Life System Modeling and Intelligent Computing: International Conference on Life System Modeling and Simulation, LSMS 2010, and International ... Computer Science and General Issues)

Lecture Notes in Computer Science Commenced Publication in 1973 Founding and Former Series Editors: Gerhard Goos, Juris Hartmanis, and Jan van Leeuwen

Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Alfred Kobsa University of California, Irvine, CA, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen TU Dortmund University, Germany Madhu Sudan Microsoft Research, Cambridge, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max Planck Institute for Informatics, Saarbruecken, Germany

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Kang Li Minrui Fei Li Jia George W. Irwin (Eds.)

Life System Modeling and Intelligent Computing International Conference on Life System Modeling and Simulation, LSMS 2010 and International Conference on Intelligent Computing for Sustainable Energy and Environment, ICSEE 2010 Wuxi, China, September 17-20, 2010 Proceedings, Part I

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Volume Editors Kang Li The Queen’s University of Belfast, Intelligent Systems and Control School of Electronics, Electrical Engineering and Computer Science Ashby Building, Stranmillis Road, Belfast BT9 5AH, UK E-mail: [email protected] Minrui Fei Shanghai University, School of Mechatronical Engineering and Automation P.O.Box 183, Shanghai 200072, China E-mail: [email protected] Li Jia Shanghai University, School of Mechatronical Engineering and Automation P.O.Box 183, Shanghai 200072, China E-mail: [email protected] George W. Irwin The Queen’s University of Belfast, Intelligent Systems and Control School of Electronics, Electrical Engineering and Computer Science Ashby Building, Stranmillis Road, Belfast BT9 5AH, UK E-mail: [email protected]

Library of Congress Control Number: 2010933354 CR Subject Classification (1998): J.3, I.6, I.2, C.2.4, F.1, I.2.11 LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues ISSN ISBN-10 ISBN-13

0302-9743 3-642-15620-7 Springer Berlin Heidelberg New York 978-3-642-15620-5 Springer Berlin Heidelberg New York

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Preface

The 2010 International Conference on Life System Modeling and Simulation (LSMS 2010) and the 2010 International Conference on Intelligent Computing for Sustainable Energy and Environment (ICSEE 2010) were formed to bring together researchers and practitioners in the fields of life system modeling/simulation and intelligent computing applied to worldwide sustainable energy and environmental applications. A life system is a broad concept, covering both micro and macro components ranging from cells, tissues and organs across to organisms and ecological niches. To comprehend and predict the complex behavior of even a simple life system can be extremely difficult using conventional approaches. To meet this challenge, a variety of new theories and methodologies have emerged in recent years on life system modeling and simulation. Along with improved understanding of the behavior of biological systems, novel intelligent computing paradigms and techniques have emerged to handle complicated real-world problems and applications. In particular, intelligent computing approaches have been valuable in the design and development of systems and facilities for achieving sustainable energy and a sustainable environment, the two most challenging issues currently facing humanity. The two LSMS 2010 and ICSEE 2010 conferences served as an important platform for synergizing these two research streams. The LSMS 2010 and ICSEE 2010 conferences, held in Wuxi, China, during September 17–20, 2010, built upon the success of two previous LSMS conferences held in Shanghai in 2004 and 2007 and were based on the Research Councils UK (RCUK)-funded Sustainable Energy and Built Environment Science Bridge project. The conferences were jointly organized by Shanghai University, Queen's University Belfast, Jiangnan University and the System Modeling and Simulation Technical Committee of CASS, together with the Embedded Instrument and System Technical Committee of China Instrument and Control Society. The conference program covered keynote addresses, special sessions, themed workshops and poster presentations, in addition to a series of social functions to enable networking and foster future research collaboration. LSMS 2010 and ICSEE 2010 received over 880 paper submissions from 22 countries. These papers went through a rigorous peer-review procedure, including both pre-review and formal refereeing. Based on the review reports, the Program Committee finally selected 260 papers for presentation at the conference, from amongst which 194 were subsequently selected and recommended for publication by Springer in two volumes of Lecture Notes in Computer Science (LNCS) and one volume of Lecture Notes in Bioinformatics (LNBI). This particular volume of Lecture Notes in Computer Science (LNCS) includes 55 papers covering 7 relevant topics.

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Preface

The organizers of LSMS 2010 and ICSEE 2010 would like to acknowledge the enormous contributions from the following: the Advisory and Steering Committees for their guidance and advice, the Program Committee and the numerous referees worldwide for their significant efforts in both reviewing and soliciting the papers, and the Publication Committee for their editorial work. We would also like to thank Alfred Hofmann, of Springer, for his continual support and guidance to ensure the highquality publication of the conference proceedings. Particular thanks are of course due to all the authors, as without their excellent submissions and presentations, the two conferences would not have occurred. Finally, we would like to express our gratitude to the following organizations: Chinese Association for System Simulation (CASS), IEEE SMCS Systems Biology Technical Committee, National Natural Science Foundation of China, Research Councils UK, IEEE CC Ireland chapter, IEEE SMC Ireland chapter, Shanghai Association for System Simulation, Shanghai Instrument and Control Society and Shanghai Association of Automation. The support of the Intelligent Systems and Control research cluster at Queen’s University Belfast, Tsinghua University, Peking University, Zhejiang University, Shanghai Jiaotong University, Fudan University, Delft University of Technology, University of Electronic Science Technology of China, Donghua University is also acknowledged.

July 2010

Bohu Li Mitsuo Umezu George W. Irwin Minrui Fei Kang Li Luonan Chen Li Jia

LSMS-ICSEE 2010 Organization

Advisory Committee Kazuyuki Aihara, Japan Zongji Chen, China Guo-sen He, China Frank L. Lewis, USA Marios M. Polycarpou, Cyprus Olaf Wolkenhauer, Germany Minlian Zhang, China

Shun-ichi Amari, Japan Peter Fleming, UK Huosheng Hu,UK Stephen K.L. Lo, UK Zhaohan Sheng, China

Erwei Bai, USA Sam Shuzhi Ge, Singapore Tong Heng Lee, Singapore Okyay Kaynak, Turkey Peter Wieringa, The Netherlands

Cheng Wu, China Guoping Zhao, China

Yugeng Xi, China

Kwang-Hyun Cho, Korea

Xiaoguang Gao, China

Shaoyuan Li, China Sean McLoone, Ireland Xiaoyi Jiang, Germany Kok Kiong Tan, Singapore Tianyuan Xiao, China Donghua Zhou, China

Liang Liang, China Robert Harrison, UK Da Ruan Belgium Stephen Thompson, UK Jianxin Xu, Singapore Quanmin Zhu, UK

Steering Committee Sheng Chen, UK Tom Heskes, The Netherlands Zengrong Liu, China MuDer Jeng, Taiwan, China Kay Chen Tan, Singapore Haifeng Wang, UK Guangzhou Zhao, China

Honorary Chairs Bohu Li, China Mitsuo Umezu, Japan

General Chairs George W. Irwin, UK Minrui Fei, China

International Program Committee IPC Chairs Kang Li, UK Luonan Chen, Japan

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Organization

IPC Regional Chairs Haibo He, USA Wen Yu, Mexico Shiji Song, China Xingsheng Gu, China Ming Chen, China

Amir Hussain, UK John Morrow, UK Taicheng Yang, UK Yongsheng Ding, China Feng Ding, China

Guangbin Huang, Singapore Qiguo Rong, China Jun Zhang, USA Zhijian Song, China Weidong Chen, China

Maysam F. Abbod, UK Vitoantonio Bevilacqua, Italy Yuehui Chen, China

Peter Andras, UK Uday K. Chakraborty, USA Xinglin Chen, China

Costin Badica, Romania

Minsen Chiu, Singapore Kevin Curran, UK Jianbo Fan, China

Michal Choras, Poland Mingcong Deng, Japan Haiping Fang, China Wai-Keung Fung, Canada Xiao-Zhi Gao, Finland Aili Han, China Pheng-Ann Heng, China Xia Hong, UK Jiankun Hu, Australia

Tianlu Chen, China Weidong Cheng, China Tommy Chow, Hong Kong, China Frank Emmert-Streib, UK Jiali Feng, China Houlei Gao, China Lingzhong Guo, UK Minghu Ha, China Laurent Heutte, France Wei-Chiang Hong, China Xiangpei Hu, China

Peter Hung, Ireland

Amir Hussain, UK

Xiaoyi Jiang, Germany Tetsuya J. Kobayashi, Japan Xiaoou Li, Mexico Paolo Lino, Italy Hua Liu, China Sean McLoone, Ireland Kezhi Mao, Singapore Wasif Naeem, UK Feng Qiao, China Jiafu Tang, China Hongwei Wang, China Ruisheng Wang, USA Yong Wang, Japan Lisheng Wei, China Rongguo Yan, China Zhang Yuwen, USA Guofu Zhai, China Qing Zhao, Canada Liangpei Zhang, China Shangming Zhou, UK

Pingping Jiang, China

IPC Members

Huijun Gao, China Xudong Guo, China Haibo He, USA Fan Hong, Singapore Yuexian Hou, China Guangbin Huang, Singapore MuDer Jeng, Taiwan, China Yasuki Kansha, Japan Gang Li, UK Yingjie Li, China Hongbo Liu, China Zhi Liu, China Fenglou Mao, USA John Morrow, UK Donglian Qi, China Chenxi Shao, China Haiying Wang, UK Kundong Wang, China Wenxing Wang, China Zhengxin Weng, China WeiQi Yan, UK Wen Yu, Mexico Peng Zan, China Degan Zhang, China Huiru Zheng, UK Huiyu Zhou, UK

Aim`e Lay-Ekuakillel, Italy Xuelong Li, UK Tim Littler, UK Wanquan Liu, Australia Marion McAfee, UK Guido Maione, Italy Mark Price, UK Alexander Rotshtein, Ukraine David Wang, Singapore Hui Wang, UK Shujuan Wang, China Zhuping Wang, China Ting Wu, China Lianzhi Yu, China Hong Yue, UK An Zhang, China Lindu Zhao, China Qingchang Zhong, UK

Organization

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Secretary-General Xin Sun, China Ping Zhang, China Huizhong Yang, China

Publication Chairs Xin Li, China Wasif Naeem, UK

Special Session Chairs Xia Hong, UK Li Jia, China

Organizing Committee OC Chairs Shiwei Ma, China Yunjie Wu, China Fei Liu, China OC Members Min Zheng, China Yijuan Di, China Qun Niu, UK

Banghua Yang, China Weihua Deng, China Xianxia Zhang, China

Yang Song, China Tim Littler, UK

Reviewers Renbo Xia, Vittorio Cristini, Aim'e Lay-Ekuakille, AlRashidi M.R., Aolei Yang, B. Yang, Bailing Zhang, Bao Nguyen, Ben Niu, Branko Samarzija, C. Elliott, Chamil Abeykoon, Changjun Xie, Chaohui Wang, Chuisheng Zeng, Chunhe Song, Da Lu, Dan Lv, Daniel Lai, David Greiner, David Wang, Deng Li, Dengyun Chen, Devedzic Goran, Dong Chen, Dongqing Feng, Du K.-L., Erno Lindfors, Fan Hong, Fang Peng, Fenglou Mao, Frank Emmert-Streib, Fuqiang Lu, Gang Li, Gopalacharyulu Peddinti, Gopura R. C., Guidi Yang, Guidong Liu, Haibo He, Haiping Fang, Hesheng Wang, Hideyuki Koshigoe, Hongbo Liu, Hongbo Ren, Hongde Liu, Hongtao Wang, Hongwei Wang, Hongxin Cao, Hua Han, Huan Shen, Hueder Paulo de Oliveira, Hui Wang, Huiyu Zhou, H.Y. Wang, Issarachai Ngamroo, Jason Kennedy, Jiafu Tang, Jianghua Zheng, Jianhon Dou, Jianwu Dang, Jichun Liu, Jie Xing, Jike Ge, Jing Deng, Jingchuan Wang, Jingtao Lei, Jiuying Deng, Jizhong Liu, Jones K.O., Jun Cao, Junfeng Chen, K. Revett, Kaliviotis Efstathios, C.H. Ko, Kundong Wang, Lei Kang,

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Organization

Leilei Zhang, Liang Chen, Lianzhi Yu, Lijie Zhao, Lin Gao, Lisheng Wei, Liu Liu, Lizhong Xu, Louguang Liu, Lun Cheng, Marion McAfee, Martin Fredriksson, Meng Jun, Mingcong Deng, Mingzhi Huang, Minsen Chiu, Mohammad Tahir, Mousumi Basu, Mutao Huang, Nian Liu, O. Ciftcioglu, Omidvar Hedayat, Peng Li, Peng Zan, Peng Zhu, Pengfei Liu, Qi Bu, Qiguo Rong, Qingzheng Xu, Qun Niu, R. Chau, R. Kala, Ramazan Coban, Rongguo Yan, Ruisheng Wang, Ruixi Yuan, Ruiyou Zhang, Ruochen Liu, Shaohui Yang, Shian Zhao, Shihu Shu, Yang Song, Tianlu Chen, Ting Wu, Tong Liang, V. Zanotto, Vincent Lee, Wang Suyu, Wanquan Liu, Wasif Naeem, Wei Gu, Wei Jiao, Wei Xu, Wei Zhou, Wei-Chiang Hong, Weidong Chen, WeiQi Yan, Wenjian Luo, Wenjuan Yang, Wenlu Yang, X.H. Zeng, Xia Ling, Xiangpei Hu, Xiao-Lei Xia, Xiaoyang Tong, Xiao-Zhi Gao, Xin Miao, Xingsheng Gu, Xisong Chen, Xudong Guo, Xueqin Liu, Yanfei Zhong, Yang Sun, Yasuki Kansha, Yi Yuan, Yin Tang, Yiping Dai, Yi-Wei Chen, Yongzhong Li, Yudong Zhang, Yuhong Wang, Yuni Jia, Zaitang Huang, Zhang Li, Zhenmin Liu, Zhi Liu, Zhigang Liu, Zhiqiang Ge, Zhongkai Li, Zilong Zhao, Ziwu Ren.

Table of Contents – Part I

The First Section: Intelligent Modeling, Monitoring, and Control of Complex Nonlinear Systems Stabilization of a Class of Networked Control Systems with Random packet Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minrui Fei, Weihua Deng, Kang Li, and Yang Song

1

Improved Nonlinear PCA Based on RBF Networks and Principal Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xueqin Liu, Kang Li, Marion McAfee, and Jing Deng

7

Application of Partical Swarm Optimization Algorithm in Field Holo-Balancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guangrui Wen, Xining Zhang, and Ming Zhao

16

Analyzing Deformation of Supply Chain Resilient System Based on Cell Resilience Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yonghong Li and Lindu Zhao

26

Multi-objective Particle Swarm Optimization Control Technology and Its Application in Batch Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Li Jia, Dashuai Cheng, Luming Cao, Zongjun Cai, and Min-Sen Chiu

36

Online Monitoring of Catalyst Activity for Synthesis of Bisphenol A . . . . Liangcheng Cheng, Yaqin Li, Huizhong Yang, and Nam Sun Wang

45

An Improved Pyramid Matching Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jun Zhang, Guangzhou Zhao, and Hong Gu

52

Stability Analysis of Multi-channel MIMO Networked Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dajun Du, Minrui Fei, and Kang Li

62

Synthesis of PI–type Congestion Controller for AQM Router in TCP/AQM Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Junsong Wang and Ruixi Yuan

69

A State Identification Method of Networked Control Systems . . . . . . . . . . Xiao-ming Yu and Jing-ping Jiang Stabilization Criterion Based on New Lyapunov Functional Candidate for Networked Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Qigong Chen, Lisheng Wei, Ming Jiang, and Minrui Fei

77

87

XII

Table of Contents – Part I

Development of Constant Current Source for SMA Wires Driver Based on OPA549 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yong Shao, Enyu Jiang, Quanzhen Huang, and Xiangqiang Zeng High Impedance Fault Location in Transmission Line Using Nonlinear Frequency Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Min-you Chen, Jin-qian Zhai, Zi-qiang Lang, Ju-cheng Liao, and Zhao-yong Fan Batch-to-Batch Iterative Optimal Control of Batch Processes Based on Dynamic Quadratic Criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Li Jia, Jiping Shi, Dashuai Cheng, Luming Cao, and Min-Sen Chiu

95

104

112

Management Information System (MIS) for Planning and Implementation Assessment (PIA) in Lake Dianchi . . . . . . . . . . . . . . . . . . . Longhao Ye, Yajuan Yu, Huaicheng Guo, and Shuxia Yu

120

Integration Infrastructure in Wireless/Wired Heterogeneous Industrial Network System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Haikuan Wang, Weiyan Hou, Zhaohui Qin, and Yang Song

129

Multi-innovation Generalized Extended Stochastic Gradient Algorithm for Multi-Input Multi-Output Nonlinear Box-Jenkins Systems Based on the Auxiliary Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jing Chen and Xiuping Wang

136

Research of Parallel-Type Double Inverted Pendulum Model Based on Lagrange Equation and LQR Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jian Fan, Xihong Wang, and Minrui Fei

147

A Consensus Protocol for Multi-agent Systems with Double Integrator Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fang Wang, Lixin Gao, and Yanping Luo

157

A Production-Collaboration Model for Manufacturing Grid . . . . . . . . . . . . Li-lan Liu, Xue-hua Sun, Zhi-song Shu, Shuai Tian, and Tao Yu

166

The Second Section: Autonomy-Oriented Computing and Intelligent Agents Parallel Computation for Stereovision Obstacle Detection of Autonomous Vehicles Using GPU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhi-yu Xu and Jie Zhang

176

Framework Designing of BOA for the Development of Enterprise Management Information System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shiwei Ma, Zhaowen Kong, Xuelin Jiang, and Chaozu Liang

185

Table of Contents – Part I

XIII

Training Support Vector Data Descriptors Using Converging Linear Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hongbo Wang, Guangzhou Zhao, and Nan Li

196

Research on Modeling and Simulation of an Adaptive Combat Agent Infrastructure for Network Centric Warfare . . . . . . . . . . . . . . . . . . . . . . . . . . Yaozhong Zhang, An Zhang, Qingjun Xia, and Fengjuan Guo

205

Genetic Algorithm-Based Support Vector Classification Method for Multi-spectral Remote Sensing Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yi-nan Guo, Da-wei Xiao, and Mei Yang

213

Grids-Based Data Parallel Computing for Learning Optimization in a Networked Learning Control Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lijun Xu, Minrui Fei, T.C. Yang, and Wei Yu

221

A New Distributed Intrusion Detection Method Based on Immune Mobile Agent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yongzhong Li, Chunwei Jing, and Jing Xu

233

Single-Machine Scheduling Problems with Two Agents Competing for Makespan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Guosheng Ding and Shijie Sun

244

Multi-Agent Asynchronous Negotiation Based on Time-Delay . . . . . . . . . . LiangGui Tang and Bo An

256

The Third Section: Advanced Theory and Methodology in Fuzzy Systems and Soft Computing Fuzzy Chance Constrained Support Vector Machine . . . . . . . . . . . . . . . . . . Hao Zhang, Kang Li, and Cheng Wu

270

An Automatic Thresholding for Crack Segmentation Based on Convex Residual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chunhua Guo and Tongqing Wang

282

A Combined Iteration Method for Probabilistic Load Flow Calculation Applied to Grid-Connected Induction Wind Power System . . . . . . . . . . . . Xue Li, Jianxia Pei, and Dajun Du

290

Associated-Conflict Analysis Using Covering Based on Granular Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shuang Liu, Jiyi Wang, and Huang Lin

297

Inspection of Surface Defects in Copper Strip Based on Machine Vision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xue-Wu Zhang, Li-Zhong Xu, Yan-Qiong Ding, Xin-Nan Fan, Li-Ping Gu, and Hao Sun

304

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Table of Contents – Part I

BIBO Stability of Spatial-temporal Fuzzy Control System . . . . . . . . . . . . . Xianxia Zhang, Meng Sun, and Guitao Cao

313

An Incremental Manifold Learning Algorithm Based on the Small World Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lukui Shi, Qingxin Yang, Enhai Liu, Jianwei Li, and Yongfeng Dong

324

Crack Image Enhancement of Track Beam Surface Based on Nonsubsampled Contourlet Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chunhua Guo and Tongqing Wang

333

The Class-2 Linguistic Dynamic Trajectories of the Interval Type-2 Fuzzy Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liang Zhao

342

The Fourth Section: Computational Intelligence in Utilization of Clean and Renewable Energy Resources Strategic Evaluation of Research and Development into Embedded Energy Storage in Wind Power Generation . . . . . . . . . . . . . . . . . . . . . . . . . . T.C. Yang and Lixiong Li

350

A Mixed-Integer Linear Optimization Model for Local Energy System Planning Based on Simplex and Branch-and-Bound Algorithms . . . . . . . . Hongbo Ren, Weisheng Zhou, Weijun Gao, and Qiong Wu

361

IEC 61400-25 Protocol Based Monitoring and Control Protocol for Tidal Current Power Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jung Woo Kim and Hong Hee Lee

372

Adaptive Maximum Power Point Tracking Algorithm for Variable Speed Wind Power Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Moo-Kyoung Hong and Hong-Hee Lee

380

Modeling and Simulation of Two-Leaf Semi-rotary VAWT . . . . . . . . . . . . . Qian Zhang, Haifeng Chen, and Binbin Wang

389

The Fifth Section: Intelligent Modeling, Control and Supervision for Energy Saving and Pollution Reduction Identification of Chiller Model in HVAC System Using Fuzzy Inference Rules with Zadeh’s Implication Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yukui Zhang, Shiji Song, Cheng Wu, and Kang Li An Improved Control Strategy for Ball Mill Grinding Circuits . . . . . . . . . Xisong Chen, Jun Yang, Shihua Li, and Qi Li

399 409

Table of Contents – Part I

Sliding Mode Controller for Switching Mode Power Supply . . . . . . . . . . . . Yue Niu, Yanxia Gao, Shuibao Guo, Xuefang Lin-Shi, and Bruno Allard

XV

416

The Sixth Section: Intelligent Methods in Developing Vehicles, Engines and Equipments Expression of Design Problem by Design Space Model to Support Collaborative Design in Basic Plan of Architectural Design . . . . . . . . . . . . Yoshiaki Tegoshi, Zhihua Zhang, and Zhou Su Drive Cycle Analysis of the Performance of Hybrid Electric Vehicles . . . . Behnam Ganji, Abbas Z. Kouzani, and H.M. Trinh

425 434

The Seventh Section: Computational Methods and Intelligence in Modeling Genetic and Biochemical Networks and Regulation Supply Chain Network Equilibrium with Profit Sharing Contract Responding to Emergencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ating Yang and Lindu Zhao

445

Modeling of the Human Bronchial Tree and Simulation of Internal Airflow: A Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yijuan Di, Minrui Fei, Xin Sun, and T.C. Yang

456

Robust Semi-supervised Learning for Biometrics . . . . . . . . . . . . . . . . . . . . . Nanhai Yang, Mingming Huang, Ran He, and Xiukun Wang

466

Research on Virtual Assembly of Supercritical Boiler . . . . . . . . . . . . . . . . . Pi-guang Wei, Wen-hua Zhu, and Hao Zhou

477

Validation of Veracity on Simulating the Indoor Temperature in PCM Light Weight Building by EnergyPlus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chun-long Zhuang, An-zhong Deng, Yong Chen, Sheng-bo Li, Hong-yu Zhang, and Guo-zhi Fan Positive Periodic Solutions of Nonautonomous Lotka-Volterra Dispersal System with Delays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ting Zhang, Minghui Jiang, and Bin Huang An Algorithm of Sphere-Structure Support Vector Machine Multi-classification Recognition on the Basis of Weighted Relative Distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shiwei Yun, Yunxing Shu, and Bo Ge Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

486

497

506

515

Table of Contents – Part II

The First Section: Advanced Evolutionary Computing Theory and Algorithms A Novel Ant Colony Optimization Algorithm in Application of Pheromone Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Peng Zhu, Ming-sheng Zhao, and Tian-chi He Modelling the Effects of Operating Conditions on Motor Power Consumption in Single Screw Extrusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chamil Abeykoon, Marion McAfee, Kang Li, Peter J. Martin, Jing Deng, and Adrian L. Kelly Quantum Genetic Algorithm for Hybrid Flow Shop Scheduling Problems to Minimize Total Completion Time . . . . . . . . . . . . . . . . . . . . . . . Qun Niu, Fang Zhou, and Taijin Zhou Re-diversified Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . Jie Qi and Shunan Pang Fast Forward RBF Network Construction Based on Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jing Deng, Kang Li, George W. Irwin, and Minrui Fei A Modified Binary Differential Evolution Algorithm . . . . . . . . . . . . . . . . . . Ling Wang, Xiping Fu, Muhammad Ilyas Menhas, and Minrui Fei

1

9

21

30

40

49

Research on Situation Assessment of UCAV Based on Dynamic Bayesian Networks in Complex Environment . . . . . . . . . . . . . . . . . . . . . . . . Lu Cao, An Zhang, and Qiang Wang

58

Optimal Tracking Performance for Unstable Processes with NMP Zeroes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jianguo Wang, Shiwei Ma, Xiaowei Gou, Ling Wang, and Li Jia

69

Typhoon Cloud Image Enhancement by Differential Evolution Algorithm and Arc-Tangent Transformation . . . . . . . . . . . . . . . . . . . . . . . . . Bo Yang and Changjiang Zhang

75

Data Fusion-Based Extraction Method of Energy Consumption Index for the Ethylene Industry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhiqiang Geng, Yongming Han, Yuanyuan Zhang, and Xiaoyun Shi

84

XVIII

Table of Contents – Part II

Research on Improved QPSO Algorithm Based on Cooperative Evolution with Two Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Longhan Cao, Shentao Wang, Xiaoli Liu, Rui Dai, and Mingliang Wu

93

Optimum Distribution of Resources Based on Particle Swarm Optimization and Complex Network Theory . . . . . . . . . . . . . . . . . . . . . . . . . Li-lan Liu, Zhi-song Shu, Xue-hua Sun, and Tao Yu

101

The Model of Rainfall Forecasting by Support Vector Regression Based on Particle Swarm Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . Shian Zhao and Lingzhi Wang

110

Constraint Multi-objective Automated Synthesis for CMOS Operational Amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jili Tao, Xiaoming Chen, and Yong Zhu

120

Research on APIT and Monte Carlo Method of Localization Algorithm for Wireless Sensor Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jia Wang and Fu Jingqi

128

Quantum Immune Algorithm and Its Application in Collision Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jue Wu, LingXi Peng, LiXue Chen, and Lei Yang

138

An Artificial Bee Colony with Random Key for Resource-Constrained Project Scheduling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yan-jun Shi, Fu-Zhen Qu, Wang Chen, and Bo Li

148

The Second Section: Advanced Neural Network and Fuzzy System Theory and Algorithms Combined Electromagnetism-Like Mechanism Optimization Algorithm and ROLS with D-Optimality Learning for RBF Networks . . . . . . . . . . . . Fang Jia and Jun Wu

158

Stochastic Stability and Bifurcation Analysis on Hopfield Neural Networks with Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xuewen Qin, Zaitang Huang, and Weiming Tan

166

EMD-TEO Based Speech Emotion Recognition . . . . . . . . . . . . . . . . . . . . . . Xiang Li, Xin Li, Xiaoming Zheng, and Dexing Zhang A Novel Fast Algorithm Technique for Evaluating Reliability Indices of Radial Distribution Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mohammoud M. Hadow, Ahmed N. Abd Alla, and Sazali P. Abdul Karim

180

190

Table of Contents – Part II

An Improved Adaptive Sliding Mode Observer for Sensorless Control of PMSM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ran Li and Guangzhou Zhao Clustering-Based Geometric Support Vector Machines . . . . . . . . . . . . . . . . Jindong Chen and Feng Pan A Fuzzy-PID Depth Control Method with Overshoot Suppression for Underwater Vehicle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhijie Tang, Luojun, and Qingbo He Local Class Boundaries for Support Vector Machine . . . . . . . . . . . . . . . . . . Guihua Wen, Caihui Zhou, Jia Wei, and Lijun Jiang

XIX

199

207

218

225

Research on Detection and Material Identification of Particles in the Aerospace Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shujuan Wang, Rui Chen, Long Zhang, and Shicheng Wang

234

The Key Theorem of Learning Theory Based on Sugeno Measure and Fuzzy Random Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Minghu Ha, Chao Wang, and Witold Pedrycz

241

Recognition of Fire Detection Based on Neural Network . . . . . . . . . . . . . . Yang Banghua, Dong Zheng, Zhang Yonghuai, and Zheng Xiaoming

250

The Design of Predictive Fuzzy-PID Controller in Temperature Control System of Electrical Heating Furnace . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ying-hong Duan

259

Stability Analysis of an Impulsive Cohen-Grossberg-Type BAM Neural Networks with Time-Varying Delays and Diffusion Terms . . . . . . . . . . . . . Qiming Liu, Rui Xu, and Yanke Du

266

The Third Section: Modeling and Simulation of Societies and Collective Behaviour Characterizing Multiplex Social Dynamics with Autonomy Oriented Computing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lailei Huang and Jiming Liu

277

A Computational Method for Groundwater Flow through Industrial Waste by Use of Digital Color Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Takako Yoshii and Hideyuki Koshigoe

288

A Genetic Algorithm for Solving Patient- Priority- Based Elective Surgery Scheduling Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yu Wang, Jiafu Tang, and Gang Qu

297

XX

Table of Contents – Part II

A Neighborhood Correlated Empirical Weighted Algorithm for Fictitious Play . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hongshu Wang, Chunyan Yu, and Liqiao Wu

305

Application of BP Neural Network in Exhaust Emission Estimatation of CAPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Linqing Wang and Jiafu Tang

312

Dynamic Behavior in a Delayed Bioeconomic Model with Stochastic Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yue Zhang, Qingling Zhang, and Tiezhi Zhang

321

The Fourth Section: Biomedical Signal Processing, Imaging, and Visualization A Feature Points Matching Method Based on Window Unique Property of Pseudo-Random Coded Image . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hui Chen, Shiwei Ma, Hao Zhang, Zhonghua Hao, and Junfeng Qian

333

A Reconstruction Method for Electrical Impedance Tomography Using Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Min-you Chen, Gang Hu, Wei He, Yan-li Yang, and Jin-qian Zhai

342

VLSI Implementation of Sub-pixel Interpolator for AVS Encoder . . . . . . . Chen Guanghua, Wang Anqi, Hu Dengji, Ma Shiwei, and Zeng Weimin

351

The Fifth Section: Intelligent Computing and Control in Distributed Power Generation Systems Optimization of Refinery Hydrogen Network . . . . . . . . . . . . . . . . . . . . . . . . . Yunqiang Jiao and Hongye Su Overview: A Simulation Based Metaheuristic Optimization Approach to Optimal Power Dispatch Related to a Smart Electric Grid . . . . . . . . . . Stephan Hutterer, Franz Auinger, Michael Affenzeller, and Gerald Steinmaurer

360

368

Speed Control for a Permanent Magnet Synchronous Motor with an Adaptive Self-Tuning Uncertainties Observer . . . . . . . . . . . . . . . . . . . . . . . . Da Lu, Kang Li, and Guangzhou Zhao

379

Research on Short-Term Gas Load Forecasting Based on Support Vector Machine Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chao Zhang, Yi Liu, Hui Zhang, Hong Huang, and Wei Zhu

390

Network Reconfiguration at the Distribution System with Distributed Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gao Xiaozhi, Li Linchuan, and Xue Hailong

400

Table of Contents – Part II

XXI

The Sixth Section: Intelligent Methods in Power and Energy Infrastructure Development An Autonomy-Oriented Computing Mechanism for Modeling the Formation of Energy Distribution Networks: Crude Oil Distribution in U.S. and Canada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Benyun Shi and Jiming Liu

410

A Wavelet-Prony Method for Modeling of Fixed-Speed Wind Farm Low-Frequency Power Pulsations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Daniel McSwiggan and Tim Littler

421

Direct Torque Control for Permanent Magnet Synchronous Motors Based on Novel Control Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sizhou Sun, Xingzhong Guo, Huacai Lu, and Ying Meng

433

The Seventh Section: Intelligent Modeling, Monitoring, and Control of Complex Nonlinear Systems A Monitoring Method Based on Modified Dynamic Factor Analysis and Its Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Xueyan Yin and Fei Liu

442

A Novel Approach to System Stabilization over Constrained Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Weihua Deng, Minrui Fei, and Huosheng Hu

450

An Efficient Algorithm for Grid-Based Robotic Path Planning Based on Priority Sorting of Direction Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aolei Yang, Qun Niu, Wanqing Zhao, Kang Li, and George W. Irwin

456

A Novel Method for Modeling and Analysis of Meander-Line-Coil Surface Wave EMATs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shujuan Wang, Lei Kang, Zhichao Li, Guofu Zhai, and Long Zhang

467

The Design of Neuron-PID Controller for a Class of Networked Control System under Data Rate Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lixiong Li, Rui Ming, and Minrui Fei

475

Stochastic Optimization of Two-Stage Multi-item Inventory System with Hybrid Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuli Zhang, Shiji Song, Cheng Wu, and Wenjun Yin

484

Iterative Learning Control Based on Integrated Dynamic Quadratic Criterion for Batch Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Li Jia, Jiping Shi, Dashuai Cheng, Luming Cao, and Min-Sen Chiu

493

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Table of Contents – Part II

Impedance Measurement Method Based on DFT . . . . . . . . . . . . . . . . . . . . . Xin Wang

499

A 3D-Shape Reconstruction Method Based on Coded Structured Light and Projected Ray Intersecting Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hui Chen, Shiwei Ma, Bo Sun, Zhonghua Hao, and Liusun Fu

505

Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

515

Stabilization of a Class of Networked Control Systems with Random Packet Loss Minrui Fei1, , Weihua Deng1 , Kang Li2 , and Yang Song1 1

School of Mechatronical Engineering and Automation, Shanghai University, Shanghai, 200072, China [email protected], [email protected], y [email protected] 2 School of Electronics, Electrical Engineering and Computer Science, Queen’s University Belfast, United Kingdom [email protected]

Abstract. This paper addresses the problem of stabilizing of a class of Networked Control Systems (NCSs) based on both the communication and network properties. Random packet loss together with Signal-toNoise Ratio (SNR) constrained channels are studied and stabilization conditions are given in discrete time domain. A numerical example is presented and shown that unstable poles and packet dropouts significantly affect the SNR requirement for stabilizing the NCSs.

1

Introduction

Network Controlled Systems (NCSs)[1-2] have drawn a lot of interest in recent years and a number of progress has been made on its theoretic. Currently, the majority of researches ignore the limitations on the communication and mainly consider the characteristics of the network such as the network-induced delays[3], data loss[4] and so on. From the stability point of view of NCSs, the impacts of communication, for instance, the quantization error[5], constraint of SNR[6], etc. are equally important. So it is important to consider the two factors, i.e. the network and communication in the design of NCSs. Recently the factors of communication have been taken into account as well. SNR[7-9] is a major issue that were discussed in these research papers. This problem was firstly studied in [7] and discussed in detail in [8]. In [8] the conditions of stabilization over SNR constrained channel are derived in both continuous and discrete time domain. But the characteristics of networks such as network induced delays and dropouts of packet were not analyzed together with SNR attribute in their above works. Further, it is not easy to compute the numerical solutions due to the absence of proper linear matrix inequality (LMI) formulation. In this paper, we extend the aforementioned works. LMI approach is used to simplify the numerical implementation of the result derived in [8]. And ran

Corresponding author.

K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 1–6, 2010. c Springer-Verlag Berlin Heidelberg 2010 

2

M. Fei et al.

Fig. 1. Control over an AWGN channel in network environment

dom packet dropouts is considered together with the SNR constraint and the stabilization criterion of NCS is established. Notations: The closed unit disk and its complement are denoted as D and ¯ C respectively. The expectation operator is denoted as E. The size of signal is D measured by L2 and L∞ norm, n(k)2L∞ = sup E{nT (t)n(t)} and n(k)2L2 = ∞  2 n(k) . k=0

2

Control over an AWGN Channel with Random Packet Dropouts

Here we will consider the packet dropouts together with the channel SNR constraint. The discrete-time NCS in Fig 1 is given by x(k + 1) = Ax(k) + B νˆ(k)

(1)

where νˆ(k) = θ(k)ν(k) is control input. Hence the system can be further reformulated as x(k + 1) = Ax(k) + Bθ(k)ν(k)

(2)

where θ(k) is a 0-1 random variable with a probability distribution given by  α i=0 Pr{θ(k) = i} = 1−α i=1 where 0 ≤ α ≤ α ¯ ≤ 1 is the probability of packet losses. The controller and channel are chosen as u(k) = −Kx(k).

(3)

v(k) = n(k) + u(k)

(4)

Stabilization of a Class of NCSs with Random Packet Loss

3

where u(k) is the channel input, v(k) is the channel output, and n(k) is zeromean AWGN with power spectral density Sn (ω) = Φ, namely, its variance. The power in the channel input is defined as u(k)pow = E{uT (k)u(k)} and satisfies u(k)pow < P

(5)

where P > 0 is predetermined input power level. Thus the closed-loop system is given as x(k + 1) = (A + BKθ(k))x(k) + θ(k)Bn(k).

(6)

If the system is stable, then power spectral density of u(t) as [8] can be rewritten as 2 Su (ω) = |T (s)| Sn (ω) where T (s), s = jw is the continuous-time closed loop transfer function from n(t) to u(t). u(t)pow has the following definition u(t)pow =

1 2π



∞

−∞

Su (ω)dω .

Thus (5) becomes P > upow = T 2H2 Φ

∞ 1 where T H2 = ( 2π |T (jw)|2 dω)1/2 is H2 norm of T (s). It is obviously that −∞ (5) is equivalent to the form of SNR constraint 2

T H2
0, 0 ≤ α ≤ α ¯ ≤ 1, the discrete-time NCS (51) exists a state ¯ satisfies feedback H2 control law , if there exist Q > 0, Z > 0 and K ⎡ ⎤ ¯ T BT −Q QAT 0 QAT + K ⎢ ⎥ A −α−1 Q 0 0 ⎢ ⎥t0:

Ek 1 e−λ2t0 ( AEk + F ) + t0 (D* − C*t0 ) + 2C*t0t + [C2 − (2C* + BD* )]eλ2t + A AB AB − A2 e−λ3t0 (2C* + AD* )]eλ3t +[C3 + 2 B − AB

ε (t ) =

(32)

To summarize, we can obtain the relationship between the deformation value of the supply chain resilient system and time when suffering risks stress as Equation (5): ⎧ D* Ek 1 D* Ek 1 λ2t * * * * ⎪− A + A + AB ( AEk + F − 2C − AD ) + [ A − A − AB − A2 ( AEk + F − 2C − AD )]e ⎪ ⎪+ 1 [ AEk + F − 2C* − AD* ]eλ3t + t (C*t + D* ) t ≤ t0 ⎪⎪ B2 − AB ε (t ) = ⎨ −λ2t0 ⎪ Ek + 1 ( AEk + F ) + t (D* − C*t ) + 2C*t t + [C − e (2C* + BD* )]eλ2t 0 0 0 2 ⎪ A AB AB − A2 ⎪ −λ3t0 ⎪+[C + e t > t0 (2C* + AD* )]eλ3t 3 2 ⎪⎩ B − AB

(33)

3 A Numerical Simulation Assume the internal study abilities of the two supply chain members are μ11=10 and μ21=15, the external study abilities are μ12=5 and μ22=15, the recovery abilities when

Analyzing Deformation of SC Resilient System Based on Cell Resilience Model

33

facing internal risks are E11=45 and E21=40, the recovery abilities when facing external risks are E12=30 and E22=30, and the stress satisfies k=0.1 and t0=40. Fig 2 is a numerical simulation, which describes the changing relationship between the deformation value of a supply chain resilient system and time when suffering a risks stress.

 Fig. 2. Curve of deformation value with time increasing

Fig. 2 shows when a supply chain resilient system suffers a risks stress, a system deformation would take place immediately. From the assumption, it is well known that when t ≤ 40 , the risks stress is increasing gradually from zero. And the deformation value of the system caused by the risks stress increases gradually from zero as well. The relationship between the deformation value and time is close to quadratic polynomial. Therefore, it is easy to know that the relationship between the deformation value and the risks stress is close to quadratic polynomial as well. This section of the curve illustrates that when supply chain risks occur and increase gradually, how a supply chain resilient system reacts under the influence of the study ability and recovery ability of the supply chain members. When t > 40 , the risks stress is constant. That is, supply chain risks reach the maximum and are not changing with time. Meanwhile, the deformation value of the system arisen from the risks increases rapidly and the speeds of deformation value increment are faster than those when t ≤ 40 . The relationship between the deformation value and time is close to linearity. Therefore, it is easy to know that the relationship between the deformation value and the risks stress is close to linearity as well. And this section of the curve illustrates the reaction of a supply chain resilient system when the supply chain risks develop to a stable state. The numerical simulation results accord with the theoretical analysis. From the analysis and numerical simulation results, it is well known that when a supply chain resilient system suffers risks, change on the system states would occur. When the risks increase gradually, the states change increases as well. Moreover, the states change is related with the sustained time of risks, the risks amount and the system resilience (study ability and recovery ability).

34

Y.H. Yang and L.D. Zhao

4 Conclusions When facing complex external environments and internal structure, a supply chain resilient system would come through a process from growth to crisis, then conversion, and at last renovation, which is called spiral rise process [24]. In the paper, based on the similarity between supply chain system and cell organism, we build a supply chain resilient model with two members, and research quantitatively the relationship between the deformation value of the supply chain resilient system and time when suffering a gradually increasing risks stress, coming to an accurate mathematical expression of the two factors. The research results also present the relationship between the risks influence and the supply chain system resilience (learning ability and recovery ability). From the results, the managers could see the change process of the supply chain system and how the supply chain system respond when suffering risks and find out strategies to reduce the negative influences. It provides a new method for supply chain risks management. Research on supply chain resilience is a complex work, and only some situations are analyzed and discussed in this paper. For further research, we can see three aspects: to analyze the deformation of supply chain system with more members; to build a supply chain resilient model when there is information sharing among members; to research the influence of study ability and recovery ability on the system deformation.

Acknowledgment This work was supported by the National Key Technology R&D Program of China (No. 2006BAH 02A06).

References 1. Mallak, L.: Putting organizational resilience to work. Ind. Manage. 40, 8–13 (1998) 2. Carpenter, S., Walker, B.: From metaphor to measurement: Resilience of what to what? Ecosyst. 4, 765–781 (2001) 3. Anderson, S.: Business + IT = Resilience. Contingency Plann. Manage. 10, 216–232 (2003) 4. Vogus, T.J., Sutcliffe, K.M.: Organizational resilience: towards a theory and research agenda. In: IEEE International Conference on Systems, Man and Cybernetics, Montreal, ISIC 2007, pp. 3418–3422 (2007) 5. Goldspink, C., Kay, R.: Organizations as self-organizing and sustaining systems: A complex and autopoietic systems perspective. Int. J. Gen. Syst. 32, 459–474 (2003) 6. Gunderson, L.: Ecological resilience-In theory and application. Annu. Rev. Ecol. Syst. 31, 425–439 (2000) 7. Reichhart, A., Holweg, M.: Creating the customer-responsive supply chain: a reconciliation of concepts. Int. J. Oper. Prod. Manage. 27, 1144–1172 (2007)

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8. Holling, C.S.: Simplifying the complex: The paradigms of ecological function and structure. Eur. J. Oper. Res. 30, 139–146 (1987) 9. Christopher, M., Peck, H.: Building the resilient supply chain. Int. J. Logist. Manage. 15, 1–29 (2004) 10. Lee, H.L.: The Triple-A Supply Chain. Harvard Bus. Rev. 82, 102–112 (2004) 11. Sheffi, Y.: Preparing for a big one. Manuf. Eng. 84, 12–15 (2005) 12. Rice, J.B., Caniato, F.: Building a secure and resilient supply network. Supply Chain Manage. Rev. 7, 22–30 (2003) 13. Snyder, L.V., Shen, Z.-J.M.: Managing disruption to supply chains. Forthcoming in The Bridge (National Acad. Eng.) 36 (2006) 14. Muckstadt, J.A., Murray, D.H.: Guidelines for collaborative supply chain system design and operation. Inf. Syst. Frontiers: Special Issue on Supply Chain Manage. 3, 427–453 (2001) 15. Haywood, M., Peck, H.: Improving the management of supply chain vulnerability in UK aerospace manufacturing. In: Proceedings of the 1st EUROMA/POMs Conference, Lake Como, pp. 121–130 (2003) 16. Kong, X.Y., Li, X.Y.: Creating the resilient supply chain: The role of knowledge management resources, Wireless Communications, Networking and Mobile Computing. In: 4th International Conference WICOM 2008, Dalian, pp. 1–4 (2008) 17. Chien, S., Sung, K.L., Skalak, R., Usami, S., Tözeren, A.: Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane. Biophys. J. 24, 463–487 (1978) 18. Schmid-Schönbeina, G.W., Sung, K.-L.P., Tozeren, H., et al.: Passive mechanical properties of human leukocytes. Biophys. J. 36, 243–256 (1981) 19. Chien, S., Sung, K.-L.P., Schmid-Schönbeina, G.W., et al.: Rheology of leukocytes. Ann. N. Y. Acad. Sci. 516, 333–347 (1987) 20. Schmid-Schönbeina, G.W.: Leukocyte kinetics in the microcirculation. Biorheology 24, 139–151 (1987) 21. Sunga, K.L., Donga, C., et al.: Leukocyte relaxtion properties. Biophys. J. 54, 331–336 (1988) 22. Zhao, L.D.: Analysis on supply chain resilience based on cell resilience model. Logist. Technol. 28, 101–104 (2009) (in Chinese) 23. Li, Y.H., Zhao, L.D.: Analyzing supply chain risk response based on resilience model. Syst. Eng. Theory Methodol. Appli. (in press) (2010) (in Chinese) 24. Zhao, L.D: Supply chain risks management. China Materials Press, Beijing (2008) (in Chinese)

Multi-objective Particle Swarm Optimization Control Technology and Its Application in Batch Processes Li Jia1, Dashuai Cheng1, Luming Cao1, Zongjun Cai1, and Min-Sen Chiu2 1 Shanghai Key Laboratory of Power Station Automation Technology, Department of Automation, College of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200072, China 2 Faculty of Engineering, National University of Singapore, Singapore [email protected]

Abstract. In this paper, considering the multi-objective problems in batch processes, an improved multi-objective particle swarm optimization based on pareto-optimal solutions is proposed. In this method, a novel diversity preservation strategy that combines the information on distance and angle into similarity judgment is employed to select global best and thus guarantees the convergence and the diversity characteristics of the pareto front. As a result, enough pareto solutions are distributed evenly in the pareto front. Lastly, the algorithm is applied to a classical batch process. The results show that the quality at the end of each batch can approximate the desire value sufficiently and the input trajectory converges; thus verify the efficiency and practicability of the algorithm. Keywords: Batch process; Muti-objective; Pareto-optimal solutions; Particle swarm optimization.

1 Introduction Recently, batch processes have been used increasingly in the production of low volume and high value added products, such as special polymers, special chemicals, pharmaceuticals, and heat treatment processes for metallic or ceramic products [1]. For the purpose of deriving the maximum benefit from batch processes, it is important to optimize the operation policy of batch processes. Therefore, Optimal control of batch processes is of great strategically importance. In batch processes, production objective changes dynamically with custom demands characterized by presence of multiple optimal objectives which often conflict with each other. This raises the question how to effectively search the feasible design region for optimal solutions and simultaneously satisfy multiple constraints. In the field of multiple optimizations, there rarely exists a unique global optimal solution but a Pareto solution set. Thus the key is how to find out the satisfied solutions from Pareto solution set. To solve it, the traditional and simple method is to transfer the muti-objective functions into single objective function, and then the mature methods used in single objective optimization can be employed. But the drawback of this K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 36–44, 2010. © Springer-Verlag Berlin Heidelberg 2010

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method is that only one solution can be available at each time, which makes it difficult for finding out enough satisfied solutions distributing in the Pareto solution set. Recently the particle swarm optimization (PSO) algorithm has showed its powerful capacity for multi-objective optimization, which is a stochastic global optimization approach derived from the feeding simulation of fish school or bird flock [1]. But at first PSO is designed for numerical problems, considering nothing about muti-objective problems. If the particle swarm optimization (PSO) algorithm is directly adopted into muti-objective problems, there will be some shortcomings, such as the choosing of Pareto set and the global best update strategy. To circumvent those drawbacks, a novel iterative muti-objective particle swarm optimization technique for batch processes is proposed in this paper. In the proposed method, the selection of the global optimal solution by using similarity judgment is presented to direct next decision such that it can acquire the Pareto front which is closer to the true Pareto optimum. The advantage is that there are enough Pareto solutions being distributed evenly in the Pareto front. This paper is organized as follows. The preliminaries knowledge is described in Section 2. The proposed novel iterative muti-objective particle swarm optimization is discussed in Section 3. Batch simulation results are presented in Section 4. Finally, concluding results are given in Section 5.

2 Preliminaries 2.1 Multi-objective Optimization Problem in Batch Processes The objective in operating batch process is to maximize the amount of the final product and minimize the amount of the final undesired species. This can be formulated as a multi-objective optimization problem

min ⎡⎣ f1 ( x ) , f 2 ( x ) , L , f m ( x ) ⎤⎦ s.t. gi ( x ) ≤ 0 i = 1, 2,L , k hi ( x ) = 0

(1)

i = 1, 2, L , p

Where x = [ x1 , x2 , L , xn ] ∈ R n , fi ( x ) i = 1, 2,L , m , gi ( x ) ≤ 0 i = 1, 2,L , k and T

hi ( x ) = 0 i = 1, 2, L , p are respectively decision vector, M objective functions k inequality constraints and p equality constraints. In this study, the batch time is divided into T segments of equal length. Without loss of generality, the multi-objective optimal control problem can now be stated to determine the optimal control policy in the time interval 0 ≤ t ≤ t f .

Before proceeding, the following definitions are given. Definition 1-Pareto solution: X ∗ ∈ Ω is a Pareto solution, if ∀X ∈ Ω , fi ( X ) > f i X ∗ holds i = 1,L, n , where n and Ω are decision vector dimension

( )

and feasible domain, respectively.

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Definition 2-Pareto dominance: A decision vector u is said strictly dominate vector v (denoted u p v ) if and only if ∀i ∈ {1,L, n} : fi ( u ) ≤ f i ( v ) and

∃j ∈ {1,L , n} : f j ( u ) < f j ( v ) . u weakly dominate v (denoted u p v ) if and only if

∀i ∈ {1,L , n} : fi ( u ) ≤ fi ( v ) . Definition 3- Pareto optimal set: The set of all Pareto solutions in the decision variable space is called the Pareto optimal set. Definition 4- Pareto front: The corresponding set of objective vectors is called the Pareto front. 2.2 Foundation of Particle Swarm Optimization

The PSO heuristic algorithm was first proposed by Kennedy and Eberhart, which was inspired by simulation of a simplified social model[5]. It is one of the modern heuristic algorithms and can generate a high-quality solution with shorter calculation time and stable convergence characteristic than other stochastic methods, such as genetic algorithm (GA) and evolutionary strategy (ES). Another advantage is that PSO algorithm does not use crossover and mutation operation which makes the computation simpler. Moreover, in PSO algorithm, a fixed population of solutions is used and all the solutions randomly distributed in the feasible domain. In PSO, the member of the population is called particle, which modifies its memorized values as the optimization routine advance. The recorded values are: velocity, position, best previous performance and best group performance. The ith particle is commonly represented as pi = ( pi1 ,pi2 ,L ,piD ) ; its velocity is represented as vi = ( vi1 ,vi2 ,L , vid ,L ,viD ) ; its best position in history is represented as pi = ( pi1 , pi 2 ,L , pid ,L , piD ) named particle best ( pbest ) .the whole position’s best position is represented as p g = pg1 ,pg2 ,L , pgd ,L ,pgD named global best ( gbest ). The general algorithms for the adjustment of these velocities and positions are:

(

)

(

)

(

vidk +1 = ω vidk + c1r1 pid − zidk + c2 r2 p gd − zidk

)

pidk +1 = pidk + vidk +1

(2)

(3)

where ω is the inertia of a particle, c1 and c2 are constraints on the velocity toward

global and local best, r1 , r2 ∈ U ( 0,1) , Usually c1 and c2 are set 2.

ω = ωmax −

ωmax − ωmin kmax

×k

(4)

ωmax is the initial weight, ωmin is final weight, kmax is maximum number of generations, k is current number of iterations.

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3 Pareto-optimal Solutions Based Multi-objective Particle Swarm Optimization (PSO) Control Multi-objective PSO algorithms should guarantee the convergence and the diversity characteristics of the Pareto front, thus the mission of it is to set an appropriate diversity strategy for the Pareto front and global best update mechanism. In this section, we design a novel method to choose global best location ( gbest ) by using the notations of distance and angle. 3.1 The Similarity of Two Points

In the preceding section, we propose a new definition of the similarity of two points. This definition includes information on distance and angle. To this end, the following similarity number, si , is defined: −

1

si , q = γ

2πσ

d ( xi − xq )

e

( )

( )

+ (1 − γ ) cos θi ,q , if cos θi ,q ≥ 0

2σ 2

(5)

where γ is a weight parameter and is constrained between 0 and 1, σ is mean of maximum value range of xi .and the Euclidian between xi and xq can be defined as:

(

)

And the angle θi , q for point xi and where xi =

( xi − xq ) ( xi − xq ) xq defined as: cos (θi ,q ) = ( xi ' xq ) ( xi '

d xi , xq =

(6) xq

)

xi ' xi .

xq ( )

cos θ i, q < 0

xi

( )

cos θi, p > 0

xp

θi,q θi,p

xq Fig. 1. Illustration of angle measure

It is important to note that Eq.(5) will not be used to compute the similarity particle si between xq and xi if cos θ i ,q is negative. For simplicity, this point is illustrated in the two dimensional space as shown in Fig.1, where xq denotes the vector

( )

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perpendicular to xq . it is clear that x p which lies in the right of xq is more similar to xq then xq which lies in the left of xq .the use of cosine function to discriminate the directionality between xi and xq indicates that these two vectors are dissimilar if cosine x is negative, and hence the q in the reference group will be discarded. 3.2 The Selection of the Global Optimal Solution ( gbest )

By using the similarity among particles in pareto optimal set, the proposed selection of global best gbest is different from those that select the particle with maximum or minimum objective, and it needs to acquire a Pareto front with evenly distribution. Firstly, the similarities between the ith particle and all particles in Pareto optimal set will be calculate. We denote si , j , j = 1, 2,..., N , N is the number of particles in the Pareto optimal set. Next the particle k in the Pareto optimal set which has the minimum similarity with the ith particle as the gbest of the ith particle. f2 ( x )

f1 ( x )

Pareto particles in Pareto Front Particles in feasible domain Fig. 2. The Selection of the global optimal solution

For a given problem, the tuning of γ results more possible particles to choose a gbest , which will ensure the convergence and the diversity of the Pareto front. In Fig.4, in order to facilitate the analysis, suppose that there are only two points A and B on the Pareto front. Those particles that have more choice lie in the shadow area which is enclosed by line L1 , line L2 and Pareto front. It is noted that all points in L1 has an equal angle to A and B , while all points in L2 has an equal distance to A and B . Evidently, the proposed algorithm guarantees the convergence and the diversity characteristics of the Pareto front by using the notation of similarity. 3.3 Algorithm Steps

In summary, the following describes the steps to find out the optimal control solution by using above-mentioned approach and the workflow of the proposed algorithm is shown in Fig.5:

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f2 ( x )

L2

q1

q2

L1

q3

0

B

f1 ( x )

Pareto particles in Pareto Front Particles in feasible domain Fig. 3. The Selection of the global optimal solution

Step 1: Initialization. Set N, pbesti , gbesti , xi and vi . Step 2: Calculate the maximin fitness for all particles; sort all particles as the non-dominated solutions whose maximin value is less than zero. Update the non-dominated set based on the domination relation. Step 3: Renew pbesti based on the particles’ history information. Step 4: Iterate through the whole swarm population. For the ith particle, calculate its similarity with all the particles in the non-dominated set. And choose particle whose similarity is max as it’s gbesti . Step 5: Update the population based on the particle history information and the whole population history information. Step 6: Go back to Step 2, until a termination criterion is not met. If terminated, then calculate performance measures in the final iteration.

4 Application to Batch Processes The process reactor used in this section was taken from papers [10-13], the mechanism k1 k2 can then be expressed through the short notation A ⎯⎯ → B ⎯⎯ → C , and the mechanistic model of the fed-batch ethanol fermentation process is described as follow:

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dx1 = −4000 exp ( −2500 / T ) x12 dt dx2 = 4000 exp ( −2500 / T ) x12 − 6.5 × 105 exp ( 5000 / T ) x2 dt where x1 and x2 represent the dimensionless concentrations of A and B , T is temperature of the reactor and is scaled to dimensionless value Td = (T − Tmin ) (Tmax − Tmin ) , t f is fixed 0.1 h , and the values of Tmin and Tmax

(7)

the as are

298 k and 398 k ,respectively. The initial conditions are x1 ( 0 ) = 1 and x2 ( 0 ) = 1 , and the constraint on the control u = Td is 0 ≤ Td ≤ 1 . As far as we know that in the related articles the performance index is to maximise the concentration of B at the end of batch. They all ignore the concentration of A , and hypothesize that concentration of A meet the requirements under all conditions. In reality, for some reason we don’t want too much C , so we should limit the amount of A , so as to reduce the concentration of C . Or we have not enough A . Pareto curve 0.7 0.65 0.6

fun2

0.55 0.5 0.45 0.4 0.35

( A)

0.1

0.15

0.2

0.25

0.3 fun1

0.35

0.4

0.45

0.5

0.75 concentration of A 0.7 0.65

valueof object

0.6 0.55 0.5 0.45 0.4 0.35 0.3 0.25

( B)

0

0.1

0.2

0.3

0.4

0.5 time

0.6

0.7

0.8

0.9

1

0.65 concentration of B 0.6

valueof object

0.55 0.5 0.45 0.4 0.35 0.3 0.25

(C )

0

0.1

0.2

0.3

0.4

0.5 time

0.6

0.7

0.8

0.9

1

Fig. 4. (A)Productivity-yield Pareto-optimal front for case batch process,(B)concentration of A with optimal time of operation,(C) concentration of B with optimal time of operation

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We consider a multi-objective optimal control problem where maximum the concentration of B and minimum the concentration of B simultaneously. The multi-objective optimal control problem can now be formally defined as:

⎧⎪ max imum Ctf ( B) ⎨ ⎪⎩ min imun Ctf ( A )

(8)

For the convenience of calculation, a little trick which put a maximum problem to a minimum problem is used

⎧⎪ max imum C ( B) desired − Ctf ( B) ⎨ min imun Ctf ( A ) ⎪⎩

(9)

C ( B )desired is the expected the concentration of C . When C ( B)desired − Ctf ( B ) = 0 , it means that the concentration of C has reached its maximum. The application of the multi-objective optimization algorithm for maximum generations of 30 gives the results are shown in Fig.6. The Pareto front between the C ( B ) desired − Ctf ( B ) and the Ctf ( A ) is shown in Fig.6 A and Fig.6 B and C present the variation of the C ( B)desired − Ctf ( B) and the Ctf ( A ) with the time of operation, respectively.

5 Conclusions In batch processes there exist lots of multi-objective problems. Traditionally, simple method based on gradient theory is applied to obtain the solution of such problems using weighted approaches. But it can not obtain all possible solutions. Recently particle swarm optimization (PSO) algorithm has showed its powerful capacity for multi-objective optimization because of their capability to evolve a set of Pareto solutions distributed along the Pareto front. According to the situation of batch process, an improved multi-objective algorithm is proposed in this paper. Firstly, we utilized the concept of similarity of two particles to improve multi-objective particle swarm algorithm. The similarity concept that combines distance and angle element can guarantee the convergence and the diversity characteristics of the Pareto front. Then some benchmark functions were used to test the algorithm. The results show that the improve algorithm is able to produce a convergence and spread of solutions on the Pareto-optimal front. Lastly, a batch process example illustrates the performance and applicability of the proposed method. Acknowledgement. Supported by Research Fund for the Doctoral Program of Higher Education of China (20093108120013), Shanghai Science Technology commission (08160512100, 08160705900, 09JC1406300 and 09DZ2273400), Grant from Shanghai Municipal Education commission (09YZ08), Shanghai University, "11th Five-Year Plan" 211 Construction Project and Innovation Project for Postgraduate Student Granted by Shanghai University (SHUCX102221).

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Reference 1. Xin, L.J.: PSO-based Multi-objective Optimization Algorithm Research and Its Applications (2006) 2. Hu, X., Eberhart, R.: Multiobjective optimization using dynamic neighborhood particle swarm optimization. In: Proceedings of the Evolutionary Computation, pp. 1677–1681 (2002) 3. Parsopoulos, K., Vrahatis, M.: Particle swarm optimization method in multiobjective problems. ACM, 603–607 (2002) 4. Mostaghim, S., Teich, J.: Strategies for finding good local guides in multi-objective particle swarm optimization (MOPSO), pp. 26–33 (2003) 5. Kenned, Y.J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks, Piscataway, NJ, USA, pp. 1942–1948. IEEE, Los Alamitos (1995) 6. Fieldsend, J., Everson, R., Singh, S.: Using unconstrained elite archives for multiobjective optimization. IEEE Transactions on Evolutionary Computation 7, 305–323 (2003) 7. Senior Member in IEEE, Leung, Y. W., Wang, Y.P.: U-measure a quality measure for multiobjective programming. IEEE Transactions on Systems, Man, and Cybernetics. Part A, Systems and humans (2003) 8. Zhang, L.B.: Research on Optimization Algoruth Base on Particle Swarm Optimization and Differential Evolution (2007) 9. Wei, J.X.: Evolutionary Algorithms for Single-Objective and Multi-Objective Optimization Problems (2009) 10. Liu, H., Jia, L., Liu, Q.: Batch-to-batch control of batch processes based on multilayer recurrent fuzzy neural network. In: Proceedings of the International Conference on Intelligent Systems and Knowledge Engineering. Atlantis Press, France (2007) 11. Lu, N., Gao, F.: Stage-based process analysis and quality prediction for batch processes. Industrial and Engineering Chemistry Research 44, 3547–3555 (2005) 12. Li, J.: Run-to-run product quality control of batch processes. Journal of Shanghai University (English Edition) 13, 267–269 (2009) 13. Ray, W.: Advanced process control. McGraw-Hill Companies, New York (1981)

Online Monitoring of Catalyst Activity for Synthesis of Bisphenol A Liangcheng Cheng1, Yaqin Li1, Huizhong Yang1, and Nam Sun Wang2 1

Institute of Measurement and Process Control, Jiangnan University, Wuxi, Jiangsu, 214122, P.R. China 2 Department of Chemical & Biomolecular, University of Maryland, College Park , MD, 20742, US {Cheng Liangcheng,Li Yaqin,Yang Huizhong, Nam Sun Wang,yhz}@jiangnan.edu.cn

Abstract. In the synthesis of bisphenol A, it is necessary to monitor the catalytic activity of ion exchanger catalyst online. A new online method to monitor the catalyst activity is proposed. Factors affecting catalyst activity are taken into consideration to compute its value using support vector machine and mathematical regression. Simulation and real operation results confirm the effectiveness of this method. Keywords: bisphenol A, catalyst activity, online monitoring, soft sensing.

1

Introduction

Bisphenol A (BPA) is an important starting material for producing epoxy resins and polycarbonates, which is manufactured by ion exchanger resin catalyzed acetone and phenol[1]. In the real plant, it is needed to know the produced BPA content to guide the field operation of BPA production[2-3]. Traditionally laboratory analysis is applied to get the BPA content. Because of this large time delay, laboratory analysis can provide little useful information for real-time plant operation. To solve this problem, soft sensing method[4] is used to achieve online measurement of BPA content. By combining kinetic model and support vector machine (SVM) method, the model of BPA production process can be constructed and BPA content monitored. To achieve higher reaction rate, ion exchanger resin is used as catalyst. Presence of the ion exchanger resin increases the reaction rate significantly and improves the selectivity also[5-7]. The catalyst activity should be included in the soft sensing model of BPA production process and its value needs to be online monitored. Despite the significance of catalyst activity, in literature it is possible to find surprisingly small number of papers devoted to technological aspects of BPA catalyst[8-12]. This paper proposes a novel method of online monitoring the catalyst activity for synthesis of BPA by constructing soft sensing model of catalyst activity using mathematical regression and SVM method. K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 45–51, 2010. © Springer-Verlag Berlin Heidelberg 2010

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2 Experiment For the BPA production is used solid acid ion exchanger resin as the catalyst. The synthesis is carried out in the fixed-bed reactor. Phenol and acetone flow into the reactor. The mixture of those raw materials passes through the fixed-bed reactor of acid ion exchanger resin catalyst. The synthesis yields bisphenol A and water as well as some reaction by-products. By using all kinds of sensors and DCS systems, most important process data such as the flow of phenol and acetone, reactor temperature and pressure can be measured online. Those real time data are displayed on monitors and meanwhile recorded into database. It is needed to analyze sample mixture in the laboratory to get these data necessary for the study on BPA reaction.

3 Results and Discussion 3.1 Reaction Kinetics Many studies have devoted to the reaction kinetics of BPA synthesis by considering the above mentioned factors and quite a lot of reaction mechanisms have been proposed. Some mechanisms have proved effective by laboratory experiments. However, few of them can be applied to online computation of produced BPA content and some other data. It is because that most variables in the kinetic equations cannot be measured online through existent sensors. For the online monitoring of BPA content, after considering the reaction mechanism[8-12] and making mathematical transformation and simplification, a new kinetic equation of BPA reaction can be proposed. The BPA content can be expressed as follows,

X =

at 1 + bt

(1)

where X is BPA content, a and b are two variables, and t is the reaction time. Then the reaction velocity r can be given by r=

dX a = dt (1 + bt )2

(2)

The remaining time E is defined as

E (t ) =

1

τ

e−t τ .

(3)

So the BPA content can be written as ∞

∞

0

∞

a 1 −t τ a e −t τ e dt + C = ∫ dt + C 2 τ 0 (1 + bt ) 2 0 (1 + bt ) τ

X = ∫ rE (t ) dt + C = ∫

where C is the concentration of BPA at the inlet.

(4)

Online Monitoring of Catalyst Activity for Synthesis of Bisphenol A

Let v = e −t τ , t = −τ ln v, dt =

47

−τ dv v

Then

X =

−τ 1 dv + C = a ∫ dv + C τ ∫1 (1 − bτ ln v) 2 v − b (1 τ ln v) 2 0 a

0

1

v

(5)

Taken the reaction temperature T into consideration, the variable a is expressed as

a = k0 exp(

−E −K ) = k0 exp( ) RT T

(6)

where k0 , K , E , R are all constants. Thus Eq.5 changes to 1

1 dv + C τ (1 ln v) 2 − b 0

X = k0 e − K T ∫

(7)

With the catalyst activity α considered, Eq.7 finally changes to 1

1 dv + C − b (1 ln v) 2 τ 0

X = α k0 e − K / T ∫

(8)

In the above kinetic equation, all the variables expect α and b can be measured online. To make this equation used in the real plant, soft sensing models are constructed to compute α and b . This paper discusses the modeling of catalyst activity α . 3.2 Catalyst Characters

For the BPA production is used solid acid ion exchanger resin as the catalyst. According to theories it has been pointed out that about five factors can cause the deactivation of the acid ion exchanger resin catalyst, including metal ions, methanol, hydrogen donor, high temperature and water[13-18]. 3.3 Numerical Simulation of Catalyst Activity 3.3.1 Restrictions for Modeling and the Solutions It is well known that the data selected as assistant variables of soft sensing models should be measurable online. All the above mentioned factors except reaction temperature cannot be measured by sensors. In this paper the support vector machine method (SVM)[19] is used to build a model describing their relationship. SVM is a novel learning method based on Statistical Learning Theory which can solve small sample learning problem better. SVM is now widely used in industrial processes where nonlinearity and limited number of data exist. Compared to the above mentioned factors, the service time of the catalyst has clearer relationship with its activity. Mathematical regression is used to derive an equation to describe this relationship.

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3.3.2 Model Description For the modeling of the ion exchanger resin catalyst activity were available the following operational data: whole reaction mixture input (kg/h), phenol input (kg/h), acetone input (kg/h), temperature at the reactor inlet (T), production of BPA (%wt). Using the above operational data besides the service time of the catalyst, the soft sensing model of catalyst activity is expressed as follows,

α = f (t ) + g ( flow, rate, T )

(9)

In Eq. α is the catalyst activity which is substituted by the conversion rate of acetone. t is the service time of the catalyst. f (t ) is a quadratic polynomial derived by mathematical regression describing the relationship of service time and catalyst activity. flow , rate and T stand for the flow of mixture input, the flow ratio of phenol to acetone and reaction temperature respectively. g ( flow, rate, T ) represents the effect of load, ratio of phenol to acetone and reaction temperature on the catalyst activity, which is in the form of a SVM model. In the real plant after inputting these process parameters into the model the catalyst activity can be computed online. With the increasing of its service time the catalyst activity decreases. This trend is irreversible, which can be expressed through a decreasing function. Considering its simple form and practical usage, a quadratic polynomial is applied in this paper,

α1 = f (t ) = a1t 2 + a2 t + a3

(10)

where α1 is catalyst activity and an (n = 1, 2,3) are coefficients which need to be computed. To calculate the unknown coefficients in the quadratic polynomial, nonlinear regression is used. Nonlinear regression is a useful technique for creating models to explain relationship between variables[20]. The value of three coefficients were obtained, which provides basis for the soft sensing model. Then in the output of the SVM model is the difference between computed and real catalyst activity and the inputs are the load of the catalyst, reaction temperature and the flow ratio of phenol to acetone. 3.3.3 General Results A batch of process data records of the assistant variables and the corresponding laboratory analysis of the acetone conversion rate at the outlet of the reactor with the service time of the catalyst are selected as data samples for modeling. Using the SVM algorithm, soft sensing model based on SVM is constructed through training data. The mean relative error, maximum relative error and mean squared error (MSE) are shown in Table 1. Table 1.Training error of soft sensing model

catalyst activity BPA content

mean relative error 0.835% 1.21%

max relative error 1.15% 3.29%

MSE 0.0086 0.29

Online Monitoring of Catalyst Activity for Synthesis of Bisphenol A

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Table 2. Testing error of soft sensing model

catalyst activity BPA content

mean relative error 0.847% 1.28%

max relative error 2.38% 3.27%

MSE 0.0095 0.30

To evaluate the generalization performance of the SVM model, some process data records are employed to test the model. The testing errors are shown in Table.2. For soft sensing models, the ability of generalization is a more important criterion for judging the performance of models. To confirm the model performance in real production, twenty process data records collected in October are employed. The results are shown in Fig.1, Fig.2 and Table.3. 1

22

21

catalyst activity

BPA content(wt% )

0.95

0.9

0

2

4

6

8 10 12 sample number

14

16

18

19

18

17

real estimated 0.85

20

20

Fig. 1. Estimated and real value of catalyst activity

16

real estimated 0

2

4

6

8 10 12 sample number

14

16

18

20

Fig. 2. Estimated and real value of BPA

Table 3. Error of soft sensing model

catalyst activity BPA content

mean relative error 0.92% 1.76%

max relative error 2.56% 3.82%

MSE 0.011 0.32

From Fig. 1, Fig.2 and Table.3, it can be found that the performance of the soft sensing model is satisfactory for the commercial production in the real plant, which can reflect the change of the catalyst activity and BPA content at the reactor outlet. As a result the BPA production becomes more efficient and the business more profitable.

4 Conclusions The catalytic activity of ion exchanger resin is studied and the method of its online monitoring proposed. The kinetic mechanisms of BPA reaction and catalyst deactivation are the basis of soft sensing model. Nonlinear regression is applied to describe the decreasing trend of catalyst activity. Its difference with the real value is

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assumed to be caused by the changes of load, reaction temperature and flow ratio of phenol to acetone. Then a soft sensing model based on SVM is constructed taken those three factors as inputs to estimate that difference. Combined with the quadratic polynomial obtained through nonlinear regression the soft sensing model can estimate the catalyst activity online. The simulation results and real production prove the satisfactory performance of the model for the online monitoring of catalyst activity.

References 1. Peng, Q.: Technical progress and application of bisphenol a at civil and abroad. Thermosetting Resin 19(3), 25–28 (2004) 2. Prokop, Z., Hankova, L., Jerabek, K.: Bisphenol A synthesis- modeling of industrial reactor and catalyst deactivation. Reactive & Functional Polymers 60, 77–83 (2004) 3. Kawase, M., Inoue, Y., Araki, T., Hashimoto, K.: The simulated moving-bed reactor for production of bisphenol A. Catalysis Today 48, 199–209 (1999) 4. Lin, B., Reckeb, B., Knudsen, J.K.H., Jørgensen, S.B.: A systematic approach for soft sensor development. Computers and Chemical Engineering 31, 419–425 (2007) 5. Jerabek, K., Wanghun, L.: Comparison for the kinetics of bisphenol A synthesis on promoted and unpromoted ion exchanger catalysts. Collect Czech Chem. Commun. 54(2), 321–325 (1989) 6. Mingyang, H., Qun, C., Xin, W.: Study on Stability of Catalyst for Bisphenol A Synthesis. Chemical Industry and Engineering Progress 24(3), 274–277 (2005) 7. Hsu, J.-P., Wong, J.-J.: Kinetic modeling of melt transesterification of diphenyl carbonate and bisphenol-A. Polymer 44, 5851–5857 (2003) 8. Kruegera, A., Balcerowiaka, W., Grzywa, E.: Reasons for deactivation of unpromoted polymeric catalysts in bisphenol A synthesis. Reactive & Functional Polymers 45, 11–18 (2000) 9. Wang, L., Jiang, X., Liu, Y.: Degradation of bisphenol A and formation of hydrogen peroxide induced by glow discharge plasma in aqueous solutions. Journal of Hazardous Materials 154, 1106–1114 (2008) 10. Chen, C.-C., Cheng, S., Jang, L.-Y.: Dual-functionalized large pore mesoporous silica as an efficient catalyst for bisphenol-A synthesis. Microporous and Mesoporous Materials 109, 258–270 (2008) 11. Tai, C., Jiang, G., Liu, J., Zhou, Q., Liu, J.: Rapid degradation of bisphenol A using air as the oxidant catalyzed by polynuclear phthalocyanine complexes under visible light irradiation. Journal of Photochemistry and Photobiology A: Chemistry 172, 275–282 (2005) 12. Baohe, W., Nianyong, Y., Jing, Z., Xin, J., Zongli, Z.: Reaction kinetics of bisphenol A synthesis catalyzed by thiol-promoted resin. Journal of Tianjin University 39(4), 428–431 (2006) 13. Hongming, F., Gang, J.: Studies on optimization of bisphenol A production process with ion exchanger as catalyst. Technology & Testing 10, 38–40 (2001) 14. Gates, B.C.: Catalytic Chemistry [M]. Wiley, New York (1992) 15. Xiwang, Q., Hongfang, C.: Reaction kinetics of bisphenol A synthesis catalyzed by sulfonic acid resin. Petrochemical Technology 25(9), 620–624 (1996) 16. Jinlai, Q., Wenwen, Z., Mingyang, H., Qun, C.: Catalysts for Synthesis of Bisphenol A. Chemical Industry and Engineering Progress 23(7), 710–717 (2004)

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17. Li, F.B., Li, X.Z., Liu, C.S., Liu, T.X.: Effect of alumina on photocatalytic activity of iron oxides for bisphenol A degradation. Journal of Hazardous Materials 149, 199–207 (2007) 18. Jerabek, K., Hankova, L., Prokop, Z., Lundquist, E.G.: Relations between morphology and catalytic activity of ion exchanger catalysts for synthesis of bisphenol A. Applied Catalysis A: General 232, 181–188 (2002) 19. Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, NY (1995) 20. Morada, S., Shachamb, M., Brenner, A.: Utilization of collinearity in regression modeling of activated sludge processes. Chemical Engineering and Processing 46, 222–229 (2007) 21. Yan, W., Shao, H., Wang, X.: Soft sensing modeling based on support vector machine and Bayesian model selection. Computers and Chemical Engineering 28, 1489–1498 (2004)

An Improved Pyramid Matching Kernel Jun Zhang, Guangzhou Zhao, and Hong Gu College of Electric Engineering, Zhejiang University, Hangzhou, China, 310027 {kenny007,zhaogz,ghong}@zju.edu.cn

Abstract. The pyramid matching kernel (PMK) draws lots of researchers’ attentions for its linear computational complexity while still having state-of-theart performance. However, as the feature dimension increases, the original PMK suffers from distortion factors that increase linearly with the feature dimension. This paper proposes a new method called dimension partition PMK (DP-PMK) which only increases little couples of the original PMK’s computation time. But DP-PMK still catches up with other proposed strategies. The main idea of the method is to consistently divide the feature space into two subspaces while generating several levels. In each subspace of the level, the original pyramid matching is used. Then a weighted sum of every subspace at each level is made as the final measurement of similarity. Experiments on dataset Caltech-101 show its impressive performance: compared with other related algorithms which need hundreds of times of original computational time, DP-PMK needs only about 4-6 times of original computational time to obtain the same accuracy. Keywords: dimension partition, bags of features, SVM, pyramid matching, kernel function, object recognition.

1 Introduction In the object recognition field, much recent work has shown the great strength of bags (sets) of local features [1-4]. Global image features, such as color or grayscale histograms or even raw pixels of image, are sensitive to real world imaging conditions. Whereas local descriptors (i.e., SIFT, PCA-SIFT), since its invariant to common image transformation, it can be more reliably detected and matched across images of same object under different view points ,poses, or lighting conditions. However, one set of features, i.e., an image of people’s face may be represented by a set of local descriptors with different facial parts, may be expected that the number of features will be vary across examples due to different imaging conditions, or inconsistent detections by the interest operator, and the size of each set may be too large to endure even square time complexity in number of size. Kernel based learning methods, which include SVM, kernel PCA, and Gaussian Processes, are widely used for their generalization ability and efficiency. However, traditional kernels are designed for fixed-length vector input, not for bags of varying number features. Existing kernel-based approaches particularly designed for bags of features [5-7], each suffers from some of the following drawbacks: two bags need the K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 52–61, 2010. © Springer-Verlag Berlin Heidelberg 2010

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same number features; needs square or even cubic time that makes large feature set sizes impractical; kernels that are not positive-defined. Hence, how to approximate correspondences between bags of features precisely and rapidly remains a challenging work.

2 Related Work Recently, Grauman and Darrell [1, 8, 9] proposed pyramid matching kernel (PMK) algorithm to find an approximate correspondence between two sets. The pyramid matching simply maps bags of unordered features to multi-resolution histograms and computes a weighted histogram intersection aimed to find implicit correspondences based on the finest resolution histogram cell where a matched pair features first appears. Since the pyramid matching’s linear time computation and performance state-of-the-art. It quickly draws a lot of researchers’ attentions [2-4, 10-15]. The original PMK lost all images’ spatial information. So spatial pyramid matching (SPM) algorithm is proposed to take images’ geometric information into count[3]. Experiments demonstrate SPMK’s good performance in natural scene categories. Since SPM may need to cluster 200 or more types, this largely increases the computational time, and the structure of the algorithm is much more complicated too. As the feature dimension increases, original PMK suffers from distortion factors that increase linearly with the feature dimension. Grauman and Darrell[2] proposed a new pyramid matching kernel—Vocabulary Guide-PMK. Because of hierarchy clustering, the algorithm becomes more complicated and the computation time is much longer. Recent work in object recognition and image classification has shown that significant performance gains can be achieved by carefully combining multi-level positive-defined kernel function. Siyao Fu et al. [14]proposed a multiple kernel learning method which alternatively solving SVM and optimizing multi-kernel weights to get a good kernel weights. Yi Liu et al.[4]proposed Dimension-Amnesic PMK which utilizes Gaussian distribution to generate multiple matrixes, and then uses these matrixes to map features to low dimension feature space, then do traditional PMK operates in it. Junfeng He et al. [15]presented a method which also cares about the weights optimization utilizing QP method.

3 Improved Pyramid Matching Kernel 3.1 Pyramid Matching Kernel Pyramid matching kernel approximates the optimal partial matching by computing a weighted intersection over multi-resolution histograms. Specifically, G G G G G G let X = {x1 , x2 ," , xm } , Y = { y1 , y2 ," , yn } be two bags of d-dimensional features in In this example, two 1-D feature sets are used to form two histogram pyramids. Dotted lines are bin boundaries, dashed line indicates a match already formed at a finer resolution level, and solid line represents a new pair matched at this level. If we

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Fig. 1. The 1-D pyramid matching example

use weights suggested by Grauman & Darrell, we get the similarity between the two L −1 1 1 1 sets: K = ∑ wi N i = 1× 3 + × 1 + × 1 + × 1 = 3.875 . 2 4 8 i =0 G G feature space S , where, xi , yi are local features. We define feature extraction function Ψ as:

Ψ ( X ) = [ H 0 ( X )," , H L −1 ( X )]

(1)

Where, X ∈ S , L = ⎢⎡log 2 D ⎥⎤ + 1 , D is the range of feature space. H i ( X ) is a

histogram vector formed over points in X using d-dimensional bins of side length 2i ,

H i ( X ) has dimension ri = ( D 2i ) , so Ψ ( X ) is pyramid histogram: the bottom bins d

in the finest-level H 0 are small enough that each unique point falls into its own bin, and at the top coarsest level H L −1 , all points fall into a single bin. Hence the pyramid matching kernel function is defined as: L −1

K ( X , Y ) = ∑ wi Ni

(2)

N i = I ( H i ( X ), H i (Y )) − I ( H i −1 ( X ), H i −1 (Y )),

(3)

i =0

j = ri

I ( H i ( X ), H i (Y )) = ∑ min( H i ( X )( j ) , H i (Y )( j ) )

(4)

j =1

Here, wi is a weight at level i , H i ( X )( j ) denotes the count of the j th bin of H i ( X ) . Since the pyramid match has been proved [8] satisfying Mercer’s condition, so it is valid for use as a kernel in any existing learning methods that require Mercer kernels. 3.2 Improved Pyramid Matching Kernel

According to Grauman & Darrell[8], the expected value of the pyramid match cost is bounded:

An Improved Pyramid Matching Kernel

E[ K ( X , Y )] ≤ (Cd log 2 D + d )Θ( M ( X , Y ; π * ))

55

(5)

Where C represents a constant, and Θ( M ( X , Y ; π * ) indicates the optimal partial match cost. That means the pyramid match cost is linear in the feature dimension. When dealing with high dimensional feature spaces, the expected cost is large, accuracy may decrease. Several algorithms have been proposed to solve it[2-4]. For instance, G G specifically, suppose two 128-dimensional vectors: x = (1,1," ,1, 63) , y = (1,1," ,1,1) , according to the original PMK algorithm, let D=64. So at level 0, two vectors will fall G G into their own bins; at level 1, x will fall into bin x = (2, 2," , 2, 64) , while y will fall into bin y = (2, 2," , 2, 2) ; and continue, until at level 6—the coarsest level, they won’t fall into the same bin and match (as if the two vectors haven’t matched with other vectors). Such vectors like these, between each other have a large similarity, but, actually they will just match at coarsest level, which makes little contribution to similarity between bags of features.

Fig. 2. A model of hierarchical random partition (4 levels)

As a matter of fact, to any two feature vectors, which level will match is depend on the dimension which has largest distance. To previous example, other dimensions except last one all have zero distance. Nevertheless, the last dimension has distance 62, which determines their matched level (coarsest). But in high dimension feature space, some large distances dimensions occur easily. Base on this, some dimension reduction strategies—such as PCA, LLE—are proposed. Yi Liu et al[4] presented a dimension amnesic method aimed to solving high dimension problem. However, its increasing computation time ruined PMK’s strength: speed; Grauman & Darrell’s VG-PMK still has to deal with clustering time. The join of hierarchy cluster largely increases the computational time; SPMK always do PMK operator on two-dimension coordinates, but its former’s traditional cluster to all feature space takes much time. All above strategies may solve high dimension feature problem, but their largely increased computational time making them imperfect. Therefore, this paper proposes another strategy called Dimension Partition PMK— DP-PMK, which need only little couples of original PMK computation time, but still comes up with all other strategies in accuracy. Its main idea is to consistently divide the high dimension feature space into several low dimension feature space, and do the PMK operate in each dividing feature space, then make a weighted sum as the

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correspondence between the original bags of features. As the DP-PMK doesn’t add new complex algorithms, its only extra computation time is spend on partition of the feature, which is small compared with other proposed algorithms. Specifically, DPPMK makes hierarchical random partition to generate T levels feature spaces. At level 0, feature space consists of original bags of features with dimension d , we do PMK operates; and at level 1, we randomly divide original bags of features into two subspaces; and so on, at level t, we choose the largest dimension subspace from sets of subspaces generated from level t-1, and divide it into two subspaces: Original feature space makes the top level, and at each level, divide the largest dimension of previous level leading one more in number of subspace than previous level. L −1 ⎧ ′ = K wit ( dt1 ) Nit ( dt1 ) ∑ t ⎪ ⎪ i =0 , (dt1 + dt 2 ) = max{d( t −1)π 0 , d( t −1)π1 ," , d (t −1)π t−1 } ⎨ L −1 ⎪ K ′′ = wt ( dt 2 ) N t ( dt 2 ) i i ⎪⎩ t ∑ i =0

(6)

Where, d ( t −1)π j covers all previous subspaces’ dimensions. Since the pyramid match is determined by the largest distance between two vectors, for instance, suppose G G G x = (1, 2," , 62,1), y = (1, 2," , 62, 63), and z = (63, 62," , 2,1) , these three vectors will G all match at coarsest level between, so we can’t obtain that z is alien. But if we divide feature space into two subspaces, we can easily get the large similarity between x and y, leaving z still abnormal. Hence we propose our matching kernel function: T

K = ∑ α t ( K t′ + Kt′′− ωt Kt∑−1 ) + Kbase

(7)

t =1

Where, α t is weight for each level, and Kt∑−1 is the kernel function from level t-1 which will be divided by level t because of its largest dimension, ωt is coefficient of that kernel with ωt ∈ [0, 2] . Kbase is a base kernel to assure its non-zero diagonal elements of K. 3.3 Analysis of DP-PMK 3.3.1 Efficiency A key aspect of our improved method is that we maintain the original PMK’s linear time computation, and doesn’t increase too much–will show in experiment, while still have high accuracy. According to Grauman & Darrell’s paper, the computational T

i =t

complexity of original PMK is O(dmL) , so DP-PMK has O(∑∑ dti mL ) , and t =1 i = 0

T

i =t

T

i =t

since ∑∑ dti mL =(∑∑ dti )mL = TdmL , 0 ≤ T ≤ 4 , when it comes to the partition t =1 i = 0

t =1 i = 0

time, if we don’t create new memory, pyramid matching always be done in d-

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dimension feature space, different dimensions use different indices. Hence DP-PMK only increases T times of original computational time. 3.3.2 Kernel Enhancements Only positive semi-define kernels guarantee an optimal solution to kernel-based algorithms based on convex optimization, which includes SVM. According to Mercer’s theorem, a kernel is p.s.d if and only if it corresponds to an inner product in some feature space [16]. First let us rewrite the kernel function at each level as: K t′ + Kt′′− ω K t∑−1 = Kt′ + Kt′′ − 2 K t∑−1 + (2 − ωt ) K t∑−1 , here we set ωt ∈ [0, 2] . Suppose there are two bags of features having the same size, so the pyramid matching is one-one matching: Every feature has its unique matching feature. If we divide features into two, since matching level is depend on the largest distance of dimension between, so after partition, these two sub-features will one stay at original level and the other fall into a finer level—if they don’t match with others—making the kernel function much larger, and if they do match with others this means the matches can only be finer. When these two bags of features have different number of features, the matching kernel also always makes better. Hence, for any two being matched bags of features K t′ + K t′′ ≥ 2 Kt∑−1 . So if we set ωt = 2 , for example, an input set compared against itself—no changes after dividing—will get zero value, and some couples of vectors like previous x and y, will get large value, while x and z still small, so, any kernel mostly measured by changes of number of the similar dimensions after partition which is more reliable compared with kernel measured by largest distance of dimension, and such kernel can somehow overcomes the memorize effect[8]; and if we set ωt = 0 , we get a purely Mercer kernel, since kernels are closed under summation and scaling by a positive constant [16], and as is shown in [8], pyramid kernel is a Mercer kernel. Hence ωt is a coefficient trades off between a purely Mercer kernel and a kernel whose diagonal elements equal to zero (without base kernel). If we set ωt = 2 , we will get all diagonal elements equal to zero, that means selfsimilarity is zero which is unacceptable; hence we add a base kernel for the use of SVM. In experiments we set

K base = β K orignal

(8)

Where, K orignal is the original kernel of PMK, since K orignal has diagonal that is significantly larger than off-diagonal entries[8]. β is the coefficient, β ∈ (0,1] . According to the matrix theory, increasing diagonal elements make the leading principal minors of the matrix greater or equal to zero, which makes a positive semi-define kernel. In applications, we set a lowest dimension (dim=8) to avoid partitioning an over too low dimension.

4 Experiments The Caltech-101 dataset contains 9,197 images comprising 101 different classes, plus a background class, collected via Google image search by Fei-Fei et al.[17]. Caltech-101

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is one of the most diverse object databases available today; some sample images are shown in Fig. 3. For this dataset, a Harris detector[18] is used to find interest points in each image, and SIFT-128[19] descriptor is used to compose the feature sets. In the following, we provide results to empirically demonstrate our matching’s accuracy and efficiency on real data, and we compare it with the original pyramid matching kernel and VG-PMK. For each method, a one-versus-all SVM classifier is trained for each kernel type, and the performance is measured via 10 runs of kernel computation. In experiments, we set α t = 1 and wit = 1 d 2i , the same as[8].

Fig. 3. Example images from Caltech-101 dataset. Three images are shown for each of 15 of the 101 classes. 0.5 PMK DP-PMK 0.45

Mean Accuracy (10 runs)

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Fig. 4. A preliminary study of DP-PMK

Here, we randomly select 15 classes from Caltech-101, and use at most 60 images of each class to compose SIFT-128 feature sets, the number of training images is 30. β = ωt = 1 , T=2. From the figure, DP-PMK can easily get at least 10% higher accuracy than the original PMK. Next, we randomly select 15 classes from Caltech-101 (called Caltech-15)—shown in table 1—to optimize related parameters, here we choose an order and optimized each parameter separately before moving to the next. Our goal is to find parameter values that could be used for any dataset, so our choosing of parameter values is careful.

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Table 1. Selected Caltech-15

revolver garfield cannon

joshua_tree octopus louts

headphone strawberry emu

okapi ceiling-fan schooner

Motorbikes stegosaurus cougar-face

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Fig.5. shows different levels to Caltech-15, left plot shows the mean accuracy according to different levels. As level increases, the accuracy increases. But consider the related time spend (right plot), we choose T=4. Base Kernel to Caltech-15 0.8

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Fig. 6. The result of parameter tuning for enhancements to DP-PMK. From the figure, we set ωt = 2 and β = 0.6 .

Finally we make a comparison with PMK and VG-PMK using SIFT-128 descriptors. For VG-PMK , we set k=10 and L=5, suggested by[2]. From table 2, to obtain the same accuracy, DP-PMK spends only about 6 times of original computational time while VG-PMK needs about 250 times of original computational time, which shows DP-PMK’s impressive performance.

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Pyramid matching method PMK DP-PMK VG-PMK

Mean accuracy 0.229293 0.623569 0.621212

Total computation time (s) 41.58 248.76 1082.2

5 Conclusion We have introduced an improved pyramid matching kernel with much less computation time, while still maintains high accuracy, when dealing with high dimension feature (such as SIFT-128) space. Our DP-PMK consistently divides the feature space into several low dimension feature subspaces to avoid distortion factors, in each subspace, the original PMK operates there, and the similarity is measured by a weight sum to each subspace. Compared with other state-of-the-art approaches which need hundreds of times of original computational time, DP-PMK needs only about 46 times of original computational time to obtain the same accuracy. However, DP-PMK’s performance doesn’t improve much using PCA-SIFT descriptor, one reasonable explanation may be that PCA-SIFT is a low dimension feature ( 1) or the arrives at the controller using more than one sampling period (τsc data arrives at the controller is out-of-order based on the time stample, then the controller will read out the most recent data yi (k − 1) from the buffer and utilize it as y¯i (k). A diagonal matrix Mp (k) is defined to describe every generalized sensor status at sampling instant k by  1 valid (2) [Mp (k)]ii = 0 invalid then, for the buffers in the controller node, we have y¯(k) = Mp (k)y(k) + (I − Mp (k))y(k − 1).

(3)

where y(k), y¯(k) denote the plant’s output, and the output received by the controller, respectively. Similarly, we can define a matrix Mσ (k) to describe all generalized actuators status at the sampling instant k by  1 valid [Mσ (k)]jj = (4) 0 invalid then, for the buffers in the actuator node, we have u(k) = Mσ (k)¯ u(k) + (I − Mσ (k))¯ u(k − 1).

(5)

where u ¯(k), u(k) denote the control signal from the controller, and the control signal received by the plant at the sampling instant k, respectively. From (1)-(5), the MIMO NCS model with multi-channel buffering strategy can be obtained ⎧ x(k + 1) = Ax(k) + Bu(k) ⎪ ⎪ ⎨ y(k) = Cx(k) (6) u(k) + (I − Mσ (k))¯ u(k − 1) ⎪ u(k) = Mσ (k)¯ ⎪ ⎩ y¯(k) = Mp (k)y(k) + (I − Mp (k))y(k − 1) From (6), the data that the controller can make use of are some sampling values from previous sampling periods. The state observer can be used to estimate the state vector, and the estimated values are then used to compute the control law. Consider the following state observer x ˆ(k + 1) = Aˆ x(k) + B u ¯(k) + L(¯ y(k) − yˆ(k)).

(7)

where L is the observer gain. We use a state feedback law u ¯(k) = K x ˆ(k).

(8)

where K is feedback gain. Considering the state observer (7) and using (8) and (6) gives x ˆ(k + 1) = (A + BK − LC)ˆ x(k) + LMp (k)Cx(k) + L(I − Mp (k))Cx(k − 1).

(9)

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Define e(k + 1) = x(k + 1) − x ˆ(k + 1), from (6) and (9) we obtain ¯ σ (k)K − LM ¯ p (k)C)x(k) + (A − B M ¯ σ (k)K − LC)e(k) e(k + 1) = (B M ¯ ¯ ¯ σ (k)Ke(k − 1). (10) + (−B Mσ (k)K + LMp (k)C)x(k − 1) + B M ¯ σ (k) = Mσ (k) − I, M ¯ p (k) = Mp (k) − I. where M Using (8) and e(k), x(k + 1) becomes x(k + 1) = (A + BMσ (k)K)x(k) − BMσ (k)Ke(k) ¯ σ (k)Ke(k − 1). ¯ σ (k)Kx(k − 1) + B M − BM

(11)

Combining (10) and (11), we have 

     x(k + 1) A00 A01 A¯ x(k) = + ¯00 A10 e(k + 1) A10 A11 e(k)

A¯01 A¯11



x(k − 1) e(k − 1)

 (12)

¯ σ (k)K − LM ¯ p (k)C, where A00 = A + BMσ (k)K, A01 = −BMσ (k)K, A10 = B M ¯ ¯ ¯ ¯ ¯ ¯ p (k)C, A11 = A−B Mσ (k)K −LC, A00 = −B Mσ (k)K, A01 = −B Mσ (k)K +LM ¯ ¯ ¯ ¯ A10 = B Mσ (k)K, A11 = B Mσ (k)K. From (12), the closed-loop system can be viewed as a switched system with time varying parameters. If we can find a Lyapunov function V that makes the ΔV always less than 0, then the system is asymptotically stable.

3

Stability Analysis of Multi-channel MIMO NCSs

Theorem 1: If there exist symmetric positive-definite matrices P , Q, M , N and real matrices K , L such that ⎡ M −P 0 0 0 ((A + BMσ (k)K)T )P ⎢ ∗ N −Q 0 0 ((−BMσ (k)K)T )P ⎢ ¯ σ (k)K)T )P ⎢ ∗ ∗ −M 0 ((−B M ⎢ ¯ ⎢ ∗ ∗ ∗ −N ((B Mσ (k)K)T )P ⎢ ⎣ ∗ ∗ ∗ ∗ −P ∗ ∗ ∗ ∗ ∗ ⎤ (13) ¯ p (k)C)T )Q ¯ σ (k)K − LM ((B M ¯ σ (k)K − LC)T )Q ⎥ ((A − B M ⎥ ¯ σ (k)K)T )Q ⎥ ((B M ⎥ ik , τ k is the time delay, which denotes the time from the instant ik T when the sensor nodes sample sensor data from a plant to the instant when actuators transfer data to the plant. When {i1 , i2 , L} = {1, 2, L} , it means that no packet dropout occurs in the transmission. If ik +1 = ik + 1 , it implies that T + τ k +1 > τ k . Obviously, U∞k =1[ik T + τ k , ik +1T + τ k +1 ) = [ 0, ∞ ) . In this paper, we assume that u (t ) = 0 before the first control signal reaches the plant and a constant τ > 0 exists such that (ik +1 − ik )T + τ k +1 ≤ τ ( k = 1, 2, L) . Equation (3) can be viewed as a general form of the NCSs model, where the effect of the network-induced delay and data packet dropout are simultaneously considered. With these models, the stabilization criterions are derived in the next section.

3 Main Results Before the development of the main result, the following lemma will be used. Lemma1 [12](Schur complement theorem): Given any symmetric matrix S = S T . ⎡S S = ⎢ 11 ⎣ S 21

S12 ⎤ S 22 ⎥⎦

(4)

r×r

where S11 ∈ R , S12 , S 21 , S 22 are known real matrices with proper dimensions. The following three conditions are equivalent (1) S < 0 (2) S11 − S12 S 22−1S12T < 0 and S22 < 0

(5)

(3) S 22 − S12T S11−1 S12 < 0 and S11 < 0

、

Lemma2 [12]: Given any symmetric matrix Q = QT , and constant matrix H E with appropriate dimension, if F (t ) is an uncertain matrix function with Lebesgue measurable elements and satisfies F T (t ) F (t ) ≤ I , in which I denotes the identity matrix of appropriate dimension. Then

Q + HF (t ) E + E T F T (t ) H T < 0

(6)

If and only if there exists positive constant ε > 0 such that

Q + ε −1 HH T + ε E T E < 0

(7)

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In the following, the sufficient condition for convergence is given. Theorem 1: considering the closed-loop system (3), given a positive constant τ , if there exist constant matrix P = PT > 0 , Q = QT > 0 , R = RT > 0 and Z = Z T > 0 with proper dimensions such that the LMI (10) holds.

⎡Ξ τ AKT ⎤ 0 , R = RT > 0 , Z = Z T > 0 , N = ⎡⎣ N1T N 2T N 3T ⎤⎦ and M = ⎡⎣ M 1T M 2T M 3T ⎤⎦ with proper dimensions such that the LMI (15) holds.

⎡Π τ AKT ⎢ −1 ⎢ * −τ Z ⎢* * ⎢ * ⎢⎣ *

τN 0 −τ Z *

τM ⎤

⎥ 0 ⎥ , the name of each child node as the name of each user configuration attribution, the ID of each child node as the ID of corresponding object, and the attributions of each child node as the user defined ones. This can realize the analysis and binding of front pages to each attribute. To analysis and bind the configuration files, we first put JDOM packet into the project, then programmed a JavaBeans file by calling JDOM library functions. This JavaBeans file can not only selectively read the configuration data form SQL2005 database and form a correspondingly XML file, but also analyse the generated configuration files and get all of its attributes to react them on front pages by using JavaScript, as shown in Fig.4. Due to this kind of bilateral effect, the BOM can be generated and configured with good flexibility. 3.2 Transmitting the Configuration Files Usually, the transmission between front web pages and data is triggered by server response after user clicking the corresponding web control By using such traditional way to transmit XML configuration files developer cannot achieve the goal of configuring pages flexibly, since the web page was also refreshed according to corresponding response once the web control was triggered and hence the state of page could not meet users' demand. To solve this problem, one can employ AJAX to transmit these files. Normally, in order to transmit XML files by using AJAX, one need firstly using JavaScript to create a XmlHttpRequest object whose Open function can be used to send data or XML documents to server synchronously or asynchronously with POST or GET method.

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Fig. 4. XML configuration files created by JDOM

Fig. 5. XML JSF way of AJAX

Different from the traditional transmission mode of AJAX, this paper use AJAX mode combining with JSF (JavaServer Faces) method. Its principle is shown in Fig.5, where the XmlHttpRequest object was used to send strings or XML files to a Servlet which is written in the JSTL code of JSF page. The Servlet was then used to call operational functions in JavaBeans to achieve the required operation purpose. The following gives the key code segment used to write such Servlet:

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<jsp:scriptlet> response.addHeader("Cache-Control", "no-cache"); response.addHeader("Expires", "Thu, 01 Jan 1970 00:00:01 GMT"); request.setCharacterEncoding("UTF-8"); String date1=null; date1=(String)request.getParameter("method"); if(date1!=null){ String mystr=null; ajaxbean.setRequest(request); mystr=ajaxbean.getResponseXML(); response.setContentType("text/html;charset=UTF -8"); response.getWriter().print(mystr); response.getWriter().close(); } It can be seen that the Servlet code open up a channel for data transfer between the front and JavaBean. The using of request and response objects can facilitate the data transfer. Then, the background operations will be performed in the JavaBean, and the results will be returned to front client. The methodology designed here is used to fetch data between BOM Configurator and the background database. 3.3 Construction and Configuration of Middleware Integrated middleware was constructed in the design idea of large scale components customize techniques, after the whole business was divided according to application and organized by its particular function. The divided granularity should be proper. Smaller granularity would break an integral business function or process, which would do harm to its reassemble and extend in business level. The larger ones would cover too many business functions in it, which would reduce flexibility and suitability. After a well business separation, the basic middleware could be configured to meet business needs. The normal time sequences for the configuration is shown in Fig.6. First the UI send a configure command to JSP by using AJAX. The Servlet give a redirection heading for JavaBean controller to the command. In the controller, there would be a configuration process. First identify and determine which basic module would be configured from the command info, here the basic module registration make the identification and the fetch of XML file easy to do. After analysis the XML file, the property of basic module could be configured according to the file by using Javascript. Different configuration corresponds different business function, which should meet the demand of the reconfiguration.

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Integrated middleware can work with the interaction between BOM register and BOM configurator. The function of BOM register is for the registration of components library. The basic middleware and its data and configuration file are tied together with the help of BOM register.

Fig. 6. Operational time sequence of BOM configurator

4 Application Example The above mentioned designing method was successfully used in the development of a management information system for a large scale coal machine manufacturing factory. The business of this factory has following characteristics: 1)

2)

3) 4)

Carrying out the designing and manufacturing of customers’ order oriented goods, which express multiple variety with short-run production and long production cycle. Along with the shortening period of the order, the temporary supplementary orders will increase in number. Therefore, in order to shorten the period of whole production of the factory, the general or semi-general purpose components and parts with long production cycle must be produced in advance. It will result in the increase in stock of components and parts. Since there are lot of situations of components and parts borrowing during the production, the statistics of lacked components and parts is difficulty. Due to complex and variety of working procedure for units production, the accounting of working hours is extremely difficulty.

Hence, it is necessary to create a corresponding business information model, that is the layer of VSP, for the development of management information system software for this factory. The proposed BOM method just provides the foundation for this work.

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In this system, a BOA based production management information software system was developed, which combined with model driven architecture to generate application software framework from the management and administration model of this factory. It employed visualized interface development tools and implemented ten functions and processes, shown in Fig.7.

Fig. 7. Schematic diagram of business in the application example

As a factory level application, the system was three layer framework using J2EE platform based B/S structure as a whole, shown in Fig.8. The AJAX technology was used for communication between clients and server. The database was developed by using SQLSERVER 2005 with XML function to be competent at non-structural data in the application, such as the structure of product’s fabrication, the routine of part’s machining and user’s work direction tree, etc.

Fig. 8. J2EE application used in the example

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As a production management system, we use the List component which is a list box with different optional components. With the design method of BOA, we built different modules according to different businesses. The internal process of the list is shown in Fig.9. It triggered by events of customs to choose different options, then to call backstage function method and to read data from database.

Fig. 9. Flowcharts of List

Except the list component, the table component and some other components are also redeveloped for a better fitting in this system. The table component of JSF have good performance and appearance. But it can not work well with BOA designings. Improved table component, which could cooperate well with AJAX, as it can be refreshed to update cells in both client and server, can satisfy the design method of BOA. And, a well designed report print component was developed in the BOA framework. It can solve the problem of the weakness in customize and adaptiveness of requirements in web report generation. In addition, some special components for this system were also designed. Which include: the order form generation component that would work with client agreement; the client information organization component that would add update or delete items according to the information of client company; the basic sales price component that would organize the products prices; the store components for input and output of the products which can generate bills and current account changes; the web IM component which can make the communication between workers in production management easier. All these special components were integrated together and made the system suited for this factory application. Since most of manufacturing factories now have multiple products and large number of complicated standard parts, even distinguishing feature on their business processes, it is difficult using general-purpose standardized ERP software to adapt their specific characteristics. However, due to its heterogeneous, loosely coupled distributed characteristics, the BOA framework can be a good choice to meet the needs of different customers and to reduce development cycle.

5 Conclusion The presented three-layer structure model of BOA and its designing method employed SunJavaStudioCreator as development platform for its BOM and configuration software. It combined JSF visualized components into AJAX heterogeneous transmission technology and used JDOM to generate and analyse the properties configuration files of XML format, which can produce different page styles by using JavaScript tool and realize reusable modules with same business processes

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or functions and reduce software development cycle. It was successfully applied in the development of an enterprise management information system for a large scale coal machine manufacturing factory.

References 1. Dong, C.L., Guo, S.S.: The research of ERP reconfigurable mode based on the theory of evolution. Manufacturing Automation Journal 6, 15–18 (2008) 2. The Business Architecture of BOA, http://www.tongtech.com/products/boadetail.jsp 3. Johnson, D., White, A., Charland, A.: Enterprise Ajax: building robust Ajax applications. Prentice Hall PTR, New Jersey (2008) 4. Zhou, H.B.: Convert database to XML programming by JDOM. J. Computer Knowledge and Technology 2, 182–183 (2006) 5. Dudey, B., Lehr, J., Willis, B., Mattingly, L.R.: Mastering JavaServer Faces. Publishing House of Electronics Industry, Indiana (2005) 6. Jacobi, J., Fallows, J.R.: Pro JSF and AJAX: Building Rich Internet Components, pp. 3–20. USA Press (2006) 7. Gallardo, M.d. , Martínez, J., Merino, P., Rosales, E.: Using XML to implement abstraction for Model Checking. In Proceedings of the 2002 ACM Symposium on Applied Computing, SAC 2002, pp.1021–1025. ACM, New York (2002)

Training Support Vector Data Descriptors Using Converging Linear Particle Swarm Optimization Hongbo Wang, Guangzhou Zhao, and Nan Li College of Electrical Engineering, University of Zhejiang, Hangzhou, Zhejiang Province, China {whongbo,zhaogz,happyapple}@zju.edu.cn

Abstract. It is known that Support Vector Domain Description (SVDD) has been introduced to detect novel data or outliers. The key problem of training a SVDD is how to solve constrained quadratic programming (QP) problem. The Linear Particle Swarm Optimization (LPSO) is developed to optimize linear constrained functions, which is intuitive and simple to implement. However, premature convergence is possible with the LPSO. The LPSO is extended to the Converging Liner PSO (CLPSO), which is guaranteed to always find at least a local optimum. A new method using CLPSO to train SVDD is proposed. Experimental results demonstrate that the proposed method is feasible and effective for SVDD training, and its performance is better than traditional method. Keywords: Support Vector Domain Description; Constrained Quadratic Programming; Linear Particle Swarm Optimization; Premature Convergence; Converging Linear Particle Swarm Optimization.

1

Introduction

Support Vector Machines (SVM)[1,2]are a recently developed class of classifier architectures, derived from the structural risk minimization principle, which have a remarkable growth in both the theory and practice in the last decade. Support Vector Data Description (SVDD)[3] can be viewed as a smooth extension of SVM. It represents one class of known data samples in such a way that for a given test sample it can be recognized as known, or rejected as novel. Training SVM requires solving a quadratic problem (QP) with box and linear equation constraints. This problem often involves a matrix with an extremely large number of entries, which requires huge memory and computational time for large data applications. Practical techniques decompose the problem into manageable subproblems, which may be solved by numeric packages. Chunking methods suggested in [4] reduce the matrix’s dimension and is suitable to large problems. Decomposition methods [5, 6] break down the large QP problem into a series of smaller subproblems, and need a numeric QP optimizer to solve each of these problems. The most extreme case of decomposition is Sequential Minimal Optimization (SMO)[7], K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 196–204, 2010. © Springer-Verlag Berlin Heidelberg 2010

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which solves the smallest possible optimization problem at each step. Most of the above approaches have been employed successfully to solve the learning of SVM. Particle Swarm Optimization (PSO)[8,9] is a swarm intelligent optimization method. It can find solution quickly in high dimensional space by its stochastic and multipoint searching ability. Using PSO to train SVM has been put forward recently, and this is really a novel tentative. For the non-constraint optimization problem, the linear particle swarm optimization (LPSO)[10] for linearly constrained problem was presented, and applied for training SVM[11]. In this paper, LPSO is introduced for SVDD training. To address the issue of premature convergence, a new parameter was introduced to LPSO, which guarantees the LPSO always finding a local minimum[12,13]. The new method was called Convergence Linear Particle Swarm Optimizer (CLPSO).

2

Support Vector Data Description

Given a set S = {x1 , , xn } , SVDD attempts to find a hyper-sphere (i.e. F ( R, a) ), with centre a and radius R , that contains all the patterns in S . The volume of this hypersphere R should be minimized. To allow for the presence of outliers in the training set, slack variables ξi ≥ 0 are introduced. The primal optimization problem is defined as

min

F ( R, a ) = R 2 + C ∑ ξ i

∀i

(1)

i

where the variable C gives the trade-off between simplicity (volume of the sphere) and the number of errors (number of target objects rejected). This has to be minimized under the constrains xi − a

2

≤ R 2 + ξi

∀i

(2)

The optimization problem can be translated into Lagrange problem L( R, a, α i , ξi ) = R 2 + C ∑ ξi − ∑ α i {R 2 + ξ i − ( xi2 − 2axi + a 2 )} − ∑ γ i ξi i

i

i

(3)

with Lagrange multipliers α i ≥ 0 and γ i ≥ 0 . By solving the partial derivatives of L, we obtain

∑α i

i

= 1 , C − α i − γ i = 0 , a = ∑ α i xi i

(4)

Equation (3) can be rewritten as Lagrange form of ai with above constraints max

L = ∑ α i ( xi ⋅ xi ) − ∑ α iα j ( xi ⋅ x j ) i

i

(5)

In order to have a flexible data description, as opposed to the simple hyper-sphere discussed above, a kernel function K ( xi , x j ) = Φ ( xi ) ⋅ Φ ( x j ) is introduced. After

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applying the kernel and using Lagrange optimization, the SVDD function using kernels becomes max

L = ∑ α i K ( xi , xi ) − ∑ α iα j K ( xi , x j ) i

i

0 ≤ αi ≤ C, ∑αi = 1 i

(6)

(7)

It can be observed that only data points with non-zero ai are needed in the description of the data set, therefore they are called support vectors of the description. Given the support vectors xi , a test sample z is accepted when K ( z , z ) − 2∑ α i K ( z , xi ) + ∑ α iα j K ( xi , x j ) ≤ R 2 i

i, j

(8)

Optimizing the functions in (5) and (6) is a Quadratic Programming (QP) problem with linear constraints (7). Generally the SVDD is used to describe large data sets. Solving the above problem via standard QP techniques becomes intractable, because the quadratic form of (6) needs to store a matrix whose size is equal to the square of the number of training samples.

3 3.1

Particle Swarm Optimization and Improvement Basic Particle Swarm Optimization

PSO differs from traditional optimization methods, in which a population of potential solutions is used in the search. The direct fitness information instead of function derivatives or other related knowledge is used to guide the search. This search is based on probabilistic, rather than deterministic, transition rules. The basic PSO is as follows. Each particle pi is a potential solution to the collective goal, usually to minimize a fitness function f . Each particle has a corresponding position and velocity, denoted as pi = ( pi1 , , pin ) and vi = (vi1 , , vin ) , i = 1, 2 , m respectively, where m is the number of particles and n is the dimension of the solution. PSO uses the following equations to update the particle’s velocity and position during evolution.

vit,+j1 = wt vit, j + c1r1 j ( pbestit, j − pit, j ) + c2 r2 j ( pg tj − pit, j )

(9)

pit,+j1 = pit, j + vit,+j1

(10)

Where t is the current generation, w is the inertia weight, c1 and c2 are coefficients, and r1 j , r2 j are evenly distributed random number in [0,1] , which embodies the stochastic nature of the algorithm. pbesti = ( pbesti1 , , pbestin ) is the best solution found by particle i , whereas pg = ( pg1 , , pg n ) is the best found by the whole population up to now.

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199

Linear Particle Swarm Optimization

A new PSO algorithm, the Linear PSO, is developed specifically with linear constraints. Traditionally, the velocity and position update equations, shown in equations (7) (8), are specified separately for each dimension of a particle. In LPSO, particles update their velocity using the under-mentioned formula. vit +1 = wt vit + c1r1t ( pbestit − pit ) + c2 r2t ( pg tj − pit )

(11)

pit,+j1 = pit, j + vit,+j1

(12)

where the same random number r1 , r2 are adopted to update each component of the velocity vector. This approach has the advantage that the flight of particles is defined by standard linear operations on vectors, and hence it is referred to as a Linear Particle Swarm Optimizer (LPSO). 3.3

Improvement of Particle Swarm Optimization

Suitable inertia weight w provides a balance between global and local explorations, thus requiring less iteration on average to find a sufficiently optimal solution. In general, w is set according to the following equation w = 0.5

itermax − iter + 0.4 itermax

(13)

Where iter and itermax are the current and the maximum number of iterations respectively. A constriction factor K has been introduced to PSO, which improves the ability of PSO to constrain and control velocities[14]. K=

2 2 − r − r 2 − 4r

(14)

where r = r1 + r2 , r > 4 , and the LPSO is then vit +1 = K ( wt vit + c1r1t ( pbestit − pit ) + c2 r2t ( pg t − pit ))

(15)

If vit,+j1 is too high, particles might fly past good solutions. If vit,+j1 is too small, particles may not explore sufficiently. The parameters Vmax and Vmin = −Vmax should be determined. In many experiences, Vmax was often set at 10% ∼ 20% of the max position. The original PSO algorithm has a potentially dangerous property: if a particle’s current position coincides with the global best position, the particle will only move away from this point. This may lead to premature convergence of the algorithm. To address this issue, the Convergence Particle Swarm Optimizer (CPSO) was developed in [12] [13]. In this algorithm, the velocity update for the global best particle is

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changed to force it to search for a better solution in an area around the position of that particle. Let τ be the index of the global best particle, then pbestτ = pg

(16)

Change the velocity update equation (11) for the global best particle τ using vτt +1 = − xτt + pg t + ρ tϑτt

(17)

Where ρ t is a scaling factor and ϑ t ∼ UNIF ( −1,1) n with the property that Aϑ t = 0 . Since xτt +1 = vτt +1 + xτt = pg t + ρ tϑτt

(18)

The new position of the global best particle will be its personal best pg t , with a random vector ρ tϑτt . It is only the global best particle that is moved with equations (17) and (18), and all other particles in the swarm are still moved with the original equations (11) and (12). This new algorithm, referred to as CLPSO is guaranteed, in the limit, to always find at least a local minimum.

4

SVDD Training Based on CLPSO

From the mathematical model of SVDD (6) (7), we can learn that the variables need to be optimized are the coefficients of support vectors, so the particle can be coded as p = (α1 , , α n ) and the fitness function is selected as f ( p ) = ∑ α i K ( xi , xi ) − ∑ α iα j K ( xi , x j ) i

i

(19)

For the training of SVDD is a quadratic programming problem with box and linearly equation constraints according to the requirements of CLPSO, the position of the particle must satisfy constraints (7). We initialize the particle’s position with pij = C ⋅ rand () , where rand () is evenly distributed random number in [0,1] , and the following is the method to tune up the position to fulfill the box restriction. n

d = ∑ pij ; j =1

delta = d − 1 ; while delta > ε

{

if

delta > ε

{

s = delta / n;

if

{

pij + s < C

pij = pij + s;

}

and

pij + s > 0

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} else

{

s = − delta / n ; if

}

{

pij − s < C

pij = pij − s ;

and

pij − s > 0

}

n

d = ∑ pij Y j ; j =1

delta = d − 1 ;

}

The velocity of particle is set to be zero. Thus, the Lagrange multipliers p satisfy constraints (7). The procedure of CLPSO to train SVDD is as shown below: 1. Initialize 1) Set all parameters of CLPSO. 2) Set current generation t = 0 . 3) Initialize the velocity vector to zero; Initialize the particle’s position randomly and then adjust each particle to satisfy the constraints (7) by above method. 4) Evaluate values of fitness function of f ( p ) for each particle; Set pbesti0 = pi0 and

pg 0 = max( pbesti0 , i = 1,

, m)

.

2. Optimize 1) Update inertia weight w using (11). 2) Generate random number r1 and r2 ; Calculate constriction factor K using (14). 3) Update the velocity of the global best particle using (17), and update the velocity of the other v > Vmax particles using (15); For any components, if i , j , vi , j = Vmax vi , j < Vmin vi , j = Vmin then ; If , then .

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4) Update particle position using (10); For any component, if pi , j > C , then pi , j = C ; If pi , j < 0 , then pi , j = 0 ; and then using the same method as in initialization to tune up the other position to satisfy the linear equation constraint. 5) Evaluate values of fitness function of f ( p ) for each particle; Update pbestit and pg t . 6) The current iteration number is set to t + 1 ; If t > itermax , then pg t is the solution of the problems. Else, return to Step 1) and repeat the above procedure again.

5

Experimental Results

In order to show the performance of the proposed method and its efficiency, we present two groups of experiments both on artificial ellipse dataset and real dataset from UCI Repository of Machine Learning Databases. The kernel functions of SVDD in two x − xj experiments are selected as Gaussian kernel function K ( xi , x j ) = exp(− i 2) .

σ

The limiting value of C was chosen to be 1, and the other parameters are selected as r1 = 2.8 , r2 = 1.3 , r = r1 + r2 = 4.1 , Vmax = 0.3 , Vmin = −0.3 . As we know that the population size has influence on the convergence and performance of the PSO. Artificial Ellipse Dataset (Fig. 1) was used for analyzing the effect of the population size. Ellipse Data 4

y

3

2

1

0

0

5

10 x

15

20

Fig. 1. Artificial Ellipse Dataset

Fig.2 shows the comparison of the running time and iteration steps for population sizes of 5 to 100 particles. The Max Iteration Steps was selected as 500. As it can be

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Training Iteration Training Time

2 1 0 -1 -2 -3

0

20

40

60

80

100

Fig. 2. The dashed line denotes the training iteration steps of CLPSO. The solid line denotes the training time of CLPSO.

seen that the more particles in the population, the smaller the iteration steps. However, increasing the population sizes resulted in more training time. The experiments showed that a population of 20 to 50 is best in terms of both sides. We selected 409 (16-dimensional) training points (known class = ’A’) from Letter Image Recognition Data and 171(19-dimensional) training points of ‘BUS’ features from Vehicle Silhouettes Data Set. Correctly classified rate was defined as CR = correctly classified / Total Testing . As shown in Table 1, in all of the two datasets, the LPSO can obtain better result of CR than SMO. Table 1. Comparison of SMO and CLPSO on UCI data set

UCI dataset

Dim

Size of training set

Size of testing set

Letter Recognition

16

409

2013

Vehicle

6

18

171

Name of algorithm

Correct Rate (FR)%

SMO

86.38

CLPSO

92.00.

SMO

85.11

CLPSO

89.89

188

Conclusion

SVDD training is a quadratic programming (QP) problem. This paper proposed a method to solve the optimization by PSO, which finds solution by its stochastic and multipoint searching ability. The results of experiment show the new way is successful and accurate. Acknowledgments. This work is supported by National Natural Science Foundation of China (60872070) and Key Scientific and Technological Project of Zhejiang Province (Grant No. 2007C11094, No. 2008C21141).

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Reference 1. Vapnik, V.N.: The nature of statistical learning theory. Springer, Heidelberg (2000) 2. Cortes, C., Vapnik, V.: Support-vector networks. Machine Learning 20, 273–297 (1995) 3. Tax, D.M.J., Duin, R.P.W.: Support vector data description. Machine Learning 54, 45–66 (2004) 4. Vapnik, V.N., Kotz, S.: Estimation of dependences based on empirical data. Springer, New York (2006) 5. Osuna, E., Freund, R., Girosi, F.: Support vector machines: Training and applications (1997) 6. Osuna, E., Freund, R., Girosi, F.: An improved training algorithm for support vector machines. Citeseer (1997) 7. Platt, J.C.: Fast training of support vector machines using sequential minimal optimization (1999) 8. Kennedy, J., Eberhart, R.: Particle swarm optimization (1995) 9. Yuan, H., et al.: A modified particle swarm optimization algorithm for support vector machine training (2006) 10. Paquet, U., Engelbrecht, A.P.: New particle swarm optimiser for linearly constrained optimization 11. Paquet, U., Engelbrecht, A.P.: Raining support vector machines with particle swarms (2003) 12. Paquet, U., Engelbrecht, A.P.: Particle swarms for equality-constrained optimization. Submitted to IEEE Transactions on Evolutionary Computation 13. Bergh, F., Engelbrecht, A.P.: A new locally convergent particle swarm optimizer (2002) 14. Eberhart, R.C., Shi, Y.: Comparing inertia weights and constriction factors in particle swarm optimization. IEEE, Piscataway (2000)

Research on Modeling and Simulation of an Adaptive Combat Agent Infrastructure for Network Centric Warfare Yaozhong Zhang, An Zhang, Qingjun Xia, and Fengjuan Guo Department of Electronic and Information, Northwestern Ploytechnical University, Xi’an 710129, China {zhang_y_z,zhangan}@nwpu.edu.cn, [email protected], [email protected]

Abstract. In order to shift from platform centric warfare to Network Centric Warfare (NCW) for the military simulation, a new adaptive combat agent model is designed that with some special sub-agent advisor. The sub-agent advisor can perform like a specialist to carry out the management of sensors, situational assessment, tactical decision-making, combat mission, and communication management. So we can demonstrate realistic and valid behaviors of military entities in a Computer Generated Forces (CGF) simulation. It provides an effective training environment to exhibit advanced coordination and cooperation capability of military units in NCW with high resolution simulation. Keywords: Network Centric Warfare; tactical decision-making; computer generated force; simulation; Agent.

1 Introduction Agent-based models borrow heavily on a biological analogy. Now it has widely used in all kinds of complex system, such as ecosystem, economic system, society system and the military system [1]. An agent is a physical or virtual entity that has the ability: a) which is capable of acting in an environment; b) which can communicate directly with other agents; c) which is driven by a set of tendencies; d) which possesses resources of its own; e) which is capable of perceiving its environment; f) whose behavior tends towards satisfying its objectives [2]. So agent-based models are very appropriate for simulate the military entities, such as artificial soldiers. We can recognizing warfare as a complex adaptive system, it requires a set of agents that are individually autonomous; it means that each agent can determines its actions based on its own state and the state of the environment, without explicit external command. It has opened the doors for a number of agent-based distillation combat systems to emerge. This includes the Irreducible Semi-Autonomous Adaptive Combat (ISAAC) and the Enhanced ISAAC Neural Simulation Toolkit (EINSTein) from the US Marine Corps Combat Development Command, the Conceptual Research Oriented Combat Agent Distillation Implemented in the Littoral Environment (CROCADILE) [3]. K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 205–212, 2010. © Springer-Verlag Berlin Heidelberg 2010

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However existing agent-based distillation combat systems were developed mainly on platform centric warfare and current agent architectures, which limit their ability to test the character of NCW. So we need to develop a new framework for the adaptive combat agent which can reflect the very character of information war and can leading to the fundamental shift from platform centric warfare to NCW.

2 Adaptive Combat Agent Infrastructure In NCW the soldiers rich with variegated information. The sensor-to-shooter time is greatly reduced. The soldiers in the battle field may take actions based on their own raw intelligence from sensor's displays or coordination each other instead of waiting for commands. They must operate in task forces, coalition forces, and joint operations where unit and equipment capabilities vary greatly[4]. The technology shift from platform centric warfare to NCW brings much embarrassment to the combat simulation. The primary architecture of agent is difficult to demonstrate realistic and valid behaviors of military entities. So we need a new systematic Infrastructure that can support the challenge like sensors manage, situation awareness, decision making and missions manage. In our research a new Adaptive Combat Agent (ACA) is adopted which with a special sub-agents layer. 2.1 Top Structure of ACA with Special Advisor In NCW the growing trend in the military simulation community is for greater degrees of system interoperability, resource distribution, entity and aggregate behavioral complexity. So our ACA must be designed and implemented for these varying degrees of integration. The new infrastructure of ACA in our research is shown in Fig.1.

Fig. 1. Top structure of combat agent with advisor

The ACA has a sub-agents layer that is building up with four specialist advisor. These advisors roughly correspond to the reality that a soldier's work flows in NCW. This design allows the implementation of different artificial intelligence techniques to be applied to their appropriate categories of problems. It also provides facilities to abstract the interfaces for specifically function and simulations. The key to this approach is the implementation of advisors which are sub-agents with special knowledge and skills.

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2.2 Microstructure of the Sub-agent Advisor The four advisors in Fig.1 have the same common microstructure as shown in Fig.2.

Fig. 2. Microstructure of Sub-Agent Advisor

The advisor controls the interfaces to receives and stores external information or to interact with other ACA. The data received through interfaces can be translated into internal representations which represent its perceptions of the battlefield environment. The choice of internal structures can depend on the level of abstraction required or the advisor’s special ability in order to deal the information efficiently and effectively. The advisor can receive external command from its direct leadership which has the higher privilege. The inference engine is the key to the advisor which derived from expert system shells and processing control rules to utilize the battlefield information. This open architecture is very convenient for other features such as neural networks, genetic algorithm, case-based reasoning, and machine learning which can be easily added to the inference engine. 2.3 Sensor Manage Advisor Sub-agent The functional frame of Sensor Manage Advisor (SMA) is shown in Fig.3.

Fig. 3. Sensor manager advisor functional frame

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The SMA sub-agent can collect the battlefield data (including terrain databases, hostile unit etc) according to the detect task. Raw data from SMA can be translated into valid battlefield data and send to the Situation Advisor (SA) where the Common Operation Picture (COP) is constructed. The command of sensor strategy control or work mode control is from the Mission Mange Advisor (MMA). In NCW the sensor’s ability is expand rapidity, so we can test the new features of the sensor without to develop the simulation from scratch. We can only do this by adding new services to the SMA. 2.4 Situation Advisor Sub-agent The functional frame of SA is shown in Fig.4.

Fig. 4. Situation advisor functional frame

Here we can see that the battlefield data from SMA first be translated into the internal representation which be called battlefield information. From this information and the history information the inference engine of SA can acquire the situation awareness and the prediction of the situation. Finally the SA can construct the Common Operation Picture (COP) and submit to the Tactical Decision Advisor (TDA). In NCW the agent rich with variegated information from the information network. How to verify the information each other and construct the COP are becoming complex and difficult. With SA we can test the new fusion arithmetic and other theory for the situation awareness. 2.5 Tactical Decision Advisor Sub-agent The functional frame of TDA is shown in Fig.5.

Fig. 5. Tactical decision advisor functional frame

As we know TDA works under conditions best described as "the fog and friction of war". TDA must first interpret his understanding as a set of alternative courses of actions (this is called decision-making). Then he must be able to select the best course of action from those alternatives (this is called mission-making). In NCW TDA must also submit the mission’s collaboration and cooperation request to the MMA.

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2.6 Mission Manage Advisor Sub-Agent The functional frame of MMA is shown in Fig.6. Sensor Manage Advisor

Mission Effectiveness Tactical Decision Advisor

Mission Collaboration

Mission Cooperation

Action selection

Action

Mission Manage Advisor Other Agents

Fig. 6. Mission manage advisor functional frame

In NCW how to exhibit advanced coordination and cooperation of military units (which are found on a real battlefield) is paramount to the MMA. The MMA deals with diverse types of missions in different contexts. MMA can submit the best action using the optimization techniques and it can also monitor the mission effectiveness.

3 Software Design of the Adaptive Agent Combat System Since the beginning of computer simulations, military analysts and programmers have developed different combat simulations for every scale of combat operations[5][6]. Adaptive Agent Combat System (AACS) in our research is belong to high-resolution combat models, which are detailed models of warfare, represent individual combatants as separate entities with numerous attributes. Each agent in AACS has four advisors as described above which can act as a real solder in network centric warfare environment.

Fig. 7. Software structure of the AACS

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The AACS try to explore combat as a self-organized emergent phenomenon, and take a bottom-up, synthesis approach, vice the more traditional top-down approach. It is developed with object oriented C++ code. The software structure is shown in Fig.7. Its running snapshots are shown in Fig.8.

Fig. 8. Snapshots of the AACS

4 Scenario Analysis In our simulation the blue agent force was selected as two squads; each squad has 25 entities and their common target. The red agent was also selected as two squads; each squad has 25 entities and their common target to be protected. The detailed parameters are shown in table1. Table 1. Simulation parameters

Agent Blue Group1 Blue Group2 Blue Group1 Blue Group2

Velocity Detect Detect Weapon Hit Fire Range Cycle Equip prob range (s) (unit) (unit)

Target position

Initially amount

Initially position

25

(300,100)

1

100

5

3

0.1

100

(300,480)

25

(150,100)

1

100

5

3

0.1

100

(450,480)

25

(200,300)

1

100

5

3

0.1

100

25

(350,300)

1

100

5

3

0.1

100

With this scenario, we analyzed the combat outputs with four different settings of blue agent's sensor ability in the same conditions while holding all other parameters the same. The different settings of blue agent’s sensor ability including the detect range and detect cycle. As we know the ability of reconnaissance is the key to NCW, so with this scenario we can easily contrast the advantage that the changes of sensor’ ability to the combat. The simulation was run 500 times for each setting and the result was shown in Fig.9.

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Fig. 9. Agent loss graph according to vary sensor capability

From the analyses results we can see that as the blue agent's sensor ability increases, its loss decreases while the red agent's loss increases. Because with the dominance of sensor information the blue agent can predict possible courses of actions, they can provide an assessment of possible future actions. The goal of our research is to provide a useful tool to the military simulation for the NCW. From the result we can see that the AACS had the potential to be a useful aid to situation awareness and decision-making. With AACS we can easily analysis the advanced characteristics such as the superiority of information, the coordination and cooperation capability of military units in NCW with high resolution simulation.

5 Conclusion The ACA in our research can demonstrate realistic and valid behaviors of military entities. It can provide an effective training environment or predictive capability for the military simulation in NCW. The ACA simulation software is very convenient to exhibit advanced coordination and cooperation ability of military units that required in NCW. From the simulation result we can see that the Infrastructure of ACA not only coincides with real-world models but it also provides many software engineering advantages as well.

References 1. Parunak, H., Sven, B.: Entropy and Self-Organization in Multi-Agent Systems. In: Proceedings of the International Conference on Autonomous Agents, pp. 124–130 (2001) 2. Jilson, E.W., Mert, E.: Modeling Conventional Land Combat in a Multi-Agent System Using Generalizations of the Different Combat Entities and Combat Operations. Master’s Thesis, Naval Postgraduate School (2001) 3. Yang, A., Abbass, H.A., Sarker, R.: Landscape dynamics in multi-agent simulation combat systems. In: Webb, G.I., Yu, X. (eds.) AI 2004. LNCS (LNAI), vol. 3339, pp. 39–50. Springer, Heidelberg (2004)

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4. Functional Description of a Command Agent. Lockheed Martin Corporation, ADST-IICDRL-023R- 96OO237A (1997) 5. Hencke, R.B.: An Agetn-based Approach to Analyzing Information and Coordination in Combat. Master’s Thesis, Naval Postgraduate School (1998) 6. David, T., Lee, L.: Testing a New C2 Model of Battlefield Information Sharing and Coordination. In: The 14th ICCRTS, Washington, DC (2009)

Genetic Algorithm-Based Support Vector Classification Method for Multi-spectral Remote Sensing Image Yi-nan Guo, Da-wei Xiao, and Mei Yang School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou, Jiangsu221008 P.R. China [email protected]

Abstract. The traditional classification methods based on asymptotic theory for multi-spectral remote sensing image need the infinite training samples, which is impossible to be satisfied. Support vector classification (SVC) method based on small samples overcome above difficulty. However, the values of hyperparameters in SVC directly determine the method’s performance, which are randomly selected. In order to obtain the optimal parameters, genetic algorithms (GAs) are introduced. Experimental results indicate that this method can not only save time for classification, but also improve the generalization of the SVC model. Keywords: remote sensing image, classification, genetic algorithms, parameters selection.

1 Introduction In remote sensing images, different cultures are reflected by different brightness and spatial position. Each objects has its own spectral and spatial information, hence feature vectors, which characterize various types of objects, distribute in different feature space [1]. Therefore, classification for remote sensing image is to partition different cultures by computers. Useful features are extracted through analyzing the spectrum and spatial information. Then these features are classified into nonoverlapping feature space. At last, each image pixel are mapped into corresponding feature space[2]. Multi-spectral images have high resolution, multi-band and massive data. So they more require high quality classification [3]. In traditional classification methods for remote sensing image: minimum distance method [4-5] is easy to fall into local optimum because only the local characteristics are considered. But it has better performance for block objects. Maximum likelihood classification method [4] needs the probability distribution function of each class to be normal distribution. However, the selected samples may deviate from normal distribution. Although the radial basis neural network [5] is good for classification of block object, it is not ideal in classification of confusion region. Above conventional methods based on asymptotic theory for multi-spectral remote sensing image need the infinite training samples, which is impossible to be satisfied. Support vector machine (SVM) based on structural risk minimization [6] K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 213–220, 2010. © Springer-Verlag Berlin Heidelberg 2010

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has stronger generalization. It is fit for solving the nonlinear or high dimensions problems with small samples. However, the learning ability of SVM depends on the values of parameter in SVM models. By now parameters selection of SVM-based classification method for remote sensing image is always determined by experience. This lead to unstable and worse classification results. So genetic algorithm is introduced to obtain optimal parameters of SVC model for multi-spectral remote sensing image in the paper. GA-based classifier can not only save time, but also improve the generalization of models.

2 Least Square Support Vector Machine (LS-SVM) 2.1 The Principle of LS-SVM Traditional SVM with the inequality constraints is based on structural risk minimization. It is used to solve nonlinear, high dimension problems with small samples. However, the computational complexity is increasing as the training samples is more. In order to decrease the computational complexity, LS-SVM is proposed. It uses ε i2 as loss function to convert the traditional SVM with inequality constraints into equality constraints. Suppose a given set has n samples. xi ∈ X = Rn and

yi ∈Y = {1,− 1} respectively denote the input and output of i-th sample.

， y )，L ，( x ， y

T = {( x1

1

n

n

)} ∈ ( X × Y ) n

(1)

Based on above set, LS-SVM can be described by the following optimal problem: ω

1 1 n 2 ω + C ∑ ε i2 2 2 i =1 y i (( ω • x i ) + b ) = 1 − ε i

min

， b， ε s.t

； i = 1，L ， n

(2)

Its dual form is: min α

1 2 n

s .t

∑

i=1

n

n

∑ ∑ i=1

y iα

y i y jα iα

j

(Φ ( x i ) • Φ ( x

j

)) −

j=1

i

n

∑

α

j

j =1

= 0

，

C ≥ α

i

≥ 0

，

， ，

i = 1 L

n

(3)

Here, C is the hyper-parameter. Its value directly influences the performance of LSSVM. So how to obtain the optimal value of hyper-parameter is a key problem. 2.2 Multi-classification Method Classification for remote sensing images using LS-SVM is a multi-classification problem in fact. However, LS-SVM is usually used in binary classification problems. So it is necessary to convert a multi-classification problem into many binary classification problems. At present, some specific methods have been given[7-9], such as One-Against-All(OAA), One-Against-One(OAO), Error-Correcting Output Code(ECOC), Minimum Output Code( MOC) and so on.

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In these methods: 1)There exists impartible area using OAA because it is asymmetric between the number of training samples belong to positive class and negative class. But the binary classifiers needed to be trained are less. 2)The impartible area is less whereas the trained binary classifiers are more when OAO is adopted. 3)When ECOC is used, the training speed is quicker. But the accuracy is inconsistent as it is repeatedly used under the same conditions. 4)MOC method is fastest, best precision and recognition rate.

3 GA-based Parameter Optimization for LS-SVM Model 3.1 Parameters Optimization for LS-SVM Model According to LS-SVM dual form shown in formula(3), we know that two parameters are needed to be optimized. They are C and kernel parameter. However, there are different kernel parameters in different kernel functions. Here, Gaussian radial basis function (RBF) is used as kernel function. Its expression is shown as follows:

K (x

，x′) = exp( − x − x′

2

σ 2)

(4)

where σ is variance. It controls radial coverage of RBF. In this paper, C and σ are parameters needed to be optimized.In order to use GA for parameter selection in LS-SVM model, the methods mentioned in Section2.2 are adopted to pre-process the training samples and test samples so as to convert multiclassification problem into binary classification problems. 3.2 Design GA Operations Code. Two parameters in LS-SVM classification method are formed into individual in genetic algorithm. Considering the optimized parameters are real-number, each individual is coded by two real-numbers shown as x = (C , σ ) . Selection Operator. Random rank selection and elitist preserved strategy are used as selection operator. Detailed selection operation is shown as follows: Step1: The individuals with the highest or lowest fitness values are finded from current population. If the best individual in current population is better than the individuals in preserved set, this individual will be saved in preserved set. Then the worst individual in current population is substituted by the best individual in preserved set. Step2: Aiming at any individual, N individuals are randomly selected from the population and compared with it. The individuals with less dominated individuals are preserved into the population in next generation. Step3: Repeated above procedure for m times, the population in next generation is obtained. Here, m is the population size.

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Crossover Operator. Arithmetic crossover operator is adopted. Two new individuals are generatd by linear combination with two individuals. Suppose two individuals are

x A (t ) , x B (t ) . The new individuals after crossover operation are: ⎧⎪ x A ( t + 1) = ax B ( t ) + (1 − a ) x A ( t ) ⎨ ⎪⎩ x B ( t + 1) = ax A ( t ) + (1 − a ) x B ( t )

(5)

where a ∈ (0,1) is constant. Mutation Operator. Non-uniform mutation operator is used. Taken C as example, '

mutation operator is shown as follow. Here, C and C denote the parameter before and after mutation. Suppose [C min , C max ] is the bound of this variable. ⎧⎪ C + Δ ( t C' = ⎨ ⎪⎩ C + Δ ( t

，C − C) ，C − C )

， ( 0， 1) = 1

if random ( 0 1 ) = 0

max

if random

min

(6)

Let y expresses C max − C or C − C min . Δ (t , y ) ∈ [0, y ] denotes stochastic number satisfying non-uniform distribution. Fitness Function. The fitness function is used to evaluate individuals. Here, error rate of LS-SVM model is used as the fitness function, expressed as follows: N

min st

f (C i , σ i ) =

∑ YP j =1

j

≠ Yj i = 1, 2 , L , m

N

C min ≤ C ≤ C max ; σ

min

≤σ ≤σ

(7)

max

where N is the number of training samples. YPj and Yj are the predictive and true classification result. [Cmin , Cmax] and [σmin,σmax] are searching bound of C and σ. Termination Condition. The genetic algorithm is stopped when the deviation satisfies a given value expressed by ε or the maximum generation is reached. Then we get the optimal solution.

4 Simulation and Analysis In order to verify the rationality of the proposed method, we apply it to the classification for remote sensing image. Aiming at the optimization model in Setion 3.1, GA-based SVC model is realized adopting MATLAB. In all experiments, we select the same training and testing samples. In multi-spectral remote sensing images, massive data information are contained. So the cultures are easy to be recognised. However, the redundant data increases the difficulty for image processing. Therefore, they need to be pre-processed. The processed original remote sensing images used in experiments are shown in Fig.1. Here, the size of each picture is 197×119.

Genetic Algorithm-Based SVC Method for Multi-spectral Remote Sensing Image

(a) band 1

(b)band 2

(e) band 5

(c )band 3

(f) band 6

217

(d)band 4

(g) band 7

Fig. 1. 7 bands of original remote sensing image

(a)Cross-validation Optimization Method We use cross-validation method to select hyper-parameters in LS-SVM classification model. Four coding methods, including OAO,OAA,ECOC,MOC are adopted. Based on ten traning samples, simulation results show in Tab 1. Table 1. Simulation result adopting cross-validation method Code

MOC

ECOC

OAA

OAO

Time(s)

62.156

91.281

137.08

334.11

In general, multi-classification problems are converted to multi-binary classification problems. According to the coding theory of multi-classifier, there are three binary classifiers needed to be trained in LS-SVM model using MOC coding method. In OAA-based classification method, seven binary classifiers are trained. Twenty one binary classifiers are trained in OAO-based classification method. However, in ECOC-based classification method, the number of decision functions expressed by L determines the number of binary classifiers. In this paper, L=4. Considering the number of training binary classifiers and the running time shown in Table 1, we know that the domination rank of above four coding methods are MOC f ECOC f OAA f OAO. It is obvious that the coding method influences the hyper-parameter selection in the model. Aiming at original multi-spectral remote sensing images in Section 4.1, the classification result adopting above four coding methods are shown in Fig 2. In all figures, the black parts are impartible. From Fig 2, we know that MOC-based classification method is the best one. There are too many impartible area using OAA and OAO coding methods. In addition, OAO coding method needs much running time. Therefore, we use MOC and ECOC to compare the classification performances.

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(a)MOC

(b)ECOC

(c)OAA

(d)OAO

Fig. 2. Classification results adopting MOC,ECOC, OAA, OAO

Taking different number of training samples, the accuracy rate of different coding methods are shown in Tab 2. Table 2. The Accuracy rate of different coding methods Number of training Data Coding method

Accuracy

10

20

OAA

MOC

OAA

MOC

0.9

0.8857

0.8786

0.9143

The classification results adopting cross-validation method with MOC and ECOC coding methods are shown in Fig 3 and Fig 4.

(a )MOC

(b ) ECOC

Fig. 3. Classification results adopting cross-validation method with MOC and ECOC(the number of training samples=10)

(a )MOC

(b ) ECOC

Fig. 4. Classification results adopting cross-validation method with MOC and ECOC(the number of training samples=20)

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From Tab 2 and Fig 3-4, we know that no matter how the accuracy rate of MOC method is, it’s classification result is much better than ECOC because there are less impartible area. Therefore, this coding method is suitable to be used in LS-SVM classification model for remote sensing images. It is obvious that the coding method used in SVC model significantly influences the classification performances for remote sensing images. (b)Comparison between cross-validation method and GA-based method. Parameters in GA-based LS-SVM classification method are shown in Tab 3. From Tab 1, we know running time of MOA-based cross-validation method is least. So we use it to compare the performance with GA-based classification method. Simulation results are shown in Tab 4. Table 3. GA’s parameters Crossover Probability

Mutation Probability

Population Size

Accuracy

Termination Generation

0.8

0.03

10

0.001

50

[Cmin, Cmax] [σmin,σmax] [1,1000]

[0,1]

Table 4. Comparison of performance between cross-validation and GA method number of training Data

10

methods

Crossvalidation

running time(s)

62.156

20

60

GA

Crossvalidation

GA

GA

9.625

290.78

19.906

173.42

It is obvious that running tims of GA-based method is less than cross-validation method aiming at the same training data. When the training data is three times to cross-validation method, GA-based method also has the better performance. Therefore, it is better to use GA to select the LS-SVM hyper-parameters. By comparing simulation results shown in Fig 5, the classification effect of methods adopting optimal hyper-parameters are better than experience-based method without hyper-parameters optimization. Through compared with Fig.1, GA-based method has the most precise classification. The impartible area is obviously less. Therefore, it is necessary to optimize the hyper-parameters in LS-SVM classification model for remote sensing images.

(a)Experience method

(b)Cross-validation method

(c) GA-based method

Fig. 5. Classification result with three methods

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In conclusion, we know that GA-based LS-SVM classification method for remote sensing images not only has less running time, but also has best classification results. It also improves the generalization of the model. So it is important for multiclassification problem to optimize hyper-parameters of SVC model and adopt suitable code method.

5 Conclusions The traditional classification methods based on asymptotic theory for multi-spectral remote sensing image need the infinite training samples, which is impossible to be satisfied. Support vector classification method based on small samples can overcome above difficulty. However, the values of hyper-parameters in SVC directly determine the method’s performance, which are randomly selected. In order to obtain the optimal parameters, genetic algorithms are introduced. Experimental results indicate that this method can not only save time for classification, but also improve the generalization of the SVC model. The new optimization method used in SVC for remote sensing image will be the next work. Acknowledgments. This work was supported by National Natural Science Foundation of China under Grant 60805025 and Qinglan Project of Jiangsu.

References 1. Du, F.L., Tian, Q.J., Xia, X.Q.: Expectation and Evaluation of the Methods on Remote Sensing Image Classifications. Remote Sensing Technology and Application 19, 521–524 (2004) 2. Zhou, F., Pan, H.P., Du, Z.S.: The classification of RBF neural network based on principal component analysis to multispectrum satellite remote-sensing images. Computing Techniques for Geophysical and Geochemical Exploration 30, 158–162 (2008) 3. Yang, Z.S., Guo, L., Luo, X., Hu, X.T.: Research on segmented PCA based on ban selection algorithm of hyperspectral image. Engineering of Surveying and Mapping 15, 15–18 (2006) 4. Liu, Q.J., Lin, Q.Z.: Classification of remote sensing image based on immune network. Computer Engineering and Application 44, 24–27 (2008) 5. Tan, K., Du, P.J.: Hyperspectral Remote Sensing Image Classification Based on Radical Basis Function Neural Network. Spectroscopy and Spectral Analysis 28, 2009–2013 (2008) 6. Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995) 7. LI, X.C.: A Remote-sense Image Classification Technology Based on SVM. Communications Technology 42, 115–117 (2009) 8. Mathur, A., Foody, G.M.: Multiclass and binary SVM classification: Implications for training and classification users. Geoscience and Remote Sensing Letters 5, 241–245 (2008) 9. Gou, B., Huang, X.W.: SVM Multi-Class Classification. Journal of Data Acquisition & Processing 21, 334–339 (2006)

Grids-Based Data Parallel Computing for Learning Optimization in a Networked Learning Control Systems* Lijun Xu, Minrui Fei1,**, T.C. Yang2, and Wei Yu3 1

Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, Shanghai 200072, China 2 University of Sussex, UK 3 CSK Systems(Shanghai) Co., LTD, Shanghai 200002, China [email protected], [email protected], [email protected], [email protected]

Abstract. This paper investigates a fast parallel computing scheme for the leaning control of a class of two-layered Networked Learning Control Systems (NLCSs). This class of systems is subject to imperfect Quality of Service (QoS) in signal transmission, and requires a real-time fast learning. A parallel computational model for this task is established in the paper. Based on some of grid computing technologies and optimal scheduling, an effective scheme is developed to make full use of distributed computing resources, and thus to achieve a fast multi-objective optimization for the learning task under study. Experiments of the scheme show that it indeed provides a required fast on-line learning for NLCSs. Keywords: Grids, Parallel computing, Optimization, Real-time.

1 Introduction A networked control system (NCS)[1] is the control system whose sensors, actuators and controllers are closed over communication networks, which has been widely used in control field due to various advantages including modular system design with greater flexibility, low cost of installation, powerful system diagnosis and ease of maintenance. We have already proposed two-layer networked learning control system (NLCS[2-3]) architecture that is suitable for complex plants. Due to complexity and varieties of data sources, learning agents consume a large amount of computing resources and cannot satisfy real-time [4] requirements. Grid as a shared service-oriented computing is becoming a focus, which has more powerful computing capabilities, having broad application prospects [5]. Here, grid computing *

This work is supported by National Natural Science Foundation of China under Grant 60774059, the Excellent Discipline Head Plan Project of Shanghai under Grant 08XD14018, Shanghai Science and Technology International Cooperation Project 08160705900 and Mechatronics Engineering Innovation Group project from Shanghai Education Commission. ** Corresponding author. K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 221–232, 2010. © Springer-Verlag Berlin Heidelberg 2010

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is established into two-layer NLCS to meet real-time and QoS requirements of the system through learning scheduling tasks parallelization and fast grid computing. Genetic algorithm (GA) [6] is a class of stochastic optimization inspired by the behavior of Darwin organic evolution. To improve the performance of original GA and avoid trapping to local excellent situations, we construct a new quantum solutions expression and adaptive crossover and mutation probability for multi-objective optimization to seek the optimal decision of network resources allocation. The rest of the paper is organized as follows: Section 2 introduces a two-layer architecture networked control system. Section 3 presents a learning scheduling optimization scheme and efficient solving method of quantum-inspired adaptive genetic algorithm. Section 4 establishes learning task parallel computing. Section 5 provides the experimental results. Finally, a brief conclusion is given in Section 6.

2 System Description In this paper, two-layer networked learning control system architecture [2-3] is introduced as shown in Fig.1,with the objectives to achieve better control performance, better interference rejection and to increase adaptability to varying environment. Local controller connects with sensors and actuators, which are attached to the complex plant via the bottom layer communication network, typically some kind of field bus dedicated to real-time control. Local controller also communicates with computer system which typically functions as a learning and scheduling agent through the upper layer communication network. The general architecture can be used in many industrial applications for distributed plants especially in power systems.

Fig. 1. Two-layer networked learning control system (NLCS)

The learning and scheduling agent update knowledge continuously online, finding the underlying laws. Online optimization improved control performance. Because of the complexity of learning control algorithm and consumption of a large number of

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computing resources, and network is typically some kind of existing local area network (LAN), wide area network (WAN), or possibly the Internet, network service quality (QoS) and delay are uncertainties, real-time requirements are not satisfied. Grid and grid scheduling, to some extent, can integrate these network nodes over the existing IT architecture to achieve dynamically sharing and collaboration of CPU, memory and database resources. Through the parallel task scheduling and grid services, the learning and scheduling unit in upper layer network reached high-speed computing to enhance service performance and real-time requirements.

3 Optimization of Networked Learning Control System The scheduling of a NLCS mainly allocates network resources and schedules the information transmission of control loops. Using the scheduling scheme, the control system may satisfy the requirements of real time and some restricted control tasks. In addition, it can ensure that the information of control tasks is transmitted during a certain communication time in order to improve the network utilization. 3.1 Multi-objective Optimization Problem in NLCS Multi-objective optimization(MOO) method dynamically adjusts the sampling of each loop, and using possible smallest bandwidth requirements to achieve optimal control performance. The MOO problem according to [7] with described rules becomes:

min

n

n

i =1

i =1

J = ∑ (α i + β i ti ) + γ i ∑ bi

(1)

subject to C T b ≤ U d (1 − ω )

(2)

bimin ≤ bi ≤ bimax

(3)

bi = bimin , if ei ≤ eith

(4)

We use Rights Law compounding system control performances called integral absolute error (IAE) and bandwidth consumption, aiming at minimize demand for bandwidth under the best system performance to the single-objective function. Where γ i is the weight coefficient. (2) is global availability of bandwidth in NLCS, where

b = [ b1 , b2 " bn ] , C = [1,1, " ,1] and percentage ω is introduced which is the T

T

proportion of network bandwidth reserved for other functions. (3) describes bandwidth consumption of subsystem

bi is bound by [bimin , bimax ] . Some expert

knowledge[8] is applied to the rules as part of constraints. Control loops require only

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less bandwidth to maintain the transmission of information near the equilibrium point.

eith expresses a sufficiently small error thresholds of the i th control loop. Obviously, the conventional mathematical programming is very difficult to solve the optimization problems and achieving real-time except some heuristic modern optimization algorithms. In this paper, an adaptive genetic algorithm will be given to solve the multi-objective scheduling optimization problem and data parallelization and grid computing technology will be utilized to achieve real-time control in NLCS. 3.2 Solving Method of A Quantum-Inspired Adaptive Genetic Algorithm In the analysis of network load distribution, the key is to find a optimal allocation scheme for subsystems. Genetic Algorithm (GA)[9] imitates biological evolution based on natural selection, which is a stochastic optimization method of biological evolution process imitation. Due to the adaptation of nonlinear multi-objective optimization and characteristics of parallelizable, we present a quantum-inspired adaptive genetic algorithm to solve the above optimization problems in NLCS. The crossover probability Pc and mutation probability Pm of our adaptive genetic algorithm are respectively:

⎧ b3 ( f max − f ' ) ' ⎧ b1 ( f max − f ) , f ≥ f , f ≥ f avg avg ⎪ ⎪ Pc = ⎨ f max − f avg , Pm = ⎨ f max − f avg ⎪b , ⎪b , f < f avg f ' < f avg ⎩ 2 ⎩ 4 Where

(5)

f max is the largest fitness value of population, f avg is the average , f the

larger fitness value in two individuals for crossover, for mutation and

f ' is fitness value of individuals

b1 , b2 , b3 , b4 are empirical constants. The crossover and mutation

probability of adaptive GA can automatically change with fitness. From the perspective of quantum mechanics, a new genetic algorithm model is proposed. This model is based on the DELTA potential, which has quantum behavior. The new genetic algorithm is simple and easy to achieve and have advantages of less adjustable parameters, with good stability and convergence. The basic unit of information in quantum computation [10] is the qubit. A qubit is a two-level quantum system and can be represented by a unit vector of a two dimensional Hilbert space

(α , β ∉ ^) :

ψ =α 0 + β 1 ,

α + β =1 2

2

(6)

The state of a qubit can be changed by the operation with a quantum gate. Inspired by the concept of quantum computing, PSO is designed with a novel Q-bit

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representation, a Q-gate as a variation operator, and an observation process. A Q-bit individual as a string of n Q-bits is defined as (7).

⎡α tj1 α tj 2 α tjm ⎤ q =⎢ t t " t ⎥ ⎢⎣ β j1 β j 2 β jm ⎥⎦ t j

(7)

In this paper, PSO use the appropriate Q-gate, by which operation the Q-bit should be updated as the step of mutation. The following rotation gate is used as a Q-gate in PSO, such

⎡cos(Δθ ) − sin(Δθ ) ⎤ U (Δθ ) = ⎢ cos(Δθ ) ⎥⎦ ⎣sin(Δθ )

(8)

θi = s(α i , βi ) × Δθi

(9)

1 (α i∗ , β i∗ )

Δθ

(α i , βi )

0

Fig. 2. Polar plot of the rotation gate for qubit individuals

⎡α i∗ ⎤ ⎡α i ⎤ ⎡ cos(Δθi ) − sin(Δθi ) ⎤ ⎡α i ⎤ ⎢ ∗ ⎥ = U (Δθi ) ⎢ ⎥ = ⎢ cos(Δθi ) ⎥⎦ ⎢⎣ β i ⎥⎦ ⎢⎣ β i ⎥⎦ ⎣ βi ⎦ ⎣sin(Δθi )

(10)

Where Δθ is a rotation angle of each Q-bit toward state depending on its sign. 3.3 Parallel Task Model Data parallel calculation mode[11] is single program multiple data (SPMD). The parallel task load of parallelizable quantum-inspired adaptive genetic algorithm will be divided into finite tasks, which were the smallest division of original mission, being mapped to independent resources and no causal relationship implementation.

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Fig. 3. Dynamic Data Parallel Task Model

Figure 3 shows the dynamic data parallel mode. Subtask segmentation unit is responsible for a clear delineation of rules, who divides total task into sub-task groups. Subtask scheduling unit provides allocation mapping for each subtask execution unit. Subtask execution unit processes sub-task groups and send results to integration unit. Subtasks integration unit receive all the partial results from subtask execution units and collecting using the analysis results to assembly achieve specific application logic. Reasonable population Individual evaluation parallel computing achieved distributed desktop systems and cluster resource sharing.

4 Grids 4.1 Grid Model Grid system is defined as finite set

R in available grid computing resource M :

R = {R1 , R1 ," , RM }

Fig. 4. Grid Services Architecture

(11)

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Under the condition of performance and time constraints, parameters of resources depend on the executive function of specific subtasks and computational complexity. Grid computing resources are multi-site and distributed workstations, parallel machines or clusters connected through the wide area network to achieve local and remote applications. Figure 4 shows the services architecture of the grid resources. If the number of subtasks is ni ∈ N 0 and resource is Ri , Tpi is processing time :

Tpi = pi + t pi ni Where

(12)

pi is the execution initial offset and t pi is the proportionality constant of

processing time and the scale of sub-mission among allocate resources. We get the communication time:

Tci = di + tci ni Where

(13)

d i is the communication initial offset and tci is the proportionality constant

of execution time and the scale of sub-mission among allocate resources. Therefore, we will obtain the total execution time Ti as follows:

Ti = Tpi + Tci = pi + d i + t pi ni + tci ni = ( pi + di ) + (t pi + tci )ni

(14)

⎧e + t n with ni > 0 ⇒ Ti = ⎨ i i i , ei = pi + d i , ti = t pi + tci with ni = 0 ⎩0

(15)

4.2 Grid Matching Strategy Scheduling server served as a provider to achieve job service, which needed to make rational use of the grid resources needed to complete the job request that the users submitted. Scheduling is composed by multiple independent processes and each process periodically checks the database state to check the task partitioning, scheduling, results validation, results of integration and delete files and so on. MultiQoS constraints based grid selection task scheduling approach packaged the individual fitness evaluation process into moderate-sized independent task unit to assign to computing nodes, achieving the control of the multi-objective genetic algorithm implementation process. (1) Tasks Division Scheduling server divides the population of each generation and allocates computing nodes to each individual through the real-time requirements. (2) Processing the Requests of Computing Nodes The daemons of computing nodes send timing requests to the scheduling server. The server returns a response message after receiving the request, which contains a set of tasks unit descriptions and URL address of related data files. According to this

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address, computing nodes download the specified file of objective function value at the local calculation via the standard HTTP protocol. When task is completed, results are automatically uploaded to the server, and at the same time sending a request to the server to apply for a new task unit. (3) Multi-QoS Constraints Based Grid Choice Task Scheduling Tasks with QoS requirements are of different groups, processing according to their QoS levels. Relatively high QoS of tasks always have the higher priority to access to resources, avoiding low QoS tasks occupy resources given to high QoS task which may lead to be forced to wait in a queue for the higher one. According to the Prediction of system performance, we obtain the expectations of the completion time and its standard deviation for the tasks in different groups which meet the requirements of QoS, then calculated relative standard deviation on the overall mean value by the standard deviation value. Relative standard deviation can effectively express the dispersion of the task. Min-Min algorithm is utilized scheduling system when the degree of dispersion is relatively small; while large, the scheduler option is of using Max-Min algorithm. Finally, different QoS groups via cycle and round robin selection get a QoS guided more excellent performance Min-Min results. (4) Implement of Optimal Control Algorithm Scheduling server traces the task units and the corresponding results of the state track records in the database. Once checked the state change, the scheduling server send them to the appropriate processes to deal with and sort out the results after finishing calculating all the objective functions. Scheduling server decide whether to produce the next generation or sort, starting a new round of iteration according to the above results. Optimized shape parameters are satisfied within a reasonable range.

5 Experimental Analysis In this section, we present the experimental analysis and results in order to operate and evaluate scheduling optimization strategy and show the validity of quantuminspired adaptive genetic algorithm in NLCS. Also we compared the effectiveness of parallel computing grid with no introducing condition.

Fig. 5. Experimental Network Topology

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Table 1. System Configuration of Grid Computing Resource Nodes Grid Nodes

Learning Unit 2 Intel E3200 2.4G

Scheduling Server Intel Xeon 2.0

OS

Learning Unit 1 Intel Core(TM)2 Quad Q8300 @ 2.5GHz 4GB SATA 600G 10M/100M Adaptive RHEL 5

2GB SATA 320G 10M/100M Adaptive RHEL 5

4GB 200G Raid 1 Dual NIC 100M RHEL 5

Software Virtualization

JDK1.5 GT4 No

JDK1.5 GT4 No

JDK1.5 GT4 No

IP

218.242.4.25

58.198.109.24 7

222.66.167.22 9

CPU

RAM HD NIC

Grid resources Intel Xeon 2.3

8GB 300G Raid 1 Dual NIC 100M Windows Server 2008 JDK1.5 GT4 Hyper-V (2 nodescluster) 222.66.167.230~32

Network topology of the experimental operating environment is shown in Fig. 5, using four computers (Table 1) as the data nodes and computing nodes which are configured in three different network segments of Internet. Two hosts are distributed learning units who act as grid tasks clients. Meanwhile the hosts deploy parallel computing-related services in the grid service container. Therefore, the learning units are both clients and computing resources. The scheduling server manages grid service with the installation for the Web server of Apache Tomcat v5.0. Another computer runs three virtual machines via Hyper-V management as grid resources nodes. Globus Toolkit4 GT4 grid platform is utilized in the experimental environment. For quantum-inspired adaptive genetic algorithm, the number of individuals takes 50 and the maximum evolutionary generation is 500. The crossover probability coefficients are b1 = 0.5, b2 = 0.9 and mutation ones are b3 = 0.02, b4 = 0.05 ,

（ ）

Discrete accuracy is set 0.01 in the test environment. Table 2. Dynamic Process Simulation of Grid Computing Resource Nodes

Time 5s 10s Virtual Machine(Grid Nodes) 1 √ √ 2 √ √ 3 √

15s

20s

25s

30s

√

√ √

√ √ √

√

The first experiment sticks to 50 population size to the requirements of quantuminspired adaptive GA. We test the resources of grid nodes on one host of virtual machines(VM). Table 2 established whether the VM is available online, servering as a grid node in the experimental time, where “√” means the VM is working.

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Figure 6 shows the resources utilization of all grid nodes for the corresponding experiments time. Dimension of longitudinal coordinates is percentage, which expresses the resource occupancy. We test 6 different switching states, simulating the dynamic process of grid nodes, that is, new entrants to grid nodes and unexpected circumstances for the offline grid node machine and cannot be used as grid resources.

Fig. 6. Resources utilization of grid nodes for six states

Figure 7 is the timing diagram of total resource consumption for the three virtual hosts, simulating the above experimental conditions of the rate for total grid resources nodes, which reflects the service capability of dynamic grid, that is, resources providing capacity for the client requests in the circumstances of the dynamic changing of grid nodes. In the case of one to three working fictitious host computer respectively, we can see the output overall resource utilization held stationary.

Fig. 7. Total resources utilization of all grid nodes

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Table 3. Parallel computing grid optimization results comparison

Parallel grid number (population size 50) 1 2 3 Population size (the number of parallel grid is 3) 10 30 MPI (Population size is 50 and the number of parallel grid is 3)

Optimizati on time (s) 12.906s 8.456s 6.834s

Network utilization 23.8% 30.4% 34.7%

4.872s 5.768s

33.1% 33.5%

8.936s

26.8%

Statistical results (Table 3) show that the average efficiency achieved 30.5% under the grid environment and meanwhile the number of parallel efficiency increases varying with the increase of population. Through the experiments, we found advantages of GT4-based grid data parallel computing for optimization in NLCS are: (1) Fast calculation and can realize real time; (2) High-performance computing resources in wide area network is utilized for distributed coordination; (3) A reasonable division of tasks and dynamic computing nodes designation for those different computational tasks can reasonably be allocated to appropriate computing nodes; (4) No extra trenchant demanding in the configuration. Relative to the parallel computing tools MPI, grid-based platform for parallel processing have been improved of its limitations. The top advantage of the designed grid computing platform based parallel optimization service are achieving learning optimization parallel online computing on wide-area specifically for the characteristics of wide-area. Meanwhile, grid monitoring components can real-time monitor and register the performance of all computing nodes in grid system, providing suitable computational capabilities for parallel computing and a rational allocation of computing tasks to computing nodes. Grid service is proved to improve QoS and real time of the system.

7 Conclusion An integrated optimization design of grid based data parallel computing in a twolayer architecture networked learning control system is proposed. After the establishment of learning task parallel computing model, distributed computing resources are integrated into high-performance computing environment via grid technology and optimization scheduling. Approached to grid services, we realized multi-objective optimization and grid fast computing, solving the problems of data parallel computing, learing real-time and network QoS in two-layer NLCS. Experimental results show the scheme improves the network utilization and control

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performance of the system .Consequently, our next steps are proposing more efficient algorithm and considering some uncertainties and more restrictive conditions in grid model, such as such as limited time and cost grid, heterogeneous network of Windows and Linux, virtualization, multi-task concurrency and internet-based grid security requirements, intending to solve more complex and time-consuming problems according to reality in NLCS.

References 1. Yang, T.C.: Networked control system: a brief survey. IEEE Proc.-Control Theory Appl. 153, 403–412 (2006) 2. Du, D.J., Fei, M.R., Li, K.: A two-layer networked learning control system using actorcritic neural network. Applied Mathematics and Computation 205, 26–36 (2008) 3. Du, D.J., Fei, M.R., Hu, H.S.: Two-layer networked learning control using self-learning fuzzy control algorithms. Chinese Journal of Scientific Instrument 28, 2124–3131 (2007) 4. Battisha, M., Elmaghraby, A.: Adaptive tracking of network behavioral signals for real time forensic analysis of service quality degradation. IEEE Transactions on Network and Service Management 5, 105–117 (2008) 5. Grimshaw, A., Morgan, M.: An Open Grid Services Architecture Primer. IEEE Computer 42, 27–34 (2009) 6. Dieter, D.: A Decomposition-Based Genetic Algorithm for the Resource-Constrained Project-Scheduling Problem. Operations Research 55, 457–469 (2007) 7. Xu, L.J., Fei, M.R.: A Hybrid Quantum Clone Evolutionary Algorithm-based Scheduling Optimization in a Networked Learning Control System. In: Proceedings of the 22th Chinese Control and Decision Conference (CCDC 2010), Xuzhou, China (2010) 8. Li, Z.X.: Optimal control and scheduling of system with resource constraints. Control Theory & Applications 26, 97–102 (2009) 9. Wang, C.S., Chang, C.T.: Integrated Genetic Algorithm and Goal Programming for Network Topology Design Problem With Multiple Objectives and Multiple Criteria. IEEE Transactions on Networking 16, 680–690 (2008) 10. Andrea, M., Enrico, B., Tommaso, C.: Quantum Genetic Optimization. IEEE Trans. on Evolutionary Computation 12, 231–241 (2008) 11. Nadia, R.: Time and Cost-Driven Scheduling of Data Parallel Tasks in Grid Workflows. IEEE Systems Journal 3 (2009)

A New Distributed Intrusion Detection Method Based on Immune Mobile Agent* Yongzhong Li1, Chunwei Jing1, and Jing Xu2 1

School of Computer Science and Engineering, Jiangsu University of Science and Technology 212003 Zhenjiang, China 2 College of Information Engineering,Yancheng Institute of technology,Yancheng, China [email protected]

Abstract. Intrusion detection system based on mobile agent has overcome the speed-bottleneck problem and reduced network load. Because of the low detection speed and high false positive rate of traditional intrusion detection systems, we have proposed an immune agent by combining immune system with mobile agent. In the distributed intrusion detection systems, the data is collected mostly using distributed component to collect data sent for processing center. Data is often analyzed in the processing center. However, this model has the following problems: bad real time capability, bottleneck, and single point of failure. In order to overcome these shortcomings, a new distributed intrusion detection method based on mobile agent is proposed in this paper by using the intelligent and mobile characteristics of the agent. Analysis shows that the network load can be reduced and the real time capability of the system can be improved with the new method. The system is also robust and fault-tolerant. Since mobile agent only can improve the structure of system, dynamic colonial selection algorithm is adopted for reducing false positive rate. The simulation results on KDD99 data set have shown that the new method can achieve low false positive rate and high detection rate. Keywords: Immune agent; Mobile agent; Network security; Distributed intrusion detectiont.

1 Introduction An intrusion detection system (IDS) is used to detect unwanted attempts at accessing, manipulating, and disabling computer system by either authorized users or external perpetrators, mainly through a network, such as the Internet. The IDS responds to the suspicious activity by resetting the connection or by reprogramming the firewall to block network traffic from the suspected malicious source [1]. It can remedy the deficiency of firewall effectively. Intrusion detection has experienced four stages: based on host, based on multihosts, based on network, and based on distributed intrusion detection. Traditional *

This paper is supported by Research fund of University of Jiangsu Province and Jiangsu University of Science and Technology’s Basic Research Development Program (No. 2005DX006J).

K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 233–243, 2010. © Springer-Verlag Berlin Heidelberg 2010

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intrusion detection systems are centralized and based on a monolithic architecture. Data are collected on a single machine by looking at log files or network flow and are analyzed on a single computer, which has some defects both in the structure and in the detection technology. So distributed intrusion detection system (DIDS) appears. It becomes a research focus in the field of intrusion detection. Reference [2] presented a distributed information-gathering step, but centralized on analyzing process. The Graph-based Intrusion Detection System (GrIDS) [3] and Event Monitoring Enabling Responses to Anomalous Live Disturbances (EMERALD) [4] are IDS that use a hierarchical approach in a more sophisticated way. The hierarchical approach seems to show better scalability by allowing local analyses at distributed monitoring areas. However, a monitor operating at the highest level may induce single point of failure. When the topology of current network is changed, it causes a change of network hierarchy, and the whole mechanism for aggregation of local analysis reports must be changed. Autonomous Agent for Intrusion Detection (AAFID) is the first attempt to use autonomous agents for network intrusion detection by Spafford and Crosbie in [5]. In AAFID, nodes of the IDS are arranged in a hierarchical structure in a tree. Agents in AAFID were not mobile. Current DIDS mostly use distributed component to collect data, and then send collected data to processing center. These models solve the problem of distributed data acquisition effectively in wide bandwidth network. However, they have bad real time capability, bottleneck problem, and single point of failure because of the central processing node. The above-mentioned problems can be solved by utilizing the intelligent, mobile, and self-adaptive characteristics of agent and its distributed collaborative calculation capability [6] − [7]. False positive rate and false negative rate are other import aspects that IDS must consider. In [8], the authors stated similarities between the defenses of natural immune systems and computer security: both must discriminate self and non-self to protect a complex system from inimical agent. Be inspired of immune system, Kim and Bentley in [9] have proposed dynamic clonal selection algorithm and shown that this algorithm could reduce false positive rate. In this paper, dynamic clonal selection algorithm is adopted. Detectors are embedded in agents. With their communication mechanism, detection agents can detect cooperatively. Using the mobile characteristic of agent, detection agent can move to local host, and thus it can reduce network load and improve real-time capability. The model is full distributed. The rest of the paper is structured as follows: In section 2, we study about Immune system and mobile agent. The overall design model based on immune mobile agent is described in Section 3. Simulation results are shown in Section 4. Section 5 is the conclusions.

2 Relative Knowledge 2.1 Immune System The immune system [10] − [13] is a complex network of organs and cells responsible for the organisms defense against alien particles. Among a large number of different

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innate and acquired cells, lymphocytes play a central role. Lymphocytes are classified into two main types: B-cells and T-cells. B-cells are antibody-secreting cells and T-cells kill antigens or help or suppress the development of B-cells. Both originate from bone marrow, and they are developed by the bone marrow and the thymus, respectively. Before leaving the bone marrow and the thymus, maturing B- and T-cells have to pass the last test-negative selection. Mature B- and T-cells that pass the negative selection are released from the bone marrow and thymus, respectively. The development of B-cells and T-cells are shown in Fig. 1.

Fig. 1. Development of B-cells and T-cells

Both B-cells and T-cells continuously circulate around the body in the blood and encounter antigens for activation and evolution. The antibodies of B-cells, which recognize harmful antigens by binding to them, are activated directly or indirectly. When B-cell antibody receptors bind to antigen epitopes with strong affinity above a threshold, they are directly activated. When B-cell antibody receptors fasten to antigen epitopes with weak affinity, MHC molecules try to find some hidden antigens inside cells. When MHC molecules find them, they transport them on the surface of B-cells. The receptors of T-cells are genetically structured to recognize the MHC molecule on the B-cell surface. When the T-cell binds to an MHC molecule with strong affinity, it sends a chemical signal to the B-cell, which allows it to activate, grow, and differentiate. Clonal selection is immediately followed with B-cells activate. The more specific antigens B-cells bind to, the more chance being selected for cloning they have. When antigens activated B-cells, they produce memory cells for the reoccurrence of the same antigens in the future. Therefore, the secondary response is quickly. Fig 2 shows the generation of memory cells via clonal selection of B-cell, which are direct activated and indirect activated, respectively.

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Fig. 2. Generation of memory cell

2.2 Mobile Agent Mobile agent is a type of software agent, with the feature of autonomy, social ability, learning, and most import, mobility [14]. Mobile agent can transport its state from one environment to another with its data intact and still be able to perform appropriately in the new environment. When a mobile agent decides to move, it saves its own state, transports this saved state to the next host and resumes execution from the saved state. Fig. 3 illustrates the work processing of mobile agent.

Fig. 3. Work processing of mobile agent.

Mobile agent has many advantages. Mobile agent makes computation move to data, it can reduce network load. Because the actions are dependent on the state of the host environment, it is dynamic adaptation. It can operate without an active connection between client and server, so it has the capability of faults tolerance to network. Because of the mobility and cooperative of agent, mobile agent has extensive application range, such as network management, information retrieval. However, communication security is a problem that must face. It can be solved by encrypting when transfer. This is not belonging to the range of discussion of this paper.

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Mobile agent neither brings new method to detect for IDS nor increases detection speed for some kind of attracting. Nevertheless, it improves the design, construct, and execute of IDS obviously.

3 The Intrusion Detection Model Based on Immune Mobile Agent 3.1 System Architecture Be inspired of immune system, this paper combines immune mechanism with mobile agent, and constructs some immune agents to monitor and detect attraction on the network. Each immune agent can be regarded as immune cell. Like B-cells and Tcells circulating around the body in the blood and preventing the body by suppressing or killing the foreign invaders, immune agents roam on the network, and monitor and detect attacking. Fig.4 presents the architecture of intrusion detection based on immune mobile agent. It composes of central control agent (C-agent), detection agent (B-agent), memory agent (M-agent), and response agent (K-agent). C-agent runs in the server and plays a role of manger. B-agent and M-agent travel though the network in order to detect attacking. If any attacking is detected by B-agent or M-agent, K-agent is activated and responds to it immediately.

Fig. 4. Architecture of intrusion detection system based on immune agent

The function of each component in this model is described as follows: C-agent. C-agent is a kind of agents, which mainly manage, coordinate, and control roaming agent on the network. Its function is similar to that of bone marrow and thymus. It can create, dispatch, and recall agent. Once B-agent is created, it can work continually without the connection between server and client. Although we adopt server and client model, it does not induce single point of failure.

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B-agent. Each B-agent contains a set of mature detectors. The function of B-agent is similar to that of B-cells. B-agent strays on the network to monitor intrusion. If antigen comes, B-agent is activated, and it will move to the local host to detect whether intrusion occurs. M-agent. Each M-agent contains a set of memory detectors. It imitates the mechanism of secondary response in immune system. If antigen comes and M-agent exists, M-agent is activated, and they will be detected by M-agent firstly. If it does not match these antigens, B-agent will detect continually. It can improve the speed of detecting known intrusion. K-agent. The function of K-agent is analogous to that of T-cells. If any intrusion is detected by B-agent or M-agent, K-agent will be activated immediately. It will act in response to it by disconnecting suspicious connection, locking account, or restricting login. Collect-agent. The function of collect-agent is to collect data, which are foundation of intrusion detection system. It can collect data based on host and based on network. Collect-agent in this paper mainly captures network packet. In order to improve efficiency of detection, collect-agent needs to extract useful property of data packet besides of capturing data packet. 3.2 Generation of Detectors Detectors play an important role in intrusion detection. The more attacking features these detectors have, the higher detection rate the system has. The less normal network features these detectors contain, the less false positive rate the system has. Kim presents dynamic clonal selection algorithm and experiment shows it can reduce false positive rate with high detection rate [9]. When detectors are generated, they are embedded in mobile agent. Suppose that there are N mature detectors in total and each B-agent can carry n detectors, the system will generate ⎡⎢ N / n ⎤⎥ B-agents. These agents with detectors roam on the network and realize the distributed computing. The dynamic selection algorithm is described in detail as follows: Step1: create an immature detector population with random detectors, and perform negative selection by comparing immature detectors to self-antigens. Because of negative selection, the immature detectors binding any self-antigen are deleted from the immature detector population and then new immature detectors are generated until the number of immature detectors becomes the maximum size of a non-memory detector population. The same processes continue for the tolerance period (T) number of generations. When the total number of generations reaches T, some immature detectors whose age reaches T, which were born at generation 1, become mature detectors. Step2: at generation T+1, mature detectors start to detect new antigen set. If any mature detector matches an antigen, the match count of a mature detector increases by one. After all the given antigen are compared with all the existing mature detectors, the system will check whether the match counts of mature detectors are larger than a

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pre-defined activation threshold (A) and whether the ages of mature detectors meet a pre-defined life span (L). If the match count of a mature detector is larger than A, it becomes a memory detector. If the age of a mature detector meets L, the mature detectors are deleted from the mature detector population. Any antigens detected by activated mature detectors are deleted, and the remaining antigens are presented to the immature detectors for negative selection. If the number of existing immature detectors and mature detectors is less than the maximum size of a non-memory detector population, generate immature detectors with random detectors until they are equal. Step 3: at generation T+2, when memory detectors match any antigen and the detected antigen bind any self-antigen, the memory detector are added to immature detectors. In addition, if the detected antigen does not bind self-detectors, it is removed directly. The remaining antigens are matched by mature detectors and the process is the same as the period of T+1.

4 Simulations 4.1 Design Guidelines In this section, we present the details of results on KDD 99 data set, and the achieved false positive rate and detection rate. Data sets. In order to survey and evaluate research in intrusion detection, the 1998 DARPA Intrusion Detection Evaluation Program was managed by MIT Lincoln Labs. Lincoln Labs set up an environment to acquire nine weeks of raw TCP dump data for a local-area network (LAN) simulating a typical U.S. Air Force LAN. They operate the LAN as if it was a true Air Force environment, but peppered it with multiple attacks. KDD99 data set is the data set, which was obtained from the 1998 DARPA. The data set is composed of a big number of connection records. Each connection is labeled as either normal or as an attack with exactly one specific attack type. Attacks in the data set can be classified into four main categories namely Denial of service (DOS), Remote to User (R2L), User to Root (U2R) and Probe. In our experiment, we only used 10 percents of the raw training data (kddcup.data_10_percent) for training and the test data set (corrected.gz) for testing. It is important to note that the test data is not from the same probability distribution as the training data, and it includes specific attack types not in the training data. The test data contains of 20 types of training attack and 17 types unknown attacks. The 37 types attacks are classified into four categories as follows: DOS: {back, land, Neptune, pod, smurf, teardrop, processtable, udpstorm, mailbomb, apache2} R2L: {ftp_write, guess_passwd, imap, multihop, phf, warezmaster, sendmail, xlock, snmpguess, named, xsnoop, snmpgetattack, worm} U2R: {buffer_overflow, loadmodule, perl, rootkit, xterm, ps, httptunnel, sqlattack} Probing: {ipsweep, nmap, portsweep, satan, mscan, saint} For each connection, there are 41 features. Among them, 32 features are continuous variables and 9 features are discrete variables. Table 1 demonstrates the network data

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feature labels. Among these features, some are redundant and some contribute little to the intrusion detection process [15]–[16]. Considering efficiency, we select features 1, 2, 3, 5, 6, 7, 8, 9, 15, 16, 18, 19 and 20 to compose of detector and choose statistical features 20 to 41 except for 30 to be collaborative signal. Among the aforementioned features, 1, 5, 6, 8, 9, 16, 18, 19, 20 and all-statistical features are continuous. We should make them discrete. Take the feature of src-bytes for example: we can use much less, less, normal, more and much more to express bytes from source to destination. Moreover, the value of them is 000, 001, 010, 011, and 100, respectively. Fig. 5 shows its membership functions. Table 1. Network data feature labels Label 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Network data Network data Label Label Network data feature feature feature duration 15 su_attempted 29 same_srv_rate protocol-type 16 num_root 30 diff_srv_rate service 17 num_file_creations 31 srv_diff_host_rate flag 18 num_shells 32 dst_host_count src_bytes 19 num_access_files 33 dst_host_srv_count dst_bytes 20 num_outbound_cmds 34 dst_host_same_srv_rate land 21 is_host_login 35 dst_host_diff_srv_rate wrong_fragment 22 is_guest_login 36 dst_host_same_src_port_rate urgent 23 count 37 dst_host_srv_diff_host_rate hot 24 srv_count 38 dst_host_serror_rate num_failed_login 25 serror_rate 39 dst_host_srv_serror_rate logged_in 26 srv_serror_rate 40 dst_host_rerror_rate num_compromised 27 rerror_rate 41 dst_host_srv_rerror_rate root_shell 28 srv_rerror_rate

p( x − μ ≥ ε ) ≤

σ2 ε2

(1)

According to Chebyshev's inequality (1) and the proportion of normal and attack data in KDD99, the values of variables in Fig. 5 are shown as follows: a = μ − 2σ

， b = μ − σ ， c = μ ， e = μ + σ ， d = μ + 2σ

(2)

For all collaborative signals, we use normal, suspicious and abnormal to express them, and the process is the same as the above. The value is 00,01 and 10 respectively. When the inherence character of the detector matches one antigen, this antigen is not always pathogen. Only in the abnormal circumstance, which is likely induced by it, it will be considered an attack. That is why the collaborative signals are adopted in this paper. When a detector matches an antigen, and there is an abnormal or suspicious feature in the collaborative signals, this antigen will be taken for an attack. Otherwise, it will be taken for a normal behavior. Considering possibility of incomplete studying, for the sake of reducing undetected rate, when the number of abnormal and suspicious feature exceed threshold, the antigen will be taken for attack behavior.

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This paper implemented on IBM’s aglet toolkit, which is composed of a set of java-based mobile software agents that carry out specific tasks on the network and collaborate on the problem of network intrusion detection. In the simulation, aglet is installed in three computers. Among them one is as sever, and others are as clients. When detectors are generated, they are embedded in agents. Utilizing aglet, agents can be dispatched, cloned, and recalled.

Fig. 5. Features of detector

4.2 Simulation Results Test of Robust and Fault-tolerant of the system. When the system is start-up, Bagent in one host is broken off in order to observe its effect to the system. Experiment shows that system can discover the invalidated agent and then create and dispatch new agent to this host. One node invalidate does not induce disability of the system. This indicates that the system is robust and fault-tolerant. Detection result. The size of non-memory detectors is defined as 100000, the training data is divided into self-antigen set and non-self antigen set. In addition, in our experiment, self-antigen set and non-self antigen set are classified into four antigen clusters. Moreover, the iterative generation is set 200. Analysis shows that the value of T is inversely proportional to detection rate and false negative rate. The larger value of T equals the less activated detectors the system has. However, if the value of T is small, immature detectors do not have enough time to experience the process of self-tolerance. Experiment shows that when T increases, the drop in FP is much shaper than the drop in TP. The value of L and N are inversely proportional to false negative rate and proportional to detection rate. In addition, the larger value of A can reduce false negative rate. Simulation results show the best results, as shown in table 2, when T, L, N and A equal to 5, 20, 1 and 5, respectively. In table 2, comparing with winning entry of KDD’99 Classifier Learning Contest, the proposed approach has a good performance in detecting DOS, Probe, U2R attack and Normal behavior. Nevertheless, the performance of detecting R2L is poor. This is because the packet of R2L is slightly different from the packet of normal. How to improve the ability of the detecting R2L and U2R is the future work.

242

Y. Li, C. Jing, and J. Xu Table 2. Comparison with winning entry of KDD’99 Classifier Learning Contest Detection Result Data TP of the winning entry TP of the proposed approach Normal(60593)

99.5%

98.127%

DOS(229853)

97.1%

97.565%

Probe(4166)

83.3%

90.494%

U2R(228)

13.2%

71.491%

R2L(16189)

8.4%

0.371%

5 Conclusions In this paper, a new distributed intrusion detection model based on immune mobile agent is proposed. Dynamic clonal selection algorithm and mobile agent are described in detail. The simulation results showed that our model is efficiently to classify the anomaly profile from the normal profile. Our model has following advantages. First, the model realized that computing move to data by utilizing mobile agent. Therefore, real time capability is improved and bottleneck problem is overcome. Second, compared with other hierarchical model, it surmounts single point of failure. Dependability of the system is enhanced. In addition, the system is robust and faulttolerant. Third, false positive rate is low and true positive rate is high by adopting dynamic clonal selection algorithm. Acknowledgments. This paper is supported by Research fund of University of Jiangsu Province and Jiangsu University of Science and Technology’s Basic Research Development Program (No. 2005DX006J ).

References 1. Axelsson, V.: Intrusion detection systems: A survey and taxonomy. Technical Report No 99–15, Chalmers University of Technology, Sweden 2. Hunteman, V.: Automated information system–(AIS) alarm system. In: 20th NIST-NCSC National Information Systems Security Conference, pp. 394–405. IEEE Press, New York (1997) 3. Staniford Chen, S., Cheung, S., Crawford, R., et al.: Grids: a graph based intrusion detection system for large networks. In: 19th National Information System Security Conference. National Institute of Standards and Technology, vol. 1, pp. 361–370. IEEE Press, Los Alamitos (1996) 4. Porras, P.A., Neumann, P.G.: MERALD: event monitoring enabling responses to anomalous live disturbances. In: 20th National Information Systems Security Conference, National Institute of Standards and Technology, pp. 11–13. IEEE Press, Los Alamitos (1997)

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5. Spafford, E.H.: Intrusion detection using autonomous agent. Computer Networks 3(4), 547–570 (2000) 6. Dasgupta, D., Brian, H.: Mobile security agent for network traffic analysis. In: DARPA Information Survivability Conference and Exposition II (DISCEX-II), Anaheium, CA, pp. 332–340. IEEE Press, Los Alamitos (2001) 7. Jansen, W., Mell, P., Karygiannis, T., Marks, D.: Mobile agents in intrusion detection and response. In: 12th Annual Canadian Information Technology Security Symposium, pp. 12– 18. IEEE Press, Ottawa (2000) 8. Hofmeyr, S.A., Forrest, S., Somayaji, A.: Intrusion detection using sequences of system calls. Journal of Computer Security 6, 151–180 (1998) 9. Kim, J., Bentley, P.: Towards an artificial immune system for network intrusion detection: an investigation of dynamic clonal selection. In: Congress on Evolutionary Computation, Honolulu, pp. 1015–1020 (2002) 10. Kim, J., Bentley, P., Aickelin, U., et al.: Immune system approaches to intrusion detectiona review. Natural Computting 6, 413–466 (2007) 11. Aickelin, U., Greensmith, J., Twycross, J.: Immune system approaches to intrusion detection–a review. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 316–329. Springer, Heidelberg (2004) 12. Glickman, M., Balthrop, J., Forrest, S.: A machine learning evaluation of an artificial immune system. Evolutionary Computation 13(2), 179–212 (2005) 13. Gomez, J., Gonzalez, F., Dasgupta, D.: An immune-fuzzy approach to anomaly detection. In: 12th IEEE International Conference on Fuzzy Systems (FUZZIEEE), vol. 2, pp. 1219– 1224. IEEE Press, Los Alamitos (May 2003) 14. Carver, C., Hill, J., Surdu, J., Pooch, U.: A methodology for using intelligent agents to provide automated intrusion response. In: IEEE Systems, Man, and Cybemetics Information Assurance and Security Workshop, West Point, New York, pp. 110–116 (2000) 15. Zainal, A., Maarof, M.A., Shamdudd, S.M.: In.: Feature selection using rough set in intrusion detection. In: Proc. IEEE TENCON, p. 4 (2006) 16. Kim, B.j., Kim, I.k.: Kernel based intrusion detection system. In: Proc. IEEE ICIS, pp. 6 (2005)

Single-Machine Scheduling Problems with Two Agents Competing for Makespan Guosheng Ding1,2 and Shijie Sun1 1

Department of Mathematics, Shanghai University, Shanghai, China 2 School of Science, Nantong University, Nantong, China

Abstract. This paper considers the single-machine scheduling problems in which two distinct agents are concerned. Each agent has a set of jobs with different release times, and both of them expect to complete their respective jobs as early as possible. We take the makespan of each agent as its own criterion and take the linear combination of the two makespans as our objective function. In this paper, both off-line and online models are considered. When preemption is allowed, we present an exact algorithm for the off-line model and an optimal algorithm for the on-line model. When preemption is not allowed we point out that the problem is NP-hard for the off-line model and give a (2+1/θ)-competitive algorithm for the on-line model. We also prove that a lower bound of the competitive ratio for the later model is 1 + θ/(1 + θ), where θ is a given factor not less than 1.

1

Introduction

In recent years, management problems in which multiple agents compete on the usage of a common processing resource are receiving increasing attention in different application environments, such as the scheduling of multiple flights of different airlines on a common set of airport runways, of berths and material/people movers (cranes, walkways, etc.) at a port for multiple ships, of clerical works among different “managers” in an office and of a mechanical/electrical workshop for different uses [1]; and in different methodological fields, such as artificial intelligence, decision theory, and operations research. A number of papers investigate the multi-agent scheduling problems, and mainly in the two-agent setting. Baker and Smith [5] analyze the computational complexity of combining linearly the agents’ criteria into a single objective function. Agnetis et al. [1] and Agnetis et al. [2] study both the problems of finding a single Pareto-optimal solution and enumerating the whole set of Pareto-optimal solutions for two agents. Agentis et al. [3] extend their research to multi-agent problems. Ng et al. [14] studied minimum weighted completion time for one agent subject to a given permitted number of tardy jobs for the second agent. Cheng et al. [6] studied in this context the objective of minimum number of tardy jobs. Cheng et al. [7] obtained several complexity results for single machine problems 

This work is partially supported by Grant 08KJD110014.

K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 244–255, 2010. c Springer-Verlag Berlin Heidelberg 2010 

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with max-form criteria. Liu and Tang [9] and Liu et al. [10] provided polynomialtime solutions for single machine problems with deteriorating jobs. And Liu et al. [11] introduce an aging effect and a learning effect into the two-agent single machine scheduling. Wan et al. [16] also considered several two-agent scheduling problems with deteriorating jobs, in which process times of jobs of one agent are deteriorating. Lee et al. [8] focused on minimizing total weighted completion time, and introduced fully polynomial-time approximation schemes and an efficient approximation algorithm with a reasonable worst case bound. Agnetis et al. [4] introduced an efficient branch and bound algorithm for minimizing total weighted completion of one agent subject to various constraints on the second agent’s performance. Mor and Mosheiov [13] introduced a polynomial time solution for the problem of minimizing maximum earliness cost of one agent, subject to a bound on the maximum earliness cost of the second agent. On the other hand, there have been a number of research on on-line scheduling because it establishes a bridge between deterministic and stochastic scheduling. And in practice, it is often the case that a very limited amount of information is available when a decision must be made. But until now the on-line model of the multi-agent scheduling has not been discussed. In this paper We take the makespan of each agent as its own criterion and take the linear combination of the two makespans as our objective function, and both off-line and on-line models are considered. This paper is organized as follows. In section 2, we introduce the model and the notation. Section 3 discusses off-line models where preemption is allowed or not. In section 4, we consider the on-line models and provide an optimal on-line algorithm when the jobs are preemptive, and a (2 + 1/θ)-competitive on-line algorithm when preemption is not allowed, where θ is a given weighted factor which is not less than 1. Finally, in section 5, we make a conclusion and some suggestions for future research.

2

Model and Notation

There are two competing agents, called agent A and agent B. Each of them has a set of jobs to be processed on a common machine. The agent A has to execute the job set J A = {J1A , J2A , . . . , JnAA }, whereas the agent B has to execute the job set J B = {J1B , J2B , . . . , JnBB }. For each job JhA (JkB ) there is a processing B A B time pA h (pk ) and a release time rh (rk ). Let σ indicate a feasible schedule of the n = nA + nB job, i.e., a feasible assignment of starting times to the jobs of both agents. The start times of job JhA and JkB in σ are denoted as ShA (σ) and SkB (σ), and the completion times are denoted as ChA (σ) and CkB (σ), or simply ShA , SkB , ChA , and CkB whenever these do not generate confusion. A B We use Cmax (σ) and Cmax (σ) to denote the completion times of agent A and A B A agent B in σ, or simply Cmax and Cmax . So, Cmax = max{C1A , C2A , . . . , CnAA }, B B B B Cmax = max{C1 , C2 , . . . , CnB }. A B We take Cmax +θCmax as our objective function, where θ > 0 is a given factor that helps us to distinguish the two agents’ relative importance, and use Cmax

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to denote the makespan of all jobs which belong to both agent A and agent B. In the remainder of our paper, if all jobs of a certain agent are completed, then we say that the agent is completed. And jobs are numbered by nondecreasing release date.

3 3.1

Off-line Models A B 1 | rj , pmtn | Cmax + θCmax

A B Consider an arbitrary instance of the problem 1 | rj , pmtn | Cmax + θCmax . We assume, of an optimal schedule, the completion times of agent A and agent B A∗ B∗ ∗ ∗ are Cmax and Cmax , and the makespan of all the jobs is Cmax . Thus, Cmax = ∗ ∗ A B max{Cmax , Cmax }

Algorithm 1. At first, regardless agent A, make agent B completed as early as possible. Namely, every time there is a B-jobs available, we process the schedulable jobs of agent B according to the nondecreasing order of their release times, while putting agent A aside. Secondly, according to the nondecreasing order of release times of the jobs of agent A, process them on the machine as early as possible. Then obtain a A B (σ1 ) + θCmax (σ1 ). schedule, called σ1 . Denote objective1 = Cmax Analogously, schedule agent A firstly and then schedule agent B, both in the nondecreasing order of their jobs release times. Then obtain σ2 and denote A B (σ2 ) + θCmax (σ2 ). objective2 = Cmax A B Finally, Cmax (σi∗ ) + θCmax (σi∗ ) = min{objective1 , objective2}, is the optimal value. A + Theorem 1. Algorithm 1 yields an optimal schedule for 1 | rj , pmtn | Cmax B θCmax .

Proof. Assume that σ ∗ is an optimal schedule. Then the optimal objective value is A B A B (σ ∗ ) + θCmax (σ ∗ ). Since preemption allowed, max{Cmax (σ ∗ ), Cmax (σ ∗ )} = Cmax A B A B max{Cmax (σ1 ), Cmax (σ1 )} = max{Cmax (σ2 ), Cmax (σ2 )}. As algorithm 1 says, agent B is completed in σ1 as early as possible. So is agent A in σ2 . Thus B B A A Cmax (σ ∗ ) ≤ Cmax (σ1 ) and Cmax (σ ∗ ) ≤ Cmax (σ2 ). Therefore, whichever agent ∗ A ∗ B A B is completed firstly in σ , Cmax (σ ) + θCmax (σ ∗ ) ≤ Cmax (σi∗ ) + θCmax (σi∗ ) = min{objective1 , objective2} 3.2

A B + θCmax 1 | rj | Cmax

1 2 Theorem 2. The problem 1 | rj | Cmax + θCmax is NP-hard.

Proof. The proof is based on the fact that the Partition problem [12] can be 1 2 reduced to 1 | rj | Cmax + θCmax . a2 , . . . , at , does there exist a subset S ⊂ Partition. Given positive integers a1 ,   T = {1, 2, . . . , t} such that i∈S ai = i∈T −S ai ?

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J12 F 2

F 2

F +1

+1

1 2 + θCmax is NP-hard Fig. 1. 1 | rj | Cmax

 Define F = i∈T ai . Assume that agent A has t jobs with p1i = ai and ri = 0, (i ∈ T ), agent B has a job with p21 = 1 and r12 = F/2, and y = 1+F +θ(F/2+1). If Partition has a solution, then the job of agent B may start its processing immediately after it is released, while the jobs of agent A are just divided into two 1 2 +θCmax = 1+F +θ(1+F/2) = y. equal parts, as illustrated in Figure 1. So Cmax 1 2 If 1 | rj | Cmax + θCmax has a solution, then the jobs of agent B can not start 1 2 its processing strictly after time F/2, otherwise Cmax + θCmax > 1 + F + θ(1 + F/2) = y, that is, the job of agent B has to start its processing at time F/2, and all the jobs of agent A have to completed not later than F + 1. Then, Partition has a solution.

4

On-line Models

4.1

A B 1 | online, rj , pmtn | Cmax + θCmax

A B In this section, for the objective function Cmax + θCmax , we use OP T, ALG and ALG2 to denote the values corresponding to an optimal schedule, a schedule constructed by an arbitrary on-line algorithm and a schedule constructed by algorithm 2 respectively.

Theorem 3. The competitive ratio of any on-line algorithm for the problem A B 1 | online, rj , pmtn | Cmax + θCmax is at least 1 + θ/(1 + θ + θ2 ). Proof. Consider the following instance. At time 0, agent A has a job J1A with B B B r1A = 0 and pA 1 = a; agent B has a job J1 with r1 = 0 and p1 = b = θa. A If some on-line algorithm schedules these jobs in order of J1 , J1B , then job J1B can not be completed before time t = a + b. In this case, at time t = a + b, a new job of agent A, J2A , is released , and its processing time is ε (ε is an arbitrary small number). Corresponding to this case, ALG ≥ a+ b + ε + θ(a+ b) ≈ a+ b + θ(a+ b) ALG ≥ a+b+θ(a+b) = 1 + 1+ bθ+θ b = and OP T = a + b + ε + θb ≈ a + b + θb. So, OP T a+b+θb a

a

θ 1 + 1+θ+θ 2. Analogously, if the on-line algorithm schedules these two jobs released at time 0 in order of J1B , J1A , then job J1A can not be completed before time t = a + b. In this case, at time t = a + b, a new job of J2B is released, and its processing time is ε. Now, ALG ≥ a + b + θ(a + b + ε) ≈ a + b + θ(a + b) and OP T = a+b+θ(a+b) ALG 1 θ a+θ(a+b+ε) ≈ a+θ(a+b). So, OP T ≥ a+θ(a+b) = 1+ a +θ a +θ = 1+ 1+θ+θ 2 .

Thus,

ALG OP T

≥1+

θ 1+θ+θ 2 .

b

b

A B Assume jobs J1A , J2A , . . . , JA of agent A and J1B , J2B , . . . , JB of agent B have t t been known at a certain time t. Schedule agent A jobs, schedule agent B jobs,

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and schedule both agent A and agent B jobs, respectively, on one machine for minimizing makespan. Three sequences are obtained. And their makespans are denoted by at , bt , and Dt . Algorithm 2. At any time t, if the jobs of only one agent are known and to be processed, then process this agent’s jobs. If there remain both agent A and agent B jobs to be processed, then compare (Dt − at )/θ and Dt − bt . When (Dt − at )/θ ≥ Dt − bt , process agent A jobs; otherwise process agent B jobs, where at , bt > 0. Theorem 4. Algorithm 2 is (1 + A B Cmax + θCmax .

θ 1+θ+θ 2 )-competitive

for 1 | online, rj , pmtn |

Proof. First, for an arbitrary instance known at time t, we prove that the agent whose jobs are completed last in the optimal schedule is the same as the one whose jobs are completed last in the resulting schedule of algorithm 2. If the jobs of only one agent are known and to be processed, then this agent’s jobs are last completed in both the optimal schedule and the resulting schedule of algorithm 2. If there remain both agent A and agent B jobs to be processed at time t, then at , bt > 0. In the optimal schedule, if agent B jobs are last completed, then its objective value must be no more than that of the other schedule in which agent A jobs are last completed. So, at + θDt ≤ Dt + θbt , i.e., (Dt − at )/θ ≥ Dt − bt . In this case, algorithm 2 make agent B jobs completed last. Similarly, If agent A jobs are last completed in the optimal schedule, then they are also last completed in the resulting schedule of algorithm 2. In the following of the proof, assume agent B jobs are last completed in the optimal schedule. So they are also last completed in the resulting schedule of algorithm 2. If agent A jobs are last completed in the optimal schedule, the proof process is similar. In the worst case, algorithm 2 postpone agent A jobs, such that the ratio 

CA

+θC B





CA

+θC B

∗

max max max ρ = ALG2 = Cmax is very large. Thus how large can ρ be A∗ +θC B ∗ A∗ B∗ OP T = Cmax max max +θCmax in the worst instance? In order to make ρ larger, the worst instance has the follow properties:

1. there must be all agent A jobs and some small agent B jobs released at time 0, such that (Dt − at )/θ < Dt − bt , (t = 0); moreover some small agent B jobs are released continuously in this later time, such that this inequality holds for the longest time; 2. there must be only a block, which consists of both agent A and B jobs in the optimal schedule, where a block means a batch of jobs processed contiguously; also there is only a block in the resulting schedule of algorithm 2. ∗

A (= But for the worst instance, the last agent A job is delayed at most θCmax A∗ θat=0 ). In fact, the inequality (Dt − at )/θ < Dt − bt holds from time 0 to θCmax . A∗ And from time 0 to θCmax , those small agent B jobs are processed continuously.

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Because agent B jobs are completed last in both the optimal schedule and the B∗ A∗ A∗ resulting schedule of algorithm 2, Cmax ≥ Cmax + θCmax . So, 

ρ=

∗

∗

∗

∗

∗

A B A A B Cmax + θCmax θCmax + Cmax + θCmax θC A ≤ = 1 + A∗ max B ∗ ∗ ∗ ∗ ∗ A B A B Cmax + θCmax Cmax + θCmax Cmax + θCmax ∗

A θ θCmax = (1 + ) . ∗ ∗ A A A∗ ) Cmax + θ(Cmax + θCmax 1 + θ + θ2 The proof is completed and we also know that algorithm 2 is optimal for A B 1 | online, rj , pmtn | Cmax + θCmax .

≤ 1+

4.2

A B + θCmax 1 | online, rj | Cmax

Theorem 5. The competitive ratio of any on-line algorithm for problem 1 | A B online, rj | Cmax + θCmax is at least 1 + θ/(1 + θ). Proof. Consider the following instance. The first job J1A of Agent A is released at time 0 and its processing time is pA 1 . The on-line algorithm schedules the job at time S. Depending on S, either no jobs are released any more or job J1B with processing time pB 1 = ε is released at time S + ε1 (ε1 is another arbitrary small A number). In the first case we get a ratio of ALG/OP T = (S + pA 1 )/p1 ; in the S+pA +θ(S+pA +ε)

S+pA +θ(S+pA )

ALG 1 1 1 1 second case we get a ratio of OP ≈ . T ≥ S+ε1 +ε+pA S+pA 1 +θ(S+ε1 +ε) 1 +θS   A A A S+p S+p +θ(S+p ) ALG 1 1 1 Hence, OP , . The algorithm may choose S so as T ≥ max pA S+pA +θS 1

1

A to minimize this expression. As (S + pA 1 )/p1 is increasing and

decreasing with S, the best choice for S is S = desired ratio of 1 + θ/(1 + θ).

θpA 1 /(1

A S+pA 1 +θ(S+p1 ) S+pA +θS 1

is

+ θ). Then we get the

Note that we can also use the example of theorem 4 to show that any online algorithm that schedules a job as soon as the machine is available has a competitive ratio of 1 + θ. If θ is a large number, then the ratio becomes terrible. A B Before giving our algorithm for 1 | online, rj | Cmax + θCmax , we introduce two conditions at a certain time t, condition 1. There exists at least one unscheduled agent A job such that A A its processing time is not more than 1+θ θ t (for any Ji ∈ J , this condition θ pA guarantee that SiA ≥ max{riA , 1+θ i }); condition 2. There exists at least one unscheduled agent B job such that its processing time is not more than (1 + θ)t (for any JiB ∈ J B , this condition 1 guarantee that SiB ≥ max{riB , 1+θ pB i }). Here, we define JaA as the current unscheduled agent A job which has the smallest release time among those whose processing times are not more than 1+θ B θ t. Similarly, we define Jb as the current unscheduled agent B job which has the smallest release time among those whose processing times are not more than (1 + θ)t.

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Algorithm 3. Assume at a certain time t, the machine is freed, then, a. if only condition 1 is satisfied, then we start processing JaA ; if only condition 2 is satisfied, then we start processing JbB ; b. if both of the two conditions are satisfied, then compare the values of  B  i:riB ≤t pi A pi and , θ A i:ri ≤t



pB  i:rB ≤t i i then if i:rA ≤t pA ≤ , start processing JaA ; otherwise start processing i θ i JbB ; c. if none of the two conditions are satisfied, then we keep the machine idle until at least one of the two conditions is satisfied.

Note that according to algorithm 3, at a certain time t, if a job of agent A is to be started, then at least condition 1 must be satisfied; similarly, if a job of agent B is to be started then at least condition 2 must be satisfied. Theorem 6. Algorithm 3 is 2 + 1/θ-competitive for problem 1 | online, rj | A B Cmax + θCmax . It can be seen easily that this competitive ratio approaches the lower bound of theorem 5 as θ is very large. In what follows, we prove theorem 6 by the smallest counterexample strategy. If there exists one or more counterexamples of algorithm 3 whose competitive ratio is strictly larger than 2 + 1/θ, then there must exist a counterexample with the smallest total number of jobs. Here we assume that the “smallest” counterexample is composed of nA jobs of agent A and nB jobs of agent B, and denote it by I. Lemma 1. The schedule given by algorithm 3 for I includes at most two cases: 1. the schedule consists of a single block, where a block means a batch of jobs processed contiguously; 2. the schedule consists of two blocks, the first one includes the jobs of agent A and/or agent B, the second one only includes the jobs belonging to one of the two agents. Proof. If the last block of the schedule given by algorithm 3 for I includes the jobs of both agent A and agent B, then the schedule consists of only this block. This is because if there exist other blocks before it then the jobs of these blocks do not influence the schedule decision of algorithm 3 concerning the jobs of the last block, and vice versa, and the deletion of them will result in a counterexample with fewer total jobs. If the last block of the schedule given by algorithm 3 for I includes only some jobs of agent A. – There do not exist other blocks including only some jobs of agent A before the last block because the deletion of those blocks result in a counterexample with fewer total jobs.

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– Once there exists one block including the jobs of both agent A and agent B, or one block including only some jobs of agent B, immediately before this last block. There does not exist any more blocks before because the deletion of them result in a counterexample with fewer total jobs. If the last block of the schedule given by algorithm 3 for I includes only some jobs of agent B, the proof is analogous to the above. Hence, lemma 1 holds. For convenience, we use ALG3(I) and OP T (I) to denote the objective function values of I under algorithm 3 and the optimal schedule respectively, and use i i∗ Cmax (I) and Cmax (I) to denote the completion times of I corresponding to the schedule given by algorithm 3 and the optimal schedule, respectively, i = A, B. Without loss of generality we assume that there exists at least one job released at time 0. Lemma 2. Algorithm 3 is 2 + 1/θ-competitive when it acts on I and results in case 1 of lemma 1. Proof. Suppose that under algorithm 3, case 1 of lemma 1 occurs. Denote this schedule by π and denote the optimal schedule by π ∗ . In π ∗ agent A, or agent B is last completed. Case 1.1. agent A is last completed in π ∗ . In order to bound B Cmax (I) B ∗ (I) Cmax

A B Cmax (I)+θCmax (I) A∗ (I)+θC B ∗ (I) , Cmax max

we are dedicated to obtain the ratio of

firstly . If all jobs of agent A are scheduled after all jobs of agent B in π , then according to 2, we know that alljobs of agent B are not to be started condition n2 n2 B∗ B B B∗ later than j=1 pB j /(1 + θ). As Cmax ≥ j=1 pj , we get Cmax (I)/Cmax (I) ≤ 1 + 1/(1 + θ). If at least one job of agent A is scheduled before some of agent B jobs, we denote the last such a job of agent A by JsA , denote the jobs of agent B immediately after B B JsA in π by JlB , Jl+1 , . . . , Jl+u in turn, u ≥ 0, and denote a certain job(it may not A exist) before Js by Jk which belongs to either agent A or agent B. B Case 1.1.1. pB l+j ≤ (1 + θ)rl+j , j = 0, 1, . . . , u.

π has at most two subcases, as illustrated in Figure 2: d. rlB > SsA ; e. rlB ≤ this time, we might as well assume Sk ≤ rlB ≤ Ck ) .

SsA (at

rlB

? · · · JsA

rlB

B ··· JlB · · · Jl+u

? · · · Jk · · · JsA

B ··· JlB · · · Jl+u

e d B Fig. 2. Two subcases for pB ≤ (1 + θ)r l+j l+j

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A For subcase d in Figure 2, according to condition 1, we get pA s ≤ Ss (1 + θ)/θ. B A A B B B By rl  > Ss , we have ps < rl (1 + θ)/θ. So we get Cmax (I) < rl + rlB (1 + u B B θ)/θ + j=0 pB l+j . Based on the hypothesis pl+j ≤ (1 + θ)rl+j , j = 0, 1, . . . , u and the property of algorithm 3 that the jobs satisfying condition 1 or 2 are processed in the nondecreasing order of their release times,  we obtain rlB ≤ u B B B∗ B rl+1 ≤ · · · ≤ rl+u . So, it is easy to see Cmax (I) ≥ rl + j=0 pB l+j . Thus, B Cmax (I) B ∗ (I) Cmax


(1 + θ)rl+i . u B B Note that at this time j=0 pl+j > (1 + θ)rl , and this indicates that job JlB u is released before time j=0 pB l+j /(1 + θ).  π also has at most two subcases, as illustrated in Figure 3: f. uj=0 pB l+j /(1 +  u A θ) > SsA ; g. j=0 pB /(1 + θ) ≤ S (at this time, we might as well assume s l+j u B Sk ≤ j=0 pl+j /(1 + θ) ≤ Ck ).

u

j=0

u

pB l+j /(1 + θ)

? · · · JsA

j=0

B ··· JlB · · · Jl+u

f

pB l+j /(1 + θ)

? · · · Jk · · · JsA

B ··· JlB · · · Jl+u

g B Fig. 3. Two subcases for pB l+i > (1 + θ)rl+i

A 1+θ For subcase f in Figure 3, according to condition 1, we have pA s ≤ Ss θ < u u B B B pl+j 1+θ u j=0 pl+j 1+θ j=0 pl+j B B B∗ + j=0 j=0 pl+j . As Cmax (I) ≥ 1+θ θ and Cmax (I) < 1+θ 1+θ θ + B u Cmax (I) 1 1 1 B j=0 pl+j , C B ∗ (I) < 1 + θ + 1+θ < 2 + θ . u

max

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253

B Similar to subcase e in Figure 2, for subcase g in Figure 3, we have Cmax (I) ≤  nB B B  p p n B B i=1 i i=1 i + + i=1 pi , where the first item in the right hand represents 1+θ θ the upper bound of the initial waiting time of the machine, the second item represents the upper bound of the sum of the processing times of jobs of agent A completed before JlB . nB B C B (I) 1 1 1 B∗ As Cmax (I) ≥ i=1 pi , then Cmax B ∗ (I) ≤ 1 + θ + 1+θ < 2 + θ .  nB

max

∗

B B So, for case 1.1, we obtain Cmax (I)/Cmax (I) ≤ 2 + 1/θ.

By the hypothesis of case 1.1, all the jobs of π are processed contiguously and in π ∗ agent A is last completed. Therefore, the sum of the processing times A∗ of the block is at most Cmax (I). If the first job of the block is of agent A, θ A∗ then the possible initial waiting time of the machine is at most 1+θ Cmax (I), θ A A∗ that is, Cmax (I) ≤ (1 + 1+θ )Cmax (I). Similarly, if the first job of the block is of agent B, then the possible initial waiting time of the machine is at most 1 θ A∗ A∗ 1+θ Cmax (I) ≤ 1+θ Cmax (I). Thus, no matter whether the first job of the block θ A A∗ is of agent A or agent B, we have Cmax (I) ≤ (1 + 1+θ )Cmax (I). So, for case 1.1, we get

ALG3(I) OP T (I)

∗

≤

∗

A B θ (1+ 1+θ )Cmax (I)+θ(2+ θ1 )Cmax (I) A∗ (I)+θC B ∗ (I) Cmax max

< 2 + 1θ .

Case 1.2. agent B is last completed in π ∗ . ∗

B Here the sum of the processing times of the block is at most Cmax (I). Corresponding to the case in which the first job of the block is of agent A or agent B, we θ A B B∗ A B get max{Cmax (I), Cmax (I)} ≤ (1 + 1+θ )Cmax (I) or max{Cmax (I), Cmax (I)} ≤ 1 B∗ (1 + 1+θ )Cmax (I).

So we obtain 2+

ALG3(I) OP T (I)

1 θ.

=

A B Cmax (I)+θCmax (I) A∗ (I)+θC B ∗ (I) Cmax max

∗

≤

∗

B B θ θ (1+ 1+θ )Cmax (I)+θ(1+ 1+θ )Cmax (I) B ∗ (I) θCmax

=

Lemma 3. Algorithm 3 is 2 + 1/θ-competitive when it acts on I and results in case 2 of lemma 1. Proof. For case 2 of lemma 1, π consists of two blocks, the first one includes the jobs of agent A and/or agent B, the second one only includes the jobs belonging to one of the two agents. Case 2.1. The second block only consists of some jobs of agent A. Denote them A A by JlA , Jl+1 , · · · , Jl+h , h ≥ 0. A A If pA l+j ≤ rl+j (1 + θ)/θ, j = 0, 1, . . . , h, then by algorithm 3, Cmax (I) = ∗ A Cmax (I). A that pA If there exists at least one pA l+i , 0 ≤ i ≤ h, such l+i> rl+i (1 + θ)/θ, then h A h A θ A h Cmax (I) j=0 pl+j + j=0 pl+j 1+θ θ A A h = 1 + 1+θ . j=0 pl+j > rl (1 + θ)/θ. Thus, C A∗ (I) ≤ pA max

1.1, so we have

j=0

l+j

A B Cmax (I) Cmax (I) θ A∗ (I) ≤ 1 + 1+θ . The ratio C B ∗ (I) is Cmax max B Cmax (I) ALG3(I) B ∗ (I) ≤ 2 + 1/θ, and OP T (I) ≤ 2 + 1/θ Cmax

So, for case 2.1,

the same as in case

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Case 2.2 The second block only consists of some jobs of agent B, and denote B B them by JlB , Jl+1 , · · · , Jl+v , v ≥ 0. B If pB l+j ≤ (1 + θ)rl+j , j = 0, 1, . . . , v, then by algorithm 3, we get ∗

B B A B Cmax (I) = Cmax (I). Considering Cmax (I) < Cmax (I), we obtain B∗ B∗ Cmax (I)+θCmax (I) ∗ A B ∗ (I) Cmax (I)+θCmax

ALG3(I) OP T (I)


(1 + θ)rl+i , u  ul+i B B 1 B u p + p Cmax (I) j=0 l+j j=0 l+j 1+θ 1 B B u then j=0 pl+j > (1 + θ)rl . So C B∗ (I) ≤ ≤ 1 + 1+θ . pB max

A B For Cmax (I) < Cmax (I), we have

1+

1 θ

+

1 1+θ

+

1 θ(1+θ)

≤2+

ALG3(I) OP T (I)

1 θ.

j=0 l+j ∗

≤

∗

B B 1 1 (1+ 1+θ )Cmax (I)+(1+ 1+θ )θCmax (I) A∗ (I)+θC B ∗ (I) Cmax max

≤

At last, through lemma 2 and lemma 3 we know that the “smallest” counterexample I does not exist. This completes the proof of theorem 6. Example 1. Consider the following instance in which agent A has a job J1A with θ B B B r1A = 0, pA 1 = 1 and agent B has a job J1 with r1 = ( 1+θ )+0 , p1 = 0. Scheduling the two jobs according to algorithm 3 results in a schedule in which J1A θ θ is completed at 1 + 1+θ and J1B is completed at 1 + 1+θ too. But it can be θ B and J1A shown easily that in an optimal solution J1 is completed at time 1+θ θ is completed at 1 + 1+θ . So, when θ is sufficiently large, the competitive ratio of algorithm 3 for this instance 1+

θ 1+θ

1+

θ 1+θ ) θ θ 1+θ

+ θ(1 +

θ 1+θ

+

≈

θ 1+θ θ 1+θ

1+

=2+

1 . θ

This particular instance implies that the algorithm 3’s competitive ratio can be achieved when θ is sufficiently large.

5

Conclusions

We consider the single-machine scheduling problems in which two distinct agents are concerned. Each agent has a set of jobs with different release times, and both of them expect to complete their respective jobs as early as possible. We take A B the makespan of each agent as its own criterion and take Cmax + θCmax as our objective function. In this paper, both off-line and on-line models are considered. For off-line model, corresponding to the preemptive case, we provide an exact algorithm. For on-line model, we construct an optimal on-line algorithm in case the jobs can be preempted. When preemption is not allowed, we give a lower bound of the competitive ratio of the problem, and construct an on-line algorithm with competitive ratio approaching this lower bound as θ large enough. There remain two future research directions. First, several different combinations of the agent’s other objective functions can be investigated thoroughly, especially for on-line case. Second, our work can be extended to include other machine environments, especially the parallel machine environment.

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References 1. Agnetis, A., Mirchandani, P.B., Pacciarelli, D., Pacifici, A.: Nondominated schedules for a job-shop with two competing users. Comput. Math. Organ. Theory 5, 191–217 (2000) 2. Agnetis, A., Mirchandani, P.B., Pacciarelli, D., Pacifici, A.: Scheduling problems with two competing agents. Oper. Res. 52, 229–242 (2004) 3. Agnetis, A., Pacciarelli, D., Pacifici, A.: Multi-agent single machine scheduling. Ann. Oper. Res. 150, 3–15 (2007) 4. Agnetis, A., Pascale, G., Pcciarelli, D.: A Lagrangian approcah to single machine scheduling problem with two competing agent. J. Scheduling 12, 401–415 (2009) 5. Baker, K.R., Smith, J.C.: A multiple-criterion model for machine scheduling. J. Scheduling 6, 7–16 (2003) 6. Cheng, T.C.E., et al.: Multi-agent scheduling on a single machine to minimize total weighted number of tardy jobs. Theoretical Computer Sci. 362, 273–281 (2006) 7. Cheng, T.C.E., Ng, C.T., Yuan, J.J.: Multi-agent scheduling on a single machine with max-form criteria. Europen J. Oper. Res. 188, 603–609 (2008) 8. Lee, K., Choi, B.-C., Leung, J.Y.-T., Pinedo, M.: Approxiation algorithms for multi-agent scheduling to minimizing total weighted completion time. Information Processing Lett. 109, 913–917 (2009) 9. Liu, P., Tang, L.: Two-agent scheduling with linear deteriorating jobs on single machine. In: Proceedings of the 14th Annual International Conference on Computing And Combinatorics, Dalian, China, pp. 642–650 10. Liu, P., Tang, L., Zhou, X.: Two-agent group scheduling with deteriorating jobs on a single machine. Int. J. Adv. Manuf. Technol. 47, 657–664 (2010) 11. Liu, P., Zhou, X., Tang, L.: Two-agent single-machine scheduling with positiondependent processing times. Int. J. Adv. Manuf. Technol. 48, 325–331 (2010) 12. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, San Francisco (1979) 13. Mor, B., Mosheiov, G.: Scheduling problems with two competing agents to minimize minamx and minsum earliness measures. Europen J. Oper. Res. (2010) doi:10.1016/j.ejor, 03003 14. Ng, C.T., Cheng, T.C.E., Yuan, J.J.: A note on the complexity of the problem of two-agent scheduling on a single machine. J. Comb. Optim. 12, 387–394 (2006) 15. Potts, C.N., Kovalyov, M.Y.: Scheduling with batching: A review. Eur. J. Oper. Res. 120, 228–349 (2000) 16. Wang, G., Vakati, R.S.R., Leund, J.Y.-T., Pinedo, M.: Scheduling two agents with controllable processing times. Europen J. Oper. Res. 205, 528–539 (2010) 17. Yang, W.H., Liao, C.J.: Survey of scheduling research involving setup times. Int. J. Sys. Sci. 30, 143–155 (1999)

Multi-Agent Asynchronous Negotiation Based on Time-Delay LiangGui Tang1 and Bo An2 1

College of Computer Science and Information Engineering, Chongqing Technology and Business University, Chongqing, P.R. China, 400067 2 Dept. of Computer Science, University of Massachusetts, Amherst, USA, MA 01003 [email protected], [email protected]

Abstract. In the Electronic Commerce applications based on MAS (MultiAgent Systems) etc., because every agent may have different negotiation strategy, reasoning mode, and that for diverse negotiation offers, the time spending in strategy computing, resource allocation and information transmission of the agent are different, so that one to many negotiation generally is asynchronous or with time-delay. This paper puts forward a mechanism with time-delay for one to many negotiation and give a negotiation control mode of multi-agents; considering the aspects of this negotiation including time dependent, opponent influence and other negotiation threads, this paper analyzes the negotiation flow for one to many negotiation with timedelay, designs sub-negotiation strategies for multi-agents; and then discusses when to offer in one to many negotiation with time-delay; brings forward a method for determining the number of negotiation opponents. The research of one to many negotiation with time-delay will improve its applicability and make agent-based automatic negotiation satisfy the needs of practical application. Experimental results validate the correctness and validity of our methods. Keywords: Multi-Agent Systems, Asynchronous Negotiation, Time-Delay.

1 Introduction Agent-based E-Commerce has greatly improved the efficiency and automation of E-Commerce [1][2][3][4]. In agent-based E-Commerce, consumer buying behavior can be divided into six stages [4]: need identification, product brokering, merchant brokering, negotiation, purchase and delivery, service and evaluation. The purpose of negotiation is to reach agreement on deal items between consumers and producers, such as price, quality, transportation, post-selling service, etc. The process of negotiation is similar to that in real life, generally including offering, offer evaluation, counteroffer generation, etc. According to the number of sellers and buyers participating in negotiation, agentbased automatic negotiation can be divided into three cases [5]: one to one negotiation (bilateral negotiation), many to many negotiation and one to many negotiation. In K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 256–269, 2010. © Springer-Verlag Berlin Heidelberg 2010

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most Multi-Agent Systems, various auction mechanisms are adopted to realize the function of one to many negotiation. The limitations of auction mechanisms are: (1) auction mechanisms rely mostly on rigid rules and are highly structured; (2) auction mechanisms lack of flexibility; (3) it is difficult for agents to individuate their strategies; (4) agents lack of interaction during the auction process. While one to many negotiation are more flexible, for example, agents can adopt different negotiation strategies with different negotiation opponents, negotiation can be taken under different negotiation environment and negotiation protocol, etc. A negotiation cycle refers to the time spent in a round of negotiation. In existing one to many negotiation mechanisms [6][7][8] and systems (such as CSIRO’s ITA[7], MIT’ s Tete-a-Tete[9], Vrije University’s NALM[10]), the negotiation cycles are the same when agent negotiates with many opponents, which means agent’s negotiation with many opponents is synchronous. But in actual negotiation, because different agents have different strategies, reasoning mechanisms, and that for diverse negotiation offers, the time spending in strategy computing, resource allocation and information transmission of the agent are different, so that one to many negotiation generally is asynchronous or with time-delay.

2 Negotiation Frame and Control Strategy Negotiation is a dynamic interactive process for reaching agreement. During negotiation, agents exchange offers reflecting of their beliefs, desires and intentions. In order to make our discussion brief, we suppose: all agents are rational; we take the negotiation about the price of a certain product between a buyer and many sellers as background. One to many negotiation structure mainly have centralized control mode and the hierarchy structure. The centralized structure consists of only one complex and powerful agent conducting negotiation with many opponents (as in Fig.1). The centralized structure is simple and has high efficiency with small number of sellers. But when the number of sellers increases, the calculating cost of buyer increases, the processing speed slows down and the buyer’s negotiation efficiency decreases. An alternative method is using hierarchy structure, in which the buyer consists of a control agent and several sub-negotiation agents, and negotiation is composed of several sub-negotiation threads (as in Fig.2). When negotiation begins, the control agent creates several sub-agents (i.e. sub-buyers here) equal with the number of sellers and each sub-agent negotiates with unique seller separately. During negotiation, the control agent manages and coordinates the negotiation of each subagent based on certain strategy. Compared with the centralized structure, hierarchy structure can fit Asynchronous Negotiation to the diverse negotiation offers, and which has good expansibility, dynamic distribution and system stability, a failure of one sub-negotiation thread will not result in the failure of whole negotiation process. Base on the hierarchy structure, a buyer needs to make decision on two levels of negotiation strategy: negotiation control strategy and sub-negotiation strategy for each

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agent. Negotiation strategy of each sub-agent is consistent with that in one to one negotiation [11][12]. Negotiation control strategy refers to rules controlling the whole negotiation process and coordinating all sub-negotiation threads.

Fig. 1. Centralized structure

Fig. 2. Hierarchy structure

Based on the analysis of Rahwan and Kowalczyk[6], we categorize the negotiation strategies for control agent into three kinds: (1) Desperate strategy: All sub-negotiation threads are independent, i.e. subagents don’t know the negotiation information of other sub-negotiation threads, and control agent is anxious to end the negotiation. Once a sub-agent finds an acceptable offer, control agent accepts it and stops other sub-negotiation threads. If several acceptable offers are found out at the same time, control agent chooses the one with the highest utility. (2) Patient strategy: All sub-negotiation threads are independent, but control agent is not anxious to end the negotiation. When one sub-agent finds an acceptable offer, other sub-negotiation threads go on. Once all sub-negotiation threads complete, control agent chooses the one with the highest utility. (3) Optimized patient strategy: All sub-negotiation threads are not independent. During negotiation, each sub-agent clearly knows the negotiation information of other sub-negotiation threads and adjusts its negotiation strategy accordingly. Optimized patient strategy regards all sub-negotiation threads as a whole. All sub-negotiation threads are interactive, and it can avoid unnecessary bargaining process. Given the condition that the control agent is not anxious to end negotiation, optimized patient strategy has the best negotiation performance.

3 One to Many Asynchronous Negotiation As former statement, one to many negotiation is generally asynchronous. The reasons causing one to many negotiation asynchronous include: (1) agents locating in different positions in network have different communication distance, and the factors affecting communication quality (QoS), e.g., bandwidth, congestion, network failure, may result in different communication delay; (2) agents with different reasoning mechanisms, processing capability, computing speed, allocating resource have

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259

different processing time; (3) according to strategies, agents may decide to postpone sending offers, even though offers have already been proposed successfully. Definition 1: The response action of agent-buyer b when receives seller

i ’s offer

offer sit at time t is defined as ACTbi ,t (offer sit ) , which is denoted as follows: ⎧ reject if Bit >= Tbi . ⎪ i ACT (offer s ) = ⎨ agree if U b (offer sit ) ≥ U bi (offer bit −1 ) ⎪ offer b i otherwise b ⎩ i ,t b

t i

(1)

Definition 2: Compromising degree refers to how much agent compromises in negotiation. Suppose kit represents the compromising degree of agent

i in the tth

negotiation round. If agent is a buyer, its offer in this round is defined as follows:

offer bit = (1 + kit ) × offer bit −1 ; Else if agent is a seller, its offer in this round is defined as:

offer sit = (1 − k it ) × offer sit −1 . Fig.3 shows the flow of one to many negotiation with time-delay. Compared with the flow of one to many negotiation without time-delay, all negotiation threads are asynchronous. We also suppose the negotiation begins with seller’s offering.

Fig. 3. The flow of one to many negotiation with time-delay

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3.1 The One to Many Negotiation Strategy with Time-Delay While adopting the hierarchy architecture, the negotiation between one buyer and several sellers consists of several threads of bilateral negotiation between sub-buyers and sellers. Given the condition that the control agent takes the optimized patient strategy, each sub-buyer needs to make a decision on its negotiation strategy. Different from generic bilateral negotiation, sub-agent needs to take negotiation information of other sub-agents into account. After analyzing the main factors affecting sub-agent’s decision making, we design three kinds of strategies: time, opponent and other negotiation threads dependent strategies. (1) Time dependent strategy T Strategy T takes it into account that the remaining negotiation time’s effect on negotiation strategies, i.e. agents’ sensitivity to time. Agents’ sensitivity to time embodies how the left negotiation time affects negotiation strategies, for example, if an agent has a time deadline by which an agreement should be in place, it will concede more rapidly as deadline approaches. Generally, the remaining negotiation time has a remarkable effect on negotiation strategy [13] [14]. From buyer’s perspective, formula pt = (1 + (t / Tmax ) β ) × p0 ( β > 0 ) can be used to express the remaining time’s effect on negotiation strategy, where

pt represents buyer’s offer at time t , Tmax represents the negotiation deadline, and p0 represents the buyer’s first offer. The change of p t with the remaining time has the following characteristics (as showed in Fig.4):

Fig. 4. The effect of the remaining time on negotiation strategy

① When β = 1 ,

p t linearly increases, which means the remaining negotiation

time has a consistent effect on agents’ negotiation strategy.

Multi-Agent Asynchronous Negotiation Based on Time-Delay

② When β > 1 , at the beginning of negotiation, p

t

261

changes little. Agents make

little compromise at the beginning of negotiation, but make great compromise when negotiation is to be closed. When 0 < β < 1 , the change of the slope is decreasing. Agents are eager to

③

reach an agreement as quickly as possible, and they make great compromise at the first few negotiation iterations. With negotiation’s ongoing, agents make less and less compromise. Buyer can decide the value of parameter β according to its practical situation. Similarly, when a seller negotiates with several buyers, β formula pt = (1 − (t / Tmax ) ) × p0 , ( β >0 ) can be used to express the remaining negotiation time’s effect on the seller’s negotiation strategy. Suppose kbit [T ] is the compromising degree of sub-buyer

i according to strategy

T in the tth negotiation round, and ksit [T ] is the compromising degree of sub-seller i according to strategy T in the tth negotiation round, where sub-seller

i represents the

ith sub-negotiator of seller when it negotiates with several buyers. We get: kbit [ Τ ] =

1 + ( B it / T bi ) β b

i

.

(2)

1 − ( Bit / Tsi ) β s . ks [ Τ ] = i 1 − ( Bit −1 / Tsi ) β s

(3)

1 + (B

t −1 i

i b

/T )

β bi

i

t i

Sub-buyer i and sub-seller

i make a decision on the value of parameter β bi and β s i

according to their practical situation. (2) Opponent dependent strategy O Agent decides its compromising degree according to that of its opponent. If its opponent makes great compromise, agent will do the same; otherwise agent will compromise little. In addition, with the increase of negotiation opponents, agent will make less and less compromise, because it has more and more chance to reach an agreement.

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Opponent dependent strategy O takes it into account that the effect of the offers of other sub-agents’ negotiation opponent’s on agent’s compromising degree. Generally, if negotiation opponent makes little compromise, agent also makes relatively little compromise, whereas agent will make great compromise. In addition, in generic bilateral negotiation, a buyer only negotiates with one seller, and if the seller quits negotiation, the buyer would bear great loss, so the buyer will cherish the only chance of reaching an agreement, i.e. making relatively great compromise. In one to many negotiation, a buyer negotiates with several sellers at the same time. If the negotiation with a seller fails, it would be possible that buyer reaches an agreement with one of other sellers, so the buyer mostly makes relatively little compromise. Suppose kbit [O ] represents the compromising degree of sub-buyer strategy O in the

i according to

t th negotiation round, ksit [O ] represents the compromising degree

of sub-seller i according to strategy O in the

t th round of negotiation, and we get: offer s it . ) offer s it −1

(4)

offer bit −1 − 1) . offer bit − 2

(5)

kbit [O ] = γ b × (η b ) n × (1 − ks it [O ] = γ s × (η s ) n × ( Where 0 < η b ≤ 1 and 0 < η s ≤ 1 .

(3) Other negotiation threads dependent strategy P Agent also decides its compromising degree according to the negotiation information of other sub-negotiation threads. Compared with offers of other subbuyers’ opponents, if its negotiation opponent’s offer is relatively smaller, agent will make great compromise; otherwise agent will compromise little. When the control agent adopts the optimized patient strategy, all negotiation threads are not mutual independent. While making a decision on its compromising degree, in order to avoid unnecessary negotiation process, single sub-agent should take the information of other negotiation threads into account. For example, a buyer negotiates with three sellers at the same time. In a certain cycle, sub-buyer 1 receives seller 1’s offer 50, and sub-buyer 1 knows the offers of seller 2 and seller 3 are 30 and 40 respectively, i.e. the lowest offer buyers receive is 30. In order to avoid unnecessary negotiation process, sub-buyer 1’s offer to seller 1 in the next round will be not higher than 30. Similarly, sub-buyer 2’s and sub-buyer 3’s offers to seller 2 and seller 3 will also be not higher than30. In addition, the lower seller’s offer is, the more compromise its opponent makes. Because negotiation is with time-delay, when a buyer negotiates with n sellers, given the condition that buyer adopts the optimized patient strategy, each sub-buyer will not immediately calculate the counteroffer to its negotiation opponent once

Multi-Agent Asynchronous Negotiation Based on Time-Delay

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receiving its opponent’s offer, but wait to get negotiation information of other negotiation threads, in order to avoid unnecessary negotiation process. numbt represents the number of offers buyer receives in the

t

th

negotiation round,

t represents the lowest offer buyer receives in the t th 0 < numbt ≤ n and offer smin

negotiation round. Similarly, when a seller negotiates with represents the number of offers seller receives in the

t

th

n buyers, num st negotiation round,

t represents the highest offer seller receives in the t th 0 < num st ≤ n and offer bmax

negotiation round. numbt

numst

i =1

i =1

t t offer smin = min(offer sit ) , offer bmax = max(offer bit )

Suppose kbit [ P ] represents the compromising degree of sub-buyer strategy P in the

i according to

t th negotiation round, kbit [ P ] represents the compromising degree of

sub-seller i according to strategy P in the

t th negotiation round, and we get:

t t ⎧γ 1 × ( offer smin ≥ offer bit −1 offer sit ) if offer smin ⎪ . kb [ P] = ⎨ t t −1 t −1 × − γ offer s offer b offer b otherwise ( ) ⎪⎩ 2 i i min

(6)

t t −1 ⎧γ 3 × ( offer bit offer bmax ≤ offer sit −1 if offer bmax ) ⎪ . ksit [ P ] = ⎨ t −1 t t −1 otherwise ⎪⎩γ 4 × ( offer si − offer bmax ) offer si

(7)

t i

(

)

(

Where

)

0 < γ 1 , γ 3 ≤ 1 and γ 2 , γ 4 ≥ 1 .

The selection of negotiation strategy T, O and P synthetically takes it into account that the most important factors affecting agents’ decision making in bilateral negotiation and the characteristics of one to many negotiation. Agents participating in negotiation can select and combine these strategies according to their practical situation, and then make a decision on their compromising degree. Suppose kit be agent’s compromising degree in the

t th negotiation round, and we get:

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k it = wT k it [T ] + wO k it [ O ] + w P k it [ P ] .

(8)

Where 0 ≤ wT , wO , wP ≤1 and wT + wO + wP = 1 . In generic bilateral negotiation, time factor usually has a remarkable effect on negotiation strategy. We use strategy T to express the remaining negotiation time’s effect on its compromising degree. During negotiation, rational agent will pursue its greatest utility, and strategy O emphasizes negotiation opponent’s strategy’s effect on its compromising degree. Given the condition that the control agent adopts the optimized patient strategy, sub-agent needs to take the information of other negotiation threads into account, to avoid unnecessary negotiation process. 3.2 Main Factors Affecting Negotiation Performance Here we discuss factors having influence on negotiation performance in certain negotiation environment (e.g., negotiation protocols, negotiation strategies, etc.). The main factors include: MAS is a distributed environment, where agents interact with each other through network. Meanwhile negotiation highly depends on time, so communication quality and network’s QoS will affect both negotiation strategies and negotiation results. Factors affecting communication quality include: data quantity, network bandwidth, transfer delay, network failure, etc. In one to many negotiation, the control agent will perform functions such as controlling and coordinating negotiation of sub-agents: negotiation management, e.g., selection of negotiation strategies, decision making of when to offer, communication, etc.; offer evaluation; counter offer generation, etc. Given a certain negotiation environment, the main factor affecting negotiation effect is distributing process loads and the opportunities to offer. (1) The number of negotiation opponents Suppose that there are n agents participating in one to many negotiation, taking the worst situation into account (means that every two agents negotiate, i.e. many to many negotiation), negotiation between n agents forms a complete diagram. The effect of the increase of negotiation opponents on Distributing Process Capability (DPC Load, DPC_L ): the worst situation of n agents taking one to many negotiation is that agents negotiating with each other. We get: DPC_L ≈ O (n 2 ) . So that it is not the more negotiation opponents the better. In one to many negotiation, buyer needs to making a decision on how many negotiation opponents to negotiate in order to reach the best negotiation result. Fig.5 shows negotiation results’ changing with the number of negotiation opponents when taking the effect of the increase of negotiation opponent on negotiation performance into account, where we can find that: with less number of

Multi-Agent Asynchronous Negotiation Based on Time-Delay

265

opponents, agreed price decreases with the increase of negotiation opponent; with greater number of opponents, the agreed price increases with the increase of negotiation opponents.

Fig. 5. Negotiation result’s changing with the number of negotiation opponents

When buyer needs to make a decision on the number of sellers, the number of sellers can be calculated by formula (9), where N represents the maximum of the number of sellers, product),

p min represents the cost of negotiation object (bargaining

p0 represents the finally agreed price, kdpc _ l is the parameter reflecting the

influence of sellers’ increase on communication quality, and ko _ l is the parameter reflecting the other influence of sellers’ increase on buyer’s processing capability. n = arg min((1 − (

（

）

x β ) ) × ( p0 − pmin ) + pmin ) × 1 + kdpc_l × x 2 + ko _ l × x ,0 < β < 1 . N

(9)

Similarly , when a seller needs to make a decision on the number of buyers, the number of buyers can be calculated by formula (10), where N represents the maximum of the number of buyers, (bargaining product),

p min represents the cost of negotiation object

p0 represents the finally agreed price, kdpc _ l is the parameter

reflecting the influence of buyers’ increase on communication quality, and ko _ l is the parameter reflecting the influence of buyers’ increase on seller’s processing capability.

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（

）

x n = arg max((1 + ( )β ) × ( p0 − pmin ) + pmin ) × 1 − kdpc _ l × x2 − ko _ l × x ,0 < β < 1 . N

(10)

(2) The decision making of when to offer In one to many negotiation with time-delay, negotiation threads are asynchronous, and sub-agents should make a decision on when to offer. In practical environment, agents don’t clearly know opponents’ negotiation strategies, processing mechanisms, and can’t forecast communication time, so the situation is greatly complex. Hence, the decision making of when to offer is a key problem for all sub-agents. We give a algorithm with the fixed ratio based negotiation plan. In a certain negotiation round, after certain sub-agent firstly receives offer from its opponent, it waits until the number of sub-agents having received offers reaches a fixed ratio, then all sub-agents having received offers begin to generate new offers. This algorithm describes the decision making process of when to offer according to the fixed ratio based plan. It uses a queue Q to store offers. Suppose the fixed ratio is R, 0 < R ≤ 1 . Begin 1) q = null ; 2) While R > Lengthq / n

insert ( offer ) ; End While 3) All the offers in queue Q, Sub-agents begin to generate new offers respectively; 4)If negotiation succeeds, turn End begin; Otherwise, turn to step 2). End begin

In this algorithm, because some negotiation threads may break up during negotiation, the sellers’ number n may constantly change. Fig.6 and Fig.7 reflect different fixed ratio’s effect on final agreed price. According to the fixed ratio based plan, in each negotiation round, after certain sub-agent firstly receives offer from its opponent, it waits until the number of subagents having received offers reaches a fixed ratio, then all sub-agents having received offers begin to generate new offers. Similarly, it is difficult for sub-buyer to choose a fixed ratio and get good negotiation result. We can find that the negotiation

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result’s changing with fixed ratio is also not monotonic. If the greatest reflecting time difference of sellers is little, greater fixed ratio can get better result (as showed in Fig.6). If the greatest reflecting time difference of sellers is greater, less fixed ratio can get better result (as showed in Fig.7).

Fig. 6. Fixed ratio based plan with little time dependent

Fig. 7. Fixed ratio based plan with great time dependent

4 Conclusion Agent based automatic negotiation has highly promoted the intelligence of agentbased E-commerce. Compared with auction mechanisms, one to many negotiation is more flexible and interactive. Practical one to many negotiation mechanisms mostly are with time-delay, and the research of one to many negotiation with time-delay will

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enlarge its applicability and make agent-based automatic negotiation meet the needs of practical application. In this paper, we analyze analyzes the structures of one to many negotiation, the strategies of control agent, and the flow of one to many negotiation without timedelay. Then the concept of one to many negotiation with time-delay is put forward, and its flow is analyzed. We design three basic negotiation strategies for sub-agents, and propose the decision making mechanisms of when to offer and how many opponents to negotiate. Experimental results validate the correctness and validity of our methods. Because most MAS work in a heterogeneous, distributed and complicated environment, our strategies and mechanisms still need to be validated in practical application. We can extend the single-attribute one to many negotiation brought out in this paper to multi-attributes many to many negotiation. The future work includes: (1) the building of a test bed for one to many negotiation; (2) studying on the characteristics of one to many negotiation with time-delay in dynamic environment;(3) research of the learning mechanisms in one to many negotiation, etc. As a work just beginning, there is still a long way to go before applying one-to-many negotiation into practical commerce application.

Acknowledgments This research is supported by the Key Science Technology Project and the Science Foundation of Chongqing under Grant No.CSTC-2005AC2090 and No.CSTC2006BB2249, supported by the Science Technology Project of Chongqing Municipal Education Commission under Grant No. KJ060704, and the Doctor Foundation of CTBU under Grant No. 09-56-12.

References 1. He, M.H., Jennings, N.R., Leung, H.F.: On Agent-Mediated Electronic Commerce. IEEE Transactions on Knowledge and Data Engineering 15(4) (July/August 2003) 2. Yarom, I., Rosenschein, J.S., Goldman, C.V.: The role of middle-agents in electronic commerce. IEEE Intelligent Systems 18(6), 15–21 (2003) 3. Youll, J.: Agent-based electronic commerce: opportunities and challenges. In: Fifth International Symposium on Autonomous Decentralized Systems, pp. 26–28 (March 2001) 4. Guttman, R.H., Moukas, A.G., Maes, P.: Agent-mediated electronic commerce: a survey. Knowledge Engineering Review 13(2), 143–152 (1998) 5. Kim, J.B., Segev, A.: A Framework for Dynamic eBusiness Negotiation Processes. In: Proceedings of the IEEE International Conference on E-Commerce (CEC’03) 6. Rahwan, I., Kowalczyk, R., Pham, H.H.: Intelligent agents for automated one-to-many ecommerce negotiation. Australian Computer Science Communications 24(1), 197–204 (2002) 7. Kowalczyk, R., Bui, V.: On Constraint-based Reasoning in e-Negotiation Agents. In: Dignum, F., Cort, U. (eds.) Agent-Mediated E-Commerce III (2003)

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8. Brazier, F.M.T., Cornelissen, F., Gustavsson, R., Jonker, C.M., Lindeberg, O., Polak, B., Treur, J.: Compositional Design and Verification of a Multi-Agent System for One-toMany Negotiation. In: Proceedings of the Third International Conference on Multi-Agent Systems, ICMAS-98, p. 8. IEEE Computer Society Press, Los Alamitos (1998) (in press) 9. Guttman, R.H., Moukas, A.G., Maes, P.: Agent-mediated Electronic Commerce: A Survey. Knowledge Engineering Review 13(3) (1998) 10. Brazier, F.M.T., Cornelissen, F., Gustavsson, R., Jonker, C.M., Lindeberg, O., Polak, B., Treur, J.: A multi-agent system performing one-to-many negotiation for load balancing of electricity use. Electronic Commerce Research and Applications 1(2), 208–224 (2002) 11. Kraus, S.: Automated negotiation and decision making in multi-Agent environments. In: Multi-Agents systems and applications. Springer, New York (2001) 12. Faratin, P., Sierra, C., Jennings, N.R.: Negotiation Decision Functions for Autonomous Agents. Int. Journal of Robotics and Autonomous Systems 24(3-4), 159–182 (1998) 13. Sim, K.M., Choi, C.Y.: Agents that react to changing market situations. IEEE Transactions on Systems, Man, and Cybernetics, Part B 33(2), 188–201 (2003) 14. Jennings, N.R., Faratin, P., Lomuscio, A.R., Parsons, S., Sierra, C., Wooldridge, M.: Automated negotiation: Prospects, methods and challenges. International Journal of Group Decision and Negotiation 10(2), 199–215 (2001) 15. Faratin, P., Sierra, C., Jennings, N.R.: Negotiation Decision Functions for Autonomous Agents. Int. Journal of Robotics and Autonomous Systems 24(3-4), 159–182 (1998) 16. Sycara, K.: Multi-Agent Systems. Artificial Intelligence 19(2), 79–92 (1998)

Fuzzy Chance Constrained Support Vector Machine Hao Zhang1, Kang Li2, and Cheng Wu1 1

Department of Automation, Tsinghua University, Beijing 100084, China 2 Queen’s University Belfast, UK

Abstract. This paper aims to improve the performance of the widely used fuzzy support vector machine (FSVM) model. By introducing a fuzzy possibility measure, we first modify the original inequality constraints of FSVM optimization model as chance constraints. We fuzzify the distance between training data and the separating hyperplane, and use a possibility measure to compare two fuzzy numbers in forming the constraints for the FSVM model. By maximizing the confidence level we ensure that the number of misclassifications is minimized and the separation margin is maximized to guarantee the generalization. Then, the fuzzy simulation based genetic algorithm is used to solve the new optimization model. The effectiveness of the proposed model and algorithm is validated on an application to the classification of uncertainty in the hydrothermal sulfide data in the TAG region of ocean survey. The experimental results show that the new fuzzy chance constrained SVM model outperforms the original SVM model. Keywords: Fuzzy SVM, Possibility measure, Chance constrained programming, Fuzzy simulation, Genetic algorithm.

1 Introduction Support Vector Machine (SVM), originally proposed by Vapnik [1] has shown to be able to solve a wide range of classification problems due to its excellent learning performance, and has become a hotspot in the field of machine learning. However, there are still a few issues and limitations yet to be solved. For example, the effectiveness of SVM classifiers can be reduced if there exists noise or outlier in the data as SVMs are quite sensitive to noise. Lin [2-4] proposed Fuzzy Support Vector Machine (FSVM) to improve the SVM model by introducing the membership function. When training separating hyperplane, different data sample has its own contribution to the hyperplane according to the membership. A data point located at the interior of a class has a relatively higher degree of membership, while the noise or outliers have a relatively lower membership. The classification performance of SVM can be significantly improved if the impact of the noise or outliers on hyperplane of SVM can be further reduced. However, in the original FSVM model, membership is only used as the weight on the slack variables. [5] introduced the fuzzy chance constrained programming into FSVM for training K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 270–281, 2010. © Springer-Verlag Berlin Heidelberg 2010

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fuzzy data. In this model, they used crisp equivalents to solve the optimization problem, which relax a support vector to a neighborhood centering around it. Using the possibility measure to frame the constraints in the optimization problem, [6] further established the following model:

r max f ( x )

r s.t. Pos {ξ | gi ( x , ξ ) ≤ 0} ≥ α i , i = 1, 2,L , p.

ξ is

a fuzzy parameter,

r gi ( x , ξ ) are constraint functions and α i are predetermined

confidence level. To solve this problem, [6] proposed two methods: crisp equivalent method and fuzzy simulation method based genetic algorithm. Although [5] introduced the chance constrained programming into the SVM model, the possibility measure was only used for the relaxation of the data points to the neighborhoods, and the optimal points were obtained in these neighborhoods to eliminate noise or outliers. In this paper, we use the basic idea of linear separability to fuzzify the distance between training data and the separating hyperplane, and then use a possibility measure to frame the constraints of FSVM model. By maximizing the confidence level we ensure that the number of misclassifications is minimized and the separation margin is maximized to guarantee the generalization. The effectiveness of the proposed model and algorithm is verified by an application to the classification of the uncertainty of hydrothermal sulfide data in ocean survey TAG region. The experiment results show that the new fuzzy SVM model outperforms the original SVM model. This paper is organized as follows. Section 2 is the preliminaries. Section 3 introduces the new fuzzy chance constrained SVM (FCSVM). In section 4 the fuzzy simulation based on genetic algorithm is used to solve the new model. Section 5 presents the numerical experiments and Section 6 concludes the paper.

2 Preliminaries We consider SVM model to classify between two classes of data, and the training data set is defined as:

r r r ( x1 , y1 ), ( x2 , y2 ),L , ( xl , yl ) ∈ℜn × {±1}, yi = +1, −1. r

with xi

(1)

= ( x1 ,L , xn )T , yi = +1 denotes positive data, yi = −1 denotes negative.

SVM is used for searching for an optimal hyperplane, separating the two classes of data correctly. If the training data set is linearly separable, there exists vector

r ( w, b) ,

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r

where w is normal vector of the optimal hyperplane, b ∈ R is the bias, holding the following inequalities:

r r w T x i + b ≥ 1, for all yi = +1.

r r wT xi + b ≤ −1, for all yi = −1. the above inequalities can be written uniformly as

(2)

r r yi ( wT xi + b) ≥ 1. The decision

function is given as:

r r r f ( x ) = sgn( wT x + b).

(3)

SVM is constructed based on the structure risk minimization principle in statistical learning theory [8], so taking misclassification into account, slack vector

r

ξ = (ξ1 , ξ 2 ,Lξl ) has been introduced to relax training data that violates constraint (2), and the training model is formulated as the following quadratic programming problem [1]: l 1 2 w + C ∑ ξi 2 i =1 rT r ⎧ y ( w xi + b) ≥ 1 − ξi s.t. ⎨ i ⎩ ξi ≥ 0, i = 1,L , l.

min

(4)

3 Fuzzy Chance Constrained Support Vector Machine Definition 1: (Dubois and Prade, 1998)[9] Let X be a nonempty set, of all subset of X , mapping Pos : the mapping satisfy: (1)

Pos(φ ) = 0.

(2)

Pos ( X ) = 1.

(3) Pos (U t∈T At ) = Sup Pos ( At ). t∈T

P( X ) is the set

P( X ) → [0,1] is called possibility measure, if

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273

% be the fuzzy set on X . For every λ ∈ [0,1] , the necessary and Theorem 1 [8]: Let A sufficient condition for any x1 ∈ X

，x

2

∈X

{

Aλ = x | A% ( x) ≥ λ

， α ∈[0,1] , we have:

}

to be s convex set is that for

{

}

A% (α x1 + (1 − α ) x2 ) ≥ min A% ( x1 ), A% ( x2 ) .

X = ℜn is n dimension Euclidean space, A% is the fuzzy set % is convex. on X . If for all λ ∈ [0,1] Aλ is a convex set, then we call fuzzy set A

Definition 2 [8]: Let

，

Definition 3 [8]: Let (1) a% is the convex fuzzy set on X ; (2)

∃a1 , a2 ∈ X and a1 ≤ a2 , ∀x ∈ [ a1 , a2 ] , a% ( x) = 1 and lim a% ( x) = 0 , then a% is x →±∞

called a fuzzy number on X . Definition 4: (Liu, 1998) [6]. Let a% and measure [16] of

b% are two fuzzy numbers, then the possibility

a% ≤ b% is defined as:

(

)

Pos(a% ≤ b% ) = Sup{min a% ( x), b% ( y ) | x, y ∈ R, x ≤ y}. Definition 5: (Enhanced Semi-trapezoidal membership function) [8] Let a% be a fuzzy number, so its enhanced semi-trapezoidal membership function is defined as:

⎧ 0, when x ≤ a1 ⎪ ⎪ x − a1 a% ( x) = ⎨ , when a1 < x ≤ a2 ⎪ a2 − a1 ⎪⎩ 1, when a2 < x.

a1 , a2 are real numbers. (Triangular membership function) [8] Let b% is a fuzzy number, so its triangular membership function is defined as:

⎧ x + 1 − m, when m − 1 ≤ x ≤ m ⎪ b% ( x) = ⎨− x + 1 + m, when m − 1 ≤ x ≤ m ⎪ 0, other . ⎩

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H. Zhang, K. Li, and C. Wu

m is a real number, which is the center of triangular membership function.

% has an enhanced semi-trapezoidal membership Theorem 2: Let fuzzy number 1 a1 = 0 and a2 = 1 , and b% is a fuzzy number % ≤ b% ) is equivalent to with triangular membership function, so the possibility Pos (1

function with the two parameters being

the following inequalities:

1, when m ≥ 1 ⎧ ⎪⎪1 + m Pos(1% ≤ b% ) = ⎨ ，when − 1 ≤ m < 1 2 ⎪ ⎩⎪ 0，when m < −1.

(5)

The above inequalities are also illustrated in Fig. 1.

Fig. 1. (a). When m ≥ 1

Fig. 1. (b). When −1 ≤

m 0

(3)

2.2 Equivalent Control

In [3], a relationship between HM-based SM controller and PWM-based SM controller has been established. Two key results are useful: First, in the SMC, the discrete control input u can be theoretically replaced by a smooth function known as the equivalent control signal ueq. Second, at a high switching frequency, the equivalent control is effectively a duty-cycle control. Based on this useful establishment, the control input u can be modified into a pulse width modulation as ueq during every duty cycle with two switching input u+ and u−. An equivalent control law which forces the system state variables trajectory to the sliding surface can represent the duty ratio control. When the state variable phase trajectory is on the sliding surface, the following conditions must be satisfied: ٛ

S ( x ) = 0, S ( x ) = 0

(4)

Thus the equivalent control signal ueq can be described as: −1

ueq = − ⎡⎣ K T g ( x ) ⎤⎦ K T f ( x )

(5)

2.3 PWM-Based SMC

The conventional PWM control is widely used in DC-DC converters, in which the control input u is switched between ‘1’ and ‘0’ once per switching cycle for a fixed small duration Δ . The time instance where the switching occurs is determined by the sampled value of the state variables at the beginning of each switching cycle. Duty ratio d is then the fraction of the switching cycle in which the control holds the value 1. It is normally a smooth function of the state vector x, and it is denoted by d(x) , where 0 < d(x) 0 S i S < 0, i.e,. ⎨ ⎩ S ( x) < 0

if S ( x) < 0 if S ( x) > 0

(8)

3 Sliding Mode Control for a Buck Converter The Buck converter is one type of the basic DC-DC converters used in industries. We present a practical design of PWM-based SMC application -for a buck converter. Our focus in this design is the application of SMC to converter operating in continuous current mode (CCM), and the discontinuous current mode (DCM) is not discussed here.

Fig. 1. The buck converter

Taking the output voltage error and its differential and integral portions as the state variables, the Buck converter shown in Fig.1 can be described as a form of state-space description:

xٛ = Ax + Bu + D Assuming that

(9)

Vref is constant and capacitor ESR is zero, then

⎡0⎤ ⎡ 0 ⎡ 0 ⎤ 1 0⎤ ⎢Vref ⎥ ⎢ 1 ⎢ Vin ⎥ 1 ⎥ A= ⎢− − 0⎥, B = ⎢− ⎥, D= ⎢ ⎥, u∈{0,1} ⎢ LC⎥ ⎢ LC RC ⎥ ⎢ LC⎥ 0 0⎦ ⎣ 1 ⎣ 0 ⎦ ⎣0⎦

(10)

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Y. Niu et al.

Where L is the inductance value, R is the load resistance, C is the capacitance value, and Vin represents the input voltage. 3.1 System Modeling for Sliding Mode Controller

The surface of the SMC at the stable equilibrium point, S (x) = 0 can be detailed as: S ( x ) = K T xٛ

(11)

S( x ) = k1 x1 + k2 x2 + k3 x3 = k1 x1 + k2 xٛ1 + k3 ∫ x1dt = 0

(12)

Or

Where, x1, x2 and x3 are respectively the voltage error and its differential and integral portions. As mentioned above, the equivalent control signal ueq has been proven equivalent to PWM duty ratio d for SMC. Then the derivation of the PWM-based SMC can be achieved by the equivalent control on the sliding surface S. Substituting x = V − V and x = x = − dV / dt into equation (5), then: 1

ueq =

1 Vin

ref

out

2

1

out

⎡ ⎤ ⎛ k1 1 ⎞ dVout ⎛k 1 ⎞ + LC ⎜ 3 − ⎢Vref − LC ⎜ − ⎟ ⎟ (Vref − VOUT ) ⎥ ⎢⎣ ⎥⎦ ⎝ k2 RC ⎠ dt ⎝ k2 LC ⎠

(13)

Where ueq is continuous and equals to PWM duty ratio d , and 0 < ueq =d 0, which means all the coefficients x1, x2, x3must be with the same sign. Secondly, extracting the time differential, the S (x) = 0 can be rearranged into a stand second-order system form:

s 2 + 2ζωn s + ωn 2 = 0

(19)

Where the values of damping ratio ζ is:

ζ = K1 / 2 K 3 K 2

(20)

Since ζ > 0 then K1 must be positive. Recalling that K1, K2, K3 must be with the same sign, thus finally all the coefficients should be positive for stable operation.

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4 Simulation and Experimental Results The time domain behavior of the proposed SMC is verified on a buck converter using Matlab/simulink, where the Buck converter circuit elements are: Vin=3V, L=4.7uH, C=22uF, R=5Ω and switching frequency fs=1MHz. The simulation mode is shown as Fig.2. To comply with the design equations regarding with the stability and the transient response, the choice for system dynamic performance should be considered with the trade-off between ωn and ξ , where large of simulations have been carried out. Finally we set the bandwidth of the SMC response fω at one-fifteenth of the switching frequency f s , i.e., f s = 15 × ωn ( 2π ) , and choose the damping ratio ξ = 1 . Thus the sliding parameters are determined as: K1 K 2 = 4π f s 15 and K3 K 2 = 4π 2 f s 2 152

Fig. 2. The model of the SMC for a buck converter

Fig.3 shows that the output voltage follows the reference by a slope function until steady state. Then the load suddenly changes from 0.3A to 0.46A (R: 5Ω→3.3Ω), Fig. 4 shows the transient response of the SMC at switching frequency 1MHz. It can be seen that the dynamic response of SMC is satisfying, where the transient response is very fast. Vout

1.5058

2.5

transient output voltage at 4MHz

1.5037 1.5012 1.4987 output Voltage: V / div

2

1.5

1

1.4962 1.4937 1.4912 1.4887 1.4862 1.4837 1.4812

0.5

1.4787 1.4762

0 0

1

2

3

Fig. 3. Output voltage Vout

Time

4

1.4737

2.5

2.55

2.6

2.65

2.7 2.75 Time: s / div

2.8

2.85

2.9 -4

x 10

Fig.4. Dynamic response of SMC when load changes from 0.3A to 0.46A

The functionality of the controller designed and proposed DPWM are experimentally verified using a discrete buck converter with 3.0V input and 1.5V output voltage. The voltage feedback is performed by a 10-bit A/D converter AD9203, and the digital PWM is realized in an 11-bit hybrid DPWM architecture [10]. The implementation of the proposed digital controller DPWM-based is performed on a Xilinx XC2VP30 FPGA with an external 32MHz system clock. A

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423

VHDL design approach is used to synthesize the controller with Xilinx ISE development software. The test platform is pictured in Fig.5.

Fig. 5. Experimental test platform

Fig.6 shows the steady-state output voltage and the corresponding PWM signal in steady state operation at 4MHz. It can be seen that the system has favorable steadystate performance. Fig.7 shows the transient output voltage of SMC

when load

varies from 0.3A to 0.46A. These results prove that the dynamic response of SMC is very fast ( qij , we need to add new production cost λij for the increased order

+

* quantity qij − qij because the original production plan has been changed; * when qij < qij , then we need to spend new disposal expense λij for the left over

−

* products qij − qij .

5 Numerical Examples In this section, we apply the two-stage prediction–correction method [13] to a numerical example, which consists of two manufacturers and two retailers. In the example, we assume that the demands associated with the retail outlets follow a uniform distribution. Hence, we assume that the random demand Pj of retailer distributed in [0, b j ] , j = 1, 2 . The distribution function of Pj is expressed as: ⎧ 0, ⎪ Pj ( x ) = ⎨ x ⎪b ⎩ j

otherw ise x ∈ [0, b j ]

j = 1, 2 .

The other functions are given by:

cij (qij ) = 0.5qij2 + 3.5qij , i = 1, 2; j = 1, 2 .

j is

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A.T. Yang and L.D. Zhao

f1 (q) = 2.5q1m2 + q1m q2m + 2q1m ; f 2 (q) = 2.5q2m 2 + q1m q2m + 2q2m .

c1 (Q ) = 0.5 ( q11 + q21 ) ; c2 (Q ) = 0.5 ( q12 + q22 ) . 2

2

Assume ρ j = 100 ; v j = 10 ; g j = 10 , gij = 10 ; φij = 0.8 . We set bj = 10 when no emergencies happen. The algorithm is implemented in MATLAB and converges well, (see Fig. 2). The convergence criterion used is X k − max[ X k − F ( X k ), 0] ≤ 0.001 and * * * yields the following equilibrium state pattern: q11 = q12* = q21 = q22 = 3.0935 ; * ρ11* = ρ12* = ρ21* = ρ22 = 23.0955 . Then we have the profits of manufacturers and

retailers: ∏1m = ∏ 2m = 64.8152 , ∏1r = ∏ 2r = 366.4327 .

Fig. 2. The convergence of the simulation

We respectively set different φij , the results are given by Table 1. Through bargaining, manufacturers and retailers can determine the parameter of the profit sharing contract. So, the supply chain network can achieve coordination by adjusting the wholesale price from manufacturer i to retailer j . Suppose that the demand scale increased suddenly because of emergencies. Suppose that the demands still follow a uniform distribution, while just the parameter b j has altered. Set bj = 15 , λij+ = 1, i = 1, 2; j = 1, 2 and the profit sharing contract parameter φij = 0.8 . If the retailers still hold the order quantities as bj = 10 ,

SCN Equilibrium with Profit Sharing Contract Responding to Emergencies

453

then their profits will decline while the profits of manufacturers increase (see column 3 in Table 2). So, the retailers prefer to order as the new equilibrium state when

bj =15 . By using the two-stage prediction–correction algorithm, we can obtain the * * following equilibrium state pattern: q11* = q12* = q21 = q22 = 3.8921 ; * * * * ρ11 = ρ12 = ρ21 = ρ22 = 30.1269 . Table 1. The profit sharing contract with different parameters

φij

qij*

ρij*

∏ im

1 0.95 0.90 0.85 0.80 0.75

3.0935 3.0935 3.0935 3.0935 3.0935 3.0935

32.9430 30.4811 28.0192 25.5573 23.0955 20.6336

36.4527 43.5432 50.6337 57.7241 64.8152 71.9057

However, when the equilibrium state has changed, the profits of manufacturers decline compared to no emergencies situation. That is, the supply chain network equilibrium state is broken because of the emergent events. Hence, the manufacturers and retailers have to adjust the profit sharing contract parameter to achieve a new supply chain network coordination state. In this example, we set φij = 0.7 , under this circumstance both the profits of manufacturers and retailers have increased (see column 5 in Table 2). Therefore, we can conclude that the profit sharing contract can coordinate the supply chain network when emergences happen. Table 2. The order plan with emergencies parameters

bj

10

15

15

15

φij

0.8

0.8

0.8

0.7

qij

3.0935

3.0935

3.8921

3.8921

ρij

23.0955

40.9346

30.1269

24.5298

∏

64.8152

124.6811

47.4936

99.9440

366.4327

306.3442

902.8282

537.0326

m i

∏

r j

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6 Conclusions This paper studies the supply chain network equilibrium model with the profit sharing contract under random demand. Contracts in the supply chain network are tools which can coordinate and improve the profit allocation of decision makers. However, when emergencies happen, the demands may change suddenly and the equilibrium state will be broken. In this situation, through numerical examples we show that the manufacturers and retailers can adjust the contracts parameters together to achieve a new supply chain network equilibrium state. That is to say, the profit sharing contract has an anti-emergency ability. We only introduce the profit sharing contract to coordinate the supply chain network in this paper. There are some other contracts that may have this ability, such as quantity discount, buy back, option contract and so on. So, we can try to study and compare these contracts in future work.

Acknowledgment This work was supported by the National Key Technology R&D Program of China (No. 2006BAH 02A06).

References 1. Nagurney, A., Dong, J., Zhang, D.: A supply chain network equilibrium model. Transp. Res. Part E: Logist. Trans. Rev. 38, 281–303 (2002) 2. Dong, J., Zhang, D., Nagurney, A.: A Supply Chain Network Equilibrium Model with Random Demand. Eur. J. Oper. Res. 56, 194–212 (2004) 3. Chee, Y.W., John, J., Hans, H.H.: Supply chain coordination problems: literature review. Working Paper No. 08–04 (2004) 4. Cachon, G.: Supply chain coordination with contracts. In: Handbooks in Operations Research and Management Science: Supply Chain Management. Kluwer Academic Publishers, Dordrecht (2003) 5. Giannoccaro, I., Pontrandolfo, P.: Supply chain coordination by revenue sharing contracts. Int. J. Prod. Econ. 89, 131–139 (2004) 6. Teng, C.X., Hu, Y.X.: The study of supply chain network equilibrium model with contracts. In: Second International Conference on Innovative Computing, Information and Control, ICICIC, Kumamoto, p. 410 (2007) 7. Ritchie, B., Brindley, C.: An emergent framework for supply chain risk management and performance measurement. J. Oper. Res. Soc. 58, 1398–1411 (2007) 8. Zhu, H.J., Tian, Y.: Research on the classification and grading system of emergencies in supply chain emergency management. In: International Conference on Management Science and Engineering-16th Annual Conference Proceedings, ICMSE, Moscow, pp. 513–517 (2009) 9. Yu, H., Chen, J., Yu, G.: How to coordinate supply chain under disruptions. Systems Engineering- Theory & Practice 25, 9–16 (2005)

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10. Cao, E.B., Lai, M.Y.: Supply chain coordination under disruptions with revenue sharing contract. J. of Wuhan Uni. of Sci. & Tech. (Natural Science Edition) 30, 557–560 (2007) (in Chinese) 11. Sun, L., Ma, Y.H.: Supply chain coordination in emergent events using a revenue-sharing contract. J. of Beijing Uni. of Chem. Tech. 35, 97–99(2008) (in Chinese) 12. Teng, C.X., Hu, Y.X., Zhou, Y.S.: Supply chain network equilibrium with stochastic demand under disruptions. Systems Engineering- Theory & Practice 29, 16–20 (2009) (in Chinese) 13. Fu, X.L.: A two-stage prediction-correction method for solving monotone variational inequalities. J. Comput. Appl. Math. 214, 345–355 (2008)

Modeling of the Human Bronchial Tree and Simulation of Internal Airflow: A Review Yijuan Di1, Minrui Fei1,*, Xin Sun1, and T.C. Yang2 1

Shanghai Key Laboratory of Power Station Automation Technology, Shanghai University, Shanghai, 200072, China 2 University of Sussex, UK [email protected], [email protected], [email protected], [email protected]

Abstract. Human bronchial tree is breath passage between pulmonary capillary vessel and fresh air and it is a key part of the human respiratory system. Clinical experience shows that abnormal or diseases of the respiratory system often occur at some bifurcated segments of the bronchial tree. Therefore, for better diagnosis and treatment of such diseases, it is necessary to investigate morphology structure of human bronchial tree and its internal airflow dynamics. In this paper, approaches for the modeling of bronchial tree are outlined based on the morphology structure data obtained from the two sources, i.e. anatomical experiments and CT/MRI. In addition, the simulation of airflow in bifurcating airways is summarized from the aspect of simulation methods and CFD. Finally, possible future research is suggested to develop: (1) a universal dynamic model of the airflow in the bronchial tree; and (2) a user-friendly software package for modeling and simulation. Keywords: Bronchial Tree, Airflow, Modeling, Simulation, Anatomical Experiments, CT/MRI, CFD.

1 Introduction In human breathing physiology, the bronchial tree is breath passage between pulmonary capillary vessel and fresh air and it is a key part of the respiratory system. Some diseases, e.g. tumor, chronic obstructive pulmonary disease (COPD), obstructive sleep apnea syndrome (OSAS), commonly occur in the airways of bronchial tree and seriously affects human body health [1-4]. Therefore, it is necessary to study human bronchial tree for better diagnosis and treatment these diseases. The two major points in the research of human bronchial tree are (1) morphological modeling of bronchial tree; and (2) the airflow simulation in bifurcating airways. These two points have become the most basic and revealing problems in the general case of breathing physiology, which can provide useful information for operation plan, drug particle delivery pattern, pollution dispersion, etc. *

Corresponding author.

K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 456–465, 2010. © Springer-Verlag Berlin Heidelberg 2010

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As the medical ethics, experiments data of bronchial tree can not be directly measured from human living body and direct airflow simulation in human bifurcating airways can not be made. Thus, anatomic experiment and two advanced medical imaging, i.e. X-ray computerized tomography (CT) and magnetic resonance imaging (MRI), has become main approaches to extract the data from human bronchial tree. And fluid characterization on the airflow in bifurcating airways was often investigated in animals. In the 1960s, anatomic experiment firstly became the method of extraction structure data from bronchial tree for generating morphology structure models of bronchial tree [5-18]. However, the data obtained has deviated from actual structure data of human bronchial tree, which may result in incorrect conclusion and limit the research on bronchial tree. With the development of computational capability and advanced medical imaging, CT/MRI makes it possible to generate real 3D bronchial tree models for internal airflow dynamics simulation [19-26]. In the following, the modeling approaches of human bronchial tree are categorized based on two data sources, i.e. anatomical experiments and CT/MRI. The simulation of airflow in bifurcating airways is then reviewed from the view of simulation methods and computational fluid dynamics (CFD). Finally, the problems and prospects in modeling of bronchial tree and airflow simulation are briefly illustrated.

2 Modeling of Human Bronchial Tree According to the sources of morphology structure data, modeling of human bronchial tree can be classified into two categories, as shown in Fig.1.

Fig. 1. Modeling of human bronchial tree

2.1 Modeling Based on Anatomical Experiments In 1963, by measuring the length and the diameter of each bronchium in bronchial tree of five normal volunteers, Weibel [5] proposed a symmetric model, which took the human lung as 23 generations regularly bifurcated airways, while the effect of airway branching asymmetry was neglected. Horsfield et al. [6, 7] presented an asymmetric model with the spatial location of airways neglected. Although these two classical models were developed based on careful measurements, none of them included information on the angle between two successive bifurcation planes. In 1980, to account for the 3-dimensional (3D) nature of the airway system, an asymmetrical model of the upper trachea-bronchial tree was proposed by WenJia [8]. In this model, the orientation angle of each tube relative to its parent tube was chosen

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from the two solutions computed from the measured gravitational inclination and the branching angle. In later research, numerous studies on bifurcating flow have been performed to investigate the effect of bifurcation on airflow pattern and particle deposition et al. They considered the human lung as either symmetric bifurcation airways [3, 9-12], or asymmetric airways [13-18], and most of these model were based on the Weibel model or Horsfield model. However, actual human bronchial tree airways show distinct irregular features, and the regular airway models may not reflect the realistic flow characteristics in the human bronchial tree. 2.2 Modeling Based on CT/MRI As the emergence of CT/MRI, numerous studies on bronchial tree no longer simply depended on anatomical experiments. CT/MRI, as an in-vivo and non-invasive tool, showed the significant improvements and accuracy increase in morphological modeling of human bronchial tree [19-26]. The 3D mathematical morphology (3DMM), diffusion limited aggregation (DLA), energy-based modeling and fractal representations were used to develop a 3D model of the human airway tree [19]. Results showed morphometric characteristics of the bronchial tree were in good agreement with those reported. Using a semi-transparent volume rendering technique, a realistic 3-D model of the bronchial tree structure was developed [20] based on CT scans. In this study, the tree segmentation was performed by a DLA-based propagation. Merryn et al. [21] modeled entire conducting airway system in human bronchial tree by a volume-filling algorithm to generate airway centerline locations within detailed volume descriptions of the lungs. Curvilinear airway centerline and diameter models had been fitted to human bronchial tree extracted data from CT scanners. Subsequently, MRI was combined with CT together to extract morphology structure data from human bronchial tree, e.g. Montesantos et al. [22] generated a hybrid conceptual model based on MRI and high-resolution CT. A novel layer-bylayer searching algorithm was presented to reconstruct branches of human airway tree from point clouds obtained from CT/MRI [23]. Once the searching direction was fixed in each lay, the topological relationship between branches and the relative location of each branch was identified. Furthermore, in 2001, a 4-dimensional (4-D) NURBS-based cardiac-torso (NCAT) phantom was developed by Segars [24] based on 4-D tagged MRI and respiratory-gated CT. By this NCAT phantom, few model of the airway tree was built. For example, Garrity et al. [25] combined a segmentation technique with an algorithmic technique formulated by Kitaoka et al. [19], and developed a dynamic respiratory model for the individual lobes of the lungs and for the bronchial tree.

3 Simulation of Airflow in Bifurcating Airways In this section, the simulation of airflow in bifurcating airways is firstly summarized from the aspect of simulation methods and CFD. Then, the simulation methods mainly are elaborated from experimental simulation and numerical simulation.

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3.1 Simulation Based on Methods Over the last few decades, airflow simulation in bifurcating airways of human bronchial tree has been largely studied base on mechanical properties and dynamics properties of lung. The simulation methods of airflow in bifurcating airways are shown in Fig. 2.

Fig. 2. The simulation method of airflow in Bifurcating airways

Experimental Simulation Methods. Numerous experimental investigations have been performed in the past few decades to estimate the airflow in the human respiratory airways. In 1978, based on a multialveolar model described by a graph, a method was proposed by Chauvet [26] to deal with ventilator inequalities to investigate the variation of press and velocity. Through a Y-shaped tube bifurcation, a stead streaming displacement of fluid elements was observed on the oscillatory velocity vector field [27]. In this research, the relationship among displacement, Reynolds (Re) and alpha was studied. Ben [28] analyzed the gaseous dispersion of gas mixing in the human pulmonary airway by bolus response methods and found that gaseous dispersion was strongly related to flow velocity and it matched well with the theory of turbulent or disturbed dispersion. Snyder et al. [29] investigated the flow energy loss, and found that the flow energy loss was nearly independent of flow direction. An analysis of these observations suggested that kinetic energy factors, not shear stresses, accounted for most of the energy dissipated in central airways and in simple bifurcating sections. The pressure-flow relationship at high-frequency and low stroke volume was measured in human upper and central airways by a respiratory tract model [30]. Plotted against Re/β (ratio between Reynolds and Womersley numbers), the normalized instantaneous pressure drop was generally smooth throughout the range of Re/β except for the appearance of a transition at the lowest frequency, suggesting the onset of turbulent flow. By 3-D laminar flow profiles measured, the secondary flow retarded the onset of local flow separation by convecting axial

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momentum into the boundary layer, which was adjacent to the diverging wall of the bronchial tube [31]. Kulkarni et al. [32] studied the airflow in first four generations of the bronchial tree based on a 2-D, fluid mechanical model. The computation results for an asymmetric breathing cycle showed that preferred flow was proximal to the trachea, areas of recirculation, and time-averaged expiratory shear stresses at the airmucus interface. In Popwell’s study [33], the simulation of airflow was carried out under different frequency, tidal volume and Reynolds through a model casted in a transparent silicone elastomer. In recent years, the oscillatory flow in human lung airways down to the 6- generation through the branching network was studied by digital particle image velocimetry (DPIV) [34]. It was used to analyze lung ventilation during breathing under rest conditions and for high frequency ventilation (HFV). In additional, a distributed model of bronchial tree based on Weibel model was proposed by Ginzburg et al. [9] to simulate the global dynamic characteristics of human lung. In the resulting model, local mechanical characteristics of each airway were represented by RCL circuits, and parameters of the electrical components were determined from local physiological data. The global resistance to airflow and the dynamic compliance of bronchi decreased as the forced oscillation frequency increased. Numerical Simulation Methods. While current in-vivo experimental techniques can only reliably provide total or regional airflow features, numerical simulations can often provide much more detailed information in both space and time and it has become the effective ways to study airflow dynamics in bifurcating airways [11-12, 15-16, 19, 35-40]. The methods of numerical simulations for airflow can be approximately classified into six categories: The control volume method (CVM): The fluid flow in bifurcations of a symmetric tree was investigated by Andrade et al. [15] by the simulation of a 2D Navier-

Stokes and continuity equations, which was solved for the velocity and pressure fields by CVM. Flow distribution was significantly heterogeneous at an increased Reynolds number. At low Reynolds number, the flow distribution throughout the airways was quite uniform while the nonlinear contribution from the inertial terms became relevant at high Reynolds number. Liu et al. [11, 16] studied the inspiratory flow characteristic in symmetric and asymmetric three-generation lung airway respectively. By the simulation of three-dimensional laminar Navier-Stokes equations based on CVM, relations between Reynolds number and flow characteristics, including flow patterns and pressure drop, was established. The finite element method (FEM): FEM was applied to numerically study steady inspiratory and expiratory flow in a symmetrical bifurcating airway model [35]. In this research, most of the important flow features observed in experiments were captured in the numerical simulation. The numerical simulation of fluid flow with high-frequency and low-tidal-volume ventilation was carried out by FEM in the first 6-generations of human bronchial tree [36]. Results indicated preferred flow proximal to the trachea, areas of recirculation, and time-averaged expiratory shear stresses at the air-mucus interface. Yang et al. used FEM to calculate the nonlinear deformation of the thin-wall structure of 3-generation airway [37]. The deformation of the

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collapsible tube increased the resistance to the fluid flow and formed a jet that altered the downstream flow pattern significantly. The finite difference method (FDM): Airflow fields within bronchial airway bifurcations were computed by solving the three-dimensional Navier-Stokes equation with FDM [38]. The large eddy simulation (LES): LES resolves large-scale energy-containing turbulent eddies and parameterizes small-scale unresolved eddies and has become an important numerical simulation methods of fluid mechanics. Luo [39] employed LES method to study the transitional and turbulent airway flow during inspiration in a single asymmetric bifurcation model. The influence of the non-laminar flow on the patterns and the particle paths was investigated in both 2D and 3D models. Results indicated that the differences in geometry can heavily influence the nature of the flow. Transitional and turbulent flow within the trachea and bronchial of asymmetric upper airways during high frequency oscillatory ventilation (HFOV) were also investigated by using LES [40]. The finite volume method (FVM): By the use of FVM, transient laminar inhalation with a realistic inlet waveform was simulated in an asymmetric out-of-plane human upper airway model. Results showed that the flow fields are similar to those obtained with equivalent Reynolds numbers at steady state. Stronger axial and secondary velocities occurred at all upper branch locations during flow deceleration because of the dynamic lingering effect [19]. The fluid network theory: Based on the fluid network theory, Lai et al. [12] investigated a three-element model of lumped parameter. The pressure and flow rate distributions in different positions of the lungs during normal respiration and partial bronchial obstruction were compared. 3.2 Simulation Based on CFD For the limitations [3] of experimental method and simulation analysis, i.e. complexity of questions and high-cost, computational fluid dynamics (CFD) simulation has become a powerful and often indispensible tool for studying airflow in realistic and complicated airway geometry[3, 37, 41-45]. CFD simulations can provide not only 3D flow pattern within the airways, but also detailed particle deposition patterns. Lin et al. [41] studied the upper and intra-thoracic airways and their role in determining central airflow patterns by CFD technique. The presence of turbulent laryngeal jet on air flow in the human intra-thoracic airways was found to increase the maximum localized wall shear stress by three-folds. It was found that turbulence could significantly affect airway flow patterns as well as tracheal wall shear stress. Some airflow simulations in human bronchial airways operated by CFD were compared with experimental measurements and good agreements have been obtained. For example, Rochefort et al. [42] carried out both experimental study and CFD simulation on the same human proximal airways, and they found the velocity agreement between measurement and calculation was within 3%. Main and secondary

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flow velocity intensities were similar, as were velocity convective patterns. This combined numerical and experimental approach of flow assessment in realistic human airway geometries confirmed the strong dependence of airway flow patterns on local and global geometrical factors. The CFD-simulated flow features qualitatively had a good agreement with the PIV-measured. More recently Ma et al. [43] investigated the CFD predictions of flow field and particle trajectory with experiments within a scaled-up model of alveolated airways. At 12 selected cross section, the velocity profiles obtained by CFD was in agreement with those by particle image velocimetry (within 1.7% on average), and the CFD predicted trajectories also matched well with particle tracking velocimetry experiments. Different from above mentioned studies only considering a straight smooth airway, Yang et al. [3] investigated the effect of COPD on respiratory flow (airflow pattern, airflow rate and pressure drop) on four different four-generation models based CFDsimulation Laminar Navier-Stokes equation. The calculation showed that the flow separation existed in the conjunction region. In a bifurcation airway, the re-circulation cells generated both upstream and downstream blocked the air from entering the downstream branches. Additional, some CFD commercial software programs in the market has got application in airflow investigation in human bronchial tree, such as, FIDAP and FLUENT. McHugh et al. [36] studied the fluid flow from high-frequency and lowtidal-volume ventilation in bronchial tree based on FIDAP CFD package. The air flow pattern and flow rate distribution in human lung model were numerically studied using low Reynolds number (LRN) k-ω turbulent model [44] and the CFD solver FLUENT. Compared with the laminar flow, the secondary flow of turbulent flow was weaker than that of the laminar flow, and the turbulent axial flow velocity profile was more flat in the center of the tube. The ratio of the air flow rate between left and right lobes was insensitive to Reynolds number.

4 Problems and Prospects From all above mentioned, a large number works on the modeling of human bronchial tree and the simulation of airflow in bifurcation airways has been generally performed, but there still exist some problems on them: (1) It can be found that these models or simulation methods was special and individual, lack of the universal property model or method between them. (2) The modeling of human bronchial tree and internal airflow simulation were studied from the viewpoint of microscopic levels (such as organ levels) while the respiration investigation from molecular levels in the bronchial tree also has made [45, 46]. However, there hasn’t a synthetic study both from the microscopic levels and from the molecular levels. (3) The modeling and simulation works are far from practical use. For these issues, it is necessary to further develop a universal variable-parameter dynamic model for better study realistic dynamical respiratory motion. This model can be based on advanced medical imaging, biomechanics and mathematical methods.

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Currently, there are some commercial software programs in the global market for research and clinical applications [47, 48]. However, by using the published algorithms or the commercial software programs in the market, many flaws occur in the generated geometries, which impair the use of the models directly. Therefore, for improving surgical operation, recovery of postoperative respiratory function and particle disposition, a user-friendly software package combined the geometries with workable numerical models for modeling of bronchial tree and internal airflow dynamics simulation is suggested to develop. Acknowledgments. This research is supported by Mechatronics Engineering Innovation Group project from Shanghai Education Commission, The graduate student innovation fund of Shanghai University under Grand SHUCX101015.

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Robust Semi-supervised Learning for Biometrics Nanhai Yang, Mingming Huang, Ran He, and Xiukun Wang Department of Computer Science and Technology, Dalian University of Technology, 116024 Dalian, China

Abstract. To deal with the problem of sensitivity to noise in semi-supervised learning for biometrics, this paper proposes a robust Gaussian-Laplacian Regularized (GLR) framework based on maximum correntropy criterion (MCC), called GLR-MCC, along with its convergence analysis. The half quadratic (HQ) optimization technique is used to simplify the correntropy optimization problem to a standard semi-supervised problem in each iteration. Experimental results show that the proposed GRL-MCC can effectively improve the semi-supervised learning performance and is robust to mislabeling noise and occlusion as compared with GLR. Keywords: Biometrics, Semi-supervised Learning, Robust, Correntropy.

1 Introduction With the advent of information age, data collection and storage competency is greatly improved. Discovery and extraction of useful information from the mass data becomes common requirement of bioinformatics and biometrics field. Since labeling often requires expensive human labor, one often faces a lack of sufficient labeled data. However, large numbers of unlabeled data can be far easier to obtain. In 1992, the concept of “semi-supervised” is proposed for the first time, which uses a large number of unlabeled data to assist insufficient labeled data for learning. In the recent decades, graph-based semi-supervised learning (SSL) have been becoming one of the hottest research area in SSL field, which models the whole data set as an undirected weighted graph, whose vertices correspond to the data set, and edges reflect the relationships between pair wise data points. In practice, during collecting data, noise may occur. Taking image data as an example, the training data may contain undesirable artifacts due to image occlusion, illumination, or image noise. At the same time, for supervised learning, mislabeling of training data may occur and deteriorate the performance of the learning model. Therefore, noisy problem has been received considerable interests from the machine learning and data mining communities. In graph-based SSL, noise problem has not been covered thoroughly. [1] proposed a heuristic method to remove the bridge points that connect different classes; [2] proposed a robust graph-based SSL method which can determine the similarities between pairwise data points automatically and is not K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 466–476, 2010. © Springer-Verlag Berlin Heidelberg 2010

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sensitive to outliers. Most existing methods adopt heuristic strategy to resolve the noise problem and hence lack of theory foundation. Gaussian-Laplacian Regularized (GLR) framework is a classical framework, most of traditional graph-based SSL algorithms are based on it [3][4][5]. This paper analyzes the effect of noise on GLR, which is based on least square criterion and is sensitive to noise [6]. To solve this problem, we propose a robust semi-supervised learning framework based on maximum correntropy criterion (MCC) [6][7], called GLR-MCC, along with its convergence analysis. The half quadratic (HQ) optimization technique is used to simplify the correntropy optimization problem to a standard semi-supervised problem in each iteration, then a greedy algorithm is proposed to increase the objective function until convergence. Promising experimental results on the UCI databases and face databases demonstrate the effectiveness of our method. The remainder of this paper is organized as follows. In section 2, we briefly review GLR method. In section 3, we discuss robust GLR-MCC framework and present an algorithm based on half quadratic to optimize it. We give the experimental results in section 4 and summarize this work in section 5.

2 GLR In SSL, we are given a set of data points l

Χl = { x i }i =1 are

labeled, and Χu

n

= { x i }i =l +1 are

Χ = {x 1,...xl , xl +1,..., x n } ∈ Rd

unlabeled. Each xi

∈X

where

is drawn from a

fixed but usually unknown distribution p(x ) . In the graph-based SSL methods, model the whole data set as a graph G = (V , E ) .V is the vertex set, which is equivalent to the data set, and E is the edge set. Associated with each edge eij ∈ E is a nonnegative, weight wij

≥ 0 reflecting

how similar datum i is to datum j. If there is no edge present

between samples xi and xj , w ij = 0 . The basic assumption behind graph-based SLL is the cluster assumption [8][9], which states that two points are likely to have the same class label if there is a path connecting them that passed through the regions of high density only. Zhou et al. [10] further explored the geometric intuition behind this assumption: 1) nearby points are likely to have the same label, and 2) points on the same structure (such as a cluster or a submanifold) are likely to have the same label. Note that the first assumption is local, whereas the second one is global. The cluster assumption tells us to consider both the local and global information contained in the data set during learning. According to the cluster assumption, the general geometric framework for SSL seeks an optimal classification function f by minimizing the following objective Η( f ) = ηC (x L ) + βS ( f )

(1)

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where C(.) denotes the loss function, which measures loss between the predictive labels and original labels, and S (f ) reflects the intrinsic geometric information of the marginal distribution p(x ) . The reason why we should punish the geometrical information of f is that in SSL, we only have a small portion of labeled data (i.e. l is small), which are not enough to train a good learner by purely minimizing the structural loss of f . Therefore, we need some prior knowledge to guide us to learn a good f . What p(x ) reflects is just such type of prior information. Moreover, it is usually assumed [20] that there is a direct relationship between p(x ) and p(y | x ) , i.e. if two points xi and xj are close in the intrinsic geometry of p(x ) , then the conditional distributions p(y | x 1 ) and p(y | x 2 ) should be similar. In other words, the conditional probability distribution p(y | x ) should vary smoothly along the geodesics in the intrinsic geometry of p(x ) . GLR framework aims to solve the following optimization problem: l

n

n

f = arg min ∑ (fi − yi )2 + ζ ∑ ∑ (fi − f j )2 wij f

i =1

(2)

i =1 j =1

where the former is the loss item, the latter is the smoothness item. T f = ⎡⎣ f1, f2,..., fl ,..., fn ⎤⎦

,

fi

is the classifier.

y = [y1, y2 ,...yl ,...yn ]T

,

yi

is the original label.

The smoothness item can be approximated by n

n

∑ ∑ (fi − fj )2 wij

(3)

= f T Lf

i =1 j =1

where L is the graph Laplacian L = D − W ∈ \n×n , adjacency graph, D

= diag (∑ i w1i ,...,∑ i wni ) .Then

wij

are the edge weights in the data

the total loss we want to minimize

becomes l

f = arg min ∑ ( fi − yi )2 + ζ f T Lf f

(4)

i =1

By setting ∂J / ∂f = 0 we can get that f = (J + ζ L)−1Jy

(5)

where J ∈ \n×n is a diagonal matrix with its ( i, i ) -th entry, y is a n × 1 column vector with its i -th entry ⎧ ⎪ 1, if x i is labeled; J (i, i ) = ⎪ , y(i ) = ⎨ ⎪ 0, otherwise, ⎪ ⎩

⎧⎪ yi , if x i is labeled; ⎪⎨ ⎪⎪ 0, otherwise ⎩

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Since (2) is based on l2 norm, noise will significantly impair objective function. GLR’s performance will decrease rapidly when noise occurs [6].

3 Robust SSL Based on MCC Theoretical analysis and experiment results [6] demonstrate that correntropy criterion can be very useful in non-Gaussian noise, especially in the impulsive noise environment. 3.1 Problem Formulation Recently, the concept of Maximum Correntropy Criterion (MCC) was proposed for ITL [11][19]. MCC is a local criterion of similarity and is very useful for cases when the noise is nonzero mean, non-Gaussian, with large outliers [6]. The correntropy is a generalized similarity measure between two arbitrary scalar random variables A and B, defined by Vσ (A, B ) = E [kσ (A − B)]

(6)

where kσ (.) is a kernel function that satisfies Mercer’s theory [12] and E[.] is the expectation. In practice, the joint probability density function is often unknown and only a finite number of data

{(ai , bi )}ni =1

are available, which leads to the sample

estimator of the correntropy: n  1 Vσ (A, B ) = ∑ kσ (ai − bi ) n i =1

(7)

The correntropy has a clear theoretic foundation and some important properties [13], such as symmetric, positive and bounded. Substituting Gaussian kernel function g(x ) = exp(−

||x ||2

σ2

) into

(7) and combing (4), we get following maximum correntropy

problem: l

E (f ) =

n

i =1

l

=

∑ exp(− i =1

T

n

∑ g(fi − yi ) + ζ ∑ ∑ g(fi − fj )wij i =1 j =1

2

( fi −yi ) σ2

n

n

) + ζ ∑ ∑ exp(− i =1 j =1

T

where f = ⎡⎣ f1, f2,..., fl ,..., fn ⎤⎦ , y = ⎡⎣ y1, y2,..., yl ,..., yn ⎤⎦ .

(8) ( fi − fj )2 σ2

)wij

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The optimal solution f is obtained by maximizing (8) according to Karush-KuhnTucker (KKT) conditions. As observed in (8), the former is a loss item: if yi is mislabeled at initial and fi is labeled correctly, fi ≠ yi , then we regard yi as outlier and expect it has small contribution to the objective; if yi is labeled correctly at initial and its corresponding data is the outlier, we can’t correctly evaluate fi, and hence we also expect fi has small contribution to the objective. The latter is a smoothness item, note that we hope the same label points are likely nearby according to the cluster assumption. If fi and fj have the same label, then xi and xj are potentially in the same cluster, and wij is may have a high value. If fi and fj belong to different classes, then xi and xj are potentially in different clusters, and wij should be low. We also recognize that it is hard to find a closed form for (8) due to its nonlinear. Hence the objective of (8) is difficult to be directly optimized. In the next section, we introduce an approximate strategy to optimize it. 3.2 Optimization Algorithm via Half Quadratic In ITL, the half-quadratic technique [11][14][15], expectation maximization (EM) method [16] and conjugate gradient algorithm [17] can be utilized to solve nonlinear ITL optimization problem. Here, we follow the lines of [18] and derive an algorithm to solve (8) based on the half-quadratic technique. Based on the theory of convex conjugated functions [13], we can easily derive the following proposition Proposition 1: There exists a convex conjugated function of g(x ) , such that, g(x , σ) = exp(−

||x ||2 σ

2

) = sup (p

||x ||2

p ∈R−

σ2

− ϕ(p))

(9)

and for a fixed x , the maximum is reached at p = −g(x , σ) . Substitute (9) into (8), we have the augmented objective function in an enlarged parameter space Eˆ(f , P,Q) =

l

∑ ( pi i =1

( fi −yi )2 σ2

)

n

n

⎛ − ϕi (pi ) + ζ ∑ ∑ ⎜⎜⎜qij ⎝ i =1 j =1

( fi − fj )2 σ2

⎞ − φij (qij ) ⎟⎟⎟ wij ⎠

(10)

where P is diagonal matrix, and P (i, i) = pi and Q = [qij ] ∈ \n×n store the auxiliary variables introduced in half quadratic optimization. According to the Proposition 1, we have that for a fixed f , the following equation holds. E ( f ) = sup Eˆ( f , P ,Q ) P ,Q

(11)

Then we can conclude that maximizing E (f ) is identical to maximizing the augmented function Eˆ(f , P,Q ) .

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max E (f ) = max Eˆ(f , P,Q ) f

471

(12)

f ,P ,Q

Then we can divide into two steps to solve this problem: 1) Calculate auxiliary variations P and Q : pi = exp(−

( fi −yi )2 σ

2

) , qij = exp(−

( fi − f j )2 σ2

)

2) Substitute P and Q into (11), we get: l

arg max ∑ exp(− f

( fi −yi )2 ( fi −yi )2 σ2

i =1

)

σ2

n

n

+ ζ ∑ ∑ exp(−

( fi − fj )2 ( fi − fj )2 σ2

i =1 j =1

)

σ2

wij

(13)

By transforming smoothness item, we can easily get: n

n

∑ ∑ exp(− i =1 j =1

( fi − fj )2 ( fi − fj )2 σ2

)

σ2

wij = f T L ′f

where L ′ = D ′ − W ′ ,W ′ is the new weight matrix, wij ′

(14)

= exp(−

( fi − f j )2 σ2

)wij , D ′ is

a diagonal

matrix D ′(i, i ) = ∑ j Wij ′ . By derivation, we obtain the solution of (12) f = (J ′ + ζ L ′)−1J ′y

(15)

where J ′ = diag([p1,..., pn ]) , y is the a n × 1 column vector ⎧⎪ y , if x i is labeled; y(i ) = ⎪⎨ i ⎪⎪ 0, otherwise ⎩

All above is about two-class case, it is easy to extend GLR-MCC algorithm to multiclass classification problems. Suppose there are c classes, we can obtain the solution F = (J ′ + ζ L ′)−1J ′Y

(16)

where both F and Y are matrixes, ⎡f ′ ⎢ 11 ⎢ ⎢f ′ F = ⎢ 21 ⎢ ... ⎢ ⎢f ′ ⎢⎣ n 1

⎡y ′ y ′ ... f1k ′ ⎤⎥ ⎢ 11 12 ⎥ ⎢ ⎢ y21′ y22′ f22′ ... f2k ′ ⎥ ⎥,Y = ⎢ ⎢ ... ... ... ... ⎥ ... ⎥ ⎢ ⎥ ⎢y ′ y ′ fn 2′ ... fnk ′ ⎥ ⎢⎣ n 1 n2 ⎦ f12′

... y1k ′ ⎤⎥ ⎥ ... y2k ′ ⎥ ⎥, k =c. ... ... ⎥ ⎥ ... ynk ′ ⎥⎥ ⎦

Intuitively, (16) is not the standard labels, so we propose a greed algorithm to seek a local optima. fi ′ = [ fi1′ fi 2′ ... fik ′ ] ∈ \d , we should discrete it to get the standard labels at first which can’t guarantee to increase the value of (13); then we adopt the greed algorithm to calculate a optimal solution, i.e., if the solution after discreting can’t increase the value of (13), we retain original value, otherwise replace it; finally

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we make use of the F value as Y in the next iteration, and recompute (16) until convergence. The main procedure of GLR-MCC is summarized as follows: Algorithm 1: GLR-MCC l

n

Input: Χ = { x1,...xl , xl +1,..., xn } ∈ Rd , Χl = { x i }i =1 are labeled, Χu = { x i }i =l +1 are unlabeled. Output: The labels of all the data points. Step 1. Calculate W ; Step 2. Repeat (a)Calculate W ′ by wij ′ = exp(−

( fi − f j )2

σ2

)wij ,

and calculate L ′ by L ′ = D − W ′ (b) Calculate J ′ by (15) and F by (16) (d) Adopt the greed algorithm to calculate the labels (discrete F ) Until all the labels are convergence to a fixed point. 



Proposition 2. Denote E t  E (f t , P t ,Qt ) is the function in the t-th iteration, then the 

sequence {E t }t =1,2,... generated by GLR-MCC converges. Proof: According to [11] and the step 2 of Algotithm1, we have     E ( f t , P t ,Q t ) ≤ E ( f t , P t +1,Q t ) ≤ E (f t , P t +1,Q t +1 ) ≤ E (f t +1, P t +1,Q t +1 )

The function increases at each iteration maximization step. Therefore, the sequence  {E t }t =1,2,... is non-decreasing. We can easily verify that E (f ) is bounded (property of 

correntropy [6]), and by (12) we get that E (f t , P t ,Q t ) is also bounded. Consequently we can conclude that GLR-MCC will converge.

4 Experiments

、

In this section, we verify the robustness of our proposed GLR-MCC algorithm and compare the performance with GLR method. Three UCI Databases ORL and Yale face databases are selected for performance evaluation. Details of these datasets are shown in Table 1. Table 1. Datasets used in experiments Datasets Balance-scale Sonar Tic-Tac-Toe(TTT) ORL Yale

Dimension 4 60 9 1024 1024

Classes 3 2 2 40 15

Instances 625 208 958 400 163

Feature real number real number real number non-negative non-negative

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In all the experiments, training and testing samples are randomly selected from each dataset and semi-supervised learning accuracy is reported. In all the figures, the x-axis represents the percentage of randomly labeled samples, and the y-axis is the average classification accuracy over 50 independent runs. Traditional graph construction methods typically decompose the graph construction process into two steps, graph adjacency construction and graph weight calculation. For graph adjacency construction, there exist two widely used methods: ε -ball neighborhood and k-nearest neighbors. For graph weight calculation, there exist three frequently used approaches•1) Gaussian Kernel 2) Inverse Euclidean Distance 3) Local Linear Reconstruction Coefficient. In our experiments, we adopt k-nearest neighbors and Gaussian Kernel to calculate W . K-nearest neighbors: The samples x i and x j are considered as neighbors if x i is among the k-nearest neighbors of x j or x j is among the k-nearest neighbors of x i where k is a positive integer and the knearest neighbors are measured by the usual Euclidean distance. Gaussian Kernel: ⎧ − || xi − x j || ⎪ δ Wij = ⎨e ⎪⎩ 0

2

i is j ' s neighbor i isn ' t j ' s neighbor

In all of the experiments, k is set to 20, σ is set to 0.1. 4.1 UCI Datasets We applied GLR-MCC and GLR to three UCI data sets in UCI machine learning repositories: Balance–scale Sonar and TTT. Balance-scale database was generated to model psychological experimental results. Each example is classified as having the balance scale tip to the right, tip to the left, or be balanced. The attributes are the left weight, the left distance, the right weight, and the right distance. The correct way to find the class is the greater of (left-distance × left-weight) and (right-distance × rightweight). If they are equal, it is balanced. Sonar data set contains signals obtained from a variety of different aspect angles, spanning 90 degrees for the cylinder and 180 degrees for the rock. Tic-Tac-Toe (TTT) database encodes the complete set of possible board configurations at the end of tic-tac-toe games, where "x" is assumed to have played first. We randomly select 5% of training samples as mislabeling noise. Table 2. Classification accuracy on mislabeling noise

Datasets Balancescale Sonar TTT

40% 89.70 77.45 81.77

GLR 60% 90.40 80.32 82.82

70% 90.38 83.91 82.87

40% 91.66 79.34 82.27

GLR-MCC 60% 92.54 82.88 83.40

70% 93.93 85.84 84.37

Table 2 shows the results of different methods under mislabeling noise. GLR-MCC achieves the highest average correct classification rate on all testing datasets. Since

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the mislabeling noise changes the relationship of neighborhood near the boundary of different classes, GLR’s performance decreases rapidly as number of training samples becomes smaller. Since GLR-MCC tries to reduce the contribution of noise points, it can efficiently deal with the mislabeling noise so that it performs better than GLR. 4.2 ORL and Yale Face Datasets In real face recognition system, it is necessary to label large amount of training facial images to learn a robust classifier. But during collection of facial images, two types of noise maybe occur. The one is mislabeling noise and the other is image noise. The mislabeling noise occurs when we mislabel one person’s facial image to another; and the image noise occurs when the person’s face is close to border of the camera so that we can only crop part of the face. In this experiment, we use ORL and Yale face databases to validate different methods under above two noises. The ORL database contains ten different images of each of 40 distinct subjects. The images were taken at different times, varying the lighting, facial expressions and facial details. The Yale face database consists of 165 gray-scale images of 15 individuals. There are 11 images per subject, with variations of facial expressions or different configurations. Each facial image is in 256 grey scales per pixel and cropped into size of 32 × 32 pixels by fixing the positions of two eyes. For each individual images are randomly selected for training and the rest are used for testing. And 5% facial images per person is randomly selected as noisy samples.

95 average classification accuracy(%)

average classification accuracy (%)

Fig. 1. Cropped facial images and their corresponding noisy images on ORL database

90 85 80 75 GLR-MCC GLR

70 65 40

50

60

70

80

percentage of randomly training points

(a) ORL

90

75

70

65 GLR-MCC GLR

60

55 40

50

60

70

80

percentage of randomly training points

(b) Yale

Fig. 2. Average classification accuracy on mislabeling noise

90

average classification accuracy (%)

average classification accuracy(%)

Robust Semi-supervised Learning for Biometrics

90 85 80 75

GLR-MCC GLR

70 40

50

60

70

80

percentage of randomly training points

(a) ORL

90

475

72 70 68 66 64 62

GLR-MCC

60

GLR

58 40

50

60

70

80

90

percentage of randomly training points

(b) Yale

Fig. 3. Average classification accuracy on image noise

Fig.2 shows the results of different methods under mislabeling noise. The average correct classification rate of GLR-MCC is clearly higher than that of GLR, at 60% the correct classification rate of GLR-MCC is significantly better than GLR. The results demonstrate that GLR-MCC provides an efficient method under mislabeling noise. Fig.3 shows the results of different methods under noisy images. Similar to mislabeling noise, the average correct classification rate of GLR-MCC is higher than that of GLR, GLR-MCC rises noticeably at 60%. When training samples are small, noise has significant effect on the results. Since GLR-MCC can remove the noise images, the results are better than GLR. Experimental results illustrate that GLRMCC is robust against training noise for both images and labels.

5 Conclusion In this paper, we propose a novel robust GLR-MCC framework based on MCC. It utilizes MCC as objective to replace GLR’s least squares criterion, and hence is not sensitive to outliers theoretically. This method firstly calculates graph weight, then calculates labels according to our objective. Lastly a greedy strategy is proposed for optimizing the problem based on the half quadratic technique, along with its convergence analysis. Experiments on recognition tasks have demonstrated GLRMCC is robust against noise comparing with GLR. In our future work, we will focus on the theoretical analysis and accelerating issues of our algorithm.

Acknowledgments This work was supported by DUT R & D Start-up costs.

References 1. Wang, F., Zhang, C.S.: Label propagation through linear neighborhoods. IEEE Transactions on Knowledge and Data Engineering 20(1), 55–67 (2008) 2. Wang, F., Zhang, C.S.: Robust self-tuning semi-supervised learning. Neurocomputing 70, 2931–2939 (2007)

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3. Belkin, M., Matveeva, I., Niyogi, P.: Regularization and Semi-supervised Learning on Large Graphs. In: Shawe-Taylor, J., Singer, Y. (eds.) COLT 2004. LNCS (LNAI), vol. 3120, pp. 624–638. Springer, Heidelberg (2004) 4. Zhou, D., Bousquet, O., Lal, T.N., Weston, J., Scholkopf, B.: Learning with Local and Global Consistency. In: NIPS 16 (2004) 5. Zhu, X., Ghahramani, Z., Lafferty, Z.: Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions. In: International Conference on Machine Learning, ICML (2003) 6. Liu, W., Pokharel, P.P., Principe, J.C.: Correntropy: Properties and application in nongaussian signal processing. IEEE Transactions on Signal Processing 55(11), 5286–5298 (2007) 7. He, R., Hu, B.G., Yuan, X.T., Zheng, W.S.: Principal Component Analysis Based on Nonparametric Maximum Entropy. Neurocomputing (2009) 8. Chapelle, O., Weston, J., Scholkopf, B.: Cluster kernels for semi-supervised learning. Advances in Neural Information Processing System 15, 585–592 (2003) 9. Chapelle, O., Weston, J., Scholkopf, B.: Cluster kernels for semi-supervised learning. In: NIPS 15 (2003) 10. Zhou, D., Bousquet, O., Lal, T.N., Weston, J., Scholkopf, B.: Learning with Local and Global Consistency. In: NIPS 16 (2004) 11. Liu, W.F., Pokharel, P.P., Principe, J.C.: Correntropy: Properties and Applications in NonGaussian Signal Processing. IEEE Transactions on Signal Processing 55(11), 5286–5298 (2007) 12. Vapnik, V.: The Nature of Statistical Learning Theory. Springer, New York (1995) 13. Rockfellar, R.: Convex analysis. Princeton Press, Upper Saddle River (1970) 14. He, R., Hu, B.G., Yuan, X.T.: Robust discriminant analysis based on nonparametric maximum entropy. In: Asian Conference on Machine Learning (ACML), NanJing, China (2009) 15. Nikolova, M., Ng, M.K.: Analysis of half-quadratic minimization methods for signal and image recovery. Society for Industrial and Applied Mathematics 27(3), 937–966 (2005) 16. Yang, S.H., Zha, H.Y., Zhou, S.K., Hu, B.G.: Variational graph embedding for globally and locally consistent feature extraction. In: ECML PKDD, pp. 538–553 (2009) 17. Grandvalet, Y., Bengio, Y.: Entropy Regularization (2006) 18. Yuan, X.T., Hu, B.G.: Robust feature extraction via information theoretic learning. In: International Conference on Machine Learning, ICML (2009) 19. He, R., Hu, B.G., Zheng, W.S., Guo, Y.Q.: Two-stage Sparse Representation for Robust Recognition on Large-scale Database. In: Twenty-Fourth AAAI Conference on Artificial Intelligence, AAAI-10 (2010) 20. Belkin, M., Niyogi, P., Sindhwani, V.: Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples. Journal of Machine Learning Research 7(11), 2399–2434 (2006)

Research on Virtual Assembly of Supercritical Boiler Pi-guang Wei, Wen-hua Zhu, and Hao Zhou CIMS and Robot Center, Shanghai University, Shanghai 200072, China [email protected]

Abstract. Supercritical boiler is an important measure to solve problems like electricity shortage or energy intensity, with its high combustion efficiency. As supercritical boiler is a large and complex product, it may appear some problems of collision, location error, or assembly order reverse in assembling process. In order to solve these problems, this paper studies the virtual assembly technology of supercritical boiler. This includes the establishment of model of supercritical boiler, the transformation technology of the model and the Lightweight model technology. Taking 600MW supercritical boiler as an example, a virtual assembly simulation is established in virtools environment. Although the supercritical boiler product contains about 100,000 parts, this technique can achieve fluency of virtual assembly process. It also realizes higher humanmachine interaction, and guilds the assembly process of supercritical boiler. Keywords: Virtual Assembly; Supercritical Boiler; Virtual Reality; Virtools; Lightweight model; Interaction.

1 Introduction On February 16, 2005, "Kyoto Protocol" signed by Parties of "United Nations Framework Convention on Climate Change" provides that developed countries reduce the emission of greenhouse gas by 5.2% based on 1990, between 2008 to 2012[1]. In response to this request, to cope with the problems such as increasingly serious energy intensity, power shortage, low energy utilization, environmental pollution, we need to research and develop the technology of supercritical boiler with its high combustion efficiency. As supercritical boiler is a large and complex product, the assembly process of supercritical boiler is also a complex process. In the process of supercritical boiler assembly, there may be some series problems such as collision occurred, spatial error, reverse sequence of assembly because of the incomprehension of previous design and plans. While most way of boiler assembly process is using welding, the boiler assembly is an irreversible process at the same time. Therefore, the assembly process problems, will greatly influence the whole project, or even result in a huge waste. Address the issues raised above, many people have done the correlative research. Xiangping Zhou puts forward some management measures, to ensure the normal operation of the supercritical boiler assembly[2]. Wanlong Shi an engineer from the Third Engineering Company of Heilongjiang Province studies the Discussion of installation procedure for 660 MW tower type supercritical boiler in northern part of K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 477–485, 2010. © Springer-Verlag Berlin Heidelberg 2010

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China[3]. These measures made a significant contribution to solve the problems in the supercritical boiler assembly. But now, as the greatly development of virtual reality technology, can we use this technology of virtual assembly to solve the problem. The answer is yes. Today's virtual assembly technology has greatly developed. Washington University and The American National Standards Institute of Technology together develop the VADE(Virtual Assembly Development Environment)[4]; Jung from Bielefeld University developed such virtual assembly system CODY based on the knowledge [5], this system has an important characteristic which supports natural language to take simple assembling orders to achieve more natural human-machine interaction; Zhuhua Liao form Institute of Plasma Physics tells about assembling characteristic of EAST, presents movement model of overhead crane, user interface model and structure of multi-3D scene[6]; Jianhua LIU from Beijing Institute of Technology proposed a virtual assembly-oriented multi-layer exact collision detection algorithm based on the analysis of the problem in the virtual assembly environment[7]. CIMS/ERC, Tsinghua University develops a virtual assembly supported system (VASS), with which a product can be analyzed, simulated and pre-assembled virtually[8]. Based on the studies of virtual assembly above, in order to solve the problems in the assembly of supercritical boiler, this paper puts forward the concept of virtual assembly of supercritical boiler. A virtual assembly simulation is established in virtools environment after studying the structure of supercritical boiler, making full use of lightweight technology. The technology of virtual assembly can realize the virtual assembly process of products with more than 10,000 parts. The hardware requirements also are not very high, and it’s no need to develop special program. The only thing need is to define the simple chart to realize the complex process of products virtual assembly, which can highly realize human-machine interaction.

2 The Technologies of Virtual Assembly 2.1 The Analysis and Planning of Supercritical Boiler Model Supercritical boiler is one of the main three components, which compose the thermal power plant. A supercritical boiler generally contains about 100,000 parts, while the cost of a supercritical boiler can reach 3 to 4 billion and its size is very large. Because of the complexity of its structure, the supercritical boiler assembly process is a huge and complex process. However, in this complex process we can still find some of the regular rules. Generally, the process of steel frame assembly is before the process of the inside parts assembly such as the heating surface assembly, the pressure parts assembly and so on. Boiler assembly mainly takes the bulk approach. To reduce the amount of high-altitude operations and to accelerate the construction schedule, assemble local components in the ground at first which will be installed on the whole boiler. Therefore, we can grasp the main part of the virtual assembly during the boiler assembly process, ignore the small details and the partial assembly. In summary of boiler assembly process, the sequence of boiler virtual assembly must meet the following requirements: Steel installation must start from front furnace to back

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furnace, while installations of left and right side start at the same time and install the steel on each layer separately from bottom to top. The heating surface and pressure parts are assembled by division, which divided into the vertical section of wall, spiral section wall, ash bucket, superheater, reheater, after the smoke well, rigid beams, roof piping, air-type expansion device, start the separator and other components. 2.2 Lightweight Model Technologies Because the model is very large and complex, we need to lightweight the model, if we want to accomplish the virtual assembly of the supercritical boiler with only one common computer. Based on the research of modeling character and virtual environment as well as the lightweight mode, we take methods as follows. Simplifying the Meshes. The 3d models depend on the meshes, which contains material, texture and animation. We can see the relationships between them in fig 1. In the test of the virtual environment, through the precision of the model meshes, the spatial capacity can be greatly reduced. Also during the test, it is definitely clear that the description of the meshes take an 80% percentage of the all the data. For the boiler product, it contained huge amount of parts, however, in the virtual environment the same models with different serial have the same meshes. As to these kinds of models, they could share the same meshes rather than corresponding to the mesh of their own. Meanwhile, for some parts with simple structure but fine mesh, we can use the special plug-in to simplify the mesh. Comparing the parts before simplification, the spatial capacity of the model reduced to 60%.

Fig. 1. The figure tells about the relationships of mesh, model, material, texture and animation

3DXML Lightweight Technology. 3DXML is one kind of technology which is used to describe the 3d data in a simple and agile way, which is launched by Dassault System in June 2005. LOD Technology. LOD (Level Of Detail) is one kind of lightweight technology that was created especially for the improvement of the efficiency of the modeling. It can dynamically describe the complexity of the model meshes according to the screen percentage of the model. For instance, when the model only covers a small part of the screen, we do not need to have a detailed description of its structure and the overall description of the object can meet the demands. The relationship is shown in the fig 2.

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Fig. 2. The fig instructs the mechanism of LOD

2.3 The Introduction of Virtools Virtools technology is a powerful solution for the 3d visualization and interactivity, which is mainly used in 3D timely interaction. It also can make an integration of the text, graphics, video and sound. The particular character of virtools is that it builds in hundreds of BB (Building Blocks). Though simple operations and settings, we can define the complex interactive behaviors. So it is a powerful, easy to use, and very effective development tool.

3 The Realize of Virtual Assembly of Supercritical Boiler 3.1 The Establishment of Boiler Model The Model of Heating Parts and Pressure Parts. The heating parts and the pressure parts are the main parts of the boiler design. The 3D models of these parts have already been found at the beginning of the boiler design, and we can inherit and use 3D models of these parts. The designed models of the heating parts and the pressure parts in NX can be transformed to the environment of Virtools by some intermediate format. There are two methods specifically. One way is to use VRML format in NX, and the models can be transformed to the format files with an extension of .wrl, which can be opened in Virtools directly; Another way is to use 3DXML format. As NX does not support the format, and CATIA has very good interface with 3DXML, the first step is to export the NX models into CATIA. In the process we should use STEP format file, which is a neutral file and is playing a role of a bridge in the process of transforming one format file into another. The models exported into CATIA by STEP format file can be transformed to format files of 3DXML directly, which can be loaded in Virtools directly. The Model of Steel Frame. The steel models used in the virtual simulation are also using the initial designing models such as the heating parts and the pressure parts, but the designing environment of the steel frame models are different, so all the methods

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above are not practical. The steel frame models are 3D models in AUTOCAD. Because AutoCAD and 3DS MAX all belong to Autodesk Company, and the plug-in interfaces have already been developed between 3DS MAX and Virtools, we can transform models into 3DS MAX. 3DS MAX has a very good compatibility with AutoCAD and can open AutoCAD models directly. By Virtools Export, we can export the models into files with an extension of .nmo, which can be loaded in Virtools directly. The Establishment of Scene Model. Boiler’s scene model plays an emphasized role in the virtual assembly, which aim is to enhance the realism of virtual assembly. While boiler scene design does not belong to the contents of the boiler, there is no ready-made model of the scene that can be borrowed. As the boiler scene is to enhance the effect of rendering type, we do not need to over-build scenario models seriously. We build the scene model using the SketchUp environment, which is a very simple software. This software is very suitable for building models in threedimensional design, and it is very efficiency. The established three-dimensional model can be exported as 3DS format, which can be loaded directly in the Virtools environment. 3.2 Lightweight Model In the process of converting models above, there are a lot of techniques to lightweight the model. Taking the heating parts and pressure parts for example, we can use the way of conversion into CATIA 3D XML technology to lightweight the model, while during the conversion of VRML format we use the way of the X3D(Extensible 3D) to lightweight the model. Comparing the two conversion methods, the results show that the lightweight model by adoption of 3D XML technology is smaller. As to the steel model, we use the streamlining plug of Polygon Cruncher from3D MAX to simplify the model. In the establishment of scene model, we use the 3DS format to simplify the model. All the conversion methods and lightening techniques are shown in Fig. 3.

Fig. 3. This fig tells about the conversion methods and lightening techniques

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3.3 Design of Virtual Assembly Virtual assembly of supercritical boiler is realized in the environment of virtools. It is easy to define the movements, the route, the statement of the model and the visual angle of the camera coupled with the instruction of words, sound or video. The virtual assembly includes the assembly of steel frame and internal model. Camera at the appropriate point as well as some instructions is also necessary. And in order to exhibit the virtual assembly better, higher human-machine interaction is needed as well. The Virtual Assembly of Steel Frame. In reality, the assembly is carried out from the boiler front to the boiler back as well as the left and right parts assembly at the same time. According this procedure, we simulate virtual assembly of steel frame from the front to the back, apply the presentation form layer by layer. The fig. 4. followed shows the steel assembly process. It is achieved through BB (Building Blocks) like Group Iterator Show Delay and so on to carry out the effect level by level.

、

、

Fig. 4. This fig tells about the process of steel assembly

Fig. 5. This fig tells about the procedure of internal parts assembly

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The Virtual Assembly of Inside Parts. The models inside the boiler are assembled after completing the assembly of boiler steel frame. For presenting the internal model much better, we disguise the steel frame model when it is being assembled. The assembly of internal model is mainly presented by putting all the components together. We apply the form of the assembly from top to bottom. Fig.5 shows the procedure of internal parts assembly. It is realized by BB like Show Move To and Delayer.

、

3.3.3 Design of Shifting Camera Angle. As the huge boiler model and the complexity of the boiler assembly, the boiler assembly process can not be present only by one perspective. Therefore, shifting camera angle constantly during the assembly for expressing the objects to be described is essential. In the virtools, camera is defined as an object whose position and orientation can be set by BB like Bezier Progression Position On Curve Set Position Set as Active Camera Look At and so on. It’s schema can be seen in Fig.6.

、

、

、

、

Fig. 6. The specific flowchart of Shifting Camera Angle

The Embedded Explanation. Explanations such as text or sound play a supporting role in the assembly process of boiler. A complete virtual assembly should have these factors. In the virtools environment, you can show the text by the use of Text Display, and play music by Wave Player. It is important to note that explanations must correspond to model assembly process. In order to meet this requirement we use the Sequencer and Parameter Selector. The combination of these two BBs can achieve to trigger different parameters in different times. The sequence of model assembly determines the trigger time of Sequencer, and output parameters have been pre-set in Parameter Selector. The two BBs together achieve to output the corresponding parameters at the right time. The Setting of Interaction of virtual assembly. In the virtual assembly of model, the interaction is a very important factor. Through human-computer interaction, people's initiative can be reflected. The virtual assembly process is showed in a better way and meet the people's will much more. In the virtools, it is easy to implement interaction. There are special BBs to achieve interaction between people and the computer by mouse, keyboards, joystick or other equipment. These BBs are Key Event, Push Button, Joystick Controller, Switch On Key, Mouse Waiter and so on. In the virtual assembly process of boiler, there are two virtual assembly modes. One is the automatic assembly mode, and the other is the free assembly mode. In free assembly mode, people can control perspective by mouse, keyboard and other devices. The

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switch of automatic mode and free mode is realized by BB such as Key Event, Get Current Camera, Set As Active Camera and so on. The specific flowchart is shown in fig 7.

Fig. 7. This fig tells about the specific flowchart of switching mode

4 Conclusion The virtual assembly takes a very good guidance on supercritical boiler assembly process, and is beneficial to avoid the problems of supercritical boiler assembly process. Based on the virtools environment, the virtual assembly technology is a new kind of technology. This virtual assembly technology can achieve more than 100,000 parts of virtual assembly process of products. In the establishment of virtual assembly process, it can easily integrate such factors as image, sound, video, etc. It also can achieve higher level man-machine interaction. The model lightweight process can use the common lightweight technology such as 3DXML, to expression more complex product with smaller model. Establishing the virtual assembly process doesn't need programming, and the only thing need is to define standard flowcharts, so the operation is convenient as well as easy. Acknowledgment. The project is supported by Shanghai informationization special project from Shanghai Municipal Science and Technology Committee (Project No.08DZ1124300), partially supported by the Municipal Program of Science and Technology Talents, Shanghai China. (Project No. 09QT1401300), and Shanghai Leading Academic Discipline Construction (Project No. Y0102). The authors gratefully acknowledge the encourages from Prof. Ming-lun FANG et al, and acknowledge the support of colleague in CIMS Center of Shanghai University.

References 1. Wang, D.B.: The Research On Key Technologies in Supercritical Pressure Boiler Design Platform. Shanghai University 147, 1–2 (2010) 2. Zhou, X.P.: Research On Quality Control Measures of Boiler Assembly. Guangdong Science and Technology 202, 207–208 (2008) 3. Shi, W.L.: Discussion of installation procedure for 660 MW tower type supercritical boiler in northern part of our country. Heilongjiang Electric Power 30, 311–314 (2008) 4. Jayamam, S., Jayaram, U., Wang, Y.: A virtual assembly design environment. IEEE Computer Graphics and Applications (S0272-1716) 19, 44–50 (1999)

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5. Jung, B., Hoffhenke, M., Wachsmuth, I.: Virtual Assembly with Construction Kits. In: Proceedings of DETC, ASME Design for Engineering Technical Conferences, pp. 1–7 (1997) 6. Liao, Z.H., Liu, X.P.: Design of 3D Interaction and User Interface for EAST Assembly Simulation. Journal of System Simulation 16, 2329–2343 (2004) 7. Liu, J.H., Yao, J., Ning, R.X.: Research and Realization of Collision Detection Algorithm in Virtual Assembly Environment. Journal of System Simulation 16, 1775–1778 (2004) 8. Li, Z., Zhang, L.X., Xiao, T.Y.: Introduction of a Virtual Assembly Supported System. Journal of System Simulation 14, 1150–1153 (2004)

Validation of Veracity on Simulating the Indoor Temperature in PCM Light Weight Building by EnergyPlus Chun-long Zhuang1,2, An-zhong Deng1, Yong Chen1, Sheng-bo Li1, Hong-yu Zhang1, and Guo-zhi Fan1 1

Department of Barracks’ Management and Environmental Engineering, PLA Logistic Engineering University, Chongqing 400016, China 2 College of Urban Construction and Environmental Engineering, Chongqing University, Chongqing 400030, China

Abstract. This article surveys the EnergyPlus constructions solution algorithm and heat balance method in EnergyPlus, presents the new conduction finite difference solution algorithm and enthalpy-temperature function features, describes the implementation of the module, and validates the veracity of the possible applications for the capabilities in EnergyPlus by PCM experiment dates. The most relativity difference is 12.41% and the least is 0.71% between the simulation and testing value in sequential 36h on the A envelope condition, wheras on the B envelope condition the most relativity difference is 8.33% and the least is 0.33% in sequential 72h.The results to date has shown good agreement with well established in this simulation tools and shown that the algorithm incorporated into EnergyPlus can simulate the PCM in building construction.

（PCMs）, Indoor

Keywords: Energyplus, Validation, Phase change materials temperature.

1 Introduction The use of PCMs in buildings, especially passive and active solar buildings, has received considerable interest since the first published application in 1940. The energy storage by wallboards is of particular importance to store and recover solar energy, many applications have been considered and some can be found in Refs.[1–3].Up to now, using PCMs in building materials was limited by many difficulty such as the engineering algorithm to confirm the PCMs dosage and phase change temperature in different climate area and incorporating the PCM into the wallboard ect. EnergyPlus —new programs of simulating this type of material in building fabric may allow us an easier handling and the use of PCM in a more handy way. The EnergyPlus project began in the late 1990s as an effort to combine the best features of BLAST and DOE-2, two popular energy analysis programs used internationally, into a single program [4-6]. The goal was to provide the simulation community with a single platform for model development, saving costs and time in the never K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 486–496, 2010. © Springer-Verlag Berlin Heidelberg 2010

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ending process of keeping the programs up to speed with the rapid changes in the HVAC industry and maximizing the impact that a new program might have on the architectural and engineering community. For heat transfer, EnergyPlus adopted the Conduction Transfer Function CTF solution algorithm to calculate the conduction through the common walls. For high performance building designs, for example the advanced constructions—PCM, this had been done by addition a new solution algorithm that utilized an implicit finite difference procedure in EnergyPlus. This paper surveyed the EnergyPlus constructions solution algorithm and heat balance method in EnergyPlus, presented the conduction finite difference solution algorithm features, described the implementation of the module, and validated the veracity of the possible applications for the capabilities in EnergyPlus by PCM house experiment dates.

（ ）

2 EnergyPlus Solution Algorithm 2.1 Conduction Finite Difference Solution Algorithm [4] EnergyPlus models followed fundamental heat balance principles very closely in almost all aspects of the program. However, the simulation of building surface conventional constructions had relied on a transfer function transformation carried over from BLAST. This had all the usual restrictions of a transformation-based solution: constant properties, and fixed values of some parameters. As the energy analysis field moved toward simulating more advanced constructions, such as phase changed materials (PCM), it becomes necessary to step back from transformations to more fundamental forms. Accordingly, a conduction finite difference solution algorithm has been incorporated into EnergyPlus. This did not replace the CTF solution algorithm, but complemented it for cases where the user needed to simulate phase change materials or variable thermal conductivity. It was also possible to use the finite difference algorithm for zone time steps as short as one minute, corresponding to the system time step. The algorithm used an implicit finite difference scheme coupled with an enthalpy-temperature function to account for phase change energy accurately. The One dimensional steady heat conduction process through the wall was shown as the formula (1).The implicit formulation for an internal node was shown in equation (2).

ρ

∂(c p t ) ∂τ

∂ 2t =k 2 ∂x

(1)

ρcpΔx(Ti,new −Ti,old ) k(Ti−1,new −Ti,new) k(Ti+1,new −Ti,new) Δt

=

；

Δx

+

Where: T is node temperature

i =node being modeled;

i + 1 =adjacent node to interior of construction;

Δx

(2)

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i − 1 =adjacent node to exterior of construction; new =new temperature at end of time step; old =temperature at end of previous time step;

Δt =calculation time step; Δx =finite difference layer thickness (always less than construction layer thickness);

Cp

=specific heat of material;

ρ = density of material.

Then, this equation is accompanied by a other equation—enthalpy-temperature function 3 that relates enthalpy and temperature.

hi = HTF (Ti )

(3)

Where HTF was an enthalpy-temperature function that uses user input data. The enthalpy-temperature function [7-10] is showed as the formula (4) and 5 .

where

， H = enthalpy,

⎧ 2 ⎪ ρ ∂H = k ∂ T ⎪ ∂t ∂y 2 ⎪ ⎨T y =0 = To ⎪ ⎪−k ∂T = h ⎡⎣T ( yo ) − T f ⎤⎦ ⎪ ∂y y = yl ⎩

⎪ ⎪ H / c p,s ⎪⎪ H + (T − ε )r / 2ε m T =⎨ c p , s + r / 2ε ⎪ ⎪ H − Hl ⎪Tm + ε + c p ,l ⎪⎩ Where,

c p ,s

and

c p ,l

(4)

H < Hs H s ≤ H ≤ Hl

(5)

H > Hl

;

=respectively solid state and liquid state specific heat of material

ε =the half of phase change temperaturerange ΔTpc ( K ) ; r =phase change latent heat (J·kg )；

H s and H l =respectively solid state and liquid state enthalpy of material, which

was showed as follow:

H s = c p , s (Tm − ε )

(6)

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H l = c p ,s ( Tm + ε ) + r

(7)

It turned out that there were four node types: external surface nodes, internal surface nodes, internal nodes such as shown above, and then nodes occurring at the material interfaces. The formulation of all node types was basically the same. So, equations such as (2) and (3) were formed for all nodes in a construction. Because the solution was implicit, a Gauss-Seidell iteration scheme was used to update to the new node temperatures in the construction. Because of this, the node enthalpies get updated each iteration, and then they were used to develop a variable C p if a phase change material was being

（）

simulated. This was done by including a third equation 8 for C p . Cp =

(h

i , new

− hi ,old )

(8)

Ti ,new − Ti ,old

The iteration scheme assured that the correct enthalpy, and therefore the correct

C p was used in each time step, and the enthalpy of the material was accounted for accurately. Of course, if the material was regular, the user input constant

C p was

used. The algorithm also had a provision for including a temperature coefficient to modify the thermal conductivity. 2.2

Zone Air Temperature Solution Algorithm

The zone air heat balance was the accurate method that coupled with the indoor air, outside surface heat balance and inside surface heat balance on the building fabrics, as were showed in Figure1, 2 and 3.By this method a variable adaptive time step shorter than one hour could be used for updating the system conditions. For stability reasons it was necessary to derive an equation for the zone temperature that included the unsteady zone capacitance term and to identify methods for determining the zone conditions and system response at successive time steps. From Figure 3, it could be seen that for energy storage in the zone air, a heat bal-

（9）[4],[11]:

ance equation would be similar to the following formula

CZ

dTz Nsl − = ∑QQ i + dt i=1

Nsurfaces

Nzones −

−

i ∑ hA i i ( Tsi −Tz ) + ∑ mC p ( Tzi −Tz ) + minf Cp (T∞ −Tz ) +Qsys

i=1

i=1

(9)

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Fig. 1. Outside surface heat balance

Fig. 2. Inside surface heat balance

Fig. 3. Zone air heat balance

Fig. 4. Building - Isometric View

Where: CZ

dTz = energy stored in zone air dt

N surfaces

；∑

loads

i =1

hi Ai (Tsi − Tz )

N zones −

∑ m C (T i

i =1

p

zi

； ∑Q N sl

i =1

−

i

= sum of the convective internal

；

= convective heat transfer from the zone surfaces

− Tz )

−

= heat transfer due to inter zone air mixing;

；

heat transfer due to infiltration of outside air

Qsys

m inf C p (T∞ − Tz )

—

一system output.

Where, CZ was the product of the mass of the zone air and the specific heat of air.

（10）for the

Used in conjunction with a third order finite difference approximation

derivative term and time steps between 0.1 and 0.25 hours, this method of calculating the zone air heat balance had been shown to be stable [12]. Thus, the basic heat balance approach was to set up energy balance equations using control volumes at the inside and outside faces of each surface in a particular zone as well as a control volume around the zone air.

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While a solution could be found for this system of equations, the actual solution process was the third order finite difference approximation of the derivative term, dTz 3 1 −1 ⎛ 11 ⎞ ≈ (δ t ) ⎜ Tzt − 3Tzt −δ t + Tzt−2δt − Tzt −3δt ⎟ + O(δ t 3 ) . dt t 2 3 ⎝6 ⎠

(10)

One final rearrangement was to move the lagged temperature in the derivative approximation to the right side of the equation. The explicit appearance of the zone air temperature was thus eliminated from one side of the equation. An energy balance equation that included the effects of zone capacitance was then obtained by dividing both sides by the coefficient of Tz, as was showed in formula

（11）: This was the

form currently used in EnergyPlus. Nsurfaces

Nsl .

T= t z

Nzones .

.

.

∑Q+ ∑hAT + ∑mCT +m CT +m CT i=1

i

i=1

i i si

i

i=1

p zi

inf

p∞

sys

p supply

3 1 ⎞ ⎛C ⎞⎛ −⎜ z ⎟⎜−3Tzt−δt + Tzt−2δt − Tzt−3δt ⎟ . 2 3 ⎠ ⎝δt ⎠⎝

N

Nzones . . . 11Cz surfaces + ∑hA i i + ∑mC p +minf Cp +msys C 6 δt i=1 i=1

(11)

3 Method or Experimental The most new EnergyPlus Version 3.1 was used to model a range of building specifications as specified in ANSI/ASHRAE Standard 140-2007- Standard Method of Test for the Evaluation of Building Energy Analysis Computer Programs and in the Building Energy Simulation Test (BESTEST) and Diagnostic Method. The ability of EnergyPlus to predict thermal loads was tested using a test suite of 18 cases which included buildings with both low mass and high mass construction, without windows and with windows on various exposures, with and without exterior window shading, with and without temperature setback, with and without night ventilation, and with and without free floating space temperatures. The annual heating and cooling and peak heating and cooling results predicted by EnergyPlus for 13 different cases were compared to results from 8 other whole building energy simulation programs. Based on 62 separate possible comparisons of results for the BASIC test cases, EnergyPlus was within the range of spread of results for the other 8 programs for 54 of the comparisons [13-14]. But it had not been reported on the condition for PCM building envelope in ANSI/ASHRAE Standard 140-2007 - Standard Method of Test. 3.1 Simulation Building Size and Envelope

Figure 4 showed the Building - Isometric View of southeast corner with Windows on South and north Wall. The PCM room dimension length×width×high = 1.5m×1.5m×2.0m door and windows the door was in the east wall and dimension 1.5m×0.6m window dimension:0.3m×0.4m. The wall, roof and floor adopted

； ；

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the same envelope structure, namely, in Energyplus the MATERIAL: Regular object, Material Property: Temperature Dep: CondFD, the material thermal characteristics and envelope structure were showed in table 1, 2. For the validation of using EnergyPlus to simulate the indoor air temperature in PCM house, and according to the prophase experiment projects, in Group – Surface Construction Elements: Material Property: Temperature Dep: CondFD, we adopted two kinds of phase change temperature materials, the temperature of phase change was 40 and 33 (40 phase change material, recorded as 40# PCM, the latent heat was about 80000 J/kg, 33 phase change material, recorded as 33# PCM, the latent heat was about 70000 J/kg),so two kinds of envelope was adopted in simulation, namely A and B ,which were showed as table 2. Created the 6mm thick plank materials in term of the 5kg/m 2 surface densities, and were installed between the wood board and EPS foam board according to the different design. EnergyPlus now automatically calculates the local outdoor air temperature and wind speed separately for the zone and surface exposed to the outdoor environment. The zone centric or surface centric are used to determine the height above ground. Only local outdoor air temperature and wind speed are currently calculated because they are important factors for the exterior convection calculation for surfaces and can also be factors in the zone infiltration and ventilation calculations. The Int.Surface Coeff. and Ext. Surface Coeff was 8.7 and 23 W / m2.K separately.

℃

℃ ℃

℃

3.2 Weather Data

The Solar and Wind Energy Resource Assessment (SWERA) was adopted in this simulation. The SWERA was funded by the United Nations Environment Program, and was developing high quality information on solar and wind energy resources in 14 developing countries. Typical year hourly data were available for 156 locations in Belize, Brazil, China, Cuba, El Salvador, Ethiopia, Ghana, Guatemala, Honduras, Kenya, Maldives, Nicaragua, and Sri Lanka. The data were available from the SWERA project web site.In this paper we changed the SWERA file of Fig. 5. Experiment house Chongqing area fine and put the testing outdoor dry bulb temperature into the Chongqing SWERA weather data from 8/13/2007 to 14/8/2007and 8/23/2007 to 26/8/2007. 3.3 Experiment Set-Up

The PCM light weight experiment house was showed in Figure5,the test condition was the same as the simulation condition from the aspect of envelope structure, as was expatiated before, The experiment process and method might obtain from the reference [15-16].

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Table 1. Material thermal characteristics Element Thermal conductivity (w / m·k) Thickness Thermal resistance (m2.k/w) coefficient (w / m2.k) Thermal inertia index

veneer 0.17 5mm 0.03 4.57 0.13

EPS 0.042 50mm 1.19 0.36 0.43

33#PCM 0.30 10mm 0.033 28.65 0.95

40#PCM 0.30 10mm 0.033 28.65 0.95

Table 2. Envelope structure Element A envelope out to in B envelope out to in

veneer 5mm 5mm

40#PCM 10mm 10mm

EPS 50mm 50mm

33#PCM 10mm

veneer 5mm 5mm

4 Results and Discussion 4.1 Comparison of Indoor Air Temperature

(1) Comparison of A envelope simulation and testing Fig.6 is the Comparison of the indoor temperature between the simulation and testing value in sequential 36h on the A envelope 40#PCM condition. The most relativity difference is 12.41% and the least is 0.71% between the simulation and testing value in 40#PCM condition, the simulation and testing value are consistency basically. It may be the reasons that created the error, firstly we only changed the outdoor dry bulb temperature in SWERA file of Chongqing area, and that solar radiation and wind speed condition would great effect on the indoor air temperature, secondly we do not change the weather data before 8 /13, the weather in 8/12 will influence the indoor air environment especially in summer because of the PCM building envelope thermal inertia, lastly there are some difference in the material thermal characteristics between the simulation input value and actual testing process, which will affect the validity results.

（

）

Fig. 6. Comparison of 40#PCM simulation and testing in sequential 36h

Fig. 7. Comparison of 40#+33#PCM simulation and testing in sequential 72h

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Fig. 8. Comparison of A fabric south wall interior surface temperature

Fig. 9. Comparison of B fabric south wall interior surface temperature

4.2 Comparison of B envelope Simulation and Testing

Fig.7 showed the Comparison of the indoor temperature between the simulation and testing value in sequential 72h on the B envelope 40#+33#PCM condition. The most relativity difference is 8.33%, and the least is 0.33% between the simulation and testing value on the B envelope condition, the simulation and testing value are more consistency than the A envelope. It may be the reasons that we used two PCM layers and increased the PCM dosage, which leaded to the improvement on the building envelope thermal inertia, and it weakened the influence of the outdoor air environment to the indoor. we change the outdoor dry bulb temperature from 8 /22 to 8 /27 in the weather data, this cam weaken the influence of the 8 /22 weather condition on the indoor air environment in 8 /23. So, it is very important that using feasible weather data when simulating in Energyplus. Comparison results of A and B envelope condition have shown good agreement with well established in this simulation tools and shown that the algorithm incorporated into EnergyPlus can simulate the conduction through the PCM walls and the indoor air temperature in PCM Light Weight Building 4.3 Comparison of Fabric Interior Surface Temperature (1) South Wall Interior Surface Temperature Concerning the evolutions of other walls interior temperatures being similar, we only take the south walls interior temperatures to analyse.Fig.8,9 shows the curves of mean temperatures for the interior surfaces of A and B fabric south walls for the cases with PCM material. The most relativity difference is 8.18% and 7.16% and the least is 0.54% and 0.65% between the simulation and testing value in two kinds of fabrics condition, the simulation and testing value are consistency basically. The reason that created the error was the same as the before-mentioned Comparison of indoor air temperature condition.

，

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!

Fig. 10. Comparison of A fabric roof interior surface temperature

Fig. 11. Comparison of B fabric roof interior surface temperature

(2)Roof Interior Surface Temperature Fig.10, 11 shows the curves of mean temperatures for the interior surfaces of A and B fabric south walls for the cases with PCM material. The most relativity difference is 6.65% and 6.03% and the least is 0.22% and 0.38% between the simulation and testing value.

5 Conclusions This paper validates the veracity of the possible applications for the PCM fabrics in EnergyPlus by PCM experiment dates. The most relativity difference is 12.41% and the least is 0.71% between the simulation and testing value in sequential 36h on the A envelope condition, the most relativity difference is 8.33% and the least is 0.33% in sequential 72h on the B envelope condition. The most relativity difference for south wall interior surface temperature is 8.18% and 7.16% and the least is 0.54% and 0.65% between the simulation and testing. The most relativity difference for roof interior surface temperature is 6.65% and 6.03% and the least is 0.22% and 0.38% between the simulation and testing value. The difference in the weather dates and the material thermal characteristics will bring great influence on the error between the simulation and testing value. So, it is very important that using feasible weather data and material thermal characteristics value when simulating in Energyplus. EnergyPlus can simulate the conduction through the PCM walls and the indoor air temperature in PCM Light Weight Building while maintaining all the other aspects of a detailed energy simulation. The scheme of carrying the node enthalpy along with the simulation has proven to be very robust, and provides a completely accurate accounting for the phase change enthalpy.

，

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References 1. Ismail, K.A.R., Henriquez, J.R.: Thermally effective windows with moving phase change material curtains. Applied Thermal Engineering 21, 1909–1923 (2001) 2. Stritih, U.: Heat transfer enhancement in latent heat thermal storage system for buildings. Energy and Buildings 35, 1097–1104 (2003) 3. Khudhair, A.M., Farid, M.M.: A review on energy conservation in building. Applications with thermal srorage by latent heat using phase change materials. Energy Conversion and Management 45, 263–275 (2004) 4. Berkely, L.: National Laboratory, University of Illinois, University of California. EnergyPlus 3.1Manual. LBNL in Berkeley, California (2009) 5. Jacobs, P., Henderson, H.: State-of-the-Art Review of Whole Building. Building Envelope, and HVAC Component and System Simulation and Design Tools, ARTI-21CR-60530010–30020-01 (2001) 6. Crawley, D.B., et al.: EnergyPlus: Creating a New-Generation Building Energy Simulation Program. Energy & Buildings 33(4), 443–457 (2001) 7. Guo, X.L., Kong, X.Q., Chen, S.N.: Numerical Heat Transfer. China Sciencete and Chnology Press (1988) 8. Zhou, J., Huang, S.Y.: Caculation for Phase Change Thermal Tranfer. Energy Technology (1), 11–14 (2000) 9. Zhang, Y.P., Hu, H.P., Kong, X.D., et al.: Phase Change Energy Storage-—Theory and Application. China Sciencete and Chnology Press (1996) 10. Ye, H., He, H.F., Ge, X.S.: The Comparative Numerical Investigations on the Melting Process of Form-Stable Phase Change Material Using Enthalpy Formulation Method and Effective Heat Capacity Formulation Method. Acta Energ1ae Solaris Sinica 25(4), 488– 491 (2004) 11. Richard, K., Curtis, O.: Modularization and Simulation Techniques for Heat Balance Based Energy and Load Calculation Programs: The Experience of The Ashrae Loads Toolkit and Energyplus. Building Simulation, 43–50 (2001) 12. Taylor, R.D., Pedersen, C.O., Fisher, D.E.: Elta: Impact of Simultaneous Simulation of Buildings and Mechanical Systems in Heat Balance Based Energy Analysis Programs on System Response and Control. In: Conference Proceedings IBPSA Building Simulation, Nice, France, pp. 20–22 (August 1991) 13. Energy Efficiency and Renewable Energy Office of Building Technologies, U.S. Department of Energy. EnergyPlus Testing with Building Thermal Envelope and Fabric Load Tests from ANSI/ASHRAE Standard 140-2007 Energy Plus Version 3.1.0.027 (April 2009) 14. IEA 1995. Building Energy Simulation Test (BESTEST) and Diagnostic Method. National Renewable Energy Laboratory, Golden, Colorado (February 1995) 15. Li, B.Z., Zhuang, C.L., Deng, A.: Study on improving the indoor thermal environment in light weight building combining pcm wall and nighttime ventilation. Journal of Civil, Architectural & Environmental Engineering 31(3) (2009) 16. Zhuang, C.L., Deng, A.Z., Li, S.B., et al.: The field study of temperature distribution in the floor radiation heating room with new phase change material. Journal of Center South University of Technology (14), 91–94 (2007)

Positive Periodic Solutions of Nonautonomous Lotka-Volterra Dispersal System with Delays Ting Zhang, Minghui Jiang, and Bin Huang Institute of Nonlinear and Complex System, China Three Gorges University, YiChang, Hubei 443002, China [email protected]

Abstract. In this paper, a general class of nonautonomous LotkaVolterra dispersal system with discrete and continuous infinite delays is investigated. This class of Lotka-Volterra systems model the diffusion of a single species into n patches by discrete dispersal. By using Schauder’s fixed point theorem, we prove the existence of positive periodic solutions of system. The global asymptotical stability of positive periodic solution is discussed and the sufficient conditions for exponential stability are also given. we give an example to illustrate the validity of the results in the end. The conditions we obtained are more general and it can be extended to several special systems. Keywords: Lotka-Volterra dispersal system, Positive periodic solutions, Schauder’s fixed point theorem, Global asymptotical stability, Global exponential stability.

1

Introduction

The Lotka-Volterra system forms a significant component of the models of population dynamics. In recent years, it has been usefully used in population dynamics, epidemiology, biology and any other areas in general. Because of its theoretical and practical significance, the Lotka-Volterra system has been extensively and intensively studied[1-10]. There have many papers on the study of the Lotka-Volterra type systems and it have been developed in[4,6,7,9,11]. Now the basic questions of this model are the persistence, extinction, global asymptotic behaviors, global exponential behaviors, existence of positive solutions and periodic solutions and so on. In this paper, we considered the following case of combined effects: dispersion, time delays, periodicity of environment. We study the following general nonautonomous Lotka-Volterra type dispersal system with discrete and continuous infinite time delays: x˙ i (t) = xi (t)[ri (t) − −

n   0 j=1

n  j=1

aij (t)xj (t) −

c (t, s)xj (t −∞ ij

n  j=1

+ s)ds] +

bij (t)xj (t − τij (t)) n  j=1

Dij (t)(xj (t) − xi (t)),

K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 497–505, 2010. c Springer-Verlag Berlin Heidelberg 2010 

(1)

498

T. Zhang, M. Jiang, and B. Huang

with the initial condition xi (s) = φi (s) f or s ∈ (−∞, 0], i = 1, 2, · · · , n.

(2)

where xi (t) represents the density of species in ith patch; ri (t) denotes the growth rate of species in patch i; aij (t) represents the effect of intraspecific (if i = j) or interspecific (i  = j)interaction at time t, bij (t) represents the effect of intraspecific (if i = j) or interspecific (i  = j) interaction at time t − τij (t); 0 c (t, s)x (t + s)ds represents the effect of all the past life history of the ij j −∞ species on its present birth rate; Dij (t) is the dispersion rate of the species from patch j to patch i. The model in this work can be extended to the models of [1-6]. In this paper, we assume the following assumptions hold for system (1): (H1 ) The bounded functions cij (t, s) are defined on R×(−∞, 0], and nonnegative continuous with respect to t ∈ R and integrable with respect to s on (−∞, 0] 0 such that −∞ cij (t, s)ds is continuous and bounded with respect to t ∈ R; (H2 ) τij (t) is continuous and differentiable bounded on R, τ˙ij (t) is uniformly continuous with respect to t on R and inf {1 − τ˙ij (t)} > 0; t∈R

(H3 ) ri (t), aij (t), bij (t), cij (t, s) are continuous periodic functions with period ω > 0, and for any ε > 0, there is a constant l = l(ε) > 0, such that in any interval [t, t + l], there exists ω such that the following inequalities hold: |ri (t + ω) − ri (t)| < ε, |aij (t + ω) − aij (t)| < ε,  |bij (t + ω) − bij (t)| < ε,

2

(3)

0

−∞

|cij (t + ω, s) − cij (t, s)|ds < ε.

(4)

Preliminaries

Throughout from this paper, we suppose that h(t) is a bounded function defined on R. Define hu = lim sup h(t), hl = lim inf h(t). t→∞

t→∞

Definition 1. An ω-periodic solution x∗ (t) of system (1) is said to be globally asymptotically stable, if for any positive solution x(t) of system (1), we have that lim x(t) − x∗ (t) = 0.

t→∞

Definition 2. An ω-periodic solution x∗ (t) of system (1) is said to be globally exponentially stable with convergence rate ε > 0, if for any positive solution x(t) of system (1), we have that lim x(t) − x∗ (t) = 0(e−εt ). t→∞

Definition 3. The {ζ, 1}-norm of a vector x ∈ Rn is defined by x{ζ,1} = n  ςi |xi |, ζi > 0 for i = 1, 2, · · · , n. i=1

Positive Periodic Solutions

499

Lemma 1. The solution x(t) of system (1) is said to be a positive solution if it satisfies the initial condition (2). Proof. From Eq.(1), we have that: ln xi (t) − ln xi (0) =

t

0 [ri (t) −

−

n 

0

n  j=1

aij xj (t) −

c (t, s)xj (t −∞ ij

j=1

n 

+ xi1(t)

j=1

n  j=1

bij (t)xj (t − τij (t))

+ s)ds

(5)

Dij (t)(xj (t) − xi (t))]dt.

When t is finite, then the right-hand side of Eq.(5) is also finite, thus ln xi (t) > −∞, which implies xi (t) > 0 for any finite time t > 0, i = 1, 2, · · · , n. Then this lemma can be proved.

3

The Existence of Positive Periodic Solutions

In this section, the conditions about the existence of positive periodic solutions of system (1) are derived. Theorem 1. For the system (1) of initial condition (2), if alii > 0, and there exist positive constants η, ξ such that for all i = 1, 2, · · · , n, the following inequalities hold: η ≤ lim inf xi (t) ≤ lim sup xi (t) ≤ ξ, t→∞

n 

i = ril − ( −

where ξ =

n  j=1

j=1,j=i

(6)

t→∞

auij +

n  j=1

buij +

n   0

−∞ cij (t, s)xj (t

j=1

+ s)ds)ξ (7)

u Dij > 0,

max {

riu +

i=1,2,··· ,n

n  j=1 alii

u Dij

}, η =

one positive ω-periodic solution.

min { ui }, i=1,2,··· ,n aii

then system (1) has at least

Proof. Assume x(t) = (x1 (t), x2 (t), · · · , xn (t)) is any positive solution of system (1) with initial condition (2). Define V (t) = max{xj (t)} for t ≥ 0, j = 1, 2, · · · , n. Suppose V (t) = xi (t), so xi (t) ≥ xj (t)(j = 1, 2, · · · , n). The upper right derivative of V (t)along the solution of system (1) is: D+ V (t) = x˙ i (t) = xi (t)[ri (t) − −

n   0 j=1

n  j=1

aij (t)xj (t) −

−∞ cij (t, s)xj (t

j=1

+ s)ds] +

≤ xi (t)[ri (t) − aii (t)xi (t)] + ≤ xi (t)[riu − alii xi (t) +

n 

n  j=1

n  j=1

u Dij ].

bij (t)xj (t − τij (t)) n  j=1

Dij (t)(xj (t) − xi (t))

Dij (t)xi (t)

500

T. Zhang, M. Jiang, and B. Huang

By using comparability theorem, we have lim sup xi (t) ≤ ξi , i = 1, 2, · · · , n, where ξi = {

riu +

n  j=1 alii

t→∞

u Dij

}, taken ξ =

max {ξi }, then lim sup xi (t) ≤ ξ. t→∞

i=1,2,··· ,n

On the other hand, there exists a positive constant T for t ≥ T such that x˙ i (t) ≥ xi (t)[ril − auii xi (t) −

n  j=1,j=i

auij ξ −

n  j=1

u Dij −(

n 

j=1

buij +

n   0 j=1

cu (s)ds)ξ]. −∞ ij

By using comparability theorem, we can get that lim inf xi (t) ≥ ηi , where ηi = ril −(

n  j=1,j=i

au ij +

n  j=1

bu ij +

n   j=1

0 −∞

cu ij (s)ds)ξ−

au ii

n  j=1

t→∞

u Dij

> 0. Taken η =

min

{ηi }, then

i=1,2,··· ,n

lim inf xi (t) ≥ η. Thus we can get that η ≤ lim inf xi (t) ≤ lim sup xi (t) ≤ ξ.

t→∞

t→∞

t→∞

Then (6) is proved. Then let C = C((−∞, 0], Rn ) be a banach space with the norm φ = max sup |φi (s)|. i

−∞≤s≤ω

˙ ≤ L, ξ = Let Ω = {x(s) ∈ C : ηi ≤ xi (s) ≤ ξi , i = 1, 2, · · · , n, x(s) max {ξi }}, then Ω is a convex compact set in C. Define a map F from Ω to

i=1,2,··· ,n

C:

F : φ(s) → x(s + ω, φ).

x(t) = x(t, φ) is the solution of system(1) with the initial condition xi (s) = φi (s) for s ∈ (−∞, 0). It is easy to prove that x(s ˙ + ω) ≤ L, then if φ ∈ Ω, we have x ∈ Ω, it means that F Ω ⊂ Ω. By using Schauder’s fixed point theorem, there exists φ∗ ∈ Ω such that F φ∗ = φ∗ . Thus x(t, φ∗ ) = x(t, F φ∗ ) i.e. x(t, φ∗ ) = x(t + ω, F φ∗ ). It means that x(t, φ∗ ) is a positive periodic solution of system (1). Then the proof is complete. Remark 1. From Theorem 1, we can know that the upper and lower bounds of x∗ (t) are ηi ≤ x∗i (t) ≤ ξi (i = 1, 2, · · · , n). It may be useful in the other applicated areas.

4

The Globally Asymptotical Stability

In this part, we discuss about the global asymptotical stability of positive peri+∞  odic solutions. We assume that s|cij (t, s)|ds < +∞ and τij (t) is continuously 0

−1 (t) is an inverse differentiable with τ˙ij (t) < 1. Define σij (t) = t − τij (t), then σij function of σij (t).

Positive Periodic Solutions

501

Theorem 2. Assume that system(1) has a positive ω-periodic solution x∗ (t) = (x∗1 (t), x∗2 (t), · · · , x∗n (t)), and there exist positive constants λ1 , λ2 , · · · , λn such that: n 

λi aii (t) + −

n  j=1

|aji (t)|λj −

j=1,j=i 0 λj −∞ |cji (t

− s, s)|ds

n 

−1 (t))| |bji (σji

λ −1 1−τ˙ji (σji (t)) j j=1 n  Dji (t) − λj η ≥ δi j=1

(8)

> 0,

for all i = 1, 2, · · · , n, δi > 0, λi > 0 hold, then x∗ (t) is globally asymptotically stable. Proof. Construct a Lyapunov function: V (t) =

n  i=1

n 

λi | ln xi (t) − ln x∗i (t)| +

−x∗i (s)|ds

+

n  i,j=1

λi

0

i,j=1

t

−∞ t+s

λi

t

−1 (s))| |bij (σij |x (s) −1 t−τij (t) 1−τ˙ij (σij (s)) i

(9)

|cij (θ − s, s)||xi (θ) − x∗i (θ)|dθds.

The derivative of V (t) along the solution of system (1) is: dV (t) dt

=

n  i=1

−

λi sign|xi (t) − x∗i (t)|[−aii (t)|xi (t) − x∗i (t)| n 

j=1,j=i

aij (t)|xi (t) − x∗i (t)| −

−x∗j (t − τij (t))| − +

n  i,j=1

n   0

j=1 −1 |bij (σij (t))|

λi [ 1−τ˙

−1 ij (σij (t))

−∞

n  j=1

bij (t)|xj (t − τij (t))

|cij (t, s)||xj (t + s) − x∗j (t + s)|ds]

|xi (t) − x∗i (t)|

(10)

x∗i (t

−|bij (t)||xi (t − τij (t)) − − τij (t))|] n 0  + λi [ −∞ |cij (t − s, s)||xi (t) − x∗i (t)|ds i,j=1 0 − −∞ |cij (t, s)||xi (t + s) − x∗i (t + s)|ds] n ∗  xj (t)x∗ i (t)−xi (t)xj (t) + λi Dij (t) sign|xi (t) − x∗i (t)|. xi (t)x∗ (t) i,j=1

i

And we have n  j=1

Dij (t)

∗ xj (t)x∗ i (t)−xi (t)xj (t) sign|xi (t) xi (t)x∗ (t) i

− x∗i (t)| ≤

n  j=1

Dij (t) η |xi (t)

− x∗i (t)|. (11)

Now we prove (11) in four cases: Case(1): If x∗i < xi , x∗j < xj , then we have: n  j=1

Dij (t)

∗ xj (t)x∗ i (t)−xi (t)xj (t) sign|xi (t) xi (t)x∗ (t) i

− x∗i (t)| ≤ ≤

n  j=1 n  j=1

Dij (t)|

xi (t)(xj (t)−x∗ j (t)) | xi (t)x∗ i (t)

Dij (t) |xi (t) η

− x∗i (t)|;

502

T. Zhang, M. Jiang, and B. Huang

Case(2): If x∗i < xi , x∗j > xj , then we have: n 

Dij (t)

j=1

xj (t)x∗i (t) − xi (t)x∗j (t) sign|xi (t) − x∗i (t)| ≤ 0 xi (t)x∗i (t)

Then n  j=1

Dij (t)

∗ xj (t)x∗ i (t)−xi (t)xj (t) sign|xi (t) xi (t)x∗ i (t)

− x∗i (t)| ≤

n  j=1

Dij (t) η |xi (t)

− x∗i (t)|;

Case(3): If x∗i > xi , x∗j < xj , then the proof is the same as case(1); Case(4): If x∗i > xi , x∗j > xj , then the proof is the same as case(2). Then (11) hold. Combining with (8)-(11), we have that dV (t) dt

≤− − ≤−

n 

[λi aii (t) +

i=1 n 

j=1 n  i=1

λj

0

n  j=1,j=i

n 

|aji (t)|λj −

|c (t − s, s)|ds − −∞ ji

n  j=1

j=1

λj

−1 (t))| |bji (σji

λ −1 1−τ˙ji (σji (t)) j

Dji (t) η ]|xi (t)

− x∗i (t)|

(12)

δi |xi (t) − x∗i (t)|.

Thus, we we can get that: 

n +∞ 

0

δi |xi (t) − x∗i (t)|ds ≤ V (0) − V (+∞) ≤ V (0) < +∞.

(13)

i=1

According to Theorem 1, we can know that x(t) and x∗ (t) are bounded on [0, +∞). Hence |xi (t) − x∗i (t)|(i = 1, 2, · · · , n) are bounded and uniformly continuous on [0, +∞). Then from (13) we can get that lim xi (t) − x∗i (t) = 0. t→∞

Therefore, x∗ (t) is globally asymptotically stable.

5

The Globally Exponential Stability

Theorem 3. If there exist constants ε > 0, ρ > 0, ζ1 , ζ2 , · · · , ζn such that ζi (aii − ερ) + −

n  j=1

ζj

0

n  j=1,j=i

|aji (t)|ζj −

|c (t − s, s)|e −∞ ji

−εs

n  j=1

ds −

−1 (t))| |bji (σji

ζ e −1 1−τ˙ji (σji (t)) j

n 

j=1

ζj

Dji (t) η

≥ 0,

| ln xi (t) − ln x∗i (t)| ≤ ρ|xi (t) − x∗i (t)|,

−1 ε(σji (t)−t)

(14)

(15)

for all t > 0, i = 1, 2, · · · , n and ζi > 0 hold, then x∗ (t) is globally exponentially stable with convergence rate ε.

Positive Periodic Solutions

503

Proof. Construct a Lyapunov function: n 

V1 (t) =

i=1

+ +

ζi | ln xi (t) − ln x∗i (t)|eεt n 

i,j=1 n  i,j=1

ζi ζi

t

−1 |bij (σij (s))|

|x (s) −1 t−τij (t) 1−τ˙ij (σij (s)) i

0

t −∞ t+s

−1

− x∗i (s)|eεσij

(s)

ds

(16)

|cij (θ − s, s)||xi (θ) − x∗i (θ)|eε(θ−s) dθds.

The derivative of V1 (t) along the solution of system (1) is: dV1 (t) dt

=

n  i=1

−

ζi sign|xi (t) − x∗i (t)eεt |[ε| ln xi (t) − ln x∗i (t)| − aii (t)|xi (t) − x∗i (t)| n 

aij (t)|xi (t) − x∗i (t)| −

n 

bij (t)|xj (t − τij (t)) − j=1 j=1,j=i n   0 ∗ − −∞ |cij (t, s)||xj (t + s) − xj (t + s)|ds] j=1 −1 n  −1 |bij (σij (t))| ε(σij (t)−t) ∗ + ζi eεt [ 1−τ˙ (σ |x (t) − x (t)|e −1 i i (t)) ij ij i,j=1 −|bij (t)||xi (t − τij (t)) − x∗i (t − τij (t))|] n 0  ζi eεt [ −∞ |cij (t − s, s)||xi (t) − x∗i (t)|e−εs ds + i,j=1 0 − −∞ |cij (t, s)||xi (t + s) − x∗i (t + s)|ds] n ∗  xj (t)x∗ i (t)−xi (t)xj (t) ζi eεt Dij (t) sign|xi (t) − x∗i (t)|. + xi (t)x∗ (t) i i,j=1

x∗j (t − τij (t))|

Combining with (14)-(16), we have that dV1 (t) dt

≤ −eεt −

n  i−1

n 

j=1

ζj

[ζi (aii − ερ) + 0

n  j=1,j=i

−∞ |cji (t − s, s)|e

And from (17), we know

n  i=1

n 

|aji (t)|ζj −

−εs

ds −

n  j=1

n  j=1

−1 (t))| |bji (σji

ζ e −1 1−τ˙ji (σji (t)) j

D (t) ζj jiη ]|xi (t)

−1 ε(σji (t)−t)

− x∗i (t)| ≤ 0.

(17)

ζi | ln xi (t) − ln x∗i (t)|eεt ≤ V1 (t) ≤ V1 (0), so

ζi | ln xi (t) − ln x∗i (t)| ≤ V1 (0)e−εt .

i=1

From Theorem 2, we can know that x∗ (t) is globally asymptotically stable. So there exist positive constants m1 , m2 such that m1 ≤ xi (t) ≤ m2 for all t ≥ 0, i = 1, 2, · · · , n. Thus ,there exists a constant μ such that |xi (t) − x∗i (t)| ≤ n  μ| ln xi (t) − ln x∗i (t)| for all t ≥ 0, i = 1, 2, · · · , n. Then it get that ζi |xi (t) − i=1

x∗i (t)| ≤ μV1 (0)e−εt . It means that xi (t) − x∗i (t){ζ,1} = o(e−εt ). So x∗ (t) is globally exponentially stable with convergence rate ε by Definition 2. Then this proof is complete.

504

6

T. Zhang, M. Jiang, and B. Huang

Numerical Example

In this part, we set an example to illustrate the validity of the results in our theorems. Example 1. Consider the following 3-species system which is a particular case of system (1): ⎧ dx1 (t) ⎪ ⎪ = (8 + sin t)x1 (t) − (4 + cos t)x21 (t) − (1.3 + sin 2t)x1 (t)x2 (t − π) ⎪ ⎪ dt ⎪ ⎪ ⎪ +(7 − sin t)x1 (t)x3 (t − π) + (1 + sin t)(x2 (t) − x1 (t)) ⎪ ⎪ ⎪ ⎪ +(3 + cos t)(x3 (t) − x1 (t)), ⎪ ⎪ ⎪ dx (t) ⎪ ⎪ ⎨ 2 = (9 + cos t)x2 (t) − (1 + cos t)x1 (t − π)x2 (t) − (6 + cos t)x22 (t) dt +(3.5 + cos t)x2 (t)x3 (t − π) + (4 + cos t)(x1 (t) − x2 (t)) ⎪ ⎪ ⎪ ⎪ +(1 + sin t)(x3 (t) − x2 (t)), ⎪ ⎪ ⎪ ⎪ dx3 (t) ⎪ ⎪ ⎪ dt = (5.5 + 2 sin t)x3 (t) − (0.2 + sin t)x1 (t − π)x3 (t) ⎪ ⎪ ⎪ ⎪ +(3 + cos t)x2 (t − π)x3 (t) − (7.5 + sin t)x23 (t) ⎪ ⎩ +(1 + sin t)(x1 (t) − x3 (t)) + (4 + cos t)(x2 (t) − x3 (t)). 8 x1(t) x2(t) x3(t) 7

x1(t),x2(t),x3(t)

6

5

4

3

2

1

0

5

10

15

20

25 time t

30

35

40

45

50

Fig. 1. The system converges to a positive 2π -periodic solution

with the initial condition x1 (s) = 2, x2 (s) = 3.8 + 0.7s, x3 (s) = 1.7 + 0.3s2 , s ∈ 14 14 17 32 . [−π, 0]. Then we get ξ = max { , , } = i=1,2,3 3 5 13 3

Positive Periodic Solutions

505

It is easy to verify that all the conditions required in Theorem 1 are satisfied. Then this system exists a positive solution. Fig.1 shows that the system converges to a positive 2π-periodic solution.

7

Conclusion

In this paper, some new results of the positive periodic solutions of a nonautonomous Lotka-Volterra dispersal system with discrete and continuous infinite delays are obtained. We discuss about the global asymptotical stability and global exponential stability and the existence of positive periodic solutions in this Lotka-Volterra system. The results are typical and more general, and it can be reduced in the other systems.

Acknowledgments This work is supported by the Graduate Scientific Research Creative Foundation of Three Gorges University (200945) (200946) and the Scientific Innovation TeamProject of Hubei Provincial Department of Education (T200809) and Hubei Natural Science Foundation (No.D20101202).

References 1. Meng, X., Chen, L.: Periodic solution and almost periodic solution for a nonautonomous Lotka-Volterra dispersal system with infinite delay. J. Math. Anal. Appl. 05, 84 (2007) 2. Lin, W., Chen, T.: Positive periodic solutions of delayed periodic Lotka-Volterra systems. Physics letters A 334, 273–287 (2005) 3. Meng, X., Jiao, J., Chen, L.: Global dynamics behaviors for a nonautonomous Lotka-Volterra almost periodic dispersal system with delays. Nonlinear Analysis 68, 3633–3645 (2008) 4. Liang, Y., Li, L., Chen, L.: Almost periodic solutions for Lotka-Volterra systems with delay. Commun. Nonlinear Sci. Numer. Simulat. 14, 3660–3669 (2009) 5. Teng, Z.: Nonautonomous Lotka-Volterra systems with delays. Journal of Differerntial Equations 179, 538–561 (2002) 6. Zhu, C., Yin, G.: On competitive Lotka-Volterra model in random environments. J. Math. Anal. Appl. 170, 154–170 (2009) 7. Li, Y.: Positive periodic solutions of periodic neutral Lotka-Volterra system with distributed delays. Chaos, Solitons and Fractals 37, 288–298 (2008) 8. Luo, H., Li, W.: Periodic solutions of a periodic Lotka-Volterra system with delays. Applied Mathematics and Computation 156, 787–803 (2004) 9. Faria, T.: Sharp conditions for global stability of Lotka-Volterra systems with distributed delays. J. Differential Equations 246, 4391–4404 (2009) 10. Meng, X., Chen, L.: Almost periodic solution of nonautonomous Lotka-Volterra predator-prey dispersal system with delays. Journal of Theoretical Biology 243, 562–574 (2006) 11. Lu, G., Lu, Z., Lian, X.: Delay effect on the permanence for Lotka-Volterra cooperative systems. Nonlinear Analysis. Real Word Application 10, 005 (2009)

An Algorithm of Sphere-Structure Support Vector Machine Multi-classification Recognition on the Basis of Weighted Relative Distances Shiwei Yun,Yunxing Shu, and Bo Ge Luoyang Institute of Science and Technology Henan, Luoyan, 471003, China [email protected]

Abstract. Theories on sphere-structure support vector machine (SVM) and multi-classification recognition algorithms were studied in the first place, and on this basis, in view of the issue of the difference in the hypersphere radiuses resulted from the difference in the quantity of the training samples and the discrepancy in their distributions, the concepts of relative distance and weight were introduced, and subsequently a new algorithm of sphere-structure SVM multi-classification recognition was proposed on the basis of weighted relative distances. Accordingly, the data from the UCI database were used to conduct simulation experiments, and the results verified the validity of the algorithm propose. Keywords: pattern recognition; sphere-structure SVM; relative distance; weighting.

1 Introduction Pattern classification is a kind of pattern recognition technology, which makes use of the machine system with the computer as its center to create the decision-making boundaries between the various pattern classes on the basis of decision-making theories and to recognize the class of the unknown sample through certain algorithms. In past few decades, pattern recognition technologies have been successfully applied in state inspection, fault diagnosis, character recognition, speech recognition, and image recognition, etc., which has promoted the development of artificial intelligence [1]. Support vector machine adopts the structure risk principle in statistical learning theories [2] and has realized the training of small samples and demonstrated a good generalization capability, thus to a certain extent having solved the “over-fitting problem” and the “generalization capability problem” in neural networks. Meanwhile, the adoption of the kernel technology has remarkably enhanced the processing capacity of nonlinear data, and this, to some extent, also avoids the “dimension disaster problem” and the “network scale explosion problem” in neural networks [3]. Therefore, SVM has made a new international hot spot in the research in the field of machine learning [4,5]. K. Li et al. (Eds.): LSMS/ICSEE 2010, Part I, LNCS 6328, pp. 506–514, 2010. © Springer-Verlag Berlin Heidelberg 2010

An Algorithm of Sphere-Structure SVM Multi-classification Recognition

507

SVM was proposed on the basis of the problem of dichotomy. As for the multiclassification problem, the main algorithms at present are as follows: the one-againstrest method [6], the one-against-one method [7], and the tree-based SVM method [89], etc. The basic idea of these algorithms is to use multiple hyperplanes to divide the data space, with each kind of data enclosed within an area formed by several hyperplanes, and all the kinds of data are not off the optimal hyperplanes of the SVMs. The idea of the sphere-structure SVM algorithm is as follows: in a high-dimension feature space, a hypersphere is to be created for every pattern class which can cover its training samples and has the minimum volume, so as to realize the division of the training sample space. Reference [5] proposed a sphere-structure-based SVM algorithm its multi-classification decision rules. References [6-9] proposed two kinds of improved algorithms on the basis of sphere-structure SVMs. Compared with the standard SVMs, the multi-classification recognition algorithm on the basis of spherestructure SVMs is more suitable for the multi-classification recognition problem involving more samples and is easier to extend new classes. This study proposed a new algorithm of multi-classification recognition on the basis of sphere-structure SVMs. First, for each pattern class, a hypersphere was created, which divides the sample space; for the samples to be tested, considering the quantity and distribution of the training samples, the relative distances from the samples to be tested to the spherical centers of various kinds and the corresponding weights were introduced; according to the weighted relative distances, a membership function was established, and pattern recognition was realized through the extent of the membership. Finally, simulation experiments verified the validity of the method proposed.

2 Basic Theories of Sphere-Structure SVMs Suppose X = { x1 , x2 ,", xn } as the set of the training samples for k kinds in a d d

dimension space R ; X

m

= { x1 , x2 , " , xnm } and m = (1, 2, " , k ) as the sample set m

m

m

for the m -th kind in X ; nm as the total number of m -th kind of training sample, k

∑n

m

= n . A sphere-structure SVM is to create a minimum hypersphere for each

m =1

kind of training sample and to make the hypersphere include all the training samples belonging to this kind. This question can be transformed into the following quadratic programming questions:

min Rm 2

(1)

s.t. ( xim − am )T ( xim − am ) ≤ Rm 2 , i = 1, 2," , nm

(2)

in which am and Rm respectively refers to the spherical center and the spherical radius derived from the training of

m -th sample.

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Then the slack variable

ξim

is introduced, and the quadratic programming

questions (1) and (2) can be changed into: nm

min Rm + Cm ∑ ξim

(3)

⎧⎪( xim − am )T ( xim − am ) ≤ Rm 2 + ξim s.t. ⎨ m , i = 1, 2," , nm ⎪⎩ξi ≥ 0

(4)

2

i =1

in which Cm > 0 is a regularization parameter, reflecting the relation between the spherical radius and the quantity of the samples outside the sphere. According to the KKT condition, the Lagrange Multiplier Method is used to realize the dual programs of the quadratic programming questions, just as follows: nm

nm

max L = ∑ α im ( xim ⋅xim ) − ∑ α imα mj ( xim ⋅ x mj )

(5)

⎧ nm m ⎪∑ α i = 1 s.t. ⎨ i =1 , i = 1, 2," , nm ⎪0 ≤ α m ≤ C i m ⎩

(6)

i =1

i , j =1

Solve the quadratic programming questions and get the spherical center nm

am = ∑ α im xim . i =1

Among the solutions, only a small portion satisfies α i > 0 , and the corresponding sample points are called support vectors, in which the sample points corresponding to m

0 < α i < Cm are called boundary support vectors, and these points are on the m

boundaries of the hypersphere; the sample points corresponding to α i = Cm are m

called outside support vectors, and these points are off the hypersphere. If any boundary support vector

xkm is used, the square of the spherical radius can be

calculated as:

Rm 2 = ( xkm − am )T ( xkm − am ) nm

nm

i =1

i , j =1

= ( xkm ⋅ xkm ) − 2∑ αim ( xkm ⋅ xim ) + ∑ αimα mj ( xim ⋅ x mj ) For any unknown sample point spherical center is:

(7)

x , the square of the distance from the point to the

An Algorithm of Sphere-Structure SVM Multi-classification Recognition

509

Dm 2 = ( x − am )T ( x − am ) nm

nm

i =1

i , j =1

= ( x ⋅ x ) − 2∑ αim ( x ⋅ xim ) + ∑ αimα mj ( xim ⋅ x mj )

(8)

In reality, sample points generally will not be distributed spherically. In order to make this method have more extensive practicality, just as the SVMs method, so the kernel method can be used, that is, find a nonlinear mapping ϕ , and map the sample into the high-dimension feature space. The inner product operation in the feature space can be replaced by the kernel function, therefore it is unnecessary to know the specific form of the nonlinear mapping, and thus the operation complexity will not be increased. Theories have proved that as long as the kernel function K ( x , y ) satisfies the Mercer theorem, the kernel function can represent the inner product of the two vectors within the high-dimension space [2]. At this point the quadratic programming questions (5) and (6) can be transformed into: nm

nm

max L = ∑ α K ( x ,x ) − ∑ α imα mj K ( xim , x mj )

(9)

⎧ nm ⎪ αi = 1 , i = 1, 2," , nm s.t. ⎨∑ i =1 ⎪0 ≤ α ≤ C i ⎩

(10)

i =1

m i

m i

m i

i , j =1

Solve the quadratic programming questions and get the spherical center nm

am =

∑α i =1

m m i ϕ ( xi ) . m

If any boundary support vector xk is used, the square of the spherical radius can be calculated as: Rm 2 = (ϕ ( xkm ) − am )T (ϕ ( xkm ) − am ) nm

nm

i =1

i , j =1

= K ( xkm ⋅ xkm ) − 2∑ αim K ( xkm ⋅ xim ) + ∑ αimα mj K ( xim ⋅ x mj )

(11)

For any testing sample point x , the square of the distance from x to the spherical center of the m -th sphere is:

Dm 2 ( x ) = (ϕ ( x ) − am )T (ϕ ( x ) − am ) nm

nm

i =1

i , j =1

= K ( x ⋅ x ) − 2∑ αim K ( x ⋅ xim ) + ∑ α imα mj K ( xim ⋅ x mj )

(12)

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3 Multi-classification Fuzzy Recognition on the Basis of SphereStructure SVMs 3.1 Weighted Relative Distances

The basic procedures of using the sphere-structure SVMs to conduct multiclassification recognition are as follows: first, train the various kinds of training samples and construct multiple hyperspheres to divide the sample space; then, test the testing samples and classify in accordance with certain rules. Generally, testing samples fall into three categories: (1) enclosed by only one hypersphere (as in Figure 1(a)); (2) not enclosed by any hypersphere (as in Figure 1(b)); (3) enclosed by multiple hyperspheres (as in Figure 1(c)).

Fig. 1.

Under general circumstances, because of the differences in the quantity and distribution of the training samples, the sizes of the radius of the training hyperspheres will also be different, and the longer the spherical radius, the more dispersed the samples; the more the sample points, the more concentrated the samples. The multi-classification recognition algorithms proposed in references [5-7] do not take these circumstances into account. Therefore, this study proposed a fuzzy recognition algorithm on the basis of weighted relative distances. Suppose nm as the number of the m -th kind of training sample, Rm as the m kind of spherical radius, and Dm ( x ) as the distance from the testing sample point x to the m -th spherical center, define

d m ( x ) = ωm

Dm ( x) Rm

(13)

as the weighted relative distance from point x to the m -th spherical center, in which ωm is the weight value. Define

μm ( x) =

1/ d m ( x) k

∑1/ d i =1

m

( x)

(14)

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511

as the degree of membership of point x the m -kind. Lastly, conduct pattern recognition according to the size of the membership function. The testing samples are affiliated to the kinds whose degree of membership is larger. Because the number of the sample points and the selection of the kernel function both will influence the distribution of the sample points, therefore the selection of the weight function ωm is related to the number of the training sample points and to the selection of the kernel function, namely, the weight function ωm = f ( nm , σ ) , in which σ is the parameter in the kernel function. Because the number of sample points will influence their distribution, and the size of σ will influence the compactness of the boundaries of the hyperspheres, the weight function shall bear the following properties: (1) ωm = f ( nm , σ ) is the increasing function of nm . Because the more the sample points are, the more concentrated the samples are, under the circumstance that the relative distances Dm ( x ) / Rm are identical, the probability for an unknown sample to be affiliated to the kind whose sample points are more dispersed is larger, that is, the weighted relative distances to those kinds whose sample points are fewer shall be shorter, namely, the fewer the sample points, the smaller the weight values. (2) With the strengthening of the nonlinearity of the kernel function, ωm = f ( nm , σ ) reduces the degree of differences in weight values between different kinds. Because the larger the nonlinearity of the kernel functions is, the more compact the hyperspheres will be, and correspondingly the smaller the influence of the sample number and distribution will be. Therefore, the extent of the relative changes among the weight values of different kinds shall become smaller. The specific function form of ωm is generally determined by experience or experiments. 3.2 Procedures of the Pattern Recognition Algorithm

(1) For every kind of training sample, construct respectively the corresponding minimum hyperspheres, and use equation (11) to calculate the radius of various kinds of hyperspheres; (2) Use equation (12) to calculate the distances from the samples to be tested to the spherical centers of various kinds of hyperspheres; (3) Determine the weight function, and use equation (14) to calculate the degree of membership of the samples to be tested; (4) Conduct decision-making classification according to the principle of maximum degree of membership.

4 Experimental Analysis 4.1 Simulation Experiments

In order to verify the validity of the proposed algorithm, this study adopted the Wine sample set and the Vehicle sample set from the UCI database to conduct simulation

512

S. Yun,Y. Shu, and B. Ge

experiments, in which the kernel function was the same, that is, the radial basis kernel function. For the Wine sample set, we selected three kinds of training samples, whose numbers were 20, 30, and 20 respectively, and the remaining ones were used as testing samples. The weight function adopted was ωm = f ( nm , σ ) = exp( −σ / nm

0.9 + 0.02σ

) , and

the parameter σ in the kernel function ranged from 1 to 20 with an interval of 1. Altogether 20 experiments were conducted. For the Vehicle sample set, we selected four kinds of training samples, whose numbers were 100, 108, 109, and 106 respectively, and the remaining ones were used as testing samples. The weight function adopted was ωm = f ( nm , σ ) = exp( −σ / nm

0.5+ 0.05σ

) , and the parameter σ in the

kernel function ranged from 1 to 4 with an interval of 0.2. Altogether 16 experiments were conducted. For the Ionosphere sample set, we selected two kinds of training samples, whose numbers were 42 and 75 respectively, and the remaining ones were used as testing samples. The weight function adopted was 2 +σ

ωm = f ( nm , σ ) = exp( −σ / nm ) , and the parameter σ in the kernel function ranged from 1 to 2 with an interval of 0.05. Altogether 21 experiments were conducted. For the Iris sample set, we selected three kinds of training samples, whose numbers were 12, 20 and 30 respectively, and the remaining ones were used as testing samples. 0.5 + 0.05σ The weight function adopted was ωm = f ( nm , σ ) = exp( −σ / nm ) , and the parameter σ in the kernel function ranged from 1 to 10 with an interval of 1. Altogether 10 experiments were conducted. For the Waveform sample set, we selected three kinds of training samples, whose numbers were100 200 and 300 respectively, and the remaining ones were used as testing samples. The weight function adopted was 1+ 0.05σ ωm = f ( nm , σ ) = exp( −σ / nm ) , and the parameter σ in the kernel function ranged from 2 to 6 with an interval of 0.5. Altogether 9 experiments were conducted. All the testing correctness rate and testing time of the algorithm were compared with those of the algorithm proposed in reference [5]. The results of the experiments are shown in Table 1. 4.2 Result Analysis

The experiment results suggest that testing correctness rate is mainly related to the selection of the kernel function parameters. Under the same kernel function parameter, because the algorithm in the present study took sample number and distribution into full consideration, the correctness rate of the algorithm in this study was higher than that in reference [5]. As for testing time, with the increase of the parameter of the radial basis kernel function, the testing time of the algorithm in the present study was less than that in reference [5], and the reason is as follows: with the increase of the parameter of the radial basis kernel function, there are relatively more overlapping among the hyperspheres, and for the decision function for the sample points in the overlapping space, the degree of complexity of the algorithm in reference [5] was higher, thus the algorithm used in the present study is better as far as testing time is concerned.

An Algorithm of Sphere-Structure SVM Multi-classification Recognition

513

Table 1. Comparison between algorithm in this study and algorithm in reference [5] Data sets

Wine

Vehicle

Iris

Ionosphere

Waveform

Method Method in this study Method in reference [5] Method in this study Method in reference [5] Method in this study Method in reference [5] Method in this study Method in reference [5] Method in this study Method in reference [5]

average correctness rate

highest correctness rate

testing time(s)

0.8911

0.9533

0.0766

0.8014

0.8598

0.0781

0.7305

0.7057

0.8642

0.7116

0.6918

0.9023

0.9589

0.9667

0.0305

0.9133

0.9556

0.0310

0.6461

0.7650

0.0930

0.6416

0.6923

0.0967

0.8262

0.8352

6.1911

0.8048

0.8191

6.5276

5 Conclusion On the basis of studying the multi-classification pattern recognition based on spherestructure SVMs, a kind of fuzzy multi-classification recognition algorithm was proposed on the basis of weighted relative distances. Because the decision function of this algorithm takes into full consideration the sample number and the influence of the kernel function on the distribution of the training samples, the testing correctness rate is higher. Meanwhile, because the decision function of the present algorithm only used weighted relative distances, compared with the decision function used in reference [5], its degree of complexity in calculation is smaller. Therefore, in the aspect of testing time the present algorithm is better than that in reference [5], and the present algorithm is easier to be realized. However, as for the determination of the weight function, so far there have been no unified theories to be guidance, and this is a further research direction for the present study.

References 1. Bishop, Christopher, M.: Pattern Recognition and Machine Learning. Springer, Heidelberg (2006) 2. Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, Heidelberg (1995)

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3. Zhang, X.: Introduction to Statistical Learning and Support Vector Machines. Acta Automatica Sinica 26, 32–42 (2000) 4. Gestel, T.V., Suykens, A.K., Brabanter, J.D., Moor, B.D., Vandewalle, J.: Kernel canonical correlation analysis and least squares support vector machines. In: Proceedings of the International Conference on Artificial Neural Networks (2001) 5. Zhu, M., Liu, X., Chen, S.: Solving the Problem of Multi-class Pattern Recognition with Sphere-structured Support Vector Machines. Journal of NanJing University Natural Sciences 39, 153–158 (2003) 6. Li, H., Lin, J.: Multiclass Classification Based on the One-class Classification and its Application. Journal of South China University of Technology (Natural Science Edition) 32, 82–88 (2004) 7. Wang, J., Neskovic, P., Cooper, L.N.: Bayes classification based on minimum bounding spheres. Neurocomputing 4-6(70), 801–808 (2007) 8. Wu, Q., Jia, C., Zhang, A., et al.: Improved Algorithm Based on Sphere Structure SVMs and Simulation. Journal of System Simulation 20, 345–348 (2008) 9. Gu, L., Wu, H., Xiao, L.: Sphere-structured Support Vector Machines Classification Algorithm Based on New Decision Rule. Journal of System Simulation 20, 2901–2904 (2008)

Author Index

Abeykoon, Chamil II-9 Affenzeller, Michael II-368 Alla, Ahmed N. Abd II-190 Allard, Bruno I-416 An, Bo I-256 Anqi, Wang II-351 Auinger, Franz II-368 Banghua, Yang

Fan, Guo-zhi I-486 Fan, Jian I-147 Fan, Xin-Nan I-304 Fan, Zhao-yong I-104 Fei, Minrui I-1, I-62, I-87, I-147, I-221, I-456, II-40, II-49, II-450, II-475 Fu, Liusun II-505 Fu, Xiping II-49

II-250

Cai, Zongjun I-36 Cao, Guitao I-313 Cao, Longhan II-93 Cao, Lu II-58 Cao, Luming I-36, I-112, II-493 Chen, Haifeng I-389 Chen, Hui II-333, II-505 Chen, Jindong II-207 Chen, Jing I-136 Chen, LiXue II-138 Chen, Min-you I-104, II-342 Chen, Qigong I-87 Chen, Rui II-234 Chen, Wang II-148 Chen, Xiaoming II-120 Chen, Xisong I-409 Chen, Yong I-486 Cheng, Dashuai I-36, I-112, II-493 Cheng, Liangcheng I-45 Chiu, Min-Sen I-36, I-112, II-493 Dai, Rui II-93 Deng, An-zhong I-486 Deng, Jing I-7, II-9, II-40 Deng, Weihua I-1, II-450 Dengji, Hu II-351 Di, Yijuan I-456 Ding, Guosheng I-244 Ding, Yan-Qiong I-304 Dong, Yongfeng I-324 Du, Dajun I-62, I-290 Du, Yanke II-266 Duan, Ying-hong II-259

Ganji, Behnam I-434 Gao, Lixin I-157 Gao, Weijun I-361 Gao, Yanxia I-416 Ge, Bo I-506 Geng, Zhiqiang II-84 Gou, Xiaowei II-69 Gu, Hong I-52 Gu, Li-Ping I-304 Guanghua, Chen II-351 Guo, Chunhua I-282, I-333 Guo, Fengjuan I-205 Guo, Huaicheng I-120 Guo, Shuibao I-416 Guo, Xingzhong II-433 Guo, Yi-nan I-213 Hadow, Mohammoud M. II-190 Hailong, Xue II-400 Ha, Minghu II-241 Han, Yongming II-84 Hao, Zhonghua II-333, II-505 He, Qingbo II-218 He, Ran I-466 He, Tian-chi II-1 He, Wei II-342 Hong, Moo-Kyoung I-380 Hou, Weiyan I-129 Hu, Gang II-342 Hu, Huosheng II-450 Huang, Bin I-497 Huang, Hong II-390 Huang, Lailei II-277 Huang, Mingming I-466 Huang, Quanzhen I-95

516

Author Index

Huang, Zaitang II-166 Hutterer, Stephan II-368 Irwin, George W.

II-40, II-456

Jia, Fang II-158 Jia, Li I-36, I-112, II-69, II-493 Jiang, Enyu I-95 Jiang, Jing-ping I-77 Jiang, Lijun II-225 Jiang, Ming I-87 Jiang, Minghui I-497 Jiang, Xuelin I-185 Jiao, Yunqiang II-360 Jing, Chunwei I-233 Jingqi, Fu II-128 Kang, Lei II-467 Karim, Sazali P. Abdul II-190 Kelly, Adrian L. II-9 Kim, Jung Woo I-372 Kong, Zhaowen I-185 Koshigoe, Hideyuki II-288 Kouzani, Abbas Z. I-434 Lang, Zi-qiang I-104 Lee, Hong-Hee I-372, I-380 Liao, Ju-cheng I-104 Li, Bo II-148 Li, Jianwei I-324 Li, Kang I-1, I-7, I-62, I-270, I-399, II-9, II-40, II-379, II-456 Li, Lixiong I-350, II-475 Li, Nan I-196 Li, Qi I-409 Li, Ran II-199 Li, Sheng-bo I-486 Li, Shihua I-409 Li, Xiang II-180 Li, Xin II-180 Li, Xue I-290 Li, Yaqin I-45 Li, Yonghong I-26 Li, Yongzhong I-233 Li, Zhichao II-467 Liang, Chaozu I-185 Lin, Huang I-297 Linchuan, Li II-400 Lin-Shi, Xuefang I-416 Littler, Tim II-421

Liu, Enhai I-324 Liu, Fei II-442 Liu, Jiming II-277, II-410 Liu, Li-lan I-166, II-101 Liu, Qiming II-266 Liu, Shuang I-297 Liu, Xiaoli II-93 Liu, Xueqin I-7 Liu, Yi II-390 Lu, Da II-379 Lu, Huacai II-433 Luojun, II-218 Luo, Yanping I-157 Ma, Shiwei I-185, II-69, II-333, II-505 Martin, Peter J. II-9 McAfee, Marion I-7, II-9 McSwiggan, Daniel II-421 Meng, Ying II-433 Menhas, Muhammad Ilyas II-49 Ming, Rui II-475 Niu, Qun Niu, Yue

II-21, II-456 I-416

Pan, Feng II-207 Pang, Shunan II-30 Pedrycz, Witold II-241 Pei, Jianxia I-290 Peng, LingXi II-138 Qi, Jie II-30 Qian, Junfeng II-333 Qin, Xuewen II-166 Qin, Zhaohui I-129 Qu, Fu-Zhen II-148 Qu, Gang II-297 Ren, Hongbo

I-361

Shao, Yong I-95 Shi, Benyun II-410 Shi, Jiping I-112, II-493 Shi, Lukui I-324 Shi, Xiaoyun II-84 Shi, Yan-jun II-148 Shiwei, Ma II-351 Shu, Yunxing I-506 Shu, Zhi-song I-166, II-101 Song, Shiji I-399, II-484

Author Index Song, Yang I-1, I-129 Steinmaurer, Gerald II-368 Su, Hongye II-360 Su, Zhou I-425 Sun, Bo II-505 Sun, Hao I-304 Sun, Meng I-313 Sun, Shijie I-244 Sun, Sizhou II-433 Sun, Xin I-456 Sun, Xue-hua I-166, II-101 Tan, Weiming II-166 Tang, Jiafu II-297, II-312 Tang, LiangGui I-256 Tang, Zhijie II-218 Tao, Jili II-120 Tegoshi, Yoshiaki I-425 Tian, Shuai I-166 Trinh, H.M. I-434 Wang, Binbin I-389 Wang, Chao II-241 Wang, Fang I-157 Wang, Haikuan I-129 Wang, Hongbo I-196 Wang, Hongshu II-305 Wang, Jia II-128 Wang, Jianguo II-69 Wang, Jiyi I-297 Wang, Junsong I-69 Wang, Ling II-49, II-69 Wang, Lingzhi II-110 Wang, Linqing II-312 Wang, Nam Sun I-45 Wang, Qiang II-58 Wang, Shentao II-93 Wang, Shicheng II-234 Wang, Shujuan II-234, II-467 Wang, Tongqing I-282, I-333 Wang, Xihong I-147 Wang, Xin II-499 Wang, Xiukun I-466 Wang, Xiuping I-136 Wang, Yu II-297 Wei, Jia II-225 Wei, Lisheng I-87 Wei, Pi-guang I-477 Weimin, Zeng II-351 Wen, Guangrui I-16

Wen, Guihua II-225 Wu, Cheng I-270, I-399, II-484 Wu, Jue II-138 Wu, Jun II-158 Wu, Liqiao II-305 Wu, Mingliang II-93 Wu, Qiong I-361 Xiao, Da-wei I-213 Xiaoming, Zheng II-250 Xiaozhi, Gao II-400 Xia, Qingjun I-205 Xu, Jing I-233 Xu, Lijun I-221 Xu, Li-Zhong I-304 Xu, Rui II-266 Xu, Zhi-yu I-176 Yang, Aolei II-456 Yang, Ating I-445 Yang, Bo II-75 Yang, Huizhong I-45 Yang, Jun I-409 Yang, Lei II-138 Yang, Mei I-213 Yang, Nanhai I-466 Yang, Qingxin I-324 Yang, T.C. I-221, I-350, I-456 Yang, Yan-li II-342 Ye, Longhao I-120 Yin, Wenjun II-484 Yin, Xueyan II-442 Yonghuai, Zhang II-250 Yoshii, Takako II-288 Yuan, Ruixi I-69 Yu, Chunyan II-305 Yu, Shuxia I-120 Yu, Tao I-166, II-101 Yu, Wei I-221 Yu, Xiao-ming I-77 Yu, Yajuan I-120 Yun, Shiwei I-506 Zeng, Xiangqiang I-95 Zhai, Guofu II-467 Zhai, Jin-qian I-104, II-342 Zhang, An I-205, II-58 Zhang, Changjiang II-75 Zhang, Chao II-390 Zhang, Dexing II-180

517

518 Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang, Zhang,

Author Index Hao I-270, II-333 Hong-yu I-486 Hui II-390 Jie I-176 Jun I-52 Long II-234, II-467 Qian I-389 Qingling II-321 Tiezhi II-321 Ting I-497 Xianxia I-313 Xining I-16 Xue-Wu I-304 Yaozhong I-205 Yuanyuan II-84 Yue II-321 Yukui I-399 Yuli II-484 Zhihua I-425

Zhao, Guangzhou I-52, I-196, II-199, II-379 Zhao, Liang I-342 Zhao, Lindu I-26, I-445 Zhao, Ming I-16 Zhao, Ming-sheng II-1 Zhao, Shian II-110 Zhao, Wanqing II-456 Zheng, Dong II-250 Zheng, Xiaoming II-180 Zhou, Caihui II-225 Zhou, Fang II-21 Zhou, Hao I-477 Zhou, Taijin II-21 Zhou, Weisheng I-361 Zhuang, Chun-long I-486 Zhu, Peng II-1 Zhu, Wei II-390 Zhu, Wen-hua I-477 Zhu, Yong II-120