tay, F.-E.H., Shen, L.: A Modified Chi2 Algorithm for Discretization, IEEE Transaction on Knowledge and Data Eng., 14 (3) (2002)666-670 13. Wu, Q.X., Bell, D.A.: Multi-Knowledge Extraction and Application. In: Wang, G.Y., Liu, Q., Yao, Y.Y., and Skowron, A., Eds. Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing (RFDGrC03). LNAI 2639, Springer, Berlin (2003) 274-279

A Novel Neural Network for Sensor Fusion Applied to Wood Growth Ring Moisture Measurement* Mingbao Li1, Shiqiang Zheng2, and Jun Hua2 1

School of Civil Engineering, Northeast Forestry University, No. 26 Hexing Road, Harbin, 150040, China [email protected] 2 School of Electromechanical Engineering, Northeast Forestry University, No. 26 Hexing Road, Harbin, 150040, China [email protected], [email protected]

Abstract. Wood growth ring moisture content is considered as an important measured quantity for the analysis of wood drying stress. However, wood moisture sensors working in the complicated drying conditions are intensively jammed by ambient factor parameters. In this paper, a novel functional-link neural network (FLNN) is presented for the implementation of wood moisture sensor fusion. FLNNs are single layer networks that are able to handle linearly nonseparable classes due to the dimensions of the inputs being increased by using nonlinear combinations of the input features. Simulation results have demonstrated that FLNN has a less computational complexity and a better performance compared with conventional multilayer neural networks.

1 Introduction Wood is preferred building and engineering material because it is cost effective, low in processing energy, easy to work, renewable, strong and aesthetically pleasant [1]. Before used for engineering applications, drying treatment for wood is needed. Wood growth ring moisture content is considered as an important property since it is related to many wood properties including strength, stiffness and dimensional stability. It also affects wood processing properties [2]. The accuracy measurement for moisture content in the wood growth ring is critical for the analysis of wood stress, as well as the determination of the drying schedule. In the harsh drying environment moisture content sensors are intensively influenced by ambient factors, including in-kiln temperature, equilibrium moisture content, jet flow, etc. In order to solve the noisy problems and obtain an accurate output, sensor fusion methods are adopted. Sensor data fusion approach combines data from multiple sensors (and associated databases if appropriate) to achieve improved accuracies and more specific inferences that could not be achieved by the use of only a single sensor [3]. Data fusion methods can be further classified into three categories:Probabilistic models, such as Bayesian *

This work is supported by National Natural Science Foundation of China (30371126) and by Natural Science Foundation of Heilongjiang Province of China (C0308).

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 784 – 789, 2006. © Springer-Verlag Berlin Heidelberg 2006

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reasoning, evidence theory, robust statistics; Least squares, such as Kalman filtering, regularization, set membership; intelligent fusion: such as fuzzy logic, neural networks, genetic algorithms, etc. Of those methods, sensor fusion based on artificial neural network has been more and more concerned in recent years. Much efforts have been focused on NN architectures and their design, in particular, on architectures for fast learning, on adjustable weight matrices for learning, and on fast learning algorithms [4],[5]. Most of the artificial neural network (ANN) data fusion techniques are based on multilayer feed-forward networks such as multilayer perceptron (MLP) trained with back-propagation (BP) or more improved variations of this algorithm. The problem of data fusion using MLP structure lies in that the BP learning algorithm needs a long training time because of the hidden layers. When the number of hidden layer is increased, the network will converge closer to a local minimum. The functional link neural network (FLNN) was first proposed by Pao and Takefuji [6]. According to the function approximation basic theorem proposed by Hornik, FLNN method combines linearly the input signal and expands the input signal space. In this structure, the hidden layers existing in the MLP are completely replaced by the nonlinear mappings. That simplifies the structure of MLP and makes FLNN perform faster convergence rate and less computational complexity than the former. Philip Chen et al. [7] presents an adaptive implementation of the functional-link neural network architecture together with a supervised learning algorithm that rapidly determines the weights of the network. By tests on function approximation, time-series prediction, and system identification, the simulation shows a very promising result. Also, other literatures [8],[9] proved that FLNN is an effective and valid modeling tool for sensor fusion. Based on the former work, in this paper, functional link neural network using Chebyshev polynomials is proposed for this purpose to compensate for nonlinear response characteristics and complex nonlinear dependency of the environmental parameters on the sensor characteristics and to get accuracy and reliable fusion output. The sensor fusion model based on the FLNN architecture will be built. The performance comparison with the MLP model will be discussed.

2 ANN-Based Sensor Fusion In this paper, wood growth ring moisture content measuring system employs multiple sensors when the single sensor cannot provide satisfactory accuracy or reliability. The method of data fusion combines redundant and complementary multi-sensor information. The fusion of redundant information can reduce overall uncertainty and thus increase the accuracy with which the features are perceived by the system. The redundant information provided by multiple sensors can also serve to increase reliability in the case of sensor error or failure. Neural networks provide a well-established formalism with which to model the processing of data fusion. Relations of neurons can be activated in response to the relationship between the multi-sensor data input and the desired signal or decision output.

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The neural network used in this paper is a single layer FLNN using Chebyshev polynomials. A general structure of FLNN is shown in Fig. 1. The architecture consists of two parts [16]: namely, numerical transformation part in part (A) and learning part in part (B). Numerical transformation deals with the input layer to hidden layer by approximate transformable method. The training patterns are denoted by { X k yk } , where the input pattern vector Xk be of dimension n, and the output yk be a scalar. A set of N basis functions Φ ( X k ) = [φ1 ( X k ) φ2 ( X k ) ⋅⋅⋅ φN ( X k )]T are adopted to expand functionally the input signal X k = [ x1 ( k ) x2 (k ) ⋅⋅⋅ xn (k )]T . These N linearly independent functions map the n-dimensional signal space into an N-dimensional space, that is R n → R N , n < N . As a result the Chebyshev polynomial basis can be viewed as a new input vector. Hence, there is no learning in this part. For example, consider a two dimensional input pattern X = [ x1 x2 ]T . An enhanced pattern obtained by using Chebyshev functions is given by Φ = [1 T1 ( x1 ) T2 ( x2 ) ⋅⋅⋅ T1 ( x1 )T2 ( x2 ) ⋅⋅⋅ ]T .

(1)

where Ti ( xi ) is a Chebyshev polynomial. The four kinds of the Chebyshev polynomials can be generated by the following the two term recursion formula [16] Ti +1 ( x) = 2 xTi ( x) − Ti −1 ( x ),

T0 ( x ) = 1 .

(2)

but with different choices of initial values T1 ( x1 ) = x, 2 x, 2 x − 1 and 2 x + 1 . The linear combination of these function values can be presented in its matrix form, that is S = Wĭ. Here Sk = [S1(k) S2(k) ··· Sm(k)]T, W is the m×N dimensional weight matrix. The matrix Sk is input into a set of nonlinear function ȡ(·) = tanh(·) to generate the equalized output Yˆ = [ yˆ1 yˆ 2 ⋅⋅⋅ yˆ m ]T , yˆ j = ρ ( S j ) , j =1, 2, ···, m.

ij1(x)

x1 x2

Functional

ij2(x)

™

: :

xk

Expansion

X=

x1 x2 : : xn

Sk

^y k

tanh (.)

–

e(k) ijN(x)

Upgrate Algorithm

™

+ yk

A. numerical transform part

B. learning part

Fig. 1. Structure of a functional link network

Being similar to a MLP, the FLNN uses a BP algorithm to train the neural networks. But since the FLNN has much simpler structure than a MLP, its speed of convergence for training process is a lot faster than a MLP. The detailed training algorithm and stability analysis can be found in the literature [10].

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3 Model Building and Testing In this section we present the results of sensor fusion model for wood ring moisture content measurement. Wood species and measurement method was given. Ambient factors that influence the measurement precision were analyzed. Based on those work, detailed performance studies using FLNN for these models have been carried out and an illustration of FLNN performance was analyzed. 3.1 Material and Measurement Method

The wood used for these experiments were rough-sawn, green sapwood boards, 60mm×150mm, obtained from a local sawmill in Harbin from Fraxinus mandshurica timber sourced from North China. The boards were dried in a closed-circuit drying kiln at an air velocity of 3m/s. Wood moisture content was measured by selfdeveloped sensors. In order to consider the other influenced factors for sensor fusion modeling, in-kiln air temperature was measured by a platinum resistance thermometer and the equilibrium moisture content (EMC) by a temperature-compensated capacitive element. These measured signals were controlled through Advantech® PCI–1711 data acquisition board and control software. The weight of the boards was monitored continuously by a Sartorius FA-N/FI Series Electronic Analytical Balance with a maximum capacity of 10kg and a resolution of 0.1mg. These weight data from ASTM D 4442–92 test method were used as calibration values for the actual sensor output in the modeling training and testing. In the wood drying applications, the final wood moisture content (MC) usually ranges from 7% to 12%. The ultimate phase (MC descending from approximately 25% to the ultimate MC) of the wood drying process is most crucial for the drying quality. So in this paper wood MC in the range from 7% to 25% was mainly studied. By data acquisition software and Electronic Analytical Balance, 396 input-output samples recorded with a sampling period of 10 minutes used for model building and testing were prepared. Next, these datasets were divided into two groups, 264 sets for the model training and 132 sets for the model testing. 3.2 Model Building

Before modeling, the three inputs (including MC sensor output voltage, ambient temperature and EMC output voltage) and the output (fusion value of MC output), used in the simulation study were suitably normalized so as to keep their values within 1. The reference [11] gives the mean square error (MSE) for the proposed model for inputs expanded to different number of terms along with the number of weights to be updated in the FLNN. From the comparison it becomes clear that when the order of the Chebyshev polynomial expansion is taken as two, the MSE is minimum. So for sensor fusion in this study, we have expanded the three inputs to two terms each. After forward calculations, the FLNN produces a fusion output of wood MC, which will be compared with the target pattern (from the balance reading) to obtain an error value. This error is used to update the weights of the FLNN by the improved training

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algorithm. Then, the iteration process continues till the mean square error between the desired and the FLNN output reaches a preset minimum value. After 689 iterations are made to train the FLNN model with MSE 0.089, the final weights are stored for later use for model testing. The performance of the proposed FLNN was compared with that of an MLP. For this purpose, the same data sets were also trained on a 5-3-1 multi-layer neural network (MLNN) using the BP algorithm. It takes 780 iterations to reach the training MSE 0.091. 3.3 Model Testing

In order to check the validity of the trained FLNN model, another 132 data-sets are normalized and applied to the model. The performance evaluation of the model is carried out by loading the final stored weights into the FLNN. There is no updating of the weights during testing mode and actual use of the LMCS model. To evaluate the effectiveness of the model, the FLNN fusion output of MC was computed and then compared with the actual values of MC. The similar operations were applied to the MLP model for making a comparison. True and fusion MC ranging from 12% to 20% from testing sets for MLP models and FLNN are evaluated shown in Fig. 2. The linearity of estimation in the MLP and FLNN model is quite good. It can be observed that the MLP and FLNN models are capable of estimating the wood MC quite accurately. The fusion result using the FLNN model is with the relative MC output error of 2.30% and the testing MSE of 0.653. The elapsed training time is 2.4322s on an IBM R52e–1.70GHz Notebook. For the MLP model, these performance values are 4.58%, 0.738 and 5.7239s, respectively. 0.8

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From the above observations, it is clear that the performance of the MLP model is similar or a little superior to the FLNN model. However, it must be pointed out that FLNN has the simplest architecture, and has the minimum computational requirements. The amount of computational complexity of the learning algorithm determines its efficiency during training phase and cost of hardware at the time of implementation of the model.

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4 Conclusions In this paper, we have presented sensor fusion schemes in a neural network framework to solve the nonlinearity and ambient interference problems of wood growth ring moisture content sensors. The functional link neural network (FLNN) is adopted for the implementation of wood moisture sensor fusion. FLNN eliminates the hidden layer(s) of conventional neural networks by expanding the input pattern into a high order dimensional space. Compared to the multilayer perceptron (MLP), FLNN with two terms of Chebyshev polynomial trained by a BP algorithm has the similar performance and less computational complexity. The amount of computational complexity of the learning algorithm determines its efficiency during training phase and cost of hardware at the time of implementation of the model. In addition, the testing performance of FLN model has been studied. This precision performs very well for the fusion model requirements compared with the conventional neural networks. Therefore, data fusion based on FLN is a very effective method for lumber MC measuring. Based on the above advantages, FLNN may be conveniently employed in the other fields of instrument and measurement systems to compensate the adverse effects of the environment and nonlinearities of the devices.

References 1. Usta, I.: Amenability of European Silver Fir (Abies alba Mill.) to Preservative Treatment by the Full-cell Process in Longitudinal, Tangential, Radial and Triplex Flow Pathways on the base of Wood Drying. Bldg. Environ 41, (2006) 1027–1033 2. Perréa, P., Turner, I.W.: A Heterogeneous Wood Drying Computational Model that Accounts for Material Property Variation across Growth Rings. Chem.Eng.J. 86, (2002) 117–131 3. Hall, D.L., Llinas, J.: An Introduction to Multi-sensor Data Fusion. Proc. IEEE, Vol. 85, (1997) 6–23 4. Su, J.B., Wang, J., Xi, Y.G.: Incremental Learning with Balanced Update on Receptive Fields for Multi-Sensor Data Fusion. IEEE Trans. Syst. Man Cybern. B, Cybern,Vol.34, No. 1, (2004) 659–665 5. Rao, N.S.V., Reister, D.B., Barhen, J.: Information Fusion Methods Based on Physical Laws. IEEE Trans. Pattern Anal. Mach. Intell, Vol. 27, (2005) 66–77 6. Pao, Y.H. , Takefuji, Y.: Functional-link Net Computing: Theory, System Architecture, and Functionalities. Computer, Vol.25 ,(1992) 76–79 7. Chen, Philip, C.L., Steven, R., Clair, L., Pao, Y.H.: An Incremental Adaptive Implementation of Functional-link Processing for Function Approximation, Time-series Prediction, and System Identification. Neurocomputing 18, (1998) 11–31 8. Zhang J.W. , Cao, J.: ANN-based Data Fusion for Lumber Moisture Content Sensors. Trans. Inst. Meas. Control 28, (2006) 69–79 9. Patra, J.C. ,Bos, A.: Modeling of an Intelligent Pressure Sensor Using Functional Link Artificial Neural Networks. ISA Trans. 39, (2000) 15–27 10. Weng, W.D.,Yen, C.T.: Reduced-decision Feedback FLANN Nonlinear Channel Equaliser for Digital Communication Systems. IEE Proc.-Commun 151, (2004) 305–311 11. Purwar, S., Kar, I.N., Jha, A.N.: On-line System Identification of Complex Systems Using Chebyshev Neural Networks. Applied Soft Computing, in press 2005

A Novel Reduction Algorithm Based Decomposition and Merging Strategy Feng Hu, Xinghua Fan, Simon.X Yang, and Chaohai Tao Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, P.R.China {hufeng, fanxh}@cqupt.edu.cn, [email protected], [email protected]

Abstract. In knowledge acquisition based on rough set theory, attribute reduction is a key problem. In this paper, by integrating with the idea of decomposing and merging decision tables, a novel attribute reduction algorithm with three steps is presented. First, an intact decision table is decomposed into two sub-decision tables with same condition and decision attributes, according to the decomposition strategy presented. Second, attribute reduction results of the two sub-decision tables are acquired in terms of classical attribute reduction algorithms. Third, a merging algorithm is developed, so the two sub-decision tables are merged into the intact decision table. The whole reduction process of original decision table is implemented. Experimental results demonstrate the efficiency of the proposed algorithms.

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Rough set (RS) is a valid mathematical theory to deal with imprecise, uncertain, and vague information [1]. It has been applied in many fields such as machine learning, data mining, intelligent data analyzing and control algorithm acquiring, successfully since it was developed by Pawlak in 1982 [2]. Rough set is an important method in KDD for the sake of the capability of process non-determinate information.In the research of knowledge acquisition, attribute reduction is a key problem in rough sets based knowledge acquisition, and many researchers proposed some algorithms for attribute reduction [3-7].However, these algorithms can hardly deal with large data environment, which is not convenient to the application of Rough Sets in industry, and it is urgent to find appropriate road to resolve the problem. The core idea of decomposing and merging strategy is as follow. Firstly, a very large and hard problem is decomposed into many small size and independent sub-problems with same type.Secondly,all sub-problems are processed and their solutions are acquired. Thirdly, their solutions are merged and the solution of the original large and hard problem is obtained. Combining the idea of decomposing and merging strategy, original large data sets are divided into many small data sets, then, the small data sets are processed and their solutions are merged. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 790–796, 2006. c Springer-Verlag Berlin Heidelberg 2006


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For the convenience of description, some basic notions of decision table are introduced here at first. Definition 1. A decision table is defined as S =< U, R, V, f >, where U is a non-empty finite set of objects, called universe, R is a non-empty finite set of attributes, R = C ∪ D, where C is the set(of condition attributes and D is the Vp , and Vp is the domain of the set of decision attributes, D = Ø. V = p∈R

attribute p. f : U × R → V is a total function such that f (x, p) ∈ Vp for every p ∈ R, x ∈ U . Definition 2. Given a decision table S =< U, C ∪ D, V, f >, D ={d }. All consistent element sets in S can be collected into set P s, that is, f or all Ei ∈ P s, f or all (x, y ∈ Ei ), (d(x) = d(y)). Ps is called positive element set. All inconsistent condition classes in S construct another set N s, that is, f or all Ei ∈ N s, ∃x, y ∈ Ei (d(x) = d(y)), N s is called negative element set. Definition 3. Given a decision table S =< U, C ∪ D, V, f >, C and D are its condition attribute set and decision attribute set respectively. Ps is its positive element set and Ns is its negative element set. Given an attribute subset B ⊆ C, f or all Ei ∈ P s, if Ei can satisfy one of the following two conditions: (1) There is a element set Ej ∈ P s(Ei = Ej ) , Ei and Ej have the same values for the condition attribute subset B, and different values for the decision attribute set D. (2) There is a element Ej ∈ N s , Ei and Ej have the same values for the condition attribute subset B. Then Ei is called a collision element set on attribute set B in Ps, otherwise Ei is called a non-collision element set on attribute set B in Ps. Property 1. Assume Ei is a non-collision element set on attribute set B(B ⊆ C), for any attribute set A(B ⊆ A ⊆ C), Ei is also a non-collision element set on attribute A. On the contrary, assume Ei is a collision element set on attribute set B(B ⊆ C) , for any attribute set A(A ⊆ B ⊆ C) , Ei a is also collision element set on attribute set A. Proof. According to Definition 3, it is obvious. Proposition 1. Given a decision table S =< U, C ∪ D, V, f > , let P OSP (Q) be the P positive region of Q, for any attribute set P ⊆ C, P OSP (Q) = P OSC (D) if f there is no collision element set on P in its positive element set Ps. Proof. Obviously, the proposition holds according to Definitions 2 and 3. In this paper, according to positive element sets, negative elemental sets, Property 1 and Proposition 1, decomposition and merging reduction algorithms are presented based on division and conquering strategy.

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Decomposition and Merging Reduction Algorithms

Divide and conquer strategy is adopted in decomposition and merging reduction algorithm.The algorithm can be developed by three steps: (1)By decomposition algorithm, original decision table S =< U, C ∪ D, V, f > is decomposed into two sub-decision table S1 =< U1 , C ∪ D, V, f > and S2 =< U2 , C ∪ D, V, f >,where U1 ∩ U2 = φ and U1 ∪ U2 = U . (2)Find reduction of S1 and S2 respectively:red1 and red2 ,by classic attribute reduction algorithm(such as attribute reduction algorithm based on discernibility matrix,general attribute reduction algorithm, attribute reduction algorithm based on feature choice and attribute reduction algorithm based on information entropy,etc).(3)After red1 and red2 are gained,the attribute reduction red of S is computed by merging reduction algorithm. After decision table S is divided into S1 and S2 ,their attribute reduction red1 and red2 are acquired by traditional method, which is accustomed by us and will not be discussed in this paper.In the rest part, we will pay attention to discuss merging reduction algorithm.According to property 1 and proposition 1, the algorithm is proposed as follow. Algorithm 1. Merging Reduction Algorithm of Decision Table. Input: Decision table S1 =< U1 , C ∪ D, V, f > ,its attribute reduction red1 ,its positive element set P s1 and negative element set N s1 ; Decision table S2 = < U2 , C ∪ D, V, f >,its attribute reduction red2 ,its positive element set P s2 and negative element set N s2 Output: the attribute reduction result Red of the new decision table S =< U1 ∪ U2 , C ∪ D, V, f > Setp1:(Initiating) Red = red1 ∪ red2 ,F = φ,r = 1. Step2: (Eliminating redundant positive and negative element sets). f or each N si2 in N s2 do if N si2 ∈ N s1 , then N s2 = N s2 − {N si2 }. if ∃P sj1 ∈ P s1 (1 ≤ j ≤ |P s1 |),where P sj1 and N si2 have same values in attribute set C,then P s1 = P s1 − {P sj1 }. f or each N sk1 in N s1 do if ∃P sj2 ∈ P s2 (1 ≤ j ≤ |P s2 |),where P sj2 and N sk1 have same values in attribute set C,then P s2 = P s2 − P sj2 . Setp3:(N eed it add new attributes ?) f or each P si2 ∈ P s2 do f or each P sj1 ∈ P s1 do if P si2 contradicts P sj1 on attribute set Red, let c1 , c2 , ..., cu be attributes in attribute set C − Red on which P si2 and P sj1 have different attribute values, and let br = c1 ∨ c2 ∨ ... ∨ cu ,r = r + 1.

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f or each N sk1 ∈ N s1 do if P si2 contradicts N sk1 on attribute set Red, let c1 , c2 , ..., cu be attributes in attribute set C − Red on which P si2 and N sk1 have different attribute values, and let br = c1 ∨ c2 ∨ ... ∨ cu ,r = r + 1. f or each N si2 ∈ N s2 do f or each P sj1 ∈ P s1 do if N si2 contradicts P sj1 on attribute set Red, let c1 , c2 , ..., cu be attributes in attribute set C − Red on which N si2 and P sj1 have different attribute values, and let br = c1 ∨ c2 ∨ ... ∨ cu ,r = r + 1. Setp4:(Add new attributes) Let F = b1 ∧ b2 ∧ ... ∧ bk−1 and transform F to a disjunctive formula F = (q1 ∨ q2 ∨ ... ∨ qi ∨ ... ∨ qn ). Choose the smallest term qj (qi = c1 ∧ c2 ∧ ... ∧ cl ) from F. A = {c1 , c2 , ..., cl }. Step5:(Eliminating possible existed redundant attributes) Red = red ∪ A. f or i = 1 to |Red| do P = Red; Let ci be i-th attribute in Red ; P = P − {ci }; if P osC (D) = P osP (D), then Red = P . Step6:(Return) return Red. Time complexity analysis of Algorithm 1: Let N1 be number of objects in S1 ,n1 be cardinality of element set in S1 ,Let N2 be number of objects in S2 ,n2 be the cardinality of element set in S2 .Let m be the cardinality of condition attribute set C,k be the cardinality of condition attribute set red1 ∪ red2 .Obviously, n1 < N1 and n2 < N2 .The best time complexity of algorithm 1 is :T = O(n1 × n2 ),and the worst time complexity is:T = O(n1 × n2 × m) + O(k × (n1 + n2 )2 ). The merging reduction algorithm is presented above, and the decomposition and merging reduction algorithm will be developed as follow. Algorithm 2. Decomposition and Merging Reduction Algorithm Input: Decision table S =< U, C ∪ D, V, f > Output: the attribute reduction result Red of S Step1(Decomposition) According to decomposition method of column vector, S is decomposes into two sub-decision tables S1 =< U1 , C ∪ D, V, f > and S2 =< U2 , C ∪ D, V, f >, where U1 ∪ U2 = U and U1 ∩ U2 = φ. Step2(Computing element sets of two sub − decision tables) According to Def.5,computing positive element set P s1 and negative element set N s1 of S1 , and computing positive element set P s2 and negative element set N s2 of S2 . Step3(Computing attribute reduction of sub − decision tables) By classical attribute reduction algorithm, acquiring attribute reduction red1 and red2 of S1 and S2 respectively.

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Step4(M erging reduce) By Algorithm1, red1 and red2 , computing attribute reduction Red of S. Step5(return) return Red. Since Algorithm 2 decomposes one |U |·|C ∪D| problem into two |U |·|C ∪D|/2 problems,and time complexity of Algorithm 1 is very small, Algorithm 2 will decrease the running time of reduction process of decision table to half,comparing to classic attribute reduction algorithm.And if distributed and parallel technique is adopted, the running efficiency will enhance more.

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Experimental Results

In order to test the validity of the algorithms, two classical algorithms for attribute reduction (general attribute reduction algorithm [2] , attribute reduction algorithm based on information entropy [2]) are used. The configuration of the PC in our experiments is P4 2.4G(CPU), 256M(memory), windowsXP (operation system). Data sets Heart c ls, P ima India, Crx bq ls, Liver and Abalone from UCI database are used to test. The whole data set are used as the original decision table, and it is decomposed into two sub-decision table. Attribute reductions are computed by two classical algorithms and Algorithm 2 for each original decision table. The experiment results are shown in Table 1. Where, T is running time of algorithm, its unit is second. n is the number of condition attributes in reduction results.Algorithm A represents general attribute reduction algorithm, and Algorithm B represents attribute reduction algorithm based on information entropy.original represents original decision table,subtable represents subdecision table.M ix represents mixed reduction, which means one sub-decision is reduced by general attribute reduction algorithm, and other sub-decision is reduced by attribute reduction algorithm based on information entropy.And Algorithm A , Algorithm B and M ix below Algorithm 2 are the attribute reduction algorithms of sub-decision table. Given a decision table, first it is divided into two sub-decision tables.Then,the attribute reductions of sub-decision tables are acquired by classic algorithm, and the two sub-decision tables are merged by algorithm 1.In [6], an incremental Table 1. Algorithms A and B [2] with the proposed Algorithm 2 Algorithm A original subtable T n T Heart c ls 0.157 9 0.062 P ima India 0.453 5 0.157 Crx bq ls 0.86 6 0.265 Liver 0.14 5 0.094 Abalone 15.672 6 3.907 Datasets

Algorithm B Algorithm 2 original subtable Algorithm A Algorithm B M ix T n T T n T n T n 0.234 9 0.063 0.124 9 0.127 9 0.126 9 0.718 5 0.187 0.330 5 0.376 5 0.364 5 1.609 7 0.391 0.63 6 0.791 7 0.767 6 0.11 5 0.094 0.188 5 0.188 5 0.189 5 44.39 6 8.687 8.615 6 18.2 6 13.436 6

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Table 2. Experimental results compare with incremental reduction algorithms Algorithm 1 Algorithm A Algorithm B ELA T n T n T n Heart c ls 0 9 0.01 9 0.14 9 5 0.02 5 0.39 5 P ima India 0.016 0.1 6 0.09 7 15.907 6 Crx bq ls 5 0 5 0 5 Liver disorder 0 Abalone 0.801 6 0.826 6 36.734 6 Datasets

algorithm for attribute reduction is presented, but it can not process inconsistent decision table, which needs be modified.In the paper,the algorithm is modified, namely ELA (Extended Liu’s algorithm).After the attribute reduction of one sub-decision table is obtained,another sub-decision table is added and attribute reduction is gained by ELA.The experiment results are shown in Table 2. From Table 2, it shows that running time of Algorithm 1 is far less than ELA.Of course, when the size of two sub-decision tables is not balanceable(such as one occupies 90% and the other occupies 10% of original decision table), ELA may be better than Algorithm 1.

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Rough set theory has been receiving paid more attention for its merit. Its matured theory foundation has been put to use in many fields. However,its application brings about little benefit in industry [7]. One main reason is that many algorithms in rough sets theory can not do in large data sets. Therefore, it is urgent to find more highly efficient and quicker algorithm. Based above, Rough set theory is studied and a determinant method about attribute reduction based on element set is presented. Besides, a decomposition and merging attribute reduction algorithm is proposed.The algorithm also can be regarded as an incremental algorithm for attribute reduction.It can adapt to bigger data sets, which can be embodied from simulation experimental results.

References 1. Pawlak, Z.: Rough Sets. International Journal of Computer and Information Sciences, 11 (1982) 341-356 2. Wang, G.Y.: Rough Set Theory and Knowledge Acquisition. Xi’an Jiaotong University Press, Xi’an (2001) (in Chinese) 3. Pan, D., Zheng, Q.L.: An Adaptive Searching Optimal Algorithm for the Attribute Reducts. Journal of Computer Research and Development, 38(8)(2001) 904-910 (in Chinese)

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4. Miao, D.Q., Hu, G.R.: A Heuristic Algorithm for Attribution of Knowledge. Journal of Computer Research and Development, 36(6) (1999) 681-684 (in Chinese) 5. Wang, J., Wang, J.: Reduction Algorithm Based on Discernibility Matrix: the Ordered Attributeds Method. Journal of Computer Science & technology, 16(6) (2001) 489-504 6. Liu, Z.T.: An Incremental Arithmetic for the Smallest Reduction of Attributes. Acta Electronica Sinica, 27(11) (1999) 96-98 (in Chinese) 7. Liu, S.H., Sheng, Q.J.: Research on Efficient Algorithms for Rough Set Methods. Chinese Journal of Computers, 26(5) (2003) 524-529 (in Chinese)

A Pattern Distance-Based Evolutionary Approach to Time Series Segmentation* Jingwen Yu1, Jian Yin1, Duanning Zhou2, and Jun Zhang1 1

Department of Computer Science Sun Yat-Sen University, Guangzhou, 510275, China 2 Department of Accounting & Information Systems Eastern Washington University, U.S.A [email protected]

Abstract. Time series segmentation is a fundamental component in the process of analyzing and mining time series data. Given a set of pattern templates, evolutionary computation is an appropriate tool to segment time series flexibly and effectively. In this paper, we propose a new distance measure based on pattern distance for fitness evaluation. Time sequence is represented by a series of perceptually important points and converted into piecewise trend sequence. Pattern distance measures the trend similarity of two sequences. Moreover, experiments are conducted to compare the performance of pattern-distance based method with the original one. Results show that pattern distance measure outperforms the original one in correct match, accurate segmentation.

1 Introduction Recently, the increasing use of temporal data has initiated various research and development efforts in the field of data mining. Time series are an important class of temporal data objects and can be easily obtained from financial and scientific applications. Undoubtedly, discovering useful time series patterns is important [1][2]. Time series data are characterized by their numerical and continuous nature. Hence, it needs to discretize a continuous time series into significative symbols [3][4]. This process is called “numeric-to-symbolic” (N/S) conversion, and is considered as one of the most basic processes before mining in the time series. In reference [1], the authors considered the problem of finding a set of suitable time points for segmentation with a set of pattern templates as an optimization problem and solved it with evolutionary computation by identifying the perceptually important points directly from the time domain. Reference [1] utilizes direct point to point *

This work is supported by the National Natural Science Foundation of China (60573097), Natural Science Foundation of Guangdong Province (05200302,04300462), Research Foundation of National Science and Technology Plan Project (2004BA721A02), Research Foundation of Science and Technology Plan Project in Guangdong Province (2005B10101032) and Research Foundation of Disciplines Leading to Doctorate degree of Chinese Universities(20050558017).

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distance (DPPD) for fitness evaluation to measure the similarity between time series segments and given pattern templates. However, DPPD is not an appropriate measure to evaluate the similarity of two sequences with different length because it usually doesn’t reflect the nature of similarity of two sequences. In this paper, we extend the work presented in [1], and study the limitation of distance measure based on DPPD. We present a novel distance measure based on pattern distance [5], which improves the performance of evolutionary approach [1]. For convenience, we refer [1] as DPPD (direct point to point distance) approach. The rest of this paper is organized as follows: In Section 2, we introduce the concept of perceptually important points, distance measure and analyze problems of this distance measure in the DPPD approach. In Section 3, we introduce our new distance measure for fitness evaluation in detail. In Section 4, we present the results of the evolutionary time series segmentation with new proposed distance measure and compare our work with the DPPD approach. Section 5 provides the conclusions of the paper.

2 Review of Distance Measure in Evolutionary Time Series Segmentation 2.1 Perceptually Important Points and Distance Measure In the time series mining system, the interesting and frequently appearing patterns usually can be abstractly represented by a few critical points. These points have perceptually important influences in the human vision. Based on this idea, the DPPD approach used perceptually important points (PIPs) to characterize a temporal sequence. The pseudocode of the PIP identification process is as below: function FindPIP (P,Q) Input: sequence P[1,...,m], length of pattern Q[1,...,n] Output: pattern SP[1,...,n] begin First set SP[1] := P[1] and SP[n] := P[m] Repeat Select point p[j] with highest fluctuation rate to the adjacent points in SP and add p[j] to SP until all the PIPs of P are put into SP[1,...,n],i.e., SP[I,...,n] is fully filled return SP end. After definition of PIPs, the distance between the sequence P and the query Q can be computed directly using point-to-point comparison. Suppose that: SP={(SPk ,SPkt) | k=1,...,n} denotes the PIPs extracted from sequence P, SPk and SPkt respectively denote the amplitude coordinate and time coordinate of PIPs of sequence P; and Q={(Qk ,Qkt) | k=1,...,n} has the same meaning. To take both temporal and amplitude distortion into consideration, the distance measure defined in [1] is as below:

1 n 1 n t 2 t DM ( SP, Q ) = ω × ( SP − Q ) 2 + (1 − ω ) × ¦ ¦ ( SP − Q ) . 1 1 k k n − 1 k =2 k n k =1 k

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and Ȧ1 denotes the weighting for the amplitude distance and the temporal distance, which can be considered as a parameter and can be specified by the users. 2.2 PIPs Added and PIPs Lost Problems

In reference [1], the number of PIPs for each segment is required to keep same with the length of pattern templates. Hence, there may be PIPs added or PIPs lost problems when the amount of apparently fluctuant points in a segment is more or less than the length of corresponding pattern template. (see Fig.1)

(a) PIPs added problem

(b) PIPs lost problem

Fig. 1. PIPs added and PIPs lost problems. In (a), the third PIP of segment is unfluctuating and so is redundant. The segment in (b) misses two PIPs respectively between 3rd and 4th, 6th and 7th.

The distance measure with formula (1) is based on DPPD. It is brittle when there are PIPs added and PIPs lost problems. As we see from Fig.1 (a), the added PIP between 2nd and 4th will cause the point to point mapping after the 3rd PIP warping a point, which leads to the warp of distance calculation of corresponding points. The same thing happens when there are PIPs lost problems (see Fig.1 (b)). In this case, the distance with formula (1) of two similar sequences is still very large and the DPPD measure can not reflect the actual distance of two sequences well.

3 Pattern Distance In Section 2, we have analyzed in detail the drawbacks of the distance measure based on DPPD. To overcome the misdirection caused by time warp in the point to point comparison during the evolutionary process, we propose a new distance measure based on pattern distance. It computes the dissimilarity of two given time sequences and indicates the trend similarity [6] right. Sometimes we determine whether two sequences are similar by comparing their trends. Pattern distance (PD) [5] is easy to implement and can be calculated rapidly since it doesn’t need to normalize the amplitude. Moreover, PD can overcome the problem of pattern mismatch in the DPPD approach, and it also works well when sequences appear through the time series in different resolution.

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In order to calculate the PD of two sequences, first, sequences should be converted into piecewise linear representation (PLR). The PLR sequence can be implemented by finding a series of PIPs in the sequence as mentioned in Section 2.1. Second, the PLR sequence should be converted into piecewise trend sequence [7]. We use trend m to describe the dynamic varying status for each line of the PLR sequence. There are usually three statuses: uptrend, downtrend or continuation. We define a Trend set M, which consists of three items: 1, -1, 0, respectively representing the three statuses above. According to every line’s dynamic varying status, time series represented by PLR can be converted into trend sequence S t = {(m1 , t1 ),..., (mi , t i ),..., (m N , t N )} , where

mi ∈ M and ti denotes the end time point of trend mi.

Hence, given two trend sequences S1 = {(m11 , t11 ),..., (m1i , t1i ),..., (m1 N , t1N )} and

S 2 = {(m 21 , t 21 ),..., (m 2i , t 2 i ),..., (m 2 N , t 2 N )} , when t1i = t 2i for i=1,2, …,N, the pattern distance between S1 and S2 can be calculated as below: 1 N D p (S , S ) = )× | m − m | . ¦ (t − t 1 2 1i 2i t i =1 1i 1(i −1) 1N

(2)

From above, we can see pattern distance has some good properties: first, its value varies from zero to one; second, the more similar the two trend sequences are, the closer its value is to zero; third, it is not sensitive to the noise of sampling data and time axis. Nevertheless, the corresponding end time points of two trend sequences are seldom same with each other in practice [8]. Assume T1 denotes the set of all the end time points of all trend segments from one trend sequence, and T2 denotes the same set from the other one, then a feasible method to solve the time inconsistency problem is to reconstruct the two trend sequences with time points set T1 T2. For instance, S1={ (1, 2), (0, 4), (-1, 5) } and S2={ (0, 1), (1, 5) }, so the set of all end time points of all trend segments from S1 and S2 is T={2, 4, 5} {1, 5}={ 1, 2, 4, 5 }. We divide S1 and S2 again by set T and get the two reconstructed trend sequences: S1’= { (1, 1),(1, 2),(0, 4), (-1, 5) } and S2’={ (0, 1), (1, 2), (1, 4), (1, 5) }.With aligning in time coordinate, we can directly use formula (2) calculating the pattern distance between two trend sequences.

ы

ы

4 Experimental Results In this section, we present the performance of new distance measure proposed in Section 3 and compare its results with the DPPD approach. The standard pattern templates used in our experiment include four dissymmetrical patterns as shown in Fig.2. All of their length is 9 (i.e., 9 points). In addition, we used an artificial time series generated from the stochastic combination of standard pattern templates to evaluate the segmentation results of the new distance measure and compared its results with DPPD approach. The artificial time series used in our experiments is shown as Fig.3.

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Fig. 2. Standard pattern templates

Fig. 3. Artificial time series

The evolutionary algorithm used in our approach is same with [1]. We used the same parameters for both the DPPD approach and our approach in all of our experiments. Some tests show that setting the parameters of evolutionary algorithm to following values can obtain better evolutionary results. The size of population was set to be 50, the crossover rate was set to be 0.4, the mutation rate was set to be 0.2, and furthermore, the probability of adding a time point during mutation was set to be 0.5. Before presenting the results, we will introduce two notions frequently used in this section: Notion 1. (Correct Match) It means every segment of time series is correctly matched to the corresponding expected pattern when the segmentation is approximately correct. We use CM for short. Notion 2. (Accurate Segmentation) It means not only the segmentation of a time series has a correct match, but also the time series is accurately segmented without a little warp. The accurate segmentation for a time series is unique. We use AS for short. Table 1. Comparison of different distance measures in CM & AS (MaxGen is the maximum number of generation in evolutionary approach)

MaxGen 10000 30000 50000

Direct Point to Point Distance CM AS 10 5 10 9 10 9

Pattern Distance CM AS 10 7 10 10 10 10

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In order to avoid the haphazard result, we did 10 tests for each experimental scheme and recorded every result. We recorded the number of CM and AS in the 10 tests using our proposed distance measure and compared the results with the DPPD approach. The results are shown in Table 1. From Table 1 we can see that both the new distance measure and DPPD measure always have the accurate segmentation after 50000 generations. By comparing the number of CM and AS in the 10000th, 30000th, 50000th generation, it is apparent to see both of the two distance measures can always choose the correct matched pattern template for each segment after 10000th, but pattern distance measure has better results than the DPPD approach in Accurate Segmentation since it always has accurate segmentation after 30000 generations, i.e., the new approach based on pattern distance measure is easier to find the accurate segment points than the DPPD approach.

5 Conclusion We have presented a new distance measure based on pattern distance for fitness evaluation in the evolutionary time series segmentation. Differing from the DPPD, the new distance measure is to compare the trend similarity of two sequences and so is robust to amplitude transformation, time phase, scale and baseline. We have compared the performance of the proposed distance measure with the DPPD approach. Experimental results show that pattern distance measure performs better than the DPPD approach in terms of correct match, accurate segmentation. Furthermore, pattern distance is efficient and leads to optimal solution due to its good properties.

References 1. Chung, L., Fu, T. C., R. Luk.: An Evolutionary Approach to Pattern-Based Time Series Segmentation. IEEE Trans. Evol. Comput., vol. 8, vol. 5, 1 (2004) 471-489 2. Fu, C., Chung, F. L., V. Ng, R. Luk.: Evolutionary Segmentation of Financial Time Series into Subsequences. In Proc. Congr. Evolutionary Computation, Seoul, Korea, (2001) 426-430 3. Das, Lin, K. I., H. Mmmila.: Rule Discovery from Time Series. In Proc. ACM SIGKDD Int. Conf. Knowledge Discovery Data Mining, (1998) 16-22 4. Kai, Y., Jia, W., Zhou, P., Meng, X.: A New Approach to Transforming Time Series into Symbolic Sequences. In Proc. 1st joint BMES/EMBS Conf., vol. 2, 10 (1999) 974 5. Wang, D., Rong, G.: Pattern Distance of Time Series. Journal of Zhejiang University (Engineering Science), vol. 38, no. 7, 6 (2004) 795-798 6. Yoon J, L. EE. J, Kim. S.: Trend Similarity and Prediction in Time Series Databases. In Proceedings of SPIE on Data Mining and Knowledge Discovery: Theory, Tools, and Technology II [C], Washington: SPIE (2000) 201-212 7. Wang, D., Rong, G, Li, H. L.: Variable Step Algorithm for Sub-trend Sequence Searching. Journal of Zhejiang University (Engineering Science), vol. 38, no. 12, 12 (2004) 1566-1569 8. Yu, Z., Peng, H., Zheng, Q. L..: Pattern Distance of Time Series Based on Segmentation by Important Points. In Proc. 4th Int. Conf. on Machine Learning and Cybemetics, 8 (2005) 1563-1567

A Quality Prediction Method of Injection Molding Processes Using Sub-stage PCA-SI XiaoPing Guo1,2, FuLi Wang2, and MingXing Jia2 1

Information Engineering School, Shenyang Institute of Chemical Technology, Shenyang 110142, China [email protected] 2 Information Science and Engineering School, Northeastern University, Shenyang 110004, China [email protected]

Abstract. Injection molding process, a typical multistage batch process, due to controller feedback, process or feedstock disturbances and unavailability of direct on-line quality measurements, it is difficult for on-line quality control. A quality prediction method based on sub-stage PCA-SI (subspace identification) is proposed for dedicating to capture batch-to-batch dynamic correlations among the variables in the historical data, and to capture dynamic correlation between process variables at different stages of injection molding process and final qualities, and to build a stage-based on-line quality prediction model of injection molding process. Application has demonstrated that the proposed method can not only give a valid quality prediction, but also it can effectively carry on quality closed-loop control.

1 Introduction Injection molding, an important plastic processing technology, transforms plastic granules into various products with high precision and productivity. Approximately 32% by weight of all plastics go through injection molding today, and there is hardly an industry that does not use injection molded parts in the manufacture of its products. Due to multistage, high dimensionality, dynamic, batch-to-batch variation, and also limited product-to-market time, it is difficult to develop a first-principle or knowledge-based model for quality prediction. These quality variables are typically measured off-line with appreciable delays that render simple feedback control strategies infeasible. So, on-line quality prediction method has been attracting increasing interest in unity of process safety and quality control [1]. An inherent nature of injection molding process is multiplicity of the operation stages. each stage has its own underlying characteristics and can exhibit significantly different behaviors over different stages. Now, multivariate statistical process control (MSPC) such as multi-way partial least square (MPLS) and MPCA have gained attention over the past decade noticeable by the large number of publications in this area [2]. But these methods use process variables over the entire batch course as the inputs and are linear static methods. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 803 – 809, 2006. © Springer-Verlag Berlin Heidelberg 2006

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Up to now, for multistage process modeling, Kosanovich et al. [3] and Dong et al. [4] have proposed to define the stages by operation time according to the process knowledge. Lu [1] has proposed a stage-based sub-PCA modeling method which can overcome many difficulties of MPCA-based monitoring for batch processes. Subspace identification methods (SIM) have drawn a great deal of attention in recent years, which aimed at finding a minimum-order state space model. Recently, Dorsey and Lee [5] showed how the method can be used on batch process data to derive a model capturing batch-to-batch dynamics or correlations. The main advantage is that measurements of previous batches such as delayed laboratory measurements of the quality variables can be used directly in the model for improved predictions. Thus, in this paper a quality prediction method based on sub-stage PCA-SI method is proposed for dedicating to reveal dynamic relationship between process variables at different stages and final qualities, and to build a stage-based on-line quality prediction model of injection molding process.

2 Process Description Injection molding [6], an important polymer processing technique, transforms polymer materials into various shapes and types of products. As a typical multistage process, injection molding operates in stages, among which, filling, packing-holding, and cooling are the most important phases. During filling, the screw moves forward and pushes melt into the mold cavity. Once the mold is completely filled, the process then switches to the packing-holding stage, during which additional polymer is “packed” at a high pressure to compensate for the material shrinkage associated with the material cooling and solidification. The packing-holding continues until the gate freezes off, which isolates the material in the mold from that in the injection unit. The process enters the cooling stage; the part in the mold continues to solidify until it is rigid enough to be ejected from the mold without damage. Concurrently with the early cooling phase, plastication takes place in the barrel where polymer is melted and conveyed to the front of barrel by screw rotation, preparing for next cycle. In injection molding process, product surface defect, such as jetting and record grooves, depends only on injection stage, while product dimension is mainly determined by packing holding stage. The material used in this work is high-density polyethylene (HDPE). Ten process variables are selected for modeling, that is, Nozzle Pressure, Stroke, Injection Velocity, Hydraulic Pressure, Plastication Pressure, Cavity Pressure, Screw Rotation Speed, SV1 valve opening, SV2 valve opening, and Mold Temperature, respectively. The sampling rates of these process variables are 20 ms. The operating conditions are set as follows: injection velocity is 25mm/sec; mold temperature equals 25ºC; seven-band barrel temperatures are set to be (200, 200, 200, 200, 200, 180, 160, 120) ºC; packingholding time is fixed to be 3 second. Quality variables are part weight. Totally, 60 batch runs are conducted under 19 different operation conditions, which can cover all the normal operation range. Based on these data, a stage-based PCA-SI model is developed for process analysis and quality prediction.

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3 Sub-stage PCA-SI Modeling Method 3.1 Identify Critical-to-Quality Stages Step 1. The data gathered from multistage batch process forms a three-dimensional data matrix, X( I q J q K ) where I denotes cycle number, J denotes variable number, and K denotes the number of samples within a cycle. X( I q J q K ) is unfolded, with each of the K time slabs concatenated to produce a two-way array Xnew ( I q JK ) . Based on sub-PCA stage partition strategy, a batch run is divided into several stages.

Step 2. Identify critical-to-quality stages which has the most important contribution to a quality. It is important to identify critical-to-quality stages and find out in each stage the key process variables that contribute the most to the quality variations. In this paper, the multiple coefficient of determination, R2 in multiple regression analysis, is borrowed to evaluate the accuracy of the derived stage model [7].

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2 j

2

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i

2

j

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(1)

j

i

Note that the above measure is developed for each quality variable, y j ( j  1, 2, ", J y ), not for the whole quality data sets. For the quality variables highly relevant to a certain stage, they have large R 2 in that stage, indicating that the regression model of that stage is reliable to explain the variation of these quality variables. On the other hand, for the quality variables irrelevant to that stage, they have small R 2 . The regression model can not give an accurate prediction. Under the precondition that the derived stage model has sufficiently extracted the systematic correlation between process variables and quality variables, for a certain quality variable y j , the R 2 values may indicate which stage has the most contribution to the variation of this quality variable. 3.2 PCA-SI Modeling All un-fold data of one stage represented as X ( I q m) , where I is batch numbers, and m is the number of process variables after un-fold data of the stage. :H definH a lifted output vector y containing all the measurements throughout the VWDJH. Letting the outputs measured throughout the stage be denoted as y and creating the time index  t = 0,1,..., n, y can be expressed as

 ykT = ª¬ y (1)Tk , y (2)Tk ,..., y ( n)Tk º¼

(2)

where y ( n)Tk refers to the vector of available measurements at sample time point n of RQH stage of the k th batch. The dimension of such a lifted vector is typically very

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high and may cause difficulties in applying the subspace identification algorithm. To address this problem, we first recognize that variations in the elements of yk tend to be strongly correlated since the variations are likely due to a few dominant disturbances, which affect the measurements altogether. Hence, we can use the principal component analysis (PCA) to compress the lifted on-line measurement vector to a much lower dimension. Let y represent the score vector from applying PCA to data  for y . The quality measurement vector q can then be appended to this reduced vector. The resulting data containing the compressed online data and quality data are then differenced with respect to the batch index in order to minimize the effect of no stationary batch-to-batch drifts potentially contained in the process data. Let us denote the differenced score vector by    ∆ y k = y k − y k −1 (3) Then, by applying the subspace algorithm to the differenced data, a state space model of the following form can be identification Subspace identification is a technique used to build a state space model directly from available data from the process. The following stochastic model of the process FDQEH extracted from the data using a subspace identification technique [8].

x k +1 = Ax k + K ε k  ª ∆ y k º ªC y º « » = « » xk + ε k ¬« ∆qk ¼» «¬Cq »¼

(4)

+HUH ε k represents the model’s prediction error and is a white noise sequence. In the continuous process setting, the index k refers to the current sample time. On the other hand, in the batch process setting, the index k refers to the current batch number. Hence, the dynamic correlations captured in the identified state space model are those that are present from batch to batch. Intrabatch dynamics or correlations are captured through the covariance matrix of ε k , which is typically nondiagonal. The output matrix is split into C y and C q to correspond to the reduced process measurement vector and the full quality vector. This model can allow for predictions at all time points during the batch by rewriting the model in a time-based output equation as demonstrated below. This requires us to create the following augmented form of the original model

x k = ª¬ xk

 yk

qk

qk −1 ε k º¼

T

(5)

To illustrate the handling of delayed measurements, we have also assumed that the quality variables are delayed by one batch, and appended the quality measurements from the previous batch to the state vector. The augmented model form is obtained as

A Quality Prediction Method of Injection Molding Processes

x k +1

0 ª º K º ª A 0 0 0 « » «C  A I 0 0 C  K » ª¬ I ny 0 º¼ » « y y « » = «Cq A 0 I 0 Cq K » x k + «« ª0 I nq º »» ε k +1 ¬ ¼ « » « » 0 I 0 0 » « 0 0 « » «¬ 0 » 0 0 0 0 ¼ «¬ » I  

  ¼ Φ

807

(6)

Γε

I ny and I nq are used here to indicate the identity matrices of dimensions of the reduced on-line and full off-line measurements, respectively. The model can be used in real time by creating the following time varying output equation yˆ k (t ) = H (t )Θ (ϑ x k (t t )) + ε k (t )  

 yˆ k ( t )

(7)

The residual white noise term ε is added because we have thrown some information away through PCA. We define ϑ = ª¬ 0 I ny 0 0 0 º¼ such that the current reduced  space vector y k is selected from x k. Also, Θ is the matrix containing the PCA loading vectors and expands the reduced vector to the full measurement space. H (t ) is a timevarying matrix that picks out those measurements that become available at the t th sample time. This is used together with the batch-to-batch update equation above to form a periodically time-varying system with period M, which in turn can be used to construct a Kalman filter and update the state vector based on incoming on-line measurements yk (t ) 

x k (t t ) = x k (t − 1 t − 1) + K (t ) ª¬ H (t )Θϑ x k (t − 1 t − 1) − yk (t ) ¼º , t ∈ 1, 2,..., M x k +1 (0 0) = Φ x k ( M M )

(8)

When off-line measurements are available, H(t) should be chosen to include the delayed quality variables from the state equation. This model form thus allows end product quality predictions throughout the batch based on current incoming measurements and previous batch measurements [5].

4 Experimental Results Without using any prior process knowledge, using sub-PCA based stage-division algorithm, the trajectories of an injection molding batch run is divided into four stages according to the change of local covariance structure, correspond to the four physical operation stages, i.e., injection, packing-holding, plastication and cooling stages. The final quality variables have weak relation with the plastication and cooling stage. The on-line quality prediction model is a distributed model, the weight variables are estimated by sub-stage subspace model in packing stage.

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7he predicted results of the proposed method and desired output for 23 batches using the off-line model of packing stage are shown in Fig. 1. It is clear that the predictions are much closer to the actual weight measurements, indicating significant effectivement by using data of the packing stage prediction model. Based on the substage model prediction, the packing pressure is adjusted automatically to compensate for the disturbance. Fig. 2 shows the comparison of the on-line predicted weight and the actual measurement. It is clear that they have good agreement.

5 Conclusion For injection molding process, a typical multi-stage batch process, a new quality prediction method has been applied. Firstly, Process stages are determined by analyzing the change of process covariance structure and partitioning time-slice PCA loading matrices using a new clustering algorithm. Then applying subspace identification based on PCA to un-fold stage data and quality data. In addition, a quality control scheme was established. Application has shown that the proposed methods can give a valid quality prediction.

29.6

27.2

28.8

Real measurement of Weight = 26.71 Average of predicted values = 26.74 Prediced error = 0.097% Maximum predicted error = 0.52%

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Design Prediction

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Fig. 2. On-line weight predicted results

Acknowledgement This work was supported by the National Science Foundation of China under Grant 60374003 and project 973 under Grant 2002CB312200.

References 1. Lu, N., Gao, F., Yang, Y., Wang, F.: A PCA-Based Modeling and Online Monitoring Strategy for Uneven-Length Batch Processes. Ind. Eng. Chem. Res., Vol. 43, No. 5 (2004) 3343-3352 2. Nomikos, P., Macgregor, J. F.: Multiway Partial Least Squares in Monitoring Batch Processes. Chemometrics Intell. Lab. Syst., Vol. 30, No. 1 (1995) 97-108

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3. Kosanovich, K. A., Piovoso, M. J., Dahl, K. S., MacGregor, J. F., Nomokos, P.: Multi-way PCA Applied to an Industrial Batch Process. Proceedings of the ACC (1994)1294-1298 4. Dong, D., McAvoy, T. J.: Multi-stage Batch Process Monitoring. Proceeding of ACC, Sprange E.N.M. (1995) 5. Dorsey, A., Lee, J. H.: Building Inferential Prediction Models of Batch Processes Using Subspace Identification. J. of Process Control, Vol. 13, No. 5 (2003) 397-406 6. Yang, Y.: Injection Molding: from Process to Quality Control, Ph.D. Thesis, The Hong Kong University of Science & Technology (2004) 7. Johnson, R., Wichern, D.: Applied Multivariate Statistical Analysis, Prentice Hall: Upper Saddle River, NJ (2002)

A Robust Algorithm for Watermark Numeric Relational Databases* Xinchun Cui1,2, Xiaolin Qin1, Gang Sheng3, and Jiping Zheng1 1

School of Information Science and Technology, Nanjing University of Aeronautics and Astronautics 210016, Nanjing, Jiangsu, China {cuixc, qinxcs, Zhengjiping}@nuaa.edu.cn 2 School of Information Technology and Communication, Qufu Normal University, 276826 Rizhao, Shandong, China 3 School of Operations Research and Management, Qufu Normal University, 276826 Rizhao, Shandong, China [email protected]

Abstract. This paper studies a novel method for watermarking relational databases for copyright protection. A novel technique to insert and detect watermarks using a mark bit position is proposed, together with a decision-making algorithm by pattern matching. Experimental results show that the proposed scheme is robust against various forms of attacks.

1 Introduction Digital Watermarks help to protect digital assets from unauthorized duplication and distribution by enabling provable ownership over the content. Although extensive efforts have been invested in the problem of watermarking multimedia data, little has been done to protect copyright of relational databases. As far as we know, there is only a few pioneer studies on watermarking relational databases so far [1-8], [12-13], which can be classified into several kinds according to different techniques they used. Namely, secret key based methods [1], [2], [6], [7], transform based methods [3-5], [12] and noise based methods [8], [13]. In this paper, we present a new technique to insert and detect watermarks using a mark bit position, together with a decision-making algorithm by pattern matching. In order to improve robustness, the scheme embeds a watermark into the database for several times and recovers the detected watermark by majority voting mechanism.

2 Algorithms for Watermarking Relational Databases The problem of watermarking relational databases can be modeled as follows. Suppose relation R contains primary key P and numerical attributes A0, A1, …, AȞ-1. *

This work is supported by the High-Technology Research Project of Jiangsu Province of China (No.BG2004005) and Aeronautics Science Foundation of China (No. 02F52033).

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 810 – 815, 2006. © Springer-Verlag Berlin Heidelberg 2006

A Robust Algorithm for Watermark Numeric Relational Databases

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Assume that it is acceptable to change one of ȟ least significant bits (LSB). A bit-string of length |L| is to be embedded into relation R for the purpose of copyright protection. Table 1 summarizes the important parameters used in our algorithms. Table 1. Notations used in this paper

Ș Ȟ Ȗ ȟ Ȧ k Į

Number of tuples in the relation Attribute numbers to be marked Fraction of tuples marked Number of candidate bits to be modified Number of tuples actually marked The secret key Significance level for detecting a watermark

Our technique aims to mark only numeric attributes. The data owner is responsible for deciding which attributes are suitable for marking. He also helps to decide two important parameters and , which describe the limit of modification to a database. We also suppose the adversary should not remove or modify the primary key attribute for the integrity and availability of the database.

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2.1 Insertion Algorithm A one-way hash function H helps to identify a tuple in insertion and detection phase. Usually it has the form of h = H(M), where M is the seed. Besides, It bears the following characteristics [2][11]: Given M, it is easy to compute h; Yet when given h, it is hard to compute M, such that H(M) = h; Given M, it is hard to find another message M0 such that H(M) =H(M0). Several hash functions such as MD5 and SHA are good choices for this purpose[11]. We First transform a meaningful watermark M(Plain Watermark) into a bit flow E(EMC, Encrypted Mark Code) of certain length. Next, we decide which tuple(attribute and bit) should be marked by the hash value. The remainder of h module L(k=h mod L) decides which bit of the EMC is used at one time. Since the hash result is expected to be uniform distributed, we can divide the relation into groups of varied but similar sizes. Thus we have L (the number of bits of the watermark) groups. The i-th bit of the watermark will be inserted into the i-th group. The ascending order of i ranging from 0 to L-1 naturally preserves the sequence of the marks. This is helpful in the detection phase. Finally we check the availability [3] with respect to the intended use of the data. If not acceptable, we simply give up watermarking this tuple and roll back. The watermark insertion algorithm was given as follows:

812

X. Cui et al. Algorithm 1. Watermark insertion algorithm // Insert a plain watermark M into relation R in form of EMC, return marked R // The parameters k, L, Ȗ, and Ȟ are all private to the owner. 1) calculate L-bit EMC E[L]=H(k concatenate M) // L is the length of EMC 2) foreach tuple r R do 3) t= H( k concatenate r.P) 4) if ( t mod Ȗ equals 0) then // mark this tuple 5) attribute_ index i = t mod Ȟ // mark attribute Ai 6) bit_index j = t mod ȟ // mark j th bit 7) watermark_index k= t mod L //use the k-th bit of EMC to mark // get the value of marked bit 8) mark_bit m=Ek XOR (k mod 2) 9) set the j-th least significant bit of r.Ai to m 10) if (not within_usability(new_data)) // check the availability 11) rollback 12) else commit 13) return R

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2.2 Detection Algorithm The same mechanism as in the insertion algorithm is used to recognize the marked tuples. For each marked bit, we count the numbers of its value being zeroes and ones respectively, and then use a majority voting mechanism to decide the final value of this bit. So far, we get a detected watermark. Because of the identical distribution of the hash function when seeded by the same key, the selected tuples in each group is of the same order as in the insertion algorithm. Thus we get a sequential pattern string. The watermark detection algorithm was given as follows: Algorithm 2. Watemark detection algorithm // Algorithm to return a watermark DM[ ] from relation R // The parameters k ,L, Ȗ, and Ȟ are private to the owner. 1) for s=0 to L-1 do 2) DM[s]=’’ // initialize detected mark code 3) count[s][0]=0, count[s][1]=0 // initialize counter 4) foreach tuple r R do 5) t= H( k concatenate r.P) 6) if ( t mod Ȗ equals 0) then // this tuple selected 7) i = t mod Ȟ // select attribute Ai 8) j = t mod ȟ // select j-th bit 9) k= t mod L // the k-th bit of EMC used 10) m= ( j-th LSB of r.Ai) XOR (k mod 2) // k-th bit value of EMC 11) count[k][m]=count[k][m]+1 // add the counter 12) for s=0 to L-1 // get the watermark 13) if (count[s][0]>=count[s][1]) // majority voting 14) then DM[s]=0 else DM[s]=1 // to get the final bit value 15) return DM[ ]

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A Robust Algorithm for Watermark Numeric Relational Databases

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2.3 Decision Making Algorithm As is given in 2.2, the detected mark is a sequential pattern string. So, if a pattern with rather small probability is likely to happen following a certain predefined routines decided by a secret key, we can conclude that the owner of the watermarked relation is the one who has the secret key once the pattern is detected. Algorithm 3. Decision making algorithm // to decide whether a piracy occurs; M is the plain watermark, DM is the detected EMC // The parameters k, L, , and are all private to the owner. 1) L-bit EMC E[L]=H(k concatenate M) // calculate L-bit EMC 2) matchCount=0 3) for i=0 to L-1 4) if (E[i] equals DM[i]) 5) then matchCount= matchCount+1 6) = threshold(L, ) 7) if (matchCount> ) then suspect piracy

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For a non-marked relation, the value of a certain bit can be modeled as a Bernoulli trial, so as an EMC produced by a one-way hash function. Each bit takes equal probability of being zero or one. For a special EMC string seeded by a peculiar secret key, each bit is fixed. To a certain bit of an EMC string, the probability of a corresponding bit of another string equals to what is 0.5, that is: P(Ei=DMi)=0.5 (i=0,1,

Ă/ 

(1)

Because each bit submits to independent and identical distribution, the number of matches is a random variable that has a binominal distribution. Denote the number of matches in L trials by SL. The probability of having at least N matches in L trials, the cumulative binomial probability, can be written as: P(SL > N ) = B(L, N, p ) = ¦ b(L, N, p ) L

i =n

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(2) .



So that a threshold can be deduce according to and L[1][7] The significance level Į determines how amenable the system is to false hits. By choosing a lower value of Į, we can increase our confidence that if the detection algorithm finds a watermark in a suspected relation, it probably is a pirated copy. The parameter Į is decided by the detector freely.

3 Experiments and Analysis To test the validity and robustness of this algorithm, we perform experiments on a computer running Windows XP Professional with 2.4 GHz CPU and 256MB RAM. Algorithms are implemented on Java Eclipse Platform Version 3.0 using JDBC to

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visit Microsoft Office Access 2003. We applied our algorithms to generated synthetic data with 10 attributes. The size of the generated set was 24,000. We choose MD5 as the one-way hash function, and significance level is 0.01. Subset selection attack, the attacker attempts to destroy the watermark by subsetting either tuples or attributes. We select different ratio of the original data to simulate such attacks, and the mark length is 64 with a marking frequency (Ȧ/L) of 5. Figure 1 shows the detection ratio of watermarks when subset selection attack occurs.

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Subset addition attack (mix-and-match attack) is very similar to subsetting selection attack on tuples. In this case, the attacker may randomly selects part of the watermarked relation and mixes them with similar tuples probably without watermarks to form a new relation of approximately the same size of the original one.

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Fig. 4. Comparison with related algorithm

The attacker may also modify the watermarked relation a little with an intention to destroy a watermark. He may choose to alter bits in either one certain attribute or several attributes. Figure 2 shows the detection ratio in simulative attacks. To be noted, the robustness of our algorithm has close relation with marking frequency. The higher marking frequency we get, the more robust it is. Yet a compromise between robustness and imperceptibility must be reached in implementary phase. Figure 3 illustrates the dependency of robustness on different marking frequency.

A Robust Algorithm for Watermark Numeric Relational Databases

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To compare the performance of our scheme with related algorithm, we perform our algorithms on different portions of tuples. Figure 4 shows the detection ratio of the comparison, where a stands for our algorithm, b and c stand for algorithm in [12][11] respectively.

4 Conclusion In this paper, we studied an improved scheme to embed a meaningful bit-string into numerical attributes in relational databases. The algorithm proved to have immunity to popular attacks to relational databases and need the smallest available bandwidth. In the future, we’d like to use this technique on DBMS of independent copyright.

References 1. Rakesh, A., Jerry, K.: Watermarking relational databases. Proceedings of the 28th International Conference on VLDB. (2002) 2. Rakesh, A., Peter, J. Haas, Jerry, K.: Watermarking Relational Data: Framework, Algorithms and Analysis. VLDB Journal, (2003) 157–169 3. Radu, S., Mikhail, A., Sunil, P.: Rights Protection for Relational Data. Proceedings of ACM SIGMOD, (2003) 98–109 4. Min, H., Cao, J. H.. Peng, Z. Y., Fang, Y.: A New Watermark Mechanism for Relational Data. The Fourth International Conference on Computer and Information Technology (CIT'04), (2004) 946–950 5. Radu, S., Mikhail, A., Sunil, P.: On Watermarking Numeric Sets. In Proceedings of IWDW 2002, Lecture Notes in Computer Science, CERIASTR 2001-60. Springer-Verlag, (2002) 130–146 6. Guo, F., Wang, J. M., Zhang, Z. H., Ye, X. J., Li, D. Y.: An Improved Algorithm to Watermark Numeric Relational Data. In Proceedings of WISA 2005, Lecture Notes in Computer Science, 3786 (2006) 138–149 7. Li, Y. J., Vipin, S., Sushil, J.: Fingerprinting Relational Databases:Schemes and Specialties. IEEE Transactions on Dependable and Secure Computing, 2 (1), Jan. (2005) 34–45 8. Zhang Y., Zhao D. N., Li D. Y.: Digital Watermarking for Relational Databases. Journal of PLA University of Science and Technology, 4 (5) (2003) 1–4 9. Hartung, F. M., Kutter.: Multimedia Watermarking Techniques. Proc. of the IEEE, Special Issue on Identification and Protection of Multimedia Information, 87 (1999) 1079–1107 10. David, G. A.: Query-preserving Watermarking of Relational Databases and XML Documents. PODS 2003, San Diego, CA (2003) 191–201 11. Schneier, B.: Applied Cryptography. John Wiley, New York (1996) 12. Liu, S., Wang, S. Deng, R., Shao, W.: A Block Oriented Fingerprinting Scheme in Relational Database. Proc. Seventh Ann. Int’l Conf. Information Security and Cryptology (ICISC2004) (2004) 455–460 13. Yoshioka, K. Shikata, J., Matsumoto, T.: A Method of Database Fingerprinting. Proc. 2004 Workshop Information Security Research, (2004) 112-123

A Study on the RAP Approach and Its Application Jian Cao1,2, Gengui Zhou1, and Feng Tang1 1

College of Business & Administration, Zhejiang University of Technology, Hangzhou, 310032, P.R. China [email protected] 2 Industrial Institute of Processing Control, Zhejiang University, Hangzhou, 310027, P.R. China

Abstract. Compared with traditional short-term forecasting problems, many today’s short-term forecasts encounter more elusive regularity of practical data and more complicated relationship between influencing factors. How to handle the different effects of various historical data to the forecasting results is also a trouble. By employing the properties of the adaptive modeling technique and the forecasting precise model, this paper presents a new RFF-based adaptive prediction (RAP) approach. The approach use the weighted recursive least square estimate method with variable forgetting factor to estimate model parameters, and apply the forecasting precise criterion to guarantee model optimization. By using the approach, the parameter estimates and even the structure coefficients can be automatically updated to obtain the optimal forecasting results. An illustrative example indicates that the proposed approach produces higher accurate results against with several traditional forecasting algorithms.

1 Introduction In many today’s short-term forecasting problems, some new characteristics emerge compared with traditional ones. For example, the forecasting period is shortened, the regularity of practical data is elusive and the influencing factors are increasing. Therefore, to reduce the risk of decision-making, it’s a key task for the decision-makers to apply useful tools to uncover the rules or patterns of numerous forecast-relative data. The technical literature displays a wide range of methodologies and models for the short-term forecasting [1-5], among which the statistical technology has been intensively studied and widely used over the past years. Statistical approaches generally employ two kinds of models: static models [1,2] and dynamic models [1,3-5]. Static models assume that the predicted value has a linear combination of some functional elements. The assumption reduces their adaptability and tracking capability to a changing environment. In dynamic models, the difference between the predicted and the actual value is usually considered as a stochastic process, and the analysis of this random process leads to a more accurate prediction. However, these dynamic models usually have the potential weakness of low robustness due to divergence of model parameters [4,5]. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 816 – 821, 2006. © Springer-Verlag Berlin Heidelberg 2006

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Therefore, to try to overcome the disadvantages of existing statistical methods mentioned above, a novel RFF-based adaptive prediction (RAP) approach, which could be regarded as one kind of dynamic statistical approaches, is presented in this paper. Combined with the parameter identification by recursive least square estimate algorithm with variable forgetting factor [6], the proposed approach can extract the implicitly continuously changing relation between the past data and the predicted values. By employing the forecasting precise criterion [7] to guarantee the model optimization, the approach is able to adjust its parameter estimates and even model structure coefficients to obtain the optimal forecasting results in every time period.

2 The RFF-Based Adaptive Prediction (RAP) Approach 2.1 RAP Approach Description We describe the dynamic identifiable model as a difference equation, in which the predicted value at time k can be expressed as z(k ) = −a1 z(k − 1) − a2 z(k − 2) − − ana z(k − na ) n

+ ¦[bi0ui (k − di ) + bi1ui (k − 1 − di ) + +binb ui (k − nbi − di )] + e(k )

nbi e(k)

(1)

i

i =1

where z(k) ui(k) di ai, bij na

,

actual predicted value in period k, actual value of ith influencing variable in period k, i [1,n], pure delay time of ith influencing variable, dynamic parameters of the model, number of preceding successive predicted values which are correlative to z(k), number of preceding successive values of ith influencing variable which are correlative to z(k), system disturbance which is usually regarded as white noise, i.e. E[e(k)]=0.

Щ

We define λ = [na , nb1 , , nbn , d1 ,  d n ] as the structure coefficient vector of the

proposed identifiable model. Then, we rewrite Eq. (1) as z (k ) = ϕ T (k )θ + e(k ) ,

(2)

where ij(k) is the regression vector of the known values of past predicted data and correlative variables, and ș is the parameter vector of the identifiable model, both are expressed as follows: ϕ T (k ) = [− z(k − 1),,− z(k − na ), u1 (k − d1 ), u1 (k − 1 − d1 ),, u1 (k − nb1 − d1 ), , ui (k − d i ), ui (k − 1 − d i ),, ui (k − nbi − d i ), , u n (k − d n ), un (k − 1 − d n ),, u n (k − nbn − d n )]

,

(3)

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J. Cao, G. Zhou, and F. Tang

θ T = [a1 , a2 ,, ana , b10 , b11 ,, b1nb1 ,, bi 0 , bi1 ,, binbi ,, bn0 , bn1 ,, bnnbn ] .

(4)

Let İ(k) be the estimation error which represents the difference between the actual  predicted value z(k) and the estimated predicted value z (k ) . Use Eq. (2) and note that   z (k ) is calculated by the multiplication of ijT(k) and θ , we get   (5) ε (k ) = z (k ) − z (k ) = ϕ T (k )θ + e(k ) − ϕ T (k )θ . Define the output column vector z = [z(1), z(2),, z(m)]T , the input regression matrix

φ = [ϕ (1),ϕ (2),,ϕ (m)]T , the disturbance column vector e = [e(1), e(2),, e(m)]T and the estimation error column vector ε = [ε (1), ε (2),  , ε (m)]T . Using Eq. (2) and Eq. (5), z and İ are obtained as z = φθ + e ,



(6) 

ε = z − φθ = φ (θ − θ ) + e .

(7)

In the model describing time-variant process behavior, the later information is usually more important than the earlier to influence the output. Therefore, to emphasize  the importance of the later data to θ , we define a positive weighted matrix w in the identification process, w = diag{ρ m−1 , ρ m−2 ,, ρ,1} , where ȡ is a forgetting factor, ȡ (0,1) [5]. The parameter estimates are computed by minimizing a criterion J, which is described as   (8) J = ε T wε = ( z − φθ )T w( z − φθ ) .

Щ

Theorem 1. Utilize the input and output data by time k, define the variance matrix  T P(k ) = (φ k wk φ k ) −1 and the gain matrix K (k ) = P (k )ϕ (k ) ρ k −1 , thus the solution to θ is obtained by the following set of recursive equations,

­   °θ (k ) = θ (k − 1) + K (k )[ y (k ) − ϕ T (k )θ (k − 1)] ° T −1 ® K (k ) = P(k − 1)ϕ (k )[ ρ + ϕ (k ) P(k − 1)ϕ (k )] . ° 1 T ° P(k ) = ρ [ I − K (k )ϕ (k )]P(k − 1) ¯

(9)

 Let θ (0) = 0 and P (0) = βI , where ȕ is a sufficiently large positive. This initial  approach [8] to the solution θ is efficient and effective due to its capability of fast parameters convergence.   Apply θ (k ) obtained at time k to the calculation of the forecasting value z (k + 1) at time k+1, and consider the disturbance e(k) as white noise, i.e. E[e( k )] = 0 , we have   (10) z (k + 1) = ϕ T (k + 1)θ (k ) .

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 Note that before the calculation of θ (k ) , Ȝ(k) should be determined. Different Ȝ(k)    leads to different θ (k ) , and different θ (k ) leads to different z (k + 1) . In practice, several structure coefficient vectors are determined by experts’ experience or certain searching algorithms at the very begin, thus different forecasting results in the same period will be obtained. Herein we use the forecasting precise (FP) criterion to determine the optimal forecasting value. The FP is expressed as [7]  1 k | z( j) − z r ( j) | , FPr (k ) = 1 − ¦ (11) k j =1 z( j)

Щ

 where FPr(k) and z r ( j ) is determined by the rth structure coefficient vector Ȝr(k), r [1,s], s means the number of the structure coefficient vectors. The closer the FP approximates to 1, the better the corresponding forecasting result is.  Before we obtain the optimal forecasting value z * (k + 1) , the optimal structure * coefficient vector Ȝ (k), which leads to the optimal forecasting precise FP*(k), FP*(k)=max{FPr(k), r [1,s]}, should be identified.

Щ

2.2 The Forecasting Process Based on the RAP Approach

A concise summary of steps in the approach follows: Step 1. Determine several influencing variables of the dynamic identifiable model. Step 2. Identify several structure coefficient vectors. Calculate the parameter estimates and then the corresponding forecasting result with various structure coefficient vectors, respectively. Step 3. Compute the forecasting precise with every structure coefficient vector and determine the optimal structure coefficient vector by the optimal FP, then compute the optimal forecasting value. Step 4. If the optimal FP is less than the designed threshold value, for instance, 90 percent, add several new structure coefficient vectors and iterate the step 2 and step 3.

3 An Illustrative Example In this example, we consider one influencing variable, u1(k), in the regression vector. We define that ϕT (k) = [−z(k −1),,−z(k − na ),u1 (k − d),u1 (k −1 − d),, u1 (k − nb1 − d)] , Ȝ=[na, nb1 , d] and θ T = [ a1 , a 2 ,  , a na , b0 , b1 ,  , bnb ] . 1

We primarily consider that the range of na is from 10 to 16, nb1 from 3 to 4 and d from 1 to 2. Thereby, the number of Ȝ is equal to 7×2×2=28. Giving ȡ = 0.9 and ȕ= 106, the RAP approach was implemented in Matlab 6.0.

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J. Cao, G. Zhou, and F. Tang Table 1. Historical data in the first 11 periods

Period

1

2

3

4

5

6

7

8

9

10

11

Actual predicted value z(k) 162 171 168 184 185 193 207 224 205 194 190 Influencing variable value u1(k) 17 17 18.5 18.5 18.5 19.5 19.5 19.5 18 18 18

Firstly, we give the actual data of the first 11 periods in Table 1. Another consecutive 20-period actual data are given in Table 2. Table 2 also lists the optimal forecasting values and corresponding optimal structure coefficient vectors by the RAP approach, as well as the forecasting results calculated by the MA and the ES. Table 2. Forecasting results by RAP, MA and ES

Forecasting result z*(k) Actual Influencing RAP Week predicted variable value Optimal structure coe ES ES Optimal fore MA (Į=0.4) (Į=0.8) u1(k) value z(k) -ffiients (na, n b1 ,d) -casting value 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

187 180 177 196 201 215 209 232 240 251 223 231 235 214 198 191 214 218 234 241

18 19 19 19.5 20.5 20.5 21 21 20.5 20.5 20 20 20 20 20 18.5 18.5 20 20 21

10,4,1 10,4,1 10,4,1 10,4,1 10,4,1 10,4,1 10,4,1 10,4,1 14,4,1 12,4,1 12,4,1 12,4,1 16,4,1 16,4,1 16,4,1 16,4,1 15,4,1 15,4,1 15,4,1 15,4,1

192 187 179 175 204 203 214 215 214 249 225 214 242 214 211 211 227 213 212 254

202 201 197 189 187 189 193 196 205 216 225 228 231 235 232 225 215 214 212 212

202 196 190 185 189 194 202 205 216 225 236 231 231 232 225 214 205 209 212 221

202 190 182 178 192 199 212 210 228 238 248 228 230 234 218 202 193 210 216 230

Table 3 presents the forecasting precise (FP), the mean absolute error (MAE) [7] and the mean square error (MSE) [7] statistics by using these approaches. Table 3. Precise statistics by RAP, MA and ES

Precise criteria FP MAE MSE

RAP 0.9509 10.60 171.20

MA 0.9111 18.95 505.65

ES

㧔Į=0.4㧕 0.9255 15.85 309.95

ES

㧔Į=0.8㧕 0.9380 13.25 217.35

A Study on the RAP Approach and Its Application

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As Table 3 shown, highly accuracy forecasting is achieved with periodical average errors less than 5% by the RAP approach. Because the actual predicted values are quite variable, we consider that such forecasting results are valid and no other structure coefficient vectors are required to add in this case. Table 3 also presents that all three precise statistics of the RAP are better than those of the MA and the ES. For example, the ratios of improvement in the FP criterion from the RAP reach up to 45%, 34% and 21% compared with the MA, the ES (Į = 0.4) and the ES (Į = 0.8), respectively. The results reveal a high degree of accuracy and robustness of the RAP approach.

4 Conclusions To solve problems such as elusive regularity of actual data, increasing influencing factors and different effects of various historical data to the forecasting results in many today’s short-term forecasting problems, a new RAP approach is proposed in this paper. By employing the properties of the adaptive modeling techniques, the approach can continuously update the parameter estimates and even the structure coefficients to procure the optimal forecasting results. An illustrative example has revealed that the proposed approach has the capability to tracking actual data patterns effectively and efficiently, thus more accurate forecasts can be obtained compared with some traditional forecasting approaches. Another advantage of the approach is the minimum human intervention required when we apply the approach-based system, it enhances the suitability of the approach for online application.

Acknowledgements This research work was partially supported by Research Planning Fund of Zhejiang Provincial Education Department (No.20040580) and Zhejiang Provincial Nature Science Foundation (No.Y104171).

References 1. Jae, K.S.: Strategic Business Forecasting: the Complete Guide to Forecasting Real World Company Performance. CRC Press LLC, Boca Raton (2000) 2. Zhong, Q., Chen, X.H., Liu, S.Q.: On Fuzzy Forecast of Sales Volume of Enterprise Product. Chinese Journal of Management Science. 9 (2001) 31-35 3. Kamarianakis, Y., Prastacos, P.: Space-Time Modeling of Traffic Flow. Computers & Geosciences. 31 (2005) 119-133 4. Kulendran, N., Witt, S.F.: Cointegration Versus Least Squares Regression. Annals of Tourism Research. 28 (2001) 291-311 5. Ljung, L.: System Identification Theory for the User. Prentice Hall, Englewood Cliffs (1987) 6. Fang, C.Z., Xiao, D.Y.: Process Identification. Tsinghua University Press, Beijing (1988) 7. Peiris, M.S.: Improving the Precision on Forecasting. Microelectronics and Reliability. 36 (1996) 1375-1378 8. Guo, S.L.: Stochastic Control. Tsinghua University Press, Beijing (1999)

An Analytical Model for Web Prefetching Lei Shi1,2, Lin Wei2, Zhimin Gu1, Yingjie Han2, and Yun Shi3 1

Department of Computer Science and Engineering, Beijing Institute of Technology, Beijing 100081,China [email protected], [email protected] 2 School of Information Engineering, Zhengzhou University, Zhengzhou 450052, China [email protected], [email protected] 3 Department of Information Technology, State Post Bureau, Beijing 100808, China [email protected]

Abstract. The ultimate goal of Web prefetching is to improve the quality of service on the Web. Previous studies in speculative prefetching focus on building prediction algorithms for the purpose of Web prefetching accuracy. This paper presents a theoretical analytical model on Web prefetching, based on which, different Web prefetching scheme can be developed. The discussion tries to describe a generic prefetching algorithm and provide implementation basis for Web speculative prefetching.

1 Introduction Currently, the most effective solutions for improving the retrieval rate of large distributed documents are Web caching and prefetching [1]. Prefetching can either be speculative or informed. In this paper we investigate speculative prefetching. Previous studies in speculative prefetching focus on building access models and evaluating the performance of such models in predicting future accesses. The criterion that most existing prefetch schemes apply in prefetching documents from the origin servers into proxy side or client side is usually the probability of each document being accessed in the near future or the popularity of the document. While these models are important, they do not constitute a complete framework for building optimal prefetch strategies. Most of the prefetch techniques do not consider the factors such as the size of the data items, the data access rate, and the data update rate. In this paper, we address these issues by proposing an analytical model, and based on which, presents different Web prefetching schemes. Intuitively, Web prefetching can have a better performance than those without prefetching mechanism. Our work tries to make performance analysis of Web prefetching quantitatively. Based on the analytical model, the access latency and the hit ratio metrics are discussed theoretically. Although Web caching has already widely used in the WWW, the benefits from Web caching are becoming limited due to the rapid changes of network resources, D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 822 – 827, 2006. © Springer-Verlag Berlin Heidelberg 2006

An Analytical Model for Web Prefetching

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while Web prefetching can optimize the World Wide Web in many aspects. The combination of Web prefetching and caching holds the promise of improving the QoS of Web systems. In 1994, Griffioen [3] paid attention to the modeling of Web prefetching and caching on file system. The research assumed that prefetching and caching share the same cache space, and showed that integrated Web prefetching and caching can improve the performance of cache system. In 1995, Cao [4] presented a model of integrated Web prefetching and caching on file system, and based on which, she made performance study and simulative validation. Simulations illustrated that the integrated model could reduce the elapsed times of the applications by up to 50%. In 2001, Yang [5] presented an integrated architecture for Web object caching and prefetching. The Web object prediction model was built by mining the frequent paths from past Web log data, and prefetching algorithm named Pre-GDSF was implemented. Experimental shows that integrated Web prefetching and caching system can have a better performance than those without prefetching mechanism. Our paper tries to establish an analytical model and make discussions based on the integrated architecture for caching and prefetching.

2 Analytical Model The following notations are used in the discussion. N: the total number of data items; ai: the mean access arrival rate for data item I; ui: the mean update arrival rate for data item i, i.e. the average modification cycle of data item I; Ti,d: the average delay imposed by the Internet, i.e. the interval between the request time and the response time; Ti,c: the average response time from the cache; Tc,s: the average response time from the origin server, and Ti,s=Ti,c+Ti,d; si: the size of data item i; pi: the access probability to data item i; The access probability to document i can be calculated as follows.

pi = a i

N

¦a

i

.

(1)

i =1

Assume that the access pattern of object i follows the Poisson distribution and the inter-arrival time of requests to document i is exponentially distributed:

f i (t ) = a i e − ai t .

(2)

The update interval is assumed to follow the exponential distribution with the average interval being ui. Define PAi (t ) as the probability that the last access occurs within time t in the past and

PBi (t ) as the probability that no update occurs within

time t in the past. Then, the following equations exist.

PAi (t ) = 1 − e ai t .

(3)

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L. Shi et al.

PBi (t ) = e −t / ui .

(4)

The probability of no accesses to object i in this time t is P(no accesses to object i in t time)= e

− ai t

(5)

.

Then the probability that there is at least one request to data item i during a given modification cycle is given by

gi = 1 − e − ai u i .

(6)

For an object i that is not prefetched, a current access is a hit if the last access occurred after the last update, and the probability of an access to be a hit is given as (7). For the prefetched objects, the hit ratio is 1. ∞

hi = ³ PAi (t )d PBi (t ) = 0

ai u i . ai u i + 1

(7)

2.1 Access Latency Potential sources of latency are the Web server’s heavy load, network congestion, low bandwidth, bandwidth underutilization and propagation delay. Suppose that r documents are prefetched to the cache. For simplicity, we consider three types of average delays. Ti , c refers to the response time from the cache, which means the average delay imposed by the Intranet between the request and the receiving of the response from the cache when a “fresh” or “valid” copy of the document is found in the cache. Ti , d represents the average delay imposed by the Internet, including the transmission time of the document, the round-trip time and the processing time. Ti , s refers to the response time from the origin server, which means the total average delay imposed by the Intranet and the Internet when there is no “fresh” copy of document i in the cache. Apparently, Ti , s = Ti , c + Ti , d . Let Lcache and L pref stand for the average latency for no-prefetch and prefetch cache scheme separately. The average latency L pref for a prefetch scheme can be expressed as

L pref =

N

¦ p [h T i

i = r +1

i i ,c

r

r

i =1

i =1

+ (1 − hi )Ti , s ] + ¦ piTi ,c = Lcache − ¦ pi (1 − hi )Ti ,d

(8)

r

L pref = Lcache − ¦ p i (1 − hi )Ti , d .

(9)

i =1

As seen from (9), the latency reduction is actually the benefit of Web prefetching r

gains and is determined by the parameters of

¦ p (1 − h )T i

i =1

i

i ,d

.

An Analytical Model for Web Prefetching

825

2.2 Hit Ratio Let

H cache and H pref refer to the total hit ratio for no-prefetch and prefetch scheme

separately. The total hit ratio for a prefetch scheme can be given by N

r

¦ a h + ¦a i i

H pref =

i

i = r +1

N

r

r

i =1

i =1

i =1

= ¦ pi hi + ¦ pi (1 − hi ) = H cache + ¦ pi (1 − hi ) (10)

i =1

N

¦a

i

i =1

r

H pref = H cache + ¦ p i (1 − hi ) .

(11)

i =1

r

From (11), we can find that

¦ p (1 − h ) is the increment of the hit ratio comi

i

i =1

pared with the “no-prefetch” cache scheme. 2.3 Bandwidth Let

Bcache and B pref be the transmission bandwidth for no-prefetch and prefetch

scheme separately. Thus, obtaining the expression of the transmission bandwidth required for transmitting documents from the origin servers to the cache.

B pref =

N

r

¦ a (1 − h )s + ¦ s i

i

i

i = r +1

i =1

r

i

= Bcache + ¦ [1 − ai (1 − hi )]si i =1

r

B pref = Bcache + ¦ [1 − a i (1 − hi )]s i .

(12)

i =1

From the equation above, we can see that the prefetch scheme needs an extra r

transmission bandwidth of

¦[1 − a (1 − h )]s i

i

i

than the ordinary cache scheme. To

i =1

be noticed, different from access latency and hit ratio, the transmission bandwidth can be increased or reduced, which depends on the value of the parameters.

3 Discussion Web prefetching algorithm cannot give an all-in-one solution. The criterion to choose what to prefetch can be different. If the main objective of Web prefetching is to reduce the access latency, then a good choice of the scheme is to minimize L pref . If the main objective is to increase the hit ratio of Web cache, then the kernel of the algorithm should be to maximize H pref .

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The generic prefetching algorithm can be described as follows. Algorithm Prefetching (Objective: prefetch_obj) Step 1: Pre-process the log, clean noisy records; Step 2: For each Web object do Calculate the key based on prefetch_obj; Step 3: Sort the key values above; Step 4: Prefetch the optimal ones; The total number of accessed documents is assumed 100,000. The mean update arN

rival rates are assumed to be 2 hours, i.e. 7200 seconds. The total access rate

¦a

i

is

i =1

assumed as 1 request per second. The access distribution { a i } of documents follows a Zipf-like distribution [2], which means stant, i is the rank of popularity and

pi = C / i a , where parameter C is a con-

p i is the conditional probability of the Web page

ranking i. The Zipf exponent α reflects the degree of popularity skew. The average delay imposed by the Internet

Ti , d is assumed 200ms. The size of document s i is

uniformly assumed 32 KB. Fig. 1 demonstrates the numerical results of the analysis. The objectives of the figures are maximized reduced access latency and minimized increased bandwidth. The trend of maximized increased hit ratio is similar to that of maximized reduced access latency. When the prefetch number increases, the reduced access latency increases simultaneously, but the trend becomes smoother, and the higher of Zipf-like parameter Į is, the more of the reduced access latency. Higher Į and more prefetched objects will gain more increased hit ratio. The reason is that higher Į implies the concentration of hot objects, prefetching hot objects will make more contributions to the reduced access latency. More prefetch number consumes more bandwidth, and the trend becomes steep as the prefetch number increases. The higher Į is, the relatively lower of bandwidth increased.

     

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¢ 

¢ 

¢ 



Reduced



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¢ 

¢ 

¢ 

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Increased Bandwidth





 

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Fig. 1. Reduced access latency and increased bandwidth of Web prefetching algorithm

An Analytical Model for Web Prefetching

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4 Discussions In this paper, we present an analytical model for Web prefetching and caching system. The performance metrics, the access latency, hit ratio, and bandwidth are discussed and analysed theoretically. Ongoing work includes the application and further performance analysis of the analytical model for Web prefetching.

References 1. Shi, L., Gu, Z., Pei, Y., Wei, L.: A PPM Prediction Model Based on Web Objects' Popularity. Lecture Notes in Artificial Intelligence, Vol. 3614. Springer-Verlag, Berlin Heidelberg (2005) 110–119 2. Shi, L., Gu, Z., Wei, L., Shi, Y.: Quantitative Analysis of Zipf's Law on Web Cache. In: Pan, Y., Chen, D. (eds.): ISPA 2005. Lecture Notes in Computer Science, Vol. 3758. Springer-Verlag, Berlin Heidelberg (2005) 845–852 3. Griffioen, J., Appleton, R.: Reducing File System Latency Using a Predictive Approach. In: Proceedings of USENIX Summer Conference, USENIX, Berkeley (1994) 197–207 4. Cao, P., Felten, E.W., Karlin A.R., Li K.: A Study of Integrated Prefetching and Caching Strategies. In: Proceedings of the ACM SIGMETRICS Conference on Measurement and Modeling of Computer Systems, Ottawa (1995) 171–182 5. Yang, Q., Zhang, H.H.: Integrating Web Prefetching and Caching Using Prediction Models. World Wide Web. Vol.4 (4) (2001) 299–321 6. Yu, S., Kobayashi, H.: A New Prefetch Cache Scheme. In: Proceedings of GLOBECOM '00. Vol.1. IEEE, Piscataway (2000) 350–355 7. Shi, L., Gu, Z., Wei, L., Shi, Y.: Popularity-based Selective Markov Model. In: Proceedings of IEEE/WIC/ACM International Conference on Web Intelligence, Beijing (2004) 504–507

An Optimal Interval for Computing Course and Ship Speed in Marine Gravity Survey Based on Approximate Reasoning Lihua Zhang1,2, Chong Fang2,3, Xiaosan Ge2, and Yilong Li1 1

Department of Hydrography and Cartography, Dalian Naval Academy, 667, Jiefang Road, Dalian, Liaoning, 116018, P.R. China 2 State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing,Wuhan University, 129 Luoyu Road, Wuhan, Hubei, 430079, P.R. China 3 Department of Surveying and Land Information Engineering, Central South University, Changsha, Hunan, 410083, P.R. China [email protected]

Abstract. Course and ship speed determine the accuracy of Eötvös correction which is the main error source of marine gravity survey. This paper presents a method to acquire an optimal interval for computing course and ship speed based on approximate reasoning. The computed error derived from positioning inaccuracy decreases with increasing time interval, but increasing interval also makes the computed values inaccurate to the actual. The optimal interval is concluded theoretically, and the value is acquired using a statistical method. Experiments show the proposed method good results, the reasonable interval can be gained, and accuracy of Eötvös correction can be improved.

1 Introduction Marine gravity survey is a kinetic survey, the platform (ship) of which is moving continuously. Observations of marine gravity are affected by the interferential acceleration such as horizontal and vertical acceleration, cross-coupling and Eötvös effect. In order to eliminate these influences and make marine gravity survey more accurate, a series of measures used to improve accuracy, which have been taken in instruments, work means and data processing, are introduced [1],[2],[3],[4]. Of all influences above, the Eötvös correction error is the main source lowering the accuracy of marine gravity survey. In the Eötvös correction equation, it is indicated that Eötvös correction is mostly dependant on course and ship speed. The increasing accuracy of course and speed will lead to great improvement of Eötvös correction. However, the real-time course and ship speed, which can not be obtained directly, are computed usually with positions of neighboring points. The accuracy of Eötvös correction is determined by positioning accuracy of the survey points and the method used to compute course and ship speed. To improve accuracy of Eötvös correction, it is necessary to improve accuracy of positioning system. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 828 – 833, 2006. © Springer-Verlag Berlin Heidelberg 2006

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However, accuracy of positioning is limited a certain extent. So it is useful and meaningful to optimize the interval used to calculate course and ship speed [4],[5],[6].

2 Model and Analyses 2.1 The Influence of Course and Ship Speed on Eötvös Correction The Eötvös correction formula is directly cited from reference [1] as follows:

δg E = 7.50V sin A cos B + 0.004V 2 .

(1)

Where: A —true course, B —geodetic latitude, V —speed of survey ship. In formula (1), it is shown that the computation accuracy of Eötvös effect correction depends on course, ship speed and latitude of the survey point. For the sake of estimating the influence from all errors above on Eötvös correction, it is necessary to calculate differential coefficient of formula (1). Because latitude error of survey point has been tiny influence on δg E , the correction formula can be simplified as: d (δg E ) = 7.50V cos A cos BdA + (7.50 sin A cos B + 0.008V )dV .

(2)

2.2 The Method and Analyses for Computing Course and Ship Speed Course and ship speed can be calculated using coordinates and time intervals of foreand-after survey points in survey. According to specifications for marine gravity survey, the course and ship speed are computed by expressions (3) and (4). A = arctg

V=

Where:

xi

yi − yi −1 . xi − xi −1

(3)

( x i − x i −1 ) 2 + ( y i − y i −1 ) 2 t i − t i −1

.

㧘 y —coordinates of the survey point; t − t i

i

(4) i −1 —time

interval of fore-

and-after survey points. For the reason of positioning errors, the two formulae above can be described as: y − ~y ) + ( ∆y i − ∆y i −1 ) (~ A = arctg ~ ~i −1 . ( x i − x i −1 ) + (∆x i − ∆x i −1 ) V=

(5)

(( ~ xi − ~ xi −1 ) + (∆xi − ∆xi −1 )) 2 + (( ~yi − ~yi −1 ) + (∆yi − ∆yi −1 )) 2 ti − ti −1

(~ xi , ~ yi ) —true coordinates of No. i point in a survey line errors of No. i point.

.

(6)

㧧 ∆x , ∆y —positioning i

i

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As it shows in formula (5) and (6), the longer the interval of fore-and after survey points is, the larger the values of ~x − ~xi −1 and ~ yi − ~ yi −1 are. However, the difference between fore-and-after in the positioning system ( ∆xi − ∆x i −1 and ∆yi − ∆yi−1 ) is limited and impossible to increase boundlessly with the augment of survey points interval used to calculate course and ship speed. Therefore the increase of survey point interval will partly decrease the positioning system errors’ influence on course and ship speed’s computation. Actually, the ship speed is not steady and the track is not straight so that the course and ship speed calculated from formula (5) and (6) are mean values of the former point and the current one. The longer the interval is, the more impossible the computation values are the true course and ship speed. Theoretically, the shorter interval to calculate course and ship speed will be better if positioning system is no errors. Reversely, with positioning system errors, longer interval can make the computation error of course and ship speed (caused by positioning errors) small. Theoretically there is an optimal interval for computing Eötvös correction, which makes synthetically the total error minimal. 2.3 The Mathematic Expression of Optimal Computation Interval When working on the sea, the survey ship will sway around planned survey line due to interferences as shows in Fig.1. There are corresponding curve fitting methods to fit the true track in reference [1]. Supposing that in a certain survey line, the course change rate function of the ship is A (t ) and the speed change rate function is V (t ) . In the interval

㧔 t — t 㧕, the mean course A a

b

b

from t a to tb (the course at

tb ) can be

calculated approximately by formula (3).

Fig. 1. The true curse and ship speed are changing continuously. Practically the values are computed using an approximate method according to the formula (3) and (4).

The true course of the survey ship at time

t b is

tb ~ ~ Ab = Aa + ³ A (t ) dt.

(7)

ta

~ Aa is the true course at t a . A (t ) is change rate of the course from t a to t b . The difference between the calculated value and the true value at time

~ dAb = Ab − Ab .

t b is (8)

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t b can be obtained. Theoretically, the optimal interval to calculate course and ship speed at t b is the interval t b - t a in which the Eötvös Similarly, dVb at time

㧔

㧕

correction error caused synthetically by course and ship speed is the lowest. It can be calculated using the following formula, which is based on formula (2). min(7.50Vb cos Ab cos Bb dAb + 7.50 sin Ab cos Bb + 0.008Vb )dVb ) .

Put

(9)

dAb and dVb into formula (9), calculate the time derivative and recalculate: 7.50Vb cos Ab cos Bb ( Pb − A (t )) + (7.50 sin Ab cos Bb + 0.008Vb )(Qb − V (t )) = 0.

Where:

(10)

Pb and Qb are two complex functions related to the compute interval and

positions errors. As formula (10) shows, the optimal interval is related to course, ship speed rate,

 (t ) and V (t ) are equal to 0, that is the ship has a and positioning errors. When A steady course and speed , the results with any interval will be always the same if without positioning errors. Actually, the ship speed is unsteady and the track is  (t ) and V (t ) become irregular at all time. changing so that A In fact, the optimal interval can hardly be computed from formula (10) since the functions are too complicated and the changing of positioning errors can’t be expressed with a simple mathematic expression. So it is impossible to calculate the real-time variation of course and ship speed using the optimal interval. However, position errors don’t excess a certain limit and the course and ship speed is controlled technically in survey, mean square error (MSE) of all point’s Eötvös correction will decrease if the reasonable mean interval is used in a or several surveys. The mean interval can’t be from the formula (10) directly, but an approximate value can be obtained based on statistical analyses [7]. 3 Experiment and Discussions Mean square error (MSE) of intersection discrepancies (the differences of gravity values respectively in two intersectant survey lines) is used estimate accuracy in survey. To analyze the influence of course and ship speed using different interval to compute Eötvös correction, MSEs of intersection discrepancies using different time intervals are computed in four surveys. The results are shown in table 1. As it shows in table 1 and Fig.2, the MSE of intersection discrepancies decrease quickly and then increase slowly when the interval changes from short to long. There is theoretical optimal interval from the trend of the change. However, it is not very definite for the incomplete statistics. In some range, the MSE of intersection discrepancies is lower than others’. As the figures show, the Eötvös correction error is large using the interval less than 1 minute. For example, if the interval is 1 minute, the

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L. Zhang et al. Table 1. MSEs of intersection discrepancies based on different time intervals(TI)

(a) Surveying No.1

(b) Surveying No.2

(c) Surveying No.3

(d) Surveying No.4

Fig. 2. The trends of MSE of intersection discrepancies based on different time intervals

MSE is 2.7 mGal larger than using 11 minutes in surveying No.1., 2.0 mGal larger than using 11 minutes in surveying No.2, 1.7 mGal larger than using 12 minutes in surveying No.3 and 1.2 mGal larger than using 14 minutes in surveying No.4. At one time, the MSE increase apparently if the interval is rather long (more than 30 minutes etc.). It is concluded that it is necessary to decide reasonable interval to compute Eötvös correction. Seen from the above figures, the MSEs are optimal when the time interval for computing the course and ship speed is within 10-15 minutes.

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4 Conclusions The computation inaccuracy of the course and ship speed causes the Eötvös correction error and further affects accuracy of marine gravity product. There is the optimal course and ship speed calculating interval to improve the accuracy of Eötvös correction in theory. To one or several surveys, it can be gained based on approximate reasoning.

Acknowledgments This work is supported by Program of the State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing (WKL(05)0304) and Science Foundation of Dalian Naval Academy(FZ0402512).

References 1. Liang, K., Liu, Y.: Marine Gravity and Magnetic Survey. Beijing; Surveying and Mapping Press (1996) 2. Huang M., et al.: On the Compensation of Systematic Errors in Marine Gravity Measurements. Marine Geoodesy, 22(3) (1999) 183-194 3. Huang, M., Zhai, G., Ouyang, Y.: Two-Step Processing for Compensating the Systematic Errors in Marine Gravity Measurements. Geomatics and Information Science of Wuhan University, 27(2) (2002) 251-255 4. Yi, Q., Sun, Y., Lin, Y.: A Method for Determining Gross Errors and Improving Accuracy of Marine Gravity Survey. Marine Surveying and Mapping, (2004) 24-25 5. Zhang, L., Yin, X., Sun, Y.: The Analysis of Intervals of Calculating Course and Ship Speed of Eötvös Effect Correction. Surveying and Mapping Engineering, 11 (2002) 39-42 6. Zhang, T., Gao, J., Chen, M.: The Reasonable Correction of Eötvös Effect in Marine G ravity Survey Marine Surveying and Mapping, 25 (2005) 17-20 7. Keim, D.A., Panse, C.-S.M.: A New Visual Data Mining Approach for Analyzing Large Spatial Data Sets. Proceedings of the Third IEEE International Conference on Data Mining, Melboume, Florida, USA: IEEE Computer Society (2003)

Application of Association Rules in Education Sylvia Encheva1 and Sharil Tumin2 1

Stord/Haugesund University College, Bjørnsonsg. 45, 5528 Haugesund, Norway [email protected] 2 University of Bergen, IT-Dept., P. O. Box 7800, 5020 Bergen, Norway [email protected]

Abstract. This paper is devoted to application of association rules in education. The aim is to discover association rules with some given information in the antecedent without the constraint of support threshold being involved.

1

Introduction

Association rules are often used in market basket analysis [1] for establishing associations among products purchased by a single costumer, and in medical research [4] for discovering associations among numerical, categorical, time and even image attributes. The probabilistic approach applied there deals with statements of the form ’the presence of attributes α and β often also involves attribute γ’. This paper is devoted to application of association rules in education. The aim is to discover association rules with some given information in the antecedent without the constraint of support threshold being involved. The rest of the paper is organized as follows. Related work is described in Section 2. Some definitions and statements from formal concept analysis and rule mining may be found in Section 3. The main results of the paper are placed in Section 4. The paper ends with a conclusion in Section 5.

2

Related Work

Formal concept analysis [8] started as an attempt of promoting better communication between lattice theorists and users of lattice theory. Since 1980’s formal concept analysis has been growing as a research field with a broad spectrum of applications. Various applications of formal concept analysis are presented in [5]. An excellent introduction to ordered sets and lattices and to their contemporary applications can be found in [3]. The complexity of mining frequent itemsets is exponential and algorithms for finding such sets have been developed by [7]. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 834–838, 2006. c Springer-Verlag Berlin Heidelberg 2006


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Preliminaries

A concept is considered by its extent and its intent: the extent consists of all objects belonging to the concept while the intent is the collection of all attributes shared by the objects [3]. A context is a triple (G, M, I) where G and M are sets and I ⊂ G × M . The elements of G and M are called objects and attributes respectively. For A ⊆ G and B ⊆ M , define A = {m ∈ M | (∀g ∈ A) gIm} and  B = {g ∈ G | (∀m ∈ B) gIm} so A is the set of attributes common to all the objects in A and B  is the set of objects possessing the attributes in B. Then a concept of the context (G, M, I) is defined to be a pair (A, B) where A ⊆ G, B ⊆ M , A = B and B  = A. The extent of the concept (A, B) is A while its intent is B. A subset A of G is the extent of some concept if and only if A = A in which case the unique concept of the which A is an extent is (A, A ). The corresponding statement applies to those subsets B of M which are the intent of some concept. The set of all concepts of the context (G, M, I) is denoted by B(G, M, I). B(G, M, I); ≤ is a complete lattice and it is known as the concept lattice of the context (G, M, I). For concepts (A1 , B1 ) and (A2 , B2 ) in B(G, M, I) we write (A1 , B1 ) ≤ (A2 , B2 ), and say that (A1 , B1 ) is a subconcept of (A2 , B2 ), or that (A2 , B2 ) is a superconcept of (A1 , B1 ), if A1 ⊆ A2 which is equivalent to B1 ⊇ B2 . Frequent sets [6] are sets of attributes that occur often enough to deserve further consideration. An association rule Q → R holds if there are sufficient objects possesing both Q and R and if there are sufficient objects among those with Q which also possess R [2]. A context (G, M, I) satisfies the association rule Q → Rminsup,minconf ,
| with Q, R ∈ M , if sup(Q → R) = |(Q∪R) ≥ minsup and conf (Q → R) = |G| |(Q∪R)
| |Q
|

≥ minconf provided minsup ∈ [0, 1] and minconf ∈ [0, 1].





| | The ratios |(Q∪R) and |(Q∪R) are called, respectively, the support and the |G| |Q
| confidence of the rule Q → R. In other words the rule Q → R has support σ% in the transaction set T if σ% of the transactions in T contain Q ∪ R. The rule has confidence ψ% if ψ% of the transactions in T that contain Q also contain R.

4

Looking at a Linear Algebra Test

Consider first year engineering students on bachelor level enrolled in a linear algebra course. In this particular case they are divided in units according to gender and results from a preliminary test as follows: – Unit 1 : male students with excellent score – Unit 2 : male students with very good score – Unit 3 : male students with good score

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– – – – – –

S. Encheva and S. Tumin

Unit Unit Unit Unit Unit Unit

4 5 6 7 8 9

: : : : : :

male students with satisfactory score female students with excellent score female students with very good score female students with good score female students with satisfactory score students with poor score

Fig. 1. Hasse diagram for students’ results

The goal is to find the association rules that relate students’ results from the preliminary test to the following attributes: – – – – – –

has special interst in algebra has moderate interst in algebra has no interst in algebra had an algebra course within the last year did not have an algebra course within the last year has working knowledge about polynomials

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– has no working knowledge about polynomials – has working knowledge about matrices – has no working knowledge about matrices For the sake of simplicity we limit the amount of attributes that may effect students’ performance. The corresponding Hasse diagram is shown in Fig. 1. Formal concepts presented in the Hasse diagram – {Unit 1, Unit 5}, {has special interst in algebra, had an algebra course within the last year, has working knowledge about polynomials, has preliminary knowledge about matrices} – {Unit 2, Unit 6}, {has special interst in algebra, had an algebra course within the last year, has no working knowledge about polynomials, has preliminary knowledge about matrices} – {Unit 3, Unit 7}, {has moderate interst in algebra, did not have an algebra course within the last year, has working knowledge about polynomials, has preliminary knowledge about matrices} – {Unit 4, Unit 8}, {has no interst in algebra, did not have an algebra course within the last year, has working knowledge about polynomials, has no preliminary knowledge about matrices} – {Unit 9}, {has special interst in algebra, did not have an algebra course within the last year, has working knowledge about polynomials, has no preliminary knowledge about matrices} – {Unit 1, Unit 2, Unit 5, Unit 6}, {has special interst in algebra, had an algebra course within the last year, has preliminary knowledge about matrices} – { Unit 1, Unit 3, Unit 5, Unit 7}, {has working knowledge about polynomials, has preliminary knowledge about matrices} – {Unit 1, Unit 3, Unit 4, Unit 5, Unit 7, Unit 8, Unit 9}, {has working knowledge about polynomials} – {Unit 1, Unit 5, Unit 9 }, {has special interst in algebra, has working knowledge about polynomials} – {Unit 1, Unit 2, Unit 3, Unit 5, Unit 6, Unit 7}, {has preliminary knowledge about matrices} – {Unit 1, Unit 2, Unit 5, Unit 6, Unit 9}, {has special interst in algebra} – {Unit 3, Unit 4, Unit 7, Unit 8, Unit 9 }, {did not have an algebra course within the last year, has working knowledge about polynomials} – {Unit 4, Unit 8, Unit 9 }, {did not have an algebra course within the last year, has working knowledge about polynomials, has no preliminary knowledge about matrices} – {Unit 1, Unit 2, Unit 3, Unit 4, Unit 5, Unit 6, Unit 7, Unit 8, Unit 9}, {} – {}, {has special interst in algebra, has moderate interst in algebra, has no interst in algebra, had an algebra course within the last year, did not have an algebra course within the last year, has working knowledge about polynomials, has no working knowledge about polynomials, has preliminary knowledge about matrices, has no preliminary knowledge about matrices} Some association rules that have the attribute ’has special interst in algebra’ as an antecedent are

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– If a student has special interst in algebra then he/she has had an algebra course within the last year and has preliminary knowledge about matrices with probability 72%. – If a student has special interst in algebra then he/she has preliminary knowledge about matrices with probability 59%.

5

Conclusion

In this paper association rules in education have been used for finding correlations among students’ preliminary knowledge in mathematics and their abilities to solve linear algebra related problems.

References 1. Brin, S., Motwani R., Ullmann, J.D., Tsur, S.: Dynamic Itemset Counting and Implication Rules for Market Basket Data. Proceedings of the ACM SIGKDD international conference on management of data, Tuscon, AZ, USA, (1997) 255–264 2. Carpineto, C., Romano, G.: Concept Data Analysis: Theory and Applications, John Wiley and Sons, Ltd., (2004) 3. Davey, B. A., Priestley, H. A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (2005) 4. Delgado, M., Sanchez, D., Martin-Bautista, M.J., Vila, M.A.: Mining Association Rules with Improved Semantics in Medical Databases. Artificial Intelligence in Medicine, 21(1-3) (2001)241-5 5. Ganter, B, Stumme, G., Wille, R.: Formal Concept Analysis - Foundations and Applications. Lecture Notes in Computer Science, Springer Verlag, 3626 (2005) 6. Pasquier, N., Bastide, T., Taouil, R., Lakhal, L.: Discovering Frequent Closed Itemsets for Association Rules. Proceedings of the 7th International Conference on Database Theory, Jerusalem, Israel (1999) 398–416 7. Pei, J., Han, J., Mao, R.: Closet: An Efficient Algorithm for Mining Frequent Closed Itemsets. Proceedings of the ACM SIGKDD International Workshop on Research Issues in Data Mining and Knowledge Discovery, Dallas, USA (2000) 21–31 8. Wille, R.: Concept Lattices And Conceptual Knowledge Systems. Computers and Mathematics with Applications, 23(6-9) (1992) 493–515

Associative Neighborhood According to Representative Attribute for Performing Collaborative Filtering Kyung-Yong Jung School of Computer Information Engineering, Sangji University, Korea [email protected]

Abstract. Collaborative filtering has been widely used and successfully applied to recommend items in practical application. However, collaborative filtering does not use attributes of items at all. In this paper, associative neighborhood according to the representative attribute, for the purpose of improving accuracy and performance in collaborative filtering system, is proposed. This associative neighborhood selects the associative users that have similar preferences by extracting the representative attribute that most affect the preference. The approach is empirically evaluated, for comparison with the nearest-neighbor model and k-means clustering, using the EachMovie dataset. This method was found to significantly outperform the previous method.

1 Introduction The personalized recommendation systems using collaborative filtering calculate the similarity between a specific user and each of other users who have rated the items that are already rated by the user. Since collaborative filtering is based on the ratings of the neighbors who have similar preferences, it is very important to select the neighbors properly to improve the prediction quality [7],[10]. Collaborative filtering systems use each user’s rating information on various items. The most common approach compares the rating information between users, discovers similar users, and then predicts a user preference for a certain item based on the similar preferences. Because collaborative filtering does not require any information on the contents of items, it can recommend items like music or movies, for which the contents are difficult to analyze. The similarity of preferences between a specific user and other users is computed from the correlation coefficient. Predicting preferences for a certain item is based on other users preferences for that item, and the similarity between each other. In reflecting human opinions, collaborative filtering has several advantages: filtering items that are not easily analyzed by automated processes, filtering items based on quality, and filtering serendipitous items [2]. However, collaborative filtering does not use attributes of items in any way. In this paper, the associative neighborhood according to the representative attribute, for the purpose of improving accuracy and performance in collaborative filtering systems, is presented. The term representative attribute is used for representing a primary attribute that influences the preference for the item. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 839 – 844, 2006. © Springer-Verlag Berlin Heidelberg 2006

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2 Associative Neighborhood The associative neighborhood is used through data mining for collaborative filtering. This technique is also used to promote the accuracy and performance, by reducing a high dimensional feature space using the Apriori algorithm. The accuracy of the associative neighborhood depends on the number of users for composing associative users. We show how the numbers of users for composing associative users at the Apriori algorithm are selected efficiently. 2.1 Selection of Associative User The Apriori algorithm can mine association rules using the data mining technique. The process of mining association rules between users consists of two stages. In the first stage, compositions having transaction support in excess of minimum support are found, in order to constitute a list of frequent users. In the second stage, the list of frequent users is used to create association rules from the database. As for all frequent users (L), find subset instead of all empty sets of frequent users. As for each subset (A), if the ratio of support (L) to support (A) is not less than minimum confidence, the rule of AÆ(L-A) type is displayed. The support of this rule is support (L) [3]. Table 1 reconfigures items to evaluate the preference of user transactions. Table 1. The user transaction Transaction No. 1 2 3 4

The extracted users u1 , u2 , u3 , u4 u2, u3, u5, u9, u10, u11 u1, u2, u3, u5, u6, u7, u8, u12 u3, u13, u14, u15, u16, u17

Transaction No. 5 6 7 8

The extracted users u3, u13, u18 u3, u13, u15, u19, u20 u23, u24, u25 u21, u22

The transaction number means the items to evaluate the preference, and the extracted user is to organize the candidate user set and the frequency user set. Table 2 presents the steps used for extracting the associative users using the Apriori Algorithm. Frequent 3-userset is extracted {u1, u2, u3}, {u2, u3, u5}, {u2, u5, u15}, {u3, u13, u15} according to the Apriori Algorithm. Table 2. The steps for extracting the association users using the Apriori Algorithm Candidate 1-userset u1(2) u2(3) u3(6) u4(1) u5(2) u6(1) u7(1) u8(1) u9(1) u10(1) u11(1) u12(1) u13(1) u14(1) u15(2) u16(1) u17(1) u18(1) u19(1) u20(1) u21(1) u22(1) u23(1) u24(1) u25(1)

Frequent 1-userset u1(2) u2(3) u3(6) u5(2) u13(3) u15(2)

Candidate 2-userset (u1,u2)(2) (u1,u3)(2) (u1,u5)(1) (u1,u13)(0) (u1,u15)(0) (u2,u3)(3) (u2,u5)(2) (u2,u13)(0) (u2,u15)(0) (u3,u5)(2) (u3,u13)(3) (u3,u15)(2) ( u5,u13)(0) (u5,u15)(0) (u13,u15)(2)

Frequent 2-userset (u1,u2,u3)(2) (u1,u2,u5)(0) (u1,u2,u13)(0) (u1,u2,u15)(0) (u1,u3,u5)(1) (u1,u3,u13)(0) (u1,u3,u15)(0) (u2,u3,u5)(2) (u2,u3,u13)(0) (u2,u3,u15)(0) (u2,u5,u15)(2) (u2,u5,u13)(0) (u3,u5,u13)(0) (u3,u5,u15)(0) (u3,u13,u15)(2) (u13,u15,u1)(0) (u13,u15,u2)(1) (u13,u15,u3)(0) (u13,u15,u5)(0)

Frequent 3-userset (u1,u2,u3)(2) (u2,u3,u5)(2) (u2,u5,u15)(2) (u3,u13,u15)(2)

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2.2 Associative User Pattern Generation The associative user pattern representation includes not just 2-associative users but as many as 5-associative users present in the database. At a confidence level of 85 and a support level of 25 in the Apriori algorithm, some characteristic user combinations, can be captured, where the number of users increases [5,6]. The process of generating the pattern is performed in the retrieval step, where associative users are generated in the last pass. An illustration of this is the accumulated number of associative user patterns during the process of generating the pattern for 20,864 users in Table 3. Let AU denote an associative user involved in the generation of the associative user using the Apriori algorithm. The number of associative user patterns generated using 2-AU can be seen to be larger than that in the other cases. Table 3. The generating associative user pattern and the result of clustering process

No. of Associative User Response Time (sec) Accuracy

2-AU 149,894 43 89.2

3-AU 12,936 21 92.6

4-AU 3,822 11 71.4

5-AU 191 -

In order to evaluate the performance of the clustering process in each case (2-AU, 3-AU, 4-AU, 5-AU), the Association Rule Hypergraph Partitioning algorithm (ARHP) [3,7] is used for clustering 20,864 users using association rules and hypergraph partitioning. In the case where the ARHP algorithm using AU clusters a user behavior into all of the classes except for the attribute class, this is considered to be incorrect clustering. The response time represents time of the associative user clustering process. 2-AU case exhibits very poor performance. However, the accuracy of the clustering process 2-AU is higher than using that 4-AU, but lower than that using 3-AU. The clustering process using 3-AU is much more accurate than the other cases. In addition, the 3-AU case exhibits relatively good performance. The 4-AU case exhibits very good performance. However, the accuracy of the clustering process using 4-AU is far lower than the cases. Therefore, in this case, it is appropriate to use the 3-associative users format for the pattern selection of associative user clustering.

3 Representative Attribute for Performing Collaborative Filtering The associative neighborhood according to the representative attribute is used to select the nearest associative neighbors, who have similar preferences to the active user, by extracting the representative attribute that most affect preferences [8]. Collaborative filtering involves the selection of all other users who have similar tastes or opposite tastes to the active user by means of the Pearson correlation coefficient [2],[11]. These users preferences are used in predicting the preference of a target item for the active user. However, collaborative filtering using the representative attribute only involves users that have similar tastes, in order to select a user that has higher correlation coefficient than the active user. The correlation is generally computed with the Pearson correlation coefficient.

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3.1 Extraction of Representative Attribute To overcome that collaborative filtering does not use the attributes of items at all, such that item attribution provides more efficient filtering, collaborative filtering using attributes is used, through the extraction of the representative attribute. In general, this means that user preferences for items are mainly affected by attributes. The representative attribute is defined to be the primary factors that influence the preference for a particular item. Table 4 presents the algorithm used to determine the representative attribute of an associative user. Table 4. Extraction of the representative attribute Algorithm Extraction of the representative attribute Input: Association user’s preference ൺ Value of item Output: Representative attribute ൺ RepresentativeID AttributeSum[Num_Attribute] ← 0, AttributeCount[Num_Attribute] ← 0 for Items that user rated do for Attributes of item do AttributeSum ← AttributeSum + Value of Item AttributeCount++ endfor endfor for j=1 to Num_Attribute do RepresentativeID ← Max(RepresentativeID, AttributeSum/AttributeCount) endfor for i=1 to Num_Attribute do for j=1 to Num_Gender do for k=1 to Num_Age do Representative Attribute[RepresentativeID] ← Add Associative User endfor endfor endfor return

The extraction of the representative attribute uses items rating user preferences. For the purpose of extracting the representative attribute, in this paper, the ratings of the user’s preference are summed for each attribute of the item. The attribute with the maximal summation is considered to be the representative attribute. The associative neighborhood according to the representative attribute is presented, that uses the age and gender, in order to improve the prediction quality. The users are grouped by age and gender, in order to take the relationship between age and gender, into consideration. For each age, gender grouping, derived from all of the user profiles, an active user, whose profile is composed of the average of the group preferences for each representative attribute, is created.

4 Evaluation In order to evaluate the performance of the associative neighborhood according to the representative attribute (AN-RA), grouping methods for collaborative filtering are

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compared with the nearest-neighbor model (NNM) [2],[7] and k-means clustering [1] (KMC). Experiments are performed on a subset of movie rating data, collected from the EachMovie dataset [9]. The data represents an experiment of 20,864 users, with each user rating at least 80 movies and 1,612 kinds of movie, through data integrity. To generate the associative neighborhood, users are represented as 3-associative users using the Apriori algorithm and 20,864 users. The Apriori algorithm can mine associative users at confidence 85 and support 25 and 3-association rule [5],[6]. As an experimental result, 167,729 numbers of the associative user pattern and the confidence are created in the transaction. In addition, 3-AU represents comparatively good speedup. It is relevant to use the 3-associative users format in pattern selection for the associative user pattern. The associative user pattern is grouped according to the representative attribute, using the ARHP Algorithm. In addition to the above, it is important to evaluate recall and precision. In order to quantify this with a single measurement, the F-measure is used, which is a weighted combination of recall and precision widely used in Information Retrieval [4]. 

Fig. 1. Performance of the AN-RA method compared to KMC method and NNM method

Figure 1 summarizes the performance of the three methods. In Figure 1(a), it is seen that AN-RA is more accurate than the other methods (average 89.12 for AN-RA vs. 76.36 for KMC vs. 84.62 for NNM). In Figure 1(b), it can be seen that AN-RA has higher performance than other methods (average 89.12 for AN-RA vs. 59.33 for KMC vs. 65.55 for NNM). These results are encouraging and provide empirical evidence that the use of the associative neighborhood according to the representative attribute can lead to improved performance of collaborative filtering systems.

5 Conclusion In this paper, the associative neighborhood according to representative attribute is proposed for the purpose of improving accuracy and performance in collaborative filtering systems. The associative user pattern representation that includes associative

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users instead of just single users, is proposed. It has been shown that when associative users are composed of 3-associative users, the performance of associative user grouping is most efficient. The associative neighborhood selects the associative users that have similar preferences by extracting the representative attribute that most affect the preference. The results are encouraging and provide empirical evidence that the use of the associative neighborhood according to the representative attribute can lead to improved performance in collaborative filtering systems. In the future, this method would be verified with more users, and the proposed method would be combined with hybrid filtering.

Acknowledgements We thank the DES systems research center from permitting us to use the EachMovie dataset. This research was supported by Sangji University Research Fund, 2006.

References 1. Ding ,C., He, X.: K-Means Clustering via Principal Component Analysis, In Proc. of the 21th Int. Conf. on Machine learning (2004)225-232 2. Connor, M. O., Herlocker, J.: Clustering Items for Collaborative Filtering,Proc. of the ACM SIGIR Workshop on Recommender Systems, Berkeley, CA (1999) 3. Han, E. H., Karypis G.,, Kumar, V.: Clustering based on Association Rule Hypergraphs,Proc. of the SIGMOD'97 Workshop on Research Issues in Data Mining and Knowledge Discovery (1997)9-13 4. Yu, H., Hatzivassiloglou V.:Towards Answering Opinion Questions: Separating Facts from Opinions and Identifying the Polarity of Opinion Sentences, In Proc. of the Conf. on Empirical Methods in Natural Language Processing (2003) 5. Jung, K. Y., Lee, J. H.: User Preference Mining through Hybrid Collaborative Filtering and Content-based Filtering in Recommendation System, IEICE Trans. on Information and Systems, Vol. E87-D, No. 12(2004)2781-2790 6. Ko, S. J., Lee, J. H.: Optimization of Association Word Knowledge Base through Genetic Algorithm, In Proc. of the 4th Int. Conf. on Data Warehousing and Knowledge Discovery, LNCS 2454 (2002)212-221 7. Karypis, G.: Evaluation of Item-Based Top-N Recommendation Algorithms, Technical Report CS-TR-00-46, Computer Science Dept., University of Minnesota(2000) 8. Wang, J., de Vries, A. P., Reinders, M. J.T.: A User-Item Relevance Model for Log-based Collaborative Filtering, In Proc. of the European Conf. on Information Retrieval, LNCS 3936(2006)37-48 9. MovieLens Collaborative Filtering Data Set, http://www.cs.umn.edu/research/GroupLens/, Grouplens Research Project(2000) 10. Kim, T. H., Yang S. B.: An Effective Recommendation Algorithm for Clustering-Based Recommender Systems, In Proc. of the Conf. on Artificial Intelligence, LNCS 3809 (2005) 1150-1153 11. Herlocker, J. L., Konstan J. A., Terveen, L. G., Riedl J. T.: Evaluating Collaborative Filtering Recommender Systems, ACM Transactions on Information Systems (TOIS) archive, Vol. 22, No. 1 (2004)5-53

Benchmarking a Recurrent Linear GP Model on Prediction and Control Problems Xiao Luo, Malcolm Heywood, and A. Nur Zincir-Heywood Faculty of Computer Science Dalhousie University Halifax, NS, Canada, B3H1W5 {luo, mheywood, zincir}@cs.dal.ca Abstract. In this work, a recurrent linear GP model is designed by introducing the concept of internal state to the standard linear Genetic Programming (GP), so that it has the capacity of working on temporal sequence data. We benchmarked this model over four standard prediction and control problems, which include generic even parity problem, sun spot series prediction, Lorenz Chaotic time series prediction and pole balance control problem. From the experimental results, the recurrent linear GP model appears to be very competitive compared to those algorithms relying on spatial reasoning of the temporal problem.

1

Introduction

Genetic Programming has been applied to a wide range of supervised learning problems, chiefly formulated as either classification or function approximation problems [4]. They have also seen widespread application within the context of reactive environments with delayed payoff (reinforcement learning), such as the ‘Ants’ [4] or robot control problems. In both cases, the models relay on a spatial description of the problem. However, in this work, we are interested in problems, which have temporal descriptions. Thus, pattern sequences and capacity of detecting or retaining the temporal relationships between the patterns of a sequence is now important. There are two basic solutions to build models for solving temporal problems. In the first case, the temporal dependence is encoded by the features of each pattern using some apriori information, thus reducing the problem to spatial reasoning alone. Examples of this might involve encoding the temporal property of the problem using a sliding window (shift register) of some predefined depth and resolution. Such an approach has seen wide spread application to predictive problems [9], [10] and [11]. In the second case, a recurrent learning model is employed. This means that the model has capacity to retain state across more than one pattern. Examples of recurrent models include Hidden Markov Models and recurrent neural network models. In these examples, support for reasoning about temporal aspects of the problem is provided by feedback paths internal to the model. Various evolutionary approaches have been proposed for building such models [1] and [5]. The motivation of this work is to design and implement a recurrent linearly structured GP (L-GP) model that falls in the second case and benchmark it on D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 845–850, 2006. c Springer-Verlag Berlin Heidelberg 2006


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predictive and control problems. In the following, the recurrent L-GP model is described in section 2. Results from an experimental study are presented on four different problems in section 3. Finally, conclusions are drawn and future work is discussed in section 4.

2 2.1

Recurrent Linear Genetic Programming Linear Genetic Programming

Linearly Structured Genetic Programming is based on a representation closely related to that employed by Genetic Algorithms. Specifically, individuals are constructed from a (linear) sequence of integers each of which has to be decoded into a valid instruction (syntactic closure). The decoding process effectively translates each integer into instruction. In this work, a 2-address instruction format is employed e.g., R1 = R1 + IP 3, where R1 denotes a register with index ‘1’ and IP 3 is a reference to a input with index ‘3’ or 3rd feature of the current input pattern. The specific form of linearly structured GP(L-GP) employed by this work utilizes the page-based L-GP developed in an earlier work [3]. Such a scheme enforces a fixed length representation, the basic components of which are defined as follows. – Representation: Individuals take the form of a 2-address instruction format. Individuals are described in terms of a (uniform) randomly selected number of pages, where each page has the same fixed number of instructions. – Initialization: Individuals are described in terms of the number of pages and instructions. The number of pages per individual is determined through uniform selection over the interval [1 . . . maxPages]. Defining an instruction is a two-stage process in which the mode bit is first defined(instruction type) using a roulette wheel(user specifies the proportions of the three instruction types). Secondly the content of the remaining fields is completed with uniform probability. – Selection Operators: A steady-state tournament is employed. In this case all such tournaments are conducted with 4 individuals selected from the population with uniform probability. The two fittest individuals are retained and reproduce. The children over-write the worst two individuals from the same tournament using their respective position in the population. – Variation Operators: Three variation operators are utilized, each with a corresponding probability of application. Crossover selects one page from each offspring and swaps them. Mutation has two forms. The first case is referred to as ‘Mutation’which merely Ex-OR’s an instruction with a new instruction. The second mutation operator is denoted as ‘Swap’ which identifies two instructions with uniform probability in the same individual and interchanges them. This represents the basic page-based L-GP scheme. However, the selection of the page size is problem specific. As a consequence the Dynamic Page based LGP algorithm was introduced to modify the number of instructions per page

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dynamically during the course of the training cycle [3]. Such a scheme was demonstrated to be much more robust than that of a fixed page size over a range of benchmark problems [3]. In this work, the Dynamic Page based L-GP algorithm is employed. 2.2

Recurrent L-GP

The only modification necessary to change a standard L-GP model into a recurrent model is to retain register values between sequential pattern presentations. Thus within the context of a prediction problem, the registers are never reset until the last pattern of the input sequence is reached. The prediction read from the predefined ‘output’ register(s) is to predict the next pattern following the last pattern that input into L-GP. In the case of a control problem in which a failure state might be explicitly reached, the model would be allowed to run until such a state occurs and then the registers are reset before a new initial condition is selected and the process is repeated.

3

Experiments and Results

A total of four benchmark problems are considered from a recurrent modeling context: Generic solution to the even parity problem; predictor for the Lorenz chaotic attractor; predictor for the sun spot series problem, and a controller for the pole balance problem. The GP learning parameters are summarized in Table 1. Table 1. GP Learning Parameters Data set Parity, Sun Spot, Pole Balance Lorenz Pop. Size 125 Max. Instr. 128 512 Max Tournaments 50000 500000 Num. Reg. 4 8 Function Set +, -, *, % ( Terminal Set {0, . . . , 255} {input index} P(Xover) 0.9 P(Mutation) 0.5 P(Swap) 0.9 Runs 50(25 on second pole balance problem)

3.1

Generic Even Parity

The even parity problem is a well-known early benchmark in which the basic objective was to derive a specific even parity instance using 2 input logical operators that excluded Ex-OR [4]. Here, our objective is to derive 6- and 7-parity from a training set consisting of 2-, 3-, 4- and 5-parity. The input sequence consists of bits associated with the parity case. The bits are input into recurrent

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L-GP one after another. On presentation of the last bit in the sequence the value of register R0 which acted as “output” register is compared to the label for that sequence. Fitness function is the sum square error of all training sequences. The simplest(and most typical) solution generated by recurrent L-GP to this problem consisted of only two instructions: R0(t) = R0(t − 1) − X(t); R0(t) = R(t) × R(t). X is the input sequence and X(t = 1 . . . n) corresponds the input bit in the sequence. R0 is initialized to 0 (R0(0) = 0). It is worth to mention that not only this solution is a very concise solution for 6- and 7-parity sequences but also for all n-parity sequences. 3.2

Sun Spot Time Series

The Sun Spot time series has been a benchmark prediction problem in a number of studies. The typical approach has been to use a sliding window with length n to go through the whole sequence to construct a spatial presentation of the sequence, then a predictive model f is built to predict the next time step n + 1, i.e. x(t + n + 1) = f (x(t), . . . , x(t + n)). In our system, no ‘n’ is predefined, all the patterns before x(t+1) are input to predict the x(t+1). Thus, t is dynamic. This leaves the selection of relevant previous time steps to the recurrent L-GP model. In line with previous work, the dataset is divided into training(221 patterns representing the years 1700-1920), and two test sets (Test set 1 has 35 patterns (1921-1955), Test set 2 has 24 patterns (1956-1979)). Fitness function takes the form of a normalized mean square error as shown in formula 1. N M SE(P ) =

P 1 1 $ (desired(p) − GP out(p))2 2 σ P p=1

(1)

Where σ 2 = 1535 and P is the pattern count for the dataset [9]. The best solution for this problem consists of 35 instructions. Table 2 provides a comparison of recurrent L-GP with other predictors identified in previous works on the same dataset based on their best performance. The other models provide lower errors on training and the first test partition, but degrade significantly on the second test partition, which represents the period most distant from the training partition. It is important to notice that recurrent L-GP is more consistent over the training and 2 test sets than the other approaches. 3.3

Lorenz Chaotic Attractor

Prediction of a chaotic time series has also been widely used benchmark for predictive models. Same as the case of the Sun Spot benchmark, the typical approach for this problem is to build a predictor based on the sliding window [7]. Lorenz Chaotic time series is defined over three variables by the discrete differential system, x˙ = σ(y − x); y˙ = ρx − y − yz; z˙ = xy − bz (2) where σ = 10, ρ = 28, and b = 8/3. The time series is built from an initial condition of (0, 0.01, 0) and a step size of 0.01. A total of 4000 samples from the sequence are constructed with the first

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Table 2. Comparative Results on Sun Spot Problem Model Recurrent L-GP NN [11] TAR [9] Recurrent NN [5] GP [10]

NMSE (train) 0.1077 0.082 0.097 0.1006 0.125 ± 0.006

NMSE (test1) 0.1655 0.086 0.097 0.0972 0.182 ± 0.037

NMSE (test2) 0.1708 0.35 0.28 0.4361 0.370 ± 0.06

2000 discarded to avoid any start up properties. The remaining 2000 samples are then divided equally between training and test. The fitness function is the normalized mean square error as shown in formula 1. The best results for this problem are NMSE(training)= 1.38 × 10−5 and NMSE(test)= 1.09 × 10−5 . The best solution for this problem consists of 48 instructions. In comparison, the SOM based Dynamic Learning architecture of Principe et al., produced training errors of the order 0.0011 [7], obviously worse than the performance of the recurrent L-GP model. 3.4

Pole Balance

The pole balance or inverted pendulum problem places the learning system within the role of a bang-bang controller [6]. The controller supplies a control force of ±10N to a cart on which an inverted pendulum is connected. Cart behavior is described in terms of x - the distance from the center of a track on which the cart travels -, and θ - the angle of the pendulum relative to the vertical. The state of the cart can be described in the form of a binary fail (unbalanced)/no fail (balanced) metric, where the failure state is defined by the condition, IF (|θ| >12) OR (|x| >2.4) THEN (fail) ELSE (no fail) The objective here is to evolve recurrent L-GP to produce a controller to supply force to the cart so as to keep the cart balanced as long as possible. Given a force produced by a controller, the behavior of the cart is described by a series of differential equations, modeled as an Euler discrete event simulation at a step size of 0.01 [6]. We set up two sets of experiments. One has two 2 inputs (x and θ), the other has 4 inputs (x, θ and their corresponding velocities). In line with previous GP solutions to this problem, for the training process, we set the 10 initial states of the cart (x, θ and their corresponding velocities) randomly over the interval ±0.2. We did 25 different random seed runs, all of them converged. The pole could last 8 seconds under all 10 random initializations without failure in training for both conditions of 2 and 4 inputs. In comparison with the controller evolved by Chellapilla using a macro-mutation operator based Tree structured variant of GP, the mean time a pole was balanced during training was 2.7228 seconds, with no controller solving the problem [2]. Hence, our system is significantly better.

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Conclusions

In this paper, we describe a recurrent linearly structured GP model and benchmark it on a series of prediction and control problems. This model works on sequence directly instead of using a sliding window to map the temporal data representation into spatial data representation. The results show that this model is more consistent on both the training and the test sets than the sliding window based model. Moreover, the evolved rule generated by the recurrent linear GP is a set of instructions, which are very simple. Future work will investigate the inter-relationships between solution lengths and the size of the register set and new fitness functions, which are able to express the temporal nature of the problem. We are also interested in applying such a model to text sequence analysis, and bio-oriented sequence analysis.

References 1. Angeline, P.J., Saunders, G.M., Pollack, J.B.: An Evolutionary Algorithm that Constructs Recurrent Neural Networks. IEEE Transactions on Neural Networks. 5(1) (1994) 54–64 2. Chellapilla, K.: Evolving Compuer Programs Without Subtree Crossover. IEEE Transactions on Evolutionary Computation. 1(3) (1997) 209–216 3. Heywood, M.I., Zincir-Heywood, A.N.: Dynamic Page-Based Linear Genetic Programming. IEEE Transactions on Systems, Man and Cybernetics - PartB: Cybernetics. 32(3) (2002)380–388 4. Koza, J.R.: Genetic Programming: ON the Programming of Computers by Means of Natural Selection. MIT Press, MA, (1992) 5. McDonnell, J.R., Waagen, D.: Evolving recurrent Perceptrons for Time-Series Modeling. IEEE Transactions on Neural Networks. 5(1) (1994) 24–38 6. Miller, W.T., Sutton, R.S., Werbos, P.J.: Neural Networks for Control. MIT Press,(1990) 7. Oakley H.: Two Scientific Applications of Genetic Programming: Stack Filters and Non-Linear equation Fitting to Chaotic Data. In Advances in Genetic Programming. Chapter 17. K.E. Kinnear (ed). MIT Press, MA, (1994) 369–390 8. Teller, A.: The Evolution of Mental Models. In Advances in Genetic Programming. Chapter 9. K.E. Kinnear (ed). MIT Press, MA, (1994)198–219 9. Tong, H., Lin, K.S.: Threshold autoregression, limit cycles and cyclical data. J. of the Royal Statistical Society. B 42 (1980) 245 10. Vallejo, E.E., Ramos R.: Evolving Turing Machines for Biosequence Recognition and Analysis. In Proceedings of the 4th European Conference on Genetic Programming (EuroGP 01). Springer Verlag, Berlin,(2001) 192–203 11. Weigend, A.S., Huberman, B.A., Rumelhart, R.E.: Predicting the Future: A Connectionist Approach. Int. J. of Neural Systems. 1(3) (1990) 193–209

Cognitive Computing in Intelligent Medical Pattern Recognition Systems Lidia Ogiela1, Ryszard Tadeusiewicz2, and Marek R. Ogiela2 AGH University of Science and Technology 1 Faculty of Management 2 Institute of Automatics Al. Mickiewicza 30, PL-30-059 Krakow, Poland {logiela, rtad, mogiela}@agh.edu.pl

Abstract. The paper will be presented the way of application of linguistic mechanisms of pattern recognition in development of intelligent information and recognition systems. Such methods are aimed to facilitate an in-depth analysis of the meaning for some selected medical patterns, especially in the form of spinal cord and coronary arteries images. The procedures proposed for semantic reasoning are based on the model of cognitive resonance analysis. Cognitive procedures have been applied to the task of semantic interpretation diagnostic images both from the central nervous system as well as from heart helical CT examinations. The application presented in this paper will show the great possibilities of lesion detection in the analysed structures used the grammar approach to the interpretation and classification tasks.

1 Introduction Among a great variety of Information Systems the class of Diagnosis Support Systems (DSS) are very popular due to their wide application in clinical practice. In this paper we try to show an example of a system that was prepared not only for simply diagnose, but also was oriented towards the cognitive analysis leading to understanding of pathological lesions. In medical image analysis the main objective is to determine whether there is any important disease lesions observed in the patient’s analysed organ or whether there are no such changes visible in the image. If there are any lesions, their type is analysed and the system directs its functions towards determining what disease the patient has. DSS systems operate on the basis of three main rules: image transformation, image analysis, and image classification allowing to classify all pathological features existing in the analysed image. DSS systems proposed in earlier research were used, among others, for pancreas as well as for kidney, and hand disease diagnosis. Their functioning is based on medical image recognition methods [5]. Due to the fact that DSS systems develop very rapidly, an attempt was made to construct a new class of such systems using in their operation the mechanisms of cognitive analysis. The said are to be directed at attempts to automatically understand the semantics of analysed images, and therefore at their content meaning interpretation. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 851 – 856, 2006. © Springer-Verlag Berlin Heidelberg 2006

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2 Semantic Processing of Medical Visual Patterns Cognitive analysis used in IT systems is very often based on the syntactic approach [3, 5]. For the purpose of meaning image interpretation it first uses a pre-processing operation usually composed of image coding using of terminal symbols, shape approximation, as well as some kind of filtration or segmentation. As a result of the execution of such stages it is possible to obtain a new image representation in the form of hierarchic semantic tree structures and subsequent production steps of this representation from the initial grammar symbol [5]. An intelligent cognitive system distinguishing at the stage of pre-processing image data must, in the majority of cases, perform image segmentation, identify primitive components and determine spatial as well as semantic relations between them. An appropriate classification is based on the recognition of whether a given representation of the actual image belongs to a class of images generated by languages defined by one of possible number of grammars. Such grammars can be considered to belong to sequential, tree and graph grammars while recognition with their application is made in the course of a syntactic analysis performed by the system [5]. The main element of a correctly functioning IT system supporting the medical image diagnostics is, analysis preparation of a cognitive method of disease units and pathological lesions as occurring in the spinal cord or coronary arteries. The cognitive analysis contained in the DSS-central nervous, and blood circulatory systems is aimed to propose an automatic interpretation method of these extremely complicated medical images. Such images are difficult to interpret due to the fact that various patients have various morphologies of the imaged organs. This is true both of the correct state and if there are any disease lesions. The nervous and circulatory systems, similarly as most elements of the human body, is not always correctly built and fully developed from the birth. It often occurs that such systems for the first couple of years functions correctly and only after some time there are some troubles with its functioning. Most pathological changes occurring in the central nervous system, and blood circulation are clinically diagnosed based mainly on image examination assigned to NMR or helical CT tomography.

3 Classification of Spinal Cord Images All the analysed images of spinal cord were, before their proper recognition, subject to segmentation and filtration procedures [4]. Structures shown in this way were then subject to cognitive analysis stages using the grammar described below. In order to analyse disease lesions of the spinal cord, the following attributed grammar has been proposed: Gsc= (VN, VT, P, ST), where: VN – stands for a set of non-terminal symbols (intermediary in the process of image description generation), VT – stands for a set of terminal symbols (final symbols

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describing shape features), P – stands for a production set, ST – stand for the grammar start symbol, VN = {LESION, STENOSIS, DILATATION, TUMOR, N, D, S}, VT = {n, d, s}. Apart from these, the following meaning was given to terminal elements present in the description: n∈[-11°, 11°], d∈(11°, 180°), s∈(-180°, -11°), ST =LESION P production set has been defined as in Table 1. Table 1. Production set defining changes in the Gsc grammar Lesion Dilation/cyst Neoplastic tumours Stenosis, compression Elements of the detected lesions

Grammar rules 1. LESION → DILATATION 2. DILATATION → D N S | D N | D S

3. LESION → TUMOR 4. TUMOR → D S D S | S D S N | SDSD|DSDN 5. LESION → STENOSIS 6. STENOSIS → S N D | S D |S N 7. N → n | n N 8. D → d | d D 9. S → s | s S

Semantic actions Lesion = spinal dilatation Lesion = spinal tumor

Lesion = spinal stenosis Lesion features= location; length; diameter,quantity,severity

The proposed grammar makes it possible to detect various kinds of spinal cord or meningeal stenoses characteristic for neoplastic lesions and inflammatory processes of the spinal cord. Figure 1 presents an image of the spinal cord with a visible deformation, and the diagram of the spinal cord.

Fig. 1. Spinal cord and width diagram. Diagnostic description of spinal cord lesions with paraganglioma detected as a result of cognitive analysis.

The bold area on the image represents the area of occurrence of the anomalies within the structure of the spinal cord. The set of chords, cross-cutting the spinal cord in subsequent points perpendicularly to its axis demonstrate how the width diagram was made.

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Spinal cord width diagram (Fig.1) presents the results of spinal cord morphology analysis. It is the most precious source of information when one is looking for pathological lesions and it contains all-important data about the examined fragment of central nervous system. At the same time it ignores all spinal cord image details unimportant from the diagnostic point of view. The results presented here have been achieved by the application of attribute grammar and they are an example of the cognitive approach to the medical data considered here. The type of lesion detected here has been assigned based on its location and on morphometric parameters determined by the grammar semantic procedures. In order to perform meaning analysis on spinal cord images the MISA (Medical Image Syntax Analyser) computer system has been developed. This enables the analysis and classification of spinal cord visualization analysed in this paper. Table 2. The efficiency of cognitive analysis methods directed towards discovering and understanding selected disease phenomena in the central nervous system The analysed disease lesion

Number of examined images

Spinal cord dilation Cysts Neoplastic tumours Stenoses and compression Degeneration Total

Cognitive analysis efficiency [%]

2 18 27 14

Number of correctly recognised images (lesions) 2 17 25 12

23 84

20 76

87 90,5

100 94 93 86

The application efficiency of cognitive analysis procedures, using this system, has been presented in the Table 2 and it is directed towards comparing the results obtained from the use of this system with those that one can consider as a correct diagnosis. These results are obtained as a result of the application of semantic analysis algorithms conducted in reasoning modules of the proposed system and based on semantic actions assigned to structural rules.

4 Coronary Vessel Analysis In the case of coronary vessels analysis the proper graph-based grammar describing these structures was defined so that the individual branches of the graph in the description provided identify all start and end points of coronary vessels and all bifurcations or transitions of main vessels into lower-level ones. Thus developed graph-based structure will constitute the elements of the language for defining spatial topology and correct vascularization of the heart muscle together with the potential morphological changes, e.g. in the form of stenoses in their lumen (Fig. 2).

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Fig. 2. Spatial labelling of coronary arteries and defining relations occurring between them for the right coronary artery. The grey rectangle marks the place of a major stenosis in a coronary artery.

Fig. 3. The set of productions in the form of graphs deriving the structure of coronary vessels together with the vertex characteristic description

To define the location where the vessel pathology is present in the graph of coronary arteries the following grammar is proposed.

GedNLC = ( Σ, ∆ , Γ, P , Z ) , where Σ = ΣN ∪ ΣT and is a set of both terminal and non-terminal node labels describing the examined graphs and defined as follows.

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∆ = ΣT = {right coronary artery, right marginal branch, right posterolateral branch, posterior interventricular branch} – a set of terminal node labels. ΣN = {A, B, C, I, M, P, P1, R} is a set of non-terminal node labels. Γ = {µ,1; µ,2; ν,1; ν,24; ο,19; ο,24} is a set of labels describing edges of the graph. Z = {A} is the original starting graph. P – is a finite set of productions recorded in the graph-based form and presented in Fig. 3.

5 Conclusion The research conducted by the author, based on the analysis of images with pathological lesions in central nervous system (spinal cord) and blood circulatory system (coronary arteries), have demonstrated that cognitive data analysis can be the factor that significantly enriches the possibilities of contemporary medical information systems. In particular, the described research has demonstrated that an appropriately built image grammar enables the conduct of precise analysis and the description of medical images from which important semantic information can be gained on the nature of processes and pathological lesions as found in the patient’s spinal cord or coronary vessels. It is worth emphasising that the results described in this paper have been obtained following the cognitive process, simulating an experts’ method of thinking: if one observes a deformation of the organ shown by the medical image used, then one tries to understand the pathological process that was the reason for the appearance of deformations found. One does not perform a mechanic classification for the purpose of pointing out more similar samples on the pathological image.

Acknowledgement This work was supported by the AGH University of Science and Technology under Grant No. 10.10.120.39.

References 1. Burgener, F.A., Meyers, S.P., Tan, R.K., Zaunbauer, W.: Differential Diagnosis in Magnetic Resonance Imaging. Thieme (2002) 2. Khan, M.G.: Heart Disease Diagnosis and Therapy. Williams & Wilkins, Baltimore (1996) 3. Meyer, B. A.: Pattern Recognition in Medical Imaging. Elsevier (2003) 4. Ogiela, L.: Usefulness Assessment of Cognitive Analysis Methods in Selected IT Systems. Ph. D. Thesis. AGH Kraków (2005) 5. Tadeusiewicz, R., Ogiela, M.R.: Medical Image Understanding Technology. Springer, Berlin-Heidelberg (2004)

Data Mining-Based Analysis on Relationship Between Academic Achievement and Learning Methods During Vacation Hea-Suk Kim1, Yang-Sae Moon1, Jinho Kim1, and Woong-Kee Loh2 1

Department of Computer Science, Kangwon National University 192-1, Hyoja-2 Dong, Chunchon, Kangwon 200-701, Korea {hskim, ysmoon, jhkim}@kangwon.ac.kr 2 Department of Computer Science & Advanced Information Technology Research Center Korea Advanced Institute of Science and Technology (KAIST) 373-1, Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea [email protected]

Abstract. In this paper, we systematically analyze the effect of learning methods and living style of students during vacation on academic achievement using data mining techniques. To achieve this goal, we first identify various items of learning methods and living style which can affect academic achievement. Students are surveyed over these items through an Internet online site and the data collected from students are stored into databases. Then, we present data filtering methods of these collected data to adopt data mining techniques. We also propose the methods of generating decision trees and association rules from the collected data of students. Finally, we apply the proposed methods to middle school students in a city of Korea, and we analyze the effect of learning methods during vacation on their academic achievement.

1 Introduction According to the recent advances in information technologies, many companies and organizations make great efforts to discover valuable knowledge from their huge databases. Data mining is a technique to discover such knowledge from the databases [1]. Many commercial data mining products such as SAS Enterprise Miner, IBM Intelligent Miner, and DBMiner were released and applied in a variety of fields including finance, communications, management, and marketing. Academic achievement means the procedure or the result of obtaining knowledge and skills through academic learning [3, 4], and it is usually measured by academic grades. The researches on academic achievement until recently are focused primarily on learning methods and activities for regular semesters. There has been almost no research on academic achievement for vacation, even though the whole vacation spans up to three or four months a year as the extension of regular semesters. In this paper, we systematically analyze the effect of learning methods and living style during vacation on academic achievement using data mining techniques. We D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 857 – 862, 2006. © Springer-Verlag Berlin Heidelberg 2006

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perform the analysis through the following four steps. First, we derive diverse items of learning methods and living style that can affect academic achievement. Second, we perform survey at an Internet online site to collect the student's real data on the derived items including academic grades before and after vacation. Third, we perform filtering on the collected data to adopt data mining techniques. Last, we use SAS Enterprise Miner [2] (E-Miner in short) to extract meaningful knowledge. We use the decision tree [5,6] and the association rule [7] as the data mining techniques for our analysis. The decision tree is used for analyzing the effect on academic achievement of learning methods during vacation, and the association rule for detecting the meaningful relationship between learning methods and living style during vacation.

2 Related Works There have been several researches on student's academic achievement [8, 9]. In [8], the effect on academic achievement of teaching and learning attitudes was analyzed for the course of Mathematics. In [9], the academic achievement depending on the result of Myers-Briggs Type Indicator (MBTI) test was analyzed. Most of the existing researches were focused primarily on academic achievement during regular semesters and were not interested in that during vacation. It is obvious that learning methods and living style during vacation can significantly affect academic achievement after vacation. Hence, this paper can be distinguished from the existing ones, since it systematically analyzes the variation of academic achievement before and after vacation. There also have been several researches to adopt data mining techniques in the field of education [3, 5, 9]. Reference [5] showed that, for the high-ranked students, studying at academic institutes or their learning attitude doesn't affect their grades, but that, for the mid-ranked students, those can affect their grades much. However, the paper was interested only in those two items and thus has the weakness of not covering other diverse items that can affect academic achievement such as private tutoring and Internet learning sites. Moreover, the paper did not deal with anything on learning methods and living style during vacation. On the contrary, we consider more items that affect academic achievement, and we focus on the academic achievement according to the activities during vacation in this paper. References [3, 9] adopted data mining techniques in other educational problems rather than academic achievement.

3 Analysis Methods 3.1 Deriving Mining Items We derive three categories of mining items. First, we use student's grades before and after vacation for checking the variation of academic achievement. Second, we derive direct-related items that are highly probable to affect academic achievement such as private tutoring and academic institute lessons. Third, we derive indirect-related items

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that are less probable to affect academic achievement such as habits of writing a diary and watching TV. The variation of academic achievement is measured as one of three nominal values: Ascend, Descend, and Sustained. The direct-related items are the learning methods that students intentionally carry out to promote their academic achievement. We use the following direct-related items: private tutoring for one or a few students; academic institute lessons; watching educational broadcasting; studying extra learning materials; and Internet learning sites. The indirect-related items are daily habits or activities of students during vacation that are not directly intended for promoting their academic achievement. We use three kinds of indirect-related items as follows: items in daily living (daily hours of using a computer, watching TV, and physical exercising; whether to have a boy/girl friend and communication with parents; whether to eat breakfast every morning); items indirectly related with a specific course (whether to write a diary, letters, and emails; whether to read books or manage his/her own Internet home pages); and additional items (the university hoping to enter; whether to have the experience of travel or foreign habitation). 3.2 Analysis Using Decision Trees We use decision trees [5, 6] to find the learning methods during vacation that are helpful for improving student's grades. We generate a decision tree for each course using the direct-related items explained in Section 3.1. Using the indirect-related items simultaneously makes decision trees too complex to analyze them, and thus, we do not consider the indirect-related items in generating decision trees. We apply the following two pruning rules to decision trees generated by E-Miner. The pruning rules are used to remove meaningless leaf nodes in the trees. Pruning Rule 1. The number of objects (students) in a leaf node should be at least 5% of whole objects (students). Pruning Rule 2. The ratio of change in grades between the root node and a leaf node should be more than 5%. 3.3 Analysis Using Association Rules The association rules are derived from the frequent itemsets which are the sets of items appearing commonly in the same transactions [7]. We use both direct- and indirect-related items to derive association rules. Contrary to decision trees, analyzing association rules is not difficult even when the number of items is large, since association rules have the simple form of ‘X Ÿ Y’ for itemsets X and Y. We need filtering process of collected survey data. For deriving association rules, we consider only whether a certain item appears in a transaction or not, while some of the survey data contains numeric values. Hence, we need to convert those numeric values into Boolean values of TRUE or FALSE. We convert numeric values according to their averages for each of the numeric items. We can formally define the conversion function Conv(Qi, Rj) as the following Eq. (1):

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­°True , if ans(Qi , R j ) ≥ avg(Qi ), Conv(Qi , R j ) = ® °¯False , if ans(Qi , R j ) < avg(Qi ),

(1)

where ans(Qi, Rj) is the answer given for the i-th question in the j-th student and avg(Qi) is the average of all the numeric values of the i-th question.

4 Experiments and Analysis We collected detailed real data of student's work and activities during vacation at an Internet survey site. The survey was performed on middle school students in a city of Korea whose population is about 250,000. The total number of students in the city area was 10,790, and the size of sample students participated in the survey was more than 500. Hence, the degree of confidence is above 90%, and the range of standard error is less than 5%. The period of survey was 15 days from May 17 to May 31, 2005. We first generated decision trees using only direct-related items as explained in Section 3.2. Figure 1 shows the decision tree for the course of Korean. In the figure, four nodes generated by E-Miner were discarded by the Pruning Rules 1 and 2 in Section 3.2. Hence, there left only two meaningful leaf nodes each of which can be expressed as a condition as shown in Table 1. From the conditions in Table 1, we can get the knowledge that educational broadcasting is helpful for the ascent of grades, while Internet learning sites may cause the descent of grades. Table 1. Conditions for Korean Grades

Classification Condition (Educational Broadcasting = YES) ∧ Ascend (Academic Inst. Lessons = NO) (Educational Broadcasting = NO) ∧ (Private Tutoring = NO) Descend ∧ (Internet Learning Sites = YES) The knowledge obtained from the course of English is that private tutoring is only helpful for sustaining grades, and that taking none of private tutoring, academic institute lessons, and Internet learning site lessons could rather help the ascent of grades. Also, the knowledge obtained from the course of Mathematics is that academic institute lessons help students sustain their Mathematics grades. We omit the detailed results due to space limitation. By combining the above three analysis results, we can derive the following knowledge: 1) Internet learning sites can cause the descent of grades; 2) private tutoring, which was expected to have much influence on student's grades, is actually not helpful very much; and 3) multiple adopting of several learning methods can even cause the descent of grades. We believe that the analysis results would be useful to establish student's guidelines for studying during vacation.

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Fig. 1. Decision Tree for Korean Course

We also generated association rules for two support values: 30% and 45%. Here, the confidence was fixed as 90% in both cases. In the case where the support was set to 30%, we got 24 association rules in total. Among the rules, the most meaningful one is that the students who study English and Mathematics at academic institutes also study Korean at academic institutes. However, the rule is within the scope of common sense, and can be hardly regarded to have a special meaning. We obtained four association rules with the support of 45%. As the analysis results by association rules, however, we conclude that there is no special relationship between the activities during vacation.

5 Conclusions In this paper, we proposed data mining-based methods to analyze the effect of learning methods and living style during vacation on student's academic achievement. We performed the analysis through the following steps. First, we derived diverse detailed items of learning methods and living style during vacation. Then, we performed survey collecting student's real data at an Internet online site. Finally, we generated decision trees and association rules finding the effective learning methods during vacation and analyzing the relationship between the activities during vacation. We summarize the knowledge obtained by our analysis as follows. (1) Internet learning sites can cause the descent of grades. (2) Private tutoring, which was expected to have much influence on student's grades, is actually not helpful very much. (3) Multiple adopting of several learning methods can even cause the descent of

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grades. (4) Regular lessons (and regular living style) give the most positive influence on academic achievement. We believe that the analysis result can help teachers, parents, and students themselves to establish student's guidelines for studying and living during vacation.

Acknowledgement This work was partially supported by the Ministry of Science and Technology (MOST)/Korea Science and Engineering Foundation (KOSEF) through the Advanced Information Technology Research Center (AITrc). Also, it was partially supported by the Research Grant from Kangwon National University.

References 1. Chen, M.-S., Han, J., Yu, P. S.: Data Mining: An Overview from a Database Perspective. IEEE Transactions on Knowledge & Data Engineering, Vol. 8, No. 6 (1996) 866-883 2. http://www.sas.com/technologies/analytics/datamining/miner/. 3. Aronson, J.: Improving Academic Achievement. Academic Press (2002) 4. Chall, J. S., Adams, M. J.: The Academic Achievement Challenge. Guilford Publishers (2002) 5. Bae, J.-H.: Analysis on Academic Achievement Using Data Mining. Master's Thesis, Kyunghee University, Korea (2001) 6. Agrawal, R. et al.: An Interval Classifier for Database Mining Applications. Proc. of the 18th Int'l Conf. on Very Large Data Bases (1992) 560-573 7. Agrawal, R., Srikant, R.: Fast Algorithms for Mining Association Rules in Large Databases. Proc. of the 20th Int'l Conf. on Very Large Data Bases (1994) 487-499 8. Kim, D.-H., Cho, Y.-J.: Analysis on the Level of Academic Achievement Based on Mathematics Teaching and Learning Attitudes. Education Theory & Practice, Vol. 14, No. 1 (2004) 115-132 9. Kim, B.-S., Kim, M.-J.: A Study on the Effect of Student's Characteristic Style on Academic Achievement. Korea Human Relationship Bulletin, Vol. 7, No. 1 (2002) 1-20

Database and Comparative Identification of Prophages K.V. Srividhya1, Geeta V Rao1, Raghavenderan L1, Preeti Mehta1, Jaime Prilusky2, Sankarnarayanan Manicka1, Joel L. Sussman3, and S Krishnaswamy1 1

Bioinformatics centre, School of Biotechnology,Madurai Kamaraj University,Madurai [email protected] 2 Biological Services,Weizmann Institute of Science Rehovot 76100, Israel 3 Department of Structural Biology, Weizmann Institute of Science Rehovot 76100, Israel

Abstract. Prophages are integrated viral genomes in bacteria. Prophages are distinct from other genomic segments encoding virulence factors that have been acquired by horizontal gene transfer events. A database for prophages (http://bicmku.in:8082/prophagedb http://ispc.weizmann.ac.il/prophagedb) has been constructed with data available from literature reports. To date other than bacteriophage corner stone genes based iterative searches, no other exhaustive approach unique for identifying prophage elements is available. Here we report detection of prophages based on proteomic signature comparison using a prophage proteome as reference set. This method was tested with using the database and then extended over newly sequenced bacterial genomes with no reported prophages. The approach of using similarity of proteins over a given region helped identify twenty putative prophage regions in nine different bacterial genomes.

1 Introduction Bacteriophages are viruses infecting bacteria. Bacteriophages take up two life cycles, one being lytic infects, multiplies, and lyses host bacterium during progeny release [1] whereas in the other temperate mode the phage DNA integrates with the bacterial genome and is termed as prophage. Prophages range from fully viable to cryptic. Cryptic prophages harbor mutational decay and do not result in lytic growth. Prophages can constitute as much as 10-20% of a bacterium’s genome (Escherichia coli O157:H7 strain Sakai contains 18 prophage elements constituting 16% of the genome) [2]. Prophage sequences contribute to interstrain variability [3]. At present 230 prophages have been reported in 82 bacterial genomes [4]. In addition, prophages are important vehicles for horizontal gene exchange between different bacterial species. Virulence factors in many pathogenic bacteria are observed to be located on prophage locus, indicating the possible role played by prophages in conferring pathogenicity to host bacterium [5][6][7]. The impact of prophages on bacterial evolution has been reviewed extensively [8]. Prophages do not seem to be a homogenous group and show mosaic nature. Their diverse nature is also reflected by the diversity of genome sizes ranging from 549 kb (Flex9 prophage of Shigella flexneri 2a301) to 139449kb (Bh1 prophage from Bacillus halodurans).Analysis of e14 prophage of E coli K-12 revealed the modular nature of the element [9] and provided the basis for the approach of using similarity of proteins over a given region [10]. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 863 – 868, 2006. © Springer-Verlag Berlin Heidelberg 2006

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Identifying and understanding prophage elements is medically important as some phage genes are known to increase the survival fitness of lysogens [3]. Unambiguous detection of cryptic prophages is difficult as these defective prophages may be devoid of any corner stone genes. A prophage database has been initiated with the information available from the integrated prophages of sequenced bacterial genomes. At present, the database contains 227 prophage sequences from 49 organisms and details on the twenty putative prophage regions identified in 9 bacterial genomes by protein similarity approach.

2 Methods The prophage database was constructed using PostgreSQL server at backend and PHP in front end. All genomes, proteomes and protein table files were downloaded from ftp://ftp.ncbi.nih.gov/genomes/Bacteria. Currently the database covers prophages reported by Casjens [4]. In order to identify e14 homologs, similarity searches at the protein level were done taking the twenty-three e14 proteins as query and the bacterial proteomes as target. Similarity searches were done using blastp, (local version of the WWW-BLAST) [11] using an e-value of 0.01 and Blosum62 as the scoring matrix.

3 Results and Discussion 3.1 Database for Prophage Elements Prophage database covers genome data (GC content, integration site, location, genome size) and protein data (location, protein annotation, related COG information, PDB homologs and Unfoldability index by FoldIndex©). Fig 1 represents the screenshot of prophage database homepage.

Fig. 1. Screenshot of Prophage Database home page

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3.2 Identifying Prophage Elements in Bacterial GenoMes The e14 element is a very well characterized prophage element [9], which contains all the highly conserved prophage genes like the integrase, excisionase , phage portal , cro type regulator , repressor and terminase genes elements . Genes encoding the BLAST hits for the different e14 proteins, which were within a particular distance (this distance varies from one organism to another; it is the size of the longest prophage in the organism’s genome) were then clubbed together. Any regions with two or more genes in this cluster were considered as putative prophage elements and further analyzed [10]. Fig 2 summarizes the method.

Fig. 2. Schematic representation of protein similarity method

A set of 61 bacterial genomes was chosen for prophage detection. To confirm the sensitivity of the approach bacterial genomes with prophage incorporated in prophage database data was used for comparison (BLAST hits (e < = 0.01). Out of 174 reported prophages, 87 loci were identified by protein similarity approach. Among them include 27 from E coli (K-12 O157 VT-2 Sakai, CFT073, EDL933) out of 61 reported in literature. With M. tuberculosis 3 loci were detected among the reported 6 prophages.With S.aureus strains 5 could be identified among 7 reported, 10 amongst 19 in Salmonella , 4 out of 10 in Yersinia, 9 among 15 in S.pyogenes. Samples results reflecting 14 genome sequences is presented in Table 1 . Hence the method was further extended on to genomes with no reports of prophage. Out of 9 genomes, 24 loci were identified among which 9 were found to be highly probable prophage locations. Table 2 details the prophages identified and respective organisms. For the former, prophage regions were delimited using data from the prophage database and from literature [4]. It was observed that most putative prophage regions encode hypothetical proteins suggesting that these regions need to be characterized further. Interestingly among the newly identified prophages, five are

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Table 1. Bacterial genomes and probable prophages identified using the Protein Similarity Approach method in comparison with literature reports Organism B subtilis 168

Literature reported 5

PSA detected 2

PBSX, SKIN

C. tetani E88

3

2

Cpt2, Cpt3

E. coli K12

11

4

24

16

H. influenzae Rd KW20

3

1

DLP12 ,QIN , Rac, KpLE1 Sp8 , Sp9, Sp6 , Sp4, Sp14, Sp3, Sp15, Sp1,Sp5, Sp12, Sp11 Sp7,Sp10,Sp18,Sp16, Sp17 FluMu

M. loti MAFF303099 M. tuberculosis H37Rv

3 3

1 1

Meso2 phiRv1

N. meningitidis Z2491 S. aureus N315

3 1

2 1

Pnm2 ,Pnm1 phiN315

S. enterica CT18 (serovar Typhi) S. flexneri 2a301

12

5

Sti4b, Sti8 , Sti3, Sti1,Sti7

11

3

Flex9, Flex5, Flex2

S. pyogenes M1 SF370

4

2

370.2 , 370.1

X. fastidiosa 9a5c Y. pestis KIM

9 5

1 2

XfP4 Yers3, Yers1

E. coli O157 VT-2 Sakai

Prophages Detected

Table 2. Prophage regions detected using the PSA approach from six bacterial genomes. Indicated in # are genomes with no report of prophages. Organism S. enterica LT2 (serovar Typhimurium) S. flexneri 2457T

Prophage St1

Sf1

Gene products Transposase, cyoplasmic proteins, phoQP

S. pyogenes M18 MGAS8232 S. pyogenes M3 MGAS315 P.luminescens subsp. laumondii TTO1#

Pl1,Pl2, P13 P14, 16,P17

Integrase, replication protein, helicase , mating formation Efflux, phage portal protein, transposase Transposase, antiterminator drug resistance protein DNA Invertase HIN, Mostly hypothetical proteins

Mycobacterium bovis AF2122/97 #

4 putative prophages

Integrase, transposase. Transcriptional regulatory

Sp1 Spy1

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located near dehydrogenase genes. A priori there seems to be no attributable reason to this tendency for the putative lambdoid phages to get integrated near a dehydrogenase gene in the bacterial genome. However, it must be noted that the search template e14 is also integrated at the isocitrate dehydrogenase gene in the E. coli K12 genome.

3 Conclusion A prophage database has been constructed and used to devise a prophage identification approach using similarity of proteins over a given region. Prediction of prophage related areas in genomes is problematic due to low similarity between prophage genes and the mosaic nature. Five bacterial genomes for which no prophage has been reported in the literature were analyzed in detail. It was observed that most putative prophage regions encode hypothetical proteins suggesting that these regions need to be characterized further. The database provides information on prophages, cryptic prophages and phage remnants, providing effective and efficient way to access the prophage genomes. Prophage identification can be further extended over newly sequenced genomes and incorporated into the database.

Acknowledgments We acknowledge the use of Bioinformatics centre facility funded by DBT, Govt of India, DBT and the Israel Ministry of Science and Technology (MOST) for INDOISRAEL project support, MOST’s support for the Israel Structural Proteomics Center.

References 1. Brussow, H., Hendrix, R.: Phage Genomics: Small Is Beautiful. Cell 108 (2002) 13-16 2. Canchaya, C., Proux, C., Fournous,G., Bruttin, A., Brussow, H. : Prophage Genomics. Microbiol Mol Biol Rev. 67 (2003) 238–276 3. Brussow, H., Canchaya, C., Hardt, W.D.: Phages And The Evolution Of Bacterial Pathogens: From Genomic Rearrangements To Lysogenic Conversion. Microbiol Mol Biol Rev. 68 (2004) 560-602 4. Casjens, S.: Prophages And Bacterial Genomics: What Have We Learned So Far? Mol. Microbiol, 49 (2003) 277-300 5. Waldor, M, K.: Bacteriophage Biology And Bacterial Virulence. Trends Microbiol, 6 (1998) 295-297 6. Davis, B.M., Waldor, and M.K.: Filamentous Phages Linked To Virulence Of Vibrio cholerae. Curr Opin Microbiol, 36 (2000) 35-42 7. Boyd, E.F., Brussow, H.: Common Themes Among Bacteriophage-Encoded Virulence Factors And Diversity Among The Bacteriophages Involved. Trends Microbiol, 10 (2002) 521-529 8. Canchaya,C., Fournous, G., Brussow, H.: The Impact Of Prophages On Bacterial Chromosomes. Mol Microbiol. 53 (2004) 9-18

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9. Mehta, P., Casjens, S., Krishnaswamy, S.: Analysis Of The Lambdoid Prophage Element e14 In The E.Coli K12 Genome. BMC Microbiol, 4 (2004) 1 10. Rao, G.V., Mehta, P.,. Srividhya, K.V., Krishnaswamy, S.: A Protein Similarity Approach For Detecting Prophage Regions In Bacterial Genomes. Genome Biology, 6, (2005) P11 (http://genomebiology.com/2005/6/10/P11) 11. Altschul, S.F., Gish, W., Miller, W., Myers, E.W., Lipman, D.J.: Basic Local Alignment. Search Tool. J. Mol. Biol. 215 (1990) 403-410

Dynamic Multidimensional Assignment Algorithm for Multisensor Information Fusion System Yi Xiao, Guan Xin, and He You Research Institute of Information Fusion, Naval Aeronautical Engineering Institute, Yantai 264001 P.R. China [email protected]

Abstract. Data association, one of the key and difficult problems for multitarget tracking, is the decision process of linking the measurements or the tracks deemed to be of common origin under certain criteria. All typical data association algorithms can be deducted into special Multidimensional Assignment Problem. However, present S-D assignment algorithm only associates the synchronous measurements from different sensors, which only generate the static result. In this paper, the static assignment algorithm(S-D) has been generalized to the dynamic Multidimensional Assignment Problem by means of combining the measurements set and the tracks set. The main challenge in the assignment problem is that it is NP-hard. The solution using Hopfield neural network (HNN) is presented in this paper. The simulation results illustrate that this method can decrease the computing burden greatly.

1 Introduction In recent years, considerable research has been undertaken in the field multitarget tracking[1], which is of interest in both military and civilian applications. The problem of data association[2], namely, partitioning measurements across lists (e.g., sensor scans) into tracks and false alarms so that accurate estimates of true tracks can be recovered, is a pivotal issue for the multitarget tracking problem. All typical data association algorithms can be deduced into special multidimensional assignment problem. However, present S-D assignment algorithm only associates the synchronous measurements from different sensors, which only generates the static result[2]. In this paper, the static assignment algorithm is generalized to the dynamic tracking circumstance. The dynamic multidimensional assignment algorithm is proposed and the relationship between the dynamic and static ones is discussed. The main challenge in the assignment problem is that it is NP-hard. The solution using Hopfield neural network is presented in this paper. The simulation experimental results illustrate that this method can decrease the computing burden greatly.

2 Problem Description Let us use ω p to denote the location of the target p . Suppose that there are S sensors tracking targets, the location of which is known, ie: D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 869 – 874, 2006. © Springer-Verlag Berlin Heidelberg 2006

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ω s = [ x s , y s , z s ]′ , s = 1, 2,  , S .

(1)

Sensors may be 3D radar, 2D radar or 2D passive sensors. The relationship between the true location of the target ω p , the location of the sensor ω s and the measurement m st is suggested as:

m st = H s (ω p , ω s ) .

(2)

The i s (i s = 1, 2,  , n s ) measurement from the sensors can be described as ­m st + W sis Z sis = ® ¯ a sis

if the measurement from a target if the measurement from a false alarm

.

(3)

where W sis ~ N (0, R s ) . Suppose that at the k − 1 th scan the tracking system has formed t tracks, ie U (k ) = { Xˆ i (k k ) , P i (k k )}ti =1 and the measurements set from S sensors at the k th scan is Z (k ) = {Z s (k )}Ss=1 = {{Z sis (k )}ins=1}Ss=1 . s

3 Dynamic Multidimensional Assignment Algorithm for Multi-target Tracking To include the circumstance of emerging target, we add a false target Xˆ 0 to the tracks set at k − 1 th scan. Then the tracks set becomes U (k − 1) = { Xˆ j (k − 1 k − 1) , P j (k − 1 k − 1)}tj =0 .

(4)

similarly, we can get ZU (k ) and the likelihood function of measurements set (k ) originates from the target Xˆ 0 (k − 1) is Z i1i2 is

S

Λ ( Z i1i2 is (k ) Xˆ 0 (k − 1)) =

∏[P

Ds

f ( Z sis ) ω p ]u (is ) [1 − PDs ][1−u (is )] .

(5)

s =1

Due to ω p is unknown, the Maximum Likelihood Estimation ωˆ p is used to replace the true location of the target, ie.

ωˆ p = arg max Λ ( Z i1i2 is ω p ) . ωp

(6)

Then (5) becomes S

Λˆ ( Z i1i2 is (k ) Xˆ 0 (k − 1)) =

∏[P

Ds

s =1

N ( µˆ st , Rs )]u (is ) [1 − PDs ][1−u (is )] .

(7)

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where

µˆ st = H s (ωˆ t , ω s ) .

(8)

(6) is revised as

∏[

] [

]

­ S PDs Λ is j (k ) u (is ) 1 − PDs [1−u (is ) ] j = 1, 2,  , t ° ° j . Λ ( Z i1i2is (k ) Xˆ (k − 1)) = ® sS=1 ° [ P N ( µˆ , R )]u (is ) [1 − P ][1−u (is )] j = 0 Ds Ds st s ° ¯ s =1

∏

(9)

So we have the formulation n1

t

J * = min

n2

ns

¦¦¦ ¦ c 

i1is j ρ i1is j

.

(10)

­ t n2 ns ° .. ρ i1i2 ...is j = 1; i1 = 1,2,.., n1 ° j = 0 i2 = 0 is = 0 ° t n1 ns ° ... ρ i1i2 ..is j = 1; i 2 = 1,2,..., n 2 ° ° j =0 i1 =0 is =0  ® . ° t n1 ns −1 ° ... ρ i1i2 ...is j = 1; i s = 1,2,..., n s ° j =0 i1 =0 is −1 =0 ° n1 ns ° ... ρ i1i2 ...is j = 1; j = 1,2,..., t ° = 0 = 0 i i s ¯ 1

(11)

ρ i1 i s

j = 0 i1 = 0 i2 = 0

is = 0

subject to

¦¦ ¦

¦¦ ¦

¦¦ ¦ ¦ ¦

4 The HNN Solution Continuous definite Hopfield neural network is a all-netted one with feedback. The state of each nerve cell can be described as a nonlinear dynamic equation. n u dui = ¦ Tij v j − i + I i . dt τi i =1

where

(12)

ui is the state of the ith nerve cell. And the output vi satisfies: v i = f i ( ui ) .

(13)

where Tij is the coefficient between the output of the jth nerve cell and the input of the ith one.

f i (ui ) is the output characteristic of the ith nerve cell. n is the number of

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Y. Xiao, G. Xin, and H. You

I i is the outside input. As for Hopfield neural network, the energy function related to the Tij and the outside input signal can be defined. If the proper initial the cells.

condition is given to, the system can approach to a convergence, which is the minimum to the energy function. Therefore, the target function, the restriction and the energy function can be associated. The optimization to the problem is the minimum to the energy function. According to the target function and the restriction to the track association problem, the energy function can be defined as:

E = A¦¦¦ v xi v xj + B ¦¦¦ v xi v yi x

i

j ≠i

x

i

y≠ x

2

C§ · + ¨ ¦¦ v xi − N ¸ + D ¦¦ α xi v xi 2© x i x i ¹

.

(14)

where A, B, C and D are punitive coefficients. The nerve cell state function derived from the energy function is:

du xi u § · = − xi − A¦ v xj − B ¦ v yi − C ¨ ¦¦ v xi − N ¸ − Dα xi . dt τ j ≠i y≠ x © x i ¹

(15)

The relationship between the input and the output is

v xi = f (u xi ) =

u 1 [1 + tanh( xi )] . 2 u0

(16)

while

Txi , yj = − A ⋅ δ ( x, y ) ⋅ (1 − δ (i, j )) − B ⋅ δ (i, j ) ⋅ (1 − δ ( x, y )) − C .

(17)

i= j . i≠ j

(18)

I xi = N ⋅ C − D ⋅ α ( x, i ) .

(19)

­1, ¯0,

δ (i , j ) = ® the outside input

Given nerve cell state function, the Hopfield network will approach to the state of the minimum energy with the outside input. The state of the nerve cell v xi is the relationship between the xth track from node 1 and the ith track from node 2. It denotes that they are the same track when v xi = 1 .

5 Simulation Results Suppose that there are two nodes considered in the simulations, and a 2-D radar is set in each node. The noise process standard deviations of rang and azimuth measurements from each sensor are assumed to be 170m and 0.017rad, 180m and

Dynamic Multidimensional Assignment Algorithm

873

0.017rad, respectively. A Monte Carlo simulation with 50-runs was carried out for two environments. there are 60 targets, and the maneuvers of these targets are random, and the initial positions of these targets are normally distributed in a region. The initial velocity and azimuth of these targets are uniformly distributed in 4~1200m/s and 0~2 π , respectively. The state equation of the nerve cell are written in the form of difference equation in order to simulate by using computer.

§ · u (t ) u xi (t + 1) = u xi (t ) + ς ¨¨ ¦ Txi , yj u yj (t ) − xi + I xi ¸¸ . τ © y, j ¹ punitive coefficients in (17) are A = B = C = 200 , D = 1200 and

(20)

u0 = 0.02 .

The location MMSE of one target, the correct correlate ratio and the elapsed time of each period are shown in fig.1, fig. 2 and fig.3 respectively.

 Fig. 1. Location MMSE of one target

Fig. 2. Correct correlate ratio

 Fig. 3. Elapsed time of each period

6 Conclusion Aiming at the data association problem in multitarget tracking, this paper generalizes the S-D assignment algorithm, which settle the measurement association at a certain

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time, to the dynamic tracking circumstance. A novel dynamic multidimensional assignment algorithm for multitarget tracking is proposed. The main challenge in the assignment problem is that it is NP-hard. The solution using Hopfield neural network (HNN) is presented in this paper. The simulation experimental results illustrate that this method can decrease the computing burden greatly.

References 1. Blackman,S.S., Popoli R.: Design and Analysis of Modern Tracking Systems. Norwood, MA Artech House (1999) 2. He Y.: Study on the Distributed Multisensor Information Fusion Algorithms. Tsinghua Unsiversity. (1996) 3. Roecker J.A., Phillis G.L.: Suboptimal Joint Probabilistic Data Association. IEEE Trans. AES.,Vol.29,2 (1993) 510–517 4. Bar-Shalom.Y., William.D.B.: Multitarget-Multisensor Tracking, Applications and Advances. Artech House (2001) 5. He Y., Wang G.H., Lu D.J., etc.: Multisensor Information Fusion With Applications. Beijing, Publishing House of Electronics Industry (2000) 6. Deb, S., Yeddanapudi M., Pattipati K., etc.: A Generalized S-D Assignment Algorithm for Multisensor-Multitarget State Estimation. IEEE Trans. on AES, Vol. 33,2 (1997) 523–538

᧶

Future Location Prediction of Moving Objects Based on Movement Rules* Vu Thi Hong Nhan and Keun Ho Ryu** Database and Bioinformatics Laboratory, Chungbuk National University, Korea {nhanvth, khryu}@dblab.chungbuk.ac.kr

Abstract. LBS (Location-based services) are rapidly emerging as a prominent area of deployment of geographic data management technologies. One of the research challenges posed by LBS is to support location management and spatial data mining on vehicle movement. In this paper, we introduce a method that investigates how to deduce future locations of mobile users. The idea is to employ the movement patterns of users in the past. All frequent patterns are enumerated, which are applied to produce movement rules, which are in turn employed to predict future location of moving object. Our proposed algorithms are quite efficient to enable push-driven LBS applications.

1 Introduction Mobile phones are equipped with global positioning system devices or the mobile networks. Technically, the paradigm of anytime-anywhere connectivity raises previously ad hoc challenges. It is impossible to effectively extract detailed locationbased information from the network about users’ positions in a proactive manner. Current LBS are mostly based on pull-driven approaches. The massive tracking of users in a region is impossible in this manner since it would flood the network with such location requests. Location prediction has been addressed in many studies [5], [6], [7], but there exist many deficiencies and they do not consider the sampling error over time of the past movements. This paper proposes a technique for inferring future location of mobile user. The idea is to base on user’s past movement patterns to generate movement rules, which are in turn used to predict user’s future location. In the mining process, we decompose the object space into regular spatio-temporal cubes to which points of trajectories are assigned. To make decision of cube’s size we take the uncertainty of sampled positions into account. As a result, our method is better than UMP method in [9] in regard to two aspects, namely dealing with the uncertainty of sampled positions and imposing timing constraints on moving sequences and therefore on movement rules. The rest of paper is organized as follows. Section 2 reviews relevant work followed by the problem statement in section 3. The process of predicting future location is *

This research was supported by the MIC (Ministry of Information and Communication), Korea, under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment). ** Corresponding author. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 875 – 881, 2006. © Springer-Verlag Berlin Heidelberg 2006

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presented in section 4. Section 5 shows the experimental results of the proposed method. Section 6 concludes the paper.

2 Related Work Sequential patterns [3], [4] are described as the discovery of inter-transaction patterns in large customer transaction databases. Location prediction has been addressed in many studies [5], [6], [7], [12], [13]. But there exist a lot of deficiencies as follows: assuming the existence of user movement patterns by only applying pattern matching techniques, without providing a method to discover them in the first place [6]; relying only on knowledge of the probability distribution of the mobile user’s velocity and/or direction of movement [7]; being susceptible in small deviation in object trajectories, which can cause significant degradation in prediction accuracy because they do not distinguish between regular and random movements of a moving object [5]. The approach in [9] does not consider the uncertainty of sampled points.

3 Definitions and Problem Statement A moving object database D is defined as the union of n time series of positions Di, Each Di for one object contains tuples (oid,x,y,t), where oid indicates object identifier, (x, y) shows the coordinates of the position at valid time t. Moving objects move in a two-dimensional space A⊆R2. Spatially, the positions of objects over time are mapped into the object space and the positions are then replaced by the region id, where they are located. Note that objects only can move from one region to its neighbors with respect to eight directions. Moving objects are assumed to stay in a region for a minimal time interval τ and its moving points are collected for a maximal time interval Τ defined as a temporally ordered list of region ids, denoted as with area ai indicating where object is at timestamp ti. The timing constraints are defined as τ < ti+1-ti ≤Τ, 2≤i≤m. A sequence is composed of k regions is denoted as k-pattern. We say P1 is a subpattern of another one P2 if there exists a oneto-one order preserving function g that maps regions in P1 to P2; that is, ai=g(ai) and if ai1){ AÅ(t-1)-frequent pattern obtained by dropping the last location of Ft; confÅsupport(Fk)/support(A); if(conf ≥ min_conf){ FrulesÅFrules∪{AÆFk-A) with confidence=conf&support=support(Fk)}; t--; }else contcreateÅFalse; } return Frules; Fig. 2. Function for deriving all possible rules from a given moving pattern

These derived rules enable us to predict the next location of a moving object. Assume an object trajectory P= up to now. We need to find out the rules whose antecedents are contained in P and the last location in the antecedent is bj-1. The first location of the consequents of these rules along with a value that is the sum of the confidence and the support values of the rule are stored in an array. The support of a rule is the support of the moving pattern from which the current rule is generated. This array are then sorted in descending order with respect to the sum of support and confidence values, which help us select the most confidence and frequent rule. Then the location of the first tuple that has the highest value is the user's next moving location.

5 Performance Study To evaluate performance of our proposed method, we conduct various experiments in C++, on a PC Pentium IV, 2.00GHz processor with 256MB RAM, and window XP. The tests are carried out on synthetic datasets generated by a generator that simulates moving objects. Assume that all objects travel at the same maximum velocity vmax of 17m/s in a grid 1000×1000. Datasets are generated by the following principle: on average 70% object trajectories have the average length of L in which average 30% trajectories have the same trip and the remaining trajectories are denoted as outliers, which are formed as random walk over the space. Here we set the sampling rate ∆t and the T to 12 and set temporal extent to 2. Moving patterns are mined from the trajectories in the training set by our All_MOP in [11]. The trajectories in the test set are used for evaluating the prediction accuracy of our proposed algorithm. The effectiveness of the proposed algorithm for predicting future locations is measured by the following two measures: Precision is defined the number of correctly predicted locations divided by the total number of predictions made; Recall is defined as the number of correctly predicated locations divided by the total number of locations the user visits. Recall counts the non-prediction case as an incorrect prediction.

Future Location Prediction of Moving Objects Based on Movement Rules

879

With the above values of maximal speed and sampling rate, we have chosen the resampling rate ρ=6 and r approximately 71; that means, a 14×14 grid after evaluating Precision and Recall on various granularities and re-sampling rates. Due to the limit of space, we exclude this test results here. The next experiment is conducted for tuning the parameters of our methods, which are min_sup and min_conf. Here, the best values are searched for each parameter that makes both Recall and Precision good. The total number of trajectories generated is 3500 in which the number of trajectories in training set is 3000 and the number of trajectories in test set is 500 with varying average length of L. Impact of Minimum Support Values Here we examine the effect of increasing minimum support values min_sup on recall and precision values obtained by our algorithm. The Fig. 3 shows that lowering the support threshold results in decreased precision and increased recall. Even though precision decreases the number of mined rules generally increased substantially as the support is lowered, which are useful for prediction. Since recall and precision values vary in inverse proportion when increasing min_sup, it would be the most appropriate to choose min_sup in the interval [7%, 9%]. Because we observe that recall and precision values do not change considerably for the min_sup values in that interval. L4

L8

0.8

0.9 0.8

L4

0.7

L8

0.6

0.6 Recall

Precision

1

0.4 0.2

0.5 3%

7%

9% 21%

min_sup

0 3%

7% 9% min_sup

21%

Fig. 3. Precision and Recall as a function of the min_sup for rule-based prediction algorithm

Impact of Minimum Confidence Values In this test, we investigate the impact of increasing minimum confidence values on the recall and precision of the algorithm. From the Fig. 4, we can realize that precision increases and recall decreases when increasing the confidence value. This is due to the fact that only the rules with high confidence values are used for prediction. Consequently, the number of rules used for prediction is reduced their quality gets higher. Therefore, the precision value improves as increasing min_conf. But the opposite effect on recall occurs for the increase of min_cof. This is because the decline in the rules negatively affects the number of correct predictions. So, recall decreases when increasing min_conf.

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L8

L8

L4

1

0.7

0.9

0.65

Recall

Precision

L4

0.8 0.7

0.6 0.55

0.6

0.5

10%

40%

90%

min_conf

100%

10%

40%

90%

100%

m in_conf

Fig. 4. Precision and Recall as a function of the min_conf for rule-based prediction algorithm

6 Conclusions Value-added services for mobile wireless networks, such as LBS and selective information dissemination service, are achieving an increasing importance. In this paper, we have introduced a method for predicting future locations of mobile users based on their moving patterns in the past. Moving patterns are derived based on spatio-temporal property of moving objects in application domain, viz. spatial and timing constraints. At first, the object space is decomposed into spatio-temporal units. Simultaneously, imprecision about the position in-between measurement is taken into consideration to choose spatial extent and temporal extent. Our algorithm All_MOP in [13] then enumerates all frequent patterns that are used to derive movement rules, which are then employed to make prediction of object’s future location. The experimental results demonstrate that our proposed algorithm for predicting next movement of mobile users is better than the previous ones and also quite efficient to enable push-driven LBS applications.

References 1. Meratnia, N., By, R. A. D.: Aggregation and Comparison of Trajectories. In Proc. Int. Symp. on GIS, (2002) 2. Yun, H., Ha, D., Hwang, B., Ryu, K. H.: Mining Association Rules on Significant Rare Data using Relative Support. Journal of System and Software, 67 (2003) 181-191. 3. Srikant, R., Agrawal, R.: Mining Sequential Patterns: Generalizations and Performance Improvements. In Proc. Int. Conf. EDBT, (1996) 4. Tsoukatos, I., Gunopulos, D.: Efficient Mining of Spatiotemporal Patterns. In Proc. On SSTD, Lecture Notes in Computer Science, Springer-Verlag, Berlin Heidelberg New York (2001) 5. Liu, G. Y., Gerald, M. Q.: A Predictive Mobility Management Algorithm for Wireless Mobile Computing and Communications. In Proc. of the IEEE Int. Conf. on Universal Personal Communications, New York (1995) 268-272 6. Liu, T., Bahl, P., Chlamtac, I.: Mobility Modeling, Location Tracking and Trajectory Prediction in Wireless ATM Networks. IEEE Journal on Selected Areas in Communications, 10 (1998) 922-936

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7. Rajagopal, S., Srinivasan, R. B., Narayan, R. B., Petit, X. B. C.: GPS-based Predictive Resource Allocation in Cellural Networks. In Proc. of the IEEE Int. Conf. on Networks, (2002) 229-234 8. Katsaros, D., Nanopoulos, A., Karakaya, M., Yavas, G., Ulusoy, O., Manolopoulos, Y.: Clustering Mobile Trajectories for Resource Allocation in Mobile Environments. In: Intelligent Data Analysis Conf. IDA, 2810 (2003) 319-329 9. Mamoulis, N., Cao, H., Kollios, G., Hadjieleftheriou, M., Tao, Y., Cheung, D.: Mining, Indexing, and Querying Historical Spatiotemporal Data. In Proc. of KDD, (2004) 10. Pfoser, D., Jensen, C. S.: Capturing the Uncertainty of Moving-Object Representations. In Proc. of Advances in Spatial Databases, 6th Int. Symp. SSD (1999) 111-132 11. Vu,T. H. N., Chi, J. H., Ryu, K. H.: Discovery of Spatiotemporal Patterns in Mobile Environment. In Proc. of APWeb (2006) 949-954 12. Oh, Y. B., Ahn, Y. A., Ryu, K. H.: Past Location Estimation of Mobile Objects. IC-AI (2003) 608-614 13. Chung, J. D., Paek, J.W., Lee, O. H., Ryu, K. H.: Temporal Pattern Mining of Moving Objects for Location-based Services. Dexa (2002) 331-340

Fuzzy Information Fusion for Hypergame Outcome Preference Perception∗ Yexin Song1, Zhijun Li2, and Yongqiang Chen1 1

College of Science, Naval University of Engineering, Wuhan, Hubei 430033, China [email protected], [email protected] 2 Wuhan University of Technology, Wuhan, Hubei 430063, China [email protected]

Abstract. This paper presents a novel fuzzy information fusion method for outcome preference perception in hypergame models. Firstly, a fuzzy aggregate algorithm is used to indicate the group fuzzy perception of opponent players’ outcome preference. The level sets of each group fuzzy outcome preference perception are obtained by solving linear programming models. Based on a defuzzification function associated with the level sets of fuzzy number and the Newton-Cotes numerical integration formula, the group crisp perception for opponent players’ outcome preference relation is determined. At last, the concept of most consensus winner is used to decide the crisp outcome preference vectors in the hypergame models. A numerical example is provided to illustrate the proposed method.

1 Introduction In real conflicting situations, it is quite usual that the players involved perceive the conflict differently and subjectively. Hypergame [1] is an efficient framework to deal with such situations. Contrary to the traditional game theory, the players involved in a hypergame may have incorrect subjective perception about the other players’ options, strategies, or preferences, or even be unaware of some of the players in the game. In this paper, we only consider a n-person first-level hypergame models [1-3], where each player correctly perceives the players in the game and the strategy set of the opponent players, but the players’ interpretations of the set of preference vectors can be different from one another because of misperceptions. Suppose N = {1, 2," , n} is the set of players in the hypergame model, Si , ∀i ∈ N is the set of strategies for players i, Vi is the preference vector (PV) for the player i over the

outcome space O = S1 × S2 ×"× Sn , Vij expresses player i's PV as interpreted by player j. When there is misperception, Vij will be different from Vi , so the game played by player j will be different from the one played by player i. In a first-level hypergame, ∗

This work is supported by National Natural Science Foundation of China Grant #70471031 and Scientific Research Foundation of Naval University of Engineering.

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 882 – 887, 2006. © Springer-Verlag Berlin Heidelberg 2006

Fuzzy Information Fusion for Hypergame Outcome Preference Perception

883

since each player’s game is formed by a set of perceived PVs, except the one for the player himself, the first-level hypergame can be formulated as

{

H 1 = H 10 , H 20 ," , H i0 , ", H n0

where,

H

0 j

} (∃i, j ∈ N : H

= ( V 1 j , V 2 j , " , V j , " , V n j ) T , j = 1, 2 , " , n

0 i

)

≠ H 0j .

(1)

.

It is important for a player to correctly determine preference vector Vij in (1). To get more correct preference information, the player is often consisted of a group of experts who can give their perception about opponent players’ preferences respectively. Then, how to integrate all the experts’ preference perception information is very important for the player. Song etc [5],[6] presented two novel fuzzy preference information aggregation methods in the face of opponent players’ different linguistic preference or fuzzy preference relations over outcome space perceived by different experts. In this paper, we present a new method for solving such problem based on linear programming, numerical integration and the concept of most consensus winner.

2 Information Fusion Method for Fuzzy Preference Perception In order to determine Vij in (1), suppose that player j is consisted of M experts { D j 1 , D j 2 , " , D jM } , the weight of expert D j m is expressed by a trapezoidal fuzzy number

w

jm

= (ε

jm

,ζ

jm

,η

jm

,θ

jm

)

, where,

0 ≤ ε

jm

≤ζ

jm

≤η

jm

≤θ

jm

≤1

, and expert

D jm provides his/her perception about player i's fuzzy preference relation over O

i ijm = [r ijm ] , where, trapezoidal fuzzy number expressed in the matrix form as R pq K × K rpijqm = (α

ijm pq

,β

ij m pq

,γ

ijm pq

,δ

i jm pq

)

,

ijm ijm ijm 0 ≤ α ijm pq ≤ β pq ≤ γ pq ≤ δ pq ≤ 1, m = 1, 2, " , M ; p , q = 1, 2, " , K

,

denote player i's fuzzy preference of the outcome O p over Oq perceived by D jm . 2.1 Group Crisp Perception for Opponent Players’ Preference Relation ijm Given the data Ri and w jm , m = 1, 2 , " , M , using following aggregate algorithm which is similar to the fuzzy weighted average [6], player i's fuzzy preference of the outcome O p over Oq perceived by expert group (player j) can be expressed as

M

¦ (r

ijm pq

r = f ( r , r " , r ij pq

ij pq

ij1 pq

ij 2 pq

ijM pq

, w j1 , w j 2 " , w jM ) =

⊗ w jm )

m =1

,.

M

¦ w

(2)

jm

m =1

where, ⊗ is the fuzzy multiplication operation. In the following, we first present an approach to solve rpqij λ , the λ (λ ∈ [0,1]) level set of rpqij . Discretizi the complete range of the membership [0,1] of the fuzzy number

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Y. Song, Z. Li, and Y. Chen

into the following finite number of L-values: 0 ≤ λ1 ≤ λ2 ≤ " ≤ λL ≤ 1 . For given λl , ijm ijm , w jmλl = [ w jmλl , w jmλl ] . Define l = 1, 2, " , L , denote rpijm qλ = [ r pqλ , rpqλ ] l

l

l

M M

f

ij pql

(w

j1

,w

j2

," w

) =

jM

¦

(w

jm

⋅r

m =1

ijm p q λl

)

M

¦

w

,

f

ij pql

( w j 1 , w j 2 , " w jM ) =

¦ (w

r pqλl = min{ f ij

ij pql

⋅ r pqijmλ l )

.

M

¦w

jm

(3)

jm

m =1

m =1

Theorem 1. Denote

jm

m =1

ij rpijq λ l = [ r p q λ l , r pijq λ l ]

, then

( w j1 , w j 2 ," w jM )} , rpqij λl = max{ f

ij pql

( w j1 , w j 2 ," w jM )} .

(4)

where, w jm ∈ [ w jmλl , w jmλl ] , m = 1, 2," , M . Proof: The reader is referred to the Ref. [6]. According to Theorem 1, the interval of λl level set of rpqij can be obtained by solving (4), which are two fractional programming problems. In order to solve (4), we wish to use the linear programming (LP) approach by first transforming this nonlinear problem into a linear one by using the Charnes and Cooper’s linear transformation technique [7]. The transformation procedure is described in the following. Let 1

y =

,

M

¦w

x jm = yw jm , m = 1, 2," , M . (5)

jm

m =1

Multiplying both the objective functions and the constraints by y and using the definitions given in (5), (4) can be converted into the following LP problems. LP1 : min f

ij pql

M

M

= ¦ r pqλl x jm ijm

m =1

ij LP 2 : max f pql = ¦ rpqijmλl x jm m =1

­ w jmλl y ≤ x jm ≤ w jmλl y , m = 1, 2," , M , . ­ w jmλl y ≤ x jm ≤ w jmλl y , m = 1, 2, " , M , °M °M ° ° s.t ® ¦ x jm = 1, s.t ® ¦ x jm = 1, = 1 m ° m =1 ° ° y ≥ 0, x jm ≥ 0, m = 1, 2, " , M . ° y ≥ 0, x jm ≥ 0, m = 1, 2," , M . ¯ ¯

(6)

Solving LP1 and LP2, we can obtain rpqij λ = [r ijpqλ , rpqij λ ] , l = 1, 2," , L . l

l

l

In order to determine the group (player j's) crisp perception for player i’ outcome preference relation, a defuzzification function [8] associated with the level sets of fuzzy number is defined as follows. Definition 1. Let ϕ : F → ℜ is a mapping from the set of fuzzy numbers F to the set of real numbers ℜ , if for any a ∈ F , ϕ ( a ) = 1 1 ( a λ + a λ )d λ , then the function ϕ is 2

³

0

a defuzzification function. According to definition 1,

ϕ (rpqij ) =

1 1 ij (r pqλ + rpqij λ )d λ . 2 ³0

(7)

Fuzzy Information Fusion for Hypergame Outcome Preference Perception

Dividing the interval [0,1] into four equal parts, denote

λ

j

= j / 4

,

885

j = 0 , 1, 2 , 3 , 4

,

and applying the following Newton-Cotes numerical integration formula 1 ³ f ( λ ) d λ ≈ 90 [7 f ( λ ) + 32 f ( λ ) + 12 f ( λ ) + 32 f ( λ ) + 7 f ( λ )] . 1

0

ϕ ( rpi jq )

0

1

2

3

4

(8)

can be calculated approximately as ϕ ( rpijq ) =

1 1 ij 1 ij ij ( r p q λ + r pijq λ )d λ ≈ [7 ( r p q λ 0 + r pijq λ 0 ) + 3 2 ( r p q λ1 + r pijq λ1 ) 2 ³0 180 ij ij ij + 1 2 ( r p q λ 2 + r pijq λ 2 ) + 3 2 ( r p q λ 3 + r pijq λ 3 ) + 7 ( r p q λ 4 + r pijq λ 4 )]

.

(9)

Since the algebraic accuracy of (8) is at least 5, the approximate formula (9) is more accurate. Then, using (9), we can obtain the group (player j's) crisp perception for player i’ outcome preference relation matrix R i j = [ ϕ ( rpi jq ) ] K × K . 2.2 Crisp Preference Vector in Hypergame Model (1)

We now discuss how to determine a crisp preference vector V ij in model (1) from the crisp preference relation matrix Rij . Define K ­°1 if ϕ (rpqij ) > 0.5 1 , g ijp = g ijpq = ® g ijpq . ¦ K − 1 0 otherwise q =1, q ≠ p °¯

(10)

where g ijpq expresses whether outcome O p defeats Oq or not, and g ijp is the mean degree to which O p is preferred to all the other outcomes. Assume that fuzzy linguistic quantifier Q =’most’ to be a fuzzy set defined in [0,1] and given as ­1, ° µ Q ( x ) = ® 2 x - 0.6, ° 0, ¯

for

x ≥ 0.8,

for 0.3 < x < 0.8, .

(11)

for x ≤ 0.3.

Then z ijpQ = µ Q ( g ijp ) is the extent to which O p is preferred to Q other outcomes. Finally, the fuzzy Q-consensus winner [9] is defined as a fuzzy set ij WQ = z1ijQ / O1 + z2ijQ / O2 + " + z KQ / OK .

(12)

So, the crisp preference vector Vij in model (1) can be determined according to the fuzzy Q-consensus winner W Q .

3 Numerical Example To illustrate the proposed approach, we choose the numerical example from Song [4]. Considering a two-person hypergame situation where all the players have 2 strategies. Player 1 is consisted of 3 experts ( D11 , D12 , D13 ) , whose respective

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linguistic weights are w11 = H , w12 = B, w13 = AF , and whose perception about player 2's preferences over O = {O1 , O2 , O3 , O4 } using linguistic preference relations as follows (here, use the linguistic term set L={B, VH, H, AF, F, BF, L, VL, W}, where B = Best= (0.8,1,1,1), VH = Very High = (0.6,0.8, 1,1), H = High= (0.6,0.8,0.8,1), AF=Above Fair= (0.3,0.5,0.8,1), F = Fair = (0.3,0.5,0.5,0.7), BF =Below Fair =(0,0.2,0.5,0.7), L=Low= (0,0.2,0.2,0.4), VL = Very Low= (0,0,0.2,0.4), W = Worst= (0,0,0,0.2)):

R 211 = [ rpq211 ]4× 4

ª − « BF =« «W « ¬ B

AF − VH VH

B Wº ª − « BF VL VL »» , 212 R = [ rpq212 ]4× 4 = « « L − L» « » H −¼ ¬VH

R 213 = [ rpq213 ] 4 × 4

ª − «F =« «VL « ¬B

F

VH

−

W

B

−

AF

H

AF

H

− VH B

VL − H

VL º W »» L» » −¼

W º BF »» . L » » − ¼

At first, solve the linear programming LP1 and LP2, some results about the intervals of rpqij λ = [r ijpqλ , rpqij λ ] are listed in Table 1. l

l

l

Table 1. Some results about the intervals of rpqij λ j 21

21

21

21

21

p, q

e pq 0

epq210

e pq1/ 4

epq211/ 4

e pq1/ 2

epq211/ 2

e pq 3/ 4

epq213 / 4

e pq1

p=1,q=2 p=1,q=3 p=1,q=4 p=2,q=1 p=2,q=3 p=2,q=4 p=3,q=1 p=3,q=2 p=3,q=4 p=4,q=1 p=4,q=2 p=4,q=3

0.300 0.646 0 0.039 0 0 0 0.626 0 0.695 0.542 0.600

0.875 1.000 0.257 0.700 0.317 0.342 0.305 1 0.400 1 1 1

0.350 0.700 0 0.096 0 0.008 0.016 0.680 0.050 0.750 0.603 0.650

0.834 0.975 0.212 0.650 0.272 0.303 0.262 1 0.350 1 0.981 0.950

0.400 0.754 0 0.152 0 0.017 0.033 0.735 0.100 0.805 0.664 0.700

0.792 0.952 0.167 0.600 0.228 0.262 0.218 1 0.300 1 0.964 0.900

0.450 0.808 0 0.209 0 0.029 0.054 0.789 0.150 0.859 0.725 0.750

0.750 0.932 0.122 0.550 0.183 0.221 0.174 1 0.250 1 0.950 0.850

0.500 0.862 0 0.265 0 0.044 0.077 0.844 0.200 0.913 0.785 0.800

epq211

0.708 0.913 0.077 0.500 0.139 0.178 0.130 1 0.200 1 0.939 0.800

21 ϕ (e pq )

0.596 0.854 0.083 0.376 0.114 0.140 0.127 0.867 0.200 0.902 0.815 0.800

Using (9), we can obtain the player 1's crisp perception for player 2’ outcome preference relation matrix R 21 . Then, applying (10), (11) and (12), the fuzzy Qconsensus winner can be computed as WQ = 0.733 / O1 + 0 / O2 + 0.066 / O3 + 1/ O4 . According to WQ , we can determine the crisp preference vector V21 = (4,1,3,2). The result is the same as that in [4]. It shows that the proposed method in this paper is reasonable and effective.

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4 Conclusion A novel information fusion method has been proposed in this paper for fuzzy outcome preference perception in the first-level hypergame models. A fuzzy aggregate algorithm is first used to indicate the group fuzzy perception of opponent players’ outcome preference. The level sets of each group fuzzy outcome preference perception are then obtained by solving linear programming models. Based on a defuzzification function associated with the level sets of fuzzy number and the Newton-Cotes numerical integration formula, the group crisp perception for opponent players’ outcome preference relation is determined. At last, the concept of most consensus winner is used to decide the crisp outcome preference vectors in the hypergame models. An illustrative example verifies the feasibility and effectiveness of the proposed method.

References 1. Wang, M., Hipel, K.W., Frase N. M.: Solution Concepts in Hypergames. Applied Mathematics and Computation. 34 (1989) 147-171 2. Putro, U.S., Kijima, K., Takahashi, S.: Adaptive Learning of Hypergame Situations Using a Genetic Algorithm. IEEE Transactions on Systems, Man and Cybernetics-Part A: Systems and Humans. 5 (2000) 562-572 3. Hipel, K.W., Wang, M., Frase, N. M.: Hypergame Analysis of the Falkland Island Crisis. Internat. Stud. Quart. 32 (1988) 335-358 4. Song, Y. X., Wang, Q., Li, Z. J.: A Group Decision Making Method for Integrating Outcome Preferences in Hypergame Situations. In: Lipo, W., Yaochu, J. (eds.): Fuzzy Systems and Knowledge Discovery. Lecture Notes in Artificial Intelligence, Vol 3613. Springer-Verlag, Berlin Heidelberg New York (2005) 676-683 5. Song, Y. X., Qu, Y., Liu, Z.R., etc.: Fusion and Automatic Ranking of Fuzzy Outcome Preferences Information in Hypergame Models. Proceedings of 2005 International Conference on Machine Learning and Cybernetics, 5(2005) 2711-2715 6. Liou, T.S., Wang, M. J.: Ranking Fuzzy Numbers with Integral Value. Fuzzy Sets and Systems. 50(1992) 247-255 7. Charnes, A. A., Cooper, W. W.: An Explicit General Solution in Linear Fractional Programming. Naval Res. Logist. Quat., 3(1973) 91-96 8. Song, Y. X., Yin, D., Chen, M. Y.: Decision Making with Fuzzy Probability Assessments and Fuzzy Payoff. Journal of Systems Engineering and Electronics. 1(2005) 69-73 9. Kacprzyk, J., Fedrizzi, M., Nurmi, H.: Group Decision Making and Consensus under Fuzzy Preferences and Fuzzy Majority. Fuzzy Sets and Systems, 49(1992) 21-31

Image Identification System Using MPEG-7 Descriptors* Wonil Kim1, Sanggil Kang2,**, and Juyoung Lee1 1

College of Electronics and Information Engineering at Sejong University, Seoul, Korea [email protected], [email protected] 2 Department of Computer Science, The University of Suwon, Gyeonggi-do, Korea [email protected]

Abstract. In this paper, we propose an image identification system employing MPEG-7 as feature and using neural network as the main methodology. The proposed system properly identifies whether a given image belongs to particular sports images or not. The simulation results show that the proposed system successfully identifies images with the rate of over 85%.

1 Introduction As the era of information highway begins, everyday we encounter more image data, even in some cases, than the traditional textual data. The attention and focus of information shift from textual form to multimedia form. Identifying textual information is relatively easier than that of image information, since in case of image, the low level information bears so many alternatives. Even though there are many useful image identification algorithms so far, not many of them use a standard feature such as MPEG-7 visual descriptors. This paper proposes an image identification system in which it tells whether a given image belongs to particular group of images. For example, it will tell that a given image belongs to soccer image with confidence rate from 0.0 to 1.0. The system uses MPEG-7 visual descriptors for image features and the identification module employs neural network. The usage of this system is enormous. It can be properly fit into the image filter engine for search system. In case of medical system, this system judges whether a patient’s medical image belongs to a specific case. We simulated the proposal with several sports image identification system and received above 85% results for both true positive and true negative rates. This paper is organized as follows; in the next section, we discuss background researches on image identification using MPEG-7 visual descriptors. Then, the proposed neural network based image identification system is discussed in section 3. The simulation results are explained in section 4. Section 5 concludes with some future research remarks. * **

This paper is supported by Seoul R&BD program. Author for correspondence: +82-31-229-8217.

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 888 – 893, 2006. © Springer-Verlag Berlin Heidelberg 2006

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2 MPEG-7 Descriptors and Image Processing Systems MPEG-7 is a recent emerging standard used in image classification systems. It is not a standard dealing with the actual encoding and decoding of video and audio, but it is a standard for describing media content. It uses a XML to store metadata. It solves the problem of lacking standard to describe visual image content. The aim, scope, and details of MPEG-7 standard are nicely overviewed by Sikora of Technical University Berlin in his paper [1]. There are a series of researches that use various MPEG-7 descriptors. Ro et al. [2] shows a study of texture based image description and retrieval method using an adapted version of homogeneous texture descriptor of MPEG-7. Other studies of image classification use descriptors like a contour-based shape descriptor [3], a histogram descriptor [4], and a combination of color structure and homogeneous descriptors [5]. As a part of the EU aceMedia project research, Spyrou et al. propose three image classification techniques based on fusing various low-level MPEG-7 visual descriptors [6]. Since the direct inclusion of descriptors would be inappropriate and incompatible, fusion is required to bridge the semantic gap between the target semantic classes and the low-level visual descriptors. There is a CBIRS that combines neural network and MPEG-7 standard: researchers of Helsinki University of Technology developed a neural, self-organizing system to retrieve images based on their content, the PicSOM (the Picture + self-organizing map, SOM) [7]. The technique is based on pictorial examples and relevance feedback (RF). The PicSOM system is implemented by using tree structured SOM. The MPEG7 content descriptor is provided for the system. In the paper, they compare the PicSOM indexing technique with a reference system based on vector quantization (VQ). Their results show the MPEG-7 content descriptor can be used in the PicSOM system despite the fact that Euclidean distance calculation is not optimal for all of them. Neural network has been used to develop methods for a high accuracy pattern recognition and image classification for a long period of time. Kanellopoulos and Wilkinson [8] perform their experiments of using different neural networks and classifiers to classify images including multi-layer perceptron neural networks and maximum likelihood classifier. The paper examines the best practice in such areas as: network architecture selection, use of optimization algorithms, scaling of input data, avoiding chaos effects, use of enhanced feature sets, and use of hybrid classifier methods. They have recommendations and strategies for effective and efficient use of neural networks in the paper as well. It is known that the neural network of the image classification system should make different errors to be effective. So Giacinto and Roli [9] propose an approach to ensemble automatic design of neural network. The approach is to target to select the subset of given large set of neural networks to form the most error-independent nets. The approach consists of the overproduction phase and the choice phase, which choose the subset of neural networks. The overproduction phase is studied by Partidge [10] and the choice phase are sub-divided into the unsupervised learning step for identifying subsets and the final ensemble set creation step by selecting subsets from the previous step.

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Kim et al. [11] proposed a neural network based classification module using MPEG-7. In this model, inputs for the neural network are fed from the feature values of MPEG-7 descriptors that are extracted from images. Since the various descriptors can represent the specific features of a given image, the proper evaluation process should be required to choose the best one for the adult image classification.

3 The Proposed Image Identification System 3.1 Feature Extraction Module Our system for identifying a specific sports image from various sports images is composed of two modules such as the feature extraction module and the identification module. The two modules are connected in serial form, as shown in Fig. 1. In the feature extraction module, there are three engines. From the figure, MPEG-7 XM engine extracts the features of images with XML description format. The parsing engine parses the raw descriptions to transform them to numerical values, which are suitable for neural network implementation. The preprocess engine normalizes the numerical values to the 0-1 range. By normalizing the input features, it can avoid that input features with big number scale dominant the output of the neural network identifier (NNI) for identifying a specific sports image over input features with small number scale.

Sports Image

MPEG-7 XM Engine

Parsing Engine

Feature Extraction Module

Preprocessing Engine

Neural Network Identifier

Yes No

Identification Module

Fig. 1. The proposed identification system of sports images

3.2 Identification Module Using the data set of the normalized input features and classes of sports, we can model an NNI in the identification module. Fig. 2 shows an example of the NNI with three layers. According to different MPEG-7 descriptors, the number of the input features can be various. Let us denote the input feature vector obtained from the first MPEG-7 descriptor as X = ( x1 , x 2 ,  , x Di ,  , x DN ) , here xi is the ith input feature extracted

from MPGE-7 descriptors and the subscript N is the dimension of the input features

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x1

1 (Yes)

x2 . . . . xN

. . . .

Input layer

. . . .

Hidden layer

0 (No)

Output layer

Fig. 2. An example of three layered neural network classifier

from the MPEG-7 descriptors. The identification of a specific sports image from various sports images means the binary classification of images. In other words, our system decides whether the coming sports image is a target sports image or not, using the input features. Thus, the output value is binary, i.e., 0 or 1. If the coming sports image is estimated to the target image then the output value is 1, otherwise 0. By utilizing the hard limit function in the output layer, we can have binary value, 0 or 1.

4 Simulation 4.1 Environments

We implemented our sports image identification system using 17 sports image data base consisting of Taekwondo, Field & Track, Ice Hockey, etc. As explained in the previous section, we extracted input features from query images using two MPEG-7 descriptors such as Color Layout (CL) and Homogenous Texture (HT) from the feature extraction module. The input feature values were normalized into 0-1 range. A total of 2,550 images (150 images per sports) were extracted. For training an NNI, 2,040 images (120 images each sports) were used and 510 images (30 images each sports) for test. The training and test images are exclusive. We structured the fourlayered (two hidden layers) NNI in the identification module. The hyperbolic tangent sigmoid function and hard limit function was used in the hidden layers and in the output layer, respectively. In each hidden layer, 10 nodes were connected. For training the NNI, we chose the back-propagation algorithm because of its training ability. In order to optimal weight vectors, large number of iterations (100,000) was selected. 4.2 Result

We simulated six image identification modules, such as Horse Riding, Skiing, and Swimming modules. These six modules employ either Color Layout or Homogeneous Texture descriptor as input features. Table 1 shows the performances of the proposed image identification modules.

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The true positive rates for three modules that use CL as input features show better results than those of using HT as input features. The true negative rates for all the six modules are relatively high, which is above 95%, comparing with that of true positive rates, which are around 85% on the average. This is reasonable since it is rather easier to say that a given image is not a particular image than saying a specific one. The results seem very promising and can be applied to various image processing domains. It can be easily extended to medical image processing, in which identifying a particular image belongs to a certain symptom is very critical. Also it can be implemented as the main part of image search engine or image collection engine. For a large image data base, it is very useful tool for image retrieval system. Table 1. The accuracies of the identification modules for Horse Riding, Skiing, and Swimming, each uses Color Layout and Homogeneous Texture respectively for input features (%)

Horse Riding Skiing Swimming Average

CL HT CL HT CL HT CL HT

True Positive 94.44 100.00 86.36 81.82 83.33 72.22 88.04 84.68

True Negative 96.20 94.42 93.98 96.90 95.32 94.71 95.38 95.33

False Positive 5.56 0.00 13.64 18.18 16.67 27.78 11.92 15.32

False Negative 3.80 5.58 6.02 3.10 4.8 5.29 4.86 4.67

5 Conclusion In this paper, we proposed and simulated a sports image identification system. The system uses the MPEG-7 visual descriptors as the input features for the neural network based identification modules. The results show a promising performance. Even the simulation is limited to the sports images in this paper, the idea can be easily scaled into the various areas, such as medical image processing, image search engine, and image retrieval system.

References 1. Sikora, T.: The MPEG-7 Visual Standard for Content Description – An Overview. IEEE Transactions on Circuit and Systems for Video Technology, Vol. 11, No. 6 (2001) 696-702 2. Ro, Y., Kim, M., Kang, H., Manjunath, B., Kim, J.: MPEG-7 Homogeneous Texture Descriptor. ETRI Journal, Vol. 23, No. 2 (2001) 41-51 3. Bober, M.: The MPEG-7 Visual Shape Descriptors. IEEE Transactions on Circuit and Systems for Video Technology, Vol. 11, No. 6 (2001) 716-719 4. Won, C., Park, D., Park, S.: Efficient Use of MPEG-7 Edge Histogram Descriptor. ETRI Journal, Vol. 24, No. 1 (2002) 23-30

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5. Pakkanen, J., Ilvesmaki, A., Iivarinen, J.: Defect Image Classification and Retrieval with MPEG-7 Descriptors. Lecture Notes in Computer Science, Vol. 2749. Springer-Verlag, Berlin Heidelberg, New York (2003) 349-355 6. Spyrou, E., Borgne, H., Mailis, T., Cooke, E., Arvrithis, Y., O’Connor H.: Fusing MPEG-7 Visual Descriptors for Image Classification. Lecture Notes in Computer Science, Vol. 3697. Springer-Verlag, Berlin Heidelberg, New York (2005) 847-852 7. Laaksonen, J., Koskela, M., Oja, E.: PicSOM – Self-Organizing Image Retrieval with MPEG-7 Content Descriptor. IEEE Transactions on Neural Networks: Special Issue on Intelligent Multimedia Processing, Vol. 13, No. 4 (2002) 841-853 8. Kanellopoulos, I., Wilkinson, G.: Strategies and Best Practice for Neural Network Image Classification. International Journal of Remote Sensing, Vol. 18, No. 4 (1997) 711-725 9. Giacinto, G., Roli, F.: Design of Effective Neural Network Ensembles for Image Classification Purposes. Image and Vision Computing, Vol. 19, No. 9-10 (2001) 699-707 10. Patridge, D.: Network Generalization Differences Quantified. Neural Networks, Vol. 9, No. 2 (1996) 263-271 11. Kim, W., Lee, H., Yoo, S., Baik, S.: Neural Network Based Adult Image Classification. Lecture Notes in Computer Science, Vol. 3696. Springer-Verlag, Berlin Heidelberg, New York (2005) 481-486

Improved Text Mining Methods to Answer Chinese E-mails Automatically Yingjie Lv, Qiang Ye, and Yijun Li School of Management, Harbin Institute of Technology, P.R. China, 150001 [email protected] Abstract. The rapid development of E-commerce makes it difficult to deal with large numbers of customer e-mails quickly and effectively for enterprises. In order to solve the problem, we can employ the method of answering customer e-mail automatically based on text classification techniques. Classified into some appropriate classifications, customer e-mails can be answered using previously defined reply templates which correspond to classifications. In this paper, according to the feature of Chinese customer e-mails, we mainly use improved classification technique based on concept extraction to raise reply accuracy. In the process of classification, we consider the impact of linguistic context into the concept extraction, and establish two different classification criterions (product criterion and demand criterion) to raise classification accuracy. Correspondingly, in the selection of reply template, we combine the result of product analysis with the result of demand analysis to offer customers the most appropriate reply information.

1 Introduction With the development of Internet, e-commerce is becoming widely used in the traditional business. As an important communication means through the Internet, e-mail plays an important part in the development of e-commerce. Especially for the enterprises which have undertaken e-commerce, e-mail has become a necessary approach to contact with their customers. Many famous enterprises think much of the customer e-mails because customer consciousness has gradually come to fore in the highly competitive business environment, and satisfying customer needs and offering them better services have become the basic requirements for businesses to survive. However, when more and more customers begin to use e-mails to voice their opinions or raise problems, the service departments of the enterprises will face a great challenge to deal with so many e-mails. Some large enterprises may receive thousands of customer e-mails, and treating with them by man will spend a long time and involve many employees, which results in the large cost and low customer satisfaction because of the protracted response to the customers. How to deal with this contradiction has become an urgent problem that the enterprises need to solve. After a long-term research, we find that quite a lot of customer e-mails are actually the consultation of common problems such as the function of the products, operation method, etc, which can be replied by some fixed templates. This condition offers a possibility for automatic response to e-mails by computer. Therefore, the research proposes a structure that uses D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 894 – 902, 2006. © Springer-Verlag Berlin Heidelberg 2006

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text mining techniques to implement the function. We firstly analyze the e-mails, extract the common problems to identify the customer purpose and then classify the e-mails by classification algorithm. Finally according to the result of the classification, the appropriate templates will be chosen to answer the e-mails [1]. In the meantime, special e-mails that can’t be answered by automatic processing or need to be dealt with personally by professional will be arranged into relevant product classes, so that they can be distributed automatically to relevant departments for further disposal. In this way, the enterprises can save much cost and improve work efficiency remarkably, which promotes the development of e-commerce ultimately.

2 Literature Reviews The first experiment on text classification was reported in a paper by H.P.Luhn published in 1958[2].All subsequent work reported up to about 1970 was based on Luhn’s ideas and relied mainly on the word-frequency methods while the later work was based on domain-knowledge or based on natural language understanding[3,4]. Some famous classification techniques include Decision Tree, Support Vector Machine, Neural Networks, k-Nearest Neighbors, Bayesian Classifier and so on[5~8]. With the rapid development of e-mail, text classification techniques are applied to e-mail classification which has become hot issues now. However, the purpose of most researches is to filter massive spam e-mail. In contrast, the researches aimed at the demand analysis of customer e-mails are much less. Sung-Shun Weng and Chih-Kai Liu (2004) proposed an approach to e-mail classification based on concept extraction[9]. The main process is: First, train the customer e-mails. Through an expert, some important concepts of customer e-mails can be determined and some high frequency words can be extracted to represent the concepts of customer e-mails. In the meantime, each concept can be classified into certain classification. Next, extract all concepts of the e-mails to be evaluated and compute the weight of the concepts in order to decide the classification of the e-mails. Finally, choose a relevant reply template to answer the customer e-mail. Although their research has a good effect on reply accuracy, there are still some problems remained to be solved when we use above approach to deal with Chinese customer e-mails: 1 ) In an English sentence, there is a blank every two words to distinguish them separately. But in Chinese, a sentence is composed of consecutive characters without interval marks. So we must do Chinese word- segmentation first. 2 ) The concepts composed of words cannot express the e-mail topic accurately. The weakness of concept extraction based on words is the assumption that words reflect respectively the topic and their relations are ignored. However, some concepts are related to special context, splitting sentences into single words will destroy some patterns, resulting in the inaccuracy of information expression. 3 ) Compared to regular e-mail, customer e-mail has its own feature. Usually, this kind of e-mail is used to express customers’ thought and requirement on certain product of enterprise. If we can design classification criterions in detail from different angles, the accuracy of classification will be improved.

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3 Methodology 3.1 Definition of Concept Concept used in this research refers to the common meaning expressed by a group of the same or similar expressions. For example, the following two expressions: “what is” and “what’s the meaning of” have the same meaning, so both of them belong to the same concept----the definition of certain product. The normal form of concept can be expressed as: Concept {expression1, expression2,…}. Concept extraction must depend on the actual operation of the enterprise. Experts will determine the amount and the kind of concept according to long-term work experience. After defining the important e-mail concepts, some expressions which belong to each concept will be chosen subsequently. In order to choose the most refined and suitable expressions to represent the concepts, we must train the e-mails first. Since in Chinese text, sentence is made up of consecutive Chinese characters without interval marks, we should make Chinese word-segmentation. However, the following problems arise: In one hand, the complexity of Chinese understanding usually results in some errors of Chinese word-segmentation. In the other hand, the purpose of the word-segmentation is not to distinguish every word clearly, but to extract the regular expressions. The expressions may be a word set not only a single word. That is to say, it’s possible that the union of some words shows an entire meaning. So we must combine the word-segmentation techniques based on the dictionary and the statistic of word frequency. First, we make word-segmentation by a common dictionary to get all words, and then extract the word sets with high frequency. The detailed process of word sets extraction is: From each sentence, we choose two words at random to compose word sets, and then calculate the total number of the word set occurring in all sentences. Thus, we can get all the frequencies of word sets composed of two words. According to the actual demands, we can continue to deal with the word sets composed of three words, four words… From these word sets, we choose those with high frequency as preparative expressions, and after combining the experts’ experience, we can decide the best expressions for each concept finally. After choosing the expressions of concepts, we must calculate the weight of every expression, because certain expressions may belong to different concepts and the recognition ability of every expression for the concept is different. We use Salton’s TF-IDF formula to show the expression weight of the concept.

w (t , d ) =

tf ( t , d ) × log( N / n t + 0 . 01 )

¦

t∈ d

[ tf ( t , d ) × log( N / n t + 0 . 01 )] 2

(1)

In Formula(1), w(t,d) represents the weight of expression t in concept d; tf(t,d) represents the number of times that expression t appears in concept d; N is the total number of concepts while nt is the number of concepts that include expression t.

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3.2 Generation of Classification Criterion Although we have defined some concepts to show the e-mail topic, we can’t make sure how to answer the customer e-mails according to the extracted concepts. In some cases, the same concept extracted from different e-mails may have different functions. For example, the concept “maintenance” can appear in an e-mail of complaint to certain products, and also can appear in an e-mail of acknowledgement for good after-sale service. So we must determine the classification of the e-mails. The establishment of classification criterion is the first issues to be solved. According to the purpose of the study, e-mails will be classified respectively by two different criterions: product criterion and demand criterion. Through the product analysis of an e-mail, we can make sure which kind of products the e-mail belongs to. The demand analysis of the e-mail makes us know which kind of service the customer needs. The advantages are as follows: 1 ) Showing the e-mail structure conveniently. Generally speaking, the structure of customer e-mails is quite similar. The contents are mainly some consultation and help aiming at certain products. Thus, classification by two different criterions can show the e-mail’s structure clearly. 2 ) Improving the accuracy of classification. When the e-mails are classified by product criterions, we can only focus on the analysis of special nouns because only these nouns can express the target product. In the same way, when the e-mails are classified by demand criterions, we can only focus on the analysis of some verbs, adjectives, especially some interrogative pronouns because these words can express what service the customers want. 3 ) Be convenient for further disposal. The technique of auto response can only deal with some common problems. Other e-mails with special problems that cannot be dealt with automatically will depend on manual disposal. These special e-mails which are classified by product criterion can be directly removed to relative product departments to dispose further.

Fig. 1. The relation between classifications and concepts

3.3 Classification Algorithm 1 ) Concepts extraction. Based on the dictionary made up of all expressions of the concepts, we do Chinese word-segments on the customer e-mail by Maximum Matching Method (MM). If some predefined expressions are extracted from the

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e-mail, we will conclude that the e-mail contains the concepts which the expressions belong to. After extracting all the expressions, the expressions which belong to the same concept will be summed up by their weights to get the weight of each concept for the e-mail. The formula is shown as follows: m

a j = ¦ b jk × t k

(2)

k =1

In formula (2), aj shows the weight of concept j in the e-mail, bjk is the weight of expression k in concept j, tk is the number of the times that expression k appears in the e-mail and m is the total number of expressions in concept j. 2 ) E-mail classification. In order to get the classification result, we need calculate the weight of each class by summing up all the concepts that belong to the same class. According to the result, we can conclude that the class with the most weight is the e-mail’s class. The formula is shown as follows:

Wi =

n

¦a

(3)

ij

j =1

‫ޕ‬

In formula (3), Wi shows the weight of class i in the e-mail, aij shows the weight of concept j in class i, n is the total number of concepts in class i.

Fig. 2. Generation of the templates

3.4 Reply Template Selection After we make sure the classification of an e-mail, the next step is to choose an e-mail reply template. A reply template is a standard reply format according to different classifications and concepts. The generation of templates is shown in Fig.2. The combination of a product concept and a demand concept corresponds to a template. The detailed selection process is: First, we get product classification of an e-mail according to the classification algorithm. Then from all the concepts involved in the chosen classification, we select the concept with the biggest weight in the e-mail as a benchmark product concept. Correspondingly, we do the same disposal of the e-mail

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classification by demand criterion to get a benchmark demand concept. Finally, we choose the template that the combination of the two benchmark concepts corresponds to as the proper reply template. For example, if in product analysis of an e-mail, the e-mail belongs to the class Product2 and the weight of concept3 is the biggest, and in demand analysis, the e-mail belongs to the class Demand1 and the weight of concept1 is the biggest, we will choose template3 to answer the e-mail.

4 Experiment and Result 4.1 Experiment Data Since it is difficult to get actual customer e-mails from enterprises, we thus simulate customer e-mails using similar FAQ models as our experimental data. The FAQ data involved in this experiment derived from www.chinamobile.com which mainly contains a collection of frequently asked questions regarding some daily work of this enterprise. There are customer service personnel answering the questions on-line. We collect a total of 450 questions and their answers as experiment data. 4.2 Experiment Design First, we divide the experiment data into two parts: training ones (300 groups) and ones to be evaluated (150 groups). The training data is analyzed by two criterions. According to the actual operations of the mobile communication enterprise, the training data are divided into ten product classes and three demand classes. Since product division simply depends on enterprise operations, we put emphasis on demand design. Three Demand classes are “Consultation (Questions regarding general information)’’, “Disposal (Problems regarding a curtain product to be solved)’’, “Comment (Suggestions, thanks or complaints)’’. And all concepts of demand classes are shown in Table 1. Then we begin to dispose the training data using the method proposed above. After all preparations are completed, we begin to test the unevaluated e-mails according to classification algorithm above. If the reply template generating automatically towards an e-mail coincides with actual reply information, we can conclude that classification result is correct. In order to assess system efficiency, we employ a commonly used measure in survey data. The measures are precision, recall and F-measure [10]. 4.3 Results Because this research proposes the classification method by different criterions, the result analysis should also be divided into two parts (product and demand). Classification results show that in product analysis, the accuracy is about 0.95 which is very high. This is because the concepts related to products are not confusable and generally have given expressions. So we put emphasis on the analysis of classification result by demand criterion. Considering the impact of linguistic context on the concept

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extraction, this paper uses expressions composed of words and word sets with high frequency to represent the concepts. The experiment result (Fig.3.) shows that the improvement effectively raises the accuracy of classification.

Fig. 3. Comparison of classification accuracy based on different concept forms

Table 1. The classification result by demand criterion

Class

Concept Receive Charge Cancel Consultation Modify Definition Use Cancel Disposal Charge Thanks Comment Suggestion Complaint Total

Predicted 17 25 16 12 14 12 30 8 10 3 3 150

Actual 15 28 20 13 11 9 28 8 14 3 1 150

Correct 12 19 12 9 10 9 27 6 8 3 0 115

Recall

Precision

74.0%

74.0%

86.8%

91.7%

68.8%

61.1%

76.7%

76.7%

Table 1 is the classification result by demand criterion. From the Table 1, we can draw two conclusions: (1) On the whole, the accuracy is 0.767 which is fairly high for Chinese e-mail classification. (2)Compared to the other classes, class “Disposal” with only two concepts has high classification accuracy, which indicates the number of concepts in one class has an important impact on the accuracy of classification. The classification accuracy of class “Comment” is quite low. The reason is that many e-mails which belong to “Question” or “Disposal” mix up many expressions such as “thanks”, “hope”. These polite expressions affect the extraction of actual information. So how to filter the useless expressions is an issue to be solved in future.

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5 Conclusion This paper proposes a method of automatically answering Chinese customer e-mails by using text mining techniques. Based on former researches and the feature of Chinese customer e-mails, this paper makes some major improvement as follows: 1 ) Considering the impact of linguistic context on concept extraction, in this research, concept is composed of expressions not words. In the process of choosing expressions, we not only choose the high frequency words, but also extract the word sets with high frequency as a part of the expressions. Thus, we get the best expressions of each concept. 2 ) According to the feature of customer e-mails, we propose that e-mail should be classified respectively by two different criterions: product criterion and demand criterion in order to improve the accuracy of classification. 3 ) In the selection of reply template, we combine the result of product analysis with the result of demand analysis to generate the proper reply template.

Acknowledgements The work was partially supported by the National Science Foundation of China (Grant No. 70501009) and Heilongjiang Natural and Science Fund Project (G0304). This work was performed at the National Center of Technology, Policy and Management (TPM), Harbin China.

References 1. Busemannn, S., Schmeier, S., Arens, R.: Message Classification in the Call Center, in: Proceedings of ANLP-2000,Seattle, (2000) 159-165 2. Luhn, H.P.: An Experimentin Auto-abstracting. In: International Conference on Scientific Information. Washington D.C.,(1958) 3. Rau, L F.: Conceptual Information Extraction and Retrieval from Natural Language Input. User-oriented Content-based Text and Image Handling. Proceedings of RIAO'88 Conference. MIT,(1988) 4. Wang, J.B., Du, C.L.: Study of Automatic Abstraction System Based on Natural Language Understanding.Journal of Chinese Information Processing, 9(3): (1995) 33 42 5. Aggarwal, C. C.: On Effective Conceptual Indexing and Similarity Search in Text Data. Proceedings of the 2001 IEEE International Conference on Data Mining (3–10) 6. Yang, Y.M., Liu, X.: A Re-examination of Text Categorization Methods. Proceedings of ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR'99)[C], (1999) 42-49 7. Joachims, T.: A Probabilistic Analysis of the Rocchio Algorithm with TFIDF for Text Categorization. Processing of ICML-97,the14th International Conference on Machine Learning [C]: (1997) 143 -151

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8. Joachims T: Transductive Inference for Text Classification Using Support Vector Machines.In: Proceedings of ICML-99,16th International Conference on Machine Learning [C]. Blad, Slowenien,(1999) 200-209 9. Weng, S.S., Liu, C.K.: Using Text Classification and Multiple Concepts to Answer E-mails.Expert Systems with Applications 26 (2004) 529–543 10. Wong P. K., Chan, C.: Chinese Word Segmentation Based on Maximum Matching and Word Binding Force. The 16th Intemational Conference on Computational Linguistics, Copenhagen,Denmark,(1996) 200 - 203

Improvement on ARC-BC Algorithm in Text Classification Method Yu Zhao1, Weitong Huang2, and Yuchang Lu3 1

Department of Computer Science and Technology, Tsinghua University Beijing, P.R.China [email protected] 2 Department of Computer Science and Technology, Tsinghua University Beijing, P.R.China [email protected] 3 Department of Computer Science and Technology, Tsinghua University Beijing, P.R.China [email protected]

Abstract. With the rapid development of automatic text clustering and classification, many techniques and algorithms studying have been made focused in the field of text categorization. However, there is still much work to be done for improving the effectiveness of these classifiers, and new models need to be examined. This paper introduce an ARC-BC algorithms by using of association rule mining in text categorization systems, and proposes some new concepts and improvements on ARC-BC. The experimental results show that the training time of association-rule-based classifier is comparable to other well-known text classifiers, but classification quality is slightly lower than KNN algorithm. Moreover, the improvement proposed here can well improve the classification quality and can shorten training time. In all, our investigation leads to conclude that association rule mining is a good and promising strategy for efficient automatic text categorization, and it has a large room to enhance.

1 Introduction to Text Categorization As the information technology is developing and the use of computers is widely used in almost all the fields, and the volume of text and documents are growing quickly, it is very important to find the truly relevant content for purpose. Text categorization is the problem of assigning predefined categories to text documents. So far, a lot of learning methods have been applied to this problem, including Naïve Bayes probabilistic classifiers[1], Decision Tree[4], Nearest Neighbors algorithm[3], and other learning approaches. The basic idea of Naïve Bayes probabilistic classifiers[1] is to estimate the probabilities of categories given a test document by using the joint probabilities of words and categories. The naïve part is the assumption of word independence. The assumption makes Naïve Bayes classifier far more efficient than the exponential complexity of non-naïve Bayes on Reuters reported by [1] and [2], respectively. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 903 – 908, 2006. © Springer-Verlag Berlin Heidelberg 2006

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Decision Tree[4] method is used to select informative words based on an information gain criterion, and predict categories of each document according to the occurrence of word combinations in the document. Nearest Neighbors algorithm[3] ranks the nearest neighbors of an input document among the training document, and predicts the categories of the input document. KNN[5] is an example of Nearest Neighbors algorithms. Given a new document, the KNN algorithm finds the k nearest neighbors among the training document, and uses the categories of the k neighbors to weight the category candidates.

2 Introduction to ARC-BC 2.1 Main Idea of the Algorithm [6] constructs a text classifier by extracting association rules that associate the terms of a document and its categories. To do so, we model the text documents as a collection of transactions where each transaction represents a text document, and the items in the transaction are the terms selected from the document and the categories the document is assigned to. Then, the system discovers associations between the words in documents and the labels assigned to them. The process of ARC-BC is showed in fig.1:

Fig. 1. The Process of ARC-BC

2.2 Outline of the Algorithm In the first phase, each category is considered as a separate text collection and the association rule mining, for example Apriori algorithm, applied to it. The rules generated from all the categories separately are combined together to form the classifier. In the second phase, we use the training set to evaluate the classification quality, which we will introduce it in Section 3.

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3 Methods and Improvements of Classifying a New Document 3.1 Classifying a New Document The association-rule-based text categorizer is a set of rules that assigns a category to a document if a set of terms occurs in the document. It is common that more than one rule would reinforce the assignment of one document to a class label. Definition 1: The number of rules covered The number of rules covered by each test document Ri refers to the number of rules of the ith category that is included in the test document. Definition 2: Attributive probability For each category, the probability pi of a test document belongs to this category i is

pi =

Ri

¦

20 1

Rj

[6] proposes the definition of dominance factor į, which is the proportion of rules of the most dominant category in the applicable rules for a document to classify. When į is set to a certain percentage, only the categories that have enough applicable rules representing that percentage of the number of rules applicable for the most dominant category are selected. 3.2 Improvement Based on Rule Reduction Definition 3: Category support If n categories contain a same association rule, this rule’s category support is n. Definition 4: Rule reduction Rule reduction is to take out the rules whose category support is no less than a threshold, because we regard these rules are of no sense to classify a new document. Such a simple rule reduction approach will raise problems if some category leaves no rule after this. This kind of situation will cause system failures. To solve the problem, we should adjust the number of rules generated by ARC-BC to make sure the number of rules of each category is not too small. (For example, if we find association rules by Apriori, we can adjust the minimum support of the algorithm to achieve the target.)

4 Experimental Evaluation 4.1 Experiment Conditions In the experiment, we use an Intel Pentium M PC with 1.60 GHz and 512M of main memory (approximately 500M useable when running). The programming language we use is java with jdk1.5 of runtime environment.

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4.2 Data Set We use the data set 20newsgroup, which is widely used. This data set contains 20 given groups, and 1000 documents in each group. We randomly select 5000 documents to be test documents and the rest as training document set. 4.3 Evaluations and Analysis For ARC-BC algorithm, we compare the different results when rule reduction threshold is 2, 3, 4, 5, 6, and no rule reduction, respectively. Table 1 shows the total number of rules generated from training set under the six situations mentioned above. Table 1. Total number of rules of training set Rule reduction Number of Rules

2 841

3 1027

4 1102

5 1134

6 1164

No rule reduction 1198

The result in Table 1 shows that appropriate rule reduction is good for reducing common rules of different categories.

Fig. 2. The Running time, F1 measure and Breakeven Points

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Fig. 3. F1 measure when rule reduction is 2

The results of the running time-including the time to generate rules, reduce rules and classify test documents, F1 measure[7] and breakeven points[7] under the six situations mentioned above are showed in fig.2. Fig.2 shows that the running time for ARC-BC algorithm is appropriate 40 seconds. The larger the threshold of rule reduction is, the longer it takes to run the algorithm. We can find F1 measure and breakeven points of ARC-BC -which represent the classifying quality- is getting larger as the rule reduction is getting smaller. The results shows that appropriate rule reduction is not only speed up the running time, but also improve the quality and effect of classifying effectively. Fig.3 illustrates F1 measure of each category when rule reduction threshold is 2. We find the best quality on category 9, 11 and 12. The reason why these categories share the high quality is that the association rules of these categories is characteristic, so the system can easily include the documents supposed to be in the correct category and easily exclude those are not supposed to be in the category. Category 1, 13, 14, 19 and 20, which represent alt.atheism, sci.electronics, sci.med, talk.politics.misc and talk.religion.misc in 20newsgroup set have a low classifying quality. Among these categories, the reason why sci.electronics and sci.med have a low classifying quality is that the total number of rules of the two categories is small. The reason why the other three categories share low qualities is that the categories overlap too much and there is a large quantity of common rules.

5 Conclusion This paper explores the association-rule-based ARC-BC algorithms in text categorization systems. We propose new concepts of attributive probability, etc, which help to formulize the description of the algorithm and make improvements by rule reductions on ARC-BC. The experimental results show that appropriate rule reduction is good for reducing common rules of different categories. Moreover,

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appropriate rule reduction is not only speed up the running time, but also improve the quality and effect of classifying effectively. The major advantage of association-rule-based classifier is its fast speed. The system time of ARC-BC is less than one minute, while it takes about one hour for KNN to run the algorithm. However, the classification quality of ARC-BC is 20 percent lower than KNN algorithm. How to enhance the quality is one of the most urgent and promising directions for ARC-BC to develop. In the future, we are testing more performance of ARC-BC on more other data sets to improve the algorithm, and test ARC-BC by all means to improve its classifying quality.

References 1. Lewis, D.: Naive (bayes) at forty: The Independence Assumption in Information Retrieval. In: 10th European Conference on Machine Learning (ECML-98) (1998) 4-15 2. Moulinier, I.: Is learning bias an issue on the text categorization problem? In: technical report, LAFORIA-LIP6. University Paris VI (1997) 3. Dasarathy B V.: Nearest neighbor norms: NN pattern classification techniques. Los Alamitos, CA: IEEE Computer Society Press (1991) 4. Moulinier, I. Ganascia, J.-G.,: Applying an existing machine learning algorithm to text categorization. In S.Wermter, E.Riloff, and G.Scheler, editors, Connectionist statistical, and symbolic approaches to learning for natural language processing. Springer Verlag, Germany. Lecture Notes for Computer Science series, No.1040, (1996) 5. Duda, R. O., Hart, P. E.: Pattern Classification and Science analysis, John Wiley & Son. (1973) 6. Zaiane, O. R., Antonie, M.: Classifying Text Documents by Associating Terms with Text Categories. In Proceedings of the Thirteenth Australasian Database Conference (ADC) (2002) 7. Yang, Y.: An Evaluation of Statistical Approaches to Text Categorization. In IR (1999)

Improving Structure Damage Identification by Using ICA-ANN Based Sensitivity Analysis Bo Han1, Lishan Kang1, Yuping Chen1, and Huazhu Song2 1

School of Computer Science, Wuhan University, Wuhan, Hubei 430072, China [email protected] 2 School of Computer Science and Technology, Wuhan University of Technology, Wuhan, Hubei 430072, China

Abstract. Structure health monitoring detects the nature of structure damage in an early stage by the network sensors whose signals are normally highly correlated and mixed with noise. Feature reduction methods are applied in extracting attributes,that will be input into advanced classification models. The complicated data transformation and classification procedures make it difficult to identify direct relationship between sensors and abnormal dynamic structure characteristics, especially for complex buildings with large numbers of sensors. In this study, the sensor sensitivity analysis on a structure damage identifier is applied, which integrates independent component analysis (ICA) and artificial neural network (ANN) together. The approach is evaluated on a benchmark data from University of British Columbia. The experimental results show sensitivity analysis not only helps domain experts understand the mapping from different location and type of sensors to a damage class, but also significantly reduce noise and increase the accuracy of ICA-ANN classifier.

1 Introduction Structural damage identification involves the observation of a system over time using periodically sampled dynamic response measurements from a network of sensors. State-of-Art researches in this area [1,2] mapped the task to a classification problem in machine learning community. It generally consists of two steps: feature reduction from measured multi-source sensor signals and statistical classification [3,4,5]. In the first step, the highly correlated and noisy sensor signals make it hard to perform effective feature selection. Many successful system applied independent component analysis (ICA) [6,7] or principal component analysis (PCA) to reduce signals to much lower dimension features. These independent or uncorrelated features facilitate the classification using either artificial neural networks (ANN) or support vector machines (SVM) in the second step [8,9]. However, the complicated data transformation and classification make it difficult to identify direct relationship between sensors and abnormal dynamic structure characteristics. Structure engineers are keen to explore such relationship because different type and location sensors have empirically been proved to provide varied quality information. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 909 – 914, 2006. © Springer-Verlag Berlin Heidelberg 2006

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Some redundant signals not only increase noise, but also make the input signals to a much higher dimension. The well known “dimensionality curse” degrades classification performance and also bring difficulties to analyze structure damage types and causes in details. Consequently, it is critical to identify which sensors make most contributions for a specific type of damage. The task has intensive applications since many complex buildings with different thickness, cracks and holes are increasingly constructed, and a large number of sensors will be set into structures. In this paper, we applied first-order sensitivity analysis to identify most important sensors for a classifier, which combines ICA and ANN together. The experiments, based on the benchmark data from the University of British Columbia, showed sensitivity analysis can clearly reveal the relationship between selected sensors and specific damages. By using the most sensitive signals, the ICAANN classifier significantly improves the identification accuracy.

2 Methodology 2.1 ICA-ANN Structure Damage Classifier ICA performs optimal linear transformations on multiple source signals and extracts the most informative independent components. These components work as feature inputs of an ANN, and thus a damage classification model is constructed. ICA and ANN have been widely applied in the stage of feature reduction and classification respectively. In our previous work, we successfully integrated them together to construct a reliable damage classifier. The detailed technical steps are listed in [10]. 2.2 ICA-ANN Based Sensitivity Analysis By sensitivity analysis, the classifier is regarded as an ICA-ANN black box. Its inputs are sensor signals x1, x2, …, xh, and output is status label Y. We assume each signal xi (i = 1,2,…, h) observers normal distribution with N( x i , σ i ) . By perturbing a sensor signal with a small value ∆x i , we explore how much difference a new predictor Yi will make, comparing with the predictor Yfull constructed by full set of original sensor signals. Thereby, the normalized stimulation sensitivity Si=

∆Yi / σ Yi ∆x i / σ i

=

σ i (Yi − Yfull ) , σ Yi ∆x i

where σ Yi is the standard derivation of predictor Yi. Given all sensor signals have the

same standard derivation, σi = σ j , σ Yi = σ Yi (here i, j = 1,2,…, h and i ≠ j), Si is simplified as the first-order derivative

(Yi − Yfull ) . Sorting the Si, we will rank the sen∆x i

sors signals by their sensitivity. The top features play the most important roles in the damage detection.

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The detailed algorithm is listed in Fig.1. Input: a dataset d = < T, S >, including damage status target T, and signals from q sensors, denoting as S = [ s1,s2,…, sq ]; Output: sensitive sensor lists SL; Step1: Randomly divide d into training dataset d1 and test dataset d2; Step2: Using full set of original sensor signals in d1 as input to ICA-ANN black box, train a classification model; Applying this model on d2, we get a prediction class vector Predfull; Step3: Let I = 1; ∆ = 10-8; Step4: Let Si’ = Si + ∆ ; S’ = [ s1,…,Si’,…, sq]; Step5: Using S’ in d1 as input to ICA-ANN black box, train a classification model; Applying the model on d2, we get a prediction class vector PredI; |d | 1 Step6: Compute the distance disti = | Pr ed I − Pr ed full | , where |d2| repre¦ | d 2 | *∆ l=1 sents the number of samples in d2; Step7: I = I + 1; if I ≤ q, goto Step4; Otherwise, goto step8; Step8: Sort the distance vector < dist1, dist2, …., distq > in descendent order; and the corresponding sensor signals are listed in the new order S’’ = [snew1, snew2, …, snewq]; Step9: Let J = 1; Step10: Let SL = [ snew1,…, snewj ]; Input them into ICA-ANN black box, train a classification model based on d1; applying the model on d2, we get a prediction class vector SPredj; Step11: J = J+1; if J ≤ q, goto step10; Otherwise, goto step12; Step12: Choose the best J, such that SPredj is most close to the true target vector in d2; SL = [ snew1,…, snewj ]. 2

Fig. 1. Algorithm for sensor sensitivity analysis

3 Experiments 3.1 Data Sets We selected a popular benchmark to testify the classification accuracies. It is developed by the IASC-ASCE SHM task Group at University of British Columbia. In the experiments, we mainly use seven data sets in the ambient data from this benchmark, where C01 is an undamage dataset, C02-C07 are different type of damaged datasets. The detailed data and information were shown in [11]. There are 15 attributes in each dataset. They correspond to the signals from 15 sensors located in this steel-frame. In addition, the benchmark provides an additional noise attribute, which helps researchers to study feature reduction.

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3.2 Experimental Results In the experiments, for each undamaged or damaged dataset, we randomly choose 6000 samples. Then following the steps in Fig. 2, we obtain a sorted attribute list shown in Table 1. The bold attributes denotes they have been selected into sensitive sensor list SL. The table also helps domain experts to explore different location and type of sensors to a specific damage class. Table 1. Sorted attributes list in dataset (C01-C07)

data C01 C02 C03 C04 C05 C06 C07

1st 8 10 2 15 1 2 6

2nd 6 5 4 2 14 13 5

3rd 9 11 3 13 4 9 1

4th 4 15 15 4 7 8 9

5th 12 13 1 1 6 7 12

6th 3 2 6 12 2 11 11

7th 10 4 12 6 10 15 8

8th 11 3 10 5 12 12 4

ica by all sensors in 6000 undamage data C01 5 0 -5 2 0 -2 5 0 -5 10 0 -10 5 0 -5 5 0 -5 5 0 -5 5 0 -5 5 0 -5 20 0 -20

9th 10th 11th 12th 13th 14th 15th 7 2 5 13 1 15 14 12 8 14 9 6 1 7 8 11 14 9 7 13 5 7 9 10 3 14 8 1 15 9 11 8 5 3 13 14 4 3 6 5 10 1 7 10 2 14 15 3 13

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In Fig. 2 and Fig. 3, we compare the independent components transformed from the full sensor signals and from the selected seven sensitive signals in data C01. We clearly see sensitivity analysis significantly reduced the number of extracted features from 10 to 5, so the ANN input dimension decrease much. Moreover, the number of the independent components from sensitive sensors has been reduced round 50% compared with the number of the independent component from all sensors in data C02-C07, shown in Table 2. For all seven data sets in Table 1, we counted the total occurring frequency for each selected sensitive attribute. The results are listed in Fig. 4.

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We have 7 attributes 15,12,6,4,2,11,1 with a frequency larger than 3. To confirm they are most informative features, we compute the correlation p-value between extracted independent components of these features with the additional noise attribute in datasets. If p M , and n − m + 1 = L . For clarity, we unify the notations of state nodes firstly. x j +1 ( M J − j −1k ) is denoted as the state of scale j+1. There are L finer nodes x j ( M J − j k − n) , x j ( M J − j k − n + 1) , ..., x j ( M J − j k − m) that relate to one coarse scale node x j +1 ( M J − j −1k ) . The multiscale sys-

tem does not constitute homogeneous tree of order M and a portion of the state vector in time block k ∆T overlap with that in time block (k + 1) ∆T . Supposing that the low-pass filter corresponding to the M-band wavelet is H1 , and h(0) denotes the impulse response at moment zero. Let us define H1 = [ h(m), h( m + 1),!, h(0),!, h(n)] .

(3)

ª º H j +1 = « h(m),0,0,...,0, h(m + 1),0,0,...,0, h(m + 2),..., h(n − 1),0,0,...,0, h( n ) » .   

  

  

«¬ »¼ Mj Mj Mj

(4)

where H j +1 is obtained by inserting M j zeros between every two coefficients of filter H1 . In time block k ∆T , the node at scale j+1 is obtained as what follows H j +1 = H 1 * H 2 * " H j .

(5)

where ∗ represents convolution. Letting H 1 = [1] , and x j +1 ( raw mate rial=shale parition1=H, typology=flake -> raw material=shale partition1=H, soil stratum=upper paleolith, typology=flak e -> raw material=shale Partition1=B -> raw material=shale Partition1=H -> raw material=shale Partition1=H, soil stratum= upper paleolith -> raw materi al=shale Partition1=H -> soil stratum= upper paleolith Partition1=H, raw material=shale -> soil stratum= upper paleolith Partition1=H, typology=flake -> soil stratum= upper pale olith Soil stratum=disturbance -> raw material=shale partition1=H, raw material=shale, typology=flake -> soil stratum= upper paleolith Soil stratum=disturbance -> raw material=shale partition1=H, typology=flake -> soil stratum= upper pale olith, raw material=shale partitition1=H -> soil stratum= upper paleolith, raw mater ial=shale

96.05(%) 90.99 90.40 90.33 90.19 89.61 89.53 88.93 88.44 88.23 87.75 87.30 87.29 86.73 86.17 78.23 78.04

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Rule 1 in table 2 explains that if typology is blade, then raw material is shale including confidence of 96.05%. Rule 2 explains that if soil stratum is disturbance and typology is flake, then raw material is shale including confidence of 90.00%. Also, rule 14 presents that if partition 1 is H, raw material is shale and typology is flake, then soil stratum is upper paleolith including confidence of 86.73%. Using these patterns, we know that the relic’s raw material of specific excavating site mostly composes shale. This means that shale in past specific region widely existed in the environment. Therefore, an archeologist uses this pattern to analyze and predict relic information.

5 Experimental Results The raw data consists of 15, 316 records. Fig. 1 shows experimental results. The figure presents the number of frequent itemsets and rules through fixing confidence of 60 and increasing support value two by two. In case of setting up support value of 2, the number of frequent itemsets generated is 154 and number of rules generated is 120. In case of setting up support value of 14, 16 and 18, the numbers of frequent itemsets and rules generated are 15 and 10 respectively. In case of setting up support value of 30, the numbers of frequent itemsets and rules generated are 7 and 3 respectively. Rules

Frequent itemsets



Number of itemsets and rules











































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Fig. 1. Number of frequent itemsets and rules according to support values

In the analysis of excavated relics, archeologists sometimes do not know the typology of some relics so they are very small or not described typology name because of the excavator's mistake. Especially, in the animal bone analysis, bones which are very small named fragment or scrap by analyzer because DNA information of the animal's life does not exist. Therefore, in this case archeologists can use generated rules through above experiment for extracting the unknown relic information.

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6 Conclusion and Future Work In this paper, we analyzed data on artifacts which were the paleolithic research results in Suyanggae on Jungwon region in the Republic of South Korea. And we carried the relationship analysis between each paleolithic stone relic data using ARD. We acquired the association rules that present the relationships between each relic data. Through this experimentation, we knew the relationship among partition1, parititon2, soil stratum, typology and raw material. Such a study may provide useful information concerning the specific stone relics. The future work is designing and implementing various time conversion operators that make it possible to reason the temporal data. And, we will study the integrated relationship about stone relics, animal bone, excavating sites and geological layer features.

References 1. Chen, M.-S., Han, J., Yu, P.S.: Data Mining: An Overview from Database Perspective. IEEE Transactions on Knowledge and Data Engineering, Vol. 8 (1996) 866-883 2. Yun, H., Ha, D., Hwang, B., Ryu, K.H.: Mining Association Rules on Significant Rare Data using Relative Support. Journal of Systems and Software, Vol. 69 (2003) 181-191 3. Aggarwal, C.C., Yu, P.S.: Mining Large Itemsets for Association Rules. Data Engineering Bulletin, Vol. 21 (1998) 23-31 4. Agarwal, R., Shafer, J.C.: Parallel Mining of Association Rules. IEEE Transactions on Knowledge and Data Engineering, Vol. 8 (1996) 962-969 5. Doddi, S., Marathe, A., Ravi, S.S., Torney, D.C.: Discovery of Association Rules in Medical Data. Medical Informatics and the Internet in Medicine, Vol. 26 (2001) 25-33 6. Coenen, F., Leng, P.H., Ahmed, S.: Data Structure for Association Rule Mining: T-Trees and P-Trees. IEEE Transactions on Knowledge and Data Engineering, Vol. 16 (2004) 774-778 7. Coenen, F., Goulbourne, G., Leng, P.: Tree Structures for Mining Association Rules. Data Mining and Knowledge Discovery Vol. 8 (2004) 25-51 8. Bench-Capon, T., Coenen, F., Leng, P.: An Experiment in Discovering Association Rules in the Legal Domain. 11th International Workshop on Database and Expert Systems Applications (2000) 1056-1060 9. Lee, Y.-J., Yoo, J.-Y., Kong, S.: Suyanggae Tranged-point in Korea. International Symposium on Palaeoanthropology, Commemoration on the 70th Anniersary of the Discovery of the First Skull of Peking Man at Zhoukoudian (1999) 10. Dougherty, J., Kohavi, R., Sahami, M.: Supervised and Unsupervised Discretization of Continuous Features. International Conference on Machine Learning (1995) 192-202

Pei-Radman Fusion Estimation Algorithm for Multisensor System Applied in State Monitoring Xue-bo Jin1 and You-xian Sun2 1

College of Informatics and Electronics, Zhejiang Sci-Tech University, Hangzhou, 310018, China [email protected] 2 Institute of Modern Control Engineering, Zhejiang University, Hangzhou, 310027, China

Abstract. More exact state estimation can be obtained by multisensor system. But measurement noises from different sensors are generally correlated when multisensor system applied in state monitoring. By solving the maximum eigenvalue of measurement covariances matrix, a Pei-Radman fusion estimation algorithm is developed for the practical state monitoring. The numerical example shows that the fusion method here is very simple and can obtain an optimal estimation in this special multisensor fusion system.

1 Introduction In the practice, lots of signals are needed to constitute the controllable loop of automatic control. However, some required states can’t be online-measured because of the limit of sensor technique. Each kind of sensor has its sphere of application and exact degree. So it’s very difficult to know exactly and completely the true conditions of the installation by single sensor. In the practice, many sensors are employed simultaneously to the industrial processing in order to meet some precise-production-demands. Be subjected to the restraint of sensor technique and the manufacturing cost, people often choose the same sensor to obtain redundancy messages of signals, by which the more exact estimation can be obtained [1] . However, due to the usage of same sensor, a close distance of different sensors and a jam or uncertain source in measurement environment, the measurement noises from different sensors are ordinarily correlated. Moreover, they often has the same correlation covariance[2] . The studies of [3,4] have shown that the performance of estimation results will decease greatly if the correlation can’t be correctly handled. [3, 4] use similarity transformation to decouple the correlated noise covariance and develop the optimal state fusion estimation algorithm. But it seemed so complex because they didn’t consider the peculiarity of multisensor system used for the condition monitoring of production process, i.e., people often use the same sensor. This paper studies a practical state monitoring system, in which the same sensors are employed and the multisensor system has the same measurement matrix, the same covariance of measurement noise and the same correlation covariance. The structure D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 963 – 968, 2006. © Springer-Verlag Berlin Heidelberg 2006

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of this paper is as the following: Section 2 gives the model of multi-senor system to be considered. The Pei-Radman fusion estimation is developed and the performance of the algorithm is discussed in Section 3. Finally, a simulation is given in Section 4.

2 System Model A state –space model of the form x(k + 1) = Ax(k ) + Bw(k )

(1)

yi (k ) = cx(k ) + vi (k )

(2)

is considered, where x(k ) ∈ R is the state of the system to be estimated and whose n

initial mean and covariance are known as x0 and P0 . w(k ) ∈ R h and vi (k ) ∈ R m are white noise with zero mean and independent of the initial state x(0), m E {w ( k ) w T ( j )} = Q . yi (k ) ∈ R is the measurement vector of the ith sensor, i = 1,2,3, N .Obviously, all the measurement matrices are equivalent. We define the generalized measurement equation is: ~ y (k ) = Cxˆ (k ) + v(k ) where y(k) = [ y1T (k), y2T (k),, yNT (k)]T ~ C = [c T , c T ,  , c T ]T

v(k ) = [v1T (k ), v2T (k ),, vTN (k )]T The measurement covariances of every sensor are equivalent and correlation covariances are also equivalent, noted as d and s , respectively. We have the covariance matrix §d s  s · ¸ ¨ ~ ¨s   ¸ T R = E {v(k ) v ( j )} = ¨    s¸ ¸ ¨ ¨s  s d¸ ¹ ©

3 Pei-Radman Fusion Estimation N

xˆλ (k | k ) = xˆλ (k | k − 1) + ¦ K λ i (k )[ yi (k ) − cxˆλ ( k | k − 1)] i =1

xˆλ (k | k − 1) = Axˆλ (k − 1 | k − 1) K λ (k ) = [ K λ 1 (k ), K λ 2 (k ), , K λ N (k )]

~ 1 (R ) K λ i (k ) = Pλ (k | k )c T λ−max

(3)

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the estimation covariance is ~ −1 −1 1 Pλ (k | k ) = Pλ (k | k − 1) + N * c T λ−max ( R )c

(4)

Pλ (k | k − 1) = APλ (k − 1 | k − 1) A T + BQB T

(5)

~ ~ where λmax ( R ) is the maximum eigenvalue of R . We have the following theorem to present the performance of the Pei-Radman fusion estimation algorithm.

Theorem 1. Pei-Radman fusion algorithm is optimal in the multisensor system (1) and (2). Proof We have the optimal centralized fusion estimation algorithm for the multisensor system (1) and (2) as the following [5]. ~ (6) xˆ (k | k ) = xˆ (k | k − 1) + K (k )[ y (k ) − C xˆ (k | k − 1)]

xˆ(k | k − 1) = Axˆ(k − 1 | k − 1) ~ ~ K (k ) = P(k | k )C T R −1

(7) (8)

the estimation covariance is ~ ~ ~ P −1 ( k | k ) = P −1 ( k | k − 1) + C T R −1 C

(9)

P(k | k − 1) = AP(k − 1 | k − 1) A T + BQB T (10) ~ Define Rλ = λmax ( R ) ∗ I , where I is an identity matrix. We can rewrite the PeiRadman fusion estimation algorithm as the following by the generalized measurement equation ~ (11) xˆλ (k | k ) = xˆ λ (k | k − 1) + K λ (k )[ y (k ) − C xˆλ (k | k − 1)] xˆλ (k | k ) = Axˆλ (k − 1 | k − 1)

(12)

~ K λ (k ) = Pλ (k | k )C T Rλ−1

(13)

where

the fusion estimation covariance is ~ ~ −1 −1 Pλ (k | k ) = Pλ (k | k − 1) + C T Rλ−1C

(14)

Pλ (k | k − 1) = APλ (k − 1 | k − 1) A T + BQB T

(15)

Now we consider the relation between the (6)-(10) and (11)-(15). From [6], we can ~ conclude that covariance matrix R is a Pei-Radman matrix, the maximum eigenvalue ~ of R~ is λmax ( R ) = d + ( N − 1) ⋅ s . When d and s satisfy d ≠ s, d ≠ − s + 1 , the inverse ~ ~ matrix of R is R −1 = [aij ] , where

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d + ( N − 2) ⋅ s ­ °° d [d + ( N − 2) ⋅ s ] − ( N − 1) ⋅ s 2 i = j aij = ® −s ° i≠ j 2 ¯° d [d + ( N − 2) ⋅ s ] − ( N − 1) ⋅ s

(16)

i, j = 1, 2,  N Then we have

ª a11  a1N º ªc º  c ]««    »» ««  »» = «¬a N 1  a NN »¼ «¬c »¼

~ ~ ~ C T R −1C = [c T

T

¦c

T

[aii + ( N − 1)a ij ]c

i, j i≠ j

By (16), we can obtain a ii + ( N − 1)a ij =

1 1 d + ( N − 2) s − ( N − 1) s = = ~ d [d + ( N − 2) s] − ( N − 1) s 2 d + ( N − 1) s λ max ( R )

i.e.,

~ ~ ~ C T R −1C = ¦ c T ⋅

1

º ª 1 ~ » ªc º « ( ) λ R » « » ~ T −1 ~ « max T  c ]«  » «  » = C Rλ C 1 » «c » « ~ »¬ ¼ « λ max ( R ) ¼ ¬

T ~ ⋅ c = [c

λ max ( R )

Then based on (9) - (10) and (14) - (15), we can have Pλ (k | k ) = P(k | k ) , k = 1, 2, 3, ...... . By the same method, we can also obtain

~ ~ C T R −1 =

¦c

T

[ a ii + ( N − 1) a ij ] =

i, j i≠ j

~ = C T Rλ−1

¦c

T

⋅

1

~ = [c λ max ( R )

T

ª 1 º ~ « » « λ max ( R ) » T  c ]«  » 1 » « ~ » « λ max ( R ) ¼ ¬

~ ~ ~ i.e., Pλ (k | k )C T Rλ−1 = P(k | k )C T R −1 , we can have K (k ) = K λ (k ) by (8) and (13). ~ Then, it’s proved that with the same initial conditions, i.e., P (0 | 0) = Pλ (0 | 0) and xˆ (0 | 0) = xˆ λ (0 | 0) , the optimal centralized fusion estimation algorithm (6) - (10) and the Pei-Radman fusion estimation algorithm (11) - (15) will result in the same state ~ estimation xˆ (k | k ) and the same estimation covariance P (k | k ) . Therefore, we can conclude that the Pei-Radman fusion estimation algorithm is optimal. # Now we consider the steady Pei-Radman fusion estimation. If there exists a positivedefine solution P to the ARE

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~ 1 P = APAT − AP( P + ( N * c T λ−max ( R )c) −1 ) −1 PAT + BQB T the steady Pei-Radman fusion estimation

xˆ (k + 1) = A f xˆ (k ) + B f

N

¦ y (k ) i

i =1

is given by A f = A − NKc

Bf = K

~ 1 where K = Pc T λ−max (R) .

4 Simulation Simulation results are obtained using the following: ª0.9 1 º ª 12 º x(k + 1) = « x( k ) + « » w( k ) » ¬ 0 0.5¼ ¬1 ¼ y i ( k ) = cx ( k ) + vi ( k )

ª2 1 1 º ~ « where w( k ) = N (0, q ) , q = 1 , c = [1 0] , R = «1 2 1 »» . «¬1 1 2»¼ ~ We can obtain λmax ( R ) = 4 and the steady Pei-Radman fusion filter ª 0.3645 0.8222º Af = « » ¬− 0.1778 0.0409¼

ª 0.1789 0.3567 − 0.1789º Bf = « » ¬− 0.1406 0.3184 0.1406 ¼

The results of estimation are shown in Fig.1. The ‘thick’ lines represent the real state, the ‘thin’ lines represent the results of the steady Pei-Radman fusion filter and the ‘star’ lines represent the results of the optimal centralized fusion estimation algorithm [5]. We can know this two estimation methods are completely equivalent.

5 Conclusions The state monitoring of industrial equipment is especially important to process controlling, equipment protection and fault detection. In order to obtain the more exact estimation of state, producers frequently employ several sensors to carry on the online measurement by living balances relationship between quality and the beneficial result. In order to resolve the correlation of measurement sensors, this note develop a simple fusion estimation algorithm, which can obtain the optimal estimation performance in the state monitoring of the practical premise production.

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Fig. 1. Results of the steady Pei-Radman fusion estimation

Acknowledgements This research has been supported by Zhejiang Provincial Natural Science Foundation of China grants No. M603174, Zhejiang Provincial Education Office Foundation of China grants No. 20031166, Zhejiang Provincial Young Teacher Support Plan and PH.D Foundation of Zhejiang Sci-Tech University.

References 1. Jin, X., Sun, Y.: Optimal Fusion Estimation Covariance of Multisensor Data Fusion on Tracking Problem. Proceedings of the 2002 IEEE International Conference on Control Applications, Scotland. (2002) 1288–1289 2. Roy, S., Ronald A.I.: Decentralized Linear Estimation in Correlated Measurement Noise. IEEE Transaction on Aerospace and Electronic Systems. 6 (1991) 939–941 3. Jin, X., Sun, Y.: Optimal State Estimation for Data Fusion with Correlated Measurement noise. Journal of Zhejiang University (Engineering Science). 1(2003) 60–64 4. Jin, X., Sun, Y.: Optimal Centralized State Fusion Estimation for Multi-sensor System with Correlated Measurement noise. Proceedings of 2003 IEEE Conference on Control Applications, Istanbul. (2003) 770–772 5. He, Y., Wang, G.: Multisenor Information Fusion and Its Application, Beijing, Electronics industry press. (2000) 238–241 6. Cen, J., Cen, X.: Special Matrix, Qinghua University Press (2001) 390–397

Privacy Preserving Association Rules Mining Based on Secure Two-Party Computation Weimin Ouyang1,2 and Qinhua Huang2 1

2

Management Department, Shanghai University of Sport, 200438 Shanghai, China [email protected] School of Computer Engineering and Science, Shanghai University, 200072 Shanghai, China [email protected]

Abstract. Privacy-preserving data mining in distributed or grid environment is a hot research field in recent years. We focus on the Privacypreserving association rules mining in the following situation: two parties, each having a private data set, wish to collaboratively discover association rules on the union of the two private data sets. Therefore, we put forward a novel approach for mining Privacy-preserving association rule based on secure two-party computation using homomorphic encryption technology.

1

Introduction

Data mining and knowledge discovery are hot research filed concerning the joint of artificial intelligence, database and statistics. It is developed to find previously unknown, potentially useful knowledge, rules or models [1] from large database. The presupposition of data mining and knowledge discovery is that the data is open to be used. But in real world it not necessary true. Some database may contain private information which should not be leaked out. Thus techniques of data mining without leaking the private information are needed. Research on privacy preserving data mining is for this purpose. Data mining and knowledge discovery contain many typical problems, including association rule mining, sequential patterning, classification and clustering. Correspondingly the privacy preserving data mining and knowledge discovery should be developed aimed at these problems. In this paper we addressed the problem of the privacy preserving association rule mining on vertically distributed data. Our problem is described as follows: Assume two parties, Alice and Bob, have private data set, D1 and D2, respectively, where D1 and D2 are vertical distributed database, i.e., different sites gather information about the same set of entities and collect different feature sets. These two parties will execute a certain kind of association rule mining algorithm on D1 ∪ D2 without existing of a third party. It requires the two parties must not leak their respective private information during computation. Hence we propose a secure two-party computation protocol based on homomorphic cryptography [4] to address privacy preserving association rules mining. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 969–975, 2006. c Springer-Verlag Berlin Heidelberg 2006


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The remains of this paper is organized as follows: the related work. is described in section 2, we describe the sequential pattern mining algorithm in section 3. We propose a secure two-party scalar product protocols to discover association rules in section 4 . We make our conclusions and future works in section 5.

2 2.1

Related Work Secure Two-Party Computation

The secure two-party computation problem is first proposed by Yao [5],which is extended to the secure multi-party computation(SMC) by O.Goldreich [6].The secure multi-party computation protocol based on the cryptograph secure model can compute arbitrary function in distributed network where each participant holds his inputs, while the participants do not trust each other, nor the channels by which they communicate with each other. However, the participants wish to correctly get the result of the function from their local inputs, while keeping their local data as private as possible. This is the problem of Secure Multi-party Computation (SMC). The security standard is the assumption that we have a trusted third party to whom we can give all data. The third party performs the computation and delivers only the final results. It is clear that nobody could reveal anything not inferable from its own input and the results. The goal of secure protocols is to reach this same level of privacy preservation without the trusted third party . Each party provides his input which will keep private to others. For each party it is allowed to know its input, final output and information can be deduced from them. If exists the trusted third party, the secure multi-party computation will be easy. They simply transfer their input to a trusted third party and get result from the third party respectively. Actually the trusted third party is often rarely easy to be found. Thus research on secure multi-party computation protocols is needed. The secure computation protocols are presented in the form of combined circuit with generality and simplicity in theory. As Goldreich [7] pointed out these protocols are inefficient and not applicable for data mining, which needs great deal of data input. Thus we need to develop a simplified and easily implemented secure multi-party computation aimed at specified data mining task. 2.2

Privacy Preserving Data Mining

Since R.Agrawal and R.Srikant proposed privacy preserving data mining based on random data in 2000, privacy preserving data mining has get wide attention in the field of data mining and knowledge discovery. Several techniques, including data perturbation, encryption, and secure multi-party algorithm, have been proposed in the literature, concerning data mining problems as association rule mining, classification and clustering [7]. J.Vaidya [8] proposed an algorithm to get scalar product of vectors, in which its security is based on the inability of either side to solve k equations in more than k unknowns. R.Wrigh [9] proposed

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two-party cooperation Bayesian Networks induce based on Pailliers homomorphic cryptography. But attacks on the protocols are easy to be success. According to his protocols PartB could guess out if ai is 1 or 0 by comparing e(1) and e(ai )) when PartA sends him encrypted vector e(a1 ), . . . , e(an )) to PartB, for PartB knows public key e. In this paper we propose secure scalar product computation protocol will deal with this problem.

3 3.1

Privacy Preserving Association Rule Mining Association Rule Mining

The problem of mining association rules was originally proposed by R.Agrawal. Association rule mining tries to find the association of customer shopping during a transaction, for example, 75% customer who buy A probably buy B. These rules will help the managers to optimize the stock, places of the goods and managements. In association rule mining we assumed a specified customer transaction database D, where each transaction is a set of items, such as customer ID, transaction date and products. Each customer generates no more than one transaction in the mean time. The product item attribute is binary, which denotes the item was sold or not. An itemset is a non-empty set of items. We say that a transaction support a itemset if the itemset is contained in a transaction. An itemset has support s in the transaction set if s% of transactions contain the itemset. The frequent itemset denotes the itemset with support no less than the threshold support. Assume a specified transaction database D, threshold support min suport, threshold confidence min conf , the task of association rules mining is to find out the frequent itemsets in the database and construct association rules based on min conf . 3.2

Problem Representation

we consider such a scenario: two parties,Alice and Bob,each party having a private vertically partitioned data set (denoted by D1 and D2 respectively). The two parties want to find association rule on D1 ∪ D2. For the security of data, each party can not get any information about the other except the result of algorithm computation. During this course no third (trusted or non trusted) party exists. For the sake of simplicity and without loss of generality, we make the assumptions about D1 and D2 as follows: (1) D1 and D2 contain a same number of transaction records L; (2) The identifier of ith transaction in D1 is the same as The identifier of ith transaction in D2. But the itemsets are secret to each other. (Note that the assumptions can be easily satisfied by pre-processing the data sets D1 and D2,and such a pre-processing does not need one party to send its data set to other party) Alice and Bob hold private data set D1 and D2. These two parties try to find out frequent itemsets with support no less than a specified threshold min support without leaking any private information. We say an itemset (A,B) is a frequent itemset if its support s in D1 ∪ D2 satisfies s ≥ min support.

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Approach to Privacy Preserving Association Rule Mining

The steps in association rule mining related to data access are: (1) counting of frequent 1-itemset. (2) counting of the support of candidate itemset C.Count. Because there is only one attribute (after having been mapped) contained, the frequent 1-itemset can be processed in one party, there is no need of data accessing over two parties. But for that the candidate itemset C contains 2 or more attributes, which may be distributed in two sites, the computation would requires data accessing operation over two parties. The secure computation problem of the support of candidate itemset C.Count without leaking any private information is exactly addressed in this paper. If the attributes in candidate itemset belongs to one party, the problem may be simplified as getting candidate support by directly computing the scalar product of corresponding attributes in candidate itemset. Else if they are distributed in two parties, the computation precondition of preserving private information must be well satisfied. 4.1

Homomorphic Property of the Encryption

We apply homomorphic encryption in the secure computation protocols of support counting of candidate itemset presented in this paper. A cryptosystem is homomorphic when it satisfies the property: e(a) ∗ e(b) = e(a + b). 4.2

Secure Two-Party Scalar Product Protocols

Assume C to be a k-itemset and Alice has m attributes A1 , A2 , . . . , Am and Bob have n attributes B1 , B2 , . . . , Bn , i.e., C = (A1 , A2 , . . . , Am , B1 , B2 , . . . , Bn ), where m ≥ 1, n ≥ 1, m + n = k. We denotes the j th attribute value of Ai as Aij , and j th attribute value of Bi as Bij . For simplicity, let vector ,m ,n X = (x1 , x2 , . . . , xL ), vector Y = (y1 , y2 , . . . , yL ), where Xj = i=1 Aij , Yj = i=1 Bij , (j = 1, 2, 3, . . . , L). To compute the support of candidate itemset C, Alice and Bob need to compute scalar product A1 ∗ A2 ∗ . . . ∗ Am ∗ B1 ∗ B2 ∗ . . . ∗ Bn = X ∗ Y . We have: C.Count = X ∗ Y . In the following we will describe in detail how the two parties Alice and Bob securely compute scalar product X ∗ Y in the condition of preserving respective private information. Based on the computation properties of scalar product, we have P (X) ∗ P (Y ) = X ∗ Y , where P is an arbitrary permutation between X and Y. If Bob sends vector P(Y) to Alice, as the permutation P and vector Y are only known by Bob, the probability for Alice guessing out a certain element order is 1/n and the probability for guessing out all elements order is 1/n!. But for that Alice knows X and P(X), Alice can deduce the permutation P. In order to avoid this problem, we must let Alice know P(X+R) instead of P(X), where R is a random vector generated by Bob and is known only by Bob. For the randomness

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of vector X+R, the probability of Alice guessing out permutation P is 1/n!. To securely get scalar product X ∗ Y Bob sends P(X+R) and P(Y) to Alice, then Alice computes P (X + R) ∗ P (Y ) and sends the result to Bob. Bob computes P (X + R) ∗ P (Y ) − R ∗ Y = P (X) ∗ P (Y ) = X ∗ Y . To further reduce the probability of Alice guessing out a certain elements in Y from P(Y), we randomly partition vector Y into m parts, U1 , . . . , Um , where Y = U1 + . . . + Um . Bob randomly generates a permutation Pi and send Pi (Ui )(i = 1, 2, . . . , m) to Alice. Thus the probability of Alice guessing out the order of a certain element is reduced to only 1/nm . The remained problem is how to make Alice only know P(X+R) without knowing P and R. We propose the following secure vector permutation protocols. Protocol 1: Secure Two-party Vector Permutation Protocols Input: Alice has private vector X. Bob has permutation P and random vector R. Output: Alice gets P(X+R). Begin: 1. Alice generates homomorphic encryption public key and private key pair (e,d), where e(.) is encryption and d(.) is decryption. Then Alice sends public key e to Bob. 2. Alice encrypts vector X with public key e, e(X) = (e(x1 ), . . . , e(xL )) and sends e(X) to Bob. 3. Bob encrypts vector R with public key e, e(R) = (e(r1 ), . . . , e(rL )) and computes e(X) ∗ e(R) = e(X + R). Then Bob performs random permutations on e(X+R) and gets P(e(X+R)). Send P(e(X+R)) to Alice. 4. Alice decrypts the P(e(X+R)) with private key d: d(P(e(X+R))) = P(d(e(X+R))) = P(X+R). End Based on protocol 1 we propose following secure two-party scalar product computation protocol. Protocol 2: Secure Two-party Scalar Product Protocol Input: Alice has private vector X. Bob has private vector Y. Output: Alice gets X ∗ Y . Begin: 1. Bob executes: + . . . + Um . (a) Bob randomly partitions X into m parts, where Y = U1' m (b) Bob generates m random vectors R1 , . . . , Rm . Let w = i=1 Ui Ri . (c) Bob generates m random permutations P1 , . . . , Pm . 2. Alice partitions X into m parts accordingly, where X = V1 + . . . + Vm . 3. For each i = 1, . . . , m, Alice and Bob executes: (a) By performing protocol 1, Alice gets P (Vi + Ri ). (b) Bob sends Pi (Ui ) to Alice. (c) Alice computes s' ∗ P (Vi + Ri ) = Vi ∗ Ui + Ui ∗ Ri . i = Pi (Ui ) ' m 4. Alice computes S = m i=1 si = i=1 Ui ∗ Vi = X ∗ Y + w and send S to Bob. 5. Bob computes S = S − w = X ∗ Y + w − w = X ∗ Y . Bob sends S to Alice. End

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Security Analysis

Applying above protocols, all information Alice can get from Bob is Pi (Ui ) and P (Vi + Ri )(i = 1, . . . , m) besides the final result of scalar product. Since Alice don’t know the random vector generated by Bob, permutation Pi (i = 1, . . . , m) wont be revealed to Alice, neither Ui nor Y. Because the probability of Alice guessing out a element in Y is 1/nm and she must perform guessing on all Pi (Ui ) (i = 1, . . . , m), the probability of Alice retrieving all elements in Y is (1/n!)m. Except for the final result of scalar product, all of Bob can get from Alice is e(X). Because Bob dont know private key,he cant reveals X. So, Alice and Bob can’t know the other’s private vector except the final result of scalar product. For permutation just changed the order of the elements, rather than the value of element, Alice could reveal the sum of elements in Y after she received all Pi (Ui )(i = 1, . . . , m) by the protocols. This is a shortage of the protocols, which need to be overcome in future work. 4.4

Computation and Communication Analysis

The communication cost is 4mnd, where m is security parameter, n is the number of elements in vector and d is the number of binary bits needed to represent any number by cryptosystem. The computation cost is divided into 7 parts: (1) generation of Homomorphic encryption public key pair. (2) generation of m random permutations.(3) 2L encryptions (4)one decryption (5) 3L multiplications (6) 3L additions (7) one subtraction.

5

Conclusions and Future Work

A secure two-party computation protocols for privacy preserving association rule mining based on homomorphic cryptography is presented in this paper. Performing the protocols each party do not need to transfer their data to the trusted third party. Because applying homomorphic cryptographic techniques in secure two-party computation to deal with across parties computation problem, we can guarantee that each party can maintain its data privacy. As a future work, we will study the measurement method for quantitative analysis of the security of secure two-party computation protocols in privacy preserving. The secure two-party clustering and classification also can be developed using protocols presented in this paper.

References 1. Usama Fayyad, Gregory Piatetsky-Shapiro, Padhraic Smyth.: From Data Mining to Knowledge Discovery in Databases, AI Magazine17(3), Fall (1996) 37-54 2. Rakesh Agrawal, Ramakrishnan Srikant.: Privacy-Preserving Data Mining. ACM SIGMOD (2000)439-450

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3. Rakesh Agrawal, Ramakrishnan Srikant.: Fast Algorithms for Mining Association Rules in Large Databases. VLDB (1994) 487-499 4. Paillier,P.: Public-key Cryptosystems Based on Composite Degree Residuosity Classes. IIn Advances in Cryptography-EUROCRYPT99, Prague, Czech Republic,May (1999) 223-233 5. Yao,A.C.: Protocols for Secure Computations. In Proc. Of the 23rd Annual IEEE Symposium on Foundations of computer Science (1982) 6. Goldreich,O.: Secure Multi-party Computation (working draft). http://www. wisdom.weizmann.ac.il/ oded/pp.html (1998) 7. Verykios,V.S., Bertino,E., Fovino,I. N., Provenza,L. P. , Saygin,Y.: Theodoridis State-of-the-art in Privacy Preserving Data Mining. In SIGMOD Record, (2004)http://www.sigmod.org/sigmod/record/issues/0403/ B1.bertion-sigmod-record2.pdf 8. Vaidya,J., Clifton,C.W.: Privacy Preserving Association Rule Mining in Vertically Partitioned Data. In Proceedings of the 8th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, July (2002)23-26, Edmonton,Alberta, Canada 9. Wright,R., Yang, Z.: Privacy-preserving Bayesian Network Structure Computation on Distributed Heterogeneous Data. IIn Proceedings of the 10th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD) (2004) 713-718

QuickBird Panchromatic and Multi-Spectral Image Fusion Using Wavelet Packet Transform Wenjuan Zhang1 and Jiayin Kang2 1

Department of Computer Science, HuiHai Institute of Technology, 222005 Lianyungang, P.R. China [email protected] 2 School of Information Engineering, University of Science and Technology Beijing, 100083 Beijing, P.R. China [email protected]

Abstract. In order to make use of the high spatial information of the QuickBird panchromatic (Pan) images and the essential spectral information of the QuickBird multi-spectral (MS) images, this paper presented a image fusion approach for combining QuickBird Multi-Spectral images with Panchromatic images using wavelet packet transform (WPT). Experimental results shown that the WPT approach performs effectively both in improving the spatial information and in preserving the spectral information.

1

Introduction

QuickBird satellite, launched in October 18, 2001, can currently be acquired in two different modes: the panchromatic mode with high spatial resolution of 0.61m and multi-spectral mode with a four times coarser ground resolution. To make use of QuickBird images, it is important to combine QuickBird MS image and Pan image in the same geographic spatial environment. Digital image fusion is a process of combining a lower spatial resolution digital image with a higher spatial resolution digital image to yield higher spatial resolution in the former image [1] , [2] . Image fusion technique is important for a variety of remote sensing application. Various methods for image fusion have been described earlier [3]. According to their efficiency and implementation, intensity-hue-saturation (IHS) method, principal component analysis (PCA) and Brovey transform (BT) are the most commonly used algorithms in remote sensing community. However, the problem of color distortion appears at the analyzed area after transformed by using these fusion methods [3]. In recent years, the wavelet transform (WT) with multi-resolution decomposition is a relatively popular approach. However, WT decomposes only at low frequency. Therefore, it preserves more spectral information but looses more spatial information [4]. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 976–981, 2006. c Springer-Verlag Berlin Heidelberg 2006


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Compare to WT, wavelet packet transform (WPT) decomposes simultaneously at both high frequency and low frequency [5]. That is, besides decomposes low frequency in a higher scale, WPT decomposes high frequency band in a higher scale too. In this paper, the WPT is applied to QuickBird remote sensing image fusion. Experimental results shown that the WPT performs effectively in QuickBird images fusion.

2

Remote Sensing Image Fusion Using Wavelet Packet Transform

2.1

The Theory of Wavelet Packet Transform

The WPT is a generalization of wavelet decomposition that offers a richer range of possibilities for signal analysis [6]. In wavelet analysis, a signal is split into an approximation and a detail. The approximation is then itself split into a second-level approximation and detail, and the process is repeated. For the n-level wavelet decomposition, there are n+1 possible ways to decompose or encode the signal. Fig. 1 is an example of 2D orthogonal discrete wavelet transform with three level decomposition. Basically, the wavelet decomposition is applied recursively to the scaling space only as follow: V0 = V1 ⊕ W1 = V2 ⊕ W2 ⊕ W1 = V3 ⊕ W3 ⊕ W2 ⊕ W1 = · · · .

(1)

Where ⊕ denotes the union of space (like the union of the sets).

Fig. 1. Wavelet decomposition structure

In multiresolution analysis, L2 (R) =

j∈Z

Wj show that Hilbert space L2 (R)

was decomposed into all orthogonal sum of subspaces (Wj (j ∈ Z)) according to different scaling factor j, where Wj is the closure of wavelet basis function

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φ(t)(wavelet subspace). Wj can be further decomposed according to binary frequency, such that frequency resolution was improved. In order to unify scaling subspace Vj and wavelet subspace Wj , the notations of the new subspace Ujn is introduced as follows: Uj0 = Vj ,

Uj1 = Wj ,

j∈Z.

Hence, the orthogonal decomposition of the Hilbert space L2 (R) can be unified by new subspace Ujn as follows: 0 Uj+1 = Uj0 ⊕ Uj1

j∈Z.

(2)

Define subspace Ujn is the closure space of function Wn (t), and Uj2n is the closure space of function W2n (t). Meanwhile, Wn (t) satisfies the following bi-scaling equation: √ $ g(k)Wn (2t − k) W2n (t) = 2 k∈Z

√ $ W2n+1 (t) = 2 h(k)Wn (2t − k) .

(3)

k∈Z

In EQ. 3, g(k) and h(k) are the low-pass filter coefficient and high-pass filter coefficient respectively, and they satisfy the following relationship: h(k) = (−1)k g(1 − k) . While n = 0 , EQ. 3 be transformed to: √ $ W0 (t) = 2 g(k)W0 (2t − k) k∈Z

√ $ h(k)W0 (2t − k) . W1 (t) = 2

(4)

k∈Z

Compare to the bi-scaling equation required by scaling function and to wavelet basis function in multiresolution analysis $ g(k)ϕ(2t − k) ϕ(t) = k∈Z

φ(t) =

$

h(k)ϕ(2t − k) .

(5)

k∈Z

It is clear that W0 (t) and W1 (t) degenerate into scaling function ϕ(t) and wavelet basis function φ(t) respectively. The sequences {Wn (t) n ∈ Z} is called orthogonal wavelet packet which determined by basis function W0 (t) = ϕ(t) [7]. As shown in Fig. 2, wavelet packet decomposition can be described by a quadtree.

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Fig. 2. Wavelet Packet decomposition chart

2.2

Image Fusion Scheme Using Wavelet Packet Transform

Fig. 3 illustrates the operation flow for fusing the Quickbird Pan image and Ms image by using WPT. The detailed procedures described as follows: First, three new Pan images are produced according to the histogram of R, G, B bands of MS image respectively. Second, WPT was conducted for three both produced Pan images bands and Ms images bands. Furthermore, compare the low frequency components of the decomposed Pan images bands (R, G, B) with that of the decomposed MS images bands (R, G, B) respectively, and then the bigger low frequency was selected as new Pan images bands (R, G, B) respectively. Third, an inverse wavelet packet transform (IWPT) is applied to each of the new Pan images band containing the local spatial details and one of the Ms bands. After three times of IWPT, the high spatial resolution details from the Pan image are injected into the low resolution MS bands resulting in fused high resolution MS bands.

Fig. 3. The flowchart of QuickBird image fusion based on WPT

3

Experiments and Results Evaluation

The approach presented in this paper was applied to QuickBird image database consisting of 6 areas. One of the images fusion was shown in Fig 4.

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Fig. 4. The result of image fusion between QuickBird Pan image and MS image based on WPT. (a) The original Pan image with the resolution of 0.61m, (b) the original MS image with the resolution of 2.44m, (c) merged image

Results Evaluation Considering the drawbacks of the subjective results assessment method, we utilized three existing indices for evaluating the quality of fused images [8]. Information entropy: The expression of the classical information entropy of an image is H=−

L−1 $

Pi lnpi .

i=0

where L denotes the number of gray level, pi equals the ratio between the number of pixels whose gray value equals i(0 ≤ i ≤ L − 1) and the total pixel number contained in an image. Correlation coefficient: The correlation coefficient of two images is often used to indicate their degree of correlation. The correlation coefficient is given by  corr

A B

m n ' '

 =.

(xi,j − µ(A))(x´i,j − µ(B))

j=1 i=1 m n ' '

(xi,j − µ(A))2

j=1 i=1

n ' m '

. (x´i,j − µ(B))2

j=1 i=1

where A and B are two images, xi,j and x´i,j are the elements of the image A and B respectively. µ(A) and µ(B) stand for their mean values. Warping degree: Warping degree represents the level of optical spectral distortion of a multispectral image. Its formula is 1 $$ W = |xi,j − x´i,j | . m × n j=1 i=1 n

m

where xi,j and x´i,j denote the element of the original image and the fused image. The degree of distortion increases, when W increases. The results of evaluation were listed in Table 1. From Table 1, we observed that the values of several quality indices obtained by WPT fusion method are all much larger than those generated by the WT and IHS method.

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Table 1. Evaluation results of WPT, WT and IHS methods Index

WPT

WT

IHS

Information entropy 5.152 4.793 3.834 Correlation coefficient 0.958 0.842 0.831 Warping degree 12.837 10.653 9.775

4

Conclusion

An approach for merging QuickBird high spatial resolution Pan image and Ms image was proposed after analyzing the theory of WPT. The experimental results indicated that this approach performs effectively both in improving the spatial information and in preserving the spectral information. Therefore, the fused image can be interpreted easily.

References 1. James, R.C.: Computational Considerations in Digital Image Fusion via Wavelets. Computers & Geosciences. 31 (2005) 527–530 2. Zhang, Y., Hong, G.: An IHS and Wavelet Integrated Approach to Improve PanSharpening Visual Quality of Natural Color IKONOS and QuickBird Images. Information Fusion. 6 (2005) 225–234 3. Tu, T.M., Su, S.C., Shyu, H.C., Huang, P.S.: A New Look at IHS-Like Image Fusion Methods. Information Fusion. 2 (2001) 177–186 4. Jorge, N., Xavier, O., Octavi, F., Albert, P., Vicenc, P., Roman, A.: MultiresolutionBased Imaged Fusion with Additive Wavelet Decomposition. IEEE Trans. Geosci. Remote Sensing. 37 (1999) 1204–1211 5. Cao, W., Li, B.C., Peng, T.Q.: A Remote Sesing Image Fusion Based on Wavelet Packet Transform. Remote Sensing Technology and Application. 18 (4) (2003) 248– 253 6. Manfred, F., Andreas, U.: Wavelet Packet Image Decomposition on MIMD Architectures. Real-Time Imaging. 8 (2002) 399–412 7. Wang, H.H., Peng, J.X., Wu, W.: Remote Sensing Image Fusion using Wavelet Packet Transform. J. of Image and Graphics. 9 (2002) 932–936 8. Shi, W.Z. , Zhu, C.Q., Tian, Y., Nichol, J.: Wavelet-based Image Fusion and Quality Assessment. Int. J. of Applied Earth Observation and Geoinformation. 6 (2005) 241–251

Satisfaction-Based Selection of XML Documents Sergio Andreozzi1,2 , Paolo Ciancarini1 , Danilo Montesi1, , and Rocco Moretti1,3 1

University of Bologna, Department of Computer Science, 40127 Bologna, Italy {paolo.ciancarini, danilo.montesi, rocco.moretti}@cs.unibo.it 2 Istituto Nazionale di Fisica Nucleare-CNAF, 40127 Bologna Italy [email protected] 3 Dept. of Pure and Applied Mathematics, University of Padova, 35131 Padova, Italy

Abstract. XML documents are becoming the most common approach to represent entities of the real world. Users need to select such entities based on their expectations in terms of both requirements and preferences. The selection process should deal with a potentially high number of documents representing similar entities and with the diversity of the perceived satisfactions of the users. In this paper, we present XMatch, a query language enabling the expression of users requests about the expected satisfaction over XML documents. This language improves the expressiveness of queries and supports aggregation of an high number of elementary satisfactions.

1

Introduction

XML is the de facto standard for exchanging representations of real world entities in the Internet [1]. We consider a mechanism supporting the selection of XML documents representing such entities. In particular, we focus on the users expectations that can be expressed in terms of both requirements and preferences. In our previous work [2], we started by proposing a model for the rigorous representation of entity characteristics, for the association of each of their possible values with the user satisfaction and for the aggregation of the single satisfactions in an overall score using a particular logic. In this paper, we describe XMatch, a query language enabling the expression of the user requirements and preferences based on the model defined in [2]. This language is inspired by XQuery [3] reusing a set of constructs useful for our goal and providing clauses based on our model. The application of XMatch to generic XML documents is also depicted by means of an application scenario. The paper is structured as follows: in Section 2, we introduce the XMatch language; in Section 3, we describe a generic application scenario; in Section 4, we present related works; finally, in Section 5, we draw up our conclusions.


Partially funded by PRIN Project “Middleware basato su Java per la fornitura di servizi interattivi di TV digitale”.

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 982–989, 2006. c Springer-Verlag Berlin Heidelberg 2006


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The XMatch Language

In this section, we present the XMatch language enabling to express queries over XML-based representations of generic entities. It offers the capability of describing the satisfaction degree that a user perceives as regards the possible values of the attributes of interest. The grammar rules are given only for symbols starting with the prefix XM, while the other symbols are taken from the XQuery W3C specification [3]. For a complete presentation of the language see [4]. 2.1

The Main Clause

The core part of the XMatch language is an expression defined in the grammar by the symbol XMExpr as follows: Grammar 1 XMExpr ::= XMForClause XMLetClause+ XMWhereClause XMReturnClause

The rule defining this symbol is inspired by the FLWOR (For-Let-Where-Order by-Return) expression of the XQuery language [3]. The first clause of this expression generates an ordered sequence of tuples of bound variables called the tuple stream (XMForClause). For each set of bound variables generated in this step, the second clause (XMLetClause) enables to bound one or more variables to the value returned by an elementary criterion of satisfaction (see [2] for a presentation of this concept) as regards elements belonging to the tuple stream. The third clause (XMWhereClause) enables to associate each variable defined in the second clause with a relevance category, thus defining the aggregation pattern. The fourth and last clause (XMReturnClause) is used to return the result as an XML document and allows to select a subset of solutions based on their overall satisfaction. 2.2

Generation of the Tuple Stream

As stated above, the XMForClause generates an ordered sequence of tuples of bound variables, called the tuple stream. This is a simplified version of the XQuery ForClause where only the basic constructs are maintained to select elements from an XML document and to generate the streams of the possible solutions by using the join capability. For each XMatch expression, only one XMForClause is allowed with one or more variables to be bound to different types of nodes. The URILiteral is defined in the XQuery specification and should refer to a URI that can be resolved to a file containing the data in XML format from which the set of important fragments are extracted. The OrExpr is also part of the XQuery specification. Grammar 2 XMForClause XMDocCall XMPathExpr XMPredicate

::= ::= ::= ::=

VarName "in" XMDocCall ("," "$" VarName "in" XMDocCall)* "doc(" URILiteral ")" XMPathExpr? XMPredicate? ( "/" QName )* ( "/" "@" QName )? "[" OrExpr "]"

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Expressing the Satisfaction

We describe the XMLetClause as the essential construct for defining a single elementary criterion of satisfaction. The three main categories are supported: an enumeration of all possible values returned by a measurement of an attribute, an absolute classification of these values and a relative classification [5]. Grammar 3 XMLetClause ::= "let" ( "$" VarName ":=" ( XMSimpleEnum | XMCompEnum | XMRange ) ) XMSimpleEnum ::= XMPathExpr ValueComp XMElement "satisfies" XMSatLiteral ( "," XMElement "satisfies" XMSatLiteral )* XMCompEnum ::= XMPathExprList ValueComp XMElementList "satisfies" XMSatLiteral ( "," XMElementList "satisfies" XMSatLiteral )* XMRange ::= XMPathExpr "in" XMElement "to" XMElement "satisfies" ( "with" "linear" "increment" | "with" "linear" "decrement" | "with" "around" | "not" "around" ) XMPathExprList ::= "(" XMPathExpr ( "," XMPathExpr )+ ")" XMElementList ::= "(" XMElement ( "," XMElement )+ ")" XMElement ::= ( Literal | XMPathExpr | XMAggregation ) XMSatLiteral ::= ("0"? "." Digits | "1" ) XMAggregation ::= ( "max"|"min"|"avg"|"sum"|"count" ) XMPathExpr ::= ( "/" QName )* ( "/" "@" QName )?

The values that are input for an elementary criterion of satisfaction are determined by a simplified XPath expression (XMPathExpr). A step in this expression consists only of a child forward step in its abbreviated form with a name node test according to the definitions given in the XPath 2.0 specification [6]. As stated in this specification, the result of an XPath expression is any sequence allowed by the data model. An important characteristic introduced by the new data model [8] is that there is no distinction between an item (i.e., a node or an atomic value) and a singleton sequence containing this item (i.e., an item is equivalent to a singleton sequence containing the item and vice versa). XMatch only admits as result of an XMPathExpr expression a sequence of atomic values. Besides, we have to specify how an elementary criterion of satisfaction is applied to such a type of result. Given the simplified path expression, the resulting sequence is composed by elements with the same qualified name at the same distance from the root node in the XML document. 2.4

Classifying the Satisfactions by Relevance

We explain how the association of an elementary satisfaction to a relevance category (see [2] for a presentation of this concept) is modeled in the XMatch language. Potentially, the relevance categories can be infinite, but only three of them are introduced as they are sufficient for meaningful use cases. They are defined in the XMatch language grammar by using the following string literals: essential, desirable and optional. The advantage of such a definition is the improvement of the legibility of XMatch queries. A possible approach to generalize the language to an high number of relevance categories is to use natural numbers to label them. The lower is the natural number associated to a relevance category, the more important is the satisfaction.

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Grammar 4 XMWhereClause ::= "where" ( ( XMRelevanceSubj ( "essential" | "desirable" | "optional" ) ) ( XMRelevanceSubj "essential" and XMRelevanceSubj "desirable") ( XMRelevanceSubj "essential" and XMRelevanceSubj "optional") ( XMRelevanceSubj "desirable" and XMRelevanceSubj "optional") ( XMRelevanceSubj "essential" and XMRelevanceSubj "desirable" and XMRelevanceSubj "optional") ) XMRelevanceSubj ::= ( "$" VarName "is" | XMVarNameList "are" ) XMVarNameList ::= "(" "$" VarName ( "," "$" VarName )+ ")"

| | | |

Given a set of XMLetClause expressions defining elementary satisfactions, each of them can be associated to a relevance category by using the XMWhereClause (see Example 1). This provides the meaningful information for building the aggregation pattern (see [2] for a presentation of this concept). Example 1. where ( $e1, $e2 ) are essential and $e3 is desirable

Weight and power parameters used in the aggregation pattern are considered to be part of the query processor. 2.5

Constructing the Result

We describe how the result of the query is constructed and returned. The decision is to define a clause that does not provide any transformation capability. The transformation of the result can be achieved by adding a postprocessing phase using languages like XQuery or XSLT. The XMReturnClause returns an XML document with a predefined structure as presented in Example 2. Example 2. ... ...

Each Result element contains a set of elements as generated by the XMForClause and an E attribute with the overall satisfaction associated to the solution. These elements are returned following a decreasing order with respect to the value of E. Moreover, the number of results can be limited in two ways: by asking the ‘Top K’ results and by dropping all solutions that do not reach a minimum overall satisfaction. Grammar 5 XMReturnClause ::= "return" "top" digits ( "with threshold" XMSatLiteral )?

3

An Application Scenario

In this section, we present a generic example to show how the XMatch language can be used. We consider an XML document having a structure given in Figure 1. In this document, two sets of different entities are represented: the

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T

A

A

B 9

B 5

C 5

B 3

B 10 C 28

P

P

Q 5

R 2

R 7

Q 8

R 9

R 4

Fig. 1. Tree view of the XML document (for each node, the left side contains the element QName and the right side contains the element value) Table 1. Elementary satisfactions and overall score Solution /T/A[2], /T/P[2] /T/A[1], /T/P[2] /T/A[2], /T/P[1] /T/A[1], /T/P[1]

ess E e1 e3 0.940 1 1 0.930 0.75 1 0.654 1 0 0.649 0.75 0

des e4 0.8 0.8 0.9 0.9

opt e2 0 1 0 1

entity A having the properties B and C; the entity P having the properties Q and R. Let us consider a user that requires an entity A and an entity P. For the entity A, the expectations can be synthesized as follows: the property B provides an increasing satisfaction for values starting from 6 up to 10, the property C provides a full satisfaction when the value is 5, while it provides a lower satisfaction for the value 7. For the entity P, the expectations can be synthesized as follows: the property Q provides a full satisfaction for the value 8 and it linearly decreases to 0 for values down to 6 or up to 10, the property R provides a linearly increasing satisfaction starting from the value 0 up to the value 20. For all other possible values, the satisfaction is equal to 0. The satisfactions related to the properties B and Q are reputed to be essential, the satisfactions related to the property R is is reputed to be desirable, finally the satisfaction related to the property C is reputed to be optional. These user expectations are expressed in the following XMatch query: for $A in doc("data.xml")/T/A, $P in doc("data.xml")/T/P, let $e1 := $A/B in 6 to 10 satisfies with linear increment let $e2 := $A/C eq 5 satisfies 1, 7 satisfies 0.7 let $e3 := $P/Q in 6 to 10 satisfies with around let $e4 := $P/R in 0 to 20 with linear decrement where ( $e1, $e3 ) are essential and $e4 is desirable and $e2 is optional return top 10 with threshold 0.6

Each let clause is used to express an elementary criterion of satisfaction, while the where clause describes a specific instance of the general aggregation pattern given in [2]. In Table 1, we report both the elementary satisfactions (e1, e2, e3 and e4) and the overall score (E) as resulting by the application of the method proposed in [2] mapped into XMatch. Such values have been computed by using the prototype implementation of an XMatch query engine that relies on the mapping into XQuery [?].

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Related Work

The problem of extending the expressiveness of query languages in order to consider not only user requirements, but also user preferences has been faced in different domains. In the context of Grid systems, a meaningful approach for the selection of services [9] is based on the Classified Advertisement (ClassAd) language [10,11]. This language has been designed in the context of the Condor distributed computing system [12] where it is used for discovery and allocation of resources. Its use consists of the following phases: (1) providers of computing resources submit advertisements describing their capabilities and declaring constraints and preferences for jobs that they are willing to run (constraints are boolean expressions involving constants or ClassAd attributes, while preferences are encoded in a rank that consists in defining an arithmetic expression synthesizing values used for sorting the services satisfying the constraints); (2) consumers submit advertisements describing their jobs and the desired execution environment in terms of constraints and preferences; (3) a matchmaker process matches the resource and consumer request advertisements. As regards this work, we observe that in general it is difficult to define a rank expression aggregating values from different attributes. Two important works in the databases community are proposed by Chomicki and Kießling. Chomicki describes a logical framework for formulating preferences as strict partial orders by using arbitrary logical formulas [13]. In order to embed such formulas into relation algebra, a single winnow operator that can be parameterized by a preference formula was defined. This enables the rewriting of preference formulas as SQL queries. Our language is targeted at semi-structured data and our approach has been to define a new language. As regards this work, we observe that the theoretical preference framework is mapped into the relational data model and the SQL query language. Kießling proposed a formal language for formulating preference queries based on the Best-Matches-Only (BMO) query model [14,15]. It developed a set of constructors and combinators that can be used to write preference expressions. An algebra modeling such operators was defined and extensions for both SQL (Preference SQL [16]) and XPath (Preference XPath [17]) were proposed. In our work, we focused on the XML data model and we have proposed a new language based on XQuery. Concerning this work, the theoretical preference framework is mapped into 1) the relational data model and the SQL query language and 2) the XML data model and XML path language (XPath).

5

Conclusion

In this paper, we have presented a query language enabling the expression of the user requirements and preferences over generic entities represented by means of XML documents. This language supports the mapping of attributes values into elementary satisfactions, the categorization of such satisfactions by relevance

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and the computation of an overall score. Such a score can be used to rank the various proposals and to identify the most satisfying solution as regards the users expectations. The simultaneous selection of a set of different entities is also supported. Ongoing work is targeted at completing the XMatch engine based on rewriting techniques that translate XMatch into XQuery. By this engine, we will analyze both benefits and performance issues in various application scenarios (e.g., Grid systems). Finally, the prototyping of a native XMatch engine considering optimization aspects that are specific for this language can be achieved.

References 1. Bray, T., Paoli, J., Sperberg-McQueen, C.M., Maler, E., Yergeau, F., Cowan, J.: Extensible Markup Language (XML) 1.1. W3C Recommendation 4 Feb (2004) 2. Andreozzi, S., Ciancarini, P., Montesi, D., Moretti, R.: An approach to the quantitative evaluation of grid services. To appear in Journal of Concurrency and Computation: Practice and Experience (2005) DOI: 10.1002/cpe.978 3. Boag, S., Chamberlin, D., Fernndez, M., Florescu, D., Robie, J., Simeon, J.: XQuery 1.0: An XML Query Language. (W3C Working Draft, 11 February (2005)) 4. Andreozzi, S., Montesi, D., Moretti,R.: XMatch: a Language for Satisfactionbased Selection of Grid Services. Scientific Programming Journal, Special Issue on Grids and Worldwide Computing, IOS Press, IOS Press, (2005) 299-316 5. Dujmovic, J.: A method for evaluation and selection of complex hardware and software systems. In: Proceedings of the International Conference for the Resource Management and Performance Evaluation of Enterprise Computing Systems (CMG96), San Diego, CA, USA, Dec 1996. Volume 1. (1996) 368–378 6. Berglund, A., Boag,S., Chamberlin, D., Fern´ andez, M.F., Kay, M., Robie,J., Sim´eon, J.: XML Path Language (XPath) 2.0. W3C Candidate Recommendation, Nov (2005) 7. Fern´ andez, M., Malhotra, A., Marsh, J., Nagy, M., Walsh,N.: XQuery 1.0 and XPath 2.0 Data Model. W3C Candidate Recommendation, Nov (2005) 8. XMatch2XQuery prototype implementation. http://www.cnaf.infn.it/∼andreozzi/research /xmatch/software/. May (2006) 9. Prelz, F. et Al.: Pratical Approaches to Grid Workload and Resource Management in the EGEE Project. In: Proceedings of the Conference on Computing in High Energy and Nuclear Physics (CHEP 2004), Interlaken, Switzerland. (2004) 10. Solomon, M.: The ClassAd language reference manual. Computer Sciences Department, University of Wisconsin, Madison, WI, Oct (2003) 11. Litzkow, M. J., Livny, M., Mutka, M. W.: 2003, ‘Policy Driven Heterogeneous Resource Co-Allocation with Gangmatching’. In: Proceedings of the 12th IEEE International Symposium on High-Performance Distributed Computing (HPDC 2003), Seattle, WA, USA, June (2003) 12. Litzkow, M., Livny, M., Mutka, M. W.: 1988, Condor - a Hunter of Idle Workstations. In: Proceedings of the 8th International Conference on Distributed Computing Systems (ICDCS 1988), San Jose, CA, USA, June (1988) 13. Chomicki, J.: Preference Formulas in Relational Queries. ACM Transaction on Database Systems, 28(4) (2003) 427–466

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14. Kießling, W.: Foundations of Preferences in Database Systems. In Proceedings of the 28th Very Large Database System (VLDB) Conference, Hong Kong, China, (2002) 15. Hafenrichter, B., Kießling, K.: Optimization of Relational Preference Queries. In Proceedings of the 16th Australasian Database (ADB05) Conference, Newcastle, Australia, (2005) 16. Kießling, K., K¨ ostler, G.: Preference SQL - Design, Implementation, Experiences. In Proceedings of 28th International Conference on Very Large Databases (VLDB), Hong Kong, China, Aug (2002) 17. Kießling, W., Hafenrichter, B., Fischer, S., Holland, S.: Preference XPATH: a Query Language for E-Commerce. In Proceedings of 5th Internationale Tagung Wirtschaftsinformatik, Augsburg, Germany, Sep (2001)

An Adaptive Error Detection-Recovery QOS for Intelligent Context-Awareness: AEDRQ Eung Nam Ko Department of Information & Communication, Baekseok University 115, Anseo-Dong, Cheonan, ChungNam, 330-704, Korea [email protected]

Abstract. This paper presents the design of the AEDRQ(An Adaptive Fault Tolerance QOS), which is running on RCSM(Reconfigurable Context Sensitive Middleware) for ubiquitous networks. The AEDRQ model is proposed for supporting QoS resource errors detection-recovery in the situation-aware middleware. The AEDRQ model captures the relationships between application missions, actions, QoS requirements, and resources under dynamically changing situations. A resource error detection-recovery algorithm using the AEDRQ model is suggested. We present the utility of the AEDRQ model in a QoS resource error detection-recovery example of the VOD system. We are in process of constructing middleware components such as Resource Agent, Resource Monitoring Agent, and fault tolerance QoS Agent using the error detection-recovery model and its specification. To ensure required reliability of multimedia communication systems, AEDRQ consists of 3 steps that are an error detection, an error classification, and an error recovery.

1 Introduction The development of middleware is closely related to the evolution of ubiquitous computing began in the mid of 1970s, when the PC first brought computers closer people. With the advent of networking, personal computing evolved into distributed computing. With seamless access and World Wide Web, distributed computing marked a next step toward pervasive computing, and mobile computing emerged from the integration of cellular technology with the Web. The “anytime anywhere” goal of mobile computing is essentially a reactive approach to information access, and it prepare the way for pervasive computing’s proactive ”all the time everywhere” goal[1,2]. Context awareness(or context sensitivity) is an application software system’s ability to sense and analyze context from various sources; it lets application software take different actions adaptively in different contexts[3]. In a ubiquitous computing environment, computing anytime, anywhere, any devices, the concept of situation-aware middleware has played very important roles in matching user needs with available computing resources in transparent manner in dynamic environments [4,5]. Although the situation-aware middleware provides powerful analysis of dynamically changing situations in the ubiquitous computing environment by synthesizing multiple contexts and users’ actions, which need to be analyzed over a D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 990 – 999, 2006. © Springer-Verlag Berlin Heidelberg 2006

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period of time, it is difficult to analyze reliable Quality of Service (QoS) of situationaware applications because the relationship between changes of situations and resources required to support the desired level of reliable QoS is not clear. Thus, there is a great need for situation-aware middleware to be able to predict whether all faulttolerance QoS requirements of the applications are satisfied and analyze tradeoff relationships among the fault-tolerance QoS requirements, if all fault-tolerance QoS requirements cannot be satisfied to determine a higher priority of fault-tolerance QoS requirements. In this paper, a QoS resource error detection-recovery model called “AEDRQ” is proposed for situation-aware middleware. To perform the QoS resource error-recovery, the AEDRQ model effectively captures relationships among missions (application capability requirements), fault-tolerance QoS constraints, actions (object method calls in object-oriented software development), and resources (e.g., hardware, software, network, and data resources). Section 2 describes related works as middleware for context awareness in ubiquitous computing environments. Section 3 denotes Reconfigurable Context-Sensitive Middleware (RCSM)., the AEDRQ architecture, and algorithm. Section 4 describes simulation results of our proposed AEDRQ model. Section 5 presents conclusion.

2 Related Works The Context Toolkit was built based on this conceptual framework. There were five applications that were built to assess the actual benefits of the Context Toolkit. Seminal work has been done by Anind Dey, et al. [6] in defining context-aware computing, identifying what kind of support was required for building context-aware applications and developing a toolkit that enabled rapid prototyping of context-aware applications. They have laid out foundations for the design and development of context-aware applications by proposing a conceptual framework. The proposed conceptual framework separates concerns between context acquisition and the use of context in applications, to provide abstractions that help acquire, collect and manage context in an application independent fashion and identify corresponding software components. In the Context Toolkit, a predefined context is acquired and processed in context widgets and then reported to the application through application-initiated queries and callback functions. In this Reconfigurable Context-Sensitive Middleware(RCSM), Stephen S. Yau et al. [3] proposed a new approach in designing their middleware to directly trigger the appropriate actions in an application rather than have the application itself decide which method(or action) to activate based on context. Their motivation was to extend existing context-sensitive applications by adding new context sources and to easily let multiple concurrent contexts trigger a specific action. They already build a Smart Classroom to validate this RCSM model. RCSM provides an Object-based framework for supporting context-sensitive applications. Anand Ranganathan et al. [7] have built a middleware for developing context-aware applications. This middleware is integrated into their infrastructure for Smart Spaces named GAIA. The middleware is based on a predicate model of context. This model enables agents to be developed that either use rules-based or machine learning approaches to decide their behavior in different contexts.

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With the proposed conceptual framework for building context sensitive applications and the Context Toolkit laid a foundation for context ware middleware to develop. However, while the Context Toolkit does provide a starting point for applications to make use of contexts, its middleware paradigm still forces programmers to think about how to deal with the context widget for the appropriate contextual information. In general these projects do not provide much help on how to reason about contexts. They provide reusable sensing mechanisms but lack of reusable reasoning mechanisms. They do not provide any generic mechanism for writing rules about contexts, inferring higher-level context or organizing the wide range of possible contexts in a structured format [6]. RCSM has laid a further step towards middleware models that fully support for context awareness. RCSM deals with contexts dynamically and let context-sensitive application developers focus on implementing the actions in their favorite language without worrying about details of getting contextual information from different sources. While RCSM uses contextual information dynamically, it does not provide reasoning and/or learning mechanism to help agents reason about context appropriately [3]. The middleware paradigm for context awareness agents implemented in GAIA infrastructure provides a more generic way of specifying the behavior of context-aware-ness applications using different reasoning and learning mechanism. Since all the terms used in the environment are defined in the ontology, it is easy to frame rules for inferring contexts based on these terms. The developers do not have to worry about not using inappropriate terms or concepts, since they can refer to the definitions I the ontology when in doubt [7].

3 The AEDRQ Model Based on RCSM The overview of the RCSM is described in section 3.1. The conceptual architecture of the AEDRQ model is described in section 3.2, and its environment is proposed in section 3.3. Its algorithm is presented in section 3.4. 3.1 Reconfigurable Context-Sensitive Middleware (RCSM) Figure 1 shows how all of RCSM’s components are layered inside a device. All of RCSM’s components are layered inside a device. The Object Request Broker of RCSM (R-ORB) assumes the availability of reliable transport protocols; one R-ORB per device is sufficient. The number of ADaptive object Containers (ADC)s depends on the number of context-sensitive objects in the device. ADCs periodically collect the necessary “raw context data” through the R-ORB, which in turn collects the data from sensors and the operating system. Initially, each ADC registers with the R-ORB to express its needs for contexts and to publish the corresponding context-sensitive interface. RCSM is called reconfigurable because it allows addition or deletion of individual ADCs during runtime (to manage new or existing context-sensitive application objects) without affecting other runtime operations inside RCSM. Ubiquitous applications require use of various contexts to adaptively communicate with each other across multiple network environments, such as mobile ad hoc networks, Internet, and mobile phone networks. However, existing context-aware

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techniques often become inadequate in these applications where combinations of multiple contexts and users’ actions need to be analyzed over a period of time. Situation-awareness in application software is considered as a desirable property to overcome this limitation. In addition to being context-sensitive, situation-aware applications can respond to both current and historical relationships of specific contexts and device-actions. An example of SmartClassroom is illustrated in [3]. However, it did not include fault-tolerance QoS support in the architecture. In this paper, we focus on how to represent fault-tolerance QoS requirements in situationaware middleware as RCSM.

Situation-Aware Application Objects RCSM

Optional Components RCSM Ephemeral Group Communication Service

Other Services

O S

Core Components Adaptive Object Containers (ADCs) [Providing awareness of situation] RCSM Object Request Broker (R-ORB) [Providing transparency over ad hoc communication]

Transport Layer Protocols for Ad Hoc Networks

Sensors

Fig. 1. RCSM’s integrated components

3.2 Conceptual Architecture of the AEDRQ Model We will present a conceptual model for fault-tolerance QoS requirements representation in situation-aware middleware. Our proposed AEDRQ model aims at supporting adaptive fault-tolerance QoS requirements defined in application-level missions described by a set of actions of objects by reserving, allocating, and reallocating necessary resources given dynamically changing situations. A high-level AEDRQ conceptual architecture to support adaptive fault-tolerance QoS requirements is shown in Figure 2. SA (Situation-aware Agent), RA(Resource Agent), and FTQA(Fault-Tolerance QoS Agent) are the main components shown in SituationAware Middleware box in Figure 2. Applications request to execute a set of missions to Situation-aware Middleware with various QoS requirements. A SA analyzes and

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synthesizes context information (e.g., location, time, devices, temperature, pressure, etc.) captured by sensors over a period of time, and drives a situation. A RA simultaneously analyzes resource availability by dividing requested resources from missions (i.e., a set of object methods, called actions) by available resources. It is also responsible for monitoring, reserving, allocating and deallocating each resource. Given the driven situations, A FTQA controls resources when it met errors through the RA to guarantee requested fault-tolerance QoS requirements. If there are some error resource due to low resource availability, FTQA performs QoS resource error detection-recovery. RA resolves the errors by recovering resources for supporting high priority missions. To effectively detect and recover an error for fault-tolerance QoS, we need to capture the relationships between mission, actions, its related fault-tolerance QoS requirements, and resources.

<Applications> Mission1

<Sensor>

Mission2

Situation 1

Missin n

Situation 2 <Situation-Aware Middleware> Situation-aware Agent

Action1 +QoS1

Situation n Resource Agent

Action n + QoSn Fault-Tolerance QoS Agent



R e s o u r c e 1

R e s o u r c e 2

R e s o u r c e n

Fig. 2. Conceptual Architecture of Our Proposed AEDRQ Model

3.3 An Environment of the AEDRQ Model The access requires situation-aware fault-tolerance QoS, in which the different faulttolerance can be automatically enforced according to different situations such as

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wired or wireless network environment. For example, a user issues a mission specified by Situation-aware IDL(Interface Definition Language) to watch a VOD movie service in his/her handheld device (e.g., smart phone) on street. When the user arrives at his/her home, the Situation-aware Manager captures the change of situation (e.g., location, device, and network) through sensors and transfers the VOD service continually and seamlessly from the wireless handheld device into a digital, wiredhome-networked TV set. IBM’s TSpace is used as a backbone network and Java-code phone and Desktop Computers(TV emulators) are used for demonstration. The VOD movie doesn’t restart from the beginning. With a click, the transition into another situation (i.e., from a wireless handheld device to a wired TV set) doesn’t disrupt the VOD service (non-stop VOD service). It is an example of the AEDRQ model to support non-stop VOD service from situation 1 (Location = “on street” ^ Device = “handheld” ^ network = “wireless”) into situation 2 (Location = “home” ^ Device = “Desktop Computers” ^ network = “wired”). The VOD service is initiated by the Wireless-VODservice mission. At first, the actions, related with Wireless-VODservice mission such as A11, A12, etc, are triggered by situation1. These actions make VODserver1 provide the VOD service to VOD-client1 using the related resources with satisfying two constraints, Fault-toleranceQoS1 and FramesPerSecond1. The FaulttoleranceeQoS1 constraint is forced on Error-Detection/Error-Recovery to execute error-detection at the VOD-server1 before the VOD data transmission and to execute error-recovery at the VOD-client1 just after receiving the VOD data. Since the situation-aware, adaptive VOD service mission is changed from wireless to wired network, situation2 is created and the actions for Wired-VODservice are triggered. The Fault-toleranceQoS2 and FramesPerSecond2 constraints are enforced when the actions are executed. 3.4 Algorithm of the AEDRQ Model To ensure required reliability of multimedia communication systems based on situation-awareness middleware, AEDRQ consists of 3 steps that are an error detection, an error classification, and an error recovery. AEDRQ consists of EDA(Error Detection Agent) and ERA(Error Recovery Agent). EDA consists of ED(Error Detector), EC(Error Classifier) and EL(Error Learner). EDA is an agent which plays a role in detecting, and classifying errors. ED is an agent which plays a role as an interface to interact among an application, EC and EL. As shown in figure 3, ED has functions which detect an error by using hooking techniques. EDA detects an error by using hooking methods in MS-Windows API(Application Program Interface). When an error occurs, A hook is a point in the Microsoft Windows message-handling mechanism where an application can install a subroutine to monitor the message traffic in the system and process certain types of messages before they reach the target window procedure. Windows contains many different types of hook. The roles of error and application program sharing are divided into two main parts; Abstraction and sharing of view generation. Error and application program sharing must take different from each other according to number of replicated application program and an event command. This proposed structure is distributed architecture but for error and application program sharing, centralization

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architecture is used. As shown in Fig.3, error and application program sharing windows perform process communication of message form. In the middle of this process, there are couple ways of snatching message by error and application sharing agent. ED informs EC of the results of detected errors. ED inspects applications by using hooking techniques to find an error. EC and EL deal with learning in reactive multi-agent systems. Generally, learning rules may be classified as supervised or unsupervised. KB has a registration information of creation of service handle and session manager handle by Daemon and GSM. EC can decide whether it is hardware error or software error based on learning rules by EL. In case of hardware error, it cannot be recoverable. In case of software error, it can be recoverable. This approach is based on the idea of comparing the expected error type which is generated by an EL with the actual error occurred from sites.

G G

hook table

<ES>

application

Event Distributer

G G G

Filter function

G G G G G G

Network

view /event

<ES>

view/event <ES>

Virtual app.

Virtual app.

Filter func.

Filter func.

G G

Fig. 3. Error and Application Sharing Process

4 Simulation Results To evaluate the performance of the proposed system, an error detection method was used to compare the performance of the proposed model against the conventional model by using DEVS formalism[8], [9], [10], [11], [12]. (Simulation 1) In the first simulation, we have considered composition component as shown in Table 1. The atomic models are EF, RA1, and ED1. The combination of atomic models makes a new coupled model. First, it receives input event, i.e., polling interval. The value is an input value in RA1. An output value is determined by the time related simulation process RA1. The output value can be an input value in ED1. An output value is determined by the time related simulation process ED1. We can observe the result value through transducer.

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Table 1. Atomic Model and State Variable

Component EF(genr) RA1

ED1

State Variable Poll_int Ra_re_time App_cnt Ra_re_t_a Tat_t_a

Contents Polling interval Response time The number of application program Accumulated response time RAaccumulated response time

(Simulation 2) In the second simulation, we have considered composition component as shown in Table 2. The atomic models are EF, RA2, and ED2. The combination of atomic models makes a new coupled model. First, it receives input event, i.e., polling interval. The value is an input value in RA2. An output value is determined by the time related simulation process RA2. The output value can be an input value in ED2. An output value is determined by the time related simulation process ED2. We can observe the result value through transducer. Table 2. Atomic Model and State Variable

Component EF (genr) RA2

State Variable Poll_int

Contents

Ra_re_time App_cnt

Response time The number application program Accumulated time RAaccumulated time

Ra_re_t_a ED2

Tat_t_a

polling interval

of response response

We can observe the following. The error detected time interval is as follows. Conventional method: 2*Poll_int* App_ cnt Proposed method: 1*Poll_int Therefore, proposed method is more efficient than conventional method in error detected method because of App_cnt >= 1. We have compared the performance of the proposed method with conventional method.

5 Conclusion RCSM provides standardized communication protocols to interoperate an application with others under dynamically changing situations. Since the application needs of

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middleware services and computing environment (resources) keep changing as the application change, it is difficult to analyze: whether it is possible that all faulttolerance QoS(Quality of Service) requirements are met, and what fault-tolerance QoS requirements have tradeoff relationships. In this paper, we propose a faulttolerance QoS resource model called “AEDRQ” for RCSM. An adaptive VOD(Video On Demand) system, is used as an illustrative example of the AEDRQ model and its resource error detection-recovery.The AEDRQ model is proposed for supporting QoS resource errors detection-recovery in the situation-aware middleware. The AEDRQ model captures the relationships between application missions, actions, QoS requirements, and resources under dynamically changing situations. A resource error detection-recovery algorithm using the AEDRQ model is suggested. We present the utility of the AEDRQ model in a QoS resource error detection-recovery example of the VOD system. We are in process of constructing middleware components such as Resource Agent, Resource Monitoring Agent, and fault tolerance QoS Agent using the error detection-recovery model and its specification. To ensure required reliability of multimedia communication systems, AEDRQ consists of 3 steps that are an error detection, an error classification, and an error recovery. This approach has no consideration of domino effect between processes. And we remain simulations for fault-tolerance QOS based on RCSM and QoS resolution strategies for fault-tolerance QOS based on GAIA projects as future work.

Acknowledgement I would like to thank Dr. Hoh Peter In for precious comments and suggestions.

References 1. Satyanarayanan, M.: Pervasive Computing: Vision and Challenges. Personal Communications, IEEE[see also IEEE Wireless Communications, IEEE], 8 (2001) 10-17 2. Saha, D.; Mukherjee, A.: Pervasive &omputing: A Paradigm for the 21st Century. IEEE Computer, 36 (2003) 25-31 3. Yau, S., Karim, F., Wang, Y., Wang, B., Gupta, S.: Reconfigurable Context-Sensitive Middleware for Pervasive Computing. IEEE Pervasive Computing, 1(3) (2002) 33-40 4. Yau, S. S., Karim, F.: Adaptive Middleware for Ubiquitous Computing Environments. Design and Analysis of Distributed Embedded Systems, Proc. IFIP 17th WCC, 219 (2002) 131-140 5. Yau, S. S., Karim, F.: Contention-Sensitive Middleware for Real-time Software in Ubiquitous Computing Environments. Proc. 4th IEEE Int’l Symp. on Object-Oriented Realtime Distributed Computing (ISORC 2001) (2001) 163-170 6. Dey, A.K., et al.: A Conceptual Framework and a Toolkit for Supporting the Rapid Prototyping of Context-Aware Applications. anchor article of a special issue on ContextAwareness Computing, Human-Computer Interaction HCI Journal, (2001) http://www.cc.gatch.edu/fce/contexttoolkit 7. Ranganathan, A., Campbell, R.H.: A Middleware for Context-Aware agents in Ubiquitous Computing Environments. GAIA Project (2003). http://choices.cs.uiuc.edu/gaia/papers/

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8. Zeigler, B.P., Cho, T.H., Rozenblit, J.W.: A Knowledge-Based Simulation Environment for Hierarchical Flexible Manufacturing. IEEE Transaction on Systems, Man, and Cybernetics-Part A: System and Humans, 26(1) (1996) 81-90 9. Cho, T.H., Zeigler, B.P.: Simulation of Intelligent Hierarchical Flexible Manufacturing: Batch Job Routing in Operation Overlapping. IEEE Transaction on Systems, Man, and Cybernetics-Part A: System and Humans, 27(1) (1997) 116-126 10. Zeigler, B.P.: Object-Oriented Simulation with Hierarchical, Modular Models. Academic Press, (1990) 11. Zeigler, B.P.: Multifacetted Modeling and Discrete Event Simulation. Orlando, FL: Academic, (1984) 12. Zeigler, B.P.: Theory of Modeling and Simulation. John Wiley, NY, USA, (1976), reissued by Krieger, Malabar, FL, USA, (1985)

An Efficient Method to Find a Shortest Path for a Car-Like Robot Gyusang Cho1 and Jinkyung Ryeu2,* 1

Dept. of Computer Eng., Dongyang Univ., Youngju, Korea [email protected] 2 Dept. of IT Electronic Eng., Dongyang Univ., Youngju, Korea [email protected]

Abstract. This paper proposes new formulae for Dubins’ CSC family to find the shortest smooth path between the initial and final configurations of the carlike robot. The formulae are used for finding connection points explicitly between the circle of the initial configuration and the straight line segment, and the connection point of the straight line segment and the circle of the final configuration. Fast finding the connection points(C S and S C) are very useful for a real application. The formulae have simple forms mainly because they are transformed to the origin of their original configuration, and then they are converted to standard forms which are the representative configurations of type LSL and LSR, respectively. And a simple criterion for classifying 4 types of CSC, which are necessary for deciding any type of CSC prior to the conversion to the standard form, is presented.

˧

˧

1 Introduction The classical result by Dubins[1] gives a sufficient set of paths which always contains the optimal path for a car-like mobile robot that only moves forwards from an initial position to a target position. He showed that any shortest path of the car-like mobile robot consists of exactly three path segment which are either arcs of circles of radius or straight line segments. Melzak[2], Robertson[3], and Cockayne and Hall[4] studied the accessibility regions in which the robot can reach, but all these works do not concentrate on optimality of the paths. Bui et. al.[5] proposed the synthesis problem for a car-like robot only moving forward in a plane. Then Boissonnat and Bui[6] considered that the partition of the plane w.r.t. the types of the optimal paths and found the shapes of the shortest path accessibility regions for a car that only moves forwards along optimal paths. Reed and Shepp[7] showed that the initial and final configurations define a sufficient set of 48 paths which contains the optimal path. Each of these paths has at most two cusps and five segments, which are either line segment or arcs of a circle of radius. These result has been proved again by Sussman and Tang[8] and Boissonnat et. al respectively. These authors produced a more elegant proof and added more *

Corresponding author.

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1000 – 1011, 2006. © Springer-Verlag Berlin Heidelberg 2006

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necessary conditions on the optimality of a path. They reduced the number of path types to a sufficient set of 46 paths. Boissonat[9] et. al. approached this problem using a well-known control theory. And Soueres and Laumond[10,11] proposed an alternative approach to the problem with reversals. The problem was treated by the combined Pontryagin's optimality principle with geometric reasoning. To find the shortest path using Dubins method, it is selected one of all possible paths, but it may become a problem that it takes much computation time in applications. Shkel and Lumelsky[12] proposed the logical classification scheme to extract the shortest path from the Dubins set directly, without explicitly calculating the candidate paths. This method has several number of equivalency groups, based on the angle quadrants of the corresponding pairs of the initial and final orientation angles. To reach a target configuration from an initial configuration using the Dubins method, we must know the connection point between a circle of the initial configuration and a straight line segment, and the connection point between a circle of the final configuration and the straight line segment of CSC type path respectively. Using the known initial configuration and the final configuration, we can find a rotational angle of the initial configuration and the final configuration individually. The rotational angles are used to find the two connection points. In this research, we propose formulae in Section 3, which are simple and efficient, for calculating the connection points of CSC type. Simple results are due to an adoption of standard forms for the representative LSL and LSR type. And in Section 4, we also present simple criterions for classifying 4 types of CSC, which are necessary for deciding any type of CSC prior to the conversion to the standard form.

2 2.1

Dubins Car Model and Coordinates Transformation Dubins Car Model

A position of a robot is represented by w( x, y,θ ) . The coordinates of the robot are represented by ( x, y ) and the direction is represented by ș . Dubins[1] showed that any path from an initial position to a target position can have 6 admissible paths. The shortest path consists of exactly three path segments and presents a sequence CCC or CSC, where C for an arc of circle will be denoted R for a right-arc and L for a left-arc, and S for a straight line segment. CCC includes 2 types(LRL and RLR) and CSC include 4 types(LSL, RSR, LSR, and RSL). Fig 1(a) shows RSR type, (b) for RSL, and (c) for LRL. Others not shown in this figure are represented by symmetry of the 3 types. 2.2

Coordinates Transformation

The first step of calculating a shortest path for Dubins robot is to transform an arbitrary position to an origin. The position translated by T ( a , b ) , and then rotated by R (θ ) . After all process of calculation, the position is transformed to the original position in a reverse order(Fig. 2).

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Standard forms have type LSL and type LSR. Type RSR is symmetrical to type LSL, and type LSR is symmetrical to type RSL about x-axis. Calculation of type LSL and type LSR can be applied to type RSR and type RSL in symmetrical forms, which are explained in Sec. 3.1 and 3.2. After transformation the arbitrary position to the origin, the angle of the target configuration is set to π Gfor type LSL, and 0 for type LSR. These cause the angle differences between the original and the standard form. Calculations of the difference angles are very essential for the proposed formulae. In Sec 3.3 and 3.4, the details of the formulae are shown.

(a) Type RSR of CSC

(b) Type RSL of CSC

(c) Type LRL of CCC Fig. 1. Examples of Dubins shortest paths

Fig. 2. Examples of Dubins shortest paths

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Calculation of Coordinates for a Shortest Path

3.1 The Case of Type LSL-Standard Form

The initial configuration and the final configuration are located at an arbitrary position and direction. These forms are transformed to the configuration in Fig. 3 by the coordinate transformation. Type LSL composed of (an arc of circle)-(a line segment)(an arc of circle). When a robot rotates counterclockwise(CCW) by θ i about the center C A of a circle with the rotational radius of ρ there exists a connection point PA of the circle and a straight line. And PB is a connection point of the tangent at PA and the target circle which rotate about the center CB . The length of the line PA PB is l . The robot reaches to a standard form by rotate about C B by θ f . The goal is to obtain the coordinates of PA and PB by calculating θ i and θ f after the standard form s which is the result of rotation by θ d from the position t .

Fig. 3. The standard form of type LSL

The length l equals to the distance between C A (0, ρ ) and CB ( x, y − ρ ) as the following equation.

l=

x + ( y − 2ρ ) 2

2

(1)

The angle δ between C A and CB can be calculated as follows. −1

§

· ¸ © y − 2ρ ¹

δ = tan ¨

x

(2)

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Then, θ i which rotates counterclockwise about C A is obtained.

§ ©

θi = π − ¨ δ +

π·

(3)

¸

2¹

The line C A C B runs parallel to PA PB and crosses at the right angles with PB CB . Consequently the angle ∠C AC B PC makes (π − δ ) . And then the angle θ a is obtained as follows.

θa = π − (π − δ ) −

π 2

=δ −

π

(4)

2

According to the equation (4), the angle θ f can be determined.

θ f = θa +

π 2

=δ −

π 2

+

π 2

=δ

(5)

The coordinates of PA is obtained by rotating the origin counterclockwise about

C A (0, ρ )

x A = ρ sin(θ i )

(6)

y A = ρ − ρ cos(θ i )

In the same manner, the coordinates of PB is obtained by rotating s ( x, y ) clockwise by θ f about CB ( x, y − ρ ) .

xB = x + ρ sin (θ f yB 3.2

) = y − ρ + ρ cos (θ )

(7)

f

The Case of Type LSR–Standard Form

The initial configuration of type LSR is Pi (0,0,0°) and the target configuration is

t ( x f , y f ,θ d °) . To transform to the standard form, t ( x f , y f ,θ d °) is rotated by θ d Gto s ( x, y ) . The direction of the initial configuration and the standard configuration is set to 0 degree, respectively. The rotational radius of the initial configuration is ρ Gand it is rotated counterclockwise by θ i Gabout C A . The rotation of the standard position s ( x, y ) Gcounterclockwise to the point PB Gby θ f . We set the lengthGof PA PB Gis 2l ,

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Fig. 4. The standard form of type LSR

the length of PA PC Gis l , and the distance C A PC Gis d . The distance d is represented by C A (0, ρ ) and CB ( x, y − ρ ) Gas follows.

x + ( y − 2ρ ) / 2

d=

2

2

(8)

The distance l is represented by the distance d as follows.

l=

d −ρ 2

2

(9)

The angle β Gis represented as follows. −1

§ρ· ¸ ©l¹

β = tan ¨

(10)

The angle δ Gcan be calculated as follows. −1

§ x · ¸ © y − 2ρ ¹

δ = tan ¨

(11)

Because the angle α is α = π / 2 − β , θ i can be represented as follows.

θi = π − α − δ =

π 2

+ tan

−1

§ ρ · − tan −1 § x · ¨ ¸ ¨ ¸ ©l¹ © y − 2ρ ¹

(12)

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Because the circles of the initial configuration A and the target configuration B is symmetrical to the point PC , the angle θ i is identical to θ f .

θ f = θi

(13)

The point PA is calculated by rotating the origin by θ i about C A .

x A = ρ sin(θ i ) y A = ρ − ρ cos(θ i )

(14)

The point PB Gis calculated by rotating s ( x, y ) counterclockwise by θ f about CB Gas follows. xB = x + ρ sin (θ f yB 3.3

) = y − ρ + ρ cos (θ )

(15)

f

Conversion to the Standard Form-Type LSL

In type LSL, the standard form of the target configuration is determined by setting θ s = π at the configuration s ( x, y ) as in Fig. 5. Consequently the robot toward

θ t must be rotated counterclockwise by θ d about CB . Only t ( x f , y f ) and θ t are known values.

Fig. 5. Conversion to type LSL standard form

The coordinates of C B are calculated by using these values. Then the coordinate of s ( x, y ) is obtained. The point r ( x f , y f + ρ ) is lcated from t ( x f , y f ) by distance ρ in the direction of y . And then the point is located at C B by rotating the point by θ r about t ( x f , y f ) .

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The angle θ r has the same value as θ t which is the angle of the tangent at t ( x f , y f ) as in Eq. (16).

θr = θt

(16)

Then, the center of a circle C B based on the rotation angle θ r can be obtained as following equations.

xCB = x f + ρ sin(θ t )

(17)

yCB = y f + ρ cos(θ t )

The point s ( x, y ) is located at intervals of + ρ from C B in the direction of y . Therefore the coordinates of that point are as the equation (18).

x = x f − ρ sin (θ t )

(18)

y = ρ + y f + ρ cos (θ t ) 3.4

Conversion to the Standard Form-Type LSR

In type LSR, the standard form of the target configuration is determined by setting θ s = 0 at the point s ( x, y ) as in Fig. 6. The point r ( x , y − ρ ) is located at from f

f

t ( x f , y f ) by distance − ρ in the direction of y . Then the point is moved to the point CB by rotating the point about t ( x f , y f ) by θ r . The coordinates of CB rotated counterclockwise by θ r are as the equation (19) because the angle θ r is the same as the angle θ t .

xCB = x f + ρ sin(θ t ) yCB = y f + ρ cos(θ t )

Fig. 6. Conversion to type LSR standard form

(19)

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The point s ( x, y ) is away from CB by distance + ρ in the direction of y . Therefore the coordinates of s ( x, y ) are as the following equation (20). x = x f − ρ sin (θ t ) y = ρ + y f + ρ cos (θ t )

(20)

4 The Criterion for Type Classification of CSC To calculate a feasible shortest path between the initial configuration to the final configuration using a method described in Section 3, the decision of CSC type(LSL, LSR, RSR and RSL) is preceded. In this section, the criterion for type classification of CSC is presented.

Fig. 7. Criterion for type LSR standard form

In Fig. 7, the angle between the origin and the position of the final configuration is denoted δ . If the angle is within 0-180 degree, the initial configuration type is set to type L of CSC, and the angle is within 180-360 degree, the initial configuration type is set to type R of CSC respectively. The angle θ of the initial configuration is oriented to the final point, but the angle is usually differs from the angle φ of the final configuration. If the difference between the angle φ and the angle θ is plus, the counterclockwise rotation of the final configuration is taken. If the angle difference is minus, the clockwise rotation of the final configuration is taken, vice versa. Consequently, If the angle oriented to left-half plane about θ -axis, the Left turn(CCW) is taken, and the angle oriented to right-half plane about θ -axis, the Right

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turn(CW) is taken, vice versa. But the angle should not exceed 180 degree. If the angle exceeds this limit angle, it is taken the reverse angle. To calculate the angle θ , find the distance d and l first. The equations are as follows.

d = x 2f + ( y f − ρ ) 2

(21)

l = d2 − ρ2

(22)

G

The angle α Gis represented as follows.

§ y−ρ· ¸ © x ¹

α = tan −1 ¨

(23)

At ∆C A PAt the angle β can be calculated as follows.

§l ·

β = tan −1 ¨¨ ¸¸ ©ρ¹

(24)

Therefore the angle θ Gis

θ=

π 2

+α − β

(25)

The criterion for the initial configuration is as follows. ­C initial = L, ® ¯C initial = R,

if 0 ≤ δ < π if π ≤ δ < 2π

(26)

The criterion for the final configuration is as follows. ­C final = L, °C ® final = R, °C ¯ final = 0,

if 0 < (φ − θ ) < π if − π < (φ − θ ) < 0

(27)

if (φ − θ ) = 0

5 Simulation Fig. 8 represents the result of simulation for type LSL. The initial configuration of a robot is P(150,300,225’) and the final configuration of a robot is t(399,136,90’). By equations (26) and (27), the type is classified as LSL. After Converted to the standard form, the angle θ i of the initial circle is calculated as 96.61(deg.) and the angle θ f of the final circle is calculated as 218.39(deg.). The connection point of the initial configuration obtained by applying rotational angles to the equation (6) and (7) and a straight line segment PA is calculate as (154,227). And the connection point of the final configuration and a straight line segment PB is calculated as (288,222).

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Fig. 8. Simulation case for type LSL

Fig. 9 represents the result of simulation for type LSR. The initial configuration of a robot is P(100,150,180’) and the final configuration of a robot is t(299,238,300’). By equations (26) and (27), the type is classified as LSR. After Converted to the standard form, the angle θ i of the initial circle is calculated as -112.94(deg.) and the angle θ f of the final circle is calculated as 127.06(deg.). The connection point of the initial configuration obtained by applying rotational angles to the equation (17) and (18) and a straight line segment PA is calculate as (146,82) and the connection point of the final configuration and a straight line segment PB is calculated as (208,231) respectively.

Fig. 9. Simulation case for type LSR

6 Conclusion This paper proposed an efficient method to find a shortest path for Dubins car-like robot between the initial configuration and the final configuration. We derived the formulae for calculating the rotational angles at the initial form and the final form to

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obtain the coordinates of the connection points between CĺS and SĺC in the type CSC by using the known initial and the final form values. Our method for deriving the formulae is novel and simple in comparison with other researches[10-12]. Introducing the standard forms of type LSL and type LSR makes it possible to derive these simple formulae. And we have presented simple criterions for classifying 4 types of CSC, which are necessary for deciding any type of CSC prior to the conversion to the standard form. Although the fundamental types in Dubins’ method are classified into the type CSC and type CCC, the range in our research was limited to type CSC. Some other methods are required for the type CCC because the radius of the initial form and that of the final form are overlapped in the type. In addition, a study for grafting our results on the Reeds and Shepp’s method in which moving forward and backward is possible must be performed as a further study.

References 1. Dubins, L. E.: On Curves of Minimal Length with a Constraint on Average Curvature and with Prescribed Initial and Terminal Positions and Tangents. Amer. J. Math., 79 (1957) 497-516 2. Melzak, Z. A.: Plane Motion with Curvature Limitations. J. of Soc.Indust.Appl.Math, 9(3) (1961) 471-482 3. Robertson, H. G.: Curvature and Arclength. SIAM Journal Applied Math., 19(4) (1970) 697-699 4. Cockane, E. J., Hall, G. W. C.: Plane Motion of a Particle Subject to Curvature Constraints. SIAM J. Control, 13(1) (1975) 197-220 5. Bui, X.-N., Sou`eres, P., Boissonnat, J.-D., Laumond, J.-P.: Shortest Path Synthesis for Dubins Nonholonomic Robots. In Proc. IEEE Int. Conf. Robot. Automat (1994) 2315-2320 6. Boissonnat, J. D., Bui, X. N.: Accessibility Region for a Car that Only Move Forward Along Optimal Paths. In Res. Rep. INRIA 2181, Sophia-Antipolis, France (1994) 7. Reeds, J. A., Shepp, R. A.: Optimal Paths for a Car that Goes Both Forward and Backward. Pacific Journal of Math., 2 (1990) 367-393 8. Sussmann, H. J., Tang, W.: Shortest Paths for the Reeds-Shepp Car: A Worked out Example of the Use of Geometric Techniques in Nonlinear Optimal Control. Tech. Rep. SYCON-91-10, Rutgers Univ., New Brunswick, NJ (1991) 9. Boissonnat, J.-D., Cerezo, A., Leblond, J.: Shortest Paths of Bounded Curvature in the Plane. In Proc. IEEE Int. Conf. Robot. Automat. (1992) 2315-2320 10. Sou`eres, P., Laumond, J.-P.: Shortest Path Synthesis for a Car-like Robot. in Proc. Eur. Contr. Conf. (1993) 672-688 11. Laumond, J.P., Sou`eres, P.: Metric Induced by the Shortest Paths for a Car-like Mobile Robot. in Proc. IEEE Int. Conf. Intell. Robots Syst. (1993) 1299-1304 12. Shkel, A. M., Lumelsky, V.: Classification of the Dubins Set. Robotics and Autonomous Systems, 34 (2001) 179-202

An Intelligent QOS Model for Adaptive Concurrency Control Running on Ubiquitous Computing Environments Eung Nam Ko Department of Information & Communication, Baekseok University 115, Anseo-Dong, Cheonan, ChungNam, 330-704, Korea [email protected] Abstract. This paper proposes a new model of dynamic window binding by analyzing the window and attributes of the object, and based on this, a mechanism that offers a seamless multimedia view without interfering with concurrency control is also suggested. This paper presents the design of the intelligence QOS model for adaptive concurrency control, which is running on RCSM(Reconfigurable Context Sensitive Middleware) for ubiquitous networks. RCSM provides standardized communication protocols to interoperate an application with others under dynamically changing situations. As the result of this system’s experimental implementation and analysis of the increase of delay factors accordant with the size of collaboration increase, the simulation results clearly show that the seam increases seriously in that case, and that the dynamic window binding mechanism proposed in this paper is worth implementation and effective when a large scale of collaboration is required.

1 Introduction Recently, the rapid development of mobile devices, wireless technique and low-cost, low-power, multifunctional sensor nodes have enabled the realizing of ubiquitous computing environment’s appearance possibly. We can describe ubiquitous computing as the combination between mobile computing and intelligent environment, where intelligent environment is a prerequisite to pervasive computing [1]. Context awareness (or context sensitivity) is an application software system’s ability to sense and analyze context from various sources; it lets application software take different actions adaptively in different contexts [2]. In a ubiquitous computing environment, computing anytime, anywhere, any devices, the concept of situationaware middleware has played very important roles in matching user needs with available computing resources in transparent manner in dynamic environments [3, 4,5]. Although the situation-aware middleware provides powerful analysis of dynamically changing situations in the ubiquitous computing environment by synthesizing multiple contexts and users’ actions, which need to be analyzed over a period of time, concurrency control in using multimedia shared object causes a problem of the seam in the ubiquitous computing environment. It is difficult to avoid a problem of the seam in the ubiquitous computing environment for seamless services. Thus, there is a great need for concurrency control algorithm in D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1012 – 1021, 2006. © Springer-Verlag Berlin Heidelberg 2006

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situation-aware middleware to provide dependable services in ubiquitous computing. This paper proposes a new model of dynamic window binding by analyzing the window and attributes of the object, and based on this, a mechanism that offers a seamless multimedia view without interfering with concurrency control is also suggested. Section 2 describes Reconfigurable Context-Sensitive Middleware (RCSM). Section 3 denotes concurrency control based on RCSM. Section 4 describes simulation results of our proposed algorithm. Section 5 present conclusions.

2 Reconfigurable Context-Sensitive Middleware (RCSM) In the Context Toolkit, a predefined context is acquired and processed in context widgets and then reported to the application through application-initiated queries and callback functions. In this Reconfigurable Context-Sensitive Middleware(RCSM), Stephen S. Yau et al.[2] proposed a new approach in designing their middleware to directly trigger the appropriate actions in an application rather than have the application itself decide which method(or action) to activate based on context. RCSM provides an Object-based framework for supporting context-sensitive applications. It shows how all of RCSM’s components are layered inside a device.

Situation-Aware Application Objects RCSM

Optional Components RCSM Ephemeral Group Communication Service

Other Services

Core Components

O S

Adaptive Object Containers (ADCs) [Providing awareness of situation] RCSM Object Request Broker (R-ORB) [Providing transparency over ad hoc communication]

Transport Layer Protocols for Ad Hoc Networks

Sensors

Fig. 1. Overview of Situation-Aware Middleware

All of RCSM’s components are layered inside a device. The Object Request Broker of RCSM (R-ORB) assumes the availability of reliable transport protocols; one R-ORB per device is sufficient. The number of ADaptive object Containers (ADC)s depends on the number of context-sensitive objects in the device. ADCs periodically collect the necessary “raw context data” through the R-ORB, which in turn collects the data from sensors and the operating system. Initially, each ADC

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registers with the R-ORB to express its needs for contexts and to publish the corresponding context-sensitive interface. RCSM is called reconfigurable because it allows addition or deletion of individual ADCs during runtime (to manage new or existing context-sensitive application objects) without affecting other runtime operations inside RCSM. However, it did not include concurrency control QoS support in the architecture. In the next subsection, we will present a conceptual model for concurrency control QoS requirements representation in situation-aware middleware.

3 Concurrency Control Based on RCSM In this section, we present a concurrency control mechanism for situation-aware ubiquitous computing. The environment of concurrency control is presented in Section 3.1, its architecture in Section 3.2 and its algorithm in Section 3.3. 3.1 The Environment for Concurrency Control Our proposed model aims at supporting concurrency control requirements by using dynamic window binding mechanism in order to provide ubiquitous, seamless services. An example of situation-aware applications is a multimedia distance education system. The development of multimedia computers and communication techniques has made it possible for a mind to be transmitted from a teacher to a student in distance environment. Other services of RCSM have many agents. They consist of AMA(Application Management Agent), MCA(Media Control Agent), FTA(Fault Tolerance Agent), SA-UIA(Situation-Aware User Interface Agent), SASMA(Situation-Aware Session Management Agent), and SA-ACCA(Situation-Aware Access and Concurrency Control Agent), as shown in Figure 2.

SA-SMA G

S A G S M

AMA FTA

SA-ACCA L S M

SA-UIA MCA

Fig. 2. The Environment for Concurrency Control in Situation-Aware Ubiquitous Computing

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AMA consists of various subclass modules. It includes creation/deletion of shared video window and creation/deletion of shared window. MCA supports convenient applications using situation-aware ubiquitous computing. Supplied services are the creation and deletion of the service object for media use, and media share between the remote users. This agent limits the services by hardware constraint. FTA is an agent that plays a role in detecting an error and recovering it in situation-aware ubiquitous environment. SA-UIA is a user interface agent to adapt user interfaces based on situations. SA-SMA is an agent which plays a role in connection of SA-UIA and FTA as situation-aware management for the whole information. SA-ACCA controls the person who can talk, and the one who can change the information for access and concurrency. SMA monitors the access to the session and controls the session. It has an object with a various information for each session and it also supports multitasking with this information. SMA consists of Global Session Manager (GSM), Daemon, Local Session Manager (LSM), Participant Session Manager (PSM), Session Monitor, and Traffic Monitor. GSM has the function of controlling whole session when a number of sessions are open simultaneously. LSM manages only own session. For example, LSM is a lecture class in distributed multimedia environment. GSM can manage multiple LSM. Daemon is an object with services to create session. 3.2 The Architecture for Concurrency Control To win over such dilemma for centralized or replicated architecture, a combined approach, CARV (the Centralized Abstraction and Replicated View) architecture is used to realize the application sharing agent. Figure 3 shows that teacher and students use their local windows and shared window individually.

Local window

Local window

Shared window

SA-GSM

Shared window

Local window

Shared window

Fig. 3. CARV Architecture for Concurrency Control

The shared window is a window shared by all the participants, and the modification carried out by the speaker is notified to every other participants. The local window is not shared except initial file. The tool box provides various tools for editing contents

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of both the shared window and the local window. The local window has the lecture plans which is distributed at the beginning, and enables participants to memo and browsing other parts in the lesson plans, and has functions as a whiteboard. 3.3 The Algorithm of Concurrency Control As shown in Figure 4, concurrency control inevitably occurs in a multimedia distance education environment where many users perform collaborative work at the same time.

I N I T I A T O R

(1) Issue commands with its session id, timestamp, sequence number and event type

(2) Broadcast serialized commands

(3) Start processing the command and awareness

P A R T I C I P A N T

Fig. 4. Concurrency Control in Situation-Aware Ubiquitous Computing

There may be a case where processing cannot be done in order of arrival due to variation according to present load, processing capability of each system and network delay caused by many participants putting in commands. Concurrency control solves such problems. As shown in Figure 5, when many users request for same media device at the same time, media device acquisition order is controlled. Alternation of event input sequence, according to present load, processing capability of each system and network delay cause by participants’ use of different computers is another problem that occurs in distributed network environment. We attempted to solve such command serialization problem with centralized serialization server and distributed synchronization clock method. In order to guarantee synchronization control and command serialization, SA-ACCA maintains and manages command sequence history that is mutually exchanged. All input events are transmitted with creating time of event to the serialization server. Serialization server can be processed according to the order of occurrence of events. Command serialization occurs because of necessity to process inputs from several users of different locations using same application program and to see same view. Collaborative work system must have command serialization mechanism. In order to overcome the problem mentioned earlier, while the user carries out a serialization of the object that is created in a shared window, a local window that is in coincidence with the scope is bound to the object.

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Shared View

Local Window

Shared Window View Sharing

Abstraction

Serialization

Communication

Fig. 5. A Dynamic Window Binding Mechanism in Situation-Aware Ubiquitous Computing

View

Abstraction

Central Manager

Display

input <Participant #2>

input copy back

<Participant #1>

Abstraction

Abstraction

View Man ager

Display

View Man ager

Display

Fig. 6. CARV architecture

Figure 6 shows the relationship between initiator and participant of a concurrency control for multimedia distance education system.

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This is the local image copy of a shared object that is to be created. By showing the user the abstract of an input command beforehand, the time that is needed to confirm whether the object is managed properly can be saved. This is like FIFO, and the user is allowed to continue working with at least the minimal level of confidence. Meanwhile, a communication channel for the serialization server is allocated to the local window as an attribute and then concurrency control is in progress. This is the process in which object and command that is created for the purpose of preview is on its way to perfecting window binding on the basis of its actual attributes. This transfer guarantee concurrency and at the same time increases promptness of user interaction, and consequently becomes the solution of eliminating seam from the view. If there is an object that is registered in local window but failed to be registered in shared space due to the failure during serialization process, the user will recognize this as a slight omission and will selectively try to re-input the omitted part.

4 Simulation Results To evaluate the performance of the proposed system, an error detection method was used to compare the performance of the proposed model against the conventional model by using DEVS formalism. In DEVS, a system has a time base, inputs, states, outputs based on the current states and inputs. DEVS(Discrete Event System Specification) is a formalism of being developed by Bernard P. Zeigler. The structure of atomic model is as follows [6 - 12]. M = < X, S, Y, δint, δext, λ, ta > X: a set of input events. S: a set of sequential states. Y: a set of output events. δint : internal transition function δext : external transition function λ : output function ta : time advance function For the structure of software implementation, the CACV(Centralized-Abstraction and Centralized-View) and the RARV(Replicated-Abstraction and Replicated-View) are extreme approaches to design software architecture on which distributed, collaborative applications are based. The CARV(Centralized-Abstraction and Replicated-View) architecture is also comparable with those architecture in terms of performance [12]. The perceived length of system delay the user working in a multimedia collaboration environment for situation-aware middleware to provide dependable services in ubiquitous computing seems to feel depends upon system load and structure of software the application has. The extent can be summarized as Table 1.

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Table 1. Performance Model for Software Architecture

Model CACV RARV CARV

Ts (n-1)Tf n(n-1)Tf (n-1)Tf

Tp Ta + Tv Ta Ta

Tv To Tv Ti + Tv

Traffic Model (n-1)E(e)(nFv+Fe) n(n-1) E(e)Fe (n-1)E(e)(nFi+Fe)

Total delay: Ts + Tp + Tv, Ts: serialization overhead, Tp: processing time Tv: view time, Tf: mean transfer time, Ta: abstraction time, Ti: intermediate result time, To: output transfer time, Tv: view generation time Fv: traffic of view transfer, Fe: traffic of event transfer, Fi: traffic of intermediatetx, n: number of platforms, E(e): mean input frequency

Based on the traffic property, the serialization overhead is to be calculated by examining mean transfer time Tf which is the mean value of time required to transmit event packet through out a network. For the evaluation of mean transfer time, following, formula is adopted as equation 1. Because the formula is much simplified to use only for the application layer protocols, it does not include details such as collision loss. Tf = ( m + t / 2 ) * (1 / 1 – p)

(1)

where m: frame transmission time t: propagation delay of the physical network p: traffic amount / channel capacity As it assumed that a message packet is transferred within a mean transfer time via a network, only the number of messages required to perform serialization is taken into account to evaluate the serialization overhead. In the pessimistic approach that is adopted in our project, sequence of received command input is regarded as always disordered as much as possible. Therefore the waiting time for serialization is required as in the worst case. In case of centralized architectures such as CACV and CARV, it is n-1. On the contrary, n(n-1) order of unit message transfer time is

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necessary in replicated architecture that is typical RARV. Overview of the command serialization overhead is obtained as seen by Figure 7. The figure on the vertical line means relative overheads compared with maximum value on RARV.

5 Conclusions The focus of situation-aware ubiquitous computing has increased lately. An example of situation-aware applications is a multimedia education system. The development of multimedia computers and communication techniques has made it possible for a mind to be transmitted from a teacher to a student in distance environment. This paper proposed a new model of dynamic window binding by analyzing the window and attributes of the attributes of the object, and based on this, a mechanism that offers a seamless view without interfering with concurrency control is also suggested. As the result of this system’s experimental implementation and analysis of the increase of delay factors accordant with the size of collaboration increase, the simulation results clearly showed that the seam increases seriously in that case, and that the dynamic window binding mechanism proposed in this paper is worth implementation and effective when a large scale of collaboration is required. In the future work, faulttolerance system will be generalized to be used in any environment, and we will progress the study of domino effect for distributed multimedia environment as an example of situation-aware applications. We remain these QoS for resource conflict resolution strategies as future work.

References 1. Hung, N.Q., Ngoc, N.C., Hung, L.X., Lei, S., Lee, S.Y.: A Survey on Middleware for Context-Awareness in Ubiquitous Computing Environments. Korea Information Processing Society Review (2003) 97–121 2. Yau, S., Karim, F., Wang, Y., Wang, B., Gupta, S.: Reconfigurable Context-Sensitive Middleware for Pervasive Computing. IEEE Pervasive Computing, 1(3) (2002) 33-40 3. Yau, S. S., Karim, F.: Adaptive Middleware for Ubiquitous Computing Environments. Design and Analysis of Distributed Embedded Systems, Proc. IFIP 17th WCC, Vol. 219 (2002) 131-140 4. Yau, S. S., Karim, F.: Contention-Sensitive Middleware for Real-time Software in Ubiquitous Computing Environments. Proc. 4th IEEE Int’l Symp. on Object-Oriented Realtime Distributed Computing (ISORC 2001) (2001) 163-170 5. Saha, D., Mukherjee, A.: Pervasive Computing: A Paradigm for the 21st Century. IEEE Computer, 36(3) (2003) 25-31 6. Zeigler, B. P., Cho, T. H., Rozenblit, Jerzy W.: A Knowledge-Based Simulation Environment for Hierarchical Flexible Manufacturing. IEEE Transaction on Systems, Man, and Cybernetics-Part A: System and Humans, 26(1) (1996) 81-90 7. Cho, T. H., Zeigler, B. P.: Simulation of Intelligent Hierarchical Flexible Manufacturing: Batch Job Routing in Operation Overlapping. IEEE Transaction on Systems, Man, and Cybernetics-Part A: System and Humans, 27(1) (1997) 116-126

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8. Zeigler, B. P.: Object-Oriented Simulation with Hierarchical, Modular Models. Academic Press (1990) 9. Zeigler, B. P.: Multifacetted Modeling and Discrete Event Simulation. Orlando, FL: Academic (1984) 10. Zeigler, B. P.: Theory of Modeling and Simulation. John Wiley, NY, USA (1976), reissued by Krieger, Malabar, FL, USA (1985) 11. A.I. Conception and B.P. Zeigler: The DEVS Formalism: Hierarchical Model Development. IEEE Trans. Software Eng., 14(2) (1988) 228-241 12. J. C. Lauwers and K. A. Lantz: Collaboration Awareness in Support of Collaboration Transparency: Requirements for the Next generation of Shared Window Systems. proc. of ACM CHI’90 (1990) 302-312

Analysis and Extension of S/Key-Based Authentication Schemes for Digital Home Networks Ilsun You Department of Information Science, Korean Bible University, 205 Sanggye-7 Dong, Nowon-ku, Seoul, 139-791, South Korea [email protected]

Abstract. Recently, we have proposed two S/Key based authentication schemes for secure remote access in digital home networks. However, because they, like other S/Key based schemes, focus on only authentication, they don’t provide authorization, which is one of the important security services at home network. In this paper, we analyze and extend the schemes to support the authorization service. For this goal, we propose a Lightweight Attribute Certificate (LAC) and Lightweight Authorization Protocol (LAP). Through the LAC, LAP allows clients to be seamlessly authenticated and authorized regardless of their location. Especially, this protocol where the involved parties needs only lightweight cryptographic operations can reduce computational cost with single sign-on.

1 Introduction Due to the rapid growth of the Internet technology and electronic devices, much interest has risen in digital home networks [1]. A typical home network is composed of home gateway, home appliances, mobile devices, and service providers. Especially, the home gateway plays an important role as an intermediary between the home network and external networks. It allows residential users to remotely access and control home appliances such as TVs, lights, washing machines, and refrigerators. However, in spite of such conveniences, the remote control service causes digital home networks to have various security threats such as masquerade, denial of service attacks, etc. Furthermore, handheld devices are often connected to digital home networks by wireless links and the links are especially vulnerable to passive eavesdropping, active replay attacks, and other active attacks. Therefore, it is necessary to provide strong security services in digital home networks. In particular, user authentication is a key service required for remote access control. In this paper, we study user authentication schemes that allow user to remotely access and control home appliances through home gateway. Considering both strong security and lightweight cryptographic operations, we have explored the S/Key user authentication scheme, a widely known one-time password system [2,3]. As a result, we proposed two S/Key based authentication schemes for digital home networks [4-6]. Though they achieve both strong security and efficiency, they, like other S/Key based schemes, don’t provide authorization, which is one of the important security D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1022 – 1033, 2006. © Springer-Verlag Berlin Heidelberg 2006

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services at home network. This paper analyzes and then extends the schemes to support the authorization service. For this goal, we propose a Lightweight Attribute Certificate (LAC) and Lightweight Authorization Protocol (LAP). The rest of the paper is organized as follows. Section 2 describes related works and section 3 analyzes two S/Key based authentication schemes. In section 4, we propose a Lightweight Attribute Certificate (LAC) and Lightweight Authorization Protocol. Finally, section 5 draws some conclusions.

2 Related Work Since user mobile devices tend to be resource constrained, we consider the S/Key scheme and its variants, which uses lightweight cryptographic operations such as exclusive-OR and Hash function. This section briefly describes the S/Key based authentication schemes. The S/KEY one-time password scheme is designed to protect a system against replay or eavesdropping attacks [2,3]. With S/Key, the user’s secret pass-phrase never needs to cross the network at any time such as during the authentication or passphrase changes. Moreover, no secret information needs to be stored on any system, including the server being protected. Although the S/KEY scheme protects a system against passive attacks based on replaying captured reusable passwords, it is vulnerable to server spoofing, preplay, and off-line dictionary attacks [7,9]. Several researches have been conducted to solve these drawbacks of the S/KEY scheme [4-9]. Mitchell and Chen propose two possible solutions to resist against server spoofing and preplay attacks. One is to locally store the predictable challenge in a client so that a server has no need to send the challenge in every login. The other is to digitally sign the predictable challenge. Yen and Liao propose a scheme that uses a shared tamper resistant cryptographic token, which includes a SEED, to prevent off-line dictionary attacks. Yeh, Shen and Hwang propose an one-time password authentication scheme which enhances the S/KEY scheme to resist against the above attacks. The scheme uses smart cards to securely preserve a preshared secret, SEED, and simplify the user login process. Also, it provides a session key to enable confidential communication over the network. However, since the scheme uses user's weak pass-phrase and utilizes SEED as a pre-shared secret, the exposure of the SEED causes the scheme to retain the flaws of the S/KEY scheme [11]. Consequently, the scheme cannot achieve the strength of the S/KEY scheme that no secret information needs to be stored on the server. In addition, it cannot defend against server compromises and is vulnerable to several attacks such as stolen-verifier attacks, denial of service attacks and Denning-Sacco attacks [11-13]. Lee and Chen propose an improvement on Yeh-Shen-Whang’s scheme to prevent its vulnerability from stolen verifier attacks [8,9]. With such improved security, their scheme still provides the same efficiency as Yeh-Shen-Whang’s scheme. However, it is vulnerable to denial of service (DoS) attacks and also allows a compromise of past session keys [5].

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3 Two Enhanced Authentication Schemes: LWAS and PKAS Recently, we have proposed two enhanced authentication schemes for secure remote access in digital home networks [4-6]. While the one, which is called LWAS(Light Weight Authentication Scheme), uses additional lightweight cryptographic operations to improve Yeh-Shen-Whang’s and Lee-Chen’s scheme, the other, which is called PKAS(Public Key Authentication Scheme), uses a server-side public key to improve them. In this section, we review and analyze them. 3.1 Notation and Preliminary -

K is the user secret, C is the client and S is the server SK is the server’s secret key and IPX denotes the IP address of X id denotes the user’s identity SCX denotes X’s smart card and SCNX denotes the serial number of X’s smart card N denotes a permitted number of login times and D is a random number H() denotes a collision-resistant hash function HX(m) means that the message m is hashed X times KRX denotes the private key of X and KUX denotes the public key of X PKCX denotes X.509 public key certificate of X PX(m) means that the message m is encrypted with the public key of X PX -1(m) means that the message m is encrypted with the private key of X pt denotes tth one-time password ⊕ denotes Exclusive-OR operation and | denotes concatenation

Before starting the registration stage, the client randomly generates a large number K and stores it in the smart card. 3.2 LWAS (Light Weight Authentication Scheme) LWAS is composed of three stages: registration, login and authentication stages. This section reviews the scheme and analyzes its drawbacks. It is assumed that the client initially receives SEED (= id ⊕ SK) from the server by out-of-band distribution. (1) Registration Stage Step1) C → S: id Step2) C ← S: N, H(SEED ⊕ N) ⊕ D, H(D), where SEED = id ⊕ SK Step3) C → S: p0 ⊕ D, H(p0 | D), where p0 = HN(K ⊕ SEED) At step (3), the client sends H(P0 | D) as well as P0 ⊕ D to the server. The hash value makes it possible for the server to ensure that P0 is valid, thus defending against DoS attacks. As a result of this stage, the login information P0 and N are stored at the server. In addition, the smart card stores P0.

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(2) Login Stage Step1) C → S: id Step2) C ← S: CN, H(SEED ⊕ CN) ⊕ D, H(D) ⊕ pt-1, where CN = N–t Step3) C → S: pt ⊕ H(D), where pt = HCN(K ⊕ SEED) This stage provides mutual authentication between a user and a server. (3) Authentication Stages After receiving, the server XORs the received pt ⊕ H(D) with H(D) to obtain the fresh one-time password pt. If the hash value of pt is equal to pt-1 stored in the server, then the client is authenticated. Finally, the server updates the last password with pt and the counter value with CN in its database. D, randomly generated by the server, can be used as a session key to enable confidential communication between the server and the client. (4) Analysis LWAS uses only 4 additional hash operations to solve the drawbacks of Lee-Chen’s scheme. Thus, it achieves both the strong security and good performance while being appropriate for low-power mobile devices. However, due to using SEED as a pre-shared secret, it has the following drawbacks: - Because SEED is derived from the server’s secret key SK, anyone who owns or steals a SEED can mount off-line dictionary attacks to find SK. That causes LWAS to be vulnerable to various attacks by legitimate users. - It is so difficult to securely distribute SEED. That causes LWAS to distribute SEED by out-of-band method. Thus, LWAS cannot guarantee the desired security by itself, depending on out-of-band method. - If an attacker succeeds in compromising SK, he or she can compromise all SEEDs. In this case, all clients should reinitialize their login information and smart card. Due to the difficulty of SEED distribution, the cost for recovering LWAS is highly expensive. 3.3 PKAS (Public Key Authentication Scheme) In PKAS, a server-side public key, instead of a pre-shared secret SEED, is used to improve YEH-SHEN-HWANG’s and Lee-Chen’s scheme. PKAS is composed of three stages: registration, login and authentication stages. This section reviews the scheme and analyzes its drawbacks. It is assumed that the server initially issues a smart card containing the server’s X.509 public key certificate PKCS to the user. If PKCS is expired or compromised, it can be updated through an out-of-band method. In addition to PKCS, the smart card contains a randomly generated large number D and PS-1(H(id ⊕ D)) used to authenticate the user in the registration stage. Those values are used once in the first

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registration of the user. To reinitialize the user’s login information, the client uses the large random number D shared with the server in the login stage. (1) Registration Stage Step1) C → S: id, H(SCNid ⊕ IPC), PS(D), PS-1(H(id ⊕ D)) Step2) C ← S: N, SEED, H(N ⊕ SEED ⊕ D) Step3) C → S: p0⊕ D, H(p0 | D) , where p0= HN(K ⊕ SEED) For the first registration, the client uses the D stored in the smart card to authenticate the user. To prevent denial of service attacks, the server firstly verifies the received H(SCid ⊕ IPC) before the expensive public key operations for PS(D) and PS1 (H(id ⊕ D)). Later, to reinitialize the user's login information such as SEED, N and p0, the client should pass both the login stage and the authentication stage to be mentioned below, and use the large number D shared with the server in the login stage. In this case, the client goes through step (2) - (3), omitting step (1). (2) Login Stage Step1) C → S: id, H(IPC ⊕ SCNid ⊕ pt-1), PS(D) Step2) C ← S: CN, SEED, H(CN ⊕ SEED ⊕ D) , where CN = N–t Step3) C → S: pt⊕ H(D) , where pt= HCN(K ⊕ SEED) (3) Authentication Stages Upon receiving, the server compares the hash value of the received pt with pt-1 stored in its database. If they are equal, then the user is authenticated. In this case, the server updates the last password with pt and the counter value with CN in its database, and sends the accept message to the client. Later, the randomly generated D can be used as a session key to enable confidential communication between the server and the client. Furthermore, it is used to reinitialize the user’s login information such as SEED, N and p0. (4) Analysis With a server-side public key, PKAS can overcome the problems resulted from using SEED as a pre-shared secret. However, it needs the client and server to perform expensive asymmetric cryptographic operations. Especially, on CPU-limited devices, asymmetric cryptographic operations are much slower than symmetric cryptographic operations. Moreover, it is computationally expensive or energy-intensive to perform asymmetric cryptographic operations. 3.4 Comparison Computational Cost: Tables 1 compares the computational costs of LWAS and PKAS. In comparison to LWAS, PKAS has an additional computational cost, which includes expensive asymmetric cryptographic operations. Though the additional cost results in performance degrade, it enables PKAS to overcome the drawbacks of LWAS, which is caused by a pre-shared secret SEED.

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Table 1. Comparison of the Computational Costs for LWAS and PKAS Step Reg. Step1

LWAS -

PKAS 4Hash + 4XOR + 3PK

Reg. Step2 Reg. Step3

4Hash + 5XOR (N+2)(Hash+XOR) + 2CON (N+6)Hash + (N+7)XOR + 2CON -

2Hash + 4XOR (N+2)(Hash+XOR) + 2CON (N+8)Hash + (N+10)XOR + 3PK + 2CON 2Hash + 4XOR + 2PK

4Hash + 7XOR

2Hash +4XOR (N-t+1)(Hash+XOR) (N-t+5)Hash + (N-t+9)XOR + 2PK

Reg. Total Login Step1 Login Step2 Login Step3 Login Total Auth. Total

(N-t+1)(Hash+XOR) (N-t+5)Hash + (N-t+8)XOR 2Hash + 1XOR

2Hash + 1XOR

(2N-t+13)Hash +

(2N-t+15)Hash + (2N-t+20)XOR + 5PK +

Difference +4Hash, +4XOR, +3PK -2Hash, -1XOR +2Hash, +3XOR, +3PK +2Hash, +4XOR, +2PK -2Hash, -3XOR

+1XOR, +2PK +2Hash, +4XOR, +5PK

(2N-t+16)XOR + 2CON 2CON * Hash denotes a hash operation, XOR denotes an exclusive-OR operation. PK denotes a public key operation, CON denotes a concatenation operation.

Security: In terms of security, the main difference between LWAS and PKAS is that LWAS uses SEED, which is derived from its secret SK, as a pre-shared secret. Thus, for the security comparison of two schemes, it needs to analyze the costs of breaking the server’s secret key SK and the server’s private key KRS. While Fig. 1 shows the algorithm for breaking SK in LWAS, Fig. 2 shows the algorithm for breaking KRS in PKAS. The costs for breaking SK and KRS are as follows: - n: the key size - Cskey: the cost of breaking the server’s secret key - Cpkey: the cost of breaking the server’s private key - Cxor: the cost of XOR operation - Cpk-decrypt: the cost of public key decryption operation Cskey = 2n × Cxor Cpkey = 2n × Cpk-decrypt The above cost analysis shows that PKAS is more secure than LWAS because Cpk-decrypt is much more than Cxor. Furthermore, the cost for recovering LWAS from SK compromise is expensive because it includes the re-initialization of all users’s login information and distribution of SEED. In the case of PKAS, PKCS in all users’s smart card (or handheld devices) should be updated.

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Fig. 1. Algorithm for Breaking the Server’s Secret Key in LWAS

Fig. 2. Algorithm for Breaking the Server’s Private Key in PKAS

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4 Extensions The S/Key scheme and its variants, including LWAS and PKAS, have focused on only authentication. Thus, they don’t provide authorization, which is one of the important security services at home network. In this section, we extend LWAS and PKAS to support the authorization service. For this goal, we propose a Lightweight Attribute Certificate (LAC) and Lightweight Authorization Protocol (LAP). With the LAC, the proposed protocol allows the involved parties to perform only lightweight cryptographic operations. Furthermore, it enables single sign-on (SSO), which reduces cryptographic operations, and seamless authentication and authorization between the home network and external networks. 4.1 Preliminary It is assumed that a home network is composed of a home gateway (HG), home network service providers (HS), clients (C) and external service providers. A master key mk, a short-term group key, is shared by the home gateway and home network service providers, while being updated periodically. 4.2 Lightweight Attribute Certificate (LAC) Fig. 3 illustrates the structure of a LAC, which contains attribute information such as role, group, access identity and clearance as well as a session key D. The LAC is a short-term certificate, which is digitally signed through the master key mk.

Fig. 3. Lightweight Attribute Certificate

4.3 Lightweight Authorization Protocol (LAP) LAP is divided into the out-home network and in-home network protocols. Out-Home Network Protocol: This protocol allows C in external networks to access the home network through HG. It is composed of LAC issue phase, HG authentication phase and HS authentication phase as shown in Fig. 4.

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Fig. 4. Out-Home Network Protocol

Fig. 5. In-Home Network Protocol

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In LAC issue phase, the login stage of LWAS or PKAS is performed during the steps (1)-(3). If the login is successful, HG issues a LAC to C in the step (4). Then, HG allows C to access in-home network through itself, while starting a new session between C and itself. C can prove itself as the owner of the issued LAC through the session key D established during the login stage. During the valid period of the issued LAC, if the session finishes, C needs not to perform this phase. Instead, C performs HG authentication phase to authenticate itself to HG. If this authentication is positive, C establishes a session, over which the home network can be accessed through HG. Especially, because this phase includes only lightweight cryptographic operations, it can reduce the computational costs occurred in the login stage of LWAS or PKAS. To access a home network service over the established session, C performs HS authentication phase. During HS authentication phase, HS verifies C’s LAC and H(id⊕hs⊕ts⊕D). If the verification is positive, it can be sure that C is valid. Then, it authorizes C according to the attributes included in C’s LAC. In-Home Network Protocol: This protocol is designed for the case that C is in the home network. As illustrated in Fig. 5, if C is successfully authenticated through LAC issue phase, it can directly access home network services without HG. Except for HG authentication, this protocol is same as out-home network protocol. That makes it possible for LAP to provide seamless authentication and authorization between the home network and external networks. 4.4 Analysis Through the LAC, LAP allows C to be seamlessly authenticated and authorized regardless of its location. Especially, this protocol where the involved parties needs only lightweight cryptographic operations can reduce computational cost with SSO. To analyze the performance improvement through SSO, we compare the computational cost of HS (or HG) authentication phase with that of LWAS and PKAS as follows: - CLWAS : the computational cost of LWAS’s login stage - CPKAS : the computational cost of PKAS’s login stage - CLAP : the computational cost of HS (or HG) authentication phase CLWAS = (N-t+5)×Hash +(N-t+8)×XOR CPKAS = (N-t+5)×Hash +(N-t+9)×XOR + 2×PK CLAP = 4×Hash + 10×XOR CLWAS - CLAP = (N-t+1)×Hash + (N-t-2)×XOR CPKAS - CLAP = (N-t+1)×Hash + (N-t-1)×XOR + 2×PK Because N-1 ≥ t, CLWAS - CLAP ≥ 2×Hash – XOR CPKAS - CLAP ≥ 2×Hash + 2×PK

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As shown above, while LAP can reduce at least (2×Hash – XOR) operations compared to LWAS, it can reduce at least 2×(Hash + PK) operations compared to PKAS. In particular, the client’s computational cost occurred in HS (or HG) authentication phase is (2×Hash + 5×XOR). Such cost allows LAP to support low-power mobile devices.

5 Conclusions Remote access control is an important service in the design of digital home networks. The service allows residential users to remotely access and control home appliances such as TVs, lights, washing machines, and refrigerators. However, in spite of such conveniences, the remote control service causes digital home networks to have various security threats. Therefore, it is necessary to provide strong security services in digital home networks. In particular, user authentication is a key service required for remote access control. Recently, we have proposed two S/Key based authentication schemes for secure remote access in digital home networks. However, because they, like other S/Key based schemes, focus on only authentication, they don’t provide authorization, which is one of the important security services at home network. In this paper, we analyze and extend the schemes to support the authorization service. For this goal, we propose a lightweight attribute certificate LAC and an authorization protocol LAP. Through the LAC, LAP allows clients to be seamlessly authenticated and authorized regardless of their location. Especially, this protocol where the involved parties needs only lightweight cryptographic operations can reduce computational cost with single sign-on.

References 1. Sun, H.: Home Networking. Mitsubishi Electric Research Laboratories (2004) http://www.merl.com/projects/hmnt/ 2. Haller, N.: The S/KEY One-time Password. RFC 1760 (1995) 3. Haller, N., Metz, C., Nesser, P., Straw, M.: A One-time Password System. RFC 2289 (1998) 4. You, I., Cho, K.: A S/KEY Based Secure Authentication Protocol Using Public Key Cryptography. The KIPS Transactions: Part C, 10-C(6) (2003) 5. You, I., Jung, E.: A Light Weight Authentication Protocol for Digital Home Networks. ICCSA 2006, Springer-Verlag LNCS. 3938 (2006) 416-423 6. You, I.: One-Time Password Authentication Scheme for Secure Remote Access in Intelligent Home Networks. Accepted to KES 2006 (2006) 7. Mitchell, C. J., Chen, L.: Comments on the S/KEY User Authentication Scheme. ACM Operating Systems Review, 30(4) (1996) 12-16 8. Yeh, T. C., Shen, H. Y., Hwang, J. J.: A Secure One-Time Password Authentication Scheme Using Smart Cards. IEICE Transaction on Communication, E85-B(11) (2002) 2515-2518 9. Lee, N. Y., Chen, J. C.: Improvement of One-Time Password Authentication Scheme Using Smart Cards. IEICE Transaction on Communication, E88-B(9) (2005) 3765-3767

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10. Yen, S. M., Liao, K. H.: Shared Authentication Token Secure against Replay and Weak Key Attacks. Information Processing Letters, 62 (1997) 77-80 11. You I., Cho, K.: Comments on YEH-SHEN-HWANG's One-Time Password Authentication Scheme. IEICE Transaction on Communication, E88-B(2) (2005) 751-753 12. Denning, D., Sacco, G.: Timestamps in Key Distribution Systems. Communications of the ACM, 24(8) (1981) 533-536 13. Kim, S., Kim, B., Park, S., Yen, S.: Comments on Password-Based Private Key Download Protocol of NDSS'99. Electronics Letters, 35(22) (1999) 1937-1938

Anonymous Voting Scheme on Multicast Dong-Myung Shin, Hee-Un Park, Woo-Jae Won, and Jae-Il Lee Korea Information Security Agency, 78, Garak-Dong, Songpa-Gu, Seoul, Korea {dmshin, hupark, yjwon, jilee}@kisa.or.kr

Abstract. A cryptographic scheme can be used for authentication to multicast users who exchange messages with group members or receive a multimedia service from server. But using conventional method like a group key management don't provide anonymity in above situation. Electronic voting, anonymous conference on multicast demand secure and anonymous service with transaction. In this service, other group members should not know which is selected by him/her or who select the one. Various selection processes are present in the real world. Among them, some processes are open to everyone and others allow only members to validate them. These choice and selection types have been developed using cryptography protocol model. But, further study of definite anonymous secure selection protocols based on a cryptography is needed. In this paper, we propose the anonymous secure selection to get the anonymity of an originator, and which blinds the selection result from other entities on the open network. This approach protects a selection result of an originator using one-way anonymous authentication service.

1 Introduction Multicast delivers source traffic to multiple receivers without adding any additional burden on the source or the receivers while using the least network bandwidth of any competing technology. Multicast is a bandwidth-conserving technology that reduces traffic by simultaneously delivering a single stream of information to thousands of corporate recipients. Applications that take advantage of multicast include videoconferencing, electronic voting, IPTV, corporate communications, E-learning, and distribution of software, stock quotes, and news. And there have been many researches into group key management of multicast members[1][2]. However this research limited to member authentication and data secrecy. Especially, in case of electronic voting and anonymous conferencing on multicast, additional requirements should be satisfied. For examples, other group members should not know which is selected by him/her or who select the one. Various selection processes are present in the real world. Among them, some processes are open to everyone and others allow only members to validate them. These choice and selection types have been developed using cryptography protocol model. A research for 'one-way anonymous authentication service' has been in progress to keep the anonymity of the information originator and authenticating the message based on the protocol for a specific group and information. Among them, electronic D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1034 – 1039, 2006. © Springer-Verlag Berlin Heidelberg 2006

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voting, anonymous conference, and fair E-money can be representative examples. This service is based on specific group members. Figuring out an originator's real identity from his/her transmission information is impossible but The authentication to prevent forgery and falsification of information is possible. When the illegal information is made by the originator, group members can identify him/her. Also The third party can not confirm the selected information without the originator's permission. Theses features are important means for offering safety to different sets of users with logically contradicting requirements. As you see, 'Anonymous Secure Selection Scheme' an originator processes secure selection and guarantees the anonymity of his/her identity[3]. In the open network, some researches are proposed to solve the anonymous secure selection service only in parts, but integration mechanisms have not been studied yet. Therefore in this paper, we propose the anonymous voting scheme for secure selection to get the anonymity of an originator, and which blinds the selection result from other entities on the open network.

2 Anonymous Voting Scheme for Secure Selection In this chapter, we describe the electronic voting that is based on one-way anonymous authentication services. On the open network, the efficiency of electronic voting is an interesting field on research. In spite of its importance, when the voting is operated in the open network, the electronic voting scheme has some security requirements and if these requirements are not met, the voting scheme is not to be trusted. Therefore, in this paper, we propose a new electronic voting scheme that satisfies the all the requirements. Especially we apply anonymous secure selection to the electronic voting system on multicast and analyze whether this satisfies all the requirements. The most important characteristic in the voting scheme is an ability to maintain voting security or anonymity. This means that the voting scheme must prevent the third party from knowing the relationship between the voting and the voter. The proposed scheme applies electronic voting system on multicast to satisfy security requirements. This scheme disapproves the forgery and confirming of voting result from the third party and provides private voting that satisfies the anonymity. 2.1 Symbols In this section, we describe system parameters used in the new proposed scheme. • Vi, Gi, Ti, CTA : Voter, Voting booth, Tally center, and CTA(Central Tabulate Agency) • vi, V_resulti : Voting value and result of the voter i • r_și, r_salti, r_seed : Voter i's random number ș, CTA's salt value, and Tally center's seed value • IDi : Voter i's alias identity generated by CTA

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p, q : Large prime number, p-1/q g : Integer with order q modulo p randomly chosen from [1, ..., p-1] * KS_* RZ q : *'s private key KP_* = gKS_* mod p : *'s public key EKP(S)_*, DKP(S)_* : *'s public key or private key encryption and decryption H : One-way hash function * xgi RZ q : The private key list for group signature xgi ygi = g mod p : The public key list for group certification.

Щ

Щ

2.2 System Protocol Phase 1. Preliminary phase Step 1.1 CTA (1) CTA writes out the voting list with confirming voting objects and broadcasts the information related to the voting to all voters. Voting information ĺ Vi (2) It generates a slat value r_salti and an alias identity IDi (i= {1, 2, ..., n}, which are given to voter. Here, r_salti is stored in a voting token and a voter, and voting booth can view this information. (3) CTA signs IDi, and concatenates IDj (j i) with a salt value r_saltj which are Digital Voting Token(DVT) elements. It then sends a signed and encrypted DVT with a voting booth's public key to a voting booth Gi. Note. the number of DVT is based on voter's number in a voting list. EKP_Gi(EKS_CTA(IDj||r_saltj)) ĺ Gi Step 1.2 Tally center Ti Ti generates and signs a seed value r_seed and sends a signed and encrypted r_seed along with a voting booth's public key to Gi. At this time, only Ti takes the seed value. EKP_Gi(EKS_Ti(r_seed)) ĺ Gi

ң

Phase 2. Voting phase Step 2.1 Voter Vi When the voting day, a voter Vi authenticates himself to CTA and joins a voting booth Gi on the Internet. EKS_Vi(Voting list) ĺ CTA Here, a voting list will be compared with a tally center's summary sheet, in the confirming phase. Step 2.2 Voting booth Gi He/She sends one of the DVTs to Vi randomly. DVT ĺ Vi Step 2.3 Voter Vi (1) Vi chooses two random numbers r_și and x. r_și, x R[1, 2, ..., q-1] (2) He/She selects a voting value vi.

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(3) He/She generates the voting results V_result using his/her alias identity IDi, CTA's salt value r_salti, Ti's r_seed, and r_și in this way. V_resulti = IDi || (vjҶr_seed) ||(r_salti(vi Ҷr_și) Ҷr_seed) ||... ||(vkҶr_seed) Note. V_n={selection element1, ..., selection elementn}, viЩV_n, V_sңV_n, vj, vkЩV_s (4) Vi calculates k and k' for group signcryption as follows. k = H(KP_CTAx mod p) k1 || k2 = k k' = H(KP_Tix mod p) k1' || k2' = k' (5) He/She processes the encryption and signature. • For CTA : c = Ek1(V_resulti) r = KHk2(V_resulti) R = gr mod p s = x/(r + xgrpi) mod q • For Ti : c’ = Ek1'(V_resulti) r' = KHk2'(V_resulti) R' = gr' mod p s' = x/(r' + xgrpi) mod q (6) Vi sends the generated information (c, R, s) and (c', R', s'), and send it to CTA and a tally center Ti. (c || R || s) ĺ CTA (c' || R' || s') ĺ Ti Phase 3. Confirming phase Step 3.1 CTA and Tally center Ti (1) When the voting time is over, CTA and Ti exchanger their secret information secure way. EKP_Ti(EKS_CTA(IDi||r_salti)) ĺ Ti EKP_CTA(EKS_Ti(r_seed)) ĺ CTA (2) They certify the received voting information from a voter Vi, and decrypts the voting result V_resulti. • CTA : k = H((ygi*R)s*KS_CTA mod p) k1 || k2 = k V_resulti = Dk1(c) When R = gKHk2'(V_resulti) mod p, then V_resulti is accepted. • Ti : k' = H((ygi*R')s'*KS_Ti mod p) k1' || k2' = k' V_resulti = Dk1'(c') When R' = gKHk2'(V_resulti) mod p, then V_resulti is accepted.

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Step 3.2 Voter Vi A voter concatenates r_și, IDi and a voting result to confirm, and sends this information to a tally center encrypting it with public key of CTA. At this time, a voting result to confirm is chosen in V_resulti by the voter Vi. EKP_CTA(IDi ||r_salti(viҶr_și) Ҷr_seed || r_și) ĺ TCA EKP_Ti(IDi ||r_salti(viҶr_și) Ҷr_seed || r_și) ĺ Ti Step 3.3 CTA and Tally center Ti (1) They verify vi using the received ș value from the voter and exchange information between CTA with Ti. (r_salti * (vi Ҷ r_și) Ҷ r_seed) Ҷ r_seed = r_salti * (vi Ҷ r_și) (r_salti * (vi Ҷ r_și)) / r_salti = (vi Ҷ r_și) (vi Ҷ r_și) Ҷ r_și = vi (2) Tally center Ti shows the recovered information to a voter Vi in which way. IDi||vi (3) After confirming the voting result, Ti opens the total voting results and compares number of voters with the number gotten from the voting list. v1k, ..., vnk (n = a number of voters, k Щ {voting results}) (4) CTA calculates H_V-result using one-way hash function as follows. It then compares its number of voters with the number gotten from the tally center's summery sheet. H_V-result = H(v1k Ҷ ... Ҷ vnk) Step 3.4 All voting entities They verify the total voting result. H(v1k Ҷ ... Ҷ vnk) = H_V-result Phase 4. Opening If the voting results have no problem, CTA announces the election result to all members. Status-based protocol was proposed for the safety of user location for any event in which the session is not terminated safely through the use of the flag. However it does not have a verification process for T therefore if T is altered, authentication is not possible even with transmission from associated tag. In addition if a malicious third party disrupts the last session of a tag whose flag value is 0, the next authentication protocol is processed with the flag value of 1. Here, ID of the database is renewed, but the tag is not able to renew the ID therefore, synchronization problems arise. 2.3 Analysis of Proposed Scheme In the proposed scheme, only authenticated voters can obtain entrance into the voting booth, and get the voting token that is signed digitally by CTA. Because the third party can not associate the voter to his/her voting result and IDi. Also because CTA confirms the voter using voting list, one person for one voting principle is assured. A third party can not vote for other voter and the conduct other illegal acts. After the voting is over, when the voting result is open to the public board, the other voters can

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not trace the voting value using the result. Because tally results are confirmed by only the voters, this scheme retains the receipt free and robustness in voting value and checks the conspiracy of the third party.

3 Conclusion One-way anonymous authentication service is focused on anonymity of the information originator in a group different from peer-to-peer services. Therefore when an anonymous secure selection scheme must be applied to this service, group oriented anonymous authentication can be used. In this paper, we proposed the anonymous secure selection and discussed the efficiency involved with the signcryption. The proposed scheme satisfies the anonymity with authentication, verifiability and integrity and blinds the selection result from other entities on the open network and protects a selection result of an originator using one-way anonymous authentication service.

References 1. Trappe, W., Song, J., Poovendran, R., Liu, K.J.R.: Key Distribution for Secure Multimedia Multicasts via Data Embedding. In Proc. IEEE ICASSP (2001) 1449–1452 2. Agarwal, D.A., Chevassut, O., Thompson, M.R., Tsudik, G.: An Integrated Solution for Secure Group Communication in Wide-area Networks. In Proc. of 6th IEEE Symposium on Computers and Communications (2001) 22-28 3. Viswanathan, K., Boyd, C., Dawson, E.: Secure Selection protocols. The International Conference on Information Security and Cryptology, ICISC '99 (1999) 117–131 4. Zheng, Y.: Signcryption and Its Application in Efficient Public Key Solutions. Proceedings of the Information Security Workshop (1998) 291–312 5. Cohen, J., Fischer, M.: A Robust and Verifiable Cryptographically Secure Election Scheme. Proceedings of the 26th Annual IEEE symposium on the Foundations of Computer Science (1985) 372–382 6. Benaloh, J.: Verifiable Secret-ballot Elections. Ph.D. Thesis, Yale University, Technical Report (1987) 7. Asano, T., Matsumoto, T., Imai, H.: A Scheme for Fair Electronic Secret Voting. Technical Report, IEICE Japan (1990) 21–31

CAST: Design and Implementation of Secure Context-Awareness Simulation Toolkit for Ubiquitous Computing Research Environment InSu Kim1 and YoungLok Lee2 1

Department of Information Security, Chonnam National University, Gwangju, Korea [email protected] 2 Linux Security Research Center, Chonnam National University, Gwangju, 500-757, Korea [email protected]

Abstract. This Paper is significant because it provides virtual, secure experimental environment to the S/W-major ubiquitous computing researchers who find it difficult to fabricate physical sensors. The study deals with the most important elements of ubiquitous computing, that is, the toolkit to acquire, express and safely use the context information. To do so, we introduce CAST and show how it works. CAST generates users and devices in a virtual home domain, designates their relation and acquires virtual context information. The created context information is reused by the request of application and put into use for context learning. Particularly, we have given a consideration to security in the process of context acquisition and its consumption. That is, we applied SPKI/SDSI to test if the created context information was valid information and if the application that called for the context had legitimate authority to do so. CAST not only captures virtual context information, but it also guarantees the safe sharing of the context information requested by the application.

1 Introduction Context Awareness is the most important research area in ubiquitous computing, on which many researches have recently been working on. It was because Mark Weiser, who first suggested the notion 'ubiquitous computing', noted that basically the following 4 should be reflected[20,21,22]: Human-friendly interface, Computing connection at anytime, anywhere, Calm technology, Dynamic service. Like this, Context Awareness is very important to ubiquitous computing that is intended to enable natural and convenient computer use in everyday lives regardless of location and time. Since Context Awareness is important, there have been lots of preceding researches on it. However, there are some limitations and our approach to the resolution of it is as follows:

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• The vagueness of the definition of context: Although there have been many preceding researches, there is no agreed definition of it yet. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1040 – 1055, 2006. © Springer-Verlag Berlin Heidelberg 2006

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• The difficulty in acquiring context: In real world, context information is acquired by physical sensors. However many researchers have hard time in their getting context information since they have mostly majored in S/W part rather than H/W part. For the reason, the majority of the related researchers are apt to do their modeling and research context conceptually without the real context information. • The validity of acquired context information and its safe sharing: Preceding studies on the things such as Context Toolkit have not given any consideration to security while acquiring context. That is, there have been no consideration to if the acquired context information was valid or if the application requesting the acquired context is duly authorized.

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Fig. 1. A scene from the featuring of famous Korean musical named NANTA(left) and Architecture of CAST(right)

The development of CAST(Context-Awareness Simulation Toolkit) which the study suggests was motivated while the author was watching a play in the theater. Figure 1 is a scene from the featuring of famous Korean musical named NANTA(left) and Architecture of CAST(right). The performers( of Figure 1) play with their all might and main in their gestures( ) following the scenario( ) of the playwright( ) against the stage( ) garnished with various stage properties( ). The CAST suggests will create a valid context information for us via a S/W agent concocted virtual sensor instead of a physical sensor. Just like the performers in the play moves us by their performance in their virtual lives, we are going to safely share and reuse the created context information and utilize it in the user adaptation by the context learning. The study is composed of the following. In section 2, it will take a look at related research and in section 3, it will introduce CAST. In section 4, it will discuss the feasibility and its comparison with existing research by a proposed prototype of CAST. Finally, in section 5, it will present the conclusion.

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2 Related Works There have been lots of preceding researches on Context-Awareness. Except the Context Toolkit of A.K.Dey[1,2], All preceding researches acquire context information through physical device in H/W part[6,10].

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2.1 The Context Toolkit of Dey et al. The approach of the Context Toolkit by Dey et al[1, 2, 3, 4] origins from the area of location-aware services. Its main focus is to provide a comprehensive conceptual framework together with a toolkit for representing and processing context information independent of an application, thus establishing an external customisation architecture. The context toolkit which realises only a subset of the frameworks' concepts has been implemented using Java and XML[5]. Various applications have been developed on basis of the toolkit, including, e.g., an in/out board for indicating those persons which are inside a building, a personalised information display which shows the user in front relevant information and a context-aware mailing list sending emails only to those subscribed users which are currently in a certain building. 2.2 The CIVE of Seiie Jang et al. The CIVE(Context-based Interactive system for distributed Virtual Environment) is a system that connects real world with virtual world by sharing user's context[6]. It consists of ubi-UCAM for generating user's context, NAVER for managing virtual environments, and Interface for linking ubi-UCAM with NAVER. Interface transforms contexts or commands into events that influence virtual environment, and converts events into contexts for context-based services in real environment. Especially, ubi-UCAM(a unified context-aware application model) is an essential part in developing personalized services in ubiquitous computing environment. The proposed model, consisting of ubiSensor and ubiService, enables multiple ubiServices to share object-oriented unified context that describes information of 5W1H(Who, What, Where, When, Why and How) generated by ubiSensors. 2.3 The GUIDE of Davis et al. The GUIDE system of Cheverst et al. [10,11,12,13] stems from the area of locationbased services. The focus is to provide tourists with up-to-date and context-aware information about a city via a PDA.

3 Context-Awareness Simulation Toolkit CAST that we suggest defines context with our focus on a specific domain of home, unlike the preceding researches with wide-range definitions of context. The domain can be a school, a hospital, an office or the like. • Contexthome: Context is the information that can particularize the conditions of all entities constituting home and be put into use in decisionmaking. The entity includes people, place and all objects in the actual world.

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3.1 CASThome We have used by Macromedia’s Flash MX 2004 in laying out a home environment with virtual people and devices[16,17]. We chose the technology because it's quite useful with its visual convenience and easy interface. It also has a big merit of its ability to be interlocked with external programs[18] since it supports the intercommunication function with the programs such as JAVA, C++, C# via the XMLsocket Class provided by Flash. Prosumer PDA

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Fig. 2. The devices are classified in their production and consumption of virtual context as Sensor devices and Application devices

3.1.1 Virtual Device Manager We have realized virtual S/W devices by using the Flash MX 2004[16,17] as well as the JAVA sockets. The devices are classified in their production and consumption of virtual context as Figure 2. 3.1.1.1 Sensor device(=Producer). This is a device, with no calculation capability, that only generates context information and that is classified as the following: •

Environment sensors: This is a sensor that produces physical environmental information that is exposed to everybody. • Smart tag sensors: Smart tag sensor connected to private information.

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Sensor Device should be able to transmit context-sensing information to the Context Manager of CASTmiddleware to support the context-recognition environment( -1, -2 of Figure 4). For that, sensing schema is suggested as shown in Figure 3.

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This is the information of the sensor which will provide contextrecognition service and includes the sort of sensor(temperature, humidity, location and the like) and the discriminator. <SensedValue>: This transmits the structure of the information being sensed. Its attributes include the data type and the unit.

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The sensing schema is shared with Context Manager and the sensor programmer generates sensing instance by specifying the necessary contents based on the sensing schema. The following describes the examples of sensing instance sent by the temperature sensor. <Sensing> <SensorInfo> <SensorType>temperature <SensorID>001 <SensedValue dataType="float" unit="celsius">22

3.1.1.2 Application device(=Consumer or Prosumer). A device with calculation capability with itself. Classified as the following: • Consumer: A device that just asks Context manager for context and consumes context.(TV, video, monitor, etc). • Prosumer: A device that not only asks Context manager for context to consume it, but also is able to update its private information-related context. (PDA, cellular phone, etc).

ԜԞ

To perform the service that supports context-recognition, Application Device should be capable of asking context from the Context Manager of CASTmiddleware( in Figure 4). A context request/response schema is suggested as shown in Figure 3 for the use.

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: The information on the Application Device which sent the context request/response instance to provide the context-recognition service. : It is where logical calculation is performed and the answer is either True or False. As its attributes, this supports relation calculation(,”,•,,=). (Example) "Is the temperature above 30 ?". : It is where the number of logical calculation is more than two. In other words, it is when more than two ContextConditions are repeated with either AND or OR calculation. (Example) “Is the temperature above 30 ?” AND “Is the humidity over 75%?. : It is generally a place where requires a value, a single context. (Example) “What is the temperature for now?” : It is the location(=ContextSource) and the kind(=ContextName) of the context that application device requires. (Example) The temperature in the livingroom. : It is an element where the result value from the context request is stored and it may describe the unit and data type with its attributes.

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Context request/response schema is shared with Context Manager. Application programmer generates Context request/response instance while specifying the necessary context information and condition based on the Context request/response schema. The Application sends the event(=context) subscription request of the context information required to perform the service in his own form of instance to the Context Manager via Event Manager( ). After being converted through CQC(Context Query Controller) via pre-processing(parsing) into Context Query statement, it queries to Context Repository(DB)( ) and replies the context information on the event subscription ( ). An example of the instance of Application Device requiring described in section 4.2.2.

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3.1.2 Virtual Person Manager This generates family members that belong to the virtual home environment. The profile of each member will be stored in their cellular phones and will be updated at all times. The profile will be written in SOUPA(Standard Ontology for Ubiquitous and Pervasive Applications)[7,8,9] and includes the information of their respective domain homes as well as the application device. The following shows a partial ontology description of the person Kim In-su: In-su <dev:modelNumber rdf:datatype="&xsd;string>SCH-E120 <dev:serialNumber rdf:datatype="&xsd;string>R24W114948 <dev:phoneNumber rdf:datatype="&xsd;string>017-365-8477

…..

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3.1.3 Virtual Home-Map Editor It generates a virtual home environment as the domain of CAST. A virtual home, like a home in real world, may consist of rooms, a living room, bath room and kitchen. Also, the Sensor and, Application devices generated by Virtual Device Manager will be put into appropriate places in the virtual home(Figure 7). 3.2 CASTmiddleware CASTmiddleware performs the communication role among the virtual people and devices set in CASThome. It is composed of Event Manager and Context Manager. Their respective roles are like the following. 3.2.1 Event Manager (SeJES:Secure Javaspaced-Based Event Service) Ubiquitous services must appropriately adapt to the context information of the user. In need of privacy protection and proper adaptation, context information should be generated from the accurate event information and only right possessor of the authority on the event should utilize it. The ad hoc network environment introduces fundamental new problems. One is the absence of an online server, and another is secure transient association. Authentication and Authorization are the most interesting security problems in ad hoc networking, because much of the conventional wisdom from distributed systems does not quite carry over. For solving these problems, we use SPKI/SDSI (Simple Public Key Infrastructure/Simple Distributed Security Infrastructure) certificates [15, 18]. 3.2.1.1 ACL and SPKI/SDSI Certificate. The consumer of events will have the following Name Certificate() and Authorization Certificate()[15]. The event consumer sends Name Certificate and Authorization Certificate bundled together to LRC when registering event listeners. ACL includes security policy which event producer endows the beneficiary event consumer the authority and is expressed as the Authorization Certificate. The following explains S-expression of Authorization Certificate. Bob grants subject, called InSu Kim in his local name space, its authority, “get notification 2” from Nov.20,2005 to June.18,2006. (cert (display plain) (issuer (public-key (rsa (e #010001#) (n |APsREOm+tJQsyS6f7ddzrY4A ...|)))) (subject (name InSu Kim)) (tag “get notification2”) (valid (not-before "2005-11-20_06:51:33") (not-after "2006-6-18_21:51:33")) (comment "test certificate") (signature (hash sha1 |aj5Le4mGJ1BltdNdhUm3BVxjgrw=|) (public-key (rsa (e #010001#) (n |APsREOm+tJQsyS6f7ddzrY4ACM9fmQC ...|))) (rsa-pkcs1-sha1 |mSWhfa2GBJ3YKwkEYL/7yCP3Iicw... |))

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3.2.1.2 SPKI/SDSI Certificate Manager. SSCM(SPKI/SDSI Certificate Manager) includes “Certificate Chain Discover” algorithm which carries out the work of retrieving from its certificate cache authority certificates and name certificates provided to verify the authority for the consumer to perform the given calculation[15]. 3.2.1.3 Listener Registration Controller (The first security challenge: Authorization). LRC (Listener Registration Controller) registers only the event listener of authorized consumer (Application Device) to JES. LRC sends the event type and certificate bundle which it received from consumer to SSCM for authority probation and decides by the feedback whether to register the event listener [23, 24]. The following is the process in which the certification and authorization is performed on the Application Device as the consumer of events( - of Figure 4).

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Ԙ The consumer of events retrieves ACLs via Event Manager for the event type that it wants to receive prior to trying event communication. ԙ The consumer of events verifies that it has the subscription authority for the Ԛ ԛ

event type with ACLs and its list of certificates and transmits the verified results to LRC. It requests SSCM to probe the certification package and receives the feedback. Once the subscription authority is verified, LRC records the information on the consumer of events to let the consumer register later on. The consumer of events that is verified to have the legitimate authority on the type of events requests LRC to register it as event listener. LRC downloads and registers the listener stub for the legitimate consumer of events and registers event listeners.

3.2.1.4 Event Registration Controller (The second security challenge: Authentication). ERC (Event Registration Controller) registers only the events of authenticated producer (=sensor device) and produces valid context. It tests the event type registered by producer and checks for any error for ACLs and for any overlapping of the event registered [23, 24]. The following is the process where the certification/authorization for sensor device as the event producer is performed( - of Figure 4).

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‫ ݎ‬Once the power is on, Sensor Device1, an Event producer, sends the certifica‫ݏ‬ ‫ݐ‬

tion package containing the event type that it supplies, ACLs and verifying that it has the authority to publish the events to ERC, requesting it to register as event producer. After checking for any errors, ERC requests SSCM(SPKI/SDSI Certificate Manager) to verify the certification package and to register event publication. Based on the verified value of the certification package, SSCM registers event type as well as ACLs. ERC records the information on the event producer to be able to later process the events published by event producer.

3.2.2 Context Manager The context manager processes context information coming from sensors, stores it, and converts it into high layer's context information according to the inference policy. Also, it performs dynamic query on the context information that application device

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requests. The context information, stored in the database, is reused later in the study of user sign or when the application demands. This context information is the events which application devices want, so to inference those events the context manager provides GUI for setting the inference policy. 3.2.2.1 CQC (Context Query Controller) (1) Sensor Device query processing After Sensor Device is verified( - of Figure 4), the following describes sensor device query processing.

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‫ݒݑ‬of Figure4

‫ݑ‬The Event Manager announces the advent of the sensor by transmitting the sensing instance of the sensor to the CQC of Context Manager(‫ݑ‬-1). CQC parses the instance, transforms it into a CREATE table in SQL, and generates the sensor table in the DB(‫ݑ‬-2). Of course, once the same device already exists, it must not be generated repeatedly. ‫ݒ‬If the sensing event really happens later(‫ݒ‬-1), it is transformed into INSERT or UPDATE table in SQL through CQC and is stored in the given sensor table (‫ݒ‬-2). (2) Application Device query processing After the verification of application device(Ԙ-ԛ of Figure 4), the following ԜԞ of Figure 4 describes application device query processing. Ԝ The application sends the event(=context) subscription request of the context ԝ Ԟ

nformation required to perform the service in his own form of instance to the Context Manager via Event Manager. After being converted through CQC(Context Query Controller) via pre-processing (parsing) into Context Query statement, it queries to Context Repository(DB). It replies the context information on the event subscription.

3.2.2.2 CIC (Context Inference Controller). CIC (Context Inference Controller), following given reasoning policy, re-transforms a low-level context to a high-level one, either storing through CQC or replying the query of the Application. 3.2.2.3 Context Repository. Context store is where context information is systematically arranged and stored. In the study, for the later re-use of the context, it was stored using DBMS in MySQL. 3.3 CASTadmin CASTadmin defines the relations between the device deployed in the CASThome as a domain and the person belonged to it, and generates policy and scenario. The defined relations and policy are to decide who can own and use which device. And person actually behaves following the scenario, then the subsequent virtual device is going to produce or consume context information via the communication with CASTmiddleware. The detailed explanation of it is omitted due to space consideration here.

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4 Implementation and Analysis To probe the feasibility of the suggested CAST, we implemented it in Linux/Windows OS, Macromedia’s Flash MX 2004[16,17], JDK 1.3 and Jini 1.2 development envi ronment[23,24]. We set up a scenario, and subsequently observed that virtual certified devices produce valid context information in accordance with the scenario and that authorized TV devices share and consume it. Application devices

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Fig. 5. The communication flow between CASTdevice and CASTmiddleware that takes place once Bob sits on the sofa

4.1 Scenario We realized the prototype scenario as the following: “On July 5, 2005, PM 6:00, Bob heads for home after work. In the way, he stops by a grocery store to buy some fruits. When he arrives home, the light goes on and after certification, he enters home. First, he changes his clothes in his home, then he has a brief dinner and sits on the sofa. The context manager, detecting his sitting on the sofa, turns on the TV to a channel based on Bob's appetite. He runs out to the grocery store to retrieve his wallet that he had mistakenly dropped there, with the TV on. When Bob came back, the TV is off, but turns on to the same channel that he viewed when he sits on the sofa.” 4.2 Prototype Implementation 4.2.1 Scenario process The information generated by the sofa sensor is transmitted to Context Manager through JES of Event Manager and stored there. Since the acquired information is the one that is called to turn the TV On/Off, it is automatically transmitted to the TV through JES of Event Manager. Of course, the information of whether the TV has the authority to use the context information generated will be transmitted only when it is probed in SSCM of Event Manager.

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4.2.2 Context Request/Response Instance of TV The following is the Context Request/Response Instance of TV in the livingroom. The content of the instance is "'Is there someone in the livingroom?' and 'Is someone sitting on the sofa?'". ‫ۈۊۊۍٻۂۉۄۑۄڧ‬ ‫ۍۊێۉۀێٻۏۃۂۄڧ‬

‫ۍۊێۉۀڮٻۉۊۄۏڼھۊڧ‬

‫ڄۉ ڪڃۀھۄۑۀ ڟٻڱگ‬

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Fig. 6. Demo and Prototype of our proposed CAST using JAVA, Macromidea Flash MX 2004 <ServiceID>TV 00002 pressure livingroom:sofa1 0 location Any livingroom

4.2.3 TV On/Off Algorithm The On/ Off adaptation algorithm for TV’s Context Request/Response Instance replyed by Context Manager is as follows:

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O Algorithm: TV Adaptation(TvConRequestReponse tvevent) O Input: tvevent //instance responsed by Context Manager O Method begin switch(_self.flag) //TV’s state(Off or On) begin case FALSE: // In the case of TV_OFF if((tvevent.sofa>0)ӡ tvevent.livingroom==TRUE)TvON(); case TRUE: // In the case of TV_ON if(tvevent.livingroom==FALSE) TvOFF(); end end

4.2.4 Prototype Implementation and Demo When Bob enters into living room, the location sensor detects his presence and turns the light on(Figure 6). But the TV does not go on by the Rule designated by the TV On/Off Adaptation Algorithm. If Bob sits on the sofa by clicking “Sit Down” button of sofa in living room, by the rule, the TV goes on(Figure 6). 4.3 Analysis The study suggested CAST for the purpose of acquiring, expressing and safely using context information in the previous sections and probed its feasibility by a Demo of a realistic prototype. In particular, we could find a big merit of guaranteed security in the aspects of context acquirement(=Authorization, The first security challenge) and consumption/sharing(=Authentication, The second security challenge) in Figure 7.

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We have compared and reviewed CAST realized by a prototype and preceding studies, focusing on the following[19]. • Authentication. It means which context information acquired from certain types (manual, semi-automatic, automatic) is valid, that is, if the context is attained from certified source.(The first Security challenge). • Authorization. It means whether it provides the acquired context information to only the application with due authority.(The second Security challenge) • Automation. Concerning the acquisition of context, first it has to be defined who is in charge for gathering appropriate context information, be it either a human (manual acquisition) or the system(automatic acquisition) or a combination thereof(semi-automatic acquisition). • Dynamicity. Another important aspect is when context acquisition takes place. Considering the frequency of context changes, context can be either static, i.e., determined once at application start up(e.g., the device used to select the appropriate interaction style), without considering any further changes or dynamic, i.e., determined on every change during runtime(e.g., the bandwidth to adapt the resolution of an image on the fly). • Abstraction. According to the level of abstraction where context properties are represented it should be distinguished between physical context and logical context. • Reusability. A customization approach should allow to explicitly represent context within the system, not just to intermingle context with adaptation or the application it self. An explicit representation would allow for reusability of already defined context across several applications.

5 Conclusion CAST generates users and devices in a virtual home domain, designates their relation and acquires virtual context information. In particular, CAST acquires valid context and supports the function of sharing it with only authorized applications. This is significant because it provides virtual experimental environment to the S/W-major context researchers who find it difficult to fabricate physical sensors. As a conclusion, the CAST that the study suggests has the following characteristics: First, it supports the acquisition of reusable contexts through virtual device. Second, it can have confidence in the context acquired by certification/authorization support, and application devices can safely use it. Third, it supports the experimental environment that is capable of applying a user-defined scenario through a virtual home environment configuration. Fourth, by suggesting Context Request/Response Schema of devices, any devices can instantly recognize and be deployed without having to re-modify the Context Manager in the home environment.

Acknowledgement This research was supported by the MIC, Korea, under the ITRC(Information Technology Research Center) support program supervised by the IITA(Institute of Information Technology Assessment).

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References 1. Abowd, G.D:. Software Engineering Issues for Ubiquitous computing. Int. Conf. on Software Engineering, Los Angeles, (1999) 75-84 2. Dey, A.K., Abowd, G.D.: The Context Toolkit: Aiding the Development of ContextAware Applications. Workshop on Software Engineering for Wearable and Pervasive Computing, Limerick, Ireland, June, (2000) 434-441 3. Dey, A. K., Kortuem, G., Morse, D. R., Schmidt, A.: Situated Interaction and ContextAware Computing. editorial, Personal Ubi Comp, Vol. 5 (2001) 1-3 4. Dey, A.K., Salber, D. Abowd, G.D.: A Conceptual Framework and a Toolkit for Supporting the Rapid Prototyping of Context-Aware Applications. anchor article of a special issue on Context-Aware Computing Human-Computer Interaction (HCI) Journal, Vol. 16 (2001) 97-166 5. Means,W.S., Harold,E.R.: XML in a Nutshell. A Desktop Quick Reference, O’Reilly, (2001) 6. Jang, S., Lee Y.H., Woo, W.: CIVE: Context-based Interactive System for Distributed Virtual Environment. ICAT 2004 (2004) 495-498 7. Chen, H., Perich, F., Finin, T., Anupam J.S.: SOUPA: Standard Ontology for Ubiquitous and Pervasive Applications. (2004) 258-267 8. Chen, H., Perich, F., Finin, T., Anupam J.S., Kagal, L.: Intelligent Agents Meet the Semantic Web in Smart Spaces. the IEEE Computer Society, October, (2004) 9. Chen, H., Finin, T., Joshi, A.: An Ontology for Context-aware Pervasive Computing Environments. Special Issue on Ontologies for Distributed Systems, Knowledge Engineering Review, (2003) 265-270 10. Davis, N., Cheverst, K., Mitchel, K., Efrat, A.: Using and Determining Location in a Context Sensitive Tour Guide. IEEE Computer, (2001) 35-41 11. Cheverst, K., Davies, N., Mitchell, K., Friday, A.: Experiences of Developing and Deploying a Context-Aware Tourist Guide: The GUIDE Project. Proc. Of the 6th Int. Conference on Mobile Computing and Networking (MOBICOM), Boston MA USA, ACM, Press (2000) 20-31 12. Mitchel, N.D.: The Role of Adaptive Hypermedia in a Context-aware Tourist Guide. Communications of the ACM (CACM), Vol. 45 (2002) 47-51 13. Davies, N., Cheverst, K., Mitchell, K., Efrat, A.: Using and Determining Location in a Context-Sensitive Tour Guide. IEEE Computer, Vol. 34 (2001) 35-41 14. Lee, Y.L., Lee, S.Y., Kim, I.S., Lee, H.H., Noh, B.N.: Development of Event Manager and Its Application in Jini Environment. IFIP International Conference on NCUS 2005, Nagasaki, Japan, (2005) 704-713 15. Lee, Y.L., Lee, S.Y., Park, H.M., Lee, H.H., Noh, B.N.: The Design and Implementation of Secure Event Manager Using SPKI/SDSI Certificate. IFIP International Conference on UISW 2005, Nagasaki, Japan, (2005) 490-498 16. Kaye, J., Castillo, D.: FlashTM MX for Interactive Simulation. THOMSON, 2005 17. Swann, C., Caines, G.: XML in FlashTM. QUE Publishing, (2002) 18. Liu, M. L.: Distributed Computing: Principles and Applications.PEARSON ADDISONWESLEY, (2004) 19. Kappel, G., Proll, B., Retshitzegger, W., Schwinger, W.: Customisation for Ubiquitous Web Applications: A Comparison of Approaches. International Journal of Web Engineering and Technology, Vol.1 (2003) 79-111

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20. Weiser, M.: Some Computer Science Problems in Ubiquitous Computing. Comunications of the ACM, (1993) 34-38 21. Weiser, M.: Ubiquitous Computing. Nikkei Electronics, (1993)137-143 22. Weiser, M.: The World is Not a Desktop. Interaction, (1994) 7-8 23. Bishop, P., WARREN, N.: JavaSpacesTM in Practice. Addison-Wesley, (2002) 24. Edwards, W.K.: Core JINI. 2nd edn. Prentice Hall PTR, (2000)

Support Vector Machine for String Vectors Malrey Lee1 and Taeho Jo2 1

School of Electronics & Information Engineering, ChonBuk National University, 664-14, 1Ga, DeokJin-Dong, JeonJu, ChonBuk, 561-756, South Korea [email protected] 2 SITE, University of Ottawa, Room 5010, SITE, 800 King-Edward Ave, Ottawa, Ontario, Canada K1N6N5

Abstract. This paper proposes an alternative version of SVM using string vectors as its input data. A string vector is defined as a finite ordered set of words. Almost all of machine learning algorithms including traditional versions of SVM use numerical vectors as their input data. In order to apply such machine learning algorithms to classification or clustering, any type of raw data should be encoded into numerical vectors. In text categorization or text clustering, representing documents into numerical vectors leads to two main problems: huge dimensionality and sparse distribution. Although traditional versions of SVM are tolerable to huge dimensionality, they are not robust to sparse distribution in their training and classification. Therefore, in order to avoid this problem, this research proposes another version of SVM, which uses string vectors given as an alternative type of structured data to numerical vectors. For applying the proposed version of SVM to text categorization, documents are encoded into string vectors by defining conditions of words as their features and positioning words corresponding to the conditions into each string vector. A similarity matrix, word by word, which defines semantic similarities of words, should be built from a given training corpus, before using the proposed version of SVM for text categorization. Each semantic similarity given as an element of the matrix is computed based on collocations of two words within their same documents over a given corpus. In this paper, inner product of two string vectors as the proposed kernel function indicates an average semantic similarity over their elements. In order to validate the proposed version of SVM, it will be compared with a traditional version of SVM using linear kernel functions in text categorization on two test beds.

1 Introduction SVM (Support Vector Machine) refers to a kernel based machine learning algorithm where a vector space is mapped into another vector space where training examples are linearly separable, and two hyper-planes corresponding to two classes are defined with the maximal margin between them as boundaries of classification. In SVM, the mapped space is called feature space, and a function for computing inner products of two examples mapped into the feature space is called a kernel function [4]. Examples involved in defining these hyper-planes are called support vectors [2]. Since SVM is D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1056 – 1067, 2006. © Springer-Verlag Berlin Heidelberg 2006

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tolerant to huge dimensionality of input vectors, it has been applied very popularly to text categorization where documents are represented into high dimensional numerical vectors. In 1998, Joachims initially applied SVM to text categorization and shown that SVM had better performance than NB [7]. In 1999, Drucker et al applied SVM to spam email filtering which was a real task using text categorization and shown that SVM was also the better approach than NB [3]. In 2002, Sebastiani surveyed more than ten machine learning based approaches to text categorization and concluded that SVM is the best approach among them [11]. In 2004, Park and Zhang proposed training SVM using labeled and unlabeled documents by co-training for text categorization [10]. SVM has been applied not only to text categorization, but also to other classification problems including image classification and protein classification [1,2]. These previous literatures have shown that SVM is very good approach to text categorization. However, representation of documents into numerical vectors for text categorization leads to not only huge dimensionality, but also sparse distribution. Although SVM is tolerable to the former, it is not robust to the latter, together with other traditional machine learning algorithms, such as NB, KNN, and traditional neural networks. The reason is that if numerical vectors become very sparse, they lose their discrimination for classification. In order to solve the two problems, Lodhi et al proposed a new kernel function, called string kernel, in 2002 [8]. String kernel is applicable to texts themselves without representing documents in a structured format. The advantages of string kernel are that it is applicable to documents independent of a natural language in which they are written, and that it captures semantic relations implicitly between two documents. However, it requires defining approximately 20,000 substrings; it takes very much time to compute a value of inner product between two raw texts using the string kernel. The experiments of Lodhi el al presented that their proposed kernel failed to improve the performance of SVM in text categorization on the test bed Reuter 21578 [8]. In using SVM for text categorization, this paper proposes that documents should be represented into string vectors instead of numerical vectors. A string vector refers to a finite ordered set of words, and it will be described in section 2.2. In other words, words replace numerical values in string vector. When Jo proposed a new neural network, called NTC (Neural Text Categorizer), in 2000, string vector was initially used for representing documents [5]. Recently, we discovered that string vectors are applicable not only to NTC or NTSO (Neural Text Self Organizer) [7], but also to other traditional machine learning algorithms, such as SVM, NB, and KNN, if they are modified properly. Therefore, this paper proposes a modified version of SVM where a kernel function for string vectors is employed. Since a kernel function is for computing an inner product of two mapped vectors, the inner product implies a similarity between two entities whether they are mapped or not. Based on this fact, this paper defines a kernel function for string vectors as their semantic similarity. Before using the kernel function, it requires building a similarity matrix word by word from a particular corpus. The matrix defines semantic similarities between words as normalized values and the semantic similarities are computed based on collocations of words within their same documents.

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In the experiments of this paper, the proposed version of SVM will be compared with its traditional version and NB on two test beds, NewsPage.com and Reuter 21578. The experiments in section 4 will show that the proposed version of SVM is best one among them on both test beds. On the second test bed, the proposed version of SVM is evaluated as the best one, in macro-averaged F1, rather than in microaveraged F1. This means that the proposed version works very well to sparse categories where a small number of training documents is given. This paper consists of five sections. Section 2 describes processes of encoding documents into two structured formats, numerical vectors and string vectors. Section 3 explains the brief concept of SVM, and presents kernel functions for numerical vectors and string vectors. Section 4 presents experimental results where the proposed version of SVM is compared with its traditional version and NB on two test beds. Section 5 mentions significances of this research and further researches to improve the current one, as the conclusion of this paper.

2 Text Representations Since texts are unstructured data in natural languages and computers can not process them directly, they should be encoded into structured data for processing them. This section describes two ways to do that. One is for the traditional version of SVM and NB, and the other is for the proposed version of SVM. 2.1 Numerical Vectors This subsection describes the traditional way to encode texts. In this method, texts are represented into numerical vectors. Main machine learning algorithms such as NB (Naïve Bayes), SVM (Support Vector Machine), MLP (Multi-Layer Perceptron), and Kohonen Network use numerical vectors as their input vectors. This method is necessary to apply such machine learning algorithms for text categorization and text clustering. Features given as attributes of numerical vectors representing texts are words in a collection of texts. If all of words were used as their features, their dimension would be more than 10,000; such a dimension is not feasible for text categorization and text clustering. Previous research suggested several methods of feature selection, such as mutual information, chi-square, frequency based method, and information theory based method [11]. There are three ways to define feature values in numerical vectors representing texts. The first way is to use a binary value for each word indicating its presence or absence in the text. The second way is to use the frequency of each word in each text as its value. In this way, each element is an integer. The third way is to use the weight of each word as a feature value. Such a weight is computed from the equation (1). wit = f it (log 2 N − log 2 d t + 1)

(1)

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where wit is the weight of the word, t in the text, i , f it is the frequency of the word, t in the text, i , N is the number of texts in the corpus, and d t is the number of texts including the word, t . 2.2 String Vectors This section describes string vectors as representations of documents for applying the proposed version of SVM to text categorization. A string vector refers to a finite ordered set of words. Each of such words may be mono-gram, bi-gram, or n-gram. A string vector is defined as an ordered set of words with the fixed size, independent of the length of the given document. The string vector representing the document, d i is denoted by vector,

d is = [wi1

wi 2 ... win ] , where n is the dimension of the string

s i

d . An arbitrary example of a four dimensional string vector is expressed as

[computer, software, hardware, machine]. From the given document, a bag of words is generated by indexing the document, as an intermediate representation for a string vector. Figure 1 illustrates the process of mapping a bag of words into a string vector. The dimension of a string vector is determined and the properties of words, such as the word with its highest frequency in the document, a random word in the first sentence, the word with its highest weight, or the word with its highest frequency in the first paragraph, are defined with the features of that vector. For simplicity and convenience of implementing the automatic process of encoding documents into string vectors, we defined the properties of string vectors as the highest frequent word, the second highest frequent word, the third highest frequent word, the fourth highest frequency word, and so on, in the document. In general, the dimension of string vectors is smaller than the size of bags of words. To each property given as a feature, its corresponding word is arranged so as to build a string vector.

Fig. 1. The process of mapping a bag of words into a string vector

Before performing operations on string vectors, from a particular corpus, we need to define a similarity matrix, a word by word matrix whose entries indicate similarities of all possible pairs of words. The idea of building a similarity matrix is based on the research of [2]. However, since word by word matrix defined in the literature does not provide normalized similarity values of words and a similarity between two

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identical words varies depending on their frequencies and distributions over a corpus, this research define similarities between words, differently from the previous research. In word by word matrix in this research there are words denoted by w1 , w2 ,..., wN , where N is the number of unique words in the given corpus, except stop words. It is denoted by the matrix, N by N , as follows.

ª s11 «s S = « 21 « ... « ¬sN1

s12 s22 ... sN 2

Its elements are denoted by sij (1 ≤ i, j ity, sij

... s1N º ... s2 N »» ... ... » » ... s NN ¼

≤ N ) , and defined as a semantic similar-

= sim( wi , w j ) , between two words, wi and w j . Each element,

sij (1 ≤ i, j ≤ N ) , is computed based on the collocation of two words, wi and w j , within a same document, using equation (2),

¦ (φ (w ) + φ (w )) r

sij = sim( wi , w j ) =

¦φ

p

( wi ) +

d p ∈Di

where

i

r

j

d r ∈D i ∩ D j

(2)

¦φ (w ) q

j

d q ∈D j

Di is the set of documents including the word, wi , and D j is the set of

φo (⋅) is the function of a word, unique to a function, φo (⋅) , means its occurrence, frequency, or

documents including the word, w j , and particular document,

do . The

weight computed by a particular equation, in the document,

do .

If a similarity matrix is built from a corpus by computing similarities between all possible pairs of words using equation (2), we can compute the similarity between s

two string vectors, denoted by d i

= [ wi1 , wi 2 ,..., win ] and d sj = [ w j1 , w j 2 ,..., w jn ] .

The similarity sim( wik , w jk ) between two words,

wik and w jk is obtained by

looking up the entry with the row corresponding to the word,

wik and the column

corresponding to the word, w jk or with its reverse, from the similarity matrix. The s

similarity between two string vectors di and

sim(d i , d j ) ≈ sim(d is , d sj ) =

d sj is computed using equation (3). 1 n ¦ sim(wik , w jk ) n k =1

(3)

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As illustrated in equation (3), the similarity between two string vectors is the average over the similarities of their elements.

3 Support Vector Machine This section describes the brief concept of SVM and presents kernel functions for numerical vectors and string vectors. SVM has been known as a good approach to any classification problem with respect to its theory and practice [4], and it has been applied to various classification tasks including text categorization [2]. Equation (4) models the classification of SVM trained by training examples, x1 , x 2 ,..., x m .

§ m · f (x) = sign¨ ¦ α i k (x ⋅ x i ) + b ¸ © k =1 ¹ where

αi

(4)

is a Lagrange multiplier correspond to a training example,

x i , k (⋅) is a

kernel function which computes an inner product between two mapped examples without mapping them explicitly, and b is a bias of SVM. The function defined in m

equation (4) generates 1 as its output, if the value of

¦ α k (x ⋅ x ) + b is greater i

i

k =1

than zero. Otherwise, it generates -1. The learning of SVM is the process of optimizing the given Lagrange multipliers, α 1 , α 2 ,..., α m , with the given training examples,

x1 , x 2 ,..., x m . Here support vectors are training examples whose Lagrange multipliers are non zero. For optimizing these Lagrange multipliers, SMO (Sequential Minimal Optimization) algorithm is used popularly. Its detail description is included in literatures, [10] and [2]. 3.1 Kernel Functions for Numerical Vectors This subsection presents three typical types of kernel functions for numerical vectors. These types are linear function, polynomial function, and Gaussian function. The linear function is defined in equation (5), and it means the inner product between two vectors in their original space and c is an arbitrary constant.

k (x i ⋅ x j ) = x i ⋅ x j + c

(5)

Polynomial function is defined in equation (6) and it means that a linear function defined in equation (5) is squared several times.

k (xi ⋅ x j ) = ((x i ⋅ x j ) + c )

p

(6)

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The third type of kernel function is defined in equation (7) and it could compute inner products between two vectors mapped even into a vector space with infinite dimensionality.

§ (x i − x j )2 · ¸ k (xi ⋅ x j ) = exp¨ − ¨ ¸ σ © ¹

(7)

Among these types of kernel functions, linear function defined in equation (5) is used popularly in text categorization, and there is little difference in their performance in using SVM [10]. 3.2 Proposed Kernel Function This subsection describes the proposed kernel function for string vectors. It is supposed that two documents are represented into two string vectors,

d is = [ wi1 , wi 2 ,..., win ] and d sj = [ w j1 , w j 2 ,..., w jn ] . The proposed kernel function is defined in equation (8).

(

)

(

k d is ⋅ d sj = sim d is , d sj

)

(8)

The proposed kernel function indicates a semantic similarity between two string vectors, and their semantic similarity is expressed in equation (3). Therefore, the proposed version of SVM is expressed in equation (9).

(

)

(

)

§m · § m · f (x ) = sign¨ ¦ α i k d is ⋅ d sj + b ¸ = sign¨ ¦ α i sim d is , d sj + b ¸ © k =1 ¹ © k =1 ¹

(9)

These Lagrange multipliers are optimized using SMO algorithm also in the proposed version, like the traditional version of SVM.

4 Experimental Results This section presents results of evaluating NB and two versions of SVM, on the two test beds, NewsPage.com and Reuter 21578. The NB and traditional version of SVM use 500 dimensional numerical vectors representing documents for their learning and classification, while the proposed version of SVM uses 10 dimensional string vectors in this experiment. The size of input data used in the proposed version of SVM is far smaller than that of input data in the others. This experiment is partitioned into two sets based on the test beds. The first set and the second set of this experiment are evaluations of the three approaches on NewsPage.com and Reuter 21578, respectively. In this experiment, documents are represented into string vectors for using the proposed version of SVM or numerical vectors for using the others. Dimensions of numerical vectors and string vectors representing documents are set as 500 and 10,

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respectively, in the two sets of this experiment. For encoding documents into numerical vectors, most frequent 500 words from a given training set for each test bed are selected as their features. The values of the features of numerical vectors are binary ones indicating absence or presence of words in a given document. For encoding documents into string vectors, most frequent 10 words are selected from a given document as values of its corresponding string vector. Here, features of string vectors are the most frequent word, the second most frequent word, the third most frequent word, and so on. SVM has its capacity which means the maximum value of its Lagrange multipliers, as its parameter. In this experiment, its value is set to 4.0, arbitrary, since its value influence very little on the performance of SVM. 4.1 NewsPage.com The first set of this preliminary experiment pursues the evaluation of the three approaches on the test bed, Newspage.com. This test bed consists of 1,200 news articles in the format of plain texts built by copying and pasting news articles in the web site, www.newspage.com. Table 1 shows the predefined categories, the number of documents of each category, and the partition of the test bed into training set and test set. As shown in table 1, the ratio of training set to test set is set as 7:3. Here, this test bed is called Newspage.com, based on the web site, given as its source. Table 1. Training Set and Test Set of Newspage.com

Category Name Business Health Law Internet Sports Total

Training Set 280 140 70 210 140 840

Test Set 120 60 30 90 60 360

#Document 400 200 100 300 200 1200

The task of text categorization on this test bed is decomposed into five binary classification problems, category by category. In each binary classification problem, a classifier answers whether an unseen document belongs to its corresponding category, or not. Table 2 shows the definition of training sets of the predefined categories. In table 2, ‘positive’ indicates that documents belong to the corresponding category, while ‘negative’ indicates that documents do not. For each training set, all of documents not belonging to its corresponding category are allocated as documents in negative class. For each test set, in negative class, documents are allocated as many as positive documents defined in the third column of table 1.

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Table 2. The Allocation of Positive and Negative Class in Training Set of each Category

Category Name Business Health Law Internet Sports

Positive 280 140 70 210 140

Negative 560 700 770 630 700

Total 840 840 840 840 840

Figure 2 presents the results of evaluating NB and two versions of SVM on the first test bed, NewsPage.com. In the x-axis of the graph illustrated in figure 2, the left group indicates micro-averaged F1, the right group indicates macro-averaged F1, and each individual bar within each group corresponds to one of NB and two versions of SVM. The y-axis means the value of micro-averaged or macro-averaged F1. In figure 2, ‘SVM-trad’ means the traditional version of SVM and ‘SVM-new’ means the proposed version of SVM. As illustrated in figure 2, the results show that the proposed version of SVM has the best performance in text categorization among the three approaches. They show also that the traditional approach of SVM does not have as good performance even as NB.

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

SVM-trad SVM-new NB

Micro

Macro

Fig. 2. Results of evaluating NB and two versions of SVM on NewsPage.com

4.2 Reuter 21578 The second set of this experiment is for the evaluation of the three classifiers on the test bed, Reuter21578, which is a typical standard test bed in the field of text categorization. In this experiment set, ten largest categories are selected. Table 3 shows ten selected categories and the number of training documents and test documents in each category. The partition of this test bed into training set and test set follows the version, ModApte, which is the standard partition of Reuter 21578 for evaluating text

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Table 3. Partition of Training Set and Test Set in 20NewsGroup

Category Name Acq Corn Crude Earn Grain Interest Money-Fx Ship Trade Wheat

Training Set 1452 152 328 2536 361 296 553 176 335 173

Test Set 672 57 203 954 162 135 246 87 160 76

#Document 2124 209 531 3490 523 431 799 263 495 249

clasifers [11]. The number of documents in each category is very variable as shown in table 3. Figure 3 illustrates the results of evaluating NB and two versions of SVM on the test bed, Reuter 21578. The difference of this experiment set from the previous experiment set is that SVM works slightly better than NB. In the results of this experiment set, the proposed version of SVM is evaluated as the worst approach with micro-averaged F1, but as the clearly best approach with macro-averaged F1, as illustrated in the left and right side of figure 3. The results mean that the proposed SVM works very well to sparse categories, each of which the size is very small.

0.7 0.6 0.5 SVM trad

0.4 0.3

SVM new

0.2

NB

0.1 0 Micro

Macro

Fig. 3. Results of evaluating NB and two versions of SVM on Reuter 21578

These two experiment sets validated the performance of the proposed version of SVM. Note that the proposed version of SVM used only ten dimensional string vectors as its input data, while the others used even 500 dimensional numerical vectors as their input data. Considering this point, even if the proposed version is not better than the others, but comparable to them, the proposed version is more recommendable.

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However, the proposed version requires building a similarity matrix from a particular corpus, before we apply it to text categorization. Although it takes very much time to build the similarity matrix, it can be reused continually once it is built.

5 Conclusion The significance of this research is to propose a practical version of SVM for text categorization. The proposed version of SVM has better performance than its traditional version and NB, in spite of its far smaller input size. Note that although the traditional version of SVM is tolerable to huge dimensionality of numerical vectors, it is not robust to their sparse distribution together with other traditional machine learning algorithms. This research shows that representing documents into string vectors is more practical than into numerical vectors for tasks of text categorization. A weakness of SVM including the proposed version is its applicability only to binary classification problems. As shown in equation (4) and (9), SVM classifies any entity into one of two classes: positive class and negative class. If we apply it to a multiple classification problem, we must decompose it into several binary classification problems. Other machine learning algorithms, than SVM, such as KNN, NB, and back propagation, are applicable to a multiple classification problem, without its decomposition. It is necessary to modify SVM to be applicable to a multiple classification problem without decomposing it. In addition to the proposed kernel function described in section 3.2, more kernel functions for string vectors could be defined. Current research defined only one kernel function for string vectors. In further research, we plan to define other kernel functions for string vectors and compare them with each other.

Acknowledgements This Research was supported by the MIC(Ministry of Information and Communication), Korea, under the ITRC(Information Technology Research Center) support program supervised by the IITA(Institute of Information Technology Assessment) (IITA-2005-C1090-0502-0023).

References 1. Cristianini, N., Shawe, T. J.: Support Vector Machines and Other Kernel-based Learning Methods. Cambridge University Press, London (2000) 2. Cristianini, N., Shawe-Taylor, J., Lodhi, H.: Latent Semantic Kernels, Journal of Intelligent Information Systems, 18 ( 2-3) (2002) 127-152 3. Drucker, H., Wu, D., Vapnik, V. N.: Support Vector Machines for Spam Categorization. IEEE Transaction on Neural Networks, 10 (5) (1999) 1048-1054 4. Hearst, M.: Support Vector Machines. IEEE Intelligent Systems, 13 ( 4) (1998) 18-28

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5. Jo, T.: Neural Text Categorizer: A New Model of Neural Networks for Text Categorization. The Proceedings of the 7th International Conference on Neural Information Processing, Beijing, China (2000) 280-285 6. Jo, T., Japkowicz, N.: Text Clustering Using NTSO. The Proceedings of International Joint Conference on Neural Networks, Sheraton Vancouver Wall Centre, Vancouver, BC (2006) 558-563 7. Joachims, T.: A statistical Learning Learning Model of Text Classification for Support Vector Machines. The Proceedings of the 24th Annual International ACM SIGIR, (1998) 128-136 8. Lodhi, H., Saunders, C., Shawe-Taylor, J., Cristianini, N., Watkins, C.: Text Classification with String Kernels. Journal of Machine Learning Research, 2 ( 2) (2002) 419-444 9. Park, S., Zhang, B.: Co-trained Support Vector Machines for Large Scale Unstructured Document Classification Using Unlabeled Data and Syntactic Information. Information Processing and Management, 40 ( 3) (2004) 421-439 10. Platt, J. C: Sequential Minimal Optimization: A Fast Algorithm for Training Support Vector Machines. Technical Report MSR-TR-98-14, (1998) 11. Sebastiani, F.: Machine Learning in Automated Text Categorization. ACM Computing Survey, 34 (1) (2002) 1-47

RHDP-Scheme for RFID’s Efficiency Improvement on the Ubiquitous Computing* Bok Yong Choi1, Deok Gyu Lee2, Jong Hyuk Park3, and Kwang Nam Choi1,** 1

School of Computer Science and Engineering, Chung-Ang University, Heukseok-dong, Dongjak-gu, Seoul, Korea [email protected], [email protected] 2 Division of Information Technology Engineering, Soonchunhyang University, # 646, Eupnae-ri, Shinchang-myun, Asan-si, Choongchungnam-do, Korea [email protected] 3 CIST, Korea University, 5-Ka, Anam-Dong, Sungbuk-Gu, Seoul, Korea [email protected]

Abstract. In the near future, RFID will be used at practical fields such as supply chain management, stock management, and so on. However, some barriers such as price of chipset and RFID user information privacy protection exist in widely using it in public. So, recently time-memory trade-off was disclosed to reduce the amount of calculation with user’s information privacy protecting scheme utilizing hash-chain, meeting indistinguishable forward security. However, it requires a long pre-calculation time, causing the problem of scalability. In this paper, we propose scheme (RHDP: Real-time Hash-chain Decreasing Pre-calculation) to reduce pre-calculation time that is the biggest problem in time-memory trade-off. The proposed scheme can shorten the authentication time and improve its scalability and efficiency of RFID.

1 Introduction Ubiquitous computing is a computing environment that various kinds of computers soak into people, objects, and environment are connected with each other so that this enables us to implement a computing at anytime and anywhere. As a meaning of “it is commonplace,” “it exits at the same time in every time and every where”, it is more advanced computing environment than existence home-network and mobile computing. Xerox PARC of America describes the requirements of ubiquitous computing throughout the research about computer and network as follows. The interface of it has to be invisible and embodied virtuality of real computer has to be possible at everywhere and the network has to be connected always [1-3]. The core technologies for these ubiquitous computing have RFID (Radio Frequency identification), WSN(Wireless Sensor Network)[4], Context Awareness[5, 6], etc. *

This work was supported by grant No. R01-2005-000-10940-0 from the Basic Research Program of the Korea Science & Engineering Foundation. ** Corresponding author. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1068 – 1077, 2006. © Springer-Verlag Berlin Heidelberg 2006

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Specially, in the near future, RFID will be used at practical fields such as a variety of applications including supply chain management, counterfeit prevention, automated payment, physical access control, and smart homes and offices. However, some barriers exist in widely using RFID in public. First, the current price of chipset is too expensive. It is essential to lower its manufacturing cost. Second, it relates to the RFID user’s information privacy protection. This problem is an essential characteristic accompanied by RFID. As tags are supposed to response any reader, it is possible to distinguish ID without reader identification. Points of discussion relate broadly and openly[8, 9], and the success of RFID depend on this user’s information privacy protection. RFID user’s information privacy protection methods require generally a large amount of calculation, and consequently does not match RFID’s low-cost policy. From this point of view, recently time-memory trade-off was disclosed to reduce the amount of calculation with a scheme protecting user’s information privacy utilizing hash-chain, meeting indistinguishable forward security with such restrictions improved. However, it requires a long pre-calculation time, causing the problem of scalability. In this paper, we propose RHDP-scheme to reduce pre-calculation time that is the biggest problem in time-memory trade-off. Accordingly discussion could be made on whether Real-time Hash-Chain can shorten the authentication time and improve its scalability and efficiency. The rest of this paper is organized as follows. In Section 2, we discuss Related Works including RFID system, user’s information privacy issue, security requirements, and the existing schemes. In Section 3, we described Hash-chain and Timememory trade-off. In Section 4, we describe proposed advanced scheme including architecture, a comparison of the existing scheme. We conclude and discuss future research direction in Section 5.

2 Related Works 2.1 RFID System The RFID systems consist of three components: Reader, Tag, and Application systems. Generally, an RFID tag consists of a small microchip with some data storage and limited logical functionality, and an antenna. The RF antenna allows the tag to couple to an electro-magnetic field to obtain power or to communicate with the reader or to do both. RFID tags can be distinguished based on their frequency of operation, or on powering techniques such as active, passive, or semi-passive. Passive tags have no power source of their own and therefore must depend on the electro-magnetic field created by a Reader. Passive tags normally communicate information to a reader by modulating the Reader’s RF signal [10, 11]. Application system with its security server equipped with DB controls the various information that are received from each tag such as ID, Reader Location, and Read Time. Application system receives information of tags and recognizes ID of tag. In this case, it can be eavesdropped due to the radio telecommunication between tag and Reader. In addition, anyone can obtain the output value of tag [12].

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2.2 RFID User’s Information and Privacy Issue In [7, 12], M. Ohkubo describes the RFID privacy issues: One is data leakage from RFID-tagged belongings. It can be considered as leakage of personal ID information contained in tag, and obtaining through the trace of Ids tag. ∼ Leakage Issue of personal ID: People tend to have a various kinds of item around them. For some items that are very personal such as high-valued belongings or medical records, people don’t want them to be revealed. If this information is recorded in tag, various type of user’s information could be obtained without any recognition of its owner. ∼ Behavioral tracking and personal identification Issue: If a consumer used his credit card to purchase any goods, malicious user can obtain the detailed information on the credit card through the trace of tag ID that was used in that purchasing. In order to protect the user’s information privacy from this threat, a variety of issue should be solved by technologies such as anonymity of ID or avoidance of the trace being made with a malicious intention. However, it not enough to protect user’s information with this sort of thought. That is, forward security is necessary. The malicious user can leak any confidential information contained in tag. However without the forward security, previous records contained in tag could be traced. Accordingly there is necessity to build the concept to prevent from the trace of past information. Researchers have recognized the RFID user’s information privacy issue for some time and are devising better approaches. There are another researches such as Kill command’s user’s information privacy protection [15] using hash function [16,17] or using public key algorithm [13,18,19]. No single approach is likely to be completely satisfactory. 2.3 Security Requirements on RFID Technology [10, 12, 20] In this sub-section, we discuss considered security requirements on RFID technology such as follows: ∼ Indistinguishability: Tag output must be indistinguishable from truly random values. Moreover, they should be unlinkable to ID of the tag. If the adversary can distinguish that a particular output is from a target tag, he can trace the tag. Naturally, this is included in the concept of ID anonymity. ∼ Forward security: Even if the adversary acquires the secret tag data stored in the tag, he cannot trace the data back through past events in which the tag was involved. Needless to say, the adversary who only eavesdrops on the tag output cannot associate the current output with past output. ∼ Confidentiality: To offer confidentiality at RF communication interval, the followings is considered. Developing low-power encryption algorithm equipped with encryption to reduce the amount of calculations, and both significant information and information on the application system need to be stored and transmitted after encrypting them considering the vulnerability of RF communication.

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Besides, it is necessary to be considered attacks such as Physical Attack, Eavesdropping Attack, Replay Attack, and Denial of Service attack. ∼ Physical Attack: It is possible to steal or destroy the tag in use by physical attack. Regarding denial of service and physical attack as above, which are the attack methods attributed from the mechanical and physical characteristics, they shall not be handled in this study suggesting identification protocol. ∼ Eavesdropping Attack: In case of communication between tag and reader can be eavesdropped by anyone, as it is the method of radio frequency. ∼ Replay Attack: By re-transmitting the eavesdropped contents to the justified reader, it could pretend to be a justified tag. ∼ Denial of Service Attack: Contents of communication could be distorted using the noise or disturbing frequency that has a certain frequency so that RFID system cannot be normally operated. 2.4 The Existing Schemes 2.4.1 Kill Command Scheme Tag that the Auto-ID Center supports have the following property. Each tag has a unique 8-bit password, and upon receiving the password, the tag erases itself. This scheme each password is only 8 bits long, so a malicious attacker may be able to determine some passwords in approximately 28 computations, and use this command abusively[15]. 2.4.2 Hash-Lock Scheme We supposed that tag has hash function in MIT method considering low prices of RFID tag. Certification course is like this: First, reader transmits query to tag. Second, tag forwards MetaID=H(Key) using in certification to Reader. And then reader transmits information which is sent to tag to database. Database abstracts key and ID with MetaID and transmits them to Reader. Reader transmits key to tag. If key shows no difference as compare with MetaID, all session is over by transmitting ID. This method is based on one side hash function and considered efficiency. Because of eavesdropping communication channel between reader and tag, adversary get key and certificate by producing MetaID in hash operation. Also, adversary can certificate by using fixed MetaID and re-transmitting wiretapping MetaID. Finally, hash-lock protocol doesn’t satisfy with demand terms of security as if confidentiality, integrity, and certification [16, 17]. 2.4.3 Randomized Hash-Lock Scheme This is an extension of the hash lock type scheme. It requires the tag to have a hash function and a pseudo-random generator. Certification course is like this: Reader transmits query to tag, tag forms random r and transmits h(IDk r). Reader operates all of the IDall into h(IDall r). Reader searches IDkːwhich is identical with h(IDk r) and transmits them to tag. Tag compares IDk with IDk and then all session is over.

ಹ

ː

ಹ

ಹ

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The tag output changes with each access, so this scheme cut-off tracking. However, this scheme allows the location history of the tag to be traced if the secret information in the tag is revealed. i.e., this scheme cannot satisfy the forward security requirement [16, 17].

3 Hash-Chain Scheme In this section, we also discuss hash-chain scheme in [7]. to explain properties of proposed scheme in the next section. We also discuss problems of hash-chain scheme and time-memory trade-off scheme. 3.1

Hash-Chain Scheme

Hash-chain Scheme, using hash-chain scheme, renews the confidential information within tag in order to satisfy forward security. It means it is impossible to identify the input value of hash function from the computed value of hash function. In i-th treatment, tag transmits ai = G (Si) to reader in response. Then, it calculates and renews Si+1 = H (Si) out of Si, the previous confidential information.(H and G are hash function). Reader receives ai from tag, and transmits it to application system that possesses secret s1. Application system, then, checks the formula of ai’ = G (Hi(s1)) for the right identification of tag. Next, application system transmits the ID of tag to reader. We assume that T is Tag , R is Reader , A is Application system.

Fig. 1. Hash-Chain scheme structure [7]

Figure 1 shows the structure of Hash-chain of RFID. M means the number of tags, the maximum length of Hash-chain for each tag is n. A declares H, G hash function, creates S1 the number of random, being saved in database in a pair of hash function (ID , S1), which is a confidential aggregate of S1 and ID. Tag: In the transaction within T, R 1. T sends answer ai = G(Si) to the R, 2. T renews secret si+1 = H(Si) as previous secret Si.

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Reader: In the transaction within T, R, A 1. R obtains answer ai from T, 2. R sends information ai to A through a secure channel, 3. R receive id of T from A through a secure channel. Application system: In the transaction within R, A 1. A receives information ai from R through a secure channel, 2. A finds corresponding id to ai by checking ai = G(Hi-1(S1)) for all i between 1 and n in database (1ืiืn), 3. A sends id to R through a secure channel. ∼ Security: The adversary may not eavesdrop on the radio frequency signals between tag and reader. Thus to ensure the anonymity of the tag ID, the tag should not output it’s ID or constant data. Because this scheme uses random hash value (ai , Si+1), satisfies above requirement. ∼ Efficiency: Because this scheme uses only two hash-function units(H,G), which require a small computational complexity and small gate size, will produce lowcost RFID tags. ∼ Problem: Because this scheme calculates hash (i.e., ai = G(Hi-1(S1))) in order to find an ID of ai in database, takes the huge time like O(m,n).(i.e., m is number of tag , n is hash maximum length). If m = 220 and n = 210 is required 230 which takes the time 64sec/tag. Therefore hash-chain based scheme problems in scalability and flexibility. 3.2 Time-Memory Trade-Off It is proposed to use time-memory trade-off[21] that is based on the Hellman’s theory and the optimum standard theory in Oechslin[14] to reduce hash calculating time ai = G(Hi-1(S1)) in basic concept[7]. Trade-off is the concept that reduces calculating time to search the input of output N from the hash function G. The trade-off’s principle is generally such as follows: 1. 2. 3. 4. 5. ∼

Reduction function R is defined. By F and R, chains of inputs and outputs of F can be built. First and final value of each chain is stored in table. We can find out final value of the chain from output R. We generate complete chain and find the input to F. Efficiency: Trade-off reduces time(N) calculating basic concept by two thirds. Trade-off takes 0.0016 sec, if O(m,n) Æ 1 min(mn=30) ∼ Problem: When mn is 30, it is needed pre-calculating time of 10 hours. So, it is a big problem in expansion and efficiency.

4 Proposed RHDP-Scheme This section explains Real-Time Hash-Chain scheme which reduces pre-calculation time of Time-Memory Trade-Off [21]. Though efficiently reduced the complexity which was the largest problem of basic scheme of Hash-Chain by use of Time-

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Memory Trade-Off, needed additional pre-calculation time of large amounts. Therefore, to reduce pre-calculation time, we do not calculate all hash-chain element in advance, but do calculate necessary element by Real-Time Hash-Chain uses of additional hash value cik+1 = H( aik || sik) whenever authentication occurred in the transaction within Tag and Reader. 4.1 RHDP-Scheme Design Tag save two values of sik = H(sik-1 ) and cik = H( aik-1 || sik-1) (1”i”m) (1”k”n). A value of sik is confidential information and cik is authentication information. Application system server manage cik = H( aik-1 || sik-1), IDi , sik and cnt i.e., set of k (ci , IDi , sik, cnti ) in database. A value of cnti indicates the number of times of the authentication and sik, cik are equal to tag values. Here is that ‘m’ tells the number of tags and ‘n’ tells hash maximum length.

Fig. 2. Proposed Scheme Architecture

Tag: In the transaction within T,R

཰-1 T sends answer a = G(s ) and c = H( a s ) by saved the previous transaction to the R, • ཰-2 T renews secret s = H(s ) as previous confidential s and c =H( a s ) as a was calculated in ཰-1. Reader: In the transaction within T, R, A • ཱ-1 R obtains answer c and a from T, R sends information c and a to A through a secure channel, • ၈-1 R receive ID from A through a secure channel. • ၈-2R identify T using ID . Application system: In the transaction within R, A • ི-1 A receives c and a from R through a secure channel, • ཱི-1 A finds corresponding ID using c from ི-1 for all tags in data•

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ཱི-2 If success ཱི-1, A renew s = H(s ) and c =H( a s ) in database. ཱི-3 else, A finds corresponding ID using a from R compared with a k+1



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which calculated G(Hk-1(sic)) as sic in database (cืkืn , c = cnti), (1”i”m). This situation occured network obstacle in previous communication between T and A. Therefore A not processed

• •

ཱི-4 If success ཱི-3, A renew s = H(s ) and tabase. ུ A sends ID to R through a secure channel. k+1

i

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i

ཱི-2.

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=H( aik || sik) in da-

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Fig. 3. Proposed Scheme Protocol

4.2 Proposed Scheme Analysis Proposed scheme can form chain with real-time whenever requests authentication without pre-calculation time. And occur two situation such as normal connection or abnormal connection. If normal connection, calculation time needs only hash calculation si k+1= H(si k) and cik+1 =H( aik || sik ) such as -2 in database. This scheme also can reduce huge hash-time(i,e., O(m,n)) of Hash-Chain scheme[7] with one hash-time, because application system can find IDi without hash calculation through previous calculation value cik =H( aik-1 || sik-1) in database. But if abnormal connection such as -3 process, A needs calculation time like the largest O(mni’) less than O(mn)( cnti ni’ n).

ཱི

ཱི ื ื

∼ Security: Proposed scheme is all satisfied with a indistinguishability and the forward security which are hash-chain basic property. • indistinguishability : Proposed Scheme is different every time output which calculated random values of (si k, cik , aik) by hash function in tag. • Forward security: An adversary, who eavesdrops only on the tag output, cannot relate to the current output to past output and cannot trace. Proposed Scheme ensure forward security that because cik and aik are hash values by calculated one-way function.

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∼ Scalability: Proposed scheme takes time needs only two hash calculation in normal connection. But the Hash-Chain scheme [7] take time m*n hash calculation at all times or huge pre-calculation [21]. ∼ Flexibility: Proposed Scheme easy to add and delete tag, because of only a list related to ID of tag from database.

ཱི

∼ Consideration: If abnormal connection such as -3 process, A needs calculation time like the largest O(mni’). Because this time is huge hash-time, we must found the way to solve the problem. ∼ Comparative analysis: The following is the hash-base chain, time-memory tradeoff , real-time chain comparative analysis. The proposed scheme was designed in all aspects Consideration in the results of a table 1. Table 1. Comparison between the existing schemes and the proposed scheme Compared Scheme Items

Hash-base Chain

Time-memory Trade- Proposed RHDPScheme off

Indistinguishability

Ⴜ

Ⴜ

Ⴜ

Forward security

Ⴜ

Ⴜ

Ⴜ

Confidentiality

Ⴜ

Ⴜ

Scalability

;

೰

Ⴜ

೰

Flexibility

Ⴜ

;

Ⴜ

(O : Excellent

೰: Normal X : Unsatisfied)

5 Conclusion We reviewed concept of hash-chain which can satisfy forward security, indistinguishability, and other security requirements using low-cost RFID, and then discussed scheme can improve efficiency. RFID is necessary to reduce calculation time and computational complexity of tag to meet low-cost policy. It also must satisfy security requirements refered in section 2 which can protect for user’s information privacy. We propose advanced RHDP-scheme to reduce pre-calculation time that is the biggest problem in time-memory trade-off for scalability and efficiency of RFID. Our advanced scheme use real-time Hash-chain can shorten the authentication time. The Real time Hash-chain uses 1~2 hash function and short calculation time, therefore, it satisfies above requirements. In the future, it needs to study more about exception handling and scheme which can decrease store space of DB as much as tag of application system and hash-chain. We are going to graft the proposed advanced scheme and additionally studied schemes together.

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References 1. Buxton, W.: Ubiquitous Media and the Active Office, http://www.billbuxton.com /ubicomp.html 2. Satya, M.: IEEE Pervasive Computing Magazine, http://www.computer.org/ pervasive 3. M. Weiser: Hot topic: Ubiquitous Computing, IEEE Computer (1993) 71-72 4. Akyildiz, I. F., Su, W., Sankarasubramaniam, Y., Cayirci, E.: A survey on sensor networks, IEEE Communication Magazine (2002) 102-114 5. Randell, C., Muller, H.: Context Awareness by Analyzing Accelerometer Data. http://www.cs.bris.ac.uk/Tools/Reports (2000) 226-265 6. Rye.: A Survey of Context-Awareness, MobiCom, ACM Press (1996) 97-107 7. Ohkubo, M., Suzuki, K., Kinoshita, S.: A Cryptographic Approach to “Privacy-Friendly” tag, RFID Privacy Workshop (2003) 624-654 8. Benetton undecided on use of ’smart tags. Associated Press (2003) 9. CNET: Wal-Mart cancels ’smart shelf trial (2003) 10. Finkenzeller, K.: RFID Handbook. John, Wiley and Sons (2003) 11. Ranasinghe, D. C., Engels, D. W., Cole, P. H.: Low-Cost RFID Systems: Confronting Security and Privacy, Auto-ID Labs Research Workshop (2004) 54-77 12. Ohkubo, M., Suzuki, K., Kinoshita, S.: Efficient Hash-Chain Based RFID Privacy Protection Scheme, Ubicomp-04 (2004) 36-69 13. Juels, A., Pappu, R.: Squealing Euros: Privacy Protection in RFID-enabled Banknotes, Financial Cryptography ’03 (2003) 69-85 14. Oechslin: Making a Faster Cryptanalytic Time-memory Trade-off, In Advances in Cryptology CRYPTO'03 15. Auto-ID Center: 860MHz-960MHz Class I Radio Frequency Identification Tag Radio Frequency & Logical communication Interface Specification Proposed Recommendation Version 1.0.0, MIT-AUTOID-TR-007 (2002) 85-98 16. Weis, S. A.: Security and Privacy in Radio-Frequency Identification Devices, Masters Thesis. MIT (2003) 69-98 17. Weis, S. A., Sanjay E.Sarma., Ronald, Rivest, L., Daiel W. Engels: Security and Privacy Aspects of Low-Cost Radio Frequency Identification Systems,” First International Conference on Security in Pervasive Computing (2003) 94-102 18. Kinoshita, S., Hoshino, F., Komuro, T., Fujimura, A., Ohkubo, M.: Nonidentifiable Anonymous-ID Scheme for RFID Privacy Protection. Computer and Communications Security (2002) 85-98 19. Golle, P., Jakobsson, M., Juels, A., Syverson , P.: Universal Re-encryption for Mixnets 20. Weis, S. A., Sarma, S. E., Rivest, R. L., Engels, D. W.: Security and Privacy Aspects of Low-Cost Radio Frequency Identification Systems.SPC’03 (2003) 21. Avoine, G., Oechslin, P.: A Scalable and Provably Secure Hash-Based RFID Protocol. The 2nd IEEE International Workshop on Pervasive Computing and Communication Security (2005) 65-92

A Study on the Improvement of Soldiers Training System for Using Ubiquitous Sensor Network* Seoksoo Kim1 and Soongohn Kim2 1

Hannam University, Department of Multimedia Engineering, Postfach, 306 791 133 Ojeong-Dong, Daedeok-Gu, Daejeon, South Korea [email protected] 2 Joongbu University, Department of Computer Multimedia Science, Chungnam, South Korea

Abstract. Logistics innovation is being promoted so that they can support the military campaigns and provide needed supplies to the right place and at the right time. Such information and knowledge can be best obtained through experience or a battle but this may cause a considerable loss, even including causalities. Moreover, munitions system and military strategies in modern times are for possible battles in the future rather than for solving problems at present. This document uses the definition in a narrow sense to do research on the efficient military distribution system that adopts a ubiquitous sensor network and collects information through an RFID tag.

1 Introduction The U.S. Army, the forerunner of the military distribution system that utilizes hightechnology, has presented visions of “ARMY 21” and “Army After Next,” made plans in detail by predicting the operation of the army according to varied military campaigns, making all out efforts to prepare for the future. The U.S. Army is developing a system that it can dispatch the a brigade within 96 hours, a division in 120 hours, and 5 divisions within 30 days to any place in the world. Furthermore, logistics innovation is being promoted so that they can support the military campaigns and provide needed supplies to the right place and at the right time. Such information and knowledge can be best obtained through experience or a battle but this may cause a considerable loss, even including causalities. Moreover, munitions system and military strategies in modern times are for possible battles in the future rather than for solving problems at present. So it is almost impossible to experiment, evaluate, or analyze them in an actual battle. Hence, obtaining knowledge of a war in an indirect way such as a war game is important. In a broad sense, a war game defined by Defense and Strategic University means “all sorts of simulated military operations including a field maneuver of an actual military unit, a maneuver for proficient activities of a commander and a staff officer, a map exercise such as strategy discussion and judgment in mind, thinking process used *

“This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD)”(KRF-2005-041-D00576).

D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1078 – 1083, 2006. © Springer-Verlag Berlin Heidelberg 2006

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for analysis of the enemy force and friendly force, a simulated operation by quantitative means and methods, and so on.” In a narrow sense, however, a war game means “a simulated military operation that carries out with certain rules, procedures, and resources an actual or imaginary combat condition which can’t be experimented due to many dangers.” This document uses the definition in a narrow sense to do research on the efficient military distribution system that adopts a ubiquitous sensor network and collects information through an RFID tag. The systematic distribution methods would allow the simulated military operations to be done more promptly and accurately [1].

2 Wireless Data Transmission for a Ubiquitous Environment The frequency range of an RFID tag is usually 125 KHz and 13.56 MHz, which are used for a traffic card or admission control within short distances. As 900MHz and 2.4GHz are used, the available distance becomes longer and prices, inexpensive. As a result, the technology has been introduced to various areas such distribution, logistics, the environment, transportation, and so on. Besides, more sensing abilities are added and its use is extended to medical/security/national defense areas. Technology of developing a chip, an antenna, and packaging is critical to lowering the prices to 5 cents or below and making it have a small size as well as advanced functions. In future a tag will be integrated with a super cheap price (1 cent or below), a wireless chip/sensor, and a simple function. Table.1 depicts the characteristics of an RFID by its frequency range. Technology of an RFID reader An RFID reader can read 100 tags per a second by adopting tag anti-collision algorithms but the technology aims at reading several hundreds. Since the use of mixed frequency range (13.56MHz, 900MHz, 2.4GHz) is expected, a multi-frequency/multi-protocol reader should be developed. Currently, the sensing distance and accuracy of an RFID reader appears to be limited by the function of an antenna as well as surrounding circumstances. In order to enhance the sensor function, therefore, arrangement of 2~4 antennas is used. Beam-forming antennas, which control beams by responding to the environments, will be applied in the future. Research should be done on tag anti-collision also. There must be identifier code system that gives a tag identification numbers according to regions, for the technology will employ electric tags using identification schemes to identify an object. Related technologies are EPC(96bit) system developed by EAN and UCC, which leads international distribution standardization, and u-ID(126bit) system by Japan. Meanwhile, IPv6 of 128bit is being promoted for the Internet address system, indicating that providers need to scale up global efforts to establish code system standardization [2], [3], [4].

3 The Improvement of Military Logistics System for Using RFID Classification by Kinds: Military supplies are classified according to the number of pieces, nature (expendables and non-expendables), unit prices (high and low), and so

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on. Of the various standards, classification based on their kinds is used most common [5], [6]. Classification by Functions: Military supplies are also divided by their functions such as fire power, movement, special weaponry, telecommunication and electronics, aviation and shipping, general equipment, supplies, munitions, and medical supplies (9 categories in total).

4 Army Logistics System ROKA logistics system is divided by the enterprises’ delivery types. First, supplies could be directly sent to both a supply unit and a military unit that needs the articles. Or they could be delivered to a logistics supply command and then to a military unit which needs the articles. With respect to expendables, a unit can make a request for them while it reports the status of non-expendables every quarter to expect the demand. Such system may require longer time, for the logistics supply command takes charge of the distribution but allows accuracy of an itemized statement and real-time service. In the above mentioned logistics system a quarterly report replaces a request and a channel of logistics supply collects the reports. The flow of supplies is direct delivery from an enterprise to a unit but administrative procedures are done by a support unit, creating inconsistency. And supplies are divided by their use and kinds in the system. Introduction of RFID technology to the logistics system as depicted in Figure 1 can prevent waste of a budget and other resources by prompt delivery and accurate management of supplies. In addition, though a division promises to offer required supplies when they are not in stock, the request in not made in an automatic manner Table 1. Classification Under 10 Class

Class

Σ Τ Υ Φ Χ Ψ Ω Ϊ Ϋ ά

Items

Remarks

Food

Including meals ready to eat

General supplies, tying materials, parts of a gun, clothing and individual outfits Oil, hard coal, an antifreeze solution, chemicals Construction materials, timbers

Cement, paint

Munitions

Including explosives

Individual stuffs

PX goods

Finished goods (equipment)

Parts/accessories to repair

Medicines, medical devices / equipment, parts to repair An engine, a tire

Materials for service of public welfare

The rest (Farming tools)

Medical devices/supplies

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Table 2. Classification by functions

Functions

Class Scope

Fire power

7,9

Equipment of fire power Parts to repair maintenance materials

Movement

7,9

Vehicles and trailers Part to repair and maintenance materials Part for a vehicle with various equipment

Special weaponry

7,9

Equipment designated by special weapons Parts to repair

Telecommunication & 2,7,9 Electronics Aviation and shipping

7,9

General equipment

7,9

Supplies

2,3

Goods

1,3,4

Munitions

5

Medical supplies

8

Telecommunications devices Computation equipment and expendables High price software barcode system An airplane, a ship, and the equipment Parts to repair Construction/power supply/river-crossing/duty support equipment Parts to repair Chemicals, an antifreeze solution, heating/cooking equipment Clothing, individual outfits, a tent, a tool, expendables Stable/subsidiary food Oil and hard coal Construction/engineering work materials Munitions for fire power equipment Various explosives Medical devices and their parts Medicines, sanitary/medical devices/materials

Fig. 1. Logistics System by RFID Technology

so that the supplies appear to be depleted unless the official in charge of logistics system ask for the articles. Unlike officials in higher divisions, military units do not know about the schedule when the supplies are delivered.

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Fig. 2. Logistics System by USN

Because there’s no automatic system among a division, a logistics supply command, and a logistics command, it’s hard to receive needed supplies even when they are in stock. But the introduction of RFID technology can solve the problem, providing a network for the Ministry of National Defense, the Logistics Command, a logistics supply command, and the other relevant organizations so that they can supply articles based on accurate data. A RFID reader attached to a PDA can be applied to a military operation also. The data of materials and human resources, employing RFID technology, can be used as operation data of a war game. There is a variety of kinds of a war game and The U.S. Navy defines it as a simulation of a military operation involving two or more forces who depict an actual or assumed situation. At present, such a war game is operated to understand efficient operation of air power in Korea. And the data obtained by RFID technology can extend the simulated military operations to the whole army.

5 Conclusion The logistics system of ROKA is divided by the way of delivery: direct delivery from an enterprise to both a support unit and a unit that needs supplies and the deliver to a logistics supply command which sends the supplies to a military unit. Concerning expendables, a unit can make a request, but it makes a report of non-expendables to expect the demand. The logistics system may have an advantage of responding each situation but also causes waste of time and a budget. To address the problem this document took a look at the logistics system using RFID technology. But the document has its limitations, for use of RFID in a logistics system has yet to be developed and there’re not sufficient data to prove the effect of the system. Though large-scale logistics companies are active in adopting RFID system, the analysis of the effect should be done in the near future. RFID technology is becoming a new system for automatic management of physical distribution. And it would provide the army

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logistics with a new method to control manufacturing, delivery, and human resources in real time. Army logistics system has employed high technology and this document analyzed the system of physical distribution in order to apply the data to military operations. RFID and USN discussed herein can be introduced to the logistics system and they will serve to provide data for a war game. Still, this document has its limitations because the use of RFID in a logistics system is in a development stage yet and there’re not sufficient data to prove its effect in logistics system. Though large-scale logistics companies are active in adopting RFID system, the analysis of its effect should be carried out in the near future. RFID technology is becoming a new system for automatic management of physical distribution. And it would provide the army logistics with a new method to upgrade a war game and acquire better results.

References 1. Ubiquitous IT Korea forum : http://www.ukoreaforum.or.kr/ukorea/index.php 2. Sung, M. Y.: The Optimization for SCM with RFID Technology. Journal of Engineering Science and Technology, 2 (2) (2003 ) 58-63 3. Sang, L. C., Hyeon, J. K.: A Study on the Ubiquitous Activation Plan in Logistics Distribution Parts. KLRA, 14 (3) (2004) 112-121 4. Goangmo, Y., Jinhong, B., Gyeongsig, K.: Development of Quality Information System for the Improvement of Efficiency of Small Business. Journal of the Research Institute of industrial Technology, 22 (2003) 16-19 5. McEwan, L.: Implementing RFID in the Supply Chain Wal-Mart's RFID compliance requirement has spurred interest. Textile world, 154 (4) (2004) 72-76 6. Sangyong, L.: A Study on The Improvement of Military Logistics System. Focus on the Clustering Group by Product Characteristics, National Defense University, Master's Thesis, (2004) 67-71

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Definition of Security Requirement Items and Its Process to Security and Progress Management* Eun Ser Lee1 and Sun-myoung Hwang2 1

Information & Media Technology Institute, Soongsil University [email protected] 2 Daejeon University, 96-3 Yongun-dong, Tong-gu, Taejon 300-716, South Korea [email protected]

Abstract. This paper propose the development of a security requirement items and its process of the profile and security target(ISO/IEC 15408). This paper estimate the security requirement items and progress management that manage the security requirements and the progress and its problems. For projects in similar domains, it is possible to remove security risk items and to manage progress by using security lifecycle and progress milestone, which can greatly improve the software process.

1 Introduction The focus of security engineering has expanded from one primarily concerned with safeguarding classified government data to broader applications including financial transactions, contractual agreements, personal information, and the Internet. These trends have elevated the importance of security engineering [1][2][3]. In this paper, we will propose a process related to security by ISO/IEC 15408 and a concept of security requirements[4][5][6].

2 Security Requirements for Common Criteria 2.1 Security Requirements For the development of software, the first objective is the perfect implementation of customer’s requirements. And this work may be done by very simple processes. [7][8]. Therefore, developers or analyzers must consider some security-related factors and append a few security-related requirements to the customer’s requirements. To determine this level for a given security service in a particular application, the customer and the information systems security engineer should consider the value of *

This work was supported by a grant from Security Engineering Research Center of Ministry of Commerce, Industry and Energy.

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the information to be protected, and the perceived threat environment. Guidelines for determining these values May be provided in the IATF [7]. Once a determination has been made regarding the information value and threat environment, the security engineer may decide the robustness level by determining EALs (Evaluation Assurance Levels) and SML (Strength of Mechanism Levels). 2.2 Security Profile Lifecycle The lifecycle is made by protecting the profiles in order to fulfill the security requirement. The next step is the removal of the redundant risk items. Protection profile progress and identification is as follows: 1. A protection profile developer must be provided to explain the profile of the TOE. 2. Explanation of the TOE must be provided so as to describe its product type and the character of the general IT. 3. The evaluator must have confirmation that the information has satisfied all of the evidence requirements. 4. The evaluator must have confirmation of the explanation of the TOE with regards to quality and consistency. 5. The evaluator must have confirmation of the explanation of the TOE with regards to the relationship of protection profile consistency.

Fig. 1. Ubiquitous lifecycle milestone of the protection profile

Fig. 2. Ubiquitous lifecycle milestone of the security target

This figure shows the activity of the risk item as it is removed from the security requirement during the extraction process. Each of the factors use the repeatable milestone for progress management. Each stage is as follows:

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Stage Identify the protection profile Security Environment Setting Security Target Setting Security requirement identification and extraction Definition of the security requirement Identify the security profile risk item Basis of the theory Checking of the rationale

Contents Identification and analysis the protection target for the extraction of the security requirement. H/W and S/W, personal element setting for the security. Security requirement Target Setting Identify and extraction of the security requirement using UML(or other method) Definition of the security requirement for system building Identify the security profile risk item at the domain Build of the repeatable lifecycle for the milestone(LCO, LCA) Check the rationale of the repeatable milestone and risk analysis

This figure shows provision of the activity of the security requirement extraction of the security target. Each of the factors use the repeatable milestone (LCO, LCA) for the progress management. Each stage is as follows: Table 2. Description of the security target

Stage Identify the protection target Security Environment Setting Security Target Setting Security requirement identify and extraction Definition of the security requirement Definition and assurance of the function’s security target Admission of the Security profile Basis of the theory Checking of the rationale Testing and identify of risk items

Contents Identification and analysis the protection target for the extraction of the security requirement. H/W and S/W, personal element setting for the security. Security requirement Target Setting Identify and extraction of the security requirement using UML (or other method) Definition of the security requirement for system building Definition and assurance of the security target based on the function for the system building Admission of the confirmed Security profile at its domain Build of the repeatable lifecycle for the milestone (LCO, LCA) Check the rationale of the repeatable milestone and risk analysis Testing and identification for the extraction of new risk items.

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Table 3. Description of the milestone element Milestone Element

Definition of Operational Concept

System Prototype(s)

Life Cycle Objectives (LCO) · Top- level system objectives and scope : System boundary, Environment parameters and assumptions, Evolution parameters · Operational concept : Operations and maintenance scenarios and parameters, Organizational life- cycle responsibilities (stakeholders) · Exercise key usage scenarios · Resolve critical risks

Definition of System Requirements

· Top- level functions, interfaces, quality attribute levels, including: Growth vectors and priorities, Prototypes · Stakeholders’ concurrence on essentials

Definition of System and Software Architecture

· Top- level definition of at least one feasible architecture · Physical and logical elements and relationships · Choices of COTS and reusable software elements · Identification of infeasible architecture options

Definition of LifeCycle Plan

· Identification of life- cycle stakeholders: Users, customers, developers, maintainers, interoperators, general public, others · Identification of life- cycle process model : Top- level stages, increments · Top- level WWWWWHH* by stage

Life Cycle Architecture (LCA) · Elaboration of system objectives and scope of increment · Elaboration of operational concept by increment · Exercise range of usage scenarios · Resolve major outstanding risks · Elaboration of functions, interfaces, quality attributes, and · prototypes by increment : Identification of TBD’s( (to- bedetermined items) · Stakeholders’ concurrence on their priority concerns · Choice of architecture and elaboration by increment : Physical and logical components, connectors, configurations, constraints COTS, reuse choices, Domain- architecture and architectural style choices, Architecture evolution parameters · Elaboration of WWWWWHH* for Initial Operational Capability (IOC) : Partial elaboration, identification of key TBD’s for later increments

· Assurance of consistency among elements above Feasibility · All major risks Rationale resolved or covered by risk management plan * WWWWWHH: Why, What, When, Who, Where, How, How Much. · Assurance of consistency among elements above : via analysis, measurement, prototyping, simulation, etc. Business case analysis for requirements, feasible architectures

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Use of the milestones (LCO, LCA) is essential for removal of risk and progress management. The authors of this paper have provided the repeatable cycle based on the milestone element. Progress was checked using the basis of the milestone. We are provides that the repeatable cycle based on milestone element. Also, we are checked the progress by the basis of milestone. 2.3 Assets Protected by TOE A new method for minimizing the ‘threat phrase’ of PP is combining the assets by using the concept ‘assets protected by TOE’. As mentioned earlier, next items may be the as assets of the NIDS. − − − − −

Devices or systems which consist of the NIDS. Services that some servers included in the network NIDS installed provide. Security-related data stored in the NIDS itself. Data stored in the hosts included in the network NIDS installed. Other network resources included in the network NIDS installed.

In the aspects of the security requirements and the evaluation of the IT systems, assets can be re-identified. − TOE (target of evaluation), − Assets protected by TOE • Systems not included in the TOE • Services provided • Data stored • Data transmitted This method for combining of assets is available for the PP, because the identifying of the security environments is connected to the security functional requirements included in the CC. It’s very important to keep in mind that many kinds of threat agents and attack methods may exist in the ‘assets protected by TOE. Therefore, the threat agents and the attack methods must be considered to contain all cases. For example, the phrase ‘by unauthorized methods’ is not suitable in some cases, because the ‘threat agents’ can contain the ‘authorized users’ who may comprise the confidentiality of the assets protected by TOE by accident. Therefore, the phrases about the method and threat agent can be excluded. Now, the threat description may be described as like: The confidentiality of the assets protected by TOE may be compromised. As seen at the above phrase, in the case the concept ‘assets protected by TOE’ used, the descriptions for the threat are expressed as a kind of ‘possibility’ of attack (Systems, services, and others are included in the assets protected by TOE).

3 Conclusions In this paper, we proposed a method appending some sensor network security-related requirements and process to the customer’s requirements by considering robustness level. For the development of software, the first objective is the perfect implementation

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of customer’s requirements. However, if the software developed has some critical security holes, the whole network or systems that software installed and generated may be very vulnerable. Therefore, developers or analyzers must consider some sensor network security-related factors and append a few sensor network security-related requirements to the customer’s requirements. The processes based on the refinement of the security-related requirements are considered with the processes of software implementation.

References 1. ISO. ISO/IEC 21827 Information technology – Systems Security Engineering Capability Maturity Model (SSE-CMM), (1999) 2. ISO. ISO/IEC 15408-1: Information technology - Security techniques - Evaluation criteria for IT security - Part 1: Introduction and general model, (1999) 3. ISO. ISO/IEC 15408-2: Information technology - Security techniques - Evaluation criteria for IT security - Part 2: Security functional requirements, (1999) 4. ISO. ISO/IEC 15408-3: Information technology - Security techniques - Evaluation criteria for IT security - Part 3: Security assurance requirements, (1999) 5. ISO. ISO/IEC TR 15504-1, 2, 3, 4, 5, 6, 7, 8, 9: Information technology – Software process assessment – Part 1: Concepts and introductory guide, (1998) 6. Lee, E., Lee, M.: Development System Security Process of ISO/IEC TR 15504 and Security Considerations for Software Process Improvement (ICCSA2005), LNCS 3972, Springer Verg, Berlin Heidelberg New York (2005) 7. Lee, E., Lee, K., Lee, K.: Development Design Defect Trigger for Software Process Improvement, Software Engineering Research and Applications, LNCS 3170, Springer Verg, Berlin Heidelberg New York (2003) 8. Lee, E., Kim, T.: Introduction of Development Site Security. Process of ISO/IEC TR 15504, Knowledge-Based Intelligent Information and Engineering Systems, LNCS 3174, Springer Verg, Berlin Heidelberg New York (2004)

Design and Implementation of Web Security Access Control System for Semantic Web Ontology* Eun-ser Lee1 and Sun-myoung Hwang2 1

Soong-Sil University, 511 Sangdo-dong, Dongjak-gu, Seoul 156-743, South Korea [email protected] 2 Daejeon University, 96-3 Yongun-dong, Tong-gu, Taejon 300-716, South Korea [email protected]

Abstract. The World Wide Web has incurred the problem that users are not necessarily provided with the information they want to receive, at a time when the amount of information is explosively increasing. Therefore, W3C (World Wide Web Consortium) proposes the Semantic Web as the new web paradigm to present semantic information. But there is always a security problem in Semantic Web such as WWW and the study about this is insufficient. Therefore, the authors of this paper propose that the SecuSemantic system should be used to present semantic information using ontology and prevents that users flow out the information. This system is an Access Control Matrix based access control model basically, and It is a system that prevent information leakage by user's deliberation and by user’s mistake.

1 Introduction The World Wide Web, which was introduced by Tim Berners-Lee in 1989, has brought an Internet revolution in the late 20th century because of convenience at use. But It has incurred the problem that users are not necessarily provided with the information they want to receive, at a time when the amount of information is explosively increasing. Accordingly, W3C (World Wide Web Consortium) proposes the Semantic Web[1]. The Semantic Web is defined to give clear meaning and definition to information exposed in the web, and involves extension of the web so as to enable people to work in cooperation with computers[2][3]. To show semantic information that is well defined for users according to this paradigm a study of a browser system using ontology needs to be achieved[4][5][6]. But, security problem is weighed in this Semantic Web such as World Wide Web. "exposing data hiding in documents, servers and databases “Eric Miller, Semantic Web activity lead for the W3C, said to several hundred conference participants[7] and expressed gravity of security problem. This paper propose that the SecuSemantic system should be used to present semantic information using ontology and prevents that users flow out the information. Security *

This work was supported by a grant from Security Engineering Research Center of Ministry of Commerce, Industry and Energy.

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function that proposed in this paper is not a function that users can do freely about the information that provided them. If users pass the user certification successfully, Authority of users is controlled. For example, even if a user can see semantic information because of having read authority, the user can not print, if he has not print authority. This function prevents information leakage by a mistake and by user's deliberation. It is method that prevents information leakage through client program function including web browser. Because user that pass the certification successfully can flow out the information through the browser’s function such as print, source view, screen capture etc, this method is needed[8][9][10]. Chapter 2 discusses the Semantic Web, Web Security etc., and chapter 3 describes the design and implementation of the SecuSemantic. Chapter 4 shows the results of the SecuSemantic along with its estimates, while finally chapter 5 concludes the paper.

2 System Design 2.1 Active X Web Security Module This system performs security function in client. Module that performs this security function is supplied by Active X control form, and when user connects to server, user is downloaded. The function of this module is divided into greatly two. First, the web page is included semantic information that is offered in server by encrypting state, it performs function that does decryption this. The decryption key is received when user performs login. Second, it performs various function controls of browser. It prevents the function, print, source view, screen capture etc. Control list is showed in 3.6. User receives limitation in case of not prevent unconditionally but has no authority. 2.2 User Authentication User performs login through the web. User is given access authority about semantic information from server by authenticated ID. User authentication for this is required following point. - User DB should be constructed. - User information and En/Decryption Key must be in User DB. - The access authority should be established beforehand in user and this is given when succeed login. 2.3 Ontology Agent Ontology Agent accepts information that user wants as keyword and it extracts semantic information that is correct in the keyword in Ontology that already constructed and performs function that makes it by file of html form. Ontology in this paper limits by climate field. And server encrypts this file and sends to User PC. This time, if user has read authority for the semantic information, one can show the information if not, one can’t show.

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2.4 En/Dectyption As preceding section refered, html file that made by Ontology Agent is downloaded being encrypted. User can see this file doing decryption by Active X Web Security Module that is downloaded in client. In this system, en/decryption module can do file whole to doing en/decryption but it can also offer part encryption function to reduce load. Fig. 1 is proto-type of encryption API of this system. Text strings in the web pages are encoded by providing an input value to the source string and returning the result as shown in Fig. 1. To encode the whole web page, the file pathname is given as the input value to the source string as shown.

Fig. 1. Encryption Algorithm

This ensures the security of the web page when it is downloaded to the client’s PC. 2.5 Authority Control Authorized users can get permission or limit the permission assigned during server authentication. Fig. 2 shows control list.

Fig. 2. List for Access Control

Above control function is performed in client and this system can prevent information leakage by user's mistake as well as information leakage by user's deliberation by performing relevant function. For example, read, print, source view and various function of web browser etc.

3 Result and Estimation 3.1 Result Design and implementation for SecuSemantic system discussed in the previous chapter. In this chapter the results and estimations of the authors’ system will be discussed. Fig. 3 is example Web page of this system. When user clicks each words, this system shows semantic information that use Ontology.

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Fig. 3. Example Web page

Fig. 4 shows semantic information when clicked "Climate" of example web page. This semantic information is information that is defined beforehand using Ontology.

Fig. 4. Semantic information about "Climate" that use Ontology

Fig. 4 is screen when user has read authority. If user has no read authority, the information is not seen. And fig. 5 shows screen opened by notepad.

Fig. 5. Encrypted semantic information

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This means that relevant page has encrypted, and when a user inspects in web browser, it is decrypted by real-time. Also, even if a user can show the semantic information because one has read authority, in this system a user can not perform relevant function (print, source view, screen capture) if one has no relevant authority. Fig. 6 shows that a user who has no print authority tries to print through the print menu of web browser.

Fig. 6. The screen that a user has no print authority

If summarize above function, when semantic information that user requires is transmitted from server to client, it is encrypting state, and the information is decrypted and inspected in client, and function of web browser is limited because of security although the information is inspected. 3.2 Estimation SecuSemantic that is proposed in this paper is a system that control so that user do not flow out the information as well as may show wanting semantic information using Ontology by applying security to Semantic Web that is web technology next generation. In this system, a user can inspect web page including semantic information, if he has read authority after user's authentication is succeeded, and even if the web page is inspected, if he has no more authority about relevant web page, user can not flow out the information. That is, if there is no source view authority or print authority, screen capture authority, a user can not flow out the information even if he uses special program and print screen key etc in client PC. This function is available because it is achieved in client. Therefore, this system can be called suitable system to secure about sensitive semantic information that is constructed using Ontology. Fig. 7 shows a chart providing comparisons of other relevant systems.

Fig. 7. Chart comparing other systems

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4 Conclusion Semantic Web is web technology next generation invented by Tim Berners-Lee who proposes World Wide Web. This Semantic Web by using Ontology can show more correct information that users wanted, but security about the information becomes problem. This paper proposes system that presents semantic information using ontology and prevents that users flow out the information. When semantic information that user requires is transmitted from server to client, it is encrypting state, and the information is decrypted and inspected in client, and function of web browser is limited because of security. Hereafter, by way of research tasks, Resources in web can be file, image, animation etc. as well as web page and the study of security about its information is defined in Ontology is also needed.

References 1. Semantic Web. http://www.w3.org/2001/sw/ (2001) 2. Tim, B., Semantic Web, W3C, http: //www.w3. org/2000/Talks/1206-xml2k-tbl/, (2000) 3. Tim, B., James Hendler, Ora Lassila, Scientific American article: The Semantic Web, Scientific American issue, (2001) 4. Dzbor, M., Domingue, J., Motta, E.: Magpie: Towards a Semantic Web Browser. Proc. of the 2nd Intl. Semantic Web Conf. ISWC, (2003) 5. Domingue, J., Dzbor, M., Motta, E.: Magpie: Supporting Browsing and Navigation on the Semantic Web. Proc. of Intl. Conf. on Intelligent User Interfaces (IUI), (2004) 6. Quan, D., Karger, D. R.: How to Make a Semantic Web Browser. In Proceedings International WWW Conference, New York (2004) 7. http://news.com.com/2100-1032_3-5605922.html 8. Freier, A., Karlton, P., Kocher, P.: The SSL Protocol Version 3.0. http//:www. netscape.com/eng/ssl3/3-spec.ps, (1996) 9. Dierks, T.: The TLS Protocol 1.0. RFC2246, (1999) 10. Weeks, J.: CCI-Based WebSecurity: A Design Using PGP. WWW Journal 95, (1995)

Designing of Patient-Focused Mobile Agent in the Ubiquitous Medical Examination System* Jaekoo Song1, Seoksoo Kim1,**, and Soongohn Kim2 1

Hannam University, Department of Multimedia Engineering, Postfach , 306 791 133 Ojeong-Dong, Daedeok-Gu, Daejeon, South Korea [email protected] 2 Joongbu University, Department of Computer Multimedia Science, Chungnam, South Korea

Abstract. With the improvement in information technology and the rapid adoption of automatization at both work and home, people are now enjoying a life that is more comfortable and convenient. In particular, as the automatization is becoming standard in the medical field, especially in the large hospital, the demand for system that can handle various information and data are now more than ever imperative. This paper aims to design agent system that is mobile based and decentralized, and that can provide and administer basic medical information. Its main objective is to move away from high cost centralized system to low-cost based system corresponding to small to mid-size medical information that can be effectively utilized and administered.

1 Introduction With the improvement in information technology and the rapid adoption of automatization at both work and home, people are now enjoying a life that is more comfortable and convenient. In particular, as the automatization is becoming standard in the medical field, especially in the large hospital, the demand for system that can handle various information and data are now more than ever imperative. As such, EMR (Electronic Medical Record), CPR (Computer-based Patient Record) and HIS (Hospital Information System) are deployed in the hospital with the aim of managing medical and patient information [1]. Aforesaid medical information system involves storing every sort of information and patient examination records and transmitting necessary medical prescription of diagnosed patients to relevant department through network system [2]. This system is not limited to mere administration of patient registration, examination, payment and other essential data, it is also critical in the sense that it unifies and facilitates all administration functions of the hospital [3], [4]. *

“This work was supported by the Korea Research Foundation Grant funded by the Korean Government(MOEHRD)”(KRF-2005-041-D00576). ** Corresponding author. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1096 – 1101, 2006. © Springer-Verlag Berlin Heidelberg 2006

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2 Patient Specific Mobile Agent Proposal The mobile device that users carry have all relevant information, including personal information, as well as medical information, location information, sensor information and others that will be generated and managed in real time. Moreover, the agent receives information from agent information center, and in turn, will provide latest information back to agent information center.

Fig. 1. Mobile agent Model

Mobile agent information center plays an essential role in analyzing data provided by a mobile agent and through close interaction with medical environment and via patient specific information and mobile devices; it stores vital data, including examination information, location information and sensor information. Information center also alleviates the calculation and memory limitation of patient-focused mobile agent, increasing the efficiency of the system. In addition, it processes mass size data through integrated information system and information linkage (H2) of ubiquitous medical system, which was not possible with the mobile agent alone [5]. 2.1 Patient-Focused Mobile Agent Information Classification Patient’s personal information, medical information, location information and sensor information are separated and administered. Saved information is managed in such way that if patient needs examination, it is immediately provided with appropriate medical service, resulting in highly efficient and convenient service. To administer the basic information efficiently in patient-focused mobile agent construction, the characteristics are divided as shown below in Table 1. Personal information creation and change when the patients request medical service and their personal information

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Classification Personal tion Medical tion

Define

Example

informa- When the patient request medical service name, sex, age, address, phone and their personal information number.. informa- Patient’s health. Relevant Medical information, medical schedule, x-ray, Embryo picture informa- User’s position information GPS position information

Location tion Sensor information

Sensor information that is collected Mobile device

in Body temperature, pulsation

do not initially exist in the mobile device, pertaining to service requested by the patients, the personal information will be generated in the device by the provision of agent. Following the requests of the services, patient information will be changed accordingly. Additionally, depending on the circumstances, services will be changed accordingly. Location information creation and change upon request by the medical service, it will provide the information on the whereabouts and the changes in the location. Sensor information creation and change Specific purpose sensor observes the conditions and changes in the patient’s surroundings and upon the request by medical services; it outputs the most relevant information. Additionally, depending on the circumstances, its criteria will be changed accordingly [6].

Fig. 2. Mobile agent information cycle

The patient-focused mobile agent information cycle is shown in Figure. 2. It occurs largely in agent information administration, agent information management and between hospitals. Individual information and patient’s location and sensor information is managed real time by agent information management and after transmission and analysis by agent information administration, pertinent information is changed accordingly.

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3 Patient Purpose Mobile Agent Design and Evaluation 3.1 System Design This paper proposes system design as shown in Figure 3 below, Proposed system is divided into mobile agent, agent information center and hospital system. The uppermost shows mobile agent, indicating mobile devices carried by users. At this juncture, mobile devices includes: a sensor control module that administers sensor, data management module that saves and transmits, and private information security module that protects user information, as well as an interface that provides convenience to users. Agent information center is composed of module that manages information collected from mobile agent and is largely consisted of sensor information analysis, data storage, private information encryption, and descrambling. On this point, as mobile agent and agent information requires wireless transmission, it is critical in designing a network control module to ensure secured transmission.

Fig. 3. Proposes mobile agent system design

3.2 System Construction Scenario to create the suggested system is described below. User A is using the mobile device that has sensors detecting temperature, blood pressure, and blood glucose level, and has recently been diagnosed with high blood pressure. When the sensors attached to the mobile device carried by the user detect abnormal increase in blood pressure, its purpose is to request for medical service and provide the hospital information most appropriate for the user. Testing environment for this system is described in Figure 4. In the test environment, mobile device connected to the USB represents the mobile agent used by the user, which sends information on temperature, blood pressure, and blood glucose level to “middle-way” via separate application. Current

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location of the user also sends data to special area, while the hospital also inputs information of imaginary hospital based on the location of the user. For this example, let’s say there are five hospitals, and one of the hospitals (M3) has previous history of providing medical service to the user. Here, each hospitals are located M1 to M5 distance away from the location of the user. Test result shows that depending on the intensity of the sensor information that represents emergency situation of the user, it indicates hospital M1 as the nearest, while as the sensor intensity decreases it indicates hospital M3 which has previous history of providing medical service to the user. In this system, XML type technology method is used in order to standardize information collected in various forms.

Fig. 4. Testing environment for this system

3.3 System Evaluation and Comparison As controlled system provides medical service that is based on the patient specific, it has fast response time on emergency and its system is less complicated, making it easier to adapt. The medical examination information process, using patient-focused mobile agent is as follows on Figure 5. In comparison to existing medical examination system, it proposes 5 items, as shown below in Table 2. Existing examination system is tailored to large-scale hospital, and thus, its application is limited to such institutions. However, with the proposed patient-focused mobile agent, its services are created with the individual patient

Fig. 5. The medical examination information process

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Table 2. In comparison to existing medical examination system Item

Information system

Patient focused mobile agent

System scaleG Sensing scope User information management Patient medical information portability

Large-scale system In hospital In hospital In hospital Portability is good in hospitalG Portability is bed outside

Small system Any ware Real time Real time Portability is good in hospitalG Portability is bed outsideG

on mind, and hence, its application are now applicable for small to mid-size hospitals and furthermore, patients can receive various medical services that goes beyond traditional services.

4 Conclusion The proposed patient-focused agent medical examination service moves focus from existing automated hospital focus system to patient specific medical examination service and through provision of individualized service, it prevents redundancy and eliminates unnecessary procedures. In addition, instead of adapting overtly excessive system, it is possible to adapt only required service, such as medical information system that is specifically made for medical examination service. Thus, it is possible to select small to large scale sized system depending on the cost, size and its requirement of the institution.

References 1. Mikkelsen G., Aasly J.: Concordance of Iinformation in Parallel Electronic and Paper Based Patient Records. Int. J. Med. Inf. (2001) 123-131 2. Istepanian, R. S. H., Jovanov, E., Zhang, Y. T.: Guest Editorial Introduction to The Special Section on M-Health: Beyond Seamless Mobility and Global Wireless Health-Care Connectivity. IEEE Trans. on Information Technology in Biomedicine, 8 (4) (2004) 405-414 3. Shortliffe, E. H., Perreault, L. E., Wiederhold, G. G., Fagan, L. M., Hannh, K. J., Ball, J., Wiederhold, G.: Medical Informatics: Computer Applications in Health Care and Biomedicine(CAHCB). Springer-Verlag, Heidelberg Berlin (2000) 4. Laerum H, Ellingsen G, Faxvaag A: Doctors' Use of Electronic Medical Records Systems in Hospitals: Cross Sectional Survey. BMJ, 323 (7325) (2001) 1344-1348 5. Prabhakar, A., Visweswara, G. H.: Datanet Corp Ltd., Bangalore: IT -Applications in Hospitals. Computer Applications in Hospital (ISHA), chapter. 13 6. Danny, L., Mitsuru, O.: Programming and Deploying Java Mobile Agents with Aglets. Addison-Wesley, Doug Lea (1998)

Mobile Robot Path Planning by Circular Scan Code and Circular Distance Transform Method Gyusang Cho1 and Jinkyung Ryeu2 1

Dept. of Computer Eng., Dongyang Univ., Youngju, Korea [email protected] 2 Dept. of IT Electronic Eng., Dongyang Univ., Youngju, Korea [email protected]

Abstract. The circular scan code method that is used for a local planner is suggested to avoid obstacles on the unknown environment. Detected obstacle in the circular window is converted to the bit data and then to the steering angle. Also, circular distance transform method that is used for a global planner is suggested. The shortest path is generated fast by using the method. The method to determine the steering angle and the global path generation was proved by the simulations.

1 Introduction Without any information about work space, robot may happen to meet unexpected obstacles in the pathway and the effective path planning to avoid them is required. Wall Following Method is applied to robot that is driven along the wall, but it does not always guarantee the shortest path. Potential Field Method was suggested by Khatib[1], in which obstacle and target exert repulsive and attractive force, respectively. By this method, robot can avoid the obstacle and plan the trajectory easily, but it also may fall into the local minima. Koren and Borenstein suggested Virtual Force Field Histogram method[2] and Vector Field Histogram method[3]. VFH applied occupancy grid method in modeling the environment. Direction and velocity of robot motion are calculated by using the grid map. But it also may happen to fall into the local minima in this method. Dynamic Window method was suggested by Fox[4], in which mobile robot can be controlled with high velocity in cluttered environment. Li and Bui[5] suggested path planning using fluid model and collision avoidance method. Distance transform method finds a shortest path by transforming distance from the target point to the start point on the contrary. Borgefors[6] and Zelinsky[7] are proposed a similar manner to calculate a shortest path by transforming a path. In this paper, a local path planner by circular scan code is proposed to avoid obstacles without any priori information about circumstances. Detected information on the circular window are converted to circular scan code and applied to avoid obstacles and determine steering angle. Circular distance transform method is proposed for a global path planner. D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1102 – 1107, 2006. © Springer-Verlag Berlin Heidelberg 2006

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2 Local Path Planning by Circular Scan Code Method 2.1 Generation of Circular Scan Code Obstacle window has the radius WR and is divided by vertical and horizontal lines. Window is composed of QR and QL ranges, which has data converted from obstacle to data bits. Clockwise direction increases bit number in QR region and counter-clockwise direction also increases bit number in QL region about the front vertical line.

QR = b1b2 b3  bn

(1)

QL = b1b2b3  bn

(2)

The circle with radius m centered at a mobile robot is used to express the distance between the mobile robot and obstacle. Radius of outer and inner most circle is r 1 and r m , respectively. When an obstacle is detected in r i -th circle, the number of k-th bit becomes j, namely bk = i . In Figure 1, the detected obstacle in QR is located all at r 3 and that in QL at r 3 , r 2 , r 2 and r 1 from the center, in which data are converted to the following data bits. So, the bits become QR = [3330 0000 0000] and QL = [3221 0000 0000] . 2.2 Definition of Obstacle

When any obstacle is o, this means o ⊂ S and obstacle set is defiend as follows. m

Sobs ≡ { o j : o j ⊂ S }

(3)

j =1

Subset of S is S free ≡ S − Sobs and S obs is defined in window in case that there exists at least one bit except 0. In order to define obstacle, B j includes id and count, specifying obstacle existence and its bit size, respectively. Any obstacle o j is defined by the following equations.

B j .id = " obs "

(4)

B j .count = n(bs bs +1bs + 2 bs + l −1 ) (∀bi ≠ 0, l is integer) B j .id = " obs "

(5) (6)

where n(⋅) is the function specifying the number of continuous bit. S free is the string having at least one 0 bit within window and defined as follows. B j .id = " free "

(7)

B j .count = n(bs bs +1bs + 2 bs +l −1 ) (∀bi ≠ 0, l is integer)

(8)

o jf = B j free

(9)

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Fig. 1. One obstacle is in the quadrant I and II. The obstacle occupied in quadrant I is represented by bit scan code by QR=[3333 0000 0000 0000] and in quadrant II is represented by bit scan code QL=[3221 0000 0000 0000] , where bit number 3 means 3rd radius from outer most circle, n=16.

2.3 Calculation of Steering

Steering angle and distance between target point and current point are denoted by δ t and d t , respectively. The angle size α j occupied by B j can be calculated by Eq. (10).

α j = aunit × B j .count

(degree)

(10)

Window is divided into right side QR and left side QL about vertical line. For the all data bits of QR and QL , crossable range and the corresponding steering angle can be found as the following procedures. CASE 1: B1R .id =" obs" of QR or B1L .id =" obs" of QL

1) Find the case of B Rj .count ≥ Bsafe among B Rj .id = " free " for j = 1, 2, n and calculate the minimum angle α j by Eq. (10). 2) Find the case of B Lj .count ≥ Bsafe among B Lj .id = " free " for j = 1, 2, n and calculate the minimum angle β j calculated by the same equation of α j by Eq. (10). 3) α j and β j calculated by i) and ii) determines the direction angle δ by Eq. (11).

δ = min(α j , β j ) + δ safe CASE 2: B Rj .id = " free " of QR and B Lj .id = " free " of QL

1) For the case of B1R .count + B1L .count ≥ Bsafe i) If α j ≥ 1 δ safe and β j ≥ 1 δ safe are satisfied, then δ = δ t 2 2

(11)

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ii) If α j > 1 δ safe and β j < 1 δ safe are satisfied, then δ = δ t + (δ safe − β j ) 2 2 1 iii) If α j < δ safe and β j > 1 δ safe are satisfied, then δ = δ t − (δ safe − β j ) 2 2 2) For the case of B1R .count + B1L .count < Bsafe follow the above CASE I.

3 Global Path Planning by Circular Distance Transform Circular distance transform method is for a global path planning. Bresenham midpoint circle generation algorithm is applied to find circle cells. The process of circular distance transform for the global path is described as the following steps. STEP 1 : Initialization Distance from the robot center to the target is n, a circle with radius j is represented as r j . map(x,y) is any cell on the grid map. All cells on the grid map is set to 0. STEP 2 : Generation of circles Circles r 1 , r 2 ,  , r n , where n is distance to the target, are generated by Bresenham midpoint circle generation algorithm, respectively. The center of the circle is located on the j

center of robot. The cells on any circle r are composed of equidistance cells j r j = {r1 j , r2j ,, rmj } , where m means total number of cells on circle r . Cells on any circle

r j are marked with their radius value on the grid map. Straight line segment, which start from the robot to the target point, is needed for assigning a priority of cells. If no obstacles are present, the cells of the line segment on the circle r j become path cell. STEP 3 : Construction of obstacle map

Obstacles on any circle

r j are represented by set of cells as follows o1j = {ri j , ri +j1 ,  , ri +j b }

(12)

o j = {o1j , o2j , , o pj }

(13)

where b is a size of cell cluster and p is a number of obstacle clusters on any circle r j . Cells occupied with obstacles are marked as -1 in the grid map. If cells are not occupied with obstacles, shaded regions by obstacles are also marked as -1. STEP 4 : Reconstruction of map Cells, which are occupied with -1 but not obstacles, are changed with new value after the process of reconstruction of map. A new circle t j centered at the target point is generated. An initial value of inner radius is set to higher value, and radius values are getting lower as the radius becomes large. The radius of outer most circle radius must be greater than the maximum radius of the previous circle generated in STEP 2. STEP 5 : Path selection Starting from the target cell t(x,y), the i-th chosen cell pi has the smallest values of 3x3 window. If several same cell values exist in the window, the nearest cell value to

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the line segment is selected. If the path is not optimal, the new path is reconstructed with another cell. A finite set of the chosen path P are represented as follows.

P = p1 ⊕ p 2 ⊕  ⊕ p k

(14)

where symbol ⊕ stands for concatenation of path.

4 Simulation In this simulation, the workspace is defined to 30x30 grid cells. Fig 2 (a) shows is the result of initialization (STEP 1) and circle generation process (STEP 2). Target point

(a)

(b)

Fig. 2. Simulation are performed on 30x30 grid cells. (a) shows the result of application of STEP 1 and STEP 2. -1s means that cells are obstacles or still not assigned any values. (b) shows the final result of application of STEP 3, STEP 4, and STEP 5. The circled cells shows the generated path for the robot.

Fig. 3. This simulation shows the results of circular scan code method for local path planner. 4 different situations are performed with different target points. Robot moves in a workspace safely with eight obstacles.

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is located in the center of block. From start point, circles are generated and labeled with their circle radius values. -1 are assigned to cells outside the outer most circle and a shaded region by obstacles. After obstacles are defined in a grid map(STEP 3), these -1s are reassigned in STEP 4 as shown in Fig. 2 (b). The labeled cells, from the robot to the target, are the chosen path for the robot. Fig. 3 shows simulation result of circular scan code method. Eight obstacles are laid in workspace, the robot has moved to the target point safely with help of the local planner. In the figure 4 different simulations with different target point are performed.

5 Conclusion On the partially known or perfectly unknown environment, moving the mobile robot safely to the target point is important thing. In circular scan code method that is used for a local path planner, obstacle information is applied to the determination of steering angle. This method can be easily applied to ultrasonic sensor which is widely used to mobile robot, and also the steering angle can be determined by simple calculation. Circular distance transform method is for a global path planner. The method is fast for generating the shortest robot path. The suggested methods were found to be effective for mobile robot path planning, which was proven by simulation results.

References 1. Khatib, O.: Real-time Obstacle Avoidance for robot manipulator and mobile robots. Int. J. Robotics Research, 5 (1) (1986) 90-98 2. Koren, Y., Borenstein, J.: Real-time Obstacle Avoidance for Fast Mobile Robots in Cluttered Environment. Proc. IEEE Int. Conf. Robotics and Automation, 2876 (1990) 572-577 3. Koren, Y., Borenstein, J.: The Vector Field Histogram - Fast Obstacle Avoidance for Mobile Robots. IEEE Trans. on Robotics and Automation, 7 (3) (1991) 278-288 4. Fox, D., Burgard, W., Thrum, S.: The Dynamic Window Approach to Collision Avoidance. IEEE Robotics and Automation Magazine, 4 (1) (1997) 23-33 5. Li, Z. X., Bui, T. D.: Robot Path Planning using Fluid Model. J. of Intelligent and Robotics Systems, 21 (1998) 29-50 6. Borgefors, G.: Distance transform in arbitrary dimensions. Comput. Vision, Graphics Image Processing, 27 (1984) 321-345 7. Zelinsky, A.: Navigation with Learning. Proc. IEEE/RSJ Conf. Intelligent Robot Systems (1989) 331-338

Ultrasonic Intruder Detection System for Home Security Yue-Peng Li, Jun Yang, Xiao-Dong Li, and Jing Tian Institute of Acoustics, Chinese Academy of Sciences, 100080 Beijing, China {liyuepeng, jyang, lxd, tian}@mail.ioa.ac.cn

Abstract. This paper describes a new intrusion detection system in the indoor environment, which is based on the airborne sonar technology and pattern classification. It utilizes an ultrasonic transmitter and a receiver to receive the pulse-echo. The simplest feature of echoes, envelope is extracted to train and test the pattern classifiers. The correct classification rates of K-nearest-neighbor (KNN) and Back-Propagation (BP) network classifiers are compared in this paper. Experiment results show that this system has a good performance on the intrusion detection.

1 Introduction Intrusion detection devices have been applied extensively in an alarm system for industrial applications and security purposes, which can detect unauthorized entry into the protected zone and provide an alarm signal or other notice. Security industry is growing at a rapid rate, and various video surveillance systems have been installed for monitoring of public and private places [1]. However, these systems have disadvantages: A person has to watch the video camera and the places need to be illuminated. Moreover, some intrusion detection techniques are generally based on the emission of ultrasonic waves or electromagnetic waves (for example, radar) and the system functions by exploiting the Doppler effect [2, 3]. This frequency shift between emitted and received waves is a characteristic of the reflection from a moving object, which probably indicates an intrusion. The detection system activates an alarm in response to the measured frequency shift. In practical application, these intrusion detection techniques may have high risk of false alarm. For example, disturbances such as sound waves can cause modulation of the emitted wave. This modulated wave, after processing and analysis by the receiver can be incorrectly interpreted as an intrusion, since the characteristics of modulated wave may be identical to those of the wav reflected from a real intruder inside the room or vehicle. There is also detection system based on room acoustic transfer function [4], but the burglars will flee once the audible sound is transmitted. In this paper, we focus on the processing of acoustic data to detect intruders for security. The system monitors the acoustic environment and employs sonar neural network to help reduce nuisance false alarms. The proposed method can be D.-S. Huang, K. Li, and G.W. Irwin (Eds.): ICIC 2006, LNCIS 344, pp. 1108 – 1115, 2006. © Springer-Verlag Berlin Heidelberg 2006

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applied to intrusion detection in a small room or a vehicle. Also, it can be extended to a large scale space after improvement. The use of sonar neural network for real world tasks is based on the effectiveness of biological sonar system [5-7]. Research on bats and dolphins has shown that sonar echoes can convey rich information about the environment [8-10]. It suggested that, we can extract much information from pulse-echoes for monitoring the target area. In an alternative detection system, we use a transmitter to emit ultrasonic pulses at a single frequency and a receiver to receive the echoes. The echoes are processed to extract feature vectors as input for neural network. Then the KNN and BP network are employed to implement classifiers, and classification results of the two classifiers are compared in the present paper. A cost-effective method based on the feature extraction from ultrasound echoes is targeted by this paper. Experiment results show that the developed intrusion detection system is simple to implement for indoor environment, because it is a narrow band system by using single frequency pulses, and only the simplest feature like the envelope from pulse-echo is to be extracted.

2 Methodology 2.1 Description of the Detection Method We performed experiment in a 4 × 3.5 × 3 m3 room. A piezoelectric transducer transmitted sonar pulses, each of which lasted for 20 cycles at frequency of f = 40kHz . A microphone was connected to a channel of an analog-to-digital converter sampling at 500 kHz with 12 bit resolution. The received echo was processed in a data processor to extract features. Then a classifier gave a judgment to activate an alarm or not. Figure 1 shows the flow of the method.

Fig. 1. Flowchart of detection method

2.2 Echoes

The experiment setup and configuration in the room are shown in Figure 2. The transmitter and receiver were placed in a corner of the room, named position A. It is well known, the ultrasonic intrusion detection system by using Doppler effect likely makes false alarm when a dog or cat comes into the room. For simplicity, we chose an

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Fig. 2. Positions distributed in a room. A transmitter and a microphone were laid in position A. A person and an object were located on positions B, C, D, E and F for recording echo samples.

object assumed as a dog in the experiment to test our system's performance on discrimination of circumstances. A great deal of echoes was recorded in the following four cases: (1) There was neither intruder nor object in the room; (2) An object was placed around the positions B, C, D, E and F, respectively; (3) An intruder stood on positions B, C, D, E and F, respectively; (4) An intruder continuously moved in the room. Accordingly, 100 echoes were recorded in every case, and we had a database of (1+5+5+1) ×100=1200 echoes in a total. Echoes obtained from cases (1)-(3) were used to train and test the classifier. The data in the case 4 were only used to further testing the classifier.

Fig. 3. Flowchart of echo data processing

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Fig. 4. A filtered and generalized echo when there is an intruder in the room

Figure 3 shows the flowchart of echo processing. The echoes were truncated and filtered for features extraction. According to their amplitudes, all the echoes were truncated into 60 ms . After that a band-pass filter was used to make the echoes between 25 ~ 65kHz . The filtered echoes were generalized to extract features. Figures 4 and 5 show a filtered echo recorded in a non-empty (human presence) and empty room, respectively. Obviously, there is a significant difference between the two wave forms, which contain rich information.

Fig. 5. A filtered and generalized echo when there is no intruder in the room

2.3 Feature Extraction and Classifier

In the time domain, the simplest feature, envelope vector is extracted from each echo as follows [10]: Compute each filtered echo’s envelope first. Then the envelope is segmented into more segments and the mean for each segment is computed. Each echo can be represented by a vector consisting of those means. Clearly, the vector’s dimension Dv is related to echo length LE and segment length Ls as follows:

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Dv = LE / LS

(1)

Although there are a great number of standard classifiers to be selected, the KNN and BPNN were used for simplicity. There are two phases in setting up these classifiers: First, the classifier’s structure and its internal parameters is determined using sets of feature vectors (the training phase). Secondly, another set of data was used to test the classification ability of the classifier (the testing phase). In the cases of (1), (2) and (3), 60% data is chosen from each case as a training set, i.e., totally 660 groups of processed data were used in the training phase. The rest data is selected as the testing set. Classification results were divided into two categories: 1) an intruder presence, corresponding to cases (1) and (2); 2) no intruder corresponding to case (3). Moreover, the obtained data in the case (4) was used for further system testing.

3 Experiment Results and Discussion 3.1 K-Nearest-Neighbor (KNN)

The KNN method assumes that the feature vectors are clustered into K clusters. We computed the clusters centers in the training phase, according to the distance measure and the relationship of each cluster to each class. The widely-used Euclidean distance was adopted. New data is then assigned to a cluster such that the Euclidean distance from the data point to the center is minimal. Table 1 shows the classification results. The rates of correct classifications are all lower than 85%, of which the KNN algorithm achieves 84 percent correct classification for a smaller segment length of 0.25 ms . Next we will employ the BP neural network to improve the performance of the present detection system. Table 1. Classification results of KNN with different Segment Length Ls Segment Length Ls

Vector Dimension Dv

Rate of Correct Classification

0.25 ms 0.5 ms 1.0 ms 2.0 ms

240 120 60 30

84.09% 82.73% 71.82% 68.86%

3.2 Back-Propagation Neural Network (BPNN)

The Back-Propagation (BP) learning algorithm, commonly used in the sonar research, was chosen for several reasons: 1) The available training data is applicable to the supervised learning since it was taken from known cases; 2) None of the network outputs were to be fed back to the inputs, so a feedback network was suitable; 3) A testing system was commercially available on hardware.

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The BPNN was trained and then activated by logistic sigmoid function. In the intrusion detection system, BPNN has only two output nodes. The weights were initialized to random numbers between – 0.9 and +0.9 .The amount of training was supervised so that the BPNN would not overtrain and learn irrelevant details from some individual training vectors. Table 2 shows the test results of BPNN with different Segment Length Ls . It can be seen that the bigger Ls is, the higher classification error will be. Since the accuracy of envelope description decreased with the increment of Ls , a proper selection of Ls is required with regard to good classification results and low complexity of computation. We set Ls = 1ms in the following experiments. The final network structure is shown in Figure 6. There are 60 input nodes the same number as Dv and 10 hidden nodes. Table 2. Classification results of BPNN with different Segment Length Ls Segment Length Ls

Vector Dimension Dv

Rate of Correct Classification

0.25ms 0.5ms 1.0 ms 2.0 ms

240 120 60 30

99.31% 97.27% 97.04% 88.86%

Fig. 6. BPNN structure

Table 3 shows detailed classification results with Ls = 1ms . From the table 3, it is demonstrated that this classifier can reach high rate of correct classification to avoid high false alarm. Moreover, data set of case 4 was used for further testing system performance. Consider a person moving continuously in the room, the BPNN algorithm still achieve high rate of correct classification (96%).

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Table 3. Classification results of BPNN with Ls = 1ms . The top row shows the correct results and left column the results into which the test data is classified. Rate of Correct Classification An Intruder No Intruder

An Intruder

No Intruder

99.5% 0.5%

5% 95%

3.3 Discussion

Comparison of the above algorithms indicates that, the BPNN method is superior to the KNN method with over 15% improvement of the correct classification rate. The intrusion detection system based on BPNN has a good classification capability, which is much preferred. For the KNN or BPNN-based detection system, we can further improve the correct classification rate by using more echo samples. If more positions shown in Fig. 2 are considered for testing, the number of echo samples used for training classifiers will be increased. As a result, it is possible to achieve a very high rate of correct classification, but requiring long computation time. It should be paid more attention on the balance between the computation load and classification performance for a cost-effective intruder detection system.

4 Conclusion A novel approach has been proposed for interior presence detection by utilizing sound characteristics of an enclosed space. An active sensing technology is developed based on the information contained in transmitted reflections. The new sensor system signals the presence of an intruder or object in response to the variation of the ultrasound field determined by a classifier. In this paper, the neural network is employed to process simple features and then accomplish intruder detection tasks. An important advantage of the present method is that a high and stable rate of correct classification can be achieved using the developed system. The low cost feature extraction, off-the-shelf transducers and good performance enable the detection system both affordable and effective. In near future, we will investigate on the intrusion detection by utilizing broadband ultrasonic signal. It is expected that more information could be extracted from echoes by means of time -frequency analysis.

Acknowledgements This research was partially supported by National Natural Science Foundation of China under Grant No. 10474115 and No. 60535030, and Chinese Academy of Science under Grant No. KGCX2-SW-602-7.

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References 1. Chun, C.F., Jerrat, N.: A neural network based intelligent intruders detection and tracking system using CCTV images, Proceedings of TENCON 2000,Kuala Lumpur, Ma1aysia (2000) 409-414 2. Denso Corporation: Intrusion detecting apparatus for a vehicle, United States Patent 5856778 issued on January 5. (1999) 3. Bonhoure, F.: Device for detecting the intrusion of a body in a predetermined space, United States Patent 6157293, issued on December 5. (2000) 4. Choi, Y.K., Kim, K.M., Jung, J.W., Chun, S.Y., Park, K.S.: Acoustic intruder detection system for home security, IEEE Trans. Consumer Electronics, 51 (2005) 130–138 5. Kleeman, L., Kuc, R.: Mobile robot sonar for target localization and classification, Int. J. Robot. Res., 14 (1995) 295-318 6. Kuc, R.: Biomimetic sonar system recognizes objects using binaural information, J. Acoustic. Soc. Amer., 102 (1997) 689-696 7. McKerrow, P.J., Harper, N.L.: Recognizing leafy plants with in-air sonar, Sensor Rev., 19 (1999) 202-206 8. Hartley, D.J., Suthers, R.A.: The sound emission pattern of the echolocating bat, Eptesicus fuscus, J. Acoust. Soc. Amer., 85 (1989) 1348-1351 9. Simmons, J.A., Eastman, K.M., Horowitz, S.S., O’Farrell, M.J., Lee, D.N.: Versatility of biosonar in the big brown bat, Eptesicus fuscus, ARLO 2 (2001) 43-48 10. Ecemis, M.I., Gaudiano, P.: Object recognition with ultrasonic sensors, Proc.Int. Symp. on Computational Intelligence in Robotics and Automation, CIRA'99, Monterey, Canada (1999) 250-255

Author Index

Ak, Ayca Gokhan 527 Aliskan, Ibrahim 331 Andreozzi, Sergio 982 Aung, Khin Mi Mi 158 Bae, S.M. 456, 486 Baek, Kwang-Ryul 438 Bao, Guangbin 150 Bao, Yongping 219 Bell, David 778 Cai, Yu 539 Cai, Yuanli 533 Cansever, Galip 527 Cao, Jian 816 Cao, Jun 240 Cao, TieYong 29 Cao, Xianqing 616 Chai, Tianyou 264, 428 Chang, Kyung-Bae 138, 171 Chavarr´ıa-B´ aez, Lorena 676 Chen, Chi 176 Chen, Jianhua 229 Chen, Jiaoliao 571 Chen, Keming 373 Chen, Lei 54 Chen, Liang 144 Chen, Wanmi 494 Chen, Weidong 188 Chen, Xiyuan 417 Chen, Xuhui 150 Chen, Yongqiang 882 Chen, Yuping 909 Chen, Zhimei 565 Chen, Zilong 945 Cheng, Jian 319 Cheng, Xin 176 Cho, Gyusang 1000, 1102 Choi, Bok Yong 1068 Choi, Jonghwa 578 Choi, Jung-Ki 438 Choi, Kwang Nam 1068 Chu, Jian 407, 602 Chung, I-Fang 299

Ciancarini, Paolo 982 Cui, Peiling 933 Cui, Xinchun 810 Dai, Huaping 130 Dai, Wei-di 633 Deng, Xuezhi 373 Ding, Shifei 951 Doan, Son 664 Dong, Hui 72 Du, Wenchao 219 Encheva, Sylvia

834

Fan, Liping 616 Fan, Xinghua 790 Fang, Binhao 428 Fang, Chong 828 Fang, Xin 514 Fei, Minrui 176, 494, 722 Fei, Yu 921 Feng, Chen 747 Feng, Naiqin 1 Fu, Tiaoping 229 Fu, Yuli 60 Ge, Sibo 533 Ge, Xiaosan 828 Gong, Dun-wei 319 Gong, Peng 194 Gu, Zhimin 822 Guan, Donghai 741 Guan, Jiwen 778 Gulez, Kayhan 331 Guo, Donghui 759 Guo, Ge 584, 590 Guo, Qiang 642 Guo, XiaoPing 803 Guo, Xuewu 395 Guo, Yi-Nan 319 Han, Han, Han, Han,

Bo 909 Kyungsook 596 Sangman 741 Yingjie 822

1118

Author Index

Hassan, Mohammad M. 623 He, Hanlin 469 He, Ling 463 He, Pi-lian 633 He, Yanxiang 95, 202 He, Yanzhao 565 Heywood, Malcolm 845 Ho, Tu Bao 939 Horiguchi, Susumu 664 Hou, Chaozhen 500 Hou, Zhixiang 480 Hsu, Chun-Fei 299 Hu, Chuanping 176 Hu, Feng 790 Hu, Huosheng 494 Hu, Kunyuan 654 Hu, Wei 688 Hua, Jun 784 Huang, Hsiang-Chan 450 Huang, Qinghua 12 Huang, Qinhua 969 Huang, Shiqi 144, 385 Huang, Wei 939 Huang, Weitong 903 Huh, Moon Haeng 957 Hwang, J.H. 456, 486 Hwang, Sun-myoung 1084, 1090 Ji, Guangrong 747 Jia, MingXing 803 Jia, Shixiang 275 Jian, Zi-Jie 450 Jiang, Eric 700 Jie-Liu 633 Jie, Min Seok 520 Jin, Fengxiang 951 Jin, Peng 654 Jin, Xue-bo 963 Jing, Yuan-wei 341, 463 Jo, Taeho 1056 Ju, Lincang 533 Juang, Jih-Gau 252 Jung, Kyung-Yong 839 Jung, Sungyun 438 Jung, Young Jin 124 Kang, Jiayin 976 Kang, Lishan 909 Kang, Sanggil 888 Kawasaki, Saori 939

Khan, M. Junaid 539 Khan, Mohammad A.U. 741 Kim, Chin Su 520 Kim, D.M. 486 Kim, Dohyung 596 Kim, Duk Kyung 194 Kim, Eun Hee 165 Kim, Hak Cheol 124 Kim, Hea-Suk 857 Kim, InSu 506, 1040 Kim, Jinho 857 Kim, Kyung Ok 124 Kim, Seoksoo 1078, 1096 Kim, Soongohn 1078, 1096 Kim, Wonil 888 Ko, Eung Nam 990, 1012 Kong, Young-Bae 171 Krishnaswamy, S 863 Lee, Bum Ju 957 Lee, Byungjeong 915 Lee, Chongwon 915 Lee, Deok Gyu 1068 Lee, Dong Gyu 124 Lee, Eun Ser 1084, 1090 Lee, G.A. 456, 486 Lee, Heon Gyu 957 Lee, H.J. 456, 486 Lee, H.W. 456, 486 Lee, Hyunghyo 83, 506 Lee, Jae-Il 1034 Lee, Jong Yun 957 Lee, Juyoung 888 Lee, Kang Woong 520 Lee, Malrey 1056 Lee, Myung Jin 165 Lee, N.K. 456, 486 Lee, Seungyong 83 Lee, Sungy-oung 741 Lee, W.S. 486 Lee, Yang Koo 124 Lee, Youngkoo 741 Lee, Younglok 83, 506, 1040 Lee, Yue-Shi 731 Li, Jigong 590 Li, Jun 207 Li, Ming 712 Li, Mingbao 784 Li, Ning 945 Li, Shujiang 264

Author Index Li, Sufen 654 Li, Xiao-Dong 1108 Li, Xiaoou 676 Li, Yaqin 395 Li, Yijun 894 Li, Yilong 828 Li, Yue-Peng 1108 Li, Zheng 642 Li, Zhijun 882 Liang, Wei 106 Lin, Bo-Shian 252 Lin, Chih-Min 299 Lin, Chun-Liang 450 Lin, Feng-Chu 252 Lin, Mao-Song 939 Liu, Daizhi 144 Liu, Erqi 712 Liu, Hong 373 Liu, Jian 765 Liu, Ruiming 712 Liu, Van-Tsai 450 Liu, Ya-qiu 240 Liu, Yunfeng 144, 385 Liu, Yushu 229 Liu, Zhen-hua 633 Loh, Woong-Kee 857 Lu, Jiangang 72 Lu, Yuchang 903 Luo, Xiao 845 Lv, Yingjie 894 Ma, Junjie 182 Manicka, Sankarnarayanan McGinnity, TM 778 Mehta, Preeti 863 Montesi, Danilo 982 Moon, Yang-Sae 857 Moretti, Rocco 982 Mumcu, Tarık Veli 331 Nam, Seung Woo 596 Nepal, Chirag 596 Nhan, Vu Thi Hong 875 Nian, Rui 747 Ogiela, Lidia 851 Ogiela, Marek R. 851 O˘ gul, Ersin 309 Oh, Jaewon 915 Ouyang, Weimin 969

Pan, Hui 275 Pan, Jianxin 921 Pan, Quan 933 Park, Gwi-Tae 138, 171 Park, Hee-Un 1034 Park, Jong Hyuk 1068 Park, Jong Sou 158 Park, Mi 124 Pian, Jinxiang 264 Prasad, Girijesh 778 Prilusky, Jaime 863 Qian, Weiqi 207 Qin, Xiaolin 810 Qiu, Yuhui 1 Qu, Liangsheng 48 Qv, Kai-feng 514 Raghavenderan, L 863 Rao, Geeta V 863 Ren, Shuqin 158 Ren, Tao 341 Ryeu, Jinkyung 1000, 1102 Ryu, Keun Ho 124, 165, 875, 957

863

Shen, Lincheng 546 Shen, Tao 554 Sheng, Gang 810 Sheng, Huanye 688 Shi, Changjiang 747 Shi, Lei 822 Shi, Min 41 Shi, Ren 533 Shi, Yang 207 Shi, Yongli 500 Shi, Yun 822 Shi, Zhongzhi 951 Shin, Dongil 578 Shin, Dongkyoo 578 Shin, Dong-Myung 1034 Son, Tae-Hwan 138 Song, Huazhu 909 Song, Jaekoo 1096 Song, Jian-she 554 Song, Wen-long 240 Song, Yexin 882 Srividhya, K.V. 863 Su, Hongye 407, 602 Su, Jia 514 Sun, Youxian 72, 130, 963

1119

1120

Author Index

Sun, Yuqiang 1 Sussman, Joel L.

863

Tadeusiewicz, Ryszard 851 Tan, Beihai 21, 60 Tan, Min 395 Tan, Minghao 264 Tang, Daquan 219 Tang, Feng 816 Tang, Xinting 275 Tao, Chaohai 790 Tao, Huan 35 Tian, Haiyan 753 Tian, Jing 1108 Tian, Jinwen 765 Tian, Yuan 584 Tombul, Mustafa 309 Tumin, Sharil 834 Wan, Yongle 66 Wang, Fang 1 Wang, Fanglin 712 Wang, FuLi 803 Wang, Guizeng 933 Wang, Heshou 176, 722 Wang, Hong 927 Wang, Jianying 54 Wang, Linze 608 Wang, RuJing 771 Wang, Sheng 182 Wang, Shuning 539 Wang, Xiaodong 130 Wang, Xin 287 Wang, Xue 182 Wang, Yuncheng 951 Wang, ZhenLi 29 Wang, Zhenyan 565 Wang, Zhi 130 Wang, Zhongsheng 469 Wei, Lin 822 Wei, Yanqin 494 Wen, Guangrui 48 Wen, John T. 395 Won, Woo-Jae 1034 Wu, Chisu 915 Wu, Jiangning 753 Wu, Jin 118, 765 Wu, Lei 176 Wu, QingXiang 778 Wu, Xiaofeng 722

Xi, Yugeng 188 Xia, Feng 444 Xia, Wenbo 21 Xiao, Yi 869 Xie, Jun 514 Xin, Guan 869 Xu, Fang 571 Xu, Hualong 385 Xu, Huipu 584 Xu, WanXin 771 Xue, Peng 194 Yan, Weisheng 207 Yang, Guangfei 753 Yang, Hui 287 Yang, Jie 12, 712 Yang, Jun 1108 Yang, J.Y. 456 Yang, Qingyu 533 Yang, Simon.X 790 Yang, Wenbin 176 Yang, Xiuzhen 219 Yang, Yahong 361 Yang, Yuequan 395 Yang, Zuyuan 66 Yao, Danya 539 Ye, Meiying 351 Ye, Qiang 894 Yen, Show-Jane 731 Yi, Jianqiang 395 Yi, Qingming 41 Yin, Bingkun 765 Yin, Jian 797 Yin, Zhongke 54 You, He 869 You, Ilsun 1022 Yu, Chunlai 385 Yu, Haibin 106 Yu, Jingwen 797 Yu, Jinyong 219 Yu, Lin 35 Yu, Shuanghe 474 Yuan, Liang 188 Yuan, Weiwei 741 Yuan, Zhanting 150 Yue, Heng 428 Zang, Chuanzhi 106 Zeng, Jianping 759 Zeng, Jiguo 229

Author Index Zeng, Yuanyuan 95, 202 Zha, Hongbin 373 Zhan, Hongwu 571 Zhang, Guozhong 546 Zhang, Hui 939 Zhang, Jian-hua 319 Zhang, Jian-yun 35 Zhang, Jinggang 565 Zhang, Jun 797 Zhang, Jun-xian 633 Zhang, Libin 571 Zhang, Lihua 828 Zhang, Qiuyu 150, 361 Zhang, Wenjuan 976 Zhang, Wen-Xiu 927 Zhang, Xingzhou 642 Zhang, Xining 48 Zhang, XiongWei 29 Zhang, Yin-Chao 514 Zhao, Da-yi 633 Zhao, Fuqing 361 Zhao, Juan 539

Zhao, Pei-Tao 514 Zhao, Wenhong 444 Zhao, Wenli 608 Zhao, Yu 903 Zhao, Yue-Feng 514 Zheng, Jiping 810 Zheng, Shiqiang 784 Zheng, Shuibo 176, 722 Zhong, ShaoChun 778 Zhou, Duanning 797 Zhou, Gang 945 Zhou, Gengui 816 Zhou, Lifang 559 Zhou, Lijian 747 Zhou, Luwen 559 Zhou, Xiaojie 428 Zhou, Yu-cheng 341, 463 Zhou, Yue 12 Zhu, Hai-yu 463 Zhu, Yunlong 654 Zincir-Heywood, A. Nur 845 Zou, Hongbo 407, 602

1121