EUROPEAN SYMPOSIUM ON COMPUTER-AIDED P R O C E S S E N G I N E E R I N G - 15
COMPUTER-AIDED CHEMICAL ENGINEERING Advisory Editor: R. Gani Volume 1: Volume 2: Volume 3: Volume 4: Volume 5: Volume 6: Volume 7: Volume 8: Volume 9: Volume 10: Volume 11: Volume 12: Volume 13: Volume 14: Volume 15: Volume 16: Volume 17: Volume 18: Volume 19: Volume 20:
Distillation Design in Practice (L.M. Rose) The Art of Chemical Process Design (G.L. Wells and L.M. Rose) Computer Programming Examples for Chemical Engineers (G. Ross) Analysis and Synthesis of Chemical Process Systems (K. Hartmann and K. Kaplick) Studies in Computer-Aided Modelling. Design and Operation Part A: Unite Operations (1. Pallai and Z. Fony6, Editors) Part B: Systems (1. Pallai and G.E. Veress, Editors) Neural Networks for Chemical Engineers (A.B. Bulsari, Editor) Material and Energy Balancing in the Process Industries - From Microscopic Balances to Large Plants (V.V. Veverka and F. Madron) EuropeanSymposium on Computer Aided Process Engineering-10 (S. Pierucci, Editor) EuropeanSymposium on Computer Aided Process Engineering-11 (R. Gani and S.B. Jorgensen, Editors) European Symposium on Computer Aided Process Engineering-12 (J. Grievink and J. van Schijndel, Editors) Software Architectures and Tools for Computer Aided Process Engineering (B. Braunschweig and R. Gani, Editors) Computer Aided Molecular Design: Theory and Practice (L.E.K. Achenie, R. Gani and V. Venkatasubramanian, Editors) Integrated Design and Simulation of Chemical Processes (A.C. Dimian) European Symposium on Computer Aided Process Engineering-13 (A. Kraslawski and I. Turunen, Editors) Process Systems Engineering 2003 (Bingzhen Chen and A.W. Westerberg, Editors) Dynamic Model Development: Methods, Theory and Applications (S.P. Asprey and S. Macchietto, Editors) The Integration of Process Design and Control (P. Seferlis and M.C. Georgiadis, Editors) European Symposium on Computer-Aided Process Engineering-14 (A. Barbosa-P6voa and H. Matos, Editors) Computer Aided Property Estimation for Process and Product Design (M. Kontogeorgis and R. Gani, Editors) European Symposium on Computer-Aided Process Engineering-15 (L. Puigjaner and A. Espufia, Editors)
COMPUTER-AIDED CHEMICAL ENGINEERING, 20B
EUROPEAN SYMPOSIUM ON COMPUTER-AIDED P R O C E S S E N G I N E E R I N G - 15 38th European Symposium of the Working Party on Computer Aided Process Engineering ESCAPE-15, 29 May- 1 June 2005, Barcelona, Spain
Edited by
Luis Puigjaner UPC-ETSEIB Barcelona, Spain
Antonio Espufia UPC-ETSEIB Barcelona, Spain
ELSEVIER 2005 Amsterdam Paris
- San
- Boston Diego
- Heidelberg
- San
Francisco
- London - Singapore
- New
York
- Sydney
- Oxford - Tokyo
ELSEVIER B.V. Sara Burgerhartstraat 25 P.O. Box 211, 1000 AE Amsterdam, The Netherlands
E L S E V I E R Inc. 525 B Street Suite 1900, San Diego C A 92101-4495, U S A
E L S E V I E R Ltd. The Boulevard Langford Lane, Kidlington, Oxford OX5 1GB, U K
E L S E V I E R Ltd. 84 Theobalds Road London W C 1 X 8RR UK
© 2005 Elsevier B.V. All rights reserved. This work is protected under copyright by Elsevier B.V., and the following terms and conditions apply to its use: Photocopying Single photocopies of single chapters may be made for personal use as allowed by national copyright laws. Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery. Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use. Permissions may be sought directly from Elsevier's Rights Department in Oxford, UK: phone (+44) 1865 843830, fax (+44) 1865 853333, e-mail:
[email protected]. Requests may also be completed on-line via the Elsevier homepage (http://www.elsevier. com/locate/permissions). In the USA, users may clear permissions and make payments through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA; phone: (+1) (978) 7508400, fax: (+1) (978) 7504744, and in the UK through the Copyright Licensing Agency Rapid Clearance Service (CLARCS), 90 Tottenham Court Road, London W1P 0LP, UK; phone: (+44) 20 7631 5555; fax: (+44) 20 7631 5500. Other countries may have a local reprographic rights agency for payments. Derivative Works Tables of contents may be reproduced for internal circulation, but permission of the Publisher is required for external resale or distribution of such material. Permission of the Publisher is required for all other derivative works, including compilations and translations. Electronic Storage or Usage Permission of the Publisher is required to store or use electronically any material contained in this work, including any chapter or part of a chapter. Except as outlined above, no part of this work may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without prior written permission of the Publisher. Address permissions requests to: Elsevier's Rights Department, at the fax and e-mail addresses noted above. Notice No responsibility is assumed by the Publisher for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Because of rapid advances in the medical sciences, in particular, independent verification of diagnoses and drug dosages should be made.
First edition 2005 Library of Congress Cataloging in Publication Data A catalog record is available from the Library of Congress. British Library Cataloguing in Publication Data A catalogue record is available from the British Library.
ISBN:
ISSN:
0-444-51990-4 (Part A) 0-444-51991-2 (Part B) 0-444-51987-4 (Set) 0-444-51992-0 (CD) 1570-7946 (Series)
The paper used in this publication meets the requirements of ANSI/NISO Z39.48-1992 (Permanence of Paper). Printed in The Netherlands.
C o n t e n t s - Part B Process Operation and Control A Framework for the Mixed Integer Dynamic Optimisation of Waste Water Treatment Plants using Scenario-Dependent Optimal Control J. Busch, M. Santos', J. Oldenburg, A. Cruse a n d W. M a r q u a r d t ............................. 955 On-line Fault Diagnosis Support for Real Time Evolution applied to MultiComponent Distillation S. Ferrer-Nadal, I. Ydlamos-Ruiz, M. Graells and L. Puigjaner .............................. 961
Real-Time Feasibility of Nonlinear Predictive Control for Semi-batch Reactors H. Arellano-Garcia, T. Bar,,, M. Wendt a n d G. Wozny ............................................ 967
Control of Integrated Process Networks - A Multi-Time Scale Perspective 973
M. Baldea and P. Daoutidis . .....................................................................................
Minimum-Cost Operation in Heat-Exchanger Networks 979
A. H. Gonzdlez and J. L. Marchetti ...........................................................................
An Online Decision Support Framework for Managing Abnormal Supply Chain Events M. Bansal, A. A dhitya, R. Srinivasan and i. A. Karimi ............................................. 985 Novel Scheduling of a Mixed Batch/Continuous Sugar Milling Plant using Petri nets M. Ghaeli, P. A. Bahri and P. L. Lee ........................................................................
991
Improving Short-Term Planning by incorporating Scheduling Consequences P. Hei./nen, I. B o u w m a n s and Z. Verwater-Lukszo ...................................................
997
Multi-scale Planning and Scheduling in the Pharmaceutical Industry H. Stefansson and N. Shah ......................................................................................
1003
Initiation and Inhibiting Mechanisms for Multi-tasking Control in Discrete Event Systems S. Macchietto, N. J. Alsop, R. J. B a i r d Z. P. Feng a n d B. H. Chen ....................... 1009 Model Based Parametric Control in Anaesthesia P. Dua, V. Dua and E. N. Pistikopoulos .................................................................
1015
Anti-Slug Control Experiments on a Small-Scale Two-Phase Loop H. Sivertsen a n d S. S k o g e s t a d .................................................................................
1021
Using CLP and MILP for Scheduling Commodities in a Pipeline L. Magat6o, L. V R. Arruda and F. Neves Jr .........................................................
1027
Scheduling of a Pipeless Multi-Product Batch Plant using Mixed-Integer Programming Combined with Heuristics S. Panek, S. Engell a n d C. Lessner ......................................................................... 1033 On the State-Task Network Formulation: Time Representations C. T. Maravelias ...................................................................................................... Optimization of Biopharmaceutical Experiences from the Real World
Manufacturing
with
1039
Scheduling Tools -
C. A. Siletti, D. Petrides and A. Koulouris ..............................................................
1045
vi Advances in Robust Optimization Approaches for Scheduling under Uncertainty S. L. Janak and C. A. Floudas ................................................................................. 1051 Proactive Approach to address Robust Batch Process Scheduling under Short-Term Uncertainties A. Bonfill, A. Espu~a and L. Puigjaner ................................................................... 1057 A Rigorous MINLP for the Simultaneous Scheduling and Operation of Multiproduct Pipeline Systems R. Rejowski Jr. and J. M. Pinto ............................................................................... 1063 Multicommodity Transportation and Supply Problem with Stepwise Constant Cost Function Z. Lelkes, E. Rev, T. Farkas, Z. Fonyo, T. Kovacs and I. Jones .............................. 1069 Design and Planning of Supply Chains with Reverse Flows M. I. Gomes Salema, A. P. Barbosa-P6voa and A. Q. Novais ................................ 1075 Heterogeneous Batch Distillation Processes: Real System Optimization S. Pommier, S. Massebeuf V. Gerbaud, O. Baudouin, P. Baudet andX. Joulia .... 1081 Modelling and Optimisation of Distributed-Parameter Batch and Semi-batch Reactor Systems X. Zheng, Robin Smith and C. Theodoropoulos ...................................................... 1087 Optimal Start-up of Micro Power Generation Processes P. I. Barton, A. Mitsos and B. Chachuat ................................................................. 1093 Performance Monitoring of Industrial Controllers Based on the Predictability of Controller Behavior R. A. Ghraizi, E. Martinez, C. de Prada, F. Cifuentes and J. L. Martinez ............. 1099 A Systematic Approach to Plant-Wide Control Based on Thermodynamics L. T. Antelo, I. Otero-Muras, J. R. Banga and A. A. Alonso ................................... 1105 A Multiple Model, State Feedback Strategy for Robust Control of Nonlinear Processes F. E Wang, P. A. Bahri, P. L. Lee and I. T. Cameron ............................................ 1111 A Robust Discriminate Analysis Method for Process Fault Diagnosis D. Wang and J. A. Romagnoli ................................................................................. 1117 Learning in Intelligent Systems for Process Safety Analysis C. Zhao and V. Venkatasubramanian ..................................................................... 1123 Multivariate Decision Trees for the Interrogation of Bioprocess Data K. Kipling, G. Montague, E. B. Martin and A. J. Morris ........................................ 1129 On a New Definition of a Stochastic-Based Accuracy Concept of Data Reconciliation-Based Estimators M. Bagajewicz ......................................................................................................... 1135 The Integration of Process and Spectroscopic Data for Enhanced Knowledge Extraction in Batch Processes C. W. L. Wong, R. E. A. Escott, A. J. Morris and E. B. Martin ............................... 1141 A Systematic Approach for Soft Sensor Development B. Lin, B. Recke, P. Renaudat, J. Knudsen and S. B. Jorgensen ............................. 1147
vii Application of Multi-Objective Optimisation to Process Measurement System Design D. Brown, F. MarOchal, G. Heyen a n d J. Paris ...................................................... 1153 Utilities Systems On-Line Optimization and Monitoring: Experiences from the Real World D. Ruiz, J. Mamprin, C. Ruiz, D. Nelson and G. R o s e m e ....................................... 1159 A Continuous-Time Formulation for Scheduling Multi-Stage Multi-product Batch Plants with Non-identical Parallel Units L. Fu and L A. Karimi .............................................................................................. 1165 Optimal Scheduling of Supply Chains: A New Continuous-Time Formulation A. C. S. A m a r o a n d A . P. B a r b o s a - P 6 v o a ...............................................................
1171
Effect of Pricing, Advertisement and Competition in Multisite Capacity Planning M. Bagq/ewicz ......................................................................................................... 1177 Multi-objective Optimization of Curds Manufacture N. G. Vaklieva, A. Espu~a, E. G. Shopova, B. B. Ivanov and L. Puigianer ............ 1183
Global Supply Chain Network Optimization for Pharmaceuticals R. T. Sousa, N. Shah a n d L. G. Papageorgiou ........................................................
1189
Linear Quadratic Control Problem in Biomedical Engineering L E Sanchez Chdvez, R. Morales-Mendndez a n d S. O. Martinez Chapa ............... 1195
Using Structured and Unstructured Estimators for Distillation Units: A Critical Comparison F. Bezzo, R. Muradore a n d M. Barolo .................................................................... 1201 Modeling of Complex Dynamics in Reaction-Diffusion-Convection Model of CrossFlow Reactor with Thermokinetic Autocatalysis T. TrdvniOkovd, L Schreiber and M. KubiOek ......................................................... 1207 A Design and Scheduling RTN Continuous-time Formulation P. M. Castro, A. P. B a r b o s a - P 6 v o a a n d A. Q. Novais ............................................
1213
Use of Perfect Indirect Control to Minimize the State Deviations E. S. Hori, S. S k o g e s l a d and W. H. K w o n g .............................................................
1219
Constraints Propagation Techniques in Batch Plants Planning and Scheduling M. T. M. Rodrigues a n d L. Gimeno .........................................................................
1225
Information Logistics for Supply Chain Management within Process Industry Environments M. Vegelti, S. Gonnet, G. H e n n i n g a n d H. Leone ................................................... 1231 Plant Structure Based Equipment Assignment in Control Recipe Generation Considering Conflicts with Other Batches T. Fuchino and H. Watanabe .................................................................................. 1237 IMC Design of Cascade Control M. R. Cesca and J. L. Marchetti ..............................................................................
1243
Robust Model-Based Predictive Controller for Hybrid System via Parametric Programming A. M. Manthanwar, V. Sakizlis, V. Dua and E. N. Pistikopoulos ............................ 1249
viii Model Based Operation of Emulsion Polymerization Reactors with Evaporative Cooling: Application to Vinyl Acetate Homopolymerization S. Arora, R. Gesthuisen and S. Engell ..................................................................... 1255 Event-Based Approach for Supply Chain Fault Analysis R. Sarrate, F. Nejjari, F. D. Mele, J. Quevedo and L. Puigjaner ........................... 1261
Back-off Application for Dynamic Optimisation and Control of Nonlinear Processes S. 1. Biagiola, A. Bandoni and J. L. Figueroa ......................................................... 1267
Operational Planning of Crude Oil Processing Terminals A. M. Blanco, A. B. Morales Diaz, A. Rodriguez Angeles and A. Sdnchez ............. 1273
A Hierarchical Approach to Optimize LNG Fractionation Units H. E. Alfadala, B. M. A h m a d andA. F. Warsame ................................................... 1279
First Principles Model Based Control M. Rodriguez and D. Pdrez ..................................................................................... 1285
On-line Oxygen Uptake Rate as a New Tool for Monitoring and Controlling the SBR Process S. Puig, Ll. Corominas, J. Colomer, M. D. Balaguer and J. Colprim .................... 1291 On-Line Dynamic Monitoring of the SHARON Process for Sustainable Nitrogen Removal from Wastewater K. Villez, C. Rosen, S. Van Hulle, C. Yoo and P. A. Vanrolleghem ........................ 1297 Robust Controller Design for a Chemical Reactor M. Bako~ovd, D. Puna and A. Mdsz~ros .................................................................
1303
A M1NLP/RCPSP Decomposition Approach for the Short-Term Planning of Batch Production N. Trautmann and C. Schwindt ............................................................................... 1309 A Framework for On-line Full Optimising Control of Chemical Processes P. A. Rolandi and J. A. Romagnoli .......................................................................... 1315
Wavelet-Based Nonlinear Multivariate Statistical Process Control A. H. S. Maulud, D. Wang and J. A. Romagnoli ..................................................... 1321
Anaerobic Digestion Process Parameter Identification and Marginal Confidence Intervals by Multivariate Steady State Analysis and Bootstrap G. Ruiz, M. Castellano, W. Gonzdlez, E. Roca and J. M. Lema .............................. 1327 An Efficient Real-Time Dynamic Optimisation Architecture for the Control of NonIsothermal Tubular Reactors M. R. Garcia, E. Balsa-Canto, C. Vilas, J. R. Banga andA. A. Alonso ................. 1333 Model Based Control of Solidification B. Furenes and B. Lie .............................................................................................. 1339
h-Techsight: A Knowledge Management Platform for Technology Intensive Industries A. Kokossis, R. Ba~ares-Alc(mtara, L. Jimdnez Esteller and P. Linke ................... 1345 Modelling for Control of Industrial Fermentation J. K. Rasmussen, H. Madsen and S. B. Jorgensen .................................................. 1351
ix
System-Dynamics Modelling to Improve Complex Inventory Management in a Batch-Wise Plant Z. I,'erwater-Lukszo and 7". S. Christina .................................................................. 1357 Dynamic Modeling and Nonlinear Model Predictive Control of a Fluid Catalytic Cracking Unit R. Roman, Z. K. Nag3,, F. AllgOwer and S. Agachi ................................................. 1363 Improving of Wavelets Filtering Approaches R. I.~. Tona, .4. Espu~a ~lncl L. Pui~/aner . ................................................................
1369
Supply Chain Monitoring: A Statistical Approach F. D. Me/e, E. Musulin and L. P u i ~ / a n e r . ...............................................................
1375
Closing the Intbrmation Loop in Recipe-Based Batch Production E. Mztsulin, M. d. Arbiza, A. Bon/il[ and L. Puigffaner ............................................
1381
Agent-Based Intelligent System Development for Decision Support in Chemical Process Industry ): Oao and A. Kokossis ........................................................................................... 1387 Enhanced Modelling of an [industrial Fermentation Process through Data Fusion Techniques S. Triadaphillou, E. B. Martin, G. Montague, P. Je~jkins, S. Stimpson and A. Nordon ..................................................................................................................... 1393
Implementation of Multi-Kalman Filter to Detect Runaway Situations and Recover Control R. Nomen, d. Sem/gere, E. Serra and d. Cano .......................................................... 1399 Supply Chain Management through a Combined Simulation-Optimisation Approach F. D. Mele, A. Espu~a and L. Pui~janer .................................................................
1405
Data-Based Internal Model Controller Design for a Class of Nonlinear Systems A. G. Kalnlukale and M.-S. Chiu .............................................................................
1411
Measurement-Based Run-to-run Optimization of a Batch Reaction-Distillation System A. Marchetti, B. Srinivasan, D. Bonvin, S. Elgue, L. Prat and M. C a b a s s u d ......... 1417 Nonlinear Behaviour of a Low-Density Polyethylene Tubular Reactor-SeparatorRecycle System M. H~/ele, I. Disli-Uslu, A. Kienle, I': M. Krishna, S. P u s h p a v a n a m and C.-U. Schmidt .................................................................................................................... ! 423 Control and Optimal Operation of Simple Heat Pump Cycles J. B. Jensen and S. Skogestad ..................................................................................
1429
Advanced Process Control of Pantolactone Synthesis using Nonlinear Model Predictive Control (NMPC) ('. Cormos and S. A,~zachi ........................................................................................ 1435 Design and Analysis of a Classical Controller to the Residual Oil in a Small Scale Semibatch Extractor A. F. Cust6dio, D. F. Rezende, M. R. Wolj:Maciel and R. M. Filho ....................... 1441 Optimal Sensor Network Design and Upgrade using Tabu Search M. C. Carnero, ,1. L. Hern(mdez and M. C. Sdmchez ...............................................
1447
Multiperiod Planning of Multiproduct Pipelines D. C. Cafaro andJ. Cerdd ...................................................................................... 1453
Statistical Performance Monitoring Using State Space Modelling and Wavelet Analysis A. Alawi, A. J. Morris and E. B. Martin .......................................... , ....................... 1459 Predictve Functional Control Applied to Multicomponent Batch Distillation Column D. Zumoffen, L. Garyulo, M. Basualdo and L. Jimdnez Esteller ............................ 1465 Fault Tolerant Control with Respect to Actuator Failures. Application to Steam Generator Process A. A ~touche and B. Ould Bouamama ....................................................................... ! 471
Open/Closed Loop Bifurcation Analysis and Dynamic Simulation for Identification and Model Based Control of Polymerization Reactors M. P. Vega and M. R. C. Fortunato ........................................................................ 1477 Effect of Recycle Streams on Energy Performance and Closed Loop Dynamics of Distillation Sequences S. Herndndez, J. G. Segovia-Herndndez, J. C. Cdrdenas and V. Rico-Ramirez ..... 1483 Expert System for the Control of Emergencies of a Process Plant M. L. Espasa and F. B. Gibert .................................................... , ............................ 1489 An Expert System for a Semi-Batch Pilot Scale Emulsion Copolymerisation Facility R. Chew, B. Alhamad, V. G. Gomes and J. A. Romagnoli ...................................... 1495
Integrating Data Uncertainty in Multiresolution Analysis M. S. Reis and P. M. Saraiva ................................................................................... 1501
Integrated Approaches in CAPE Integrated Process and Product Design Optimization: A Cosmetic Emulsion Application F. P. Bernardo and P. M. Saraiva ........................................................................... 1507 Design Synthesis for Simultaneous Waste Source Reduction and Recycling Analysis in Batch Processes I. Halim and R. Srinivasan ...................................................................................... 1513
Design and Control Structure Integration from a Model-Based Methodology for Reaction-Separation with Recycle Systems E. Ramirez and R. Gani ........................................................................................... ! 519
Modelling and Optimisation Collaborative Research Project
of Industrial
Absorption
Processes:
An
EC
P. Seferlis, N. Dalaouti, E. Y. Kenig, B. Huepen, P. Patil, M. Jobson, J. Kleme~, P. Proios, M. C. Georgiadis, E. N. Pistikopoulos, S. Singare, C. S. Bildea, J. Grievink, P. J. T. Verheijen, M. Hostrup, P. Harper, G. Vlachopoulos, C. Kerasidis, J. Katsanevakis, D. Constantinidis, P. Stehlik and G. Fernholz ................................. 1525
An Integrated Approach to Modelling of Chemical Transformations in Chemical Reactors T. Salmi, D. Yu. Murzin, J. Wdrngt, M. Kangas, E. Toukoniitty and V. Nieminen .. 1531
xi
An MILP Model for the Optimal Design of Purification Tags and Synthesis of Downstream Processing E. Simeonidis, J. M. Pinto and L. G. Papageorgiou ............................................... 1537 An Upper Ontology based on ISO 15926 R. Batres, M. West, D. Leal, D. Price and }I. Naka ................................................. 1543
Multi-agent Systems for Ontology-Based Information Retrieval R. Ba~ares-Alc~ntara, L. Jim~nez Esteller and A. Aldea ....................................... 1549
An Agent-Based Approach for Supply Chain Retrofitting under Uncertainty G. GuillOn, F. D. Mele, F. Urbano, A. Espu~a and L. Puigjaner ........................... 1555
Pharmaceutical Informatics: A Novel Development and Manufacture
Paradigm for Pharmaceutical
Product
C. Zhao, G. Joglekar, A. Jain, V. Venkatasubramanian and G. V. Reklaitis .......... 1561
A Web Service Based Framework for Information Integration of the Process Industry Systems Xiangyu Li, Xiuxi Li and E Qian ............................................................................ 1567 A Library for Equation System Processing based on the CAPE-OPEN ESO Interface G. Schopfer, J. Wyes, W. Marquardt and L. von Wedel .......................................... 1573 On the Optimal Synthesis of Micro Polymerase Chain Reactor Systems for DNA Analysis T. Zhelev .................................................................................................................. 1579 An Agent-oriented Approach to Integrated Process Operations in Chemical Plants M. Nikraz and P. A. Bahri ....................................................................................... 1585
Entire Supply Chain Optimization in Terms of Hybrid in Approach T. Wada, E Shimizu and J. Yoo ............................................................................... 1591 A Computer Architecture to Support the Operation of Virtual Organisations for the Chemical Development Lifecycle A. Conlin, P. English, H. Hiden, A. J. Morris, Rob Smith and A. Wright ............... 1597 An Approach for Integrating Process and Control Simulation into the Plant Engineering Process M. Hoyer, R. Schumann and G. C. Premier ............................................................ 1603 Process Integration and Optimization of Logistical Fuels Processing for Hydrogen Production F. T. Eljack, R. M. Cummings, A. F. A bdelhady, M. R. Eden and B. J. Tatarchuk 1609 A Systematic Approach for Synthesis of Optimal Polymer Films for Radioactive Decontamination and Waste Reduction T. L. Mole, M. R. Eden, 7". E. Burch, A. R. Tarrer and J. Johnston ........................ 1615 Integration of Planning and Scheduling in Multi-site Plants- Application to Paper Manufacturing S. A. Munawar, M. D. Kapadi, S. C. Patwardhan, K. P. Madhavan, S. Pragathieswaran, P. Lingathurai and R. D. Gudi .................................................. 1621
Review of Optimization Models in the Pollution Prevention and Control E. Kondili .................................................................................................................
1627
Models for Integrated Resource and Operation Scheduling A. Ha~t, M. TrOpanier and P. Baptiste ..................................................................... 1633
xii Automated Process Design Using Web-Service based Parameterised Constructors T. Seuranen, T. Karhela and M. Hurme .................................................................. 1639
Integrated Design of Optimal Processes and Molecules: A Framework for SolventBased Separation and Reactive-Separation Systems A. L Papadopoulos and P. Linke ............................................................................. 1645 A Computer-Aided Methodology for Optimal Solvent Design for Reactions with Experimental Verification M. Foli~, C. S. Adjiman and E. N. Pistikopoulos .................................................... 1651 Development of Information System for Extrusion Forming Process of Catalyst Pastes A. V. Jensa, A. A. Polunin, V. V. Kostutchenko, l. A. Petropavlovskiy and E. M. Koltsova ................................................................................................................... 1657
Integrating Short-Term Budgeting into Multi-site Scheduling G. Guill~n, M. Badell, A. Espu~a and L. Puig/aner ................................................ 1663
An Integrated Modelling Framework for Asset-Wide Lifecycle Modelling S. Sundaram and K. Loudermilk ............................................................................. 1669
AUTHOR INDEX ................................................................................................. 1675
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 ElsevierB.V. All rights reserved.
955
A Framework for the Mixed Integer Dynamic Optimisation of Waste Water Treatment Plants using Scenario-Dependent Optimal Control Jan Busch a, Marcella Santos b, Jan Oldenburg c, Andreas Cruse d and Wolfgang Marquardt a* aLehrstuhl ffir Prozesstechnik, RWTH Aachen, D-52056 Aachen, Germany bSchool of Chemical Engineering, UNICAMP, Campinas- S P - Brazil CBASF Aktiengesellschaft, D-67056 Ludwigshafen dUhde GmbH, Friedrich-Uhde-Str. 15, D-44141 Dortmund
Abstract in many real life processes, operational objectives, constraints and the process itself may change over time. This is due to changing product requirements, market demands and other external or internal influences, which constitute a certain scenario. Modelbased techniques can provide optimal solutions to the corresponding scheduling and process control problems. This paper focuses on those situations, where the objectives and constraints of plant operation depend on the scenario and therefore change over time. A framework is developed, which enables the modelling and scheduling of different operational strategies on the optimisation horizon. A case study involving a waste water treatment plant is used to demonstrate the approach. Existing expert knowledge is used to relate certain operational objectives and constraints to corresponding scenarios. It is shown that easily interpretable optimisation results are obtained. Also, the results are significantly improved as compared to a weighted average approach only approximating sequential strategies.
Keywords: online optimisation, plant scheduling, scenario-dependent optimal control, waste water treatment, mixed integer dynamic optimisation 1. Introduction With recent advances in the fields of process modelling, optimisation algorithms, computing power and practical experience, model-based techniques like online optimisation and plant scheduling have moved from being a purely academic challenge towards industrial relevance. Model-based control and scheduling require process models and models for the operational constraints and objectives. In the following, the operational constraints and objectives are defined as the operational strategy. Two typical operational strategies are to produce a certain product grade at minimum cost or at maximum throughput. Secondly, the scenario is defined to be the whole of those internal and ex-
Author to whom correspondence should be addressed:
[email protected] 956 ternal factors, which determine a suitable operational strategy, e.g. stock hold-ups, predicted market demand etc. This paper focuses on those situations, where the operational strategy depends on the present scenario, which may change over time. If such a change occurs on the time horizon which is considered in the optimisation, two or more periods (stages) with different operational strategies have to be scheduled in a way to yield optimal overall plant performance. Therefore, a framework will be proposed, which allows for the accurate modelling and scheduling of such problems, introducing the notion of scenario-dependent optimal control. a)
.
I I ]
stage
0
stage
stage
b)
stage 3
I [ 1 i st. 2 i
I
I
stage 3
I stage 1 i st. 2 i stage 3 ]
I time
time
Figure l a,b. Moving Horizon Control and Plant Scheduling
2. State of the art The types of processes considered in this work are continuous processes, for which optimal base controller set point trajectories are to be determined using dynamic real time optimisation. Disturbances on a fast time scale are not accounted for on this control level, but long-term, predictable disturbances are considered. The optimisation is iteratively performed on a moving horizon, as depicted in Fig. l a. In the following, two approaches will be introduced, which have been extensively treated in literature and which are valid for certain problem specifications. Based on this, the idea of scenariodependent optimal control will be developed. If the operational objectives and constraints are assumed to be time invariant, the horizon can be interpreted as one stage, on which the continuous optimisation problem is solved (single stage formulation). A plant scheduling problem evolves, when different products or product grades are to be produced sequentially, as e.g. in modem multipurpose plants (Papageorgiou et al., 1996). Here not only the individual production campaigns have to be optimised, but also their number, sequence and lengths. The optimisation horizon is split into stages, which correspond to the campaigns. On each stage, the process model and the operational constraints may be different. However, the operational objective is the same on all stages. Although usually performed offiine, an iterative moving horizon implementation is shown in Fig. lb.
3. Scenario-dependent optimal control 3.1 Motivation
In contrast to these approaches, this paper considers situations where the operational constraints and the objectives change over time. Abel and Marquardt (2000) have treated the case that at every point in time a critical event could take place, e.g. the burst of a rupture disc, after which it must still be possible to meet certain safety constraints
957 using a suitable operational strategy. Since the moment of failure is expected at every point in time, this leads to a high problem complexity. Here the case is considered that the sequence of operational strategies depends on predictable scenarios. The motivation to do so originates from research on the optimisation-based control of the waste water treatment plant discussed in the case study. When trying to formulate a suitable model-based operational strategy, it was found that plant operators employ two different strategies. At certain times the objective is to maximise the throughput in order to increase flexibility, at other times it is to minimise the energy consumption. The choice of a strategy mainly depends on the predicted inflow and therefore changes over time. There are several possibilities to approximate the use of scenario-dependent operational strategies, e.g. by considering a weighted average of the individual objectives. This weighted average can be expressed in a single objective function, which is valid at all times and which can be optimised using a single stage formulation. The main difficulty is assigning suitable values to the weights, which means e.g. to assign a monetary value to flexibility that is valid in all possible scenarios. However, to the authors' knowledge, no exact modelling and scheduling methodology for scenario-dependent operational strategies has been reported so far. This paper proposes such a rigorous approach, which can be interpreted as a variation of regular plant scheduling on a moving horizon. The campaigns are substituted by time periods, during which a certain operational strategy is employed. The main difference is that not only the constraints, but also the operational objectives may change from stage to stage, while the process model is always the same. The expected benefits of the are: 1. Expert knowledge concerning the strategies and the heuristics, when to employ which strategy, can be exactly represented. This might enhance the overall optimisation results as compared to approaches only approximating sequential strategies. 2. Since the optimisation results correspond to well known strategies, which are separated in time, they are more easily interpretable by plant operators. This is a key factor in enhancing the acceptance of model-based techniques in industrial settings.
3.2 Formulation of the optimisation problem K
rain Y', w/'''~ )
- N , N B -(a~e~_y~ + a, a2c~x z) Mz PL
1 gl
'fi
j:, =--~. --F,kz,, (y ~.,~- y , ) - N, + y~(N , + N,)+ y.,(a,c~y, +a, os2e=xt) ML ] Pl. I = 1 F kzL (yz.R-yz)-(crv~ vz + rztrz_~2xz)M,. +yz(N~ + NB)+),z(al~:v~ +oflc~2~2xz) ML M~ = N ~+ N B + ( u ~ )'~ + a~m_e'~_., 2+no, or no > 2+nh. For instance, if all the qo, = 0 (or qh, = 0), the index function J is constant despite of how many qhj (or qc, ) are in the network, how is the connecting
981 structure, or how is the total service duty distributed among the q~,, (or q~, ). However, performing the same heat duty in different exchanger units (with different UA) implies different utility flow rates. Thus, once the maximum heat integration is attained, different combinations of q/, (or q~: ) are still possible, which implies different use of utility streams and consequently different utility costs. This extra degree of freedom, which goes beyond heat integration, appears also when a HEN having any number of cooling and heating services goes to temporary operating points where the number of active service units complies with any of the above relationships.
3. The Optimal HEN Operation Problem Let us assume that the HEN structure and the heat exchanger areas are completely defined for a given case problem, where there are enough degrees of freedom as to perform steady-state optimisation. Assume also that all process stream targets are known, and that the convenient control structure for temperature regulation has been already defined. When the desired condition actually focus on minimum operating cost, the optimal solution can be obtained by solving the following minimization problem:
subject to - ~--'~qk - q~.(w ) - Q,
i E H,
(7)
j~C,
(8)
k E 1,he+s},
(9)
k~K i
qx +q,, (% ) - Q~ k~K~
-q, < 0
k e {1,ne + s} ,
q~. (w ) = e (w ) L (w. ) qh, ( % , ) = e,, ( % , ) L~,,
i~H, j ~ C,
(~o) (11) (12)
where ne stands for the total number of process-to-process heat-exchangers, s is the total number of serviced units, w~.i stands for the cold utility flow rate of the service unit on the hot stream i, and wl~/is the hot utility flow-rate of the service unit on the cold stream j. The supra index " in (9) indicates fully open control valve or fully closed bypass; the functions e and L are defined in the Appendix. Note that the utility costs per unit mass (c~i and chi) are included in the performance index, and that (11) and (12) are non-linear equations determining w~; and whj at the optimal operation condition. if the network structure does not include stream splits or multiple bypasses (bypass to more than one unit), excellent initialisations for the above NLP problem are obtained by first solving the associate LP for maximum heat integration; this LP uses heat flows as exclusive optimising variables and excludes the equality constraints (11) and (12).
982
4. Example Problem Figure 1 shows the sketch of a HEN composed by two process-to-process exchangers and three service units connected by one hot and two cold process streams. Table 1 gives the stream conditions, and Table 2 shows the UA values for two network designs A and B. The factor F, is assumed 1.0 in all the units, and the utility cost cci and chj are also set to 1. The first row in Table 3 shows the results obtained by solving the above optimisation problem when the design A is used. Though the problem of maximizing the utility expenses J makes no sense from the operating point of view, when this maximum is subject to the same energy recovery obtained before, an important reference solution is determined. For instance, the result in the second row of Table 3 is obtained by including the constraint q l + q2 = 115, or equivalently q~l + q~2 + q.~3 = 60, in the problem formulation. Thus, the results in rows 1 and 2 become the extremes of a set of infinite solutions maintaining the same energy recovery, but showing different levels of utility expenses. Any of these solutions in the set could be reached by minimizing the total service heat duty depending on the initialisation or the numerical method used to find the minimum. A similar numerical experience is repeated for design B, where the results show a greater cost function difference than in case A (see rows 3 and 4). Analysing the slack variables when there is an extra degree of freedom, it was noted that each extreme operation condition is associated with an active constraint (9) related to different units located in the path connecting $2 and $3. Notice that with the stream conditions in Table 1, the solutions avoid using the cooler S 1, creating the condition for an extra degree of freedom. However, when the output temperature of stream H1 is set to 50 °C, the cooler is activated and the extra degree of freedom is lost; see rows 5 and 6 where both, the min J and the constrained max J problems give the same solution for each design. Nevertheless, even though the designs A and B have the same total exchange area, they show different operation cost.
%
Figure 1: General structure of the HEN example
Csl
983 Table 1. Nominal process and service stream conditions
wc bTlet temp. ('C) Outlet temp. (°C)
H1
C1
C2
Csl
1.0 190 75
1.5 80 160
0.5 20 130
1.0 1.0 1.0 15 200 200 . . . . . .
Hs:
Hss
Table 2. UA values used in the above network
UA (case A) UA (case B)
ql
q:
5.0 5.0
2.0 2.0
q.,.1 3.0 3.0
q.,.2
q.,.s
3.0 1.0
1.0 3.0
Table 3. Effect of the extra degree offi'eedom on the operation cost.
Case A-minJ A - max J B- minJ B - max J A-min/max J B min/maxJ
q~
102.07 67.44 102.07 85.98 102.07 102.07
q:
q.,.1
12.93 47.56 12.93 29.02 31.50 31.50
0.0 0.0 0.0 0.0 6.43 6.43
q,:
17.93 52.56 17.93 34.02 17.93 17.93
q.,.s
x,t
x,.2
x,s
J
42.07 7.44 42.07 25.98 23.50 23.50
0.0 0.0 0.0 0.0 0.155 0.155
0.345 0.757 0.39 1.0 0.345 0.390
0.32 0.088 0.274 0.213 0.208 0.201
0.665 0.845 0.664 1.213 0.533 0.591
5. C o n c l u s i o n s Any HEN having nh active heaters and nc active coolers, which operates under optimal heat integration, may have an extra degree of freedom when nh > nc +2, or when nc > nh +2. The reference to active service units emphasizes that this additional optimisation space may turn on and off depending on the operating condition. The immediate consequence of this finding is that the problem formulation for HEN online optimisation has to be adapted to effectively address the minimum utility cost objective. In other words, the extra degree of freedom means that optimising service costs by directly minimising expenses associated to utility flow rates may yield additional benefits as compared to maximising heat-integration. Besides, minimising expenses associated to utility flow rates implies maximising heat-integration. Furthermore, these results also show that HEN designs based on maximum energy recovery combined with minimum total-exchange-area cost should be revised when operation cost is the main goal.
References Aguilera, N. and J. L. Marchetti, 1998, Optimising and Controlling the Operation of HeatExchanger Networks, AIChE Journal, 44 (5), 1090. Glemmestad, B., S. Skogestad, and T. Gundersen, 1999, Optimal Operation of Heat Exchanger Networks, Comput. Chem. Eng., 23,509. Marselle, D.F., M. Morari, and D.F. Rudd, 1982, Design of Resilient Processing Plants: II. Design and Control of Energy Management System, Chem. Eng. Sci., 37 (2), 259. Mathisen, K.W., 1994, Integrated Design and Control of Heat Exchanger Networks, Doctoral Thesis, University of Trondheim, Norway. UztOrk, D. and Akman, U., 1997, Centralized and Descentralized Control of Retrofit HeatExchanger Networks, Comput. Chem. Eng., 21, $373.
984 Acknowledgements
This work has received the support from Universidad Nacional del Litoral and CONICET. Appendix" M o d e l of a H e a t E x c h a n g e r in a N e t w o r k
A convenient way of writing the main equations modeling the stationary condition of a single heat exchanger is obtained from the steady energy balance and the constitutive equation for the heat transferred, namely q
= wici(Ti 0 -Ti)
- wjcj(Tj.
-T O) -
(A1)
UA(FrATn,,)
In this expression, the supra index 0 stands for inlet conditions, A is the heat-exchanger area, U is the overall heat transfer coefficient, and F r is a factor correcting the logarithmic mean temperature difference ATml to account for deviations from pure counter-current pattern. Algebraic rearranges combining the above equalities show the convenience of defining the following parameters: wjcy .__ (T~°-T~) R ___..__:_ WiC i (Tj - V°) '
Xvu
- - UA WjCj
and
B-exp{UruFv(R-l)}
- -( T_ j __ T.O )
(A2)
These three parameters help the computation of the heat-exchanger efficiency defined by 1- B 1 - RB
( T j - T ° ) for R:/:B:/:I, or ( Ti° - T° )
e
Nru for R l + Ur~:
B
1
(A3)
Combining Eqs. A1 to A3 allows writing the heat flow rate as q = q(wi, wj) = e(wi, w s ) L ( w j ) , with
L(Wj)= W/cs(Ti ° - T° )
(A4)
where L(wj) may be interpreted as the virtual amount of exchangeable energy and the efficiency e(wi,wj) defines the amount of heat transferred when a finite exchange area is available between the two fluids. Thus, the equations representing any heat-exchanger k being part of a network at the stream match (ij) are similar to Eqs. (A4), the main difference is that the heat-exchanger inlet temperatures T~° and T° are the results of previous exchanges, namely Ti° ( k ) = riiin
1 Z qli' Win i Ci
TO
(k)-
[i ~ prei(k),
i~H
(A5)
1i
Ti n 1 ~ + w~"cj ~ qtj,
l~ ~ pre~(k),
j ~ C
(A6)
lj
where the superscript in stands for inlet to the network, and prei(k) and prej(k) represent exchanges previous to k. Notice that w/or wj may be different from the nominal inlet stream flow rate because of the control valve position. Thus, the heat duty upper bound is determined by (A4) for fully open control valve or fully closed bypass, namely q< _ q° =e(wi" ,wji.~) L,twji~) - eOLo .
(A7)
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
985
An Online Decision Support Framework for Managing Abnormal Supply Chain Events Mukta Bansal, Arief Adhitya, Rajagopalan Srinivasan*, and I.A. Karimi Laboratory for Intelligent Applications in Chemical Engineering Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore
Abstract Enterprises today have acknowledged the importance of supply chain management to achieve operational efficiency, and cutting costs while maintaining quality. Uncertainties in supply, demand, transportation, market conditions, and many other factors can interrupt supply chain operations, causing significant adverse effects. These uncertainties motivate the development of simulation models and decision support system for managing disruptions in the supply chain. In this paper, we propose a new agent-based online decision support framework for disruption management. The steps for disruption management are: monitoring the KPIs, detecting the root cause for the deviation of KPIs, identifying rectification strategies, finding the optimal rectification strategy and rescheduling operates as necessary in response to the disruption. The above framework has been implemented as a decision support system and tested on a refinery case study.
Keywords: Risk Management, Optimization, Agent-Based, Uncertainty 1. Introduction In the face of highly competitive global markets, companies are pressurized to reduce costs and increase efficiency. As a consequence, they are employing new strategies which result in complex supply chains. These strategies include outsourcing, single sourcing, and centralised distribution. An efficient supply chain requires transparency among its constituent entities. Complex and lengthy supply chains lack visibility and this leads to disruptions. Unhindered and timely material, information and finance flow between different entities of supply chain is another important element. Blockage in any of these would lead to undesirable events like process shutdown, financial loss, under-supply or over-supply, etc. Hence there is a greater need for risk and disruption management. A disruption management system should be capable of detecting abnormal situations before they occur, diagnose the root cause, and propose corrective actions as required. While a complete rectification is desirable, in cases where the effect of disruption is
Author to whom correspondence should be addressed:
[email protected] 986 manifested very late, it may only be feasible to effect a partial recovery. A robust system should be capable of handling both complete and partial rectification. The challenges involved in developing disruption management system are: 1) Supply chain entities are dynamic, disparate and distributed; and 2) they are tightly linked at intra- and inter-enterprise levels and affect the performance of one another. These make the detection of disruption and the root cause difficult. Further, complex rectification strategies are needed to partially or completely overcome the disruption. For example, the implementation of a rectification strategy in some cases will need rescheduling of operations. In this paper, we propose an agent-based framework for disruption management. Intelligent agents measure key performance indicators in each supply chain entities. Disruptions are detected when these KPIs deviates from a pre-specified set points or when unplanned events are detected. Root causes are diagnosed using a causal model. Rectifications are proposed and optimised through a model of supply chain linkage. When necessary, rescheduling is performed to recover from a disruption. In this paper, we present the details of the framework and its implementation and illustrate it using a refinery supply chain. 1.1
Literature Review
There is limited literature in the area of disruption management; no general structured methodology exists to date. Sheffi et al. (2003) describe mechanisms which companies follow to assess terrorism-related risks, protect the supply chain from those risks and attain resilience. They provide classifications of disruptions, security measures and ideas to achieve resilience. They report various case studies and interviews with executives of companies. Wilson (2003) focuses only on transportation disruptions. Julka et al (2002; a, b) proposed an agent-based framework for modelling a supply chain. In their framework, the behaviour of every entity in the supply chain is emulated using an agent that imitates the behaviour of various departments in refinery. Mishra et al. (2003) reported an agent-based decision support system to manage disruptions in a refinery supply chain. In the event of a disruption, agents collaborate to identify a holistic rectification strategy using heuristic rules. In this paper, we generalize their approach and develop a model-based framework for managing supply chain.
2. Framework and Methodology for Disruption Management The proposed framework is described in Figure 1 and is capable of handling situations where 1) occurrence of a disruption is manifested only through deviations from set point and the root cause is not observable, as well as 2) cases when disruptions can be detected at source i.e., the root cause is observable. From control theory, the former needs feedback control while the latter requires a feedforward mechanism. In the general case, the steps for disruption management are carried out by the following components: KPI Monitors: To manage disruptions in supply chain, it is essential to measure key performance indicators (KPIs) and to identify their effect on the supply chain. We use stock inventory, throughput, and other similar indicators to monitor the state of each constituent of the supply chain. These can be measured at regular intervals and
987 monitored by comparing their day-to-day values against pre-specified limits. Alarms are generated when a sustained deviation in any KPI is detected. {
•
I*2PIs
,-
...... :
hffOHnatiOll of Deviation
Alarms
m
e
I) lsluptioll ( ( - ' O1 l"e c t i v e
Action 2,~e<essalT)
i
Possible Causes
I
Y os sible Re ctifi c atiOllS m
Ne~v N:hedule and ('oHecW~e Actkms k-PIs fOl each '~ • •
I ecHfi(
~ (-)primal RectifF. ation
atlOll
i
y
S Cell211 i 0
........S c ~ e d u ! e r
..........................~
"
A
[NNNN ...........
New Sdledule
Figure l. Frameworkjbr disruption management system 2.
Root Cause Identifier: Causal models are used to identify the possible causes for the alarms. Hypotheses are proposed to identify the root cause and confirmed if all expected consequences are manifested online. 3. Rectifications Proposer: The list of corrective actions to rectify the root cause is generated using a causal model, which accounts for the linkages among the supply chain entities. Each rectification strategy is simulated using a supply chain simulator and feasibility and KPIs for each scenario is evaluated. 4. Optimizer: One rectification strategy is selected based on feasibility and KPIs. 5. Scheduler: In a general case, disruption may make the existing operation schedule infeasible or sub-optimal. Optimal rectification strategy may require rescheduling of operations. Our rescheduling scheme is described in more detail in Section 2.1. 6. Coordinator: Numerous activities may be necessary to partially or completely rectify the disruption. The implementation of these rectification strategies can be coordinated by this agent. All the above steps are necessary for disruptions whose root cause is not observable. In cases where the root cause is observable, the occurrence of abnormal event triggers a comparison with KP|s. If corrective actions are found necessary steps 3 to 6 described above are implemented.
988
2.1 Methodology for rescheduling Our rescheduling approach is described in Figure 2. Implementation of the optimal rectification strategy may require changes which affect the original schedule, i.e. some operations may be cancelled or rescheduled and new operations may be necessary. These changes are reconciled with the original schedule by the scheduler agent. New schedules are generated based on heuristics taking into account relevant data from the plant hardware model. The evaluator calculates the profit of each new schedule so that the best one can be implemented.
Scheduler A~ent
n
Optimal Rectification
; ~
Strategy
1
blew schedules
:
i
'--
EvalUator
:]*-- [: :Heuristic: ~ : ] ............. ::::::::::: . . . . . . [: R e s c h e d u l e r : "~-
(.~riginal.~_~_~ ........ Schedul~~ ~ " Sales(Productiont a r g e t s ) / |
[
• Procurement (Crude
j/~/Plant [
procurementdata)
/
[.. • LogistiCs (Ships arrival)
J
"
i ,.,,o
Hardware ''" ..... , Model ""~:,
.........,. - ~ p p e ~ ~
~ p ~ °
i
".. transter rates etc,)
Figure 2. Scheduler agent of the disruption system
The rescheduler uses a heuristic multi-step block preservation strategy. An operation spanning one or more periods is considered a block if it involves no intervening change in configuration. As a corollary, adjacent blocks are separated by a change in configuration. Our approach seeks to minimize changes to blocks. First, feasibility of the disrupted schedule is checked. Second, a heuristic rescheduling strategy is employed to improve optimality of the disrupted schedule for each type of disruption. Five types of disruption have been considered: ship arrival delay, SBM/jetty unavailability, tank unavailability, equipment unavailability, and demand change. To deal with ship arrival delays, relative positions of the blocks of operation as mapped by the original schedule are maintained while adjusting the lengths of the blocks and the volumes involved in the blocks. In response to unavailability of equipment (e.g. pumps, tanks, CDUs, etc.), alternate processing strategies that can retain the blocks of operation from the original schedule are sought. To handle changes in demands, the relative positions of the blocks are kept while adjusting the volume involved in the blocks. The key here is to preserve the characteristic of the original schedule, which is the map of the blocks of operations scheduled. Finally, the objective value of the new schedule is evaluated.
3. Case Study We have implemented the above framework as a decision support system in Gensym's G2 expert system shell. In this section, we illustrate it using a case study derived from the supply chain of a Singapore refinery. Consider the scenario where there is a sudden increase in demand starting from the 41 st day. Operation therefore increases throughput
989 immediately. As a consequence, the KPI monitor finds that the crude oil inventory for the 42 ~d day has gone low and generates an alarm. The root cause identifier finds out the possible causes of the deviation: raw material delay, high demand of products, or the efficiency of process decreases such that more crude oil is required. Comparison of the actual and planned ship arrival indicates that there is no arrival delay. Similarly, a check with the operation department reveals that there is no problem with the efficiency of process. Further check with the sales department indicates that the demand is higher than previously projected by 330 kbbl. The diagnosis agent thus confirms the root cause for the low inventory alarm to be a new order on the 41 ~t day. The rectification proposer agent finds two possible rectifications: 1) postponement of other orders, and 2) emergency crude procurement. The optimizer agent evaluates the two options and flags emergency crude procurement of 330 kbbl to arrive on the 44 th day as the optimal rectification strategy. The flow of events in this case study is shown in Figure 3. The optimal rectification strategy is then passed to the scheduler agent who reschedules the operation as shown in Figure 4 and 5. The new schedule (Figure 5) includes the emergency crude and deals with the increase in demand by rescheduling operations. ...-.
['~1 " M°nit°ring~ I ow Inventory Deteot-~ L 1
~..
l 4" EmergencY ardval Crude
..."-.. ... /
"--.. \ \
", I
.. \
Day I~:--...,. __ I 41 "q.i:ii_-- ......... - - - ~ 4 _ e ,............ 2 Diagnosis .....: . . . . . '[,... High demand ,' .............
, I 44 /~.~Optimal Rectification"?'--.. 43 _----~-------------__
[ \
Emergency Crude
,]
,%. Procurement-Passed
.,M/
"--._._
to Scheduler _ _ _ j ~ -
Figure 3. Eventjlow./br the case study I
I
,i-] P~' H3 (6) I 200;
pan H5 (6) I -
~
IPanL3 (8)
44.221
80160
I
200¢
34.84 671
v
fu,,al ~(0 ~)
.
67
fugalB (0.~)
36.t3° I ° " -i
~
I ;
\
, Csystems ', , _ ~__.~. . . .
r .......
1
,
[ ~"J'Sr__i
//
......... ,
Figure 2. The flowsheet of the sugar milling case study Table 1. Storage Specoqcations (tonnes) Syrup
Magma
AMolasses
BMolasses
Ree3
Rec5
LRee
Wetsugar
Max
410
50
310
200
330
330
230
250
Initial value
1O0
20
140
110
200
200
70
25
'
994 In order to solve the scheduling problem of this case study, the model should first be created using THPN.
3.1 Model of the case Study The THPN model of the sugar mill system is depicted in Figure 3. In this model, it is assumed that there is a possible change of flowrates for the continuous processing units every half hour. While discrete transitions are used to show the batch operations, continuous units are represented by continuous transitions. In addition, discrete places between the batch operations show the availability of the materials in the previous batch processing unit and the continuous places illustrate the storages. The major benefit of the proposed model is the formulation part of the problem, which is much less complicated than traditional methods. Applying THPN for modelling and scheduling of hybrid systems, the formulation of the important constraints such as assignment constraints, material balance constraints and resource constraints will become much simpler as discussed below: • Assignment constraints: consideration of places having one token as an input to a discrete transition enforces the constraint that there should not be more than one task processed in a processing unit at any time. • Material balances constraints: the amount of inputs and outputs of a processing unit are considered as weights located on arcs connecting a transition (place) to a place (transition). • Resource constraints: for the storages with a limited capacity, a place is connected as an input to a transition (operation unit) producing the products to be stored in the associated storage. The arc connecting this place to the transition has a weight equal to the amount of the resulting products. The same amount is released as soon as the materials leave the associated processing unit. It should be noted that all the above constraints have been considered in the firing rules of transitions and there is no need to set any time consuming formulations or variables. The objective function of the system is to find a schedule with the maximum product (profit) or equivalently minimum idle time (A period during which a processing unit is not in use, but is available), within a horizon time of 16 hours. There is also a penalty of 0.1 for changes in the flowrates of continuous units. 3.2 Proposed algorithm In the proposed approach, there are two steps. First, based on some initial values for the flowrates of continuous units, the scheduling algorithm will find the optimal schedule with respect to the objective function. Second, the optimal schedule obtained is passed to the CFSQP optimisation algorithm (Lawrence et al., 1997). CFSQP will find the best flowrates for each continuous unit, which maximises the products (sugar and Cmolasses) within the obtained optimal schedule. It should be noted that before applying the proposed algorithm, the horizon time is divided into half hourly periods. This will allow the change in the flowrate of each continuous unit every half hour. The following shows the steps of the scheduling algorithm" SI" Begin with the initial marking and a large value for the lower_idle_time; set the flowrates of the continuous units to some initial values. $2" With the initial marking, check if the current transition is not enabled due to the lack of materials or space in the storage, then consider the associated idle time.
995 $3" With the initial marking, check if the current transition is enabled; determine the new marking and the usage time of each processing unit including its idle time and put them all with the old markings into one result matrix. $4: If there are more enabled transitions with the current initial marking, go to $2. $5: Check the last two rows of the result matrix and perform merging if the related transitions are not in conflict; in case of conflict check if the shared input place has enough markings (weights) to fire these two transitions simultaneously. If so perform the merging and repeat $5 for the next two rows. $6: Check the time of all the batch processing units and if there is at least one with the time of less than the horizon time go to $2. $7: If the latest total idle time of the batch processing units is less than the lower_idle_time update loweridle_time to this time. $8: If all the rows of the result matrix have been assessed, the search is complete. Output the lower_idle_time and the feasible schedule to this lower_idle_time. $9: Start checking from the last row of the result matrix upward and find the row in which the associated transition is enabled and has not been fired yet" set the marking of this row as the initial marking and go to $2. The scheduling algorithm was implemented in the C programming language and the optimal solution yields the Gantt chart shown in Figure 4. As was mentioned previously, based on the optimal schedule, CFSQP gives the best flowrate per half hour for each continuous processing unit (Table 2).
I
i
I
i
....
[-----~-;;r--]
i
j
--K1
r
~,
. . . . . . . . . .
T - ] F~
,~ ......
f,, ...........
Figure 3. Timed Hybrid Petri net (THPN) model of the sugar milling case study
996 Applying the proposed method to solve the sugar mill case study reduces the computational time from 140 seconds in the previous method (Nott, 1998), which used a sets implementation technique, to 1 second in the current study. This confirms the power of THPN for modelling and scheduling of hybrid systems. Units
12 h
P= H4
u
~
~
I
•
:
AFugal BFugal
o
........ ~
' '
•..............:............I ...................................... [
~
: ::
Pan L 1
i.
................
i
:
!i
~
! ~:
ii
i
' :
i
~
i
~
:
Pan L2 Pan L3
"
i
i
i
i
...................
i i
,
l
i
i~
i
i
i
::
r
r
i..... . . . . !
i '
i
~......... ......
Figure 4. Gantt chart of sugar milling case study Table 2. Optimal flowrates (tonnes/half hour)
Time 0-2 hours 2-14 hours 14-16 hours
fl (super) 2.04375 2.06875 2.04375
f2 (dryer) 7.0125 7.0375 7.0125
f3 (Csystem) 2.16875 2.19375 2.16875
4. Conclusions The THPN has been introduced as a suitable tool for systems with both discrete and continuous behaviour in which many of the constraints can be shown graphically. The great potential of this model for handling complicated operations in the mixed batch/continuous processes has been illustrated through a sugar milling case study, which is an example of a hybrid system. An algorithm, which is a mixture of scheduling and optimisation, is proposed to solve the scheduling problem of the case study. A substantial reduction in the computation time is achieved thereof. Division of the horizon time into a smaller period is currently being researched.
References David, R and H. Alla, 2001, On Hybrid Petri net, Discrete Event Dynamic Systems: Theory and Application, vol. 11, pp.9-40. Djavdan, P., 1993, Design an on-line scheduling strategy for a combined batch/continuous plant using simulation, Computers and Chemical Engineering, vol. 17, pp.561-567. Ghaeli, M., P.A. Bahri, P. Lee and T. Gu, 2004, Petri-Net Based Formulation and Algorithm for Short Term Scheduling of Batch Plants, Computers and Chemical Engineering, Accepted. Lawrence, C., J.L. Zhou and A.L. Tits, 1997, User's Guide for CFSQP Version 2.5: A C Code for Sloving (Large Scale) Constrained Nonlinear Satisfying All Inequality Constraints. Neville, J.M., R.Ventker and T.E. Baker, 1982, An interactive process scheduling system, the American Institute of Chemical Engineers. Nott, H.P., 1998, Modelling alternatives for scheduling mixed batch/continuous process plants with variable cycle time, Doctor of Philosophy Thesis, Murdoch University. Sicignano, A., J.D. McKeand, S.F. LeMasters, 1984, IBM Pc Schedules batch processes, cuts inventories at Houston refinery, Oil and Gas Journal, pp.63-67.
European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.
997
Improving short-term planning by incorporating scheduling consequences Petra Heijnen*, Ivo Bouwmans, Zofia Verwater-Lukszo Faculty of Technology, Policy and Management Delft University of Technology Delft, The Netherlands
Abstract Decisions in short-term planning and scheduling in multi-product multi-purpose plants are often taken in isolation from each other and may be based on conflicting objectives. This may result in decisions that are sub-optimal for the plant as a whole. A more integral perspective on the decision-making could lead to a better overall performance. This paper describes a mathematical reformulation of the short-term planning and scheduling decisions in a bi-level top-down program. It is based on a recursive formula and a smart definition of the cutting rules, which greatly reduces the complexity of the optimization. A practical case shows that the reliability of the planning results increases significantly.
Keywords: Bi-level programming, short-term planning, scheduling, optimisation, decision support
1. Introduction In a multi-product multi-purpose plant, decisions are usually taken at different locations and on different hierarchical levels, too often in isolation from each other (Shobrys et al. 2002). Together, however, these decisions influence the overall performance of the plant to a high extent. Ryu, Dua and Pistikopoulos (2003) address plant-wide planning and network decisions. This paper aims at the planning and scheduling level. Planners as well as schedulers can only decide about their own decision factors and have no control over the others, but the decisions can mutually interfere, causing far from optimal results. This happens in particular when the respective decisions are based on conflicting objectives. Therefore, a more integral perspective on short-term planning and scheduling decisionmaking in the plant is desirable to guarantee a better overall performance. Multi-level programming is a specific way of mathematically formulating such multi-level decision problems in a complex system, by incorporating the consequences of one decision on the other, aiming at a better performance of the system as a whole (e.g. Bialas et al. 1982).
Author to whom correspondence should be addressed:
[email protected] 998 In this paper, the short-term planning and scheduling decisions in a multi-product plant, aiming at different, conflicting objectives, are mathematically reformulated in a bi-level top-down program. The method is based on a recursive formula by which the scheduling objective function can be calculated. The use of this recursive formula and a smart definition of the cutting rules significantly reduce the complexity of the search for an optimal planning.
2. Short-term planning and scheduling in a multi-product plant In the short-term planning, customer orders are accepted or rejected based on a chosen criterion, which in our example is profitability. At the start of each week, the planners receive the set of customer orders from the sales department. Every customer order indicates the amount of product, the date the order should be delivered and the type of product. Since capacity is limited, only the most profitable set of orders from the order list is selected and passed on to the schedulers. In the scheduling, the orders accepted in the planning stage are sequenced minimizing the total tardiness, i.e. the total time of delivery after due date. To reduce complexity, the assumption is made here that all orders are to be produced in one reactor. The scheduling performance highly depends on the planning decision, since the schedulers have to schedule all the orders selected by the planners, whereas another selection of orders might have led to a better schedule with less tardiness. Moreover, if in the final schedule two consecutive orders are of different types of product, extra changeover costs are made, reducing the profit. The planners, however, only estimate the profit by correcting every order with a fixed sum of changeover costs, disregarding the real consequences of the scheduling process. The schedulers, in turn, have no influence on the order selection procedure. The problem situation described here might seem a little artificial, since planners and schedulers, working for the same company, should aim at a better overall performance and not only at their own objectives. Nevertheless, isolated decision making is not uncommon in practice for various reasons, such as habits, the complexity of integrated decision making, or the impossibility of unambiguously defining the influence of lowerlevel activities on strategic objectives.
2.1 Mathematical formulation of the planning and scheduling decisions Each week, the planners solve the following decision problem:
From the total set of customer orders, find the subset of orders that maximize the profit and for which the total available capacity is not exceeded. Let
C=[[cl,,di,Pi ] i E{1,2 ..... m}]
(1)
be the total set of customer orders received from the sales department, where ag is the ordered amount of product (in tons), di the due date (in working hours from the start of the week), and pi the type of product ordered. The planners should then find the binary vector x - [xl, x2, ..., Xm] for which the total profit
999 tn
P(x)-~-~(aif(pi)-c)x,
(2)
i=l
is maximized. Here, J(pi) is the profit that can be achieved with one ton of product of type p;. The decision vector x_is bounded by the constraint
~ a , t ( p i )x,
-.. ".............. LL.L._.LL£1£ . . . . . . . . . . . . . . . . . . . . . .\..~_.. :--~.._. _~. ............. ~.~-~-~NCI--cR~-I:--£-7~::::.,-~.::::::..~_.~.~.........
L 20
1 0
i 40
i 60 Valve opening %
i 80
i 1 O0
120
Figure 3. Bifurcation diagrams from experimental data (dotted line) and Storkaas' model (solid line) When the model is tuned it can be used to perform a controllability analysis on the system. This way we can predict which measurements are suitable for control, thus avoiding slug flow. The analysis shows that the system consists of the poles given in Table 1. Table 1. Poles of the system for valve openings z=O.12 and z=0.25 z
0.12 -20.3411 -0.0197 ± 0.1301i
0.25 -35.2145 0.0071 + 0.1732i
Since all poles of the system are in the LHP when using a valve opening of 12%, this valve opening results in stable flow in the pipeline. However, when the valve opening is set to 25% we get a pair of RHP poles leading to riser slugging. This could also be predicted from the bifurcation diagram in Figure 3. To stabilize the flow we have available several measurements. Four of these are topside measurements; pressure P2, density p, volume flow Fq and mass flow Fw. The fifth measurement is the inlet pressure, P1. The zeros of the system using different measurements are given in Table 2.
Table 2. Zeros of the system using different measurements at valve opening z=0.25
~'~
P2
p
Fq
p~
- 1.285
46.984 0.212
0.092 -0.0547
-3.958 -0.369 ± 0.192i
-65.587 -0.007 ± 0.076i
It is well known that stabilization (shifting of poles from RHP to LHP) is fundamentally difficult if the plant has a RHP-zero close to the RHP-poles. From this, we expect no
1025 particular problems using P1 as the measurement. Also, Fq and Fw could be used for stabilization, but we note that the steady-state gain is close to zero (due to zeros close to the origin), so good control performance can not be expected. On the other hand, it seems difficult to use O or Pg_ for stabilization because of presence of RHP-zeros. From the controllability analysis we therefore can draw the conclusion that when using only one measurement for control, the inlet pressure/:'1 is the only suitable choice.
4. Experimental results The analysis showed that using the inlet pressure P 1 w a s the only possibility when using only one measurement for control. Based on this, a PI-controller was used to control the system using this measurement. The MiniLoop was first run open loop for two minutes, with a valve opening of 30%. This is well inside the unstable area, as the bifurcation diagram shows. The result is the pressure oscillations plotted in Figure 4, which illustrates how the pressure and valve opening varies with time. Both experimental and simulated values using the simplified model are plotted. When the controller is activated after two minutes, the control valve starts working. The flow is almost immediately stabilized, even though the average valve opening is still within the unstable area. It remains that way until the controller is turned of again after 8 min. When the controller is turned off, the pressure starts oscillating again. Pl
z
g
lOO
A ~.18
g~
80
-~ 1.16
~
60
~ E
40
"E 1.12
-c_
~ 20 ,,x,
~_. 1.14
&
1.1
x
LU 1.08
0 0
2
4
6
8
10
0
2
4
6
8
10
100 ,.....,
,-.-, ...{3 ,.._,
1.18
o---1 80
1.16
m
i
.r-
tV....
N 1.12 E
._
}
6o
g
"
40
.E_ CD
2o
1.14
0_
-
1.1 1.08 0
0 2
4 6 Time [min]
8
10
0
2
4 6 Time [min]
8
Figure 4. Experin~ental and simulated results using a Pl-controller
From Figure 4 we see that the controller efficiently stabilizes the flow, confirming the results from the analysis. However, this measurement can be difficult to use in offshore installations because of its location.
1026 Using other control configurations or measurements other than the ones analyzed in this paper might be the solution if there are only topside measurements available. The plan is to test out different ways to do this in the near future. The first possibility that will be explored, is using a cascade configuration involving the topside pressure/92 and one of the flow measurements F~ or Fq. Storkaas and Skogestad (2003) have proved theoretically that this works for another case of riser slugging.
5. C o n c l u s i o n From the controllability analysis it was found that using the bottom hole pressure was the only measurement of the five measurements analyzed, that could be used for controlling the system. The experiments confirmed that the model used for the analysis was good, and that using this measurement we where able to control the flow without problems. We are, however, looking for other ways to control the flow because of the problems related to down hole measurements. When using some of the other measurements analyzed, we must use combinations of measurements in order to avoid the problems related to the zeros introduced.
References Courbot, A. (1996). Prevention of Severe Slugging in the Dunbar 16" Multiphase Pipeline. Offshore Technology Conference, May 6-9, Houston, Texas. Havre, K., Stornes, K. and Stray, H. (2000). Taming Slug Flow in Pipelines. ABB review, 4:pp. 55-63. Hedne, E and Linga, H. (1990). Supression of Terrein Slugging with Automatic and Manual Riser Choking. Advances in Gas-Liquid Flows, pp. 453-469. Sarica, C. and Tengesdal, J. (2000). A new teqnique to eliminating severe slugging in pipeline/riser systems. SPE Annual Technical Conference and Exibition, Dallas, Texas. SPE 63185. Storkaas, E. and Skogestad, S. (2003). Cascade control of Unstable Systems with Application to Stabilization of Slug Flow. Storkaas, E., Skogestad, S. and Godhavn, J. (2003). A low-dimentional model of severe slugging for controller design and analysis. In Proc. of MultiPhase '03, San Remo, Ita(v, 11-13 June
2003.
European Symposiumon Computer Aided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1027
Using CLP and MILP for Scheduling Commodities in a Pipeline Leandro Magatfio*, L.V.R. Arruda, Flfivio Neves-Jr. The Federal Center of Technological Education of Paranfi (CEFET-PR) Graduate School in Electrical Engineering and Industrial Computer Science (CPGEI) Av. Sete de Setembro, 3165, 80230-901, Curitiba, PR, Brazil Tel: +55 41 310-4707 - Fax: +55 41 310-4683
[email protected] arruda@cpgei, cefetpr.br
[email protected] Abstract This paper addresses the problem of developing an optimization structure to aid the operational decision-making in a real-world pipeline scenario. The pipeline connects an inland refinery to a harbor, conveying different types of commodities (gasoline, diesel, kerosene, alcohol, liquefied petroleum gas, etc). The scheduling of activities has to be specified in advance by a specialist, who must provide low cost operational procedures. The specialist has to take into account issues concerning product availability, tankage constraints, pumping sequencing, flow rate determination, and a series of operational requirements. Thus, the decision-making process is hard and error-prone, and the developed optimization structure can aid the specialist to determine the pipeline scheduling with improved efficiency. Such optimization structure has its core in a novel mathematical approach, which uses Constraint Logic Programming (CLP) and Mixed Integer Linear Programming (MILP) in an integrated CLP-MILP model. Moreover, a set of high-level modeling structures was created to straightforward formulate the CLPMILP model. The scheme used for integrating techniques is double modeling (Hooker, 2000), and the CLP-MILP model is implemented and solved by using a commercial tool. Illustrative instances have demonstrated that the optimization structure is able to define new operational points to the pipeline system, providing significant cost saving.
Keywords: Optimization, Scheduling, Constraint Logic Programming (CLP), Mixed Integer Linear Progralmning (MILP), and Pipeline. 1. Introduction The oil industry has a strong influence upon the economic market. Research in this area may provide profitable solutions and also avoid environmental damages. The oil distribution problem is within this context, and pipelines provide an efficient way to convey products (Kennedy, 1993). However, the operational decision-making in pipeline systems is still based on experience, and no general framework has been established for determining the short-term scheduling of operational activities in pipeline systems. The approach to address (short-term) scheduling problems is manifold, but the struggle to Author to whom correspondence should be addressed:
[email protected] 1028 model and solve such problems within a reasonable computational amount has challenged the development of new optimization approaches. In the front line of such approaches, Operational Research (OR) and Constraint Programming (CP) optimization techniques are merging. More specifically, Mixed Integer Linear Programming (MILP) and Constraint Logic Programming (CLP) are at the confluence of OR and CP fields. The integration of CLP/MILP has been recognized as an emerging discipline for achieving the best that both fields can contribute to solve scheduling problems (Hooker, 2000). Following this tendency, this paper develops an optimization structure based on CLP and MILP techniques (with their well-known complementary strengths). This structure is used to aid the scheduling of activities in a real-world pipeline scenario.
2. Problem Description The considered problem involves the short-term scheduling of activities in a specific pipeline, which connects a harbor to an inland refinery. The pipeline is 93.5 km in length, and it connects a refinery tank farm to a harbor tank farm, conveying different types of commodities (gasoline, diesel, kerosene, alcohol, liquefied petroleum gas, etc). Products can be pumped either from refinery to harbor or from harbor to refinery. The pipe operates uninterruptedly, and there is no physical separation between successive products as they are pumped. Consequently, there is a contamination area between miscible products: the interface. Some interfaces are operationally not recommended, and a plug (small volume of product) can be used to avoid specific interfaces, but plug inclusions increase the operational cost. The scheduling process must take into account issues concerning product availability, tankage constraints, pumping sequencing, flow rate determination, usage of plugs, and operational requirements. The task is to specify the pipeline operation during a limited scheduling horizon (H), providing low cost operational procedures, and, at the same time, satisfying a set of operational requirements. An in-depth problem description can be found in Magat~o (2003). 3.
Methodology
An optimization structure to address this pipeline-scheduling problem was proposed by Magat~o et al. (2004). This structure, which is illustrated in Figure 1, is based on an MILP main model (Main Model), one auxiliary MILP model (Tank Bound), a time computation procedure (Auxiliary Routine), and a database (Data Base), which gathers the input data and the information provided by the other optimization blocks. The Tank Bound task involves the appropriate selection of some resources (tanks) for a given activity (the pumping of demanded products). Its main inputs are demand requirements, product availability, and tankage constraints. As an output, it specifies the tanks to be used in operational procedures. The Auxiliary Routine takes into account the available scheduling horizon, the product flow rate, and demand requirements. It specifies temporal constraints, which must be respected by the Main Model. The Main Model, which is based on MILP with uniform time discretization, determines the product pumping sequence and it establishes the initial and the final time of each pumping activity. The final scheduling is attained by first solving the Tank Bound and the Auxiliary Routine, and, at last, the Main Model. The Main Model must respect the
1029 parameters previously determined by the Auxiliary Routine. In this paper, we also use this optimization structure, but with one fundamental difference: the Main Model is b a s e d o n a c o m b i n e d CLP-MILP approach. In the former approach, the Main Model was just based on an MILP formulation, and, depending on the problem instance, it can demand a computational effort from minutes to even hours. The Tank Bound and the Auxiliary Routine, which demand few seconds of running, are essentially the same models of Magatfio et al. (2004). For simplicity, these models are not herein discussed, and they are considered to provide input parameters to the new CLP-MILP Main Model. In order to straightforward formulate the CLP-MILP model, a set of high-level modeling structures was created (details are given in Magatfio, 2003). Thus, the model builder just needs to establish a "high-level" CLP-MILP modeling statement, and, afterwards, CLP and MILP equivalent expressions could be automatically derived. In a modeling standpoint, the MILP vocabulary, which is just based on inequalities, is poorer than the CLP vocabulary (Williams and Wilson, 1998), and the high-level structures provided and insight to overcome the modeling difference between MILP and CLP techniques. Figure 2 illustrates a high-level "if and only if' proposition that is expressed according to CLP and MILP approaches +. In this proposition, a binary variable c~. has to be set to one if and only if E/a~/xy < bk, where J is the set of variables (/E J), K is the set of constraints (kEK), akj's are constraints coefficients on continuous variables Xj'S, b~'s are requirements. Moreover, Lk's and U~'s are, respectively, lower and upper bounds, such that Lk Corn + Ioo'm - Z
m~Mo
Z
Som + loo'm --
m~Mo s°' m
Z
m~Mo
m ~ meMo'
ee- - aom +ao'm - 1 .
Operations on the same machine must not overlap: V m • M , Vo, o' • 0 m :
1037 %m - So'm < H(I - Poo'm) + H(2 - aom eo, m -Som < H . Poo'm + H(2 - aom
-
- ao,tn).eom
-So,
m >_
a o , m ) . e o , m - S o r e >_
- H "Poo'm
-
H(2 - aom
-H(I - Poo'm) - H(2 - aom
-
ao,m)
- ao, m )
3.2.4 The o b j e c t i v e f i m c t i o n
The objective function penalizes the accumulated tardiness of the final operations of all jobs. These are the mixing vessel operations MV/ which finish later than the filling operations because of the cleaning of the vessels" min ~ - Z max { d u e / - eMv/m, 0}
o
.jcJ
4. S o l u t i o n P r o c e d u r e
The commercial package GAMS/Cplex was used. Parameter studies of various Cplex parameters yielded that dpriind = 1 clearly increased the solution performance. This setting was used for the procedure described below, the other parameters were set to their default values. The heuristics used here are similar to those in (Cerda et. al., 1997). • H1 - Non-overtaking of non-overlapping jobs: if d u e / < relj, then Vm e M, Vo e O/m,O' c 0i'm : eom < So'm H2 - Non-overtaking of jobs with equal recipes: if reci = recj,/~ d u e / < due/, then Vme M, Vo e O/m,O' e O7,m : eom r, (23) B~,, = Bs,..... Vi, Vn > r; (24) ~,'_ N)~Lvi
n ' n - Ni ~aN
Finally, the balance constraints of Sundaramoorthy and Karimi (2005) can be used for the calculation of the remaining processing time on an equipment unit, instead of big-M constraints ( 13)-(16).
1043
5. E x a m p l e and C o m p u t a t i o n a l Results Model (M3) is used for the scheduling of the STN in Figure 1 (modified from Kondili et al., 1993; data given in Table 5). The scheduling horizon is 10 hours and there are three orders for 20 kg of P 1 each (with intermediate due dates at t = 4, 6 and 8 hr). The objective is to meet the orders on time and maximize the revenues from additional sales. ) P1 ($10/kg) 40% ,I
-D
4O%
IntAB
o% IntBC
Is°°/° L__. R3 I
1 B
,0°,o
I
'
©
S +90%
i e°°'°
($10/kg)
C Figure 1. State-Task Network.
Table 5. Processing data (BAn"V/B~4vin kg, a in hr, fl in hr/kg).
Unit HT RI RII DC
Task ~ B 'vnx B~4.v 50 100 25 50 40 80 100 200
H
a 1 .
fi 0 .
a . 2 2 .
R1 fi . 0 0 .
R2
a . .5 .5 .
R3
fl .
.
.04 .025 . .
a . .25 .25 .
fl .02 .0125 .5
.01
To model intermediate due dates using a continuous-time model we have to introduce additional binary variables. In model (M3), however, we only introduce a (demand) parameter in eq. (8). The example is solved using both the continuous-time model (M1) with N=8, 9 and 10, and model (M3) with At=0.5, 0.33 and 0.25 hr (solution statistics given in Table 6). Model (M1) cannot be solved to optimality within 600 CPU sec, and the best solution has an objective value of $1,797.3 (found with N=8). However, a solution with an objective value of $1,805.4 is obtained using model (M3) with At= 0.25hr (N = 40) in 542.9 CPU sec. Model (M2), in other words, yields a better solution in less time than an "accurate" continuous-time model. Moreover, good solutions are also obtained with At = 0.5 ($1,720) and At = 0.33 ($1,763.3) in less than two minutes. The Gantt chart of the optimal solution of (M3) with At = 0.25 hr is shown in Figure 2. Table 6. Computational results of models (M1) and (M3) (At in hours).
(M1)
(M3)
N=8 N=9 N=IO At=0.5 At=0.33 At=0.25 LP-rel. 2,498.9 2,539.0 2,561.4 2,081.4 2,054.7 2,095.9 Objective 1,797.3 ~ 1,783.61 1,788.4 ~ 1,720.0 1,763.3 1,805.3 CPU-sec 2 600 600 600 43.1 76.3 542.9 Nodes 114,651 71,106 65,620 2,368 1,534 5,106 Optimality gap (%) 2.03 8.71 12.3 0.5 0.5 0.5 1 Best solution found after 600 CPU sec. 2 Using GAMS 21.3/CPLEX 9.0 on a Pentium M at 1.7 GHz; solved to 0.5% optimality gap.
1044 H RI RII
I
[
0
R1-44.8 [ I I I R1-80
I
I
I
I
R2-43.8 i I I R2-60
11111II 2
[
I
4
i
R1-50 R2-80
I
[[LltL
I
6
R3-37.5 1R3-25 [ I / I R3-75.3 ]
1tl
I
R2-37.5 I I 1 R2-70
t
8
I
I
10 t (hr)
Figure 2. Gantt chart of optimal solution of (M3) with At=0.25 hr.
The scheduling of batch process remains a very hard problem and better methods are needed, especially for the solution of problems over long scheduling horizons. Nevertheless, model (M3) can be used for the solution of batch scheduling problems with intermediate release and due times, for which continuous-time models cannot be solved to optimality within reasonable time. Furthermore, it can be used for the solution of problems where holding and backlog costs are important. Finally, the proposed representation can be extended to account for continuous processes, with very good computational results. More details can be found in Maravelias (2005).
6. Conclusions In this paper we formally show that discrete-time STN models are a special case of continuous-time models. A new mixed time representation (fixed grid, variable processing times) is proposed. Computational enhancements for the solution of the proposed representation are also presented.
References Castro, P.; Barbosa-Povoa, A. P. F. D.; Matos, H. An Improved RTN Continuous-Time Formulation for the Short-term Scheduling of Multipurpose Batch Plants. Ind. Eng. Chem. Res. 2001, 40, 2059-2068. Ierapetritou, M. G.; Floudas, C. A. Effective Continuous-Time Formulation for Short-Term Scheduling. 1. Multipurpose Batch Processes. Ind. Eng. Chem. Res. 1998, 37, 4341-4359. Kondili, E.; Pantelides, C. C.; Sargent, R. A General Algorithm for Short-Term Scheduling of Batch Operations - I. MILP Formulation. Comput. Chem. Eng. 1993, 17, 211-227. Maravelias, C. T.; Grossmann, I. E. A New General Continuous-Time State Task Network Formulation for the Short-Term Scheduling of Multipurpose Batch Plants. Ind. Eng. Chem. Res., 2003, 42(13), 3056-3074. Maravelias, C. T. A Mixed Time Representation for State Task Network Models. Submitted for Publication (2005). Mockus, L.; Reklaitis, G.V. Continuous Time Representation Approach to Batch and Continuous Process Scheduling. 1. MINLP Formulation. Ind. Eng. Chem. Res. 1999, 38, 197-203. Pantelides, C. C. Unified Frameworks for the Optimal Process Planning and Scheduling. Proceedings on the Second Conference on Foundations of Computer Aided Operations. 1994, 253-274. Shah, N.; E.; Pantelides, C. C.; Sargent, R. A General Algorithm for Short-Term Scheduling of Batch Operations- II. Computational Issues. Comput. Chem. Eng. 1993, 17, 229-244. Schilling, G.; Pantelides, C. C. A Simple Continuous-Time Process Scheduling Formulation and a Novel Solution Algorithm. Comput. Chem. Eng. 1996, 20, S1221-1226. Sundaramoorthy, A.; Karimi, I.A. A Simpler Better Slot-based Continuous-time Formulation for Short-term Scheduling in Multipurpose Batch Plants. Chem. Eng. Sci., In Press, 2005.
Acknowledgements The author would like to thank Professor Ignacio Grossmann for stimulating discussions on the time representation of STN models.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.
1045
Optimization of Biopharmaceutical Manufacturing with Scheduling Tools - Experiences from the Real World Charles A. Siletti a*, Demetri Petrides a and Alexandros Koulourisb aIntelligen, Inc. New Jersey, USA bIntelligen Europe Thermi-Thessaloniki, Greece
Abstract This paper presents industrial experience with a resource-constrained batch process scheduling program. The batch process representation is loosely based on the ISA $88 batch process standard. This representation allows the import of batch process information from other software, e.g. batch process simulators. The scheduling algorithm is a non-optimization approach that proceeds in two steps. First a bottleneck analysis is done to determine a lower bound on the process cycle time, and all the batches are scheduled accordingly. Second, if conflicts remain, they are resolved by applying progressively aggressive modifications to the schedule. This approach to scheduling was tested on several biotech processes. These processes consist of a sequence of batch steps performed with dedicated equipment. The scheduling challenges in biotech processes lie in the ancillary operations: media and buffer preparation, vessel and line cleaning, and chromatography column preparation. Such operations may use shared resources and may serve to couple process suites with otherwise dedicated equipment. These considerations are further complicated by variability in process durations. Three case studies, which are based on a process for the manufacture of monoclonal antibodies (MABs), illustrate the value of a constrained-resource scheduling tool for biotech processes. In the first case study, the scheduling tool shows that auxiliary cleaning equipment can limit batch production. A second case study shows how scheduling tools can calculate the size of a purified water system. A third case study illustrates how to use scheduling tools to mitigate the effects of process variability.
Keywords: scheduling,
process modelling, biotech, pharmaceutical manufacture
1. Introduction Biotechnology manufacturing capacity is currently in very high demand. In recent years the estimated capacity utilization has been 90% for both microbial and mammalian cell culture production (S. Fox et al., 2001). Some biotech firms have estimated potential revenue losses of well over $100 million due to lack of Author to whom correspondence should be addressed:
[email protected] 1046 manufacturing capacity (R. Rouhi, 2002). Thus there is substantial motivation to improve process efficiency in biotechnology manufacturing.
1.1 Bioprocessing Overview A typical biopharmaceutical process consists of two parts: an upstream process in which a living organism produces the product in a raw form and a downstream process in which the product is purified. Most biotech upstream processes employ either microbial fermentation or mammalian cell culture. From a scheduling viewpoint, biotechnology processes generally have the following features: • They are batch processes • Primary processing equipment is dedicated to a particular processing step • Wait-time between process steps is either zero or limited • From 20 to 30 buffers may be made for each batch and each has a limited life • There is some variability in processing times especially in the upstream processes • Equipment cleaning is common after most process steps and often requires auxiliary clean-in-place (CIP) skids, which are not dedicated Biopharmaceutical manufacture is regulated, and manufacturers need to prove, through studies or clinical trials, that a process change will not adversely affect the product. Manufacturers therefore tend to avoid any direct changes in the process itself.
1.2 Scheduling Challenges For most bioprocesses, scheduling the main process does not pose a significant challenge. Because the steps usually proceed with no wait, the timing is fixed when the batch start is fixed. Scheduling challenges arise in the support operations such as cleaning and buffer preparation. Such support operations may impose unexpected limits on the process. Common utilities, such as purified water, may impose scheduling limits because they impose limits on both peak and average resource consumption. Finally, planning for process variability and failures presents a significant challenge.
2. A Scheduling Tool for Bioprocessing Most bioprocess manufacturers employ spreadsheets for process scheduling because spreadsheets are inexpensive, readily available, easy to learn and highly flexible. For more complicated situations, however, spreadsheets have very clear drawbacks including poor visualization tools and poor maintainability. Furthermore, spreadsheet solutions are usually "owned" by an individual and may be difficult to transfer to another individual or to another site. The scheduling tool and approach described in this section maintains many of the advantages of the spreadsheet approach while minimizing the disadvantages. Pekny and Reklaitis (1998) describe a generic scheduling tool consisting of graphical user interface, a representation layer, and problem formulation and solution layers.
2.1 The Interface The interface should provide both an easy means of entering and maintaining scheduling information and appropriate displays of the scheduling outputs. The equipment occupancy chart is the most popular way to display scheduling information
1047 for bioprocesses. Equipment occupancy charts, as shown in Figure 5, display Ganttstyle time-bars for equipment.
2.2 The Representation Layer The representation consists of a model for the process and its associated resources and constraints. The instructions for making a single batch of a product constitute a recipe. The recipe structure, which is loosely based on the ISA SP88 standard, consists of unit procedures and operations. A unit procedure is a primary process step and is assigned a single unit of primary equipment. Operations are individual tasks within a unit procedure. All resources other than primary equipment, i.e. auxiliary equipment, labor, materials and utilities, are associated with operations. Operation durations may be fixed or rate and/or equipment dependent. Rate dependent durations are linearly dependent on the batch size. Scheduling precedence relationships exist among operations. Specifically, an operation may have any of the following timing dependencies: (1) the operation starts at the beginning of the batch, (2) the operation starts simultaneously with a reference operation, (3) the operation starts at the end of a reference operation or (4) operation finishes at the start of a reference operation. In addition to the relationships above, an operation may have a fixed or flexible shift time. A fixed shift indicates the time after (or before) which the dependency condition is fulfilled that the operation actually starts. A flexible shift indicates the maximum time that an operation may be delayed.
2.3 The Formulation and Solution Layers There is an abundance of proposed problem formulations and solution algorithms for scheduling problems. The goal of the scheduling methodology described below is to allow a user to generate and evaluate a schedule interactively. The user enters a plan with one or more campaigns each of which consists of a number of batches of a particular recipe and either the due date or start date. The system lays out a preliminary schedule using the cycle-time analysis and conflict resolution methodology. The user may edit the resulting schedule. The system schedules a campaign by scheduling batch starts according to the estimated cycle time. The cycle time for a recipe is the average time between consecutive batch starts. The minimum cycle time, Tcycle, is estimated by the following relation from Biegler et al. (1997). Tcycle = Max(Ti/Ni) j o t i = (1, M)
(1)
77 is the duration of unit procedure i, Ni is the number of alternative primary equipment units, and M is the number of unit procedures. This estimate does not account for shared primary equipment, auxiliary equipment, or down-time, so a conflict resolution scheme is employed to ensure that the resulting schedule is feasible. Conflicts are resolved by (1) selecting other equipment, (2) adding a flexible delay, or (3) delaying the start of a batch.
3. B i o p r o c e s s i n g Case Studies The case studies draw on a process for producing a monoclonal antibody product. The process, shown in Figure 1, consists of multiple upstream suites and a single
1048 downstream suite, which is detailed in Figure 2. The upstream process is limited by the production bioreactor, which has a processing time of 12 days. Multiple upstream suites allow for a batch every 48 hours, while the downstream suite has a minimum cycle time of 33 hours. The limiting equipment in the downstream process is the buffer hold vessel, DCS- 103. Upstream(multiplesuites) Tcycle= 48 h
Downstream(singlesuite) T c y c l e = 33 h
I I..... lum H Bio- ~ Prep. reactor
PrimaryR ...... y H naietPor H I..... hange H Hydrophobic k l Final I Viralinactivation Chromatography Chromatography Chromatography Filtration Figure 1. Monoclonal Antibody Process
Monoclonal
Antibody
t '
Purification
~
Pr~ary R...... y~
#
i Protein-A
[ Buf ~V-107Tperj ePrp% ~ B7CS; ...... ~0°5 ! ILI: BITpS!I; __/ ti],]i- - ] II',]-
IEX Cfi,-;:>~,i
...... ~@
~BD~S-' 10°8! *~1~'C1-'`,_101~ .......... ............ ............ [~ II ~CS' ......... ~'lti~/~' "ii-:,O~ [' , ~ITf !p~e~I ~! ¢~} .... 'l'
.....................................................
.....
-I I Ir ~' r I
"
' I I I
r
....... ..........
I I
*
~; ~- ~- ! ~@---]!1 ~'IIEXI --L]Chr°mat I.CI 1'02°:graphy J';' ~ ...... ~;] "]i"~IE]!V; X('iiiilo~gank i"1!* --
~TIZ][2!!~S~ ~ii' 'L ]
.....
7' 7 ]--7 i.71 I~£ ocs-104 rprep3 BufferHold BufferPrep
I
I .1!i i~!~71
~
I I
ii. i_ ! if: i. :< ...... Tprep L,.;.;.t; DCS-107 5 BufferHold BufferPrep
~i'
:z
DCS-113 BufferHold
i
i!:: i!: Tprep 11
BufferPrep
I
i~
~
'
FinalProduct
" ~11
Figure2. MAB Downstream Details
3.1 Case Study 1 CIP Skids The objective is to schedule the downstream process to accommodate upstream improvements that would reduce the upstream cycle time to 36 hours. When the system is given a target cycle time of 36 hours, it reports that the process may not be scheduled. In fact target cycle times of 46, 36 and 35 hours aren't met. Target cycle times of 48, 45, and 34 hours, however, are achieved. The equipment occupancy chart in Figure 3 reveals the problem. CIP-SKID-1 is conflicting from batch to batch. The cleaning skid is used to clean the bioreactor harvest tank, V-101 and is required at the same time to clean the IEX elution buffer tank in the second batch, so the second batch is delayed at the expense of the cycle-time target.
1049 +~
iicI--P]~i~ID-[I! ......... | ........!..! ........I.i-.
I ...... D..-I--~[ ....... fl.~ ..............i ....l ........!1...... I!-1 .......I.il
..n........N.
.~
iCIP-SKID-3
! ...... In-7 ~........D
i
"
CIP-SKID-2 h clay
l---t ......f
I
! 'ill .........I " "I ,.. ],~
I,~ 1
~
i~ , .... ~i ............! ! ,
n-
nl in .~ ""~ ...... ~ " 0~..... 1,7
I,~
~
I~,~ I,,.
2
3
~'1! !" "!" "" ~ ; m . . . . ,o
~
~
![ [
~1,11.,o
4
5
Figure 3. CIP Skid Usage (Color Coded by Batch)
The key to resolving the problem lies in understanding where to add flexibility. While a delay in a step that affects the product would probably not be allowable in a biopharmaceutical process, a short delay in cleaning a vessel would be acceptable. In this example, a delay of up to 2 hours before cleaning the buffer tanks allows any cycletime target greater 33 hours.
3.2 Case Study 2 Estimating Water for Injection Requirements Purified water known as water for injection (WFI) is used extensively in bioprocesses both for the process and for cleaning vessels. A WFI system consists of a still, surge tank and circulation system. The still capacity surge vessel requirements are dependent on the production schedule. A plot of WFI consumption, shown in Figure 4, gives the basic design parameters. Under peak conditions a four-hour WFI turnover is chosen. The plot shows the instantaneous consumption (light red), the 4-hour average consumption rate (dark blue) and the 4-hour cumulative consumption (brown). The approximate still capacity can be set to peak average rate (9,000 L/h) and the vessel size to the peak 4-hour consumption (35,000 L).
~ i ................i
i: ]
."::7 i ..........i
i........"::i i t l
i ......i
i
jl I!;LJ
ii:
....
.........
,Jl '~.II; ll,f I.............
i ;':;:LAL_jI! ................ L Figure 4. WF1 Consumption
3.3 Case Study 3, Scheduling for Uncertainty An important source of uncertainty in bioprocesses arises from variability in bioreactor durations combined with the long processing times. In the MAB process above, the completion time of an upstream batch may easily vary by a day.
1050 An analysis of the cycle time shows that a 24-hour delay in the upstream process will cause a conflict in the downstream schedule. The upstream cycle time is 48 hours, and the downstream cycle time is 33 hours. A 24 hour delay in the upstream process reduces the time between consecutive branches as follows: ( 4 8 h - 24h) < 33 h. As noted earlier, the cycle-time limiting procedure is a buffer hold step. Buffers are normally made up about a day in advance and held. See the DCS equipment in the first batch in Figure 5. In an emergency, buffer preparation could reasonably be delayed as long as the buffers are ready in time for the chromatography. The user interactively resets the start times for the buffer preparation steps in batch 3 and shifts the start of batch 2 by 24 hours as shown in Figure 5. "(:i!f::!~:~:£1 : i q "
t i p ~/.~.-:~r;, ~ . . . . . ~ill i .11 ~:[~:~[~:~ . . . . . . ii. l i l t
L~i
- i N
D F , ),¢)
i
T~,.,;t
........
i .
......
li
~i
II ......
I~ . . . . . . . . . . . . .
~ ..... ~ ~
............................
.
.
.
.
.
.
.
.
.
~t [ i ~
:. . . . . . .
.....................
m..,
•
!
I
:
~
:
[
. . . . . . .
...........
.....
i~
~
.......
.... : .
.
.
i
.
.
.
.
L _ . ~ . . - ~
fill
:: . . . . .
. . . .
.
[ T : : _ ~
i
i~ :: . . . . . ¢~
~ }
)~4~. . . . . .
~ " ~ : ' ~ ~" ~.~ ~
I~ . . . . .
[~..:S, :i!:i'
v ~0t
:. . . . . . . .
i
................................
~)
.
i
ILL~_.-.J[~
~ I
i
E : : : : : : : ]
............................ ;~i;,,t- - - ~ - -
62T~T~
I
~:. . . . . . .
.... . . . . . . . .
. . . . . . . . . . . . . . . .
•
~
~
. . . . ::. . . . . .
)
.....
:. . . . . . . . . . .
.....
~__-£"
:
~~7222~
......
L__~2.2_._LJ
..............
1
.......
i]
. . . . . . .
l:lEI:]~}
. . . . . . . .
v
~ .........
i .......
•
~:" I(:t . . . . .
~ ~ : ~
[:2~:~
[:3
B:I
:,. . . . . . .
. . . . . . . . . . . . . . . .
~
i
. . . . . . .
.............................
~ ..... ~] I~ ~ l t . . . . . t ~ |l[[. [ . . . . . . . .
i
m
~ .......
. . . . .
T-'--T-
i. . . . . . .
i .
.
.
.
.... w - ~
:
...........
~ I D
•
.1]
..........
~ ,i~
II
: CL:::--"-_~:
L--LT.2::::_)
:
.....
z:::r2-~
..... ~ .....
!. . . . . . . . . . . .
(-
.
.
.
.
~
T .....~
.
.
i
I~.~:::Z~
~t . . . . . . . . . . . . .
.
.............
:. . . . . . .
:
;. . . . . . . . . . .
~
. . . . .
E
~L22]~
J :
F~:::)
....... - ; - . . . . - ~ . . . . . . . T - ~ - T - - ~
--
Figure 5. Schedule for a Delay in the Second Batch
4. Conclusion For most bioprocesses, tight constraints dictate much of the scheduling. Under such conditions interactive scheduling tools can deliver a considerable benefit even if they do not generate mathematically optimized schedules. References Biegler, L. T., I. E. Grossmann and A. W. Westerberg, 1997, Systematic Methods of Chemical Process Design, Prentice Hall, Upper Saddle River, New Jersey, 721. Fox, S., L. Sopchak and R. Khoury, 2001, A Time to Build Capacity, Contract Pharma, September. Pekny, J. and G. Reklaitis, 1998, Towards the Convergence of Theory and Practice: A Technology Guide for Scheduling~Planning Methodology, In Proceedings of Foundations of Computer-Aided Process Operations, J. Pekny and G. Blau, Eds., AIChE, 91. Rouhi, R., 2002, No Vacancy, Chemical and Engineering News, 80, 7, 84-85.
European Symposiumon ComputerAided Process Engineering- 15 L. Pui~ianerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1051
Advances in Robust Optimization Approaches for Scheduling under Uncertainty Stacy L Janak a and Christodoulos A. Floudas a* aDepartment of Chemical Engineering Princeton University Princeton, NJ 08544-5263
Abstract The problem of scheduling under uncertainty is addressed. We propose a novel robust optimization methodology, which when applied to Mixed-Integer Linear Programming (MILP) problems produces "robust" solutions that are, in a sense, immune against uncertainty. The robust optimization approach is applied to the scheduling under uncertainty problem. Based on a novel and effective continuous-time short-term scheduling model proposed by Floudas and coworkers (Ierapetritou and Floudas 1998a, 1998b; lerapetritou et al. 1999; Janak et al. 2004; Lin and Floudas 2001; Lin et al. 2002, 2003), three of the most common sources of uncertainty in scheduling problems can be addressed, namely processing times of tasks, market demands for products, and prices of products and raw materials. Computational results on a small example with uncertainty in the processing times of tasks are presented to demonstrate the effectiveness of the proposed approach.
Keywords: Process scheduling, uncertainty, robust optimization, MILP 1. I n t r o d u c t i o n The issue of robustness in scheduling under uncertainty has received relatively little attention, in spite of its importance and the fact that there has been a substantial amount of work to address the problem of design and operation of batch plants under uncertainty. Most of the existing work has followed the scenario-based framework, in which the uncertainty is modeled through the use of a number of scenarios, using either discrete probability distributions or the discretization of continuous probability distribution functions, and the expectation of a certain performance criterion, such as the expected profit, which is optimized with respect to the scheduling decision variables. Scenario-based approaches provide a straightforward way to implicitly incorporate uncertainty. However, they inevitably enlarge the size of the problem significantly as the number of scenarios increases exponentially with the number of uncertain parameters. This main drawback limits the application of these approaches to solve practical problems with a large number of uncertain parameters. A recent review of scheduling approaches, including uncertainty, can be found in Floudas and Lin (2004). Author to whom correspondence should be addressed:
[email protected] 1052 In this work, we propose a novel robust optimization approach to address the problem of scheduling under uncertainty. The underlying framework is based on a robust optimization methodology first introduced for Linear Programming (LP) problems by Ben-Tal and Nemirovski (2000) and extended in this work for Mixed-Integer Linear Programming (MILP) problems.
2. Problem Statement The scheduling problem of chemical processes is defined as follows. Given (i) production recipes (i.e., the processing times for each task at the suitable units, and the amount of the materials required for the production of each product), (ii) available equipment and the ranges of their capacities, (iii) material storage policy, (iv) production requirement, and (v) time horizon under consideration, determine (i) the optimal sequence of tasks taking place in each unit, (ii) the amount of material being processed at each time in each unit, (iii) the processing time of each task in each unit, so as to optimize a performance criterion, for example, to minimize the makespan or to maximize the overall profit. The most common sources of uncertainty in the aforementioned scheduling problem are (i) the processing times of tasks, (ii) the market demands for products, and (iii) the prices of products and/or raw materials. An uncertain parameter can be described using discrete or continuous distributions. In some cases, only limited knowledge about the distribution is available, for example, the uncertainty is bounded, or the uncertainty is symmetrically distributed in a certain range. In the best situation, the distribution function for the uncertain parameter is given, for instance, as a normal distribution with known mean and standard deviation. In this paper, we will discuss bounded uncertainty as well as uncertainty with a known distribution.
3. Robust Optimization for MILP Problems Consider the following generic mixed-integer linear programming (MILP) problem:
Min / Max crx + d r y x,y
s.t.
Ex + Fy = e Ax+By 0 is a given (relative) uncertainty level. In this situation, we call a solution (x,y) robust if: (i) (x,y) is feasible for the nominal problem, and (ii) for every l, the probability of the event
Z ~ImXm -+-Z b/kYk > Pl -3t-(~max]l,] P t ] m
is at most K, where 8 > 0 is a given
k
feasibility tolerance and K > 0 is a given reliability level. If the distributions of the random variables ~l,,,, ~lk and ~:t in the uncertain parameters are known, it is possible
1054 to obtain a more accurate estimation of the probability measures involved. Denote a new random variable ~ as the following:
-- Z
~'m l alm I Xm + ~ ~Zk I b/k l Y k - ~z I P, I
mcM l
(6)
k~K l
Assume that the distribution function of ~ is"
F;(A) - Pr{~ _ 2} - 1 - P r { ~ > 2} - 1-~c
(7)
where • is a given reliability level and the inverse function (quantile) can be represented as follows:
f~ -1 ( 1 - K:) - f(,Z,I aim
I Xm,I bzk I y~-,I p,
1)
(8)
Then, given an infeasibility tolerance, 6, and a reliability level, K, to generate robust solutions, the following so-called (e,6,~:)-Robust Counterpart (RC[~,8,K]) of the original uncertain MILP problem can be derived. The additional constraints in the RC problem:
~-'~atmXm + ~ btkyk +~f(A,I alm I xm,I btk l Yk,I p, I) ,,
k
(9)
__ p, + 6 max[1,l Pt I], v/ Several different distribution functions can be modeled this way including the uniform distribution, normal distribution, difference of normal distributions, and several discrete distributions such as Poisson or binomial (Janak et al., 2005). This robust optimization methodology can be applied to address the problem of scheduling under uncertainty, including three classes of problems: (i) uncertainty in processing times/rates of tasks, (ii) uncertainty in market demands for products, and (iii) uncertainty in market prices of products and raw materials. In this work, we will only consider uncertainty in the processing times/rates of tasks.
4. E x a m p l e P r o b l e m Consider the following example process that was first presented by Kondili et al. (1993) and has been widely studied in the literature. Two products can be produced from three feeds according to the state-task network as shown in Figure 1. The objective is to maximize the profit from sales of products manufactured in a time horizon of 12 h. The continuous-time formulation proposed by Floudas and coworkers (Ierapetritou and Floudas 1998a, 1998b; Ierapetritou et al. 1999; Janak et al. 2004; Lin and Floudas 2001; Lin et al. 2002, 2003) is used to solve this simple scheduling problem. The example is implemented with GAMS (Brooke et al., 1988) and solved using CPLEX 8.1 on a Linux 3.0 GHz workstation. The "nominal" solution is shown in Figure 2, which features intensive utilization of units U2 and U3 and an objective value (profit) of 3639. However, this solution can become completely infeasible when there is uncertainty in the processing times of the tasks. Consider the case where the uncertainty of the processing times is bounded and the (relative) uncertainty level, ~, is 15% and the infeasibility tolerance level, 8, is 10%. Then, by solving the IRC[~,8] problem, a "robust" schedule is obtained, as shown in Figure 3, which takes into account
1055 .Product 1
Heating ~
l
I
IntAB
4 o.4
( ~
Io.~ r , ,
Reaction 2 [ . . . . ~ ) ~,
Feed A
0.6
re E
I Feed B
0"8lReacti°n31
I
T0.5
0.1
_I
0
0.2
Product 2
Feed C
Figure 1. State-task networkjbr the example problem.
uncertainty in the processing times. Compared to the nominal solution, the robust solution exhibits very different scheduling strategies, such as task-unit assignments and task timings. The robust solution ensures that the robust schedule obtained is feasible with the specified uncertainty level and infeasibility tolerance. However, the resulting profit is reduced, from 3639 to 2887, which reflects the effect of uncertainty on overall production. A comparison of the model and solution statistics for the nominal and robust solutions can be found in Table 1. [30.00
U4 89_00 T2 50_00 T2
It? U2
52_00 T[ I
U1
80_00 T3 50_C~0 W3
I I 20_(210 T[ t
1
52_0 0 T1
."
I
80.00 T4
8C~_00 T2
I 5":u:u') T3
I
[
80_00 T3 50_0C~ T3
50_00 T4
[ I
4
5
6
8
7
T5
I 68.75 I T4 50_00 T4 I [ 6_00 T1 I
I
[
3
[ [8.75
T5
I
9
40:30 T3
10
11
12
Figure 2. Optimal solution with nominal processing times.
97_ 50
L[,4
I 80.0 (-i T2 50.00 T2
U3 U2
l_0 0_0 0
U1
T[
II II 3 6_0 0
II-- T[ t
0
8,0_(J(-i T3 50.130 T3
1
80.00 T3
il I I
50.00 T4
I~-
i 47.5 (-I T4 I I
72_ 1_9
T5
I
I 2219 T4
]
74.00 T2
I
T5
50.00 T4
I
I
80_ 00 T3 50.00 T3
II II
I I
i i
,c. "~
t
i
t
i
L
i
I
3
4
5
6
7
8
•~.
I
10
i
11
Figure 3. Robust solution with uncertainty level (~)of 15%, infeasibilit)' tolerance (0")of 10%.
5. Conclusions In this work, we propose a new approach to address the scheduling under uncertainty problem based on a robust optimization methodology, which when applied to MixedInteger (MILP) problems produces "robust" solutions which are in a sense immune
1056 Table 1. Model and solution statistics for the example problem.
Profit CPU Time (s) Binary Variables Continuous Variables Constraints
Nominal Solution 3638.75 0.40 64 346 489
Robust Solution 2887.19 10.10 64 346 713
against uncertainties in both the coefficients in the objective function, the left-hand-side parameters and the right-hand-side parameters of the inequality constraints. A unique feature of the proposed approach is that it can address many uncertain parameters. The approach can be applied to address the problem of production scheduling with uncertain processing times, market demands, and/or prices of products and raw materials. Our computational results show that this approach provides an effective way to address scheduling problems under uncertainty, producing reliable schedules and generating helpful insights on the tradeoffs between conflicting objectives. Furthermore, due to its efficient transformation, the approach is capable of solving real-world problems with a large number of uncertain parameters (Lin et al., 2004). References Ben-Tel, A. and A. Nemirovski, 2000, Robust solutions of Linear Programming problems contaminated with uncertain data, Math. Program. 88, 411. Brooke A., D. Kendrick and A. Meeraus, 1988, GAMS: A User's Guide, San Francisco, CA. Floudas, C.A. and X. Lin, 2004, Continuous-Time versus Discrete-Time Approaches for Scheduling of Chemical Processes: A Review, Comp. Chem. Engng. 28, 2109. Ierapetritou, M.G. and C.A. Floudas, 1998a, Effective Continuous-Time Formulation for ShortTerm Scheduling: 1. Multipurpose Batch Processes, Ind. Eng. Chem. 37, 4341. Ierapetritou, M.G. and C.A. Floudas, 1998b, Effective Continuous-Time Formulation for ShortTerm Scheduling: 2. Continuous and Semi-continuous Processes, Ind. Eng. Chem. 37, 4360. Ierapetritou, M.G., T.S. Hene and C.A. Floudas, 1999, Effective Continuous-Time Formulation for Short-Term Scheduling: 2. Multiple Intermediate Due Dates, Ind. Eng. Chem. 38, 3446. Janak, S.L., X. Lin and C.A. Floudas, 2004, Enhanced Continuous-Time Unit-Specific EventBased Formulation for Short-Term Scheduling of Multipurpose Batch Processes: Resource Constraints and Mixed Storage Policies, Ind. Eng. Chem. Res. 43, 2516. Janak, S.L., X. Lin and C.A. Floudas, 2005, A New Robust Optimization Approach for Scheduling under Uncertainty: II. Uncertainty with Known Distribution, submitted for publication. Kondili, E., C.C. Pantelides and R.W.H. Sargent, 1993, A General Algorithm for Short-Term Scheduling of Batch Operations - I. MILP Formulation, Comp. Chem. Engng. 17, 211. Lin, X., E.D. Chajakis and C.A. Floudas, 2003, Scheduling of Tanker Lightering via a Novel Continuous-Time Optimization Framework, Ind. Eng. Chem. Res. 28, 2109. Lin, X. and C.A. Floudas, 2001, Design, Synthesis and Scheduling of Multipurpose Batch Plants via an Effective Continuous-Time Formulation, Comp. Chem. Engng. 25,665. Lin, X., C.A. Floudas, S. Modi and N.M. Juhasz, 2002, Continuous-Time Optimization Approach for Medium-Range Production Scheduling of a Multiproduct Batch Plant, Ind. Eng. Chem. Res. 41, 3884. Lin, X, S.L. Janak and C.A. Floudas, 2004, A New Robust Optimization Approach for Scheduling under Uncertainty: I. Bounded Uncertainty, Comp. Chem. Engng. 28, 1069.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1057
Proactive approach to address robust batch process scheduling under short-term uncertainties A. Bonfill, A. Espufia and L. Puigjaner Universitat Polit6cnica de Catalunya, Chemical Engineering Department, ETSEIB, Diagonal 647, E - 08028 Barcelona, Spain e-mails: [anna.bonfill, antonio.espuna, luis.puigjaner]@upc.edu
Abstract A contribution is made in the area of proactive scheduling with the aim to properly define the scheduling problem explicitly incorporating the effects of short-term uncertainties. The idea is to identify a robust initial schedule with the flexibility to react to unexpected events with minimum effects. The problem is modelled using a stochastic optimization approach where not only a set of anticipated scenarios can be considered, but also the capability to react to events once they occur. A stochastic genetic algorithm is developed to efficiently identify robust schedules with minimum expectance for the wait times and idle times that commonly arise in the operation of batch processes with variable operation times and machine breakdowns. The application of the proposed modelling framework to different batch processes shows the flexibility of the identified initial schedule and highlights the importance of exploiting the information of the uncertainty at the decision stage.
Keywords: Proactive schedule, rescheduling, robustness, uncertainty. 1. Introduction Process variations and incomplete information are inherent characteristics of any process system, and flexibility to respond quickly and effectively to the dynamic and uncertain environment has become an essential feature for effective scheduling. Research in scheduling under uncertainty has mostly been focused either on reactive scheduling algorithms, implemented according to the actual situation of the plant once the uncertainty is realized or unexpected events occur, or on proactive scheduling approaches, which tend to generate schedules that are in some sense robust or insensitive to a priori anticipated uncertainties. The execution of optimal schedules based on nominal parameter values and the implementation of rescheduling strategies to face disruptions could result cumbersome and might lead to inefficient or costly reconfigurations as well as to plant nervousness. On the other hand, a robust schedule exhibits an optimum expected performance, but it is not likely to be the optimum one for the actual scenario that will finally occur. Both methodologies have usually been implemented independently, and relatively little attention has been given to the consideration of short-term uncertainties proactively (O'donovan et al., 1999; Kim and Diwekar, 2002; Jensen, 2003).
1058 The incorporation of rescheduling aspects at the time of scheduling is proposed in this work. The identification of a robust initial schedule with the flexibility to react to unexpected events with minimum effects is pursued by explicitly addressing the major effects of variable processing times and equipment breakdowns in short-term scheduling of batch processes. These effects can be characterized by their main consequences in terms of task scheduling. On one hand, if a breakdown occurs and/or the actual processing time of a task is longer than the scheduled one, the time spent by batches waiting for the availability of the next unit increases. This might lead to unexpected delays, and eventually result in quality problems for sensitive or unstable materials that force the rejection of batches with the consequent increase of operational costs. On the other hand, if processing times are shorter than the scheduled ones, idle times appear and subsequent equipment under-utilization occurs (Figure 1). The approaches proposed so far that recognize the importance of considering the uncertainty into the decision level do not explicitly address not even analyze these critical situations that can arise during the execution of the schedule. However, the knowledge of this uncertainty can be usefully incorporated at the time of scheduling to reduce the gap between theory and practice, thus reducing reschedule requirements and improving the overall plant performance avoiding the occurrence of the full force of a perturbation. It is highly desirable to balance the trade offs between robustness, rescheduling and performance, and develop an initial schedule able to absorb anticipated disruptions, thus minimizing their effect on planned activities while maintaining acceptable plant performance. Predicted schedule
°, {ii!iii{i{
o~
jii{gi~iiiig~iigii
u2
~:~ii~ii"ii~i~ii~~
................... ..............the scheduled ones "";...................... WAIT TIME (wt) []
--, wt .................. u l i:~i~ii~i~'~i~ii~{~ iiiii~i~ ...........
I
wt
o'it/ca/for unstab/e materia& ...........Shorter times than ....................... the scheduled ones
U2
~,>!.CUUT,,,,75;.7/#7..~=,~"
I I
:.-~')--~
....................................................................... ~< .................. i...;...;..,.;..~.,.i..A':R'~'/~--~', .................. ,/ .........i ! ~ , ~ " i ~ A . ; "
/
! 5-/
i
Rermery
I~{"~~ ~L'JF~ '(beginning /~k=0
....................................................................................................................................................................................................... Q# [ m 3 / h ]
of the' operation)
Figure 1 - Distribution pipeline system The refinery stores its products in dedicated tanks and these load their derivatives at predetermined amounts and initial and end time instants along the time horizon. Whenever the pipeline receives any product from the refinery, the same amount leaves it and feeds the depots at the same time in order to satisfy volume and flow rate constraints. The depots have to control their inventory levels and fulfill product demands. Due to demand variations, the pipeline operation is in most cases intermittent. Figure 1 also shows the system and the pump operating curves. The hydraulic behavior depends on the sequencing of products and their allocation inside the pipeline, the flow rate variations, the topographical profile of the pipeline and diameter variations. The pump curves operating depend on the pump types, adjustable speeds, and represent the energy that is provided by the booster stations to transfer the products. Moreover, the pipeline operating point is given by the intersection of these two curves.
3. Optimization Model The MINLP formulation is based on the previously MILP developed by Rejowski Jr. and Pinto (2004), which was however based on a discrete time formulation. The objective function is shown by equation (1).
CERp.VRp,k +
Min C = ~ k=l P
p=l D
C E D p , d . V D p , j , k .A k p=l d=l
K
P
P
D
K
+2 Z Z CP~.OPWd.k.Ak +Z 2 Z Z CONTACTp,p,.TYpa,p,,k p = l d = l k=l
p = l p'= d = l k=l
(1)
1065 The terms in brackets represent the inventory costs at the refinery and at the depots that take into account the variable time interval duration (A~). The next term accounts for the pumping costs, that are composed by the overall power consumption by the booster stations (OPWa.~.) and the time interval that the pipeline remains in operation (&). The last term corresponds to costs associated to product interface formation (Rejowski Jr. and Pinto, 2004).
3.1 Temporal and refinery constraints The refinery sends the products to its tanks in lots (i) with predefined amounts and initial and end instants, as shown in Figure 2. The temporal constraints must satisfy the operational time horizon (/-/), according to equation (2) and their initial (Ti~) and end instants (Tf ) along the transfer operation, as in equations (3) and (4), respectively. The mass balances at the refinery are given by (5) and their volumes are bounded in (6). ~:i T'- 1
R e r m e ~ w P r odu c t i o n L o t s
[
i = 1 R P I , I,~
:
7)
T~/Tf~: slta11.,,'end t h n e foi~ loading operation for product lot i composed by p r o d u c t p at t h n e / e l K ~ : Set of t i m e h l t e r v a l s that receive a product lot f r o m t h e
1
f
2
rermel.w p r o d u c t i o n
.#eL,
/~O: 1 ~ t t i m e h l t e r v a l b~fore production lot )'~ , : 1~1[ t i m e h l t e r v a l olr production lot i
I#1
--
i
I
" Tim e ~
Figure 2 - Production lots and continuous time representation K
~-'A k - H
(2)
k:l
77i
Vi
(3)
/"k - T~
Vi
(4)
Vp, d:l,k
(5)
Vp, k
(6)
~" A k
-
k _ 1, k=2,...,K
(7)
If YJ,k is true, the first pack of the segment takes the feed variable values (XTp.d,k or d = 1). The products in the pipeline are displaced from pack 1-1 to pack 1. The product stored at pack Ld can be sent to depot d (XDp,d,k) o r to the next segment (XTp.J+l.a). The velocity limits (vk) must be respected when the pipeline operates and its time interval (&) is equal to the ratio between the pack size (Uj) and the flow rate used at time k. If the segment remains idle, Yj,a is false and all packs keep their contents. Interfaces are detected when the first two packs from the segments store different products. Moreover, any pipeline segment can only be stopped if it does not contain any interfaces. The depot constraints are similar to the ones of the refinery and demands must be met at the end of the operation. Finally, Rejowski Jr. and Pinto (2004) propose integer cuts that relate demands and the initial inventory at the depots and in the segments. The temporal variables are disaggregated into two parcels. The first one (Ale) regards
XRp,k for
the pipeline operation, whereas the second ( A ,2) considers the time that the pipeline remains idle. Equations (9) and (10) state that the time that the pipeline operates at interval k must be equal to the ratio between the pipeline volume pack (Ud) and its operational flow rate
(v,.A).
Equation (11) imposes zero values to A~k whenever the
pipeline remains idle. The product velocities must take positive values when the pipeline is operative, according to (12). A~ = A~1 + A~2
vk
(8)
iX'k" (v,.A) = U~.X'S~
Vd, k
(9)
Vd, k
(10)
Vd, k
(11)
Vd, k
(12)
AL°sToP'~I - X S a
uP k] < - A 2h -< A s r o p ' I 1 -
vkL°.XSd, ~ -< vk -< vUe'xsjk
,k
X S a ,k
3.3 Flow rate and hydraulic constraints The hydraulic model is described by disjunction (13). If Yj,~ is true, the friction factor
(fd,/,k) follows equation (13a), where logical 0-1 variable XVpdt,k is multiplied by an exponential that depends on the product physical properties. The friction losses for each pack I take into account the friction factor, the pipeline internal diameter ( D i n ) , the pack extension ( L E X T I ) and the pipeline flow rate, according to (13b). The yield rates (r/k) used by the booster stations are represented by an mt-h order polynomial that depends on
1067
the velocity. The booster stations have several stages (N) that can be activated during the operation from binary variable ( NS,;~k ) and their power consumption ( PW,~/~ ) must satisfy lower and upper bounds, according to (13d). Finally, the energy balance over the pipeline is given by (13e) and the overall power consumption from (1) is given in (13f). If the pipeline remains idle, the friction factor and losses, the power consumed by the booster stations and the yield rates equal to zero, as shown by (13g) to (13k).
J]LZ.k = ,~__,XV:/.Lk.(a,,'vk ' ~' )
VI < Lj
(13a)
_
Y/,k
P
lw/;,.,., = LEX7],.,.f,.z , .,,~ /2.Di,,
,,,--cm.(.,)'"
+c,,,, (.,)
.... '+...+c .... .(,,) ..... +...+co ,,3c)
PW]°.NSj,k z.=0. This can be expressed by Equation 1, where variable Da~ is the length of interval i. Equation 2 expresses monotinicity, i.e. the cost cannot be smaller than the cost of the kth interval. Equation 3 specifies that the intervals have to be considered one after the other.
icI
1072 (2)
C>-Z(yi'Dci) ici
i~{ili~I,i>O} i~{ili~I,i-O}
Yi 1}
(5)
D a i - ba i
i ~ {i [ i ~ I , i - 1}
(6)
Oa i -
0
i ~ {i l i ~ I , i -
0}
(7)
DC i -
bc i -bc,_
i ~ {i l i ~ I , i > 0}
(8)
i ~ {i l i ~ I , i - 0}
(9)
Oc i
1
-- b c i
Tight bounds to all the non-decision variables are computed, based on the problem formulation, from bounds given to the decision variables, see Chapter 5. Note also that Equations 1-2 need not be given as equality constraints because of the monotonity of the cost function, and because the cost is minimized during the optimization.
4. Example problems Results of test runs on a middle scale and a large scale problems, given by SABMiller Europe, with charactesistics summarized in Table 1, are presented here.
Table 1. Characteristicsof the exampleproblems Problem Small Large
Processing plants 3 25
Packaging lines Products in a plant 3 13 5 100
Customer sites 67 250
Steps of cost function of plants lines 6 4 5 6
Table 2. Comparison of models Problem
Small Large
Model Multi-M Ttirkay Convex Hull New model New model
Number of equations 4,035 3,927 3,981 3,852 671,626
Number of Number of variables binary v. 5,632 66 5,632 66 5,764 66 5,632 66 1,281,201 875
Number of Solution time iterations (CPU sec) 3,384 1,046 2,350 750 1,121 453 543 312 437,364 19,357
The middle scale problem is used to compare the efficiency of some usual model formulations applied to the given problem type. The problem was solved by GAMS (Brooke et al., 1998) using CPLEX as MILP solver on a PC Pentium 4 CPU 2.4 GHz.
1073 The results are collected in Table 2. The same optimum was found in all the cases. The number of iterations and the solution time in CPU sec are shown in the last two columns. The Ttirkay model is a forward development of the Big-M technique. The Convex Hull technique applies tighter bound / better relaxation than either Big-M or Ttirkay, that is why the solution properties improve according to this sequence. Our new methodology utilizes the monotonicity property; that must be the main reason of the improvement. The lower row in Table 2 demonstrates that large scale problems become solvable with our suggested model formulation. The problem was solved using the same solver on the same machine as above. The solution was found with 1,33% relative gap between the best integer and the best relaxed solution.
5. Feasibility check and solution methodology Checking feasibility may involve examining all the binary combinations in general case. Our special formulation, however, applies binary variables in the terms of the cost function only; and a relaxed LP problem (RLP) can be generated by excluding those terms from the cost function. Any (LP) problem, see below, can be extended (and called LPV) by introducing vn (negative perturbation) and vp (positive perturbation) variable arrays: m
min min
w-
z - cx Ax
- b = 0
x > O,b > O, x e R "
,-:1
(LP)
vp-
m
~-'vp,. + ~ v n , . vn + Ax
,.:1 - b = 0
(LPV)
x > O,b > O, vp > O, v n > _ O xeR",vpeRm,vneR
m
where m is the number of equations. LPV always has a solution; LP has a solution if, and only if the optimum of LPV is w:0; if the optimum of LPV is w=0, vp*=O, vn*=O, and x*, then x* is a feasible solution of LP. If w:/:O, vp*:/:O, and/or vn*:/:O then RPV is infeasible. Which element(s) of the array v=[vn, vp] is(are) nonzero tells us which constraint(s) is(are) voilated. If there were not minimum capacity utilizations specified in the original problem then the solution of RLP would be always a feasible solution of the original problem, as well. But such minimum utilizations are specified, and binary variables related to the existence of plants cannot be excluded, involving a rather difficult problem. Instead, we check the feasibility of the most probable binary combination only; this is the case that all the plants included in the model work with some capacity. The final program is illustarted in Figure 3. The problem data are collected in MS Acces, and transformed into GAMS readable format using mdb2gms.exe (Kalvelagen, 2004). The GAMS model has three main parts. (1) First the feasibility of the problem is checked using LPV. If w:/:0 solution is found then the program stops, and reports the value of the nonzero perturbation variables. (2) RLP is solved in the other case, and provides with proper initial values for the variables. (3) Finally, the original MILP, formulated according to the new modelling equations, is solved. The results of the GAMS run is transformed into MS Access format using GDXViewer (Kalvelagen,
1074 2004). The result data can be read in MS Access, or it is transformed into graphical form by MS MapPoint. This latter form is illustrated in Figure 4. with a theoretical example including 4 processing plants and 24 customers. Circles are assigned to the customers; their size visualise the total demand of the customer, whereas circle sectors represent what parts of the demand are satisfied from different sources.
i• .........
. . . . . . . . .
Data in mdb2gms.I MS Access I ~
-"
I
J'] Solve LPV~
I
es
i •
2[Initialization
I. . . .
___
l[
Solvethe
I
I .
i
i
i
• GDX Viewe~
i
i .
i
,
~
.
i
.
i
.
i
.
i
.
i
=
~
.
i
,
i
w
~
MS Access
+
q
MS MapPoint Figure 3. Algorithm of the final program
.!!!:¸~: :i:i ..e.
::::::::::::::::::::::::::: ::::::::::P:::::::::::[
Figure 3. Graph visualization of the results of a theoretical example
6. Conclusions and recommendations The new model works well for the studied problem with objective function including terms with stepwise constant cost functions. Test on middle case problems resulted in better computation properties than Big-M or Convex Hull, and large scale problems can also be solved with it. The relaxed formulation (RLP) in its transformed form LPV, together with the elaborated GAMS program, can be successfully applied to check the feasibility of the problem prior to trying MILP solution. When RLP is infeasible, the results of LPV provides useful information on the possible reasons of the infeasibility. References
Brook, A., D. D. Kendrick and A. Meeraus, 1992, GAMS. A User's Guide. boyd & fraser, USA Kalvelagen, E., 2004, http://www.gams.com/-erwin/interface/wtools.zip Tt~rkay, M. and I.E. Grossmann, 1996, Ind. Eng. Chem. Res. 35, 2611-2623. Vidal, C.J., and M. Goetschalckx, 1997, Eur. J. Op. Res. 98, 1-18. Acknowledgements
This study was partially supported by OTKA T037191 and OTKA F046282.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1075
Design and Planning of Supply Chains with Reverse Flows Maria Isabel Gomes Salema a, Ana Paula Barbosa Pdvoa bY, Augusto Q. Novais c aCMA, FCT, UNL, Monte de Caparica, 2825-114 Caparica, Portugal bCEG-IST, Av. Rovisco Pais, 1049-101 Lisboa, Portugal CDMS, INETI, Est. do Pago do Lumiar, 1649-038 Lisboa, Portugal
Abstract A multi-product model for the design of global supply chains with reverse flows is proposed. Two levels of decisions are considered, one strategic and one tactical. The first is modelled through a macro perspective of time where the determination of the network structure and flows is accomplished. At tactical level, a micro perspective of time is considered, where production planning and inventory management are addressed in detail. A mixed integer linear programming formulation is developed which is solved with standard Branch and Bound techniques. The model accuracy and suitability are studied using a case study.
Keywords: Supply Chain design, Optimization, Reverse Logistics, Planning.
1. Introduction In modern society, used products constitute a major challenge. Governments are facing overflowed landfills, while creating legislation to shift product management responsibility towards the producers. Used/disposed products are now placed in a different perspective, as company managers perceive new business opportunities whereby these products should be returned to factories for remanufacturing/recycling. Consequently, the supply chain must be extended and no longer terminate at the end customers, but account also for the products return. Only recently the scientific community started looking into this problem. Thus the reverse logistics problem appears as an emerging field where only a limited number of models have been, so far, presented in the literature. These are essentially case study dependent and mostly consider the reverse flow on its own and not as an integral part of the supply chain. As the most generalized published models, one should refer to: Fleischmann et al. (2001), where forward and reverse flows of a given product are integrated, with no limiting capacities in the involved facilities and flows; Jayaraman et al. (2003), who proposed a MILP model for the reverse distribution problem, without taking into account the forward flow; Fandel and Stammen (2004), that proposed a MILP general model for extended strategic supply chain management, based on a twostep time structure, but where no testing of adequacy to any example/case was explored; and finally Salema et al. (2004) who developed a capacitated multi-product design
Author to whom correspondence should be addressed,
[email protected] 1076 network model where forward and reverse flows were considered, the flows differ not only in terms of structure but also in the number of products involved. Within these few works, one important area of research not yet explored, is the simultaneous design and planning of such structures (Goetschalckx et al., 2002). In the present paper, we look into this issue and propose an optimal multi-product supply chain design model where both forward and return flows are integrated considering simultaneously the design and planning of such structures. A Mixed Integer Linear Programming formulation is developed where two different perspectives are employed for the treatment of time: a macro perspective (strategic), for the determination of the network structure and flows, and a micro, more detailed perspective (tactical), for the production planning and inventory management. An illustrative case-study is solved showing the model applicability.
2. Problem Definition Figure 1 shows a schematic representation of ~ l~~ a supply chain network with reverse flows. A ~ ~ ~ two echelons forward distribution network is considered where factories are linked to ~l"llili"iiFactory iiliii:;i~i'"i"i"ii;'"i:i~' i"~ customers through warehouses. No direct
connection, factory-costumer, is allowed. The
~
Customer
~ - - ' [ : i ~ DisassemblyCentre
same applies for the reverse flow where a two Figure 1: Distribution network with echelons structure is also present, customers reverse flows. being linked to factories through disassembly centres. Again, customers cannot send their products directly to factories, since products must pass through disassembly centres. Forward and returned products might be treated as independent since we consider that original products may loose their identity after use (e.g. paper recycling paper products after use are simply classified as paper). However, if required, it is also possible to track the same product in both flows. Furthermore, a disposal option is considered within the structure in study. At the disassembly centres if collected products are found to be unsuitable for remanufacturing, a disposal option is made available. Using these structural options the model considers two levels of decisions at different time scales. A "macro time" scale, where the supply network is designed, and a "micro time" scale, where planning activities are set (e.g. macro production and/or storage planning). These time scales can be years/months, years/trimester, month/days or whichever combination suits the problem. The chosen facilities will remain unchanged throughout the time horizon while the throughput will undergo changes. Flows are not necessarily instantaneous (customers will not have their demand satisfied in the same time period when products are manufactured) and thus travelling times might be considered. A travelling time is modelled as the number of micro time periods that a product takes to flow from its origin to its destination. If all travelling times were to be set to zero, a multi-period location/allocation model would be obtained. Finally, a profit function is assumed for the objective function where revenues and transfer plus selling prices are considered. The former are defined whenever there are products flowing between facilities (from factories to warehouses or from disassembly
1077 centres to factories) and the latter whenever products are sent to customers by warehouses or collected by disassembly centres. In terms of costs different terms are identified: investment costs (whenever a facility is chosen), transportation costs, production costs, storage costs and penalty costs (for non-satisfied demand or return). In short, the proposed model can be stated as follows.
Given" • the investment costs • the amount of returned product that will be added to the new products • travelling time between each pair of network agents • the minimum disposal fraction and for each macro period and product: • customers' demand and return values, • the unit penalty costs for non satisfied demand and return, and in addition, for each micro period: • the unit transportation cost between each pair of network agents, • the maximum and minimum flow capacities, • the factory production unit costs, • the facilities unit storage costs, • the maximum and minimum production capacities, • the maximum storage capacities, • the initial stock levels, • the transfer prices between facilities, • customers' purchase and selling prices. Determine, the network structure, the production levels and storage levels, the flow amounts, and the non-satisfied demand and return volumes. So as to, maximize the global supply chain profit. 3. I b e r i a n
Case
3.1 Case description This example was created based on a company that operates in the Iberian Peninsula. This company needs to determine the network design for a supply chain that will involve two forward products (F1 and F2) and one single returned product (R1). At the strategic level customers are grouped into 16 clusters, where each cluster is named after the city it represents. Customers' clusters, from now on designated simply as customers, are respectively located in Barcelona, Bilbao, Braga, Coimbra, la Corufia, Granada, Lisbon, Madrid, Malaga, Oviedo, Porto, Santander, Saragossa, Seville, Valencia and Valladolid. Six of these cities are possible sites to locate warehouses and/or disassembly centres (Barcelona, Bilbao, Lisboa, Madrid, Porto and Sevilla). For the factories there are only two possible locations: Lisbon and Madrid. In terms of time, a macro period is defined over ten years and a micro period over twelve months per year: macro period - "year" and micro period = "month". Since the model considers a horizon of ten years, some data have to be estimated. These include the demand and return volumes as well as variations in costs over the years. These
1078 estimates were based on some assumptions: transportations costs are proportional to the distance between each city and after the first year an inflation rate of 3% (or some other convenient value) is applied to these and all other costs; if flows link cities in different countries, a tax is applied to the corresponding transportation cost namely, 6% from Portugal to Spain and 3% from Spain to Portugal; in the first year, customers' demand is made equal to a fraction of the city inhabitants (a value between 0.8 and 0.9) while in the remaining years a variation factor (ranging from 0.98 to 1.08) is considered, allowing for an increase or decrease in the demand value; in each year, customers' returns is set as a 0.8 fraction of the corresponding demand. The problem also assumes zero initial stock levels; for product recycling F1 incorporates 0.6 of product R1 and product F2 incorporates the remaining 0.4 of product R1; the disposal fraction is set to zero; minimum and maximum capacities are defined for production (0.8"106 and 1.0"106 , respectively); no limit is imposed on flows; travelling time is set to nil, which seems a reasonable assumption given the chosen time scale (years/month) and the particular geographical area under study. 3.2 Results
The resulting MILP model was solved by GMAS/CPLEX (built 21.1), in a Pentium 4, 3,40 GHz. The model is characterised by 46 337 variables (14 binary) and 5 703 constraints and took about 392 CPU seconds to solve (0% optimality gap). The optimal value found for the objective function is 96xl 09 currency units and the optimal network is characterised by a single factory location (Madrid). /
//
.o................
i--
Figure 2a: Forward networks
Figure 2b: Reverse networks
In the forward flow, the Madrid factory serves four warehouses (Bilbao, Lisboa, Madrid and Porto). The associated connections are depicted in Figure 2a: solid lines link the factory to warehouses and dotted lines connect warehouses to customers. One can see that Lisboa and Bilbao have just one customer and that Madrid acts has a geographical centre. Every warehouse supplies the customer located in the same city, while there is one single customer which is served by a warehouse outside the country (Coruna is served by Porto). The number of connections between the two countries is therefore small, which is a result of the taxation imposed for flows between countries. Finally, all customers had their demand fully supplied. In terms of the reverse network (Figure 2b), all six different locations were chosen for the disassembly centres (Barcelona, Bilbao, Lisboa, Madrid, Porto and Seville). As in
1079 the forward network, every disassembly centre serves the customer located in the same city. Concerning the tactical level of decision three different analyses can be made, respectively for production, storage and distribution. As the model produces a large wealth of information, only some examples will be presented.
Figure 3. Facto~ production plan.
In terms of production, Madrid factory operates continually at the minimum level. To meet demand fluctuations, this factory has the products returned by the disassembly centres. To illustrate the optimal production plan, the first, fourth and tenth years are depicted in Figure 3. In terms of storage, the optimal solution leads to a zero stock policy. This is a result of the negative impact that storage has on the objective function (i.e. inventory is costly). Finally in terms of distribution, four examples are given. Each one refers to a different network level. il ir :
• 11 !i!
i:i
i
i:i
.... Iliiill i!l il Figure 4. Distribution.17ows between Madrid and Lisboa.
Figure 5. Demand served to Braga's customer.
Figure 4 shows in detail the flows between the factory and the warehouse located in Lisboa. The relaxation of the capacity constraints resulted in very dissimilar flow patterns. In Figure 5, Braga's customer supplying plan is depicted. The difference between amounts supplied has to do with the simultaneity of supplies received by this customer, as noted in the third and sixth years. On the contrary, in the ninth year there are three separate visits. In the remaining years, every product is supplied in one single separate delivery. With regard to return volumes, Figure 6 shows the total return of product R1 between customers and disassembly centres. The dissimilarity among values is a consequence of
1080 the customers return volumes. Lastly, the return of Lisboa disassembly centre is depicted in figure 7. One can see that each year returns are sent to remanufacture (Madrid factory, labelled Mad) as well as to the disposal option (f0). However, the number of times these activities are performed, varies between once and twice a year. ~:~.~
i
-
.......................
o:o ~ : ~ -i...................................................... I
:~ ° ° ° ' ~
~
::~.~;~E~
.)~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
~°~ ~ ' ~
...............................
..................
I
. . . . . . . . . . . . .
......... '........ I I .... . . . . . . . . .
:~
Figure 6." Total return for the first year.
...... II i .?..l...... ...I...!..........
....... i...... iI!
¢~~ , ~
...................................................... m .......................................................
Figure 7." Lisboa disassembly centre return
flOWS.
4. Conclusions In this paper, a multi-period, multi-product design model for a supply chain network with reverse flows is proposed. Two time levels are modelled allowing the establishment of two different levels of decisions: a strategic level defining the network design of the supply chain and a tactical level defining the production, storage, distribution and returning planning. The obtained MILP formulation is fairly flexible since several products can be considered in both networks; different time units can be correlated (years/semesters, years/months, months/days...); limits can be imposed on flows, production and storage capacities; and different travelling times are allowed. The mathematical formulation which supports this model, while it is likely to increase significantly in complexity with the problem dimension, still appears as an important tool to help the decision making process at the strategic and tactical levels of the supply chain management decisions. In order to overcome the computational burden of such a formulation, different solution techniques are now being explored to speed up resolution. Further research is also being undertaken with a view to both strengthen the model formulation and to treat production planning with greater detail, with the introduction of bills of materials.
References Fandel G. and M. Stammen, 2004, Int.J.P.E. 89: 293-308. Fleischmann M., P. Beullens, J.M. Bloemhof-Ruwaard and L.N. Van Wassenhove, 2001. POM 10: 156-173. Goetschalckx M., C.J. Vidal and K. Dogan, 2002. EJOR 143: 1-18. Jayaraman V., R.A. Patterson and E. Rolland, 2003. EJOR 150: 128-149. Salema MI, AP Barb6sa-P6voa and AQ Novais, 2004. POM (submitted).
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1081
Heterogeneous Batch Distillation Processes: Real System Optimisation Pommier S6bastien a, Massebeuf Silvbre a, Gerbaud Vincent a, Baudouin Olivier b , Baudet Philippe b and Joulia Xavier a* aLaboratoire de G6nie Chimique, 118 route de Narbonne, F-31077 Toulouse Cedex 04, France bproSim SA, Stratbge OffShore, Bfitiment A - BP 2738 F-31312 Lab6ge Cedex, France
Abstract in this paper, optimisation of batch distillation processes is considered. It deals with real systems with rigorous simulation of the processes through the resolution full MESH differential algebraic equations. A specific software architecture is developed, lying on the ProSim BatchColumn simulator and on both SQP and GA numerical algorithms. The efficiency of the proposed optimisation tool is illustrated by a case study of heterogeneous batch solvent recovery by distillation. Significant economical gains are optained along with improved process conditions. For such a multiobjective complex problems, GA is preferred to SQP that is able to improve specific GA solutions.
Keywords: Optimisation, Batch Distillation, Heterogeneous Azeotrope
1. Introduction Solvent recovery is a major issue in the pharmaceutical and specialty chemical industries. In that purpose, batch distillation is a separation process of choice. For azeotropic or close-boiling mixtures, the addition of an entrainer, partially or totally miscible with one of the initial binary mixture components, is viable and its choice is the first key issue of azeotropic batch distillation. A whole set of entrainer selection rules has been published for both homogeneous and heterogeneous azeotropic distillation for the separation of azeotropic binary mixtures or close boiling components (Rodriguez Donis, 2001a and 2001b). These rules also hint at a feasible sequence of batch needed to perform the separation together with the initial feed stream location in the ternary diagram. But the optimisation of the batch sequences is a second key issue and this contribution validates a framework for the optimisation of complex distillation.
2. Problem definition The goal of batch sequences optimisation is to minimise an overall economical criterion while respecting constraints such as purity, .... It can be considered as a nonlinear constraint optimisation problem. The classical formulation involves an objective function ~ , equality constraints and inequality constraints (gi and hj respectively):
Author/s to whom correspondence should be addressed :
[email protected] 1082 Min
f (x)
gi(x) = 0
i = 1,..., ng
hj(x) < 0
j = 1,...,n h
(1)
2.1. Objective function The objective f u n c t i o n f i s the summation of six cost functions ci: Table 1. Economical cost functions taken into account in the objective function 6
cost f = Z ci object function 1 cl c: c3 c4 c5
expression
immobilisation energy load entrainer column treatment
c~ = c: = c3 = c4 =
used variable
al.t + bl a:. Q a3.L a4.E
c5 = as.R + b5
t = total separation duration Q = total required energy L = global column load E = entrainer amount added initially R = residual column load
lit
C6
tanks treatments c6 = Z a~'Tk + b6k Tk = final load of each of the nrtanks (including still) k=l
2.2. Constraints The constraints of the NLP problem are defined with respect to target purity and/or quantity specifications at the end of the distillation process. Each constraint hj is expressed as follows: (2)
h j : x k - xik obj
where x/k and X~obj are the effective and target fraction of component i in tank k.
2.3. Action variables Action variables are chosen among all the available running specifications of the batch process, that is a collection of successive tasks and the initial load of entrainer (Table 2). Table 2. Available action variables
Available action variable (* for each task i) Entrainer load Boiling duty * Subcooling temperature *
Task duration * Reflux ratio of light phase * Reflux ratio of heavy phase *
3. Problem resolution 3.1. Overall resolution software architecture The proposed optimisation methodology lies on a rigorous simulation of the considered batch processes. Most of the variables values required to evaluate the objective function and the constraints are calculated through this process simulation. From a defined column configuration and defined initial settings, a full MESH (Material balance,
1083 Equilibrium, Summation of molar fraction, Heat Balance) set of differential algebraic equation is solved using the ProSim BatchColumn software (ProSim SA, France). Main results from the batch simulations are mass and composition in each distillate tank and in the boiler, as well as the total heating and cooling duties. The economical optimisation criterion and the constraints values is evaluated from these results. These evaluations stand for the heart of the resolution software architecture, as shown in
Figure 1. Optimisation algorithms offer strategies to change the values of the action variables in order to solve the constraint minimisation problem. Simulation
Batch Column simu1ator ~~,,,,~~.~
Lsettings [
Action
i
Manager ~,q variables J criteria ~ evaluation ~ Action variab1es • Simulation '7 ~ ~ j ~ Objectivefunction value
results
simulation
1 Optimisation pack
Constraints value
objective function and constraints evaluation
optimisation
Figure 1. Optimisationsoftware architecture 3.2. Optimisation methods Two optimisation techniques are used: a SQP-based deterministic method, and a home made Genetic Algorithm as a stochastic one. The SQP algorithm is the donlp2 tool, available at www.netlib.org (Spellucci, 1998). It incorporates the exact ll-merit function and a special BFGS quasi-Newton approximation to the Hessian. The optimisation problem is strictly equation (1). The genetic algorithm is real-coded. In order to use such an unconstrained optimisation technique, the constraints are introduced into the objective function by penalty terms. The optimisation problem aims then at finding the minimum of the following it; function:
{O with
P, (x) -
80
if gi (x) -- O tf g; (x) ~ 0
{O and
Qi(x)-
oo
if hi (x) O
and Pi ° and Qi ° are weighting factors proportional the inverse of the squared tolerances on the constraints.
4. Separation of pyridine from water using toluene as entrainer 4.1 Problem settings We study the separation of the minimum temperature homoazeotropic binary mixture w a t e r - pyridine. According the Rodriguez-Donis et al. (2002) and Skouras (2004), the separation is possible using a heterogeneous entrainer. Toluene is added to the mixture, forming a minimum temperature homoazeotrope with pyridine and a minimum
1084 temperature heteroazeotrope with water. Three distillation regions exist with the w a t e r toluene heteroazeotrope being the unstable node in each region and the stable node being the pure vertexes. The distillation boundaries are strongly curved and tangent to the vapour line at the heteroazeotrope, like any residue curve in the VLLE region. During the heterogeneous batch rectification process, removal of the aqueous phase in the decanter is expected and reflux of either the non-aqueous phase or a combination of both decanter phases is possible. In this work, the whole non-aqueous decanter phase is refluxed. This operating mode is called Mode B by Skouras (2004) who described elegantly the heterogeneous batch distillation process issue and feasibility in complement to Rodriguez-Donis et al. (2002). According to Skouras (2004), the initial charge composition must be above the line p y r i d i n e - aqueous phase to make the process feasible. The batch distillation boundary has no impact on mode B process feasibility (but does on mode A, see Skouras (2004)). The residue curve/distillation boundaries have no impact on feasibility despite their curvature. Table 3. VLL and LL Thermodynamic parameters (liquid." NRTL," gas." ideal gas)
Parameter value (cal/mol)
Aijo
Ajio
otijo
Water- Toluene Water- Pyridine Toluene - Pyridine
3809.1 1779.18 264.64
2776.3 416.162 -60.34
Aijv
0.2 0.6932 0.2992
AjiT
21.182 0 0
GtijT
-7.3179 0 0
0 0 0
F o r N R T L : gij-gjj=Aijo+AijT.(T-273.15); gji-gi~=Aj~o+AjiT.(T-273.15); ~ij=Gtij0+GtijT.(T-273.15)
.....
298K LLE enveloppe
toluene [sn] (383.8K)
VLLEResidueenVeloppecurves
/#, ,W~I!,.,, \
.................................. Residue curve boundary . . . . .
......
_ j~, ~ Still path
Batch distillation boundary Vapour line Az tol-pyr [sa] (383.3K)
' / ',
o o o o Distillate path
',
/ \ '\ .~" ....................... 7\............................ ~!~ A
#
'~
/
'~z~/~,:j
/;:\,,
/%
'\\
/",X /\,,
/./,S
A+B
~~ >R
where A (a diazonium salt) is initially charged in the reactor and B (a pyrazolone) is added continuously at a constant rate. R, a dyestuff is the product and S the unwanted
1090 by-product. The reaction kinetics, operating conditions and kinetic parameters are reported in (Nienow et al., 1992). The height and diameter D of the vessel are both 0.3m. Four 0.1D strip baffles were used with a Rushton turbine with diameter DI=D/3 and clearance C=D/3. A 3-D NoZ model was constructed using 20 zones in each direction (axial, radial and circumferential -8000 zones in total) resulting in a system of 48000 ODEs which were integrated in time using DASPK (Maly and Petzold, 1996). Fig.2 shows a comparison between results from the 3-D network (diamonds) experimental results (squares) and simulation results from the literature (triangles- Nienow et al 1992) for a range of impeller rotation speeds. Simulations assuming ideal mixing (circles) over-predict the yield. Our 3-D simulations agree very well with the experiments and are in better agreement than the literature results, which are, however, close since the volume change effects are small in this case. Further parametric studies have shown that better yield can be achieved by supplying both feeds continuously from the same feed position near the tip of the impeller. These results along with results from a second case study where volume change effects were more pronounced (Paul and Treybal 1972) are presented in a forthcoming publication (Zheng et al, 2004). 0.97
0
0
0
0
0
0.96 0.95 0.94 0.93 0.92
.....~i~.....!i
~
~dtea~Mi~ng
0.91 0
50
1O0
150
200
250
300
350
Rotation Speed(RPM)
Figure 2. Comparison between yield predictionsfrom our 3-D model, and experimental and simulation results from the literature.
i~i~:!~:~~!i:~:i:!i? i~i,i:~,i~:~'~~i~:i
3 seconds
18 seconds
Figure 3. Concentration snapshots o f the product R on a vertical plane in the reactor vessel at t=3 and t = 18 s. The blue (red) colour denotes low (high) concentration.
1091 Fig. 3 shows concentration distribution profiles of species R at a vertical plane inside the reactor at t-3 and 18 s. The right side is the reactor centreline. The impeller rotation speed was 78 RPM. Blue (red) colour denotes low (high) concentration. The concentration at the top empty zones is zero. As it can be seen, areas of lower mixing intensity are the comers of the reactor, the impeller shaft and the circulating zones. As time progresses reactants in these parts eventually participate in the reactions and are converted to products or by-products.
3. Reduced model The NoZ model coupled with flow correlations typically results to systems containing (hundreds of) thousands of ODEs. The simulation of large-scale ODE-based systems is nowadays achievable in realistic CPU times with large yet reasonable memory requirements. Nevertheless, optimisation studies and optimal control design and implementation cannot be based on such large-scale systems since a huge number of function evaluations is required. In this work we have employed the Proper Orthogonal Decomposition method (POD) (Holmes et al., 1996) to extract accurate low-order models from the full-scale ones. In POD a small number of semi-empirical eigenfunctions are computed from a database of detailed full-scale simulations (or even experiments) that can capture the energy of the system i.e. can accurately describe the system in the parametric range of interest. The dynamic low-order model can then be obtained by a Galerkin projection of the governing equations onto these few basis functions. POD has been used successfully in a number of works (e.g. Rowley et al, 2004; Cizmas et al, 2003; Shvartsman et al 2000). Here the s c a l a r - v a l u e d method is employed (Rowley et al. 2004) computing POD modes for each variable (concentrations and reaction volume). We have constructed a simulation database for the case study presented above, by performing simulations using the NoZ model at 3 different rotation speeds: 39 RPM, 197 RPM and 302 RPM recording snapshots every 0.5s. It was found that 20 basis functions for each species (100 in total) and only 1 basis function for the volume were sufficient to capture 99.9 % of the energy of the system. A Galerkin projection of equations (1)-(3) onto these eigenfunctions produced a reduced model of only 101 ODEs that can accurately predict the system behaviour.
~:~:'i!!!ii!i!ii!ili!
i 3 seconds
.........
l
i 18 seconds
Figure 4.Concentration snapshots of the product R at t=3 & 18 s on a vertical plane in the reactor obtained from the reduced model. The blue (red) colour denotes low (high) concentration.
1092 In Fig. 4 concentration profiles obtained from the reduced model at the same conditions as the profiles showed in Fig. 3 are depicted. As it can be seen the agreement between the full-scale and the reduced model results is excellent both for the short term (3s) and for the longer term (18s) dynamics. It is worthwhile to note that the case simulated here (impeller speed 78 RPM) is not included in the simulation database. Results of this reduced model at other conditions also show the same agreement with results from the full model. It can be concluded that the reduced model can predict the system behaviour very well requiring much less computer memory and CPU time.
4. Conclusions We have constructed 3-D models of batch and semi-batch reactors using a network of zones discretisation. The computational domain is discretised in an appropriately large number of cells and local velocity distributions are computed by detailed flow correlations. Mass balances coupled with volumetric changes are then superimposed onto the computed flow resulting in large-scale ODE-based systems. The model can successfully predict the effects of non-ideal macro-mixing and includes a large number of important design and operating parameters than can be used for system scale-up, optimisation and control. The POD method was subsequently used to extract reduced computationally-amenable models from the full-scale ones that can be efficiently employed in parametric studies, model-based optimisation and optimal control.
References Bakker, A., A.H. Haidari and L.M. Oshinowo 2001, Chem. Eng. Prog., 97, 45. Brucato A., M. Ciofalo, F. Grisafi, R. Tocco 2000, Chem. Eng. Sci. 55,291. Cizmas, P.G., A. Palacios, T. O'Brien and M. Syamlal 2003, Chem. Engi. Sci. 58, 4417. Cui, Y.Q., R.G.J.M. van del Lans, H.J. Noorman and K. Luyben 1996, Chem. Eng. Res. Des. 74, 261. David, R., H. Muhr and J. Villermaux 1992, Chem. Eng. Sci. 47,2841. Desouza, A. and R.W. Pike 1972. Can. J. Chem. Eng. 50, 15. Holmes P., J.L. Lumley and G. Berkooz 1996, Turbulence, coherent structures, dynamical systems and symmetry, Cambridge University Press. Hristov, H.V. and R. Mann 2002, IChemE, 80, 872. Maly, T. and L.R. Petzold 1996, Appl. Numer. Math. 20, 57. Nienow, A.W., S.M. Drain, A.P. Boyes, R. Mann, A.M. E1-Hamouz, and K.J. Carpenter 1992. Chem. Eng. Sci. 47, 2825. Paul, E. L. and R.E. Treybal 1971 AIChE J. 17, 718. Platzer, B. and G. Noll 1988. Chem. Eng. Proc. 23, 13. Rahimi, M. and R. Mann 2001 Chem. Eng. Sci. 56, 763. Rowley, C.W., T. Colonius and R.M. Murray 2004 Physica D: Nonlin Phen. 189, 119. Shvartsman, S. Y., C. Theodoropoulos, R. Rico-Martinez, I.G. Kevrekidis, E.S. Titi and T.J. Mountziaris 2000 J. Proc. Control, 10, 177. Vrabel P, R.G.J.M van der Lans, K.Ch.A.M. Luyben, L. Boon and A.W. Nienow 2000, Chem. Eng. Sci. 55, 5881. Zaldivar, J. M., H. Hernfindez and C. Barcons 1996 Thermochimica Acta, 289, 267. Zheng X., R. Smith and C. Theodoropoulos, Manuscript in preparation.
European Symposium on Computer Aided Process Engineering - 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.
1093
Optimal Start-up of Micro Power Generation Processes Paul I. Barton a*, Alexander Mitsos a, and Benoit Chachuat a a
Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue (room 66-464), Cambridge, MA 02139-4307, USA
Abstract Fuel cell based systems are a promising alternative to batteries in man-portable power generation applications. These micro power generation processes must operate fully autonomously and automatically without the intervention of operators. Operational considerations are indeed so important that they influence the optimal design, following the paradigm of interaction of design and operation. This paper presents a methodology for the simultaneous optimization of design and operation of such systems. We illustrate the methodology with two case studies, focusing on the start-up procedure. A small rechargeable battery is necessary to satisfy the power demand during the start-up while the device temperature is too low for power generation. The optimization problem is formulated as minimization of the mass of fuel and battery required to heat the device up to operating temperature.
Keywords: man-portable power; micro power generation; micro fuel-cell system; optimal start-up operation; dynamic optimization
1. Introduction The widespread use of portable electric and electronic devices increases the need for efficient man-portable power supplies (up to 50 W). Currently, batteries are the predominant technology in most applications, even though they have a large environmental impact, high cost and relatively low gravimetric and volumetric energy densities; furthermore, the upper limit on performance is now being reached. Out of the alternatives that are possible, we are focusing on micro scale power generation devices based on the electrochemical conversion of common fuels and chemicals, such as hydrocarbons or alcohols, in fuel cells. These process-product hybrids have the potential to yield much higher energy densities than state-of-the-art batteries, because the above mentioned fuels have very high energy contents and fuel cells can in principle achieve very high efficiencies. Since most power consuming devices are operated periodically and have rapidly changing power demands, the dynamics and automated operation of portable power production are very important and must be considered thoroughly. In this paper, the focus is on the optimal start-up of micro power generation processes. It is most likely that the devices will be coupled with a relatively small, rechargeable battery; its role is to ensure that the power demand is met when the fuel cell is unavailable or can only Author/s to whom correspondence should be addressed: pib@mi t. edu
1094 satisfy part of the demand, to provide the energy needed to heat the stack up to a temperature at which chemical and electrochemical reactions are fast enough, or to provide an electric spark for the initiation of a combustion reaction.
2. Methodology Our methodology relies on the assumption that intermediate fidelity models can approximate the performance of the devices and can be used for optimization purposes. Our models do not require the specification of a detailed geometry and rely mainly on first-principles, containing only a minimal number of modeling parameters. This is possible because the relative importance of physical phenomena at the micro scale makes one-dimensional spatial discretization sufficient. We assume that the molar flux in the gas channels of the fuel processing reactor, fuel cell and burners is convective in the flow direction (PFR), and axial diffusion can be neglected; on the other hand we assume that diffusion in the radial direction is fast enough to ensure a uniform profile in the cross-section. These assumptions have the consequence that micro-fabricated units such as reactors or fuel cells can be approximated by an idealized model using 1-D species balances, without the inclusion of the diffusion term. We neglect the pressure drop along the gas channel and assume an ideal gas. Back-of-the-envelope calculations based on the expected device dimensions using Hagen-Poiseuille's equation provide an estimated pressure drop in the order of a few kPa, i.e., a relative pressure drop of a few percent only. We note that this value is in good agreement with the measurements for a micro-fabricated reactor made by Arana (2003). As a consequence, no solution of momentum equations is necessary. We further assume that heat transfer is fast enough, so that the temperature throughout the device, or regions of the device, is near uniform. This is typically the case at the micro-scale for silicon based reactors. Finite element simulations were also performed, which confirm this assumption. It is important to note that considering a uniform temperature allows one to not specify a particular geometry for the unit operations and their arrangement in the stack. Otherwise, not only the generality of our study would be inherently affected, but problems would also be encountered as several micro devices and components of the proposed processes are not fully developed thus far. Due to material constraints and technological limitations the start-up time will be in the order of at least one minute, much longer than the residence time of gases in the process, which is in the order of ms. We therefore assume pseudo-steady-state concentration profiles along the various units at each time instant. This assumption allows us to solve the concentration profile at each time step using an integration along the spatial axis, similar to the the steadystate case (Chachuat et al., 2004) without requiring method of lines semi-discretization of the state variables; in some cases this assumption even allows the calculation of analytical solutions for the concentration profile. It should be noted that if one wanted to explicitly calculate the material stresses developed, a fully transient model would be necessary. The objective of the start-up problem is to bring the fuel cell to its nominal temperature while minimizing the total mass (battery and fuel) required for this heat-up and meeting the nominal power demand at all times. In the case studies we assume that the battery
1095 can also be used for heat-up of the device. Additional constraints can also be specified, such as a maximum rate of change for the temperature based on structural stability considerations, or requirements concerning the emission of toxic gases. Since different operating modes are described by different sets of equations (e.g., discharging and recharging of the battery), the start-up problem is formulated as a hybrid discrete/continuous dynamic optimization problem (Lee and Barton, 2002). This optimization problem is solved by using recent developments in numerical methods for dynamic optimization with hybrid systems embedded.
3. Case Studies 3.1. Case Study 1: Butane Based Process A very promising process for micro power generation is the partial oxidation of butane, with subsequent electro-chemical conversion of the generated syngas in a Solid Oxide Fuel Cell (SOFC) (Mitsos et al., 2004a); one of the main advantages of this process is that butane has a very high energy content, and partial oxidation is an exothermic reaction. Therefore, oxidation of the fuel cell effluents is sufficient to overcome the heat losses at steady-state operation. A conceptual flowsheet for the process is shown in Figure 1; the reactor, fuel cell and catalytic burner are assumed to be thermally coupled and operate at a common uniform temperature. The drawbacks of this process are that butane partial oxidation has not yet been demonstrated at the micro-scale and limited kinetic data are available; therefore the model presented should be considered preliminary and the results qualitative rather than quantitative. air
~it +
air
re+:~q~,~r
i ..,
k
L.
'
;:.,+
~
+
+
S()F(!
.............
...............,. ........
! + =
-
•...........++ ........
+ +~'/.+:,1,:~
............. =-
T,+
-.+:,
!
~
i
;
! ........
+
..+++i+,
.+
,;
|~_~.
W~:~,~ t (i ~'
,
,
+
+
:~................................................................. ~,. powel.
+ Iauxiliarv ',
tl)~!~'~l~:!t+
+
(~~.:lt ])l.ll:
; +'
,i
................................................ l
Figure 1. Conceptual f l o w s h e e t f o r butane based process.
We now present results obtained from optimization of the butane based process at a nominal power output of 1 W and a nominal operating temperature of 1000 K. Figure 2 illustrates the optimal profile, obtained by applying a piecewise constant approximation with 50 control segments of equal duration to solve the problem. The optimal start-up procedure duration was determined to be around 150 s. The number of time intervals has an insignificant influence on the start-up performance in terms of the objective function.
1096 2
~S X
J
1.5
- -
jj ....
0
~,.oJ
¢
.2 0
~..~
0
~ ....................................
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0
20
~ . . . . . . . . . . .
40
~ .....................................
60
~
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
80
.
.
.
.
.
.
................
li00
! ......................................
120
~
.
.
.
.
.
.
.
.
.
.
.
140
:160
t,im.e (s) t200 s tack
t e n i p e 1:a t u .re
t000
.
800
© 600
400
200
0
20
4o
eo
80
100
~20
~40
160
Figure 2. Time profiles for optimal start-up of butane process.
3.2. Case Study 2: Ammonia Based Process Ammonia is often considered as a potential energy source in fuel cell systems, e.g., Metkemeijer and Achard (1994), because ammonia decomposition produces hydrogen. A drawback of this process is that ammonia is corrosive and toxic and therefore tight constraints regarding the emission of residual ammonia need to be imposed. Also, ammonia decomposition is an endothermic reaction and therefore a heat source is required. While oxidation of part of the hydrogen produced could be used to provide the necessary heat, a more promising approach Mitsos et al. (2004b) is the use of a secondary fuel with a high energy density, such as butane. In Chachuat et al. (2004), we have considered optimal steady-state operation of the process shown in Figure 3 and we now extend this work to transient operation.
1097 air
air
f
i
SOiTT"
r (.,:.~ac 1:,:::~r
~.~
" I
I { ....... --I .....
i~.1i " i i
:
b i i....... riier I
c?
I
I I ......I............. ...... I II
~
ii
....... ,
i
i
"
I
~
,:
i
~
:
.:
~ ,S/o:~:/,:
w a ~'i @
1
~Iauxilia~ i
p o ~re r o u I p u t
.............................. J
Figure 3. Conceptual lTowsheetfor ammonia based process.
The scope of this paper does not permit a detailed discussion of the start-up procedure for the ammonia based process. Instead we present how, for a fixed design, the fuel energy density (in Whr/Kg) changes as a function of the power output. This consideration is very important for the transient operation, since at start-up it is plausible to gradually increase the flow through the fuel cell. Furthermore, the power demand of power consuming devices is time varying and there is a trade-off between running a process away from its optimal operating point and consuming more energy from the auxiliary battery. In Figure 4 the design optimized for a nominal power demand of 10 W (Chachuat et al., 2004) is used and the energy density based on optimal steady-state operation is shown in comparison to the design optimized for the given power output, it should be noted that we do not consider a variation of the operating temperature, assuming that the design was done for the maximal allowable temperature, based on material constraints. The energy density is maximal at a power demand slightly higher than the one for which the system was designed (~ 10.1 W). For power demands lower than the design power output, the heat generation is small, and relatively more butane needs to be burned to compensate for the heat losses. For an increasing power output, the ammonia flowrate is increased and the fractional conversion in the reactor and fuel cell is decreased; the constraints on residual concentrations of ammonia and nitric oxide in the outlets are only met with a largely increased flow of oxygen, which results in higher requirements for heat and a higher butane flow rate. The flow rate for oxygen quickly becomes so large that the pressure drop through the system would become significant, making the process practically infeasible and also violating one of our main modeling assumptions. This case study shows that it is necessary to consider variations in the power demand during the design of the system, and a promising method is stochastic optimization.
1098
.........
I)e::,:g ~ Ol;)timized for power demand -...... Fixed d.~!~ign (oi:~timized for 10W)
200:0
!
1500
....... ~........ :.....
~ ....
i:
.i ..................~ ....S>~:> min max{Jo,... , Jm } --->Q
(3)
The overall parameter vector Q is applicable to all regimes rather than a single regime. The following equation is used to determine the pre-filter gain for SISO systems:
LimlP s ~ O
(s)(, "
G i (s)E(s))
' G i (s)E(s)] - 1
(4)
"
4. Case Studies A continuous stirred tank reactor model originally proposed by Morningred et al. (1990) and further analysed by Bartholomaus (2002) is selected as the first case study. The model is represented as:
dC~
_ q (Coo _ C~
) - k oC exp(-E' / RT)
dT : q (r o -r)+k,C~ dt V
(5) exp(-E'/RT)+
k2qc[1-exp(-k 3/q~)](r~o-r)
The nominal values of model parameters are available from Momingred et al. (1990). We treat k2qc[1-exp(-k3/qc)] together as the control variable u. The control objective is to drive the concentration Ca from the initial operating point Ca - 0.06 to the final operating point Ca = 0.16 along a specified staged trajectory by adjusting the coolant flow rate qc. The process is open loop unstable with multiple steady states. The conventional (Bartholomaus, 2002; Wang et al., 2003) and improved performances are shown in Figure 2. The system becomes open loop unstable as Ca > 0.140. It can be shown from Figure 2a that the conventional control leads to notable deviations from desired trajectory in the unstable regime. The most unacceptable fact is that when the conventional controller gain increases 10%, chaotic dynamics appear as shown in Figure 2b. This implies that the conventional controllers are of little practical significance due to the robustness concern. The newly developed control scheme allows a broad range of controller gain variations. The control variable profile and its deviations from steady state are depicted in Figures 2c and 2d, and this is easy to achieve. The number of local models is reduced from 10 (Wang et al., 2003) to 5 using
1115
the proposed approach. than 10 were used.
Previous work by Bartholomaus (2002) suggests many more
b: Chaos under Controller Gain Change
a Concentration Dynamics 0.18
0.3 Improved Performance ..........
___0.16 O
,.-...
r_r-
"5 0.25
.......
E .._~.
E .._.. =
=0.14
..... ~ 0 1. 2
,~r
0 1"
....,
Conventional Performance
~
o
'0 o
Under Conventional Control
.o ..,_, 0.2
O ..,._,
e--
~0.15 8 ~
,7
o 0.08
..........
~_r~-~-
0.1 r~.~--
=y 0.06
ill
50
100 150 Time (minutes)
0.05
200
50
0
c Control Profile in New Scheme
100 150 Time (minutes)
200
d: Control Deviation in New Scheme
1.2
0.025 ,.--...
,.-,.
~.~
_.__.r~
.,._~.
..- (
,,.---
0.02 " /" /, ,,
v-F
E 0.015
. ~. ~ r
tO
o.oi
(-"t-
•
>
>
t"---
c~ 0.005
_j'
£O.9
O
cO
"
0
0 0
o
0.8
50
100 150 Time (minutes)
-0.005
200
50
0
100 150 Time (minutes)
Figure 2. Control of a chaotic CSTR a OynBmics u n d e r T h r e e Control S c h e m e s 2.6.~ ........................,. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i:
Improved Performance
!
b: O s c i l ! t a t i o n
under Conventional Control
!.6
:
~7
2.4
1.55
i
2.2i-
....j ~
.-°
x
~
2i .~
1,81
8
~,. i ~-'
~
Convenlional Performance
,;~~ '........i
N I 4
t.6i ¸
g
,
, }.5 r...
,
..........................................i
1.4ir _('(
1.3 I
1,2i / i/ i~
1
iB
0.%
Step-up Conllrol Leading t o Undesirable Steady Stale
o12
o:~
o6
08
Dimensionless T i m e l{A:f, t~ = I 0 0 0 0 (h)
1.251
1.21 ................................................................................i 0
0.1 Dimens.ionle,ss
Time
0.2 tit r, t r = 1 0 0 0 0
Figure 3. Control of ZMC with bifurcation behaviour
0.3 (h)
200
1116 The second case study is a Zymomonas mobilis reactor. Its model was fully described by McLellan et al (1999) and further analysed by Zhang and Henson (2001). The model consists of 5 state variables. We choose biomass X as the output and dilution rate D as the manipulative variable. The conventional and modified performances can be seen in Figure 3. Figure 3a shows the performance with three different control schemes with an indication of multiple steady states. Figure 3b shows the oscillatory behaviour using conventional control schemes without state feedback. Similar to the first case study, oscillations become severe with a slightly disturbed controller gain. Both performance and robustness have been improved significantly using the proposed control scheme. Three local models are sufficient for effective control of this process. For both processes, the controller format is" (qls2+q2s+q3)/(q4s2+qss+1), and the pre-filter equation is: pi/(s+l), where q~-q5 are determined through mini-max optimisation, and the regime dependent parameter Pi is computable using Equation (4).
5. Conclusions Through the theoretical development and simulation studies on control of two nonlinear processes with chaotic dynamics, the following conclusions can be drawn: 1.
2.
3.
Although a class of non-linear processes with chaotic dynamics can be stabilised using conventional control schemes, this work has shown that robustness is the main issue preventing the industrial application of the reported methods. State feedback for pole placement is an effective strategy amenable within the framework of the multiple model approach, leading to significantly improved performance and robustness with a dramatically reduced number of local models. The mini-max optimisation techniques enable the design of a global controller without relying on membership and validity functions. An integration of mini-max optimisation, pre-filter design, state estimation using Kalman filter and state feedback leads to the development of robust, offset free control systems for nonlinear, unstable processes.
Reference Balas, G.J., J. C. Doyle, K. Glover, A. Packard and R. Smith, 1995, ~t-Analysis and Synthesis Toolbox For Use with MATLAB, The Math Works, Natick. Bartholomaus, R., 2002, Contr. Eng. Practice, 10, 941. McLellan, P.J., A.J. Daugulis J. and J. Li, 1999, Biotechnol. Prog., 15,667. Morningred, J.D., B. E. Paden, D. E. Seborg and D. A. Mellichamp, 1990, Proc. ACC, 1614. Murray-Smith, R and T. A. Johansen Eds., 1997, Multiple Model Approaches to Modelling and Control, Taylor and Frances, London. Samyudia, Y., P. L. Lee, I. T. Cameron and M. Green, 1996, Comput. Chem. Eng. 20, $919. Shorten, R., R. Murray-Smith, R. Bjorgan and H. Gollee, 1999, Int. J. Control, 72, 620.S. Wang, F.Y., P. Bahri, P.L. Lee and I.T. Cameron, 2003, Proc. PSE 2003, 1065. Zhang, Y. and M.A. Henson, 2001, Biotechnol. Prog. 17, 647.
Acknowledgements The authors would like to acknowledge the financial support from the Australian Research Council (ARC) through a Large Grant Scheme for project A 10030015.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espuna(Editors) ~>2005 Elsevier B.V. All rights reserved.
1117
A Robust Discriminate Analysis Method for Process Fault Diagnosis D. Wang* and J. A. Romagnoli Dept. of Chemical Engineering, the University of Sydney, NSW 2006, Australia
Abstract: A robust Fisher discriminant analysis (FDA) strategy is proposed for process fault diagnosis. The performance of FDA based fault diagnosis procedures could deteriorate with the violation of the assumptions made during conventional FDA. The consequence is a reduction in accuracy of the model and efficiency of the method, with the increase of the rate of misclassification. In the proposed approach, an M-estimate winsorization method is applied to the transformed data set; this procedure eliminates the effects of outliers in the training data set, while retaining the multivariate structure of the data. The proposed approach increases the accuracy of the model when the training data is corrupted by anomalous outliers and improves the performance of the FDA based diagnosis by decreasing the misclassification rate. The performance of the proposed method is evaluated using a multipurpose chemical engineering pilot-facility. Key Words: discriminant analysis, robustness, fault diagnosis, and process monitoring.
1. Introduction Chemical processes experience abnormal conditions that may lead to out-ofspecification products or even process shutdown. These abnormal conditions are often related to the same root causes. Data driven process fault diagnosis techniques are often employed in process industries due to their ease of implementation, requiring very little modelling effort and a priori information. Given that there are multiple datasets in the historical database, each associated with a different abnormal condition (root cause), the objective of fault diagnosis is to assign the on-line out-of-control observations to the most closely related fault class. Fisher discriminate analysis (FDA) is a superior linear pattern classification technique, which has been applied in industry for fault diagnosis (Russell et. al. 2000). By maximising the scatter between classes and minimising the scatter within classes, FDA projects faulty data into a feature space so that data from different classes are maximally separated. Discriminant functions are established associated with the feature space so that the classification of new faulty data is undertaken by projecting it into the feature space and comparing their scores. As a dimensionality reduction technique for feature extraction as PCA, FDA is superior to PCA because it takes into account the information between the classes and is well suited for fault diagnosis. FDA also has better performance than other techniques such as KNN and SIMCA (Chiang, et. al. 2004). to whom correspondence should be addressed:
[email protected] 1118 Even through the above advantages, there are still unsolved issues within the application of FDA approaches. One key aspect is the robustness of the approach when dealing with real data. It is known that, in FDA, the most difficult assumption to meet is the requirement for a normal distribution on the discriminating variables, which are formed by measurements at interval level. Practical examination tells us that the real plant data seldom satisfy to this crucial assumption. The data are usually unpredictable having, for example, heavier tails than the normal ones, especially when data contain anomalous outliers. This will inevitably result in the loss of performance leading in some cases to wrong modelling in the feature extraction step, which in turn leads to misclassifications of the faulty conditions. In this paper, a robust discriminant analysis method for process fault is presented. In the proposed approach, without eliminating the data in the training set, robust estimations of with-in-scatter matrix and between-class-scatter matrix are obtained using reconstructed data using M-estimator theory. A winsorization process is applied in the score space, which eliminates the effects of outliers in the original data in the sense of maximum likelihood estimation. The robust estimator used in this work is based on the Generalised T distribution, which can adaptively transform the data to eliminate the effects of the outliers in the original data (Wang et. al. 2003, Wang et. al., 2004). Consequently, a more accurate model is obtained and this procedure is optimal in the sense of minimising the number of misclassifications for process fault diagnosis.
2. Process Fault Diagnosis Using Discriminant Analysis 2.1 Discriminant analysis Let the training data for all faulty classes be stacked into a n by m matrix X ~ 9~..... , where n is the observation number and m is the variable number. The within-classscatter matrices S,,, and the between-class-scatter matrix S b contain all the basic information about the relationship within the groups and between them (Russell et. al. 2000). The FDA can be obtained by solving the generalized eigenvalue problem: Sbu k = 2~Swu k , where 2 k indicates the degree of overall separation among the classes by projecting the data onto new coordinate system represented by u;. After the above process, FDA decomposes the observation X ~ 9~"×m as (1)
X "-- T U T : £ ti~Ti i:1
2.2 Process fault diagnosis based on FDA After projecting data onto the discriminant function subspace, the data of different groups will cluster around their centroids. The objective of fault diagnosis is to assign the on-line out-of-control observations to the most closely related fault classes using classification techniques. An intuitive means of classification is to measure the distances from the individual case to each of the group centroids and classify the case into the closest group. Considering the fact that, in the chemical engineering measurements there are correlated variables, different measurement units, and different standard deviations, the concept of distance needs to be well defined. A generalized distance measure is introduced (Mahalanobis distance): O2(xi [ G, )=(x, - Y,
)vk-l(xi - Xk) T ,
where
1119
D2(x, I G~_) is the squared distance from a specific case x; to 2~, the centroid of group k, where V/, is the sample covariance matrix of group k. After calculating D 2 for each group, one would classify the case into the group with the smallest D 2 , that group is the one in which the typical profile on the discriminating variables most closely resembles the profile of this case. By classifying a case into the closest group according to D -~, one is implicitly assigning it into the group for which it has the highest probability of belonging. If one assumes that every case must belong to one of the groups, one can compute a probability of group membership for each group: P(GI, :"i)= P(xi G k / ~ P ( x i
Gi). This is a posterior
probability; the classification on the largest of these values is also equivalent to using the smallest distance.
3. R o b u s t D i s c r i m i n a n t A n a l y s i s B a s e d on M - e s t i m a t e W i n s o r i z a t i o n The presence of outliers in the training data will result in deviations of discriminant function coefficients from the real ones, so that the coordinate system for data projection may be changed. Fault diagnosis based on this degraded model will inevitably increase the misclassification rate. A robust remedy procedure is proposed here, to reduce the effects of outliers in the training data. After implementing FDA, the outliers in the original data X c 9~...... can manifest themselves in the score space. By recurrently winsorizing the scores and replacing them with suitable values, it is possible to detect multivariate outliers and replace them by values which conform to the correlation structure in the data.
3.1 Winsorization Consider the linear regression problem: y = f ( X , O ) + e ,
where: y is a n×l vector of
dependent variables, X is a n xm matrix of independent variables, and 0 is a p xl vector of parameters, e is a n xl vector of model error or residual. An estimation of parameter 0 (t~) can be obtained by optimization or least squares method. With the parameter
t}
estimated,
the
prediction
or
estimation
of
the
dependent
variable y i ( i - 1 ..... n) is given by ; ' i - If(x,, t~) and the residual is given by r~ = y , - ;,,. In the winsorization process, the variable ),~ is transformed using pseudo observation according to specified M-estimates, which characterizes the residual distribution. The normal assumption of residual data will result in poor performance of winsorization. In this work, we will fit the residual data to a more flexible distribution, i.e. the generalized T distribution, which can accommodate the shapes of most distributions one meets in practice, and then winsorize the variable y, using its corresponding influence function.
3.2 Robust discriminant analysis based on M-estimate winsorization The proposed robust estimator for FDA modelling is based on the assumption that the data in the score space follow the generalized T distribution (GT) (Wang and Romagnoli, 2003), which has the flexibility to accommodate various distributional shapes:
1120 P
f~r(u,'o,p,q)= 2crq,/PB(1/p,q)(1+ i,l,~/qo.,~)~+,,,~
-oo < .
f ,'
ii /
i~° b
1U
lr"
V . r t , "[Sbb,
..........,
2. . . .
[ //',"i
[35
.......
5
':,
Aii
~: 1%
l(]
/
i,¸
20
2q
30
35
T I
',/ i /! /
/
i i /'~ / ii/i/
i~
Latent Variable 1 Iteration 1 Split Value 1.5793
,....
/i :i::i/'/
"~
1 .)
i "a'e°'Var'ae I Iteration 2 Split Value 2.6555 , 1
. . . . . .
i La'en'Var'a 'e'1 I Iteration
Vor,,,,;:i. . . . . . . . .
1 Good
| ) "
3
, Poor
Split Value 3.278 l 1
[
Poor
1
Figure 3- Iterative decision tree Table 3- Accurac3, o/the iterative decision tree
Leaf Number
Number of Samples
Number of Samples Correctly Classified
l
12
l0
2 3 4
4 0 1
1 N/A 0
% Accuracy 83 25 N/A 0
Table 3 shows the results of the validation of the iterative decision tree. These results are comparable with both the univariate and pre-processed decision trees but the process understanding that the multivariate approach provides is much more useful to the end user than the univariate tree. The concept of using the errors as input to the next iteration of the tree means that all of the available information can be used in the development of the tree improving the information that is available to the end user.
5. Conclusions This paper has shown that where there are relationships between variables it is beneficial from a process understanding perspective to consider combinations of these variables to eliminate the correlation and assist in the decision making process. The technique suggested here is to pre-process the data using a multivariate technique such as principal components analysis and use the result of this analysis as the input into the
1134 decision tree. The use of such a technique orthogonalises the data and as a result the data fed into the tree is independent of the other variables. The second method described first produces a model relating the input to the output and then using this model, where again the inputs are orthogonal to each other, determines a decision node. The residuals from the model are then used to build another model and another node until the residuals are too small to be considered significant. Three decision tree techniques have been compared on the same data sample and it has been shown that the multivariate techniques are comparable to the univariate method in classification ability but it is important to appreciate that decisions are rarely taken in isolation and that many variables are considered in parallel when interpreting data. The multivariate tree techniques give the user this ability and consider which variables are most influential on the outcome and why this is the case. The results of the analysis indicate that for the technique to be successful there need to be many samples for training and testing and although this is a common disadvantage of using decision tree methods for data mining, the results of the validation presented here are promising.
6. References Breiman, L., J. Freidman, R. Olshen and C. Stone (1984). Classification and Regression Trees. California, Wadsworth International. Brodley, C. E. and P. E. Utgoff (1992). Multivariate Decision Trees. Amherst, University of Massachusetts: COINS Technical Report 92-82 Duda, R. O. and P. E. Hart (1973). Pattern Classification and Scene Analysis. New York, Wileyinterscience. Fayyad, U. M. and K. B. Irani (1992). "On the Handling of Continuous-Valued Attributes in Decision Tree Generation." Machine Learning 8(1): 87-102 Fayyad, U., P. Smyth, N. Weir and Djorgovski (1995). "Automated Analysis of Image Databases: results, progress and challenges." Journal of Intelligent Information Systems 4:1-19 Francis, P. J. and B. J. Wills (1999). Introduction to Principal Components Analysis. in Quasars and Cosmology. eds: G.J.Ferland and J.A.Baldwin. San Fransico, Astronomical Society of the Pacific. CS-162. Guilfoyle, C. (1986). Ten Minutes to Lay the Foundations. Proceedings of Expert Systems User, August, 16-19. Langley, P. and H. Simon, A (1995). "Applications of Machine Learning and Rule Induction." Communications of ACM 38:54-64 Larson, D. R. and P. L. Speckman (2002). Multivariate Regression Trees for Ananysis of Abundance Data. Columbia, University of Missouri: 21 Lim, T.-S., W.-Y. Loh and Y.-S. Shih (2000). "A Comparison of Prediction Accuracy, Complexity, and Training Time of Thirty-three Old and New Classifcation Algorithms." Machine Learning 40:203-229 Michie, D. (1989). Problems of Computer-Aided Concept Formation. in Applications of Expert Systems. eds: J. R. Quinlan. Wokingham, Addison-Wesley. 2. Mingers, J. (1989). "An Emprical Comparison of Selection Measures for Decision-Tree Induction." Machine Learning 3:319-342 Quinlan, J. R. (1986). "Induction of Decision Trees." Machine Learning 1(1): 81-106 Segal, M. R. (1992). "Tree-Structured Methods for Longitudinal Data." Journal of the American Statistical Association 87(418): 407-418 Wold, H. (1985). Partial Least Squares. in Encyclopaedia of Statistical Sciences. eds: S. Kotz and N. L. Johnson. New York, Wiley. 6: 581-591.
European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.
1135
On a New Definition of a Stochastic-based Accuracy Concept of Data Reconciliation-Based Estimators M. Bagajewicz University of Oklahoma 100 E. Boyd St., Norman OK 73019, USA
Abstract Traditionally, accuracy of an instrument is defined as the sum of the precision and the bias. Recently, this notion was generalized to estimators. However, the concept used a maximum undetected bias, as well as ignored the frequency of failures. In this paper the definition of accuracy is modified to include expected undetected biases and their frequency.
Keywords: Instrumentation Network Design, Data Reconciliation, Plant Monitoring. 1. Introduction Traditionally, accuracy of an instrument is defined as the sum of the precision and the bias (Miller, 1996). In a recent paper (Bagajewicz, 2004) this notion was generalized to estimators arguing that the accuracy of an estimator is the sum of the precision and the maximum induced bias. This maximum induced is the maximum value of the bias of the estimator used, that is, a result of a certain specific number of biases in the network which have not been detected. This lead to a definition of accuracy that is dependent on the number of biases chosen. Aside from many other shortcomings of the definition, two stand out as the most important: The definition has no time horizon associated to it, nor states anything about the frequency at which each sensor will fail, or the time it will take to repair it. In addition, the definition could be more realistic if expected bias, instead of maximum bias is used. In this paper, we review the definitions and discuss the results of a Montecarlo technique that can help determine an expected value of accuracy.
2. Background Accuracy was defined for individual measurements as the sum of the absolute value of the systematic error plus the standard deviation of the meter (Miller, 1996). Since the bias is usually not known, the definition has little practical value. Bagajewicz (2004) introduced a new definition of accuracy of an estimator (or software accuracy) defined as the sum of the maximum undetected induced bias plus the precision of the estimator:
1136 where
c~i ~i and (~'i are the accuracy, the maximum undetected induced bias and
the precision (square root ) of the estimator's variance Sii, respectively. In turn, the accuracy of the system can be defined in various ways, for example making an average of all accuracies or taking the maximum among them. Since this involves comparing the accuracy of measurements of different magnitude, relative values are recommended. The maximum undetected induced bias is obtained from the assumption that a particular gross error detection test is used. In the case of the maximum power measurement test, and under the assumption of one gross error being present in the system this value is given by"
(2)
g~p,1) __ z~ripl ) M a x [(jr _ s m ) i s ] Vs ~/-mss
where Z crit (p) is the critical value for the test at confidence level p, S is the variancecovariance matrix of the measurements and W = A r (ASA r)-lA (A is the incidence matrix). When a larger number of gross errors are present in the system, an optimisation model is needed. Thus, for each set T we obtain the maximum induced and undetected bias by solving the following problem: ~¢P) ( T ) - M a x (~crit,i -- Z ( S W ) i s Vs~T set
(~crit ~ "
s.t
Z
Wks(~cri', s
(3)
-- -- crit
VsET
Therefore, considering all possible combinations of bias locations, we write
~¢p,,T) _ Max 6~ p) (T)
(4) vr As it was mentioned above, this definition states what the accuracy of the system is, when and ifa certain number of gross errors are expected to take place. In other words,
it represents the worst case scenario and does not discuss the frequency of such scenario. We now discuss a new definition and how to obtain an expected value next
3. Stochastic Based Accuracy We define the stochastic based maximum induced biased as the sum over all possible nr biases of the expected fraction of time (Fn~) in which these biases are present.
gl
- Z
]
/7T
The formula assumes that a) when errors in a certain number of sensors occur they replace other existing set of undetected errors and that b) Sensors with detected errors are repaired instantaneously.
1137 Sensors have their own failure frequency, which is independent of what happens with other sensors. For example, the probability of one sensor failing at time t, when all sensors where functioning correctly between time zero and time t is ~ i - J ; ( t ) l - I [ 1 - f , . ( t ) ] , where f ( t ) i s the service reliability function of sensor / i f sensors are not repaired. When sensors are repaired, one can use availability and write
f~(t) = ri/(r~ + bt~ ), where ri is the repair rate and }_ti is the failure rate. The second issue, the repair time, is more problematic because it also affects the value of o- i , which becomes the residual precision during that period of time.
So, E[F,, ] can only be
estimated by identifying the probability of the state with the frequency of the state in the /
|
case of negligible repair time. However, when repair time is significant E[Fn~ ] i s more difficult to estimate and there are no expressions available. In addition, multiple gross errors do not arise from a simultaneous event, but rather from a gross error occurring and adding to an existing set of undetected gross errors. In addition, problem (3) assumes the worst case in which all will flag at first, but it does not say what will happen if some are eliminated. We now define the stochastic-based expected induced biased as the sum over all possible nT biases of the expected fraction of time (F,, T ) in which these biases are present. I1 T
To understand how the stochastic-based induced bias (and by extension, the stochasticbased accuracy) can be calculated. Assume that a system is bias free in the period [0, tl] and that sensor k fails at time t~. Thus, if the bias is not detected, then there is an expected induced bias that one can calculate as follows:
(k )]- El
- sw],
)dOk
where h(O k "~Sa,Ok) is the pdf of the bias q3a with mean value 8a and variance 9k" Note that we integrate over all values of 13a, but we only count absolute values, as the accuracy definition requires.
Thus, in between tl and the time of the next failure of
I-~(p 1) some sensor t2, the system has an accuracy given by °'i + E[6i ....ij~,(k)] •
In turn, if the bias is detected, the sensor is taken out of line for a duration of the repair time Ra. During this time (and assuming no new failure takes place), the system has no induced bias, but it has a lower precision, simply because the measurement is no longer used to perform data reconciliation. Thus, during repair time, the expectation of the accuracy due to detected biases is given by the residual precision~yiR ( k ) .
After a
period of time Ra. the accuracy returns to the normal value when no biases are present *'R
&i • Thus, in the interval [0, t2), the accuracy is given by [&i tl+ c~i ( k ) R k +°'i *(t2_
1138
t,. Rk)]/t2 when bias k is detected and [ o" i t,+ E[-~ ~,~,~de, ( k ) ] (t2_ t,)]/t2 when bias k is undetected. The expectation is then given by multiplying the undetected portion by the corresponding probability
(s)
P,,,,e,(k) - fa ~''' h(Ok "gk,Pk )dOk k,crit and the detected by its complement [ 1 -
P,,,d~, (k)].
Assume now that the bias in sensor k is undetected at t~ and another bias in some other sensor r occurs at h, which can be in turn detected or not detected. If it is undetected, then the expected induced bias is given by:
E[~f p,R)(k,r)] - ~k,crit ;r,cri, I[i__ SW]i k Ok + [I-- SW]iFOF{ ~k,crit ~r,cri!
(9)
h(Ok," ak,Ok )h(Or," a,.,9, )dOkdO,. where, for simplicity of presentation we have assumed that 6 k,crit and
6r,crit can be
used as integration limits. (in reality, the integration region is not a rectangle). We leave this detail for future work. In turn, if the error in sensor r is detected, then we assume that the induced bias remains. Quite clearly, the scenario shown is one of many, and while one is able to obtain the expected induced errors in each case, the problem of calculating the expected fraction of time in each state persists. Thus, we resort to Montecarlo simulations to assess this.
3.1 M o n t e c a r l o
simulations
Consider a scenario s, composed of a set of n, values of time (tl, t2,..., tns ) within the time horizon 7 ~. For each time ti, one considers a sample of one sensor failing with one of two conditions" its bias is detected or undetected. Sensors that have been biased between ti_l and ti and where undetected at ti, continue undetected. Thus, when bias in sensor k is detected, for the time between t~ and t~ +Rk we write
E[a i ]- cyi ( k ) + E
p,m, , 1,i-1 ' 12,~- , "" "~l mi,i-1
(10)
where the second term is the expected bias due to the presence of m~_l undetected errors. 1,i-1.
, ......
,.i-1
a,,~_,
a,,c,.,
v=l
(11)
1-Ih( O~, a~,p~ )dO~ v
For the interval
(t~+R~ ,ti+l), we write
r[ai ]- 6i + r[~i,undet(ll,i_l,12,i_ l ..... lmi.i_l ) ]
(12)
In turn, if the error was not detected, then we write ti+l, we write (13)
1139 The above formula is valid for k =~l,,i_ ~,v = 1.... m i ~ . Otherwise, the same formula is used, but k is removed from ~i(')...." ) (l 1 . i
1 '
l~_ . i
1 ' ....
l,,,i , i
1
)"
To obtain an average accuracy of the system in the horizon 74' and for the scenario s, the accuracy in each interval or sub-interval is multiplied by the duration of such interval and divided by the time horizon 74'. Finally all the values are added to obtain the expectation for that scenario. The final accuracy is obtained using the average of all scenarios. Finally, scenarios are sampled the following way. For each sensor a set of failure times is obtained by sampling the reliability function repeatedly and assuming that sensors are as good as new after repair (AGAN maintenance). Of these, undetectability is sampled using a pdf given by P,,,,d,,, ( k ) and its complement.
4. Example Consider the example of figure 1. Assume flowmeters with cy/=1, 2
and 3,
respectively. We also assume that the biases have zero mean and standard deviation p x =2, 4 and 6 respectively, failure rate of 0.025, 0.015, 0.005 (1/day) and repair time of 0.5, 2 and 1 day respectively. The system is barely redundant (Only one gross error can be determined, and when it is flagged by the measurement test, hardware inspection is needed to obtain its exact location. This is due to gross error equivalency (equivalency theory: Bagajewicz and Jiang, 1998).
S~
I
$3
r
Figure 1. Example
The problem was run with scenarios containing 20 event samples. A portion of one such sample is for example depicted in Table 1. Convergence is achieved very quickly (see figure 2) to a value of accuracy of 1.89. (The solid line is the average value). Comparatively the accuracy defined for maximum bias of one bias present is 6.30. This highlights the fact that using a maximum expected undetected bias is too conservative
5. Discussion and Conclusions The problems with an existing definition of accuracy have been highlighted and a new definition, which gives a more realistic value, has been presented. In addition a Montecarlo sampling technique was suggested to determine the value of the accuracy. Some shortcomings still remain: The expected value of existing undetected biases is determined using rectangular integration regions, when it is known these regions have other more complex forms. This can be addressed analytically somehow, but one can also resort to sample the bias sizes as well. All this is part of ongoing work.
1140 Table 1. Example of one scenario (Portion)
Time 15.6 43.6 62 90 100 115 150 160 170 185 189 193 208
Bias in sensor S1 S1 $2 $2 $2 S1 $3 S1 $2 $2 S1 S1 $2
Bias detected No No Yes Yes Yes Yes Yes Yes No No Yes No Yes
2.7
2.3
2.1-
1.9-
~.
1.5
.
0
20
.
.
40
.
60
80
Figure 2. Montecarlo Iterations convergence.
References Bagajewicz, M., 2004, On the Definition of Software Accuracy in Redundant Measurement Systems. To appear. AIChE J., (available at http://www, ou. edu/clas s/che- de sign/Unpub lished-p ap ers.htm). Bagajewicz M. and Q. Jiang. Gross Error Modelling and Detection in Plant Linear Dynamic Reconciliation. Computers and Chemical Engineering, 22, 12, 1789-1810 (1998). Miller R. W. Flow Measurement Engineering Handbook. McGraw Hill, (1996)
Acknowledgements Funding from the US-NSF, Grant CTS-0350501, is acknowledged.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) ~ 2005 Elsevier B.V. All rights reserved.
1141
The Integration of Process and Spectroscopic Data for Enhanced Knowledge Extraction in Batch Processes C. W. L. Wong a, R. E. A. Escott b, A. J. Morris a, E. B. Martin a* aCentre for Process Analytics and Control Technology School of Chemical Engineering and Advanced Materials University of Newcastle, Newcastle-upon-Tyne, NE1 7RU, UK bGlaxoSmithKline Chemical Development, Tonbridge, TN 11 9AN, UK
Abstract Batch process performance monitoring has been achieved primarily using process measurements with the extracted information being associated with the physical parameters of the process. More recently, there has been an increase in the implementation of process spectroscopic instrumentation in the processing industries. By integrating the process and spectroscopic measurements for multivariate statistical data modelling and analysis, it is conjectured that improved process understanding and fault diagnosis can be achieved. To evaluate this hypothesis, an investigation into combining process and spectral data using multiblock and multiresolution analysis is progressed. The results from the analysis of an experimental dataset demonstrate the improvements achievable in terms of performance monitoring and fault diagnosis.
Keywords: Multiblock; Multiresolution analysis; On-line monitoring; Batch processes. 1. Introduction Since the introduction of the Process Analytical Technology (PAT) initiative, companies in the processing industries are increasingly aware of the need to attain a detailed understanding of their processes and products. The goal of PAT is to build quality into the process and remove the final step of testing the final product, thereby achieving the ultimate goal of parametric release. To deliver against this objective, an enhanced understanding of the process and the product is required. One approach to realising this objective is through the implementation of on-line spectroscopic analysers. A second aspect is the need for on-line real time process performance monitoring. Traditionally batch process performance monitoring (Neogi and Schlags, 1998; Martin and Morris, 2002) has been performed primarily using process measurements with the extracted intbrmation being associated with the physical parameters and/or inferred chemical parameters of the process. More recently, there has been an increase in the use of process spectroscopic instrumentation for the monitoring of a process (Gurden et al., 2002). Spectroscopy provides real-time, high-quality chemically rich information, but in
Author to whom correspondence should be addressed:
[email protected] 1142 most studies, the data is analysed independently of the process data. By integrating the process (physical state) and spectroscopic (chemical state) measurements for multivariate statistical data modelling and analysis, it is hypothesised that improved process understanding and fault diagnosis can be achieved. To evaluate this belief, an investigation into combining the two data forms using multiblock and multiresolution analysis is conducted. The results of the combined analysis are compared with those attained from separate analyses undertaken on the spectral and process data. A number of approaches to combining Principal Component Analysis (PCA) and Partial Least Squares (PLS) with wavelet analysis have been proposed (Bakshi, 1998). Current methods reported in the literature have involved the selection of an appropriate scale as the basis of the monitoring scheme after the application of the wavelet transformation or alternatively applying the projection method to the decomposed scales, complicating the interpretability of the final process representations. To address this level of complexity, multiblock analysis is considered. Multiblock methods can enhance the identification of the underlying relationships between several conceptually meaningful blocks thereby summarising the relevant information both between and within the blocks in a single representation. To demonstrate the potential of the developed methodology, process and UV-visible data from a batch mini-plant is considered.
2. Methodology for Data Integration In a typical batch production environment, process information and spectra are normally acquired in separate data historians thus dividing the data into two distinct data blocks. These two blocks are conceptually meaningful since the same object is measured but the description of the state differs. Two approaches are developed in the subsequent sections and compared for combining the process and spectral data.
2.1 Multiblock Method For the first approach, the spectroscopic and process data are integrated using multiblock analysis, more specifically consensus PCA (CPCA) (Westerhuis et al., 1998). Figure 1 provides a schematic of the proposed integrated on-line monitoring scheme. The process and spectral data are divided into two base blocks and CPCA is applied. More specifically a starting super score tr is selected as the first column for one of the blocks and this vector is regressed on both blocks to give block variable loadings. The block scores tb are then calculated and combined into a super block T. The super scores are then regressed on the super block to give the super weights of the block scores with the super weight being normalised to unit length and a new super score is calculated. The procedure is repeated until the super score converges. Both the super and block scores are then used for the monitoring of the performance of the process.
2.2 Multiresolution Analysis For the second approach, integration is performed as per the first approach but the spectral data is first pre-processed using wavelet analysis. Most data generated from chemical processes is inherently multiscale and multivariate in nature. Spectral data is no exception and usually comprises a large number of wavelengths thus the interpretation of such a large and complex data matrix requires advanced techniques to
1143 reduce the dimensionality and complexity of the problem. Wavelets have been proven to be a useful tool to denoise signals and extract multiscale components (Trygg and Wold, 1998; Teppola and Minkkinen, 2000).
Super Level
Super
/ Block T [
..i.~ .....................
kl k~
............................ 2::................
kl k2
-
I
Base Level ...................
Process
tl
Spectroscopic
Wavelet t: Coefficients
Figure 1. h~tegrated on-line monitoring scheme by CPCA
in the second approach, the spectral data is decomposed using the discrete wavelet transform with the original signal being recursively decomposed at a resolution differing by a factor of two from the previous step. During the decomposition, the smallest features (noise) are first extracted, resulting in an approximate signal. From this approximation, new features are extracted, resulting in an ever more coarse approximation. This continues until the signal has been approximated to the preselected level. The differences are stored as wavelet coefficients. If all wavelet coefficients are used, the original signal can be perfectly reconstructed. In Figure 1, the dotted section is included into the CPCA but not the spectroscopic block. The size of the dataset is significantly reduced however the details are retained with the multiscale components being extracted.
3. On-line Monitoring 3.1 Process Description A simple reaction of nitrobenzene hydrogenation to aniline is considered. Eight experiments were performed of which six batches formed the nominal data set. Seven process variables were recorded every second including reactor temperature, pressure, agitator, H_~ gas feed, jacket inlet and outlet temperatures and flow rate of heating fluid with the UV-Visible spectra being recorded every 30 seconds. Two batches with predefined process deviations were also run. The first of these, batch 7, was discharged with 10% less catalyst to simulate a charging problem and to simulate a series of temperature control problem. The second batch, batch 8, simulates a series of agitator speed and pressure loss problems. The changes reflect both a change to the process as well as to the chemistry. In the application, Daubechies-4 wavelet with five decomposition levels was chosen with the last level of wavelet coefficients being considered as the spectral block as opposed to the original spectra.
1144 3.2 Data Pre-preeessing One of the challenges of data integration is to time align the disparate data sets. The process measurements may be recorded with a sampling interval of seconds but the time frame for the spectroscopic measurements is typically larger. In this study to realise the more rapid detection of a fault, a sampling rate of ten seconds was selected, hence interpolation of the spectral data was necessary. Additional pre-processing of the UVVisible spectra was required since it exhibited a baseline shift therefore a baseline correction was applied to the spectroscopic data. Since the process and spectral data blocks are three-dimensional matrices, X (I x J x K), the first step is to unfold the data to a two-dimensional array. The approach of Nomikos and MacGregor (1994) was adopted resulting in a matrix of order (I x JK). Auto-scaling was then applied to the unfolded matrices for the removal of the mean trajectories. A weighing factor was also introduced at this stage to ensure the variance of each block was unity. The weighting factor to achieve this was 1/n 1/2 where n is the number of variables in a block. The next step was to re-arrange the matrices into a matrix of order (IK x J) to enable the application of the Wold et al. (1998) approach. By adopting this procedure the issue of unequal batch length monitoring and the need to consider how to handle on-line performance monitoring is reduced. CPCA is then applied to the preprocessed data blocks with the principal component scores being used for monitoring. 3.3 Results 3.3.1 Multiblock Approach The process and spectral block scores for the first principal component for batch 7 are shown in Figure 2a and 2b. The temperature control problem is observed from Figure 2a and verified using the contribution plot (Figure 3). It is expected that a slower reaction would occur when less catalyst is charged into the vessel thereby affecting the overall kinetics of the reaction. This effect is observed in Figure 2b (spectral block) where the trajectory is observed to be out of control throughout the whole process.
0
20
40
...... ~a) 60
80
100
120
140
0
20
40
60
80
....... oc~)
100
120
140
Figure 2. Block scores of principal component one. (a) Process," (b) Spectral
1
2
3
4
5
6
7
Figure 3. Contribution plot for the process block scores
Figure 4. Super scores for principal component one for batch 7
1145 The super scores of principal component one were interrogated. Figure 4 illustrates the advantages of the multi-block approach. It summarises the deviations from the process and spectral blocks. Figure 5 shows the super scores of principal component one for batch 8. This batch has mainly process disturbances as observed from the process block scores (Figure 6) since the spectral block scores (Figure 7) revealed no out-of-control signal. Most of the process disturbances are detected from the super scores however the agitator disturbance during the period 43 - 4 9 was not detected as the main source of failure (Figure 8). This result will be compared with the multiblock-wavelet approach.
/~,\
20
40
~0
80
100
120
140
120
~.~o
tl
Figure 5. Super scores of principal component one for batch 8
Figure 6. Process block scores of principal component one Scores
--
;;;s_
20
-
|0
2
6O 80 I1 for b l o c k 2
; 100
Contrlbuhon
plot of PC
1 at Time 43 to 49
-120
1,1Q
Figure 7. Spectral block scores of principal component one
1
2
3
4
5
6
•
Figure 8. Process block scores of principal component one
3.3.2 Multiblock- Wavelets" Approach
For the multiblock-wavelet pre-processing approach, the number of variables (wavelengths) for the spectral data was significantly reduced from the original number of wavelengths, i.e. 216 to 14 wavelet coefficients, resulting in the data being compressed 15-fold. However, the process features are retained as evidenced from the coefficients shown in Figure 9 for batch 8.
21
lO
.5 [ o
20
,1o
/
80
6o
100
120
14(J
0
~ 1
2
3
4
5
6
7
tl
Figure 9. Super scores of principal component one.for batch 8
Figure 10. Contribution plot for process block scores
Interrogating the super scores of principal component one, it was observed that a similar result is obtained. The focus is on the agitator disturbance during time period 43 to 49
1146 where it shows an out-of-control signal that was not observed from the multi-block analysis. The contribution plot of the process block scores (Figure 10) confirmed the finding that the fault was primarily due to the failure of the agitator (variable 3) which consequently affected the reactor pressure (variable 2) and H2 gas feed (variable 4). The approach has been shown to have improved fault detection capability.
4. Discussions and Conclusions The area of integrated data monitoring has become increasingly more important as increased amounts of data from different data structures are recorded. However, the extraction of information and hence knowledge from such combined data structures is limited. The development of an integrated framework can help in the understanding of the process more than that of an individual model. While further fault diagnosis is required, the integrated model allows tracking back to the base models thus to address the problem accordingly. More specifically in this paper, a successful application to data integration has been proposed where the chemical and physical information are incorporated into the model but interpretation is made simpler in a single representation. Multiblock and wavelet transformation are combined providing a powerful combination of dimensionality reduction and data compression. The correlation between blocks and the multiscale nature of data were also considered. The challenges of time alignment, data scaling and weighing between blocks were discussed.
References Neogi, D. and C. Schlags, 1998, Multivariate statistical analysis of an emulsion batch process, Industrial & Engineering Chemistry Research, 37, 3971. Martin, E. B. and A. J. Morris, 2002, Enhanced bio-manufacturing through advanced multivariate statistical technologies, Journal of Biotechnology, 99, 223. Gurden, S. P., J. A. Westerhuis and A. K. Smilde, 2002, Monitoring of batch processes using spectroscopy, AIChE Journal, 48, 2283. Bakshi, B. R., 1998, Multiscale PCA with application to multivariate statistical process monitoring, AIChE Journal, 44, 1596. Westerhuis, J. A., T. Kourti and J. F. MacGregor, 1998, Analysis of multiblock and hierarchical PCA and PLS models, Journal of Chemometrics, 12, 301. Trygg, J. and S. Wold, 1998, PLS regression on wavelet compressed NIR spectra, Chemometrics and Intelligent Laboratory Systems, 42, 209. Teppola, P. and P. Minkkinen, 2000, Wavelet-PLS regression models for both exploratory data analysis and process monitoring, Journal of Chemometrics, 14, 383. Nomikos, P. and J. MacGregor, 1994, Monitoring batch processes using multi-way principal component analysis, AIChE Journal, 40, 1361. Wold, S., N. Kettaneh, H. Friden and A. Holmberget, 1998, Modelling and diagnostics of batch processes and analogous kinetic experiments, Chemometrics and Intelligent Laboratory Systems, 44, 331.
Acknowledgements Chris Wong would like to acknowledge the EPSRC, GlaxoSmithKline, the UK ORS Scheme and CPACT for financial support of his PhD.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1147
A Systematic Approach for Soft Sensor Development Bao Lin a, Bodil Recke b, Philippe Renaudat b, Jorgen Knudsen b, Sten Bay Jorgensen a* a
CAPEC, Department of Chemical Engineering, DTU Lyngby 2800, Denmark b FLS Automation Valby 2500, Denmark
Abstract This paper presents a systematic approach for development of a data-driven soft sensor using robust statistical technique. Data preprocessing procedures are described in detail. First, a template is defined based on a key process variable to handle missing data related to severe operation interruption. Second, a univariate, followed by a multivariate principal component analysis (PCA) approach, is used to detecting outlying observations. Then, robust regression techniques are employed to derive an inferential model. The proposed methodology is applied to a cement kiln system for realtime estimation of free lime, demonstrating improved performance over a standard multivariate approach.
Keywords: Multivariate regression analysis, Soft sensing, Robust statistics
1. Introduction Soft sensors have been developed as supplement to online instrument measurements for process monitoring and control. Early work on soft sensor development assumed that a process model was available. The inferential model is developed using Kalman filter (Joseph and Brosilow, 1978). In case the process mechanisms are not well understood, empirical models, such as neural networks (Qin and McAvoy, 1992; Radhakrishnan and Mohamed, 2000), multivariate statistical methods may be used to derive the regression model (Kresta et al., 1994; Park and Han, 2000; Zhao, 2003). A model-based soft sensor can be derived if a first principle model (FPM) describes the process sufficiently accurately. However, modern measurement techniques enable a large amount of operating data to be collected and stored, thereby rendering data-driven soft sensor development a viable alternative. Multivariate regression techniques have been extensively employed to develop datadriven soft sensors. Principal component regression (PCR) and partial least squares (PLS) address collinearity issues of process data by projecting the original process variables into a smaller number of orthogonal latent variables. Process measurements are often contaminated with data points that deviate significantly from the real values due to human errors, instrument failure or changes of operating conditions. Since Author to whom correspondence should be addressed:
[email protected] 1148 outlying observations may seriously bias a regression model, robust statistical approaches have been developed to provide a reliable model in the presence of abnormal observations. This paper presents a systematic approach for building a soft sensor. The proposed method using robust statistical techniques is applied to the estimation of free lime for cement kilns. The paper is organized as follows. Section 2 describes data preprocessing which includes both univariate and multivariate approaches to detect outlying observations. The robust PCR and PLS approaches are presented in section 3, followed by the illustrative application on development of a free lime soft sensor for a cement kiln. 2. D A T A P R E P R O C E S S I N G Outliers are commonly defined as observations that are not consistent with the majority of the data (Pearson, 2002; Chiang et al., 2003), including missing data points or blocks, and observations that deviate significantly from the normal values. A data-driven soft sensor derived with PCR or PLS deteriorates even in the presence of a single abnormal observation, resulting in model misspecification. Therefore, outlier detection constitutes an essential prerequisite step for a data-driven soft sensor design. A heuristic procedure has been implemented in the paper to handle missing data related to sever operating interruptions. A template is defined by the kiln drive measurement to identify missing observations, since near zero drive current data corresponds to a stop of cement kiln operation. During such a period, other process measurements will not be reliable or meaningful. In case a small block (less than 2 hour) of data is missing, interpolated values based on neighbouring observations will be inserted. If a large segment of missing data is detected, these blocks will be marked and not used to build the soft sensor. Both univariate and multivariate approaches have been developed to detect these outlying process observations. The 3a edit rule is a popular univariate approach to detect outliers (Ratcliff, 1993). This method labels outliers when data points are three or more standard deviations from the mean. Unfortunately, this procedure often fails in practice because the presence of outliers tends to inflate the variance estimation, causing too few outliers to be detected. The Hampel ident~er (Davies and Gather, 1981) replaces the outlier-sensitive mean and standard deviation estimates with the outlierresistant median and median absolute deviation from the median (MAD). The MAD scale estimate is defined as: MAD = 1.4826 median
~x i - x ' l }
(1)
where x * is the median of the data sequence. The factor 1.4826 was chosen so that the expected MAD is equal to the standard deviation a for normally distributed data. Since process measurements from the cement kiln system are not independent from each other, detecting outliers using univariate diagnostics is not sufficient, resulting in masking and swamping. Masking refers to the case that outliers are incorrectly identified as normal samples; while swamping is the case when normal samples are classified to be outliers. Effective outlier detection approaches are expected to be based on multivariate statistical techniques.
1149
Principal component analysis (PCA) is a multivariate analysis tool that projects the predictor data matrix to a lower dimensional space. The loading vectors corresponding to the k largest eigenvalues are retained to optimally capture the variations of the data and minimize the effect of random noise. The fitness between data and the model can be calculated using the residual matrix and Q statistics that measures the distance of a sample from the PCA model. Hotellings T 2 statistics indicates that how far the estimated sample by the PCA model is from the multivariate mean of the data, thus provides an indication of variability within the normal subspace. The combined Q and T~tests are used to detect abnormal observations. Given the significance level for the Q (Jackson and Mudholkar, 1979) and T 2 statistic (Wise, 1991), measurements with Q or 7"2 values over the threshold are classified as outliers. In this paper the significance level, a has the same value in the two tests, however finding a compromise between accepting large modelled disturbances and rejecting large unmodelled behaviours for outlier detection clearly needs further investigation. 3. R O B U S T
STATISTICS
Scaling is an important step in PCA. Since numerically large values are associated with numerically large variance, appropriate scaling methods are introduced such that all variables will have approximately equal weights in the PCA model. In the absence of a prior knowledge about relative importance of process variables, autoscaling (meancentering following by a division over the standard deviation) is commonly used. Since both mean and standard deviation are inflated by outlying observations, autoscaling is not suitable for handling data which are especially noisy. This paper applies robust scaling to cement kiln data before performing PCA (Chiang et al., 2003) which replace mean by median and the standard deviation by MAD. There are two types of approaches for rendering PCA robust. The first detects and removes outliers using a univariate approach then carries out a classic PCA on the new data set; the second is multivariate and is based on robust estimation of covariance matrix. An elliposidal multivariate trimming (MVT) (Devlin et al., 1981) approach is used. It iteratively detects bad data based on the squared Mahalanobis distance:
d~-(xi-xi)rS
'(xi-xi)
(2)
where x i is the current robust estimation of the location and S
is the robust
estimation of the covariance matrix. Since the data set has been preprocessed with a Hampel ident(fier, 95% of data with smallest Mahalanobis distance are retained in the next iteration. The ileration proceeds till both
X i
and S* converge. In this paper, the
iteration stops at the 10 th iteration such that at least 60% of the data is retained for the estimation of covariance matrix. Chiang et al (2003) suggested the closest distance to center (CDC) approach that m/2 observations with the smallest deviation from the center of the data is used to calculate the mean value. The CDC method is integrated such that the covariance matrix from the initialization step is not disrupted by outlying observations.
1150 Principal component regression (PCR) derives an inferential model with score vectors and free lime measurements from the lab. During the regression step, zero weights are assigned to outlying observations identified by the PCA model; a weight value of one is assigned to normal data. PLS is a multivariate statistical approach for relating input and dependent data matrices. The input data is projected onto a k-dimensional hyper-plane such that the coordinates are good predictors of dependent variables. The outlying measurements identified with an also downweighted PCA model before PLS analysis. The proposed approaches, robust PCR and weighted PLS, are applied to a data set collected from the log system of a cement kiln. 4. C A S E S T U D Y The product quality of a cement kiln is indicated by the amount of CaO (free lime) in clinker. The direct measurement is generally only available with a time delay of about an hour. In addition, the measurement also suffers from operating perturbations within the kiln and the cooler, which result in uncertain indication of the average quality. It is desirable to develop a soft sensor that is able to accurately predict the content of free lime in real time, and can be employed for effective quality control. The operating data from a cement kiln log system are used to derive a soft sensor of free lime in the clinker. There are 13 process measurements available, including kiln drive current, kiln feed, fuels to calciner and kiln, plus several temperature measurements within the kiln system. The standard measurements are logged every 10 min, whereas the laboratory analysis of free lime content of the clinker is logged approximately every 2 hours. A data block of 12500 samples is selected in this study: 6500 samples to derive the model and 6000 samples for validation. One step ahead prediction residual sum of squared errors (PRESS) between the model and measured lime content is used to select the number of principal components (PCs): Nv
PRESS
- Z
2
(3)
( ~ ( i ) - y,,, ( i ) )
i=1
where N v is the total number of samples during the validation period. It is calculated only when a new lab measurement is available. The PRESS of regression models derived with PCR and PLS are shown in Figure 1. The PCR model with 5 PCs has the minimum PRESS (23.443). The PLS analysis shows a minimum of PRESS for 2 latent variables (LVs), because PLS finds LVs that describe a large amount of variation in X and are correlated with dependent variables, Y, while the PCs in PCR approach are selected only on the amount of variation they explain in X. 6O
45
50
40
0
0
~,~ 40
35
O
C:'
0
C:,
25
1
2 (a )
3 4 5 6 7 N u m b e r of Principal Components
O
30 . ~i;,
8 (b)
N u m b e r of Principal Components
Figure 1. P R E S S o f (a) - PCR model • (b) - PLS model during validation period
1151 24
2U
.
.
.
.
.
.
.
.
"23
~.~ 22 21 L i.000 0998
J
J EI.9~,I
(a)
,
,
J
0 992
, L 0.'#8#_-, i_iN',54
, IU981)
C1996
Significance Level
l-i994
13.992 0.990
:~0(1:
0
200
' ~ ; N N N " 7 7 N N N N N T ; :
0
", ~ , ~ "
i: :I
:it
~i
::
:
200
F i g u r e 5. Effects o f convection on undulating chaotic pattern Le = 600, D a = 0.064, ~ = 690. a) v = O.O, b) v = O.1, c) v = O.5, d) v = 1.5
convection steady state wavy patterns are related to periodic oscillations of the homogeneous system with L e = 1 (Nekhamkina et al., 2000). Since the reactiondiffusion patterns examined here are far from this condition when L e is large, convection cannot contribute to steady state pattern and periodic waves occur instead.
References Chang, M. and R. A. Schmitz, 1975, Chem. Eng. Sci. 30, 21. Kapral, R. and K. Showalter, Eds., 1995, Chemical Waves and Patterns. Kluwer Academic Publisher, Dordrecht. Kohout, M., Schreiber, I. and M. Kubi6ek, 2002, Comp. and Chem. Eng. 26, 517. Kohout, M., Vani~kovfi, T., Schreiber, I. and M. Kubi6ek, 2003, in Proc. of the ESCAPE 13, Kraslawski, A. and I. Turunen, Eds., Elsevier, Amsterdam, p. 725. Merkin, J. H., Petrov. V., Scott, S. K. and K. Showalter, 1996, Phys. Rev. Lett. 76, 546. Nekhamkina, O., Rubinstein, B. Y. and M. Sheintuch, 2000, AIChE J., 46, 1632. Nekhamkina, O., Rubinstein, B. Y. and M. Sheintuch, 2001, Chem. Eng. Sci. 56, 771. Sheintuch, M. and O. Nekhamkina, 2001, Catal. Today 70, 383. Trfivni6kovfi, T., Kohout, M., Schreiber, I. and M. Kubi6ek, 2004, Proc. of the 31st Int. Conf. of the SSCHE, Markog, J. and V. Stefuca, Eds., Slovak Univ. of Technology, Bratislava. Vani6kovfi, T., Kohout, M., Schreiber, I. and M. Kubi6ek, 2003, Proc. of the BOth Int. Conf. of the SSCHE, Markog, J. and V. Stefuca, Eds., Slovak Univ. of Technology, Bratislava. Yakhnin, V. Z., Rovinsky, A. B. and M. Menzinger, 1994, Chem. Eng. Sci. 49, 3257. Yakhnin, V. Z., Rovinsky, A. B. and M. Menzinger, 1995, Chem. Eng. Sci. 49, 2853.
Acknowledgements This work has been supported by the grants MSM 6046137306 of the Czech Ministry of Education and 104/03/H 141 of the Czech Science Foundation.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1213
A Design and Scheduling RTN Continuous-time Formulation Pedro M. Castro a*, Ana P. Barbosa-Pdvoa b, Augusto Q. Novais b aDepartamento de Modelag~o e Simulag~o de Processos do INETI 1649-038 Lisboa, Portugal bCentro de Estudos de Gest~o do IST 1049-001 Lisboa, Portugal
Abstract This paper presents a general mathematical formulation for the simultaneous design and scheduling of multipurpose plants. The formulation is based on the Resource Task Network process representation, uses a periodic, uniform time grid, continuous-time representation and originates mixed integer nonlinear programs (MINLPs) or mixed integer linear programs (MILPs), depending on the type of tasks and objective function being considered. Its performance is illustrated through the solution of two batch-plant example problems that have been examined in the literature.
Keywords: Resource Task Network, Uniform-time grid, Event points
1. Introduction Multipurpose plants are general purpose facilities where a variety of products can be produced by sharing the available plant resources (raw materials, equipment, utilities and manpower) properly in time. The production of a particular product involves a sequence of operations that can be batch, semi-continuous or continuous in nature, where a particular unit is usually suitable for more than a single operation. As a consequence, multipurpose plants are more flexible and suitable for the production of small quantities of high value-added products with short life cycles, the current trend of consumers' demands in today's competitive global market. These same special characteristics however, introduce extra degrees of complexity into the design and operation of such plants. In particular, it is not possible to design a plant without considering how it will be operated, neither it is possible to schedule all the required operations without knowing the plant configuration. Hence, design and scheduling must be considered simultaneously to avoid over or under design. Several authors have addressed the design and scheduling problem of batch plants. Few, however, have based the mathematical formulations on general process representations. Barbosa-Pdvoa and Macchietto (1994) presented a discrete-time formulation that uses the maximal State Task Network (mSTN). Examples of continuous-time formulations
Author to whom correspondence should be addressed:
[email protected] 1214 are the work of Lin and Floudas (2001) for the STN and of Castro et al. (2004) for the RTN, with both assuming a short-term mode of operation. This work follows that of Castro et al. (2004) but now a periodic mode of operation is assumed. In addition, both batch and continuous tasks can now be handled. However, to avoid generating MINLPs, only equipment items characterized by size (not processing rate) will be considered. Thus, the two example problems chosen to illustrate the performance of the formulation involve the design and scheduling of batch plants.
2. Fundamental Concepts In the proposed formulation, the time horizon of interest (H) is divided into a fixed number of time intervals/slots. The interval boundaries are called event points (set T) and their exact location (Tt), as well as the cycle time (H) is unknown a priori. A single time grid keeps track of all events taking place (see Figure 1). In periodic problems, the beginning and end of the time horizon are the exact same event point. The wrap-around operator defined in eq 1 is used to overcome the problem of modelling the execution of tasks that span across two cycles and to facilitate the formulation of some constraints. i
i Cycle N
,~1 "-] 1
Slot 1
~
Slot 2
I
Slot T-1
I
2
3
/~/
I
-1--1
Slot T
I
T
l
Cycle N+I Slot 1
I
I
2
>
T+1-1
0
H
Figure 1. Uniform time grid for periodic scheduling problems ~ ( t ) - t - I T l if t > T , ~ ( t ) - t if l - eft(tl,bl) and lft(t~,bl) est(t2,b2) and lst(t2,b2) < lft(tl,bl). If any of such conditions is not satisfied est(tj,b~) has to be increased and/or lft(t2,b2) has to be reduced thus reducing respective time windows.
2.3 Constraints induced by limited intermediate storage. (Rodrigues et al.,2000) Time windows for batches producing and consuming an intermediate with limited storage capacity can be utilized to calculate storage time profiles in two limiting scenarios: i) production time allocation at eft and consumption at est and ii) production time allocation at lfl and consumption at 1st. in the first case if storage capacity is exceeded some production batches have to be delayed through est increases, in the second some consumption batches must be anticipated through lft reductions (which will reduce 1st consumption times). Which batches must have its time windows reduced is not entirely fixed but starting with the first/last batches involved in the problem allow producing lower reductions.
2.4 Constraints induced by equipment units. If a batch (t,b) is assigned to an equipment unit its time window can induce a forced occupation during a time interval. In Sadeh, 1991, the concept of slot of total reliance is introduced as the time interval (lst, eft) which necessarily will be utilized by the task if eft > 1st that is if the time window is lower than twice the processing time. Intervals of total reliance (by a batch) are not allowed to other batches assigned to the same equipment unit. This "hole" in a time window would make necessary to work with multiple disjoint time windows, which is not supported by actual constraint propagation mechanism. Nevertheless they can be taken into account in special conditions, for example when heads and/or tails originated by intervals of total reliance are useless because their extent is lower than processing time; in this case they can be eliminated thus leading to time windows reductions. In Caseau et al., 1994, conditions are presented in order to analyze in which situations a set of batches assigned to the same equipment unit lead to obligatory precedence relationships among some of them. Given a set S of batches i and a batch (t,b) not contained in S, conditions are obtained to conclude if (t,b) does not precede the entire set S, does not follow the entire set S, precedes S or is preceded by S. Earliest starting time (estS) and latest finishing time (IriS) for set S are defined as minimum est and maximum lft among the batches in the set, set processing time ptS as the sum of batches processing times. If IriS - est < ptS + pt then (t,b) does not precede the entire set and the condition est _<min(efti) holds, if additionally IriS - estS < tpS + tp then (t,b) cannot be processed among tasks i and it follows that S precedes (t,b) so that the condition est > estS + tpS can be imposed, in the same way if l f l - estS < ptS + pt then (t,b) does not follow the entire set and the condition lfl _< max(lsti) holds, if additionally I r i S - estS < tpS + tp then (t,b) cannot be processed among tasks i and it follows that (t,b) precedes S so that the condition lfl _< IriS - tpS can be imposed.
2.5 Equipment units load imposed by time windows. In Keng et al., 1988 and Sadeh, 1991 similar concepts are presented to represent the load imposed on an equipment unit by the batches assigned to it. Keng defines batch criticality as the ratio between processing time and time window span, and equipment unit cruciality function as a time function obtained summing up batches criticalities. Sadeh introduces the batch individual demand as a time function representing the likelihood that a discretized time interval be used by the batch, and the equipment unit
1228 aggregated demand summing up batches individual demands. Both authors utilize these concepts to guide constrained based search scheduling algorithms. These time functions are related to slack measures utilized by Cheng et al., 1997. The authors have proposed to utilize equipment units load as useful insight in the planning phase to evaluate plant loading and possible bottlenecks (Rodrigues et al.,2000). On the other side it can be used during the scheduling procedure to reduce the burden of the constraint propagation mechanisms, which look for possible ordering among batches in the same equipment unit discussed in the previous section. In fact forced ordering among batches is likely to occur when equipment unit load is high or in the time intervals where load is higher. Equipment unit load has been used to filter out units and time intervals where the constraint propagation mechanism is launched reducing significantly the computer effort.
3. Simple planning problem A very simple planning problem is used to illustrate time windows utilization. Four products A, B, C and D are manufactured through two stages (tasks) each. First tasks A1 and B1 share the same equipment unit U1. Tasks A2 and B2 utilize U3, C1 and D1 utilize U2, C2 and D2 utilize U4. Demand for products B, C and D is located at the end of the horizon (t = 432). There are three demands on product A at times 144, 288 and 432. Raw materials are available at t = 0. Given batchsizes the planning system leads to 8 batches for tasks A1 and A2 and 3 batches for all the other tasks. Tasks processing times are: Al(31), A2(33), B1(32), B2(32), C1(27), C2(16), Dl(21) and D2(19). Batches time windows and equipment units load (aggregated demand) are given in Figure 1. ....................~
............ ~ ~ ~ : ~ i i i : : i : : i
~ii~::i::::::~::i:;iii i:.:~
!...../.";i:; . '.~.../..:....Yi;7;i; .~ ..........................................~i....~
'. . . .~. . . . .:. . . .' . . . . . . .....................:.~..:~..:~..................=.. ..........t.......... ...:ii tl d e m a n d s for
~
i................
i
~
~
~......~ ..:~ 288
...
C1C2 t
i!
Figure 1. Equipment units load and batches time windows. Intermediate demands for product A lead to shorter time windows for initial batches of tasks A1 and A2 which leads to higher load on units U 1 and U3 at the beginning of the horizon. Suppose that the user wants to analyze if product B can be scheduled after product A as far as its batches time windows are large. With this objective earliest starting time - est of the first batch of task B1, B1/1 is modified from t = 0 to t = 280. Constraints propagation leads to the scenario of Figure 2. It can be observed that the increase in est
1229
of B 1/1 is propagated to the other batches of B 1 and to the batches of the second task B2 as could be expected. What is less evident is that that same increase leads to reductions in lft of all the batches of tasks A1 and A2. This results from propagation of capacity constraints in the utilization of equipment units U 1 and U3. Some other time windows modifications by the user can be introduced. For example as load in units U2 and U4 are low the user may want to analyze if products C and D can be delivered early or started later with a postponed delivery of raw materials. Figure 3 shows the result when due date of product C is reduced to t = 160 and for product D raw materials are made available at t = 160 and due date is reduced to t = 300. ......~ r
2._...i.. ............ ~:.: ~ . ° ' ~ . ~ i " ~
~ ........ I-I
lO0
........
~
~
~
~
~'00
:
-
-
-iI:ll:l
J
~
!
~
41:10
500
7 A1 •
III
II~?|I
I
| I]ll.'l~i
........................................ ~
I
I
~B2, .......................................................~%~;;i~,
C1
............... ,
i I._~C34~-
I @
i
!
........................... .. E : . : ......
. . . . . . . . . :. .: .'" . . .
:
'
' ,:,C2 I
:~42 I o.~ 4 ~ ! I LA i rI :~ i,~i j IIl~ ~,~l,,~iI
,
t N
a~~lRlWlJigN~ii',Niii',iii'iiiiii~!i~!ii'~
ii~{~ii~:::::::::::::::::::::::::::::: . ::/::
. ......... :. L._.22_2
. . . . .
, D2
'
................. 22_22_._._..__2
...................................'...'.2.......... 2 _ ........... 3
::~:::
i
1
[
A1
A2 ~:
~
:~
'
I B1 B2
I
c/ ~::::!+~i2&i& . . . . . . I
D1 'D2 ..................................................................................................................................................................................................... i
Figure 3. Scenario after modification of due date (C) and delivery time (D)
4. Time windows based scheduling heuristic Many existing scheduling heuristics have been introduced in recent years into commercial Advanced Planning and Scheduling systems (APS). In general they utilize a constructive or simulation approach where, at each step, a batch is selected and a start time is defined. The constructive approach of the Gantt chart allows taking into account a great number of plant and recipe constraints as far as the actual situation of the plant is known at each step. In this way a convenient/feasible start time can be defined. The
1230 main problem is batch selection. Selection often relies on a batch/task priority order defined by the user from the beginning of the scheduling procedure and/or a priority order in the choice of equipment units to treat bottlenecks first. Again bottlenecks are selected at the beginning. Batches time windows, and its maintenance through constraints propagation, allow developing scheduling heuristics with internal batch selection based on characteristics such as batches criticality, equipment units load and time interval spanned by each batch time window. Heuristics focusing on bottlenecks can benefit from updated equipment units load thus selecting at each step the unit and time interval where batches scheduling is likely to be harder. Heuristics aimed to schedule batches as soon/late as possible select the batch considering the batches whose time windows start/end earlier/later, without using the time instants where equipment units become available as the unique information for batch selection. This selection procedure coupled with candidate batches criticality allow picking up first batches with lower schedule possibilities. This in turn reduces the possibility of undesirable solutions, in the sense that some batches cannot be scheduled inside their time windows, thus implying that some due dates will not be fulfilled or raw materials deliveries must be anticipated. A heuristic aimed to schedule batches as soon as possible has been developed. The procedure utilizes a rolling time horizon and unscheduled batches criticality. Rolling horizon starts at the minimum earliest starting t i m e - est among the unscheduled batches and has a duration established by the user. Batches with est inside the rolling horizon are candidate batches for selection. One batch is selected according to equipment units' load and batch criticality. After batch allocation time windows are updated through constraints propagation as well as equipment units load. For the scenario in Figure 3 computer time was 5 seconds and all the batches were allocated inside its time windows.
5. Conclusions Interactive and/or heuristic planning and scheduling techniques in short term problems can benefit from constraints propagation over batches processing time windows. They allow to visualize and take into account the consequences of decisions that often are complex and difficult to infer. References
Erschler J., Roubellat, F., and Vernhes LP.,1976, Finding Some Essential Characteristics of the Feasible Solutions for a Scheduling Problem. Operations. Research., 24(4). Fox M.S.,1983, Constraint-directed search: a case study in job shop scheduling. Ph.D.Thesis, Carnegie Mellon University, Computer Science Department, Pittsburgh, USA. Caseau Y., and Laburthe F.,1994, Improved CLP Scheduling with Tasks Intervals. Proceedings Eleventh International Conference on Logic Programming. Santa Margherita Ligure, Italy. Keng N.P., Yun D.Y.Y., and Rossi M.,1988, Interaction Sensitive Planning System for Job-Shop Scheduling, in Expert Systems and Intelligent Manufacturing, Ed. M.D.Oliff. Elsevier. Sadeh N.,1991, Look-Ahead Techniques for Micro-Opportunistic Job Shop Scheduling. Ph.D. Dissertation, CMU-CS-91-102, School of Computer Science, Carnegie Mellon University. Cheng C., Smith S.F.,1997, Applying constraint satisfaction techniques to job shop scheduling. Annals of Operations Research (70). ILOG,1997, ILOG Solver White Paper. ILOG Inc.,Mountain View, CA, USA. Rodrigues M.T.M., Latre L.G., Rodrigues C.A.,2000, Production Planning Using Time Windows for Short-Term Multipurpose Batch Plants Scheduling Problems. Ind Eng Chem. Res., 39.
European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) g5 2005 Elsevier B.V. All rights reserved.
1231
Information Logistics for Supply Chain Management within Process Industry Environments Marcela Vegetti a, Silvio Gonnet ~, Gabriela Henning b* and Horacio Leon& INGAR/UTN Avellaneda 3657, 3000 - Santa Fe, Argentina b INTEC Gfiemes 3450, 3000 - Santa Fe, Argentina
Abstract This contribution proposes the design of an ontology that provides the foundations for the specification of intbnnation logistics processes in extended supply chains associated to process industries. The proposed ontology includes concepts and relationships that are necessary to formally describe, measure and evaluate a supply chain (SC), thus simplifying the visualization and analysis of networks. A SC ontology is a first step towards achieving a standard description of SC design and management processes.
Keywords: Supply Chain Management, Ontologies, SCOR Model 1. I n t r o d u c t i o n Nowadays, process industries are usually involved in '~extended" supply chains (ESCs), therefore they are tbrced to leave aside the traditional supply chain (SC) companycentric view (Shah, 2004). There is a real need to track and trace product-related information in extended multi-company SCs, either for management or optimization purposes or just for the observance of products liability requirements. The ESC context emphasizes the importance of information logistics (IL) as a key issue for integration. iL processes make accessible to the business management, task-specific and relevant information coming from production, management and business processes as well as from external sources (e.g. suppliers' and customers' data). The role of IL processes is to interlink business process management cycles and to mainly support the monitoring and communication activities in a SC. Thus, the supply chain management (SCM) poses not only the problem of the efficient administration of material inventories and flows but also the challenge of the efficient storage and flow of the associated information. The Supply Chain Council (Stewart, 1997) presented a general framework for the SCM, named SCOR ("Supply Chain Operations Reference Model"). It is based on the consideration that all supply chain tasks and activities can be assigned to five fundamental processes -plan, s o u r c e , m a k e , d e l i v e r a n d r e t u r n - and thus simplifies the visualization and analysis of networks. Theretbre, SCOR is a good starting point for the communication among SC stakeholders. However, it has some limitations and it is necessary to extend it in order to obtain a system of consistent concepts that could be used by all the actors and components of an ESC in a process industry environment.
author to whom correspondence should be addressed:
[email protected] 1232 In order to tackle the consistency problem, this contribution proposes the use of the ontology technology, which is discussed in the next section. The proposed ontology, called SCOntology, provides the foundations for the specification of information logistics processes in ESCs associated to process industries. It is introduced in Section 3, where the concepts and relationships that are necessary to describe, measure and evaluate a SC are discussed.
2. Towards a Supply Chain Ontology Even though many ontology definitions exist, the classical one was proposed by Gruber (1993): "an ontology is a formal, explicit specification of a shared conceptualization". A conceptualization refers to an abstract model of some phenomenon in the world, which identifies the relevant concepts of that phenomenon. Explicit means that the type of concepts used and the constraints on their use are explicitly defined. Formal refers to the fact that the ontology should be machine-understandable. Shared reflects the notion that an ontology captures consensual knowledge; so, it is not restricted to some individual, but accepted by a group. Therefore, the construction of an ontology for SCM would provide a framework for sharing a precise meaning of information exchanged during the communication among the many stakeholders involved in the SC. Although many methodologies have been proposed to build ontologies, each having different principles, design criteria and development stages, the approach of Grtininger and Fox (1995) has been selected for the development of the SCOntology. According to this approach a set of natural language questions, called competency questions, must be defined to determine the ontology scope. These questions and their answers are employed in the following step of the methodology, called conceptualization, which consists in extracting the ontology main concepts and their properties as well as relationships and axioms. IL processes have as premises to access the right information, with the right content and quality, at the right time and at the required place. But which is the right information, the right content and quality for it, as well as the right time and place to access it? In order to define the scope of SCOntology, the previous generic competency questions are reformulated as follows: i) which is the required information for each supply chain process?; ii) which is the structure and content of each piece of information?; iii) which is the place to access it?; iv) which are the processes that provide it?; v) which are the processes that consume it?; vi) when is each information piece supplied?; vii) when is it consumed?, etc. Having posed and answered these questions, the conceptualization stage will help to organize and structure the acquired knowledge using a representation language that must be independent of both the implementation language and environment. In this contribution, the well-known UML language will be employed for conceptualizing the SCOntology.
3. Defining the Conceptual Model The relevant concepts of SCOntology that arise when posing and answering competency questions are directly linked to the information associated to the ESC and the processes using it. They can be summarized as follows: (i) Information resources,
1233 defining the information and its structure; (ii) SC Processes, acting as information suppliers and clients; (iii) Locations, where processes are performed and the required information is needed, (iv) Relationships among processes and information resources, such as provider, consumer; (v) Relationships among processes, which allow tracing the information flow associated with particular workflows. A good starting point to represent a framework able to answer competency questions is to consider an enterprise model. Though there are several models available, Coordinates (Mannarino, 2001) has been chosen because it allows representing the process and product views in an integrated fashion. The main concepts are shown in Fig. 1. According to this model, a Process is employed to represent a set of activities in terms of a set of resources that participate in different ways in order to achieve the process' goals. As only certain aspects or characteristics of a Resource may be of interest to a given process, a particular perspective of the Resource (ResourcePerspective) is actually viewed by such P~'ocess. This fact is modelled by means of the Use Mode relationship that reflects the role that the Process plays in relation to the Resource Perspective. The following roles have been considered in this contribution" creates/ eliminates (non-renewable resources), produces/consumes (renewable resources), modilies, uses, and employs (exclusive usage). The incorporation of these role types extends the SCOR original approach, which only considers input and output roles. As can be interred from the previous paragraphs, processes relate among themselves indirectly by means of the resources they operate on. However, two processes can be directly linked through explicit temporal relationships. Furthermore, a Process can be described at different abstraction levels, according to the complexity of the activity that is being modelled. Hence, a process can be decomposed into subprocesses. Other concepts that take part in the model are: (i) the Organisational Unit one and (ii) the specialization of the Resource concept into Material and Information Resources. Temporal Relation ship
UseMode *
InitialState IntermediateState R e s o u r c e State FinalState
sul~process
1. *
.
Organisational Unit
Process 1..*
*
*
*
Resource Persuective
Resource 1 * i
'!
Information Resource
,
Material Resource
Figure 1. Supply Chain Conceptual Model Elements This basic conceptual model is extended with the concepts introduced in the SCOR framework, which includes three levels of process detail. At Level One (see Fig. 2), SCM is defined in terms of the following integrated core processes" Plan, Source, Make, Deliver, and Return, spanning from the suppliers' supplier to the customers' customer, and all aligned with each company's operational strategy, work, material, and information flows (Bolstorff and Rosenbaum, 2003). These processes, with the exception of Plan, are considered as Execution type of processes (Execute); thus, they are the ones that represent raw materials acquisition (Source), transformation (Make) and product distribution to customers (Deliver). Return processes are associated with receiving any returned products, having two perspectives built into them" Delive W Return- returns from customers, and Source Return- returns to suppliers. It can be seen
1234 that Plan processes cover all activities for the preparation of future material flows; thus they perform the Planning of the SC and the Execution processes. In addition, SCOR includes a series of Enable elements for each of these processes. An Enable process is a one that prepares, maintains or manages information or relationships on which planning and execution processes rely.
rocess Plan
fsco ocessl 1
1
Planning
[
Execute
[__
I Make ' Source ]supplier ~customeq ~r sup~31ier
Enable
__+
[suppl ier Del'iver J cust°me~l~ Return custol]ner Iupplier z~ , ~ I SourceReturn} DeliverReturn supplier customer
Figure 2. Supply Chain: Level I Model
The five basic elements are further divided into process categories at the next level, called Level Two or configuration level. It defines the configuration of planning and execution processes using standard categories, like make-to-stock, make-to-order, and engineer-to-order, employed by companies to fulfil customer orders. The configuration is defined by the specification of which processes are used to move materials from location (organizational unit) to location. Thus, at Level Two, the five Level One process categories (Plan, Source, Make, Deliver, and Return) are decomposed into thirteen supply chain execute process types and five plan process types (P1." Plan the whole supply chain," t:'2." Plan Source; P3: Plan Make; P4: Plan Deliver," 1,5." Plan Return). Furthermore, at this second level, Enable is also extended into five processes (EP." Enable Plan," ES: Enable Source," EM." Enable Make," ED: Enable Deliver; ER." Enable Return), one for each basic process. This decomposition is shown in Fig. 3, including the aggregation association over the SCOR process class, which specialises the processsubprocess link introduced in Fig. 1.
[eve rocess
CO rocess g
L
Plan
] p2 t
l
Planning
,
Execute
[ Sou~rce
Enable
Enabling__~E~_~~_EM I
S2~
EP E~
Figure 3. Supply Chain: A Partial View of the Level I1 Model
Fig. 3 shows the specialisation of Plan and Source processes. The Source Level Two process types (S1 - Source stocked product, $2 - Source make-to-order product, $3 Source engineer-to-order product) attempt to characterize how a company purchases raw materials and finished goods. A level two Source process is guided by the planning made by a P2 process, therefore such 1'2 process has to be performed before the execution of the corresponding Source process. This temporal relationship is refined by the Planning link. The specialization of the Make, Deliver and Return processes was done in a similar fashion, though it is not shown due to lack of space.
1235 Fig. 4 illustrates a partial view of the P1 and P2 processes and their relationships with the associated information resources. In particular, P2 is the process of comparing total material requirements (a Supply Chain Plan Information Resource) with the constrainedjbrecast (another Information Resource) created by the P1 process and generating a material requirements resource plan (Sourcing Plans information Resource) to satisfy landed cost and inventory goals by commodity type. This translates into a material release schedule that lets the buyer know the amount of product that must be purchased based on current orders, inventory and further requirements. ~ !i p2 ~ --i i
~
Resource Perspective
PI|
i
v
. . . . . - SC Plans Persp
ra'e" ] C Persp Fo ec"t'1 . . . . '
$1
~
Information Resource
i 1 SPlans Persp
I
U s e s
.
.
.
E Sourcing Plans
~,
!
t
I
ti ChainSupplyPlans I Constrained Forecast
.
Creates
..
Figure 4. A Partial View of Relevant hd'brmation to Perform some Level H Activities
Level Three defines the business processes used to transact sales, purchase and work orders, return authorizations, replenishment orders, and forecasts. Fig. 5 shows a new class, Process Element, that represents those processes. A set of Process Elements defines a level two SCOR process. In the figure, it is possible to see the definition of the S1, and $3 particular ones. At this level, the SCOR model defines work and information flows. Thus, the workflow is specified by temporal relationships. As can be seen in Fig. 5, this link type is represented by customer-supplier relationships that define the roles of the associated Processes; and the information flow is specified by the set of data that are inputs and outputs of the Process Elements. As it was mentioned before, this is included in the proposed ontology by the Use Mode relationship, that allows specifying the semantic of a process in relation to a related information resource. The proposed SCOntologv was implemented by adopting the OWL ontology language (http://www.w3. org/TR/owl-features/) and the Protdg6 2000 ontology editor (http://protege.stanford.edu/). In order to test SCOntology, a refinery industry supply chain process (Julka el al., 2002) has been modeled. Figure 6 shows a partial view of the three SCOR representation levels for the crude procurement process treated in this work. • I
~"~
Process
......
-
i
SC~OR
,. . . . . . . ~
Process r
Identify Sources
[
~±_
j
•
i
. . . . .
-
Select Final, Supply i
.
.
.
.
.
~
! ,
• Process Element
~
s =supplier i c= customer i •............................................................................................. 1
:
[Select Prod. Receive Deliveries j L Product
1 j
r %rify ~ l Product ~
,
-T~ran~
Product
J
Authorize SuppPavment
1 ]
!
•! $1 ~~-
-.--
-
~ S o[ u r c e
~> . . . .
$ 3__ 7
Figm'e 5. Supply Chain. A Partial View of the Level III Model
4. Conclusions and future work The SCOR model is a business process reference model that provides a standard description of SC planning and operational activities. Thus, these tasks could be
1236 unambiguously described and communicated among supply-chain partners, providing the basis for SC improvement. However, in its current version, the SCOR model provides partial and very abstract answers to the competency questions that could be formulated in real situations. One of its main drawbacks is the weak representation that information and data have, as well as the lousy modelling of their usage by means of the actual SC processes. Moreover, the sources of most information flows are Enable type of processes; but the SCOR model does not explicitly specify which are those processes and which information is employed in such data creation. The SCOntology presented in this contribution formalizes and extends the SCOR model in order to overcome some of these limitations. Future work will involve specifying the information flows participating at levels IIi and IV and testing the model with other case studies.
Oil supplier: OrganizationalUnit
containlr eleme~2~ eleme~
[........... ::: ::: ..... [........:OrgahizationalUnii:::::t
! i:::::S~i:i~ I: ::!S~::::i:i~__~
[ :::::: De!!vede~ : ::: :::~
[:: ::Product ::::t
pl~ii:ne3gi i ~ [: :M:] :i:~ nabling''j// ::;Product::::::J
"Use I :Creates~ __ IInf°rmati°~ ..... ~i::i:i:!Estabhsh: :::: S°urc!ng: 1 ~-:Use SourcingRes°urce Plans: t { :ResourcePerspective ,........... .
I-~l
~"~ ........*~-~'~"~! .......................... ~I !t~ N ~ %~i.
I
..[
ScheduledReceipts: Information Resourcet-- t :ResourcePerspectiv~
_..
:Use
Figure 6. Case Study: A partial view of a Refinery Supply Chain model.
References Bolstorff, P., and R. Rosenbaum, 2003, Supply Chain Excellence: A handbook for dramatic improvement using the SCOR model, Amacon. Gruber, T.R., 1993, A translation approach to portable ontology specifications, Knowledge Acquisition, vol. 5, 199- 220 G~ninger, M. and M.S. Fox, 1995, Methodology for the design and evaluation of ontologies. Workshop on Basic Ontological Issues in Knowledge Sharing. Julka, N., R. Srinivasan, and I. Karimi, 2002, Agent-based supply chain management- 2: a refinery application. Computers and Chemical Engineering, 26, 1771-1781. Mannarino, G., 2001, Coordinates, Un lenguaje para el modelado de empresas. PhD Thesis, Universidad de Buenos Aires, Argentina. Shah N., 2004, Process industry supply chains: Advances and challenges, ESCAPE 14, 123-138. Stewart, G., 1997, Supply-chain operations reference model (SCOR): The first cross-industry framework for integrated supply chain management; Logistics Information Management, 10, 62-67.
Acknowledgements This work was sponsored by ANPCyT, CONICET, Universidad Tecnol6gica Nacional and Universidad Nacional del Litoral. Authors gratefully acknowledgehelp received from these institutions.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1237
Plant Structure Based Equipment Assignment in Control Recipe Generation Considering Conflicts with Other Batches T. Fuchino* and H. Watanabe *Department of Chemical Engineering, Tokyo Institute of Technology 2-12-1, Oookayama, Meguro-ku, Tokyo, 152-8552, Japan
Abstract This paper describes the equipment assignment in a control recipe design. To produce a batch in a batch plant, equipment assignments to each task of a batch are carried out on the basis of the equipment requirement information of the master recipe. However, the equipment units satisfying the equipment requirement are not necessarily connected topologically with each other, especially in the lnultiple-path and/or the network structural batch plants. Furthermore, there is no guarantee that the assigned equipment unit does not compete with other batches on a production schedule. In this study, plant structure based equipment assignment system considering conflicts with other batches is developed.
Keywords: Control Recipe Generation, Equipment Assignment, Plant Structure, Conflict between Batches
1. Introduction The process industries are confronted with competitive situation in these days that requires production of high value added products with higher productivity and quality. Batch processes are suitable for producing such products, and their operation should be designed to realize the property of batch processes. In batch processes, the necessary information to produce a product is specified in the recipe, which is hierarchically categorized into four types; general, site, master and control recipe. To produce a batch in a batch plant, the control recipe corresponding to the batch is generated by assigning equipment to the batch and sizing the master recipe to meet the quality requirement, and it is imputed to the operating system for execution. The assignment is carried out on the basis of the equipment requirement information of the master recipe. However, even though the equipment units satisfying the equipment requirement are assigned, it does not ensure that they are topologically connected with each other. Especially, in the multiple-path and/or the network structural batch plants, there exist plural production paths and alternative equipment units for flexible operation, but certain equipment units may not be connected with pipe each other originally or temporally, if such equipment units were assigned for a batch in the control recipe, * Authors to whom correspondence should be addressed:
[email protected] 1238 production interruption, abortion of unfinished product and/or unexpected release of hazardous material would occur. It is necessary to consider the plant structural connectability on real-time in generating the control recipe to maintain productivity and safety. Furthermore, in general, multiple products and/or multiple batches are produces in a batch plant, and the equipment units are assigned to these batches simultaneously or time is shifted. When a new batch is planed to be produced in a batch plant, assignment of equipment units to the new batch can not be decided independently, because it is restricted by the other batches, to which equipment units have already assigned, and their occupancy time. Therefore, it is necessary to consider such conflicts with other batches in generating the control recipe. There are several previous studies about recipe design support environment based on ANSI/ISA-S88.01 which is an international standard (Aoyama et. al. (2002), Hoshi et. al. (2002), Kaneko et. al. (2003), and so on). These studies paid attention to the relation between plant structural properties and the operation (recipe), but not to the conflicts with other batches. On the other hand, although batch scheduling systems based on ANSI/ISA-S88.01 have been developed (such as Nortcliffe (2001)), they are not taken into consideration about the plant structural connect-ability. In this study, the control recipe generation is considered based on ANSI/ISA-S88.01 ($88.01), and plant structure based equipment assignment system considering conflicts with other batches is developed.
2. Control Recipe Generation The control recipe is generated based on the master recipe by assigning equipment to tasks and sizing the batch. In the master recipe, equipment requirements to carry out recipe procedures are specified, and the equipments satisfying these requirements should be assigned. However, in order to consider the plant structural connect-ability, not only the main equipments, but also piping and a valve should be considered as an object to be assigned. Therefore, to enumerate alternative equipment assignment, the master recipe representation and the plant structure (P&ID) representation are necessary. On the other hand, the conflicts with other batches can be detected by comparing the plant schedule and the individual batch schedule. The occupancy time of assigned equipment is calculated by their sizing, and the batch schedule can be obtained by ordering of the occupancy time of the assigned equipment. In order to avoid conflicts with other batches, dispatching rule becomes effective. Based on the above consideration, this study aims at developing the control recipe generation environment shown in Figure 1 as IDEF0 activity model. The plant structure, master recipe and scheduling information are put into the system as control of this IDEF0 model and their XML representations are provided at A5 subactivity in this study. In the plant structure representation, equipment, piping and valves are defined as objects, and the structural connections are represented by their associations. The property and specification of the objects are defined as their attributes. The master recipe representation is based on ANSI/ISA-S88.02, and the entities to describe occupancy time for respective equipment unit are defined in the recipe representation in this study. Furthermore, the schedule information is represented by the production order and time of starting the respective batches, so that the plant schedule is
1239 obtained by correlation of the schedule information and occupancy time here. On the basis of these XML representations, the control recipe is generated. In the A2 sub-activity, the alternative equipment units are enumerated by mapping the equipment requirement in the master recipe representation and properties of equipment units in the plant structure representation, and the available paths are searched to check the connect-ability by tracing the associating piping and valves, and mapping the equipment requirements and properties of piping and valves, in the A3 sub-activity. The candidate of connect-able equipment assignment is informed to A4 sub-activity, and the occupancy time is calculated. The conflict with other batches is checked and a very simple dispatching rule; time of starting is delayed if the task conflicts, otherwise reassign equipment, is applied here. Although not only conflicts with other batches but evaluation to quality, safety, etc. should be performed in this activity, only the conflict is considered here. ~-'r-':-,I:-tLICf iC,FI 12:1 B:ec+ij i r-er,I,er-,f i [:er-t if i,::at ior, ,
T r ige r" t ,::, (]e:-~e lI;at @ I] :)rat ro I F::e,::: ~pe .....
'
~'
....."
............... -F:/I ant
:--.f r-,_~i-ti~r-e B:epreser-,tat . . . . . . .
"--..
F:e,:::ir:,e
'
."
"
. "~- ....
Ik
i:]e ne r-a te
•f
F:'l:~ LJ'_-:,L,i e Eq ui p rrle nt Alte m a t i,..,e
...---@1]l._j[ ~r i(_] ~, tUI @rll~ 1]
Recipe F r Eql..l i r:,rl,er "1t
i I:.,e ['r,:,cedu re i l-:,ruer "It Requi r F:'it::, iri.g ;_=tr-,d ",,,'a + .L .,,' o t-flit. ~ ] ;1 ,7tr-i,:_-t
. .....
r :';:' Ma:--:f ~*r t~ec i r:,e ...... I.... J~::il p l a n t '.. ior, ..
~r
F ir, d tbl@
+- +
Fe:_~'d L,le Equiprr, er, t
I. ~
] ,.,,,'@'.-;
-~-I-[:;=lt-~,:Ji ,:-tar e ,,~ Eq,.Jiprnent
......
oi: Reasss ig-,rner4 rorr, C'.rTffI ict'.-_--:
I[:or-,t: r o I Re,: i r:e B'.er-, r e s e n t a t ior,
L::{..........' ..........
E:,.~t,:::h ~nd ::Set U I-I ' ~L F' r :,,.::e..-.:=. P,::, +,J++r,,J ~ .... ~ Parameter._:: ~ ~ -< ~ {, k,,la na ~e A4 Furthermore, to ensure the connect-ability, the precise connection information, which is not the connection of equipment to equipment basis, but that of equipment phase to equipment phase basis. In this study, not only the main equipment but also valves, tee, pipe and so on, appeared in the P&ID are defined as objects, and their connections are
1241 defined using equipment ID, connection port ID and connecting object ID. For example, when the connection port "1" of the equipment "E-01" is connected with the connection port "1" of the valve "MV-01" via the pipe "Pipe-001", then the relation between "E01" and "MV-01" is described as follow. E-01.1, MV-01.1, Pipe-001
3.2 Master Recipe The master recipe is described hierarchically on the basis of procedure. The formula, equipment requirement and so on are defined as property of the procedure, in this study. In order to assign the equipment which satisfies the equipment requirement, the specifications on equipment are described by using predefined property class as same as the equipment properties in the plant structure representation. On the other hand, in assigning equipment, not only the consistency with equipment requirement, but also the conflict between other batches should be checked. To detect the conflict, the occupancy time of the assigning equipment for the scheduled batches and the necessary time for the task should be compared. However, the necessary time for the task is depending to the assignment. Therefore, in this study, the necessary time is modelled as a function of equipment capacity, in this example as shown a part at "ProcedureAttribute" tag, below.
3.3 Schedule Information There are two types of scheduling information are used in this study; the plant schedule information and the batch schedule information. The former specifies sequence of batches and their preferable time of starting and finishing. The assignment of equipment is to be performed according to this order. According to the plant schedule information, the provided external XML parser generates the batch schedule information, i.e. enumerate candidates of equipment for assignment, assign feasible equipment, calculate necessary time for each task, and decide the time of starting the batch not to conflict with other scheduled batches. In the batch schedule information, finally the time of starting and finishing the batch is generated, as shown as follow. <EndTime EndTime="Wed Dec 24 09:12:00 JST 2003"/> Based on the batch schedules, the Gantt chart for the batches appeared in the plant schedule information is provided.
4. Illustrative E x a m p l e To illustrate performance of developed method to assign equipment in control recipe generation, an example problem is solved. Six batches (No l to No. 6), which are specified by the same master recipe, are scheduled for the forgoing two stages
1242 polymerization plant as shown in Figure 1. The production priority is in that order, and equipment assignment is decided one by one according to the priority specified in the schedule information. The result shown in Figure 3 as a Gantt chart of main equipment is obtained successfully. 0000 Mixer
Mixer.22
0100
0200
0300
0400
0500
0600
0700
0800
0900
1000
Batch1
0002.00
:
c2z7.30 n~
nn
Mixer,23 Reactor.2
Batch 1 0209.30 0434.30
Reactor.6 Reactor.8
B=tchl
Reactor
I
!
0434.30
i
Reactor.4
i .
.
.
.
ii i~
.
BatchE 0720.0(~ 0907.30
Reactor,5 Tank.280
Batch5 0710.00 0857.30
i
Tank
i
Tank.278
Figure 3 Result of Assignment for six batches
5 Conclusions In order to assign equipment to tasks in generating control recipe, plant structural connect-ability of equipment units and conflict with other batches should be considered. In this study, plant structure based equipment assignment system considering conflicts with other batches is developed. References ANSI/ISA-S88.01-1995 Batch Control Part 1: Models and Terminology, ISA (1995). ANSI/ISA-S88.02-2001 Batch Control Part 2: Data Structures and Guidelines for Languages, ISA (2001). Aoyama, A., I. Yamada, R. Batres and Y. Naka, Multi-dimensional object oriented approach for automatic generation of control recipes, Computers and Chemical Engineering 24 (2000) 519524. Hoshi, K., K. Nagasawa, Y. Yamashita and M. Suzuki, Automatic Generation of Operating Procedures for Batch Production Plants by Using Graph Representations, J. of Chemical Engineering of Japan 35 (2002) 377-383. JSPS PSE- 143 committee, Technical Report No.20 (1999). Kaneko, Y., Y. Yamashita, and K. Hoshi, Synthesis of Operation Procedure for Material and Energy Conversions in a Batch Plant, Lecture Notes in Artificial Intelligence 2773 (2003) 12731280 Nortcliffe, A. L., M. Thompson, K. J Shaw, J. Love and P. J. Fleming, A framework for modeling in $88 constructs for scheduling purposes, ISA Transactions 40 (2001) 295-305
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) (C22005 Elsevier B.V. All rights reserved.
1243
IMC Design of Cascade Control Mario R. Cesca a and Jacinto L. Marchetti b* a Chemical Engineering Department- Universidad Nacional de Tucumfin Av. Independencia 1800 - (4000) Tucumfin - Argentina b Institute of Technological Development for the Chemical Industry (INTEC) Gtiemes 3450, (3000) Santa Fe, Argentina
Abstract Cascade control is one of the most successful methods for enhancing single-loop performance. However, the literature about synthesis methods for designing and tuning cascade control systems appears to be rather limited. In this contribution, a model-based procedure using internal model control (IMC) approach is proposed for synthesizing the controllers transfer functions. The suggested tuning procedure determines the controller filter time constants such to assure robust stability. Simulation examples are provided to demonstrate the goodness of the synthesis method and to compare its performance with those of PID-PID cascade configuration tuned with already accepted rules.
Keywords: Cascade Control, Robust Control, IMC Design, Model Based Control 1. Introduction The robust process control has received considerable attention in the last twenty years. The IMC structure, as base for the robust controller design, is treated with great detail in Morari and Zafiriou (1989) where robust control is associated with IMC design. When addressing cascade control, the authors mention the utility of this control configuration when the secondary process is dominated by an important uncertainty. Skogestad and Postlethwaite (1996) analyze different cascade control structures, but they do not present any particular robust synthesis method. The paper of Tan et al. (2000) is one of the few contributions of robustness analysis for series cascade systems, where they propose conventional PID controllers for the inner and outer loops. Lately, Brosilow and Joseph (2002) used IMC design approach employing the Mp parameter and considered both stability and robust performance simultaneously. In this framework, the contribution by Hahn et al. (2002) presents a procedure to obtain the uncertain information in order to design robust IMC controllers. In this work, the IMC Series Cascade Control structure is studied (see Figure 1). The analysis includes robust stability conditions for tuning both controllers. Finally, the closed-loop performance and robustness of the synthesized system are compared with cascaded PID regulators tuned according to Lee et al. (1998), one of the few systematic tuning rule for cascade systems reported in the literature.
Author/s to whom correspondence should be addressed:
[email protected] 1244
d=J
d,]
r*(
Y2
y
....
Figure 1. IMC Series Cascade Control Structure
2. IMC Cascade Control Synthesis 2.1 Nominal Perfornace The primary disturbance d~, and the secondary disturbance d2 are typically analyzed when dealing with cascade control systems. In particular, the effect of the secondary disturbance on the main output Yl is considered for synthesizing the inner controller q2. Thus, the IMC design proceeds by minimizing the H2 norm of the yl error according to ~'
n nfe?dt- nll II;-nnlJ (l-G2 q2
"
q2
0
q2
2
q2) G1 d2112
(1)
On the other hand, the optimum primary controller q l is obtained by minimizing the H2 norm of the error el, caused by the primary disturbance ,:,o
min ql
f2e,
,,2
aft - min e 1 il2 Z/1
;
n i (1 - q~(if8) d~ !1i
(2)
o
Under nominal conditions (plant equal model), the time constants of the IMC filters should be chosen as small as possible. To avoid excessive noise amplification, the filter parameter should, be chosen so that the controller high frequency gain is not greater than [3 times its low frequency gain. This criterion can be expressed as
-sup] q(jm)l
~o, [q(O)J
(3)
where q(s) is the transfer function of the IMC controller. Brosilow and Joseph (2002) proposed max fl = 20, however, factors between 5 and 20 are encountered in practice. In this work, f l - 10 is adopted, which follows the standard industrial practice of limiting the high-frequency gain of PID controllers. If the controller does not have complex poles in the left-half plane, equation (2) can be transformed in the limit: [3- lim [q(jco)]
~,-,= [q(O) I
(4)
1245 2.2 Robust Stability
In order to evaluate the robust stability conditions a multiplicative description of the uncertainty is assumed. Thus, two families of models with uncertain parameters are defined as"
Hi-{Gi"
Gi (.lo~) - O~(joJ)
I
-I
i - 1,2
(5)
where in each family set, G; is the nominal model, ~.i(jo)) is the multiplicative uncertainty, and (,mi (co) stands for the largest module. The robust stability condition (Skogestad and Postlethwaite, 1996), for the inner loop is
[
I-I
I 0;Vi = 1 v 2 v ...s where Q >- 0 and R >- 0 are the weighting matrices for state and control while positive definite P is the stabilizing terminal cost for the prediction horizon N . The objective is defined over
p=l,2oroobased
on
ll,12orlooperformance criterion and
disjunction denoting logical "or" for i = 1..... s systems.
v
is
After the N ~/' time step we
enforce the solution of constrained and unconstrained problem to coincide, [17,18], by defining O~ as the positive invariant set containing origin in its interior:
O~ = I x(k)~ N",u(k)~ ~'" Kx(k)E Y, 1 [(A i + BiK)x(k)+ Gu'(k)~ X;Vw(k) e ®;Vk > 0 J
(4)
where K is the optimal feedback gain. Rewriting the system (2) in terms of constraint sets X,Y and substituting x(k) into the objective function of equation (3) and can be reformulated as tbllowing multiparametric mixed integer quadratic program.
E [~(U,Z,D,W,x(O)]
F ( x ( 0 ) ) - min U,Z,D
~,~(-)\
.~,.t. g { = : { a - ) . a : { k ) , , , ( k ) . . , { k ) , x { O ) )
0 ~ w(k) C" - w(k) "b or if Ogj < 0 ~ w(k) ~" - w(k) tb . Ow(k)
~w(k)
Thus, by substituting the sequence of critical uncertainty, w(k) c" in the constraints set g(.), a multiparametric linear program is formulated as,
Ilt(U,Z,D,x(O)) = max{gi(U,Z,D,W,x(O)} w,j • [E >__gi(U,Z,D,W,x(O) ] = mln~ N e [x(0)e X , U e Y ,We O N , D e {0,1}xs;vj = l , . . . , J
(8)
Equation (8) can then be solved using the formal comparison procedure of [ 1].
4. Design of mpRHC The feasibility constraints (7) from section 3.3 are incorporated in problem (5) to obtain the following open-loop robust predictive control problem, min ~ 0E ~ [~(U,Z D,W,x(O)] F(x(O))- U,Z,D
s.t. g(zi(k),~i(k),u(k ), w(k),x(O)) gi(U,Z,D,W,x(O)} 8
This open-loop robust predictive control problem is a bi-level optimization problem. Note that the inner minimization problem is equivalent to equation (8), which can be solved separately resulting into a set of linear feasibility constraints ~ ( . ) < 0 . Substituting it into equation (9) results in following single-level optimization problem:
1253
E[~(U,Z,D,W,x(O)]
F(x(0)) - min U.Z, D
~,~
s.t. g(zi(k),~i(k),u(k),w(k),x(O)) < O;~(U,Z,D,x(O)) < 0; ~i(k)-l;~Si(k)E
{O,1}Vi-lv...v
(10)
s;x(O)E X , U ~ y N w(k)~ 6)
i=1
R e m a r k 4.1 The solution obtained in section 4. is obtained as a piecewise affine optimal robust parametric predictive control policT as a fimction of states U(x(O))for
the critical polyhedral regions in which plant operation is stable and feasible Vw(k).
5. Design Examples Example
1: Consider the following dynamical system
x(k+l)_lll.5X(k)+z,(k)
i[
x(k)>O
.lx(k)+u(k) ~/' x(k)
x
I_i
s_0j
.......
X
:-
0.01 O
4 . . . .
~
r
I
I
--
-
0.005
I
0
0
100 200 T i m e (min)
I
I
300
I
0
I _ _
[
100 200 Time (min)
300
F i g u r e 2. S i m u l a t i o n r e s u l t s f o r 1 0 0 0 litre r e a c t o r
The rates of heat generation and removal by evaporative cooling are shown in subfigure C. It can be noticed that a significant amount of heat is taken out of the system by the proper usage of the vaporization phenomenon. The simulations clearly show the
1260 advantage of evaporative cooling in addition to the jacket cooling which is limited for highly viscous systems and for large reactors that have relatively small heat transfer areas. The temperature of the reacting mixture is maintained around 60 °C and the pressure is kept at 1 atmosphere. The vaporization rate for water is shown in subfigure E. It is observed that vaporization flux is strongly dependent on the temperature. As soon as the reaction is over, the vaporization causes the temperature to fall thus leading to its sharp decline. Since the mole fraction of vinyl acetate is very low in the gas phase due to the high rate of reaction, it was not considered in the control strategy. The value of set point (mole fraction of water in the gas phase) was chosen based on economic considerations (depending on the usage of nitrogen and increment in vaporization flux) of the reaction. Simulation runs were performed for that purpose. The set point along with the actual mole fraction of water in the gas phase is plotted in subfigure F.
4. Conclusions and Future Perspective Emulsion polymerization process offer great challenges with respect to industrial operation, optimization and control. Since the reaction is highly exothermic, the process operation is often restricted by the heat removal constraint. One of the major issues is to run the process at safe conditions but at higher reaction rates. Evaporative cooling can be used for this purpose. A model has been developed here that describes the effects of vaporization on the process conditions. The exact estimation of the molar fluxes requires knowledge of the mass transfer coefficients and the interfacial composition, area and temperature. The approach used in this work is based on Burghardt's approach. Since Burghardt's solution can be applied only when the interface and bulk compositions are known, the vapor-liquid equilibrium calculations together with diffusion equations are solved by an iterative procedure. This model was used to determine the operating set point. Two decoupled control loops are implemented to take advantage of the vaporization phenomenon. The simulation results clearly indicate the advantages of using evaporative cooling over the usual jacket cooling, which is restricted in highly viscous systems and in big reactors (due to the lower heat surface area to volume ratio). In the future, we plan to validate and to improve the results by the experiments.
References Arora, S. and R. Gesthusien, 2004, 8th International Workshop on Polymer Reaction Engineering, DECHEMA Monographs, Vol. 138. Burghardt, A., 1983, Int. Comm. Heat Mass Transfer, 10. Burghardt, A., 1984, Chemical Engineering Science, 39. Sayer, C., M. Palma and R. Giudici, 2002, Ind. Eng. Chem. Res., 41. Taylor, R., and R. Krishna, 1993, Multicomponent Mass Transfer. John Wiley & Sons, Inc., USA.
European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.
1261
Event-based Approach for Supply Chain Fault Analysis Ramon Sarrate a*, Fatiha Nejjari a, Fernando D. Mele b, J. Quevedo a and L. Puigjanerb a
Dept. d'Enginyeria de Sist., Aut. i Inf. Ind., Universitat Polit6cnica de Catalunya Rambla de Sant Nebridi, 10, E-08222, Terrassa, Spain bDept, d'Enginyeria Quimica, Universitat Polit6cnica de Catalunya ETSEIB, Av. Diagonal 647, E-08028, Barcelona, Spain
Abstract This work is a contribution to fault propagation analysis in a supply chain network. An event-based fault detection method is applied to fault propagation analysis validation. The goal of this methodology is to discover and validate fault propagation effects on system variables. This knowledge could be used to improve corrective action design in order to compensate negative effects. The methodology has been applied to supply chain fault propagation analysis over inventory data. Once validated, fault propagation effects on inventory level could be compensated by adapting the inventory control policy. Thus, unnecessary inventory holding could be reduced.
Keywords: supply chain management, discrete event system, fault detection, process monitoring, fault propagation analysis
1. Introduction Supply chain productivity and economic benefit strongly depend on the correct behaviour of each unit or activity involved. A raw material supply transport interruption or a production machine breakdown in a manufacturing plant can bring the supply chain to a decrease in efficiency, leading to unexpected economic costs. These undesired situations can be regarded as supply chain faults or incidents. Due to the interconnected nature of supply chains, fault effects usually propagate through the system, degrading, as time goes on, the overall performance. After a production machine breakdown, a manufacturing plant will lately service orders posted by a distributor. Consequently, the distributor could also be forced to delaying orders posted by its costumers, and so on. Anticipating the fault propagation effects could be beneficial in reducing the overall economic loses. Global corrective actions could be designed and planned beforehand off-line. As soon as a fault occurs, these corrective actions could be applied, compensating for fault propagation effects and thus minimizing economic loses. In the machine breakdown example, the manufacturing plant would decide to repair the damaged machine, whereas at the same time the distributor would decide to
Author/s to whom correspondence should be addressed:
[email protected] 1262 immediately post its pending orders to another manufacturing plant while production is re-established in the former. This should be preferable to just waiting for repair. In the literature, the analysis to determine how certain fault effects propagate through a system is known as fault propagation analysis. Blanke et al. (2003) propose a methodology for fault propagation analysis based on structural analysis, a technique which analyses the structural properties of mathematical models. However, whenever models are not available, their approach is not applicable. The approach proposed in this paper is based on the observation of system signals. Faults modify the normal behaviour of system signals. Discovering temporal patterns originated by faults on these signals should help in anticipating negative fault effects. Candidate fault propagation patterns could be generated by applying well-known data mining techniques as time series pattern recognition (Berndt et al., 1996) or clustering methods (Piera et al., 1991). These techniques allow for knowledge discovery. However, the observation of system signals by an expert could be enough to produce a candidate fault propagation pattern. In this paper, candidates are generated from the observation of inventory levels. Inventory data is commonly registered by companies, so it will probably always be available for analysis. A methodology has been developed that allows for checking the correlation of a fault occurrence with a candidate fault propagation pattern. This validation methodology is based on a process monitoring technique which has been previously applied to other domains such as biotechnological process supervision (Sarrate et al.,1998) or tool machine monitoring (Aguilar et al., 2001). In this work, its application has been extended and adapted to supply chain fault detection. In Section 2, a brief description of the process monitoring technique applied to fault detection is presented. Guidelines to apply this technique to fault propagation analysis validation are given at the end of this section. Section 3 is devoted to illustrate the methodology on a supply chain network. Two fault scenarios are studied and results are discussed. Some concluding remarks on this methodology are given in Section 4.
2. The Fault Analysis Methodology 2.1 Event-based fault detection Fault detection aims at determining faults present in a system and the time when they have occurred. A lot of research has been done in this field (Isermann, 1997). In Sarrate (2002) a methodology for process monitoring is proposed and applied to tool machine fault detection. This fault detection rrethodology is organized in to stages: the Interface and the Supervisor.
2.1.1. The Interface The Interj'ace analyses system signals following the sliding window paradigm, in order to detect relevant events. Under this approach, data is processed in sets con"prising a time window. A window slides over time, and is periodically sampled. For each sample, all window data is analyzed in order to produce a window attribute which constitutes new data. Output data produced by this sliding window mechanism could be analysed again following the same procedure. Applying this algorithm recursively with different kinds of analysis, the required significant information can be abstracted. For instance,
1263 signal trends can be generated by first applying a linear regression window-based analysis to obtain the slope. Next, the slope is classified over a set of intervals applying a statistical window-based analysis to obtain the mode, which represents the most probable signal trend. Interface configuration is needed to adjust window parameters. Expert system knowledge is applied for lntec/ace design and configuration.
2.1.2. The Supervisor The Supervisor is build upon an automaton which models the system behaviour. It must describe normal operation as well as all faulty situations that should be able to detect. Expert system knowledge is needed to discover which event sequences are associated to faulty situations. In the automaton, states model system states whereas transitions are associated to events.
2.2 Fault propagation analysis validation The Supervisor automaton models system behaviour as event sequences. Events are associated to relevant signal dynamics. Thus, the observation of a sequence of relevant signal dynamics allows a faulty situation to be detected. In fact, the auton~ton stores the fault propagation knowledge. Fault propagation effects are often clearly visible on system variables. Thus, the observation of signals by a system expert should provide temporal patterns that a fault originates on them. Once this information is available, the automaton can be built. Since fault detection methodology is based on fault propagation knowledge, the fault detection procedure can be used for fault propagation validation as follows" 1. A set of design signals must be available. These must correspond to normal as well as faulty behaviour. The design set could be generated by a simulation model or obtained by measurements in the real system. 2. Through expert observation of the design set, the fault detection system must be designed and configured a. Relevant signals dynamics are to be identified. The Interlace must be designed accordingly, so that it is able to detect these significant events. b. Fault propagation patterns are to be discovered. The automaton must be build, so that it models these patterns. 3. A set of validation signals must be available. The same considerations given for the design set apply. 4. The fault detection system is run on the validation set. A fault detection success validates the fault propagation knowledge. However, wrong fault detection performance indicates that the fault propagation knowledge was badly inferred.
3. Application to Supply Chain Fault Propagation Analysis 3.1. Problem statement The fault analysis methodology will be applied to a supply chain. The model interconnects 6 entities, as illustrated in Figure 1. Two types of flows are present. On the one hand, there is a material flow (raw material P and finished products A and B) from the supplier to costumers. On the other hand, there is an information flow (order) from costumers to the supplier.
1264 Supplier
Plant
Distribution centers
Retailers
]D1B~RIB~
~No,"
/
Figure 1. Supply chain network
Demand pattern has been simulated following a certain distribution probability. Given the discrete event nature of the supply chain, its model has been simulated in Matlab using Simulink and Stateflow tools. Two faulty scenarios were studied applying the fault analysis methodology developed in section 2: • Scenario 1 : A transient transport interruption of product B from P1 to D1B. • Scenario 2 : A transient production delay of product A. The goal is to discover how these events have an effect on the inventory levels of the supply chain entities. Excess inventory incurs unnecessary holding costs, while the inability to meet the costumers needs results in both loss of profit and potentially, the long term loss of costumers. The fault propagation knowledge can be used to design adequate corrective actions. For instance, once a fault has occurred and has been noticed, fault effects could be compensated adapting inventory control policies. 3.2. Results
Three design simulations were provided for the fault propagation analysis: the fault-free case, a transport interruption at 4000 s.u. for 65 s.u. and a production delay at 5000 s.u. during 700 s.u., where s.u. stands for simulation units (1 s.u. = 5 min.). Figure 2 shows the inventory levels for some relevant supply chain entities under faultfree as well as faulty conditions. Apparently, the effects that both faults have on them can be easily appreciated. Both result in a transient increase of inventory levels for different supply chain entities. The transport interruption significantly affects D1B inventory level, whereas the production delay slightly modifies D 1B and D 1A inventory levels. In order to validate these fault propagation statements, the fault propagation analysis validation methodology has been followed. For Scenario 1, the fault detection system illustrated in Figure 3 was designed a tuned. The trend detector implements the Interface. Significant trend events sequences are characterized in the Supervisor by a Stateflow automaton. Fault detection results for the design set are illustrated in Figure 4. The first plot corresponds to the D1B inventory data. It shows also the fault detection at 4160 s.u.. Trend events are detected following the sliding window paradigm, as illustrated in section 2.1.1. The second plot corresponds to slope data obtained through a linear regression window-based analysis. And the third plot corresponds to the mode obtained from a statistical window-based analysis.
1265 100 [- Fault-fre4
l
f
_i
__=:[ ............... ]". . . . . . .
D1B invi "i
. . . . . . . II'l '", "ill ""l"l .... "]t' "i "i "" " T....... r,[ .... 0 2000 4000 6000 8000 10000 ,~,~[[~. Fault'fre~ [[[[[~, i , ~ 'm [ Ill ~NIm[Wll'[
] .... _~.L
'1 "ll~ii "'i 'll"l"i 12000 14000
~~~~~~~~~[
~ i ]
"i -' p" i ' '' "' "[ 16000 18000
IIl~[
/mmmml~~~--1[
1
a 1A
inv.t 1[ Ill W'IIV~II"I'ql*lI'I~1rlll iI'f'l~t~'ll'rl"~ ~,r,llrlq '!~ I ,lrq rn1""!"11'~'f"'l'l ' ~"l 0
2000
100[
4000
T . . . . po~t int. . . . pticlltl
D1Binvi" .... 0 100 -
6000
I
6000
8000
2000
100 . ~ r o d2
D1Ain5(~v
"1
0
12000
14000
10000
16000
]
12000
]
Illli'll'l-'l'[ql"i 14000
16000
18000 __~
. . . . l~. 18000 -7
i" I i.~i "II ~II~II ~ " l ' ' l ' l ' [ ~ ' l
0
10000 _---T--[
• , , , , ~ ',3 I " " ! [ ! ! l ' _ l r " l _ ~ l l / ] l r = ~ : [ l ' ~ [ [ l ' l " l
-,~'1 '-','11~
2000 4000 Productic in delay
D1B inv.
8000
~
4000
6000
' 8000
I,.-'-I~ I"I I'pl.n.F. 10000
12000
14000
16000
18000
n delay
"I I'I II I ~
IIIlUl IqWI II r 'rpr'p'ml"l'rlqr.qpr,I
2000
4000
6000
!~'ql'~ ~q I "lI i'l'l ,~lll 11'11 ,'t'lll'l II'll!
8000 10000 12000 Time (s.u., 1 s.u 5 rain.)
14000
16000
18000
Figure 2. Design set
EUi~j~{~ZEll CJock I I
worFspace ~
I ...........
~ ___L_l-a--z-'-*r--_-____-3___ I r -it 71
/ %e~,f
Trenddeteetor .......
:~ '~-- Su;ervisor --
* start
'Normal/ r_,estat=O .
D1B_incr. 'Fmtl estat=l D 1B_decr
Figure 3. Event-based fault detection system and automaton for Scenario 1 Once designed and tuned, the fault detection system was used as a validation tool. A validation set was generated via simulation, varying fault time and duration. Table 1 summarises the validation results. As expected, the longer the fault, the better the fault detection: over 250 s.u duration success is granted. This confirms the influence of this fault on the D 1B inventory level. For Scenario 2, a similar study was developed. Another fault detection system was designed but validation results were not so satisfactory. This confirmed the slight influence of this fault on supply chain entities. In this case, fault propagation effects were not generic applicable.
4. Conclusions This work describes a methodology for fault propagation analysis and validation. Fault detection systems are designed for validation purposes. They are built from expert system knowledge, so no mathematical system descriptions or models are needed. As this fault detection system is built from fault propagation knowledge, it can be used for fault propagation validation.
1266 D1B Inventory 150
I'I
l'IIll
.~,,
o
) !.,,,,
-~,
'q
'
ll'~Ill l
~'II I 'I
"
r~-~,'~~
~" 0
2000
6000 8000 10000 12000 14000 Linear regression window-based analysis: Slope
16000
18000
0.6, :. 0.4
1 •
°iil.rr..l~f~,f.r. _o.21 0
2000
i
[~ ,'.... ,, ,n,,.n.h, ....... ~'.~w .n,a ~ , . ~ , r l~..t w ~ ¢"'pu""oW'*" 4000
[
[!
6000 8000 10000 12000 Statistical window-based analysis: Mode
[
[ ..... i
14000
[ .... r
!111 I I 11111It Ill,illill °~oI i lllll I llUli I i llill 2000
4000
6000
16000
18000
!
II IIIIlJl! ,ll Iil[i[lI!
8000 10000 12000 Time (s.u., 1 s.u. = 5 rnin)
14000
16000
18000
Figure 4. Event-based fault detection results for Scenario 1 design set Table 1. Validation results for Scenario 1 (X." wrong, ~" success)
Fault time (xl0 ~ s.u.) = ,
O ,,..~
a,
3
4
5
6
7
8
9
10
11
12
13
14
65
X
x/
X
X
X
X
X
X
X
X
X
X
]oo
x
~/ x
4
4
4
x
x
x
x
4
x
250
x/
x/
q
~/
x/
x/
~/
x/
x/
x/
x/
x/
i
An application to supply chain fault analysis has been done. Results demonstrate the usefulness of this approach. Once fault propagation analysis is validated, adequate corrective actions could be planned to compensate for fault effects. References
Piera, N. and J. Aguilar, 1991, Controlling selectivity in non-standard pattern recognition algorithms, IEEE Trans. In Syst., Man and Cybernetics, 21, 1, pp. 71-82. Berndt, D.J. and J. Clifford, 1996, Finding patterns in time series: a dynamic programming approach, In: Fayyad, U.M. et al., Eds., Advances in Knowledge Discovery and Data Mining, pp. 229-248, AAAI Press/MIT Press. Isermann, R., 1997, Supervision, fault-detection and fault diagnosis methods - an introduction, Control Engineering Practice, 5, 5, pp. 639-652. Sarrate, R., J. Aguilar and J. Waissman, 1998, On-line event-based supervision of a biotechnological process, 3'd IFAC Workshop on On-line Fault Detection and Supervision in the Chemical Process Industries, pp. 359-364. Solaize. Aguilar, J., R. Sarrate and J. Waissman, 2001, Knowledge-based signal analysis and case-based condition monitoring of a tool machine, Joint 9h IFSA World Congress and 20 th NAFIPS International Conference, pp. 286-291. Sarrate, R., 2002, Supervisi6 Intel.ligent de Processos Din~mics Basada en Esdeveniments, PhD Thesis, Universitat Politbcnica de Catalunya (in Catalan). Blanke, M., M. Kinnaert, J. Lunze and M. Staroswiecki, 2003, Diagnosis and Fault-Tolerant Control, Springer-Verlag, Berlin.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) {~:2005 Elsevier B.V. All rights reserved.
1267
Back-off Application for Dynamic Optimisation and Control of Nonlinear Processes Silvina I. Biagiola ", Alberto Bandoni b and Jos6 L. Figueroa ~* aDepartamento de Ingenieria Eldctrica y de Computadoras, Universidad Nacional del Sur-CONICET Av. Alem 1253, 8000 Bahia Blanca, Argentina bPlanta Piloto de lngenieria Quimica-CONICET La Carrindanga Kin.7; 8000 Bahia Bianca, Argentina
Abstract The operating point of a process plant is obtained through optimisation of an objective function subject to certain constraints. Typically, the resultant point lies in the boundary of the operative region. Therefore, in the presence of disturbances, the constraints may be violated and the process may be obliged to operate in an infeasible region. The goal of this paper is to present an efficient back-off algorithm to determine the operating point which guarantees feasibility even under disturbances effects. The proposed method is especially oriented to diminish the computational time associated with nonlinear processes. For this purpose, the nonlinear process is approximated by means of a piecewise linear (PWL) model which allows a substantial computational time reduction. Finally, an example is dealt with to show the application of the proposed approach. For this purpose, a nonlinear steam generating process is modelled, optimised and controlled. Keywords: back-off, canonical piecewise linear approximations, dynamic optimisation, process control
1. Introduction Applications of nonlinear optimisation problems have become very common in the process industries, especially in the area of process operations. To achieve the optimal design and operation of a process, one seeks the best design and operation which will result in a maximum profit. Therefore, in a first design stage, the operating point is usually determined to maximize (or minimize) an objective function. This cost function is normally a weighted combination of various utility costs, material costs, production costs and penalties of environmental emissions. The process model and constraints describe the interrelationship of the key variables. These constraints define a feasibility set for the possible operating points, and in most cases, the optimal operating point lies in the boundary of the set. Therefore, in the presence of disturbances, the current operating point (i.e. optimum point) might exceed some constraint value for the changed conditions. This would lead to undesirable or even unsafe operation of the plant. To avoid operating the process in an infeasible region (Figueroa et al., 1996), it is possible
Author to whom correspondence should be addressed:
[email protected] 1268 to move the operation point away from the one determined in the optimisation level and to oblige the new point to satisfy the constraints under the disturbed operation. The movement of the operation point due to the likely effect of disturbances is referred to as back-off, and was originally calculated from the desire for evaluating and comparing control strategies on the economical basis (Perkins and Walsh, 1994). Because in the process industry there is a great number of strongly nonlinear processes, the accomplishment of the back-off algorithm may become very slow or even impossible to perform. To avoid this obstacle, the optimisation problem can be turned into a linear one. In the present paper, we propose to use a canonical piecewise linear (PWL) approximation (Julifin et al., 1999) to the problem. This formulation allows the systematic description of any nonlinear function. Then, the whole procedure, i.e. the dynamic back-off analysis, the steady-state calculations, the closed-loop output predictions, are accomplished on the basis of the PWL representation of the process. The main advantages of the proposed approach are the problem simplification and the substantial calculation-time reduction. In a following stage, a controller is designed to regulate the behaviour of the plant around the designed steady-state value. The underlying idea is that the controller provides perfect control, so that the plant remains very close to its nominal operating points against disturbances and parameter variations and uncertainties on the plant characteristics. Finally, an example is presented to show the application of the introduced method. For this purpose, a nonlinear steam generating process is modelled, optimised and controlled. Computer simulations are developed for showing the performance of the optimised and controlled nonlinear process. The results obtained with the exact nonlinear approach and the approximating PWL one, are compared.
2. Back-off problem formulation The mathematical formulation of the closed-loop back-off problem can be posed as follows:
(1)
%bj[USo,%] subject to
g[Us,X(t),d] 0 such that
dV(x(t))
< 0 along all state trajectories. If a P > 0 exists, system (3) is quadratically dt stable and following statement holds: system (3) is quadratically stable if and only if there exists a positive definite matrix P>0 such that following inequalities are satisfied
A & i P + PA~L i < O, e > O, i - 1,...,n
(5)
Consider the polytopic closed-loop system (3). Then the following two statements are equivalent (Vesel2~, 2002): 1. The system (3) is robust static output feedback quadratically stabilizable. 2. There exist a positive definite matrix P = p r > 0 and a matrix F satisfying the following matrix inequality
(A i + B i F C i)T p + P(Ai + B i F C i)< 0, P > 0, i - 1 , . . . , n
(6)
1305 Consider the polytopic closed-loop system (3). Then the following three statements are equivalent (Vesel3), 2002)" 1. The system (3) is simultaneously static output feedback stabilizable with guaranteed cost oo
~(x~,~ Qx~,~ + .~,~
~.~,~)~, ~_xo~,~ ~ ~xo ~,~-
~
~ *, ~ >o
0 2. There exist matrices P > 0, Q > 0, R > 0 and a matrix F such that the following inequalities hold
(A i + BiFC i )r p + P(Ai + BiFC i )+ Q + Cri F T R F C i < O, i - 1,...,n
(8)
3. There exist matrices P > 0, Q > 0, R > 0 and a matrix F such that the following inequalities hold
Ai TP + PA i - PBiR-1Bri P + Q 0 from the following inequality
S(Q
< O, yI < S , i - 1,...,n
(12)
when 7" > 0 is any non-negative constant and S = P I. 2. Compute F from the following inequality
+
+•
1 °, i =',---,
If the solutions of (12), (13) are not feasible, either the system (3) is not stabilizable with a prescribed guaranteed cost, or it is necessary to change Q, R and 7" in order to find a feasible solution.
4. Simulation results Consider a continuous-time stirred tank reactor (CSTR) with the first order irreversible parallel exothermic reactions according to the scheme A
k, >B, A
~2 >C, where B
is the main product and C is the side product. Under the condition of perfect mixing, the dynamic mathematical model of the controlled system has been obtained by mass balances of reactants, energy balance of the reactant mixture and energy balance of the coolant. Using usual simplifications, the model of the CSTR can be described by four nonlinear differential equations
1306
dCAdt - -
Vr
/
qr + k 1 + k 2 CA + Vr CA f
(14)
dCB - _ q___LCB+ klCA + q__L d----~-
Vr
dTr --=
hlkl + h2k2
dt
IOr Cpr
dTc
_
(15)
Vr cBf
qc (Tcf
cA +
qr -~r
AhU
(Trf- Tr) + - - ( T c
AhU _Tc)+__(Tr_Tc
Vr Pr Cpr
- T~)
(16)
)
(17)
with initial conditions CA(0), cB(0), Tr(0) and Tc(0). Here, t is time, c are concentrations, T are temperatures, V are volumes, p are densities, Cp are specific heat capacities, q are volumetric flow rates, h are reaction enthalpies, Ah is the heat transfer area and U is the heat transfer coefficient. The subscripts denote .r the reactant mixture, .c the coolant, .f feed values and the superscript .s the steady-state values. The reaction rates k~, k2 are expressed as
kj =k0jex p
RTr
,j-1,2
(18)
where k0 are pre-exponential factors, E are activation energies, R is the gas constant. The values of all parameters and feed values are in Table 1.
Table 1. Parameters and inputs of the chemical reactor Vr = 0.23 m 3 V~= 0.21 m 3 qrs = 0.015 m 3 m i n 1 qc~= 0.004 m 3 m i n -1
,Or= 1020 kg m -3 Ah = 1.51 m 2 CAC= 4.22 kmol m -3 Pc = 998 kg m -3 U = 42.8 kJ m-2 min -1K-1 CBr = 0 kmol m -3 cp~ = 4.02 kJ kg-1K-I gl =El~ R = 9850 K T~f= 310 K Cpc = 4.182 kJ kg-1K-j gz=E2 / R = 22019 K T~f= 288 K
Model uncertainties of the over described reactor follows from the fact that there are four only approximately known physical parameters in this reactor:
1.6 0,1] k20 ~ [4.95 x 1026", 12.15 x 1026 ] . The nominal values of these parameters are mean values of intervals. The steady state behavior of the chemical reactor with nominal values and also with all 16 combinations of minimal and maximal values of 4 uncertain parameters was studied at first. It can be stated the reactor has always three steady states, two of them are stable and one is unstable. The maximal concentration of the product B is obtained in the unstable steady state. So, the main operating point is described by unstable steady-state values of state variables. The situation for the nominal model is shown in Figure 1, where Q~EN is the heat generated by chemical reactions and Qouf is the heat removed by the jacket and the product stream. The main operating point for the nominal model is
[c,A,CB,Tr s , ,T c,] -[1.8614kmol.m -3 1 0113kmol.m -3 338.41K,
328.06K]
1307 CB (kmol m -3 1,25
QGEN' QOUT (kJ min" ) 5000 4000
)
1,00
3000 0,75 t
2000
0,50
1000
{
0,25
0 -1000 300
310
320
330 340 mr(K)
350
360
370
0,00 300
310
320
330
340
350
360
370
T r (K)
Figure 1. Stead), state behavior of the chemical reactor for nominal values of uncertain parameters
Design of a robust stabilizing controller is based on having a linear state space model (1) of the controlled system. Linearized mathematical model has been derived under the assumption that the control inputs are the reactant flow rate qr and the coolant flow rate qc and the controlled output is the temperature of reaction mixture Tr. The other input variables are considered to be constant. The matrices of the nominal linearized model in the main operating are
A0 -
C0 -(0
-0.1479
0
-0.0226
0.0354
-0.0652
0.0057
1.3763
0
0.2118
0.0685
0
0
0.0737
-0.0928)
0
~
(10.2546 1-4.3968 Bo - 1 ' ,-123.5131 (
O
0 0 0
,
-190.7612
1 0). This model is unstable, the eigenvalues of A0 are-0.0652, 0.1195,
-0.0741+0.0310i,-0.0741-0.0310i. For 4 uncertain parameters, we have obtained 24 =16 linearized mathematical models, which differ in coefficients of Ai, Bi. These systems represent vertices of the uncertain polytopic system and they all are unstable. It was further important to find a robust static output feedback, which would be able to stabilize the whole uncertain system with the guaranteed cost expressed by (7), where Q - q~o,,,.t.diag(1, 1, 1 × 10 5, 1 × 10 5),
R - rco,,.,,t.diag(1 x 103, 1 × 103) . The parameters
of matrices Q, R have been chosen according to the values of state variables and control inputs. For finding a stabilizing output feedback controller it is necessary to solve two sets of LMIs (12), (13), each set consisting of 16 LMIs. The feasibility of the solution of (12) assures that the reactor is robust static output feedback quadratically stabilizable and the feasibility of the solution of (13) gives robust static output stabilizing controller with guaranteed cost for the whole uncertain system. For solving the LMIs, the LMI MATLAB toolbox was used. There are three parameters, which
influence
solution
and can be changed:
qco,st,rco,st,y.
In
dependence on the choice of these parameters, it was possible to find several stabilizing controllers, which stabilize the polytopic system with 16 vertices and also stabilize the reactor. For all stabilizing controllers all closed loop systems obtained for the nominal system and also for all vertices of the polytopic system are stable, e. a. all eigenvalues of all state matrices (4) of all 17 closed loop systems have negative real parts.
1308 c B (kmol m -3 )
T r (K)
339
1,04
J
1,00
338
0.96 337
0.92 336
3~
0.88
0
.
. ~'0
.
4o
.
.
t (min)
6'0
~'0
~00
084
0
.
.
~0
.
.0
.
.
6'0
8'0
~00
t (min)
Figure 2. Closed-loop response of the CSTR with robust output feedback controller
Some of the simulation results obtained with the robust static feedback controller F = [0.0023
0.0186] v are shown in Figure 2 for the nominal values of uncertain
parameters.
Conclusions
In this paper, the possibility to stabilize an exothermic chemical reactor with uncertainties working in the unstable operating point via static output feedback controller is studied. The robust controller design is converted to solving of LMI problems. A computationally simple LMI based non-iterative algorithm is used for the design of robust static output feedback controller. This algorithm is based on linear state-space representation of a controlled system. The design procedure guarantees with sufficient conditions the robust quadratic stability and guaranteed cost. The designed robust controller is able to stabilize the exothermic CSTR for the entire operating area not only for a single operating point.
References Alvarez-Ramirez, J. and R. Fermat, 1999, Robust PI stabilization of a class of chemical reactors. Systems Control Lett. 38, 219-225. Benton, I.E. and D. Smith, 1999, A non iterative LMI based algorithm for robust static output feedback stabilization, Int. J. Contr. 72, 1322-1330. Boyd, S., L. E1 Ghaoui, E. Feron and V. Blakrishnan, 1994, Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia. Ku6era, V. and C.E. de Souza, 1995, A necessary and sufficient conditions for output feedback stability, Automatica 31, 1357-1359. Syrmos, V.L., C.T.Abdallah, P.Dorato and K. Grigoriadis, 1997, Static output feedback. A survey, Automatica 33,203-210. Vesel~, V., 2004, Design of robust output affine quadratic controller, Kybernetika 40, 221-232. Vesel~, V., 2002, Robust output feedback controller design for linear parametric uncertain systems, Journal of Electrical Engineering, 53, 117-125. Yu, L. and J. Chu, 1999, An LMI approach to guaranteed cost control of linear uncertain timedelay systems, Automatica 35, 1155-1159.
Acknowledgements The authors are pleased to acknowledge the financial support of the Scientific Grant Agency of the Slovak Republic under grants No. 1/0135/03 and 1/1046/04.
European Symposiumon Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.
1309
A MINLP/RCPSP decomposition approach for the shortterm planning of batch production N orbert Trautmann a and Christoph Schwindt b aInstitute for Economic Theory and Operations Research University of Karlsruhe, 76128 Karlsruhe, Germany blnstitute for Business Administration and Economics Technical University of Clausthal, 38678 Clausthal-Zellerfeld, Germany
Abstract We present a new solution approach for short-term planning of batch production, which decomposes the problem into batching and batch scheduling. Batching converts the primary requirements for products into individual batches. We formulate the batching problem as a mixed-integer nonlinear program, which can be solved by standard software. Batch scheduling allocates the batches to scarce resources such as processing units and intermediate storage facilities. The batch scheduling problem is modelled as a resource-constrained project scheduling problem, which is solved by a novel priorityrule based method.
Keywords: Batch production; Scheduling; Decomposition; Mixed-integer nonlinear programming; Resource-constrained project scheduling
1. Introduction This paper deals with short-term planning of batch production in the process industries. In batch production mode, the total requirements of intermediate and final products are partitioned into batches. To produce a batch, at first the inputs are loaded into a processing unit. Then a transformation process is performed, and finally the batch is unloaded from the processing unit. We consider the case of multi-purpose processing units, which can operate different processes. The duration of a process depends on the processing unit used. The minimum and maximum filling levels of a processing unit give rise to lower and upper bounds on the respective batch size. Between consecutive executions of different processes in a processing unit, a changeover with sequence-dependent duration is necessary. Moreover, to avoid ongoing reactions of residuals, a processing unit needs to be cleaned before an idle time. In general, storage facilities of limited capacity are available for stocking raw materials, intermediates, and final products. Some products are perishable and must be consumed immediately after production. The product structure may be linear, divergent, convergent, or general. In the latter case, the product structure may also contain cycles. The input or output proportions are either fixed or can be chosen within prescribed bounds. For a practical example of a batch production, we refer to the case study presented in Kallrath (2002).
1310 A plant is operated in batch production mode when a large number of different products are processed on multi-purpose equipment. In this case, the plant is configured according to (a subset of) the required final products. Before processing the next set of final products, the plant has to be reconfigured, which requires the completion of all operations. In order to ensure high resource utilization and short customer lead times, the objective of makespan minimization is particularly important. That is why we consider the short-term planning problem which for given primary requirements consists in computing a feasible schedule with minimum makespan. Various solution methods for short-term planning of batch production are known from literature. Most of them follow a monolithic approach, which tackles the problem as a whole starting from a mixed-integer linear programming formulation of the problem. In those models, the period length is either fixed (time-indexed formulations, cf. e.g., Kondili et al., 1993) or variable (continuous-time formulations, see e.g., Ierapetritou and Floudas, 1998, or Castro et al., 2001). A disadvantage of the monolithic approaches is that the CPU time requirements for solving real-world problems tend to be prohibitively high (cf. Maravelias and Grossmann, 2004). To overcome this difficulty, heuristics reducing the number of variables have been developed (cf. e.g., B16mer and Gtinther, 1998). A promising alternative approach is based on a decomposition of the problem into interdependent sub-problems, as it has been proposed e.g. by Brucker and Hurink (2000), Neumann et al. (2002), and Maravelias and Grossmann (2004). The solution approach developed in what follows decomposes the short-term production planning problem into a batching and a batch-scheduling problem. Batching provides a set of batches for the intermediate and final products needed to satisfy the primary requirements. Batch scheduling allocates the processing units, intermediates, and storage facilities over time to the processing of all batches. In this paper, we use a new formulation of the batching problem as a mixed-integer nonlinear program that, in contrast to the model discussed in Neumann et al. (2002), allows for taking into account alternative processing units of different size. Moreover, we present a novel priority-rule based method for batch scheduling which is able to cope with large problem instances. The remainder of this paper is organized as follows. In Section 2 we formulate the batching problem as a mixed-integer nonlinear program. In Section 3 we show how to model the batch-scheduling problem as a resource-constrained project scheduling problem, and we sketch an appropriate priority-rule based solution method. Results of an experimental performance analysis of the new approach are discussed in Section 4. Section 5 is devoted to concluding remarks.
2. The batching problem In what follows, the combination of a transformation process and a processing unit is referred to as a task. For example, if there are three alternative processing units for the execution of a transformation process, we define three tasks for this process. Let T be the set of all tasks and let 13~ and e~ be the batch size and number of batches for task e T. By 1-I~ and 1-I+ we denote the set of input and output products, respectively, of task "c. I-I~ "-1-I~-~[1 +~ is the set of all input and output products of task i: , and
1311 FI := UFI: is the set of all products considered. In addition to 13~ and ~ , the proporc¢T
tions c ~ < 0 of all input products rce H7 and the proportions c ~ > 0 of all output products rc e 17I+ have to be determined for all tasks 1: e T such that ~{~=-
Zc~=I
rcclq +
(T~T)
(1)
rccl-I r
Batch sizes 13~ and proportions (~:~ have to be chosen within prescribed intervals [ ~ r , ~ ] and [ _ ~ , ~ ] , ot~_ S i + Pi ) and the set Ck of pairs for which j must be started immediately after the
completion of activity i. A schedule S is called process-feasible if Sj
>_- S i nt-
Sj-S
Pi + ci, if (i, j ) ~ C k (S)}
i+pi,
if(i,j)~Ck(S)
_
R° (k~
)
(7)
Now we turn to the intermediates and storage facilities, which are both represented by so-called cumulative resources (cf. Neumann and Schwindt, 2002). For each nonperishable product, there is one cumulative resource keeping its inventory. Let R r be the set of all cumulative resources. For each k ~ R r , a minimum inventory R__k (safety stock) and a maximum inventory R~- (storage capacity) are given. Each activity i s V has a demand r/k for resource k ~ R v . If r/k > 0, the inventory of resource k is replenished by r/k units at time S i + P i . If rik < 0, the inventory is depleted by -r/k units at
1313 time
S i . FOk
represents the initial stock level of resource k. Let V~+ "- {i ~ V r/k > 0}
and V~; "-{i ~ V r/~ < 0} be the sets of activities replenishing and depleting, respectively, the inventory of k ~ R Y . Schedule S is said to be storage-feasible if
Rk
S; + 6!/ for all (i,./)e E is called time-feasible. A schedule which is time-, process-, and storage-feasible is called feasible. The batch scheduling problem consists in finding a feasible schedule S with minimum makespan S,+I •
3.2 Solution procedure The priority-rule based scheduling method consists of two phases. During the first phase, we relax the storage-capacity constraints. Using a serial schedule-generation scheme, the activities are iteratively scheduled on the processing units in such a way that the inventory does not fall below the safety stock at any point in time. Deadlocks are avoided by means of a specific unscheduling technique. Based on the resulting schedule, precedence constraints between replenishing and depleting operations are introduced according to a FIFO strategy. Those precedence constraints ensure that the material-availability constraints are always satisfied. In the second phase, which again applies the serial schedule-generation scheme, the activities are scheduled subject to the storage-capacity and the precedence constraints introduced. Details of this procedure can be found in Schwindt and Trautmann (2004).
4. Computational results We have compared our decomposition approach to the time-grid heuristic by B16mer and Gfinther (1998) and to the decomposition method by Maravelias and Grossmann (2004). As a test bed we have used the 22 instances introduced by B16mer and Gt~nther, which have been constructed by varying the primary requirements for final products in the case study presented by Kallrath (2002). In addition, we have solved Example 2 discussed in Maravelias and Grossmann (2004). For solving the batching problem, we have used the Solver package by Frontline Systems. For batch scheduling, we have implemented a randomized multi-pass version of the priority-rule based solution procedure in ANSI C. All computations have been performed on an 800 MHz Pentium III personal computer.
1314 It turns out that for each of the 23 instances in the test set, the batching problem could be solved within less than 8 seconds. In each case, the optimality of the solution found could be verified by using an alternative MILP-formulation of the problem. The sizes of the resulting batch scheduling instances range from 24 to 100 operations. For all instances, within less than four minutes the priority-rule based method has either provided an optimal solution or the best solution known thus far could be improved. The results obtained for the large instances with more than 50 operations indicate that our decomposition approach scales quite well. The mean relative improvement achieved for those instances with respect to the time grid heuristic amounts to more than 35%. Moreover, the CPU time requirements have been decreased significantly compared to the time-grid heuristic and have been comparable to those reported by Maravelias and Grossmann.
5. C o n c l u s i o n s In this paper we have presented an efficient heuristic method for the short-term planning of batch production, which is based on a decomposition of the problem into a batching and a batch scheduling problem. Whereas the batching problem is formulated as a MINLP of moderate size, the batch scheduling problem is solved by a novel two-phase priority-rule based method for resource-constrained project scheduling. The decomposition heuristic is able to approximately solve problem instances of practical size in the space of a few minutes. An important area of future research will be the development of efficient online-scheduling procedures that are based on the priority-rule based method. Such an online-scheduling algorithm could be used in the Available-to-Promise module of Advanced Planning Systems for Supply Chain Management.
References B16mer, F. and H.O. Giinther, 1998, Scheduling of a multi-product batch process in the chemical industry, Comp. Ind. 36, 245. Brucker, P. and J. Hurink, 2000, Solving a chemical batch scheduling problem by local search, Annals Oper. Res. 96, 17. Brucker, P., A. Drexl, R. M6hring, K. Neumann, and E. Pesch, 1999, Resource-constrained project scheduling: notation, classification, models, and methods. Eur. J. Oper. Res. 112, 3. Castro, P., A.P. Barbosa-Pdvoa, and H. Matos, 2001, An improved RTN continuous-time formulation for the short-term scheduling of multipurpose batch plants, Ind. Eng. Chem. Res. 40, 2059. Ierapetritou, M.G. and C.A. Floudas, 1998, Effective continuous-time formulation for short-term scheduling. 1. Multipurpose batch processes, Ind. Eng. Chem. Res. 37, 4341. Kallrath, J., 2002, Planning and scheduling in the process industry, OR Spectrum 24, 219. Kondili, E., C.C. Pantelides, and R.W.H. Sargent, 1993, A general algorithm for short-term scheduling of batch operations- I. MILP formulation, Comput. Chem. Eng. 17, 211. Maravelias, C.T. and I.E. Grossmann, 2004, A hybrid MILP/CP decomposition approach for the continuous time scheduling of multipurpose batch plants, Comput. Chem. Eng. 28, 1921. Neumann, K. and C. Schwindt, 2002, Project scheduling with inventory constraints, Math. Meth. Oper. Res. 56, 513. Neumann, K., C. Schwindt, and N. Trautmann, 2002, Advanced production scheduling for batch plants in process industries, OR Spectrum 24, 251. Schwindt, C. and N. Trautmann, 2004, A priority-rule based method for batch production scheduling in the process industries. In: Ahr, D., R. Fahrion, M. Oswald, and G. Reinelt, Eds., Operations Research Proceedings 2003. Springer, Berlin, 111.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) ¢¢)2005 Elsevier B.V. All rights reserved.
1315
A F r a m e w o r k for On-line Full Optimising Control of Chemical Processes P. A. Rolandi*, J. A. Romagnoli
Centre for Process Systems Engineering Department of Chemical Engineering The University of Sydney Sydney, NSW, 2006, Australia
Abstract An increasing demand for improved productivity and better quality control has shifted the interest of the research community to nonlinear model-based control, which has a better chance to meet these requirements due to the intrinsic nonlinear nature of chemical and physical processes. Recent progress in modelling, simulation and optimisation environments (MSOEs) and open software architectures (OSAs) have created the conditions to conceive novel paradigms for advanced process control (APC) of large-scale complex process systems. However, large-scale mechanistic models have scarcely been used in control algorithms and, therefore, issues arising from embedding these process models in APC applications have not been addressed satisfactorily. In this manuscript we propose a novel framework Ibr advanced nonlinear model-based control of process systems which aspires to bring the latest advances in model-based technology closer to the Process Industries.
1. Introduction Nowadays, not only state-of-the-art MSOEs support efficiently most stages of the modelling process, but also allow the creation of large-scale mechanistic models and solution of advanced model-based activities that were impossible to engage in one decade ago (Pantelides, 2001). Additionally, as rigorous process models conforming to the CAPE-OPEN (CO) standards proliferate in the public domain of the PSE and CAPE communities, the time and eflbrt to develop large-scale mechanistic models is reduced considerably. Even though these mathematical models could be used as precursors of advanced model-based control algorithms, the research community has failed to provide a framework to use rigorous mechanistic models in APC applications. Undoubtedly, MSOEs and OSAs have driven major changes in model-based technology and will continue to promote further transformations. However, how to benefit from MSOEs and OSAs to conceive new visions and establish novel paradigms in the area of APC is still an unresolved question. In this work, we present to the research community and industry the most important aspects of the framework tbrfidl optimising control of process systems (FOCoPS) proposed by Rolandi (2004).
Author to whom correspondence should be addressed:
[email protected] 1316
2. F r a m e w o r k Definition 2.1. Control algorithm and general philosophy The framework is centred on hierarchical control architecture where multivariable constrained control and process optimisation (which were traditionally segregated into distinct layers (e.g. Qin and Badgwell, 1996)) are combined into a single hierarchical level. A rigorous mechanistic dynamic model of the process is used for this purpose. The core of the proposed control algorithm is based on the on-line iterative solution at time t = t o - A of a finite horizon open-loop optimal control problem (FHP) of the form: min ~o(t0 + P-A) ~(,).,~[,0.,0+cA]
(1)
F(2(t),x(t),y(t),u(t))- O, t ~ [t0,t 0 + P. A]
(2)
~(~(,0 ). x(,0 ). y(,0 ).. (,0))= 0
(3)
~ ( t ) - ~(t 0 + C. A), t e (to + C. A,t 0 + P. A]
(4)
~(,) ~ v ,
(5)
, ~ [,0,,0 + e A]
y(,)~ ~, , ~ [,o,,o + v . d
(6)
x(,) ~ x . , ~ [,0.,0 + P A]
(7)
The nomenclature conventions adopted in the equations above are straightforward. The symbols P , C and A denote the prediction horizon, the control horizon and the control window, respectively. Additionally, h~(t) indicates the subset of controlled input variables. In the proposed architecture, these decision variables correspond to the setpoints of the regulatory (PID) control layer. The FHP is solved via a control vector parameterisation approach, or sequential solution method, with piecewise-constant controls h-A e U . Details on feedback mechanisms and other features of the control algorithm can be found in Rolandi (2004). In the proposed framework for FOCoPS, we suggest to differentiate the objective function (i.e. Eq. (1), a primary and direct performance measure) from the series of process constraints on state and output variables that define the admissible set of trajectories (i.e. Eqs. (6) and (7), secondary and indirect measures of performance). In effect, objective functions such as productivity or overall profitability are more intuitive and natural performance measures for the purpose of simultaneous process optimisation and control than the multivariable objective function typically encountered in linear model-predictive control (LMPC) applications. However, translating the constraints arising from a control problem into equivalent terminal and path constraints of the corresponding NLP problem formulation and simultaneously guarantying the existence of a non-empty feasible region is a non-trivial problem. We will address this issue in subsequent sections of this paper. The reader may feel persuaded to think that the rupture with the multivariable constraint dynamic control (or quadratic cost) objective function and consequent reduction of the
1317 number of algorithmic parameters (i.e. elimination of weighting matrices intrinsic to any multivariable objective function) is a drawback of the proposed framework. On the contrary, in the author's opinion, it represents a paradigm shift that holds the potential for significant boost of the process systems performance due to a more realistic treatment of process constraints given by the specification of the control problem. Effectively, Prett and Garcia (1988) recognised that performance requirements cannot be appropriately reflected by the combination of multiple objectives into a single objective function. For instance, not only should control requirements be translated into appropriate relative weights, but care should also be exercised to avoid scaling problems and ill-conditioned solutions (Qin and Badgwell, 1996). Ultimately, the weights are used as tuning parameters of the control algorithm balancing the relative enforcement of admissible input and output trajectories. On the contrary, in the proposed framework, the performance of the controller is intimately associated with the structure of the control problem, that is, the characteristics of the objective function, and number and nature of the control variables and constraints. Since these reflect true specifications of the required process operation, better control performance can be expected from the proposed framework. 2.2. On-line formulation of the control problem
The framework for FOCoPS has been centred on the initiative of translating a process control problem into an equivalent NLP jbrmulation, and then converting this problem into a high-level declarative definition consistent with the native language of state-ofthe-art MSOEs. Even though this is an important conceptual breakthrough, several complications arise since the control problem is likely to be stated by the user (e.g. an operator) in a very straightforward way, with little resemblance with the conventions of modern modelling languages. In order to fulfil this vision, the FOC/APC application currently supports the following mechanisms: a) the user has the ability to communicate with the application kernel by posting a series of elementaw events describing the structure of the control problem at discrete points in time; b) concurrently, the application kernel has the capacity to translate this series of future events posted by the user into an equivalent NLP problem. The elementary event data model (EVNdm) has been suggested as an abstraction of all relevant information that should be contained in an event to make it useful for the purpose described above (Rolandi, 2004). Additionally, a dynamic optimisation object data model (DOOdm) was created to represent the high-level declaration of the NLP/FHP within the FOC/APC application. Since the conventions of gPROMS' highlevel declarative language were used to describe the mathematical form of the NLP problem, the generation of the gPROMS language input file describing a dynamic optimisation problem given by the DOOdm was straightforward. The control problem de[in#ion and solution supervisor (CPDaSS) is the software component of the FOC/APC application in charge of manipulating instances of the EVNdm and transforming them into a DOOdm. The algorithmic nature of this component is fairly involved and research is still being conducted in this area. In spite of this, a general discussion of the issues involved during such translation and associated software implementation aspects can be found in Rolandi (2004).
1318 2.3. Advanced features of the framework In industrial processing plants, input process variables may be "lost" due to hardware or software signal failure or unavailable due to direct intervention from the operator or the supervisory control system. Concurrently, constraints on output process variables may be modified due to alterations on process operation specifications. On the other hand, solution ill-conditioning may result from poor control problem definition or abnormal process performance, and an adequate modification of configuration (input and/or output variables, Eqs. (5) and/or (6)) could be used to recover from this situation. All of these circumstances cause the structure of the control problem to change dynamically. In the proposed framework for FOCoPS, changing the structure of the control problem is possible via the introduction of a series of mechanisms which allow a flexible definition of the associated on-line NLP/FHP. These mechanisms respond to the type of elementary event. At the moment ten different types are supported. PH C h a n g e ,
CH_Change and CW_Change keywords trigger changes in the prediction horizon, control horizon and control window respectively, thus affecting the nature of the multistage dynamic optimisation problem. PC C r e a t e and PC D e l e t e are used to modify the structure of piecewise-constant decision variables of the NLP problem. For instance, PC C r e a t e adds an additional control variable and/or modifies the magnitude of upper and lower bounds and initial guesses of an already-existent control variable. In addition, PC D e l e t e removes a piecewise-constant control variable from the list of decision variables. FR C r e a t e and FR D e l e t e are used for similar purposes for the case of process constraints, while FR C r e a t e F i x e d E n d P o i n g and FR D e l e t e F i x e d E n d P o i n g are special cases of the latter and are needed when the occurrence time of the elementary event is always coincident with the end of the prediction horizon. Finally, OV C h a n g e allows the user to change the process variable reflecting the objective function. At the moment, the user is the driving force in the definition of the control structure because the elementary events can only be posted by a restricted set of mechanisms. It is important to highlight, though, that such elementary events could be initiated by internal and/or other external agents to the FOC/APC application. The opportunity to modify the NLP formulation on-line by posting elementary events gives good flexibility and generality to the framework. In spite of this, it also gives rise to several non-trivial issues such as guarantying the validity and feasibility of the newly created NLP problem. Effectively, problem infeasibility or ill-conditioning may occur as a result of abnormal process operation and/or an intrinsically badly-posed control problem. In the FOC/APC application, constraint ranking and elimination was exploited as a mechanism for recuperation form infeasible solutions. In other words, when the solution of the NLP problem becomes infeasible, constraints below a priority level are eliminated from the formulation and the calculation is repeated. The NLP is considered infeasible for the purposes of implementation only when constraints above a certain priority level cannot be enforced. In addition, constraint identification and relaxation has been proposed as a complementary approach to infeasibility recuperation (Rolandi, 2004), although the lack of standard methods for communication with numerical solvers halts the implementation of this idea for the moment. Infeasibility recuperation is handled by the control problem definition and solution supervisor (CPDaSS), since the
1319 function of this component is to respond to control problem formulations that change dynamically according to endogenous or exogenous reasons.
3. Implementation State-of-the-art MSOEs such as gPROMS provide standard mechanisms to interact with the modelling and solution engine at a lower level than the conventional model development and activity execution environment. This is accomplished via the gPROMS Server (gSERVER), which allows any application to construct process models in gPROMS' native language, perform all supported model-based activities, and have full access to the mathematical description of the corresponding models and activities as specified by the GCO standard. The FOC/APC application has been implemented in C÷+ object-oriented programming language, although some components will support XML soon.
4. Results and Discussion In this manuscript, the framework is presented and exemplified through a case study. The process under consideration is a continuous cooking digester and auxiliary units. A large-scale model consisting of approximately 14000 algebraic and 1000 ordinary differential equations (DAEs) and 100 statuses within the state transition network (STNs) is the process model used by the FOC/APC algorithm. This model has been implemented in gPROMS modelling language. The communication between the virtual (simulated) process system (VPS) and the FOC/APC application is accomplished via Honeywell Experion PKS T M by means of the network application programming interface (NAPI) protocol. The viability and performance of the FOC/APC application is assessed by the following illustrative case-study. Let us assume that the results of an off-line study seeking to find the optimal transition management procedure for slowing down the production from 650.0 to 600.0 ad.ton/day is available to mill personnel. In this study, pulp yield was maximised while keeping the deviation of pulp selectivity fi'om its target operating value below a given threshold for quality control. Typically, these transition planning case-studies would be obtained under the assumption that the process system was initially operating at steady-state. Let us assume, instead, that a production rate change from 600.0 to 650.0 ad.ton/day had taken place five hours before the new transition (following similar optimality criteria, though). By doing this, we would like to support the thesis that results from off-line process optimisation and transition planning studies are useful to indicate the direction for enhancement of the process operation but are not directly applicable as control recipes unless process performance is sacrificed. The transition is accomplished by manipulating the set-point of three controllers: the chip meter speed (feed rate of wood chips), and the temperature of the lower and wash circulation heaters (.indirect column heating). Path (interior-point) and terminal (endpoint) constraints were imposed on the trajectories and final magnitude of blow-line kappa number and blow-line pulp production rate. Two additional (en-point) constraints were added for the deviation and violation of soft-control bounds of the kappa number. The prediction and control horizons were 7hr and 5hr, and the control window was l hr.
1320 Figures 1 and 2 compare the trajectories of key process variables for the transition based on process knowledge derived off-line (OFL) and that driven by the on-line FOC/APC control algorithm (ONL). It is clear that the FOC/APC application was able to manage the transition more efficiently than what operators could have done on the basis of previous process knowledge.
I ..................... oF,
............ oN,
OFL ...................ONL I ......................
I
91.0
156 155 154 °~,~153 152 151
90.5 "" =1:1= 90.0 89.5 89.0 1
2
3
4
5
6
7
8
9
[hr]
Figure 1" Kappa number trajectory.
I
5; !
0
1
2
3
4
5
6
7
8
9
[hr]
Figure 2." Lower heater set-point trajectory.
5. Conclusions This work presented a novel framework (FOCoPS) for on-line optimising control of large-scale processes. The emphasis was centred on creating a paradigm which would support the definition of a control problem in a way consistent with the structure and formalisms of high-level declarative languages and the framework imposed by the CO standards. The innovative elementary event data model was presented as a means to change the structure of the control problem dynamically due to the interaction of the APC application with the operators and the process system. A large-scale mechanistic process model of an industrial continuous pulping area was used to illustrate the framework. In this work, only key issues of the novel framework have been addressed, and no attempt has been made to compare the proposed algorithm with other standard model-based control technologies such as LMPC. However, the framework is expected to bring improved process profitability and quality control because optimisation and control occur simultaneously in the proposed architecture for FOCoPS and the FOC/APC application is centred on mechanistic process models. Overall, this paper has provided a framework for advanced process control (APC) compatible with the paradigm for open software architectures (OSA) given by the Global CAPE-OPEN (GCO) project. Naturally, the PSE, CAPE and APC community will greatly benefit from further research in the path delineated by this manuscript.
6. References Pantelides, C.C., 2001, New challenges and opportunities for process modelling, ESCAPE-11, Kolding, Denmark. Prett, D.M., Garcia, C.E., 1988, Fundamental Process Control, Butterworths, Boston. Qin, S.J., Badgwell, T.A., An overview of industrial model predictive control technology, Chemical Process Control- CPC V, CACHE, Tahoe City, California. Rolandi, P.A., 2004, PhD Thesis, University of Sydney, Australia.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1321
Wavelet-Based Nonlinear Multivariate Statistical Process Control Abd Halim S. Maulud*, Dawei Wang and Jose A. Romagnoli Process System Engineering Laboratory, Department of Chemical Engineering, University of Sydney, NSW 2006, Australia
Abstract In this paper, an approach of wavelet-based nonlinear PCA for statistical process monitoring is presented. The strategy utilizes the optimal wavelet decomposition in such a way that only approximation and the highest detail functions are used thus simplifying the overall structure and making the interpretation at each scale more meaningful. An orthogonal nonlinear PCA procedure is incorporated to capture the nonlinearity characteristic with minimum number of principal components. The proposed nonlinear strategy also eliminates the requirement of nonlinear functions relating the nonlinear principal scores to process measurements for Q-statistics as in other nonlinear PCA process monitoring approaches.
Keywords: Fault detection, Orthogonal Nonlinear PCA, Optimal multivariate wavelet decomposition
1. Introduction Principal component analysis (PCA) has been widely applied in multivariate statistical process monitoring due to its capability to extract information in multivariate environment. In practice, many processes do exhibit significant nonlinearity correlation and in these cases a linear PCA mapping results in substantial loss of information or large numbers of linear components are required to obtain the required accuracy. Several nonlinear PCA have been proposed in the literature to improve the data extraction when the nonlinear correlations among the variables exist. Wavelets have also become a promising tool in many applications due to its property of time-frequency localization. However, up to date few combinations of PCA and wavelets have been reported for process monitoring. A multi-scale-PCA strategy (Bakshi 1998; Misra et al. 2002) has been proposed to capture information in both time and frequency domains and in addition, some wavelet nonlinear PCA combination have been reported (Shao et al. 1999; Palazoglu et al. 2001) Despite these developments there are still some issues remaining on the development and implementation of wavelet based nonlinear PCA approaches. Orthogonality is a problem when dealing with nonlinear extensions of PCA strategies. In a conventional nonlinear PCA (NLPCA), the data information tends to be evenly distributed among the
Author/s to whom correspondence should be addressed:
[email protected] 1322 principal components or bottleneck layer (Chessari et al. 1995). Thus, loosing the orthogonally characteristics inherent of linear PCA. On the other hand, when wavelet decomposition is applied in process measurements, the signals are projected onto the approximation and detail coefficients. As the signals are decomposed by using discrete wavelet transform to multi-level decompositions, more information is being transferred from approximation function to detail functions. If the signal is overly decomposed, it will eventually smoothing out the underlying features in the approximation function. In this paper, an approach of wavelet-based nonlinear PCA for statistical process monitoring is presented. A significant contribution of the proposed strategy is the identification/definition of the optimal level of decomposition making possible to use only the approximation reconstruction and the highest level detail (the lowest frequency) reconstruction for process monitoring. This strategy improves the fault interpretation by separating the deterministic features and localized events. A modified Kramer's NLPCA (Kramer 1991) called orthogonal non-linear PCA (O-NLPCA) is incorporated into the strategy to improve the explained variance by maximizing the data variability in the first few principal. In addition, the number of principal components specified can be relaxed while in NLPCA the number of principal components must be optimally specified in advance. The proposed nonlinear strategy structure also eliminates a requirement of nonlinear functions relating the nonlinear principal scores to process measurements for Q-statistics monitoring as in other nonlinear PCA approaches.
2. Orthogonal Nonlinear PCA Let X be a data matrix with n number of observations and m number of dimensions. In PCA, the X matrix can be decomposed into two matrices as follows:
(1)
X = TP ~ - ~ t , p ~ i=1
where T and P are called scores and loadings matrix, respectively. If the variables in X are collinear, the first f principal components can sufficiently explain the variability in data X. Thus, the data X can be written in term of a residual, E, as; f
X-
TrPrr + E - ~
t,p~ + E
(2)
i=1
In order to improve the orthogonality property in NLPCA, the Gram-Schmidt training algorithm is applied in NLPCA in such that the nonlinear score produced are orthogonal at the end of training session (Chessari et al. 1995). A major disadvantage of this scheme is it may suffer a constraint of trade-off between the main objective (overall convergence) and the secondary objective (orthogonal principal components). In addition, the network training is quite complex as it involves iterative procedure. In this paper, a simpler alternative approach to orthogonal NLPCA is proposed. This approach utilizes the Hammerstein model concept by incorporating linear PCA into the NLPCA. In Hammerstein model, the nonlinear and linear parts are separated into two blocks as shown in figure 1. In this case, the bottleneck layer nodes are called non-orthogonal nonlinear principal components and their outputs are called non-orthogonal scores.
1323 When linear PCA is applied on non-orthogonal score, it will produce orthogonal nonlinear principal components as shown in figure 2.
X
J
Nonlinear Block
~l
L~CAr ~ h Q g ............. nn¢ipalComponents
Linear I ¥
~_
Figm'e l
The ttammerstein Model
Y MappinqNetwork
J
Non-Orthogonal Nonlinear
PrincipalComponents
Figm'e 2 • Orthogonal Nonlinear PCA
Let T is the non-orthogonal nonlinear scores matrix generated at the output of bottleneck layer. Thus, the non-orthogonal matrix T can be transformed to orthogonal matrix U; T - UP r
(3)
where P is the eigenvector matrix. Another advantage of this approach compared to conventional NLPCA is a number of bottleneck layer neurons can be relaxed as long as the number is reasonably selected.
3. Optimal Wavelet Decomposition In multi-resolution analysis theory (Mallat 1989), any signal can be approximated by successively projecting it down onto scaling function and wavelet function. The projections onto the scaling functions are known as scaling or approximation coefficients. The projection onto the wavelet functions are known as the wavelet or detail coefficients which capture the details of the signal lost when moving from an approximation at one scale to the next coarser scale. Let us define the optimal decomposition level as the highest decomposition level in which the approximation function is adequately representing the actual deterministic signal with a minimum noise for given wavelet type. In a multivariate case, each variable may have a different optimal decomposition level. In most practical application, only a single decomposition level will be applied on all variables for computational simplification. Thus, the decomposition level selected must be appropriate or optimal to ensure that the underlying features of each variable are adequately preserved in approximation function with minimum noises. In this paper, a graphical method based on PC A concept is presented to determine the optimal decomposition level for multivariate system. It is assumed that the deterministic features of the process data are continuous smooth functions. Let a PCA is being applied on the approximation reconstruction function with single-level wavelet decomposition. Recall equation (2), the E matrix consist mainly of noises. As the wavelet decomposition is recursively applied, the magnitude of matrix E is reduced as more noises have been captured by the detail fimctions. However, the compositions of thefprincipal components remain more or a less constant as the underlying features are still adequately preserved. As the decomposition level increases, at the l level some of the underlying features of the signals in the approximation function start to be lost to the
1324 detail function and the composition of the f principal components start to change significantly. This change can be detected by plotting the explained variance of the first principal component of the approximation reconstruction function for different decomposition level. An example plot is shown in figure 4. The explained variance is calculated based on the eigenvalue of the approximation reconstruction covariance matrix. The optimal decomposition level is given as (/-1) which is can be determined from the plot.
4. Wavelet-Based Nonlinear Statistical Process Control Wavelet-based nonlinear statistical process control (WNSPC) combines the optimal wavelet decomposition ability to extract the deterministic features of the process variables in the approximation reconstruction with the ability of orthogonal nonlinear PCA to extract the correlation among the variables. The proposed monitoring strategy is shown in figure 3. Orthogonal Nonlinear PCA Approximation function A I Nonlinear , ~ PCA Optimal Wavelet Decomposition & Reconstruction I Linear I D PCA Highest level v"I detail function
Y ~"
ii Linear PCA
Z
.I
"1
E
Figure 3. Wavelet Based Nonlinear Statistical Process Control
The measurement data matrix, X, is decomposed and reconstructed by using orthonormal wavelet at optimal decomposition level. Most of the noises will be filtered in this process. Only the approximation function and the lowest frequency detail function (the highest level) are retained for process monitoring. The advantage of this strategy is that the interpretation of a fault detected is more meaningful and simpler since only bi-scale is utilized. The approximation function represents the cleaned process deterministic features while the detail function represents the localized activities or stochastic features. In the multi-scale strategy, the process deterministic features are decomposed onto multi-scale which makes it difficult for interpretation. In addition, cleaned measurement data in the approximation function improves the data analysis. The orthogonal nonlinear PCA is applied onto the approximation reconstruction function as the nonlinearity characteristics are exhibited in the deterministic features. For the detail reconstruction function, a linear PCA is utilized as mostly noise is expected to be present. It is assumed that Y adequately represents the measurement data X in a compact form. Thus, the multivariate statistical process monitoring can be performed in Y instead of X. As a result, this strategy reduces the overall monitoring system to a conventional linear PCA system. The Q-statistic can be computed as in a conventional linear PCA manner between Y and Z. For the detail function, it is not necessary to apply Q-statistic because it mainly contains noises.
1325 5. S i m u l a t i o n C a s e S t u d y An irreversible exothermic reaction of A--) B is conducted in an ideal CSTR. There are 9 variables monitored and 1000 data points are generated from the simulation and are corrupted with random noise with zero mean. The Daubechies-4 wavelet is utilized in this application. Figure 4 shows the explained variance for the first principal component of approximation reconstruction at different decomposition level. Level 8 is selected as the optimal decomposition level based on normal operating data. Two types of fault have been introduced. The first fault is a step mean shift in the inlet concentration of component A, between samples 200 and 399. The second fault is a drift deterioration of the overall heat transfer coefficient of the cooling system starting from a sample 601 onward. 95% and 99% significance points are considered as warning and action limits, which are indicated by dotted and solid lines, respectively. The WNSPC utilizes three control charts (T&approximation, Q-approximation and 74-detail) compare to two control charts in conventional PCA (7': and Q). 70
2
25 .
.
.
.
.
.
.
]
i~i
e5 1.6 14 60
0
55
1
5o 06 04
45
02 401
2
3
7
8
Samples
samples
Figure 4. E. V. o/" 1"' PC
Figure 6a." T:-PCA
Figure 5b. Q-approx. 30
io
25
7
20
['
6 0
15:
4 5
2 1
°o
lOO
300
500
60o
zoo
80:)
Samples
Figure 5a." T: approx.
90o
looo
0
0
iou
zoo
4oo
500
Samples
700
8o0
Figure 5c. T2-detail
900
1000
0
100
200
400
500
Samples
600
700
80o
900
100
Figure 6b. Q-PCA
From figure 5 through 6, the mean shift can be easily detected by both WNSPC and PCA methods. This can be seen in Q-statistic plots which indicate a sharp increase that goes beyond the 99% limit at sample 200. For the T:-plots, both methods cross the 95% limit, but the WNSPC response is faster. A sudden change in mean is also warned by the T:-detail at sample 200 and 400. An advantage of O-NLPCA is being applied in the WNSPC approach can be clearly seen in the second fault. The fault is quickly detected by Q-approximation as it occurred by crossing the 95% and 99% limits at sample 515 and 539, respectively. While Q-PCA is only crossing the 95% and 99% limits at 628 and 668 respectively. This indicates that WNSPC approach is much faster compared to PCA in detecting a gradual process of characteristic change. A utilization of T:-detail plot gives some advantages. In addition its ability to warn any sudden or sharp changes (as illustrated in figure 5c), it has a potential to warn some localized events. A simulation of sensor stalled of outlet A concentration is performed
1326
from point 201 to 400 as shown in figure 7. Dotted line indicates the actual deterministic path. Both T:-approximation and Q-approximation (figure 8a-b) do not indicate any warning regarding this fault as it does not involve the mean shift or process characteristic change. However, the T:-detail (figure 8c) quickly warns that there is some localized event taking place. For PCA, the Q-PCA does indicate some warning since some points are crossing 95% limit from points 201 to 400. However, an interpretation of fault type can not be quickly addressed. This illustrates an additional advantage of this strategy as it is able to provide an initial guess of the fault types. 2-
~
•
:
.
=
,
.
--~
]
1
i
i:i
J
08
is! 1!
•
0-5 i
.
.
.
.
.
.
.
.
1 lOt
0.7!
8.
o o.5
i !
o.4!
-0.5 !
t
!
~_ 6[
I
-11 o.2 i .
-15!
..'J-:::
Ol
, "'
I l
-~"
1~o ~®
~-~00
~oo ~o
70-0 ~oo
'
0[~
....
100
200
300
400
500
600
700
800
900 1000
Samples
Samples
81 ~_
6~
~;~ Voo
~o s;o oo~ 7~o
8~ 900
Samples
~o~
Figure 9a: T:-PCA
Figure 8b: Q-approximation
Figure 7." Outlet A concentration
o~ 1~
i ,
5~
.
•
2[
i 00
I ~00
2()0
3()0 ~400
500
6~0
700
800
9~00 1000
Samples
Figure 8a. T2-approximation
Samples
Figure 8c: T:-detail
Samples
Figure 9b: Q-PCA
6. C o n c l u s i o n Wavelet-based Nonlinear Statistical Process Control strategy has been presented which utilizes optimal wavelet decomposition and orthogonal NLPCA. The strategy provides an alternative approach to uncover the nonlinear characteristic and simultaneously provide an initial fault interpretation platform.
References Bakshi, B. R., 1998, AIChE Journal 44(7), 1596-1610. Chessari, C. J., G. W. Barton and P. Watson, 1995, IEEE International Conference on Neural Networks 1, 183-188. Kramer, M. A., 1991, AIChE Journal 37(2), 233-243. Mallat, S. G., 1989, IEEE Transactions on Pattern Analysis and Machine Intelligence 11(7), 674-693.
Misra, M., H. H. Yue, S. J. Qin and C. Ling, 2002, Computers & Chemical Engineering 26(9), 1281-1293. Palazoglu, A., F. Doymaz, W. Sun, A. Bakhtazad and J. Romagnoli, 2001, ESCAPE-11 supplementary, 115-120. Shao, R., F. Jia, E.B. Martin and A.J. Morris, 1999, Control Engineering Practice 7(7), 865-879.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) ::c)2005 Elsevier B.V. All rights reserved.
1327
Anaerobic digestion process parameter identification and marginal confidence intervals by multivariate steady state analysis and bootstrap. G. Ruiz ~*, M. Castellano b, W. Gonzfilez t~, E. Rocd' and J.M. Lema ~ ~' Department of Chemical Engineering. Institute of Technology. b Department of Statistics and Operation Research. University of Santiago de Compostela. E- 15782, Spain
Abstract There are a few works related to on line steady state detection algorithms and less with parameter estimation. This work used Principal Component Analysis (PCA) for reduction of the dimension of the data space and producing independent variables, allowing the application of the multivariate Cad and Rhinehart algorithm in steady state detection. Once steady states were detected, model parameters can be calculated by steady state mass balance equations and non linear fit of data. Bootstrap method was used in order to approximate the parameters estimators distribution and confidence boundaries fbr the kinetic model. These methodologies were applied to a case of anaerobic wastewater digestion process where four different organic loading rates (OLR) were applied.
Keywords: PCA, steady state, parameter estimation, bootstrap.
1. Introduction Parameter identification l-br wastewater treatment process is usually determined by model fit to dynamical data both, in batch and continuous operation (Batstone, 1999; Markel et al, 1996: Lokshina, 1999). These methods have the disadvantage of not consider time delay in dynamic data due to unknown time dependence of data, especially due to non-ideal liquid flow pattern. Usually steady state identification is analysed by an expert or an operator, In many cases, it is not possible to count with the expert advice. Furthermore, experts are always subjected to human error in recognition of steady state, especially when measurements are noisy and process changes are slow (Szela and Rhinheart, 2002). Consequently, it is important to define an algorithm tbr steady state detection, specially an algorithm for on line steady state detection. Ruiz et al (2004) have developed a multivariate extension of the Cad and Rhinehart (1995) methodology giving good results. Because of the reduced number of steady states available from process data and because the use of mean data of steady state data sets, usually high estimation errors can arise
Author to whom correspondence should be addressed:
[email protected] 1328 from parameter identification, so it is necessary to increase as much as possible the accuracy of the identification procedure. Re-sampling of data by means of bootstrap, a technique invented by Bradley Efron (Efron, 1979; Efron and Tibshirani, 1993) with inferential purposes, will give more accuracy to parameter identification. Furthermore, it would be possible to obtain marginal intervals at a desired confidence. Statistical Inference studies how to use the information of a parameter estimator for obtaining probabilistic results about the real and unknown parameter. The bootstrap method rise from the analogy between a population and a sample from it. In the bootstrap word the sample is the population. In the present work, a steady state detection algorithm for multivariate process was used to generate a data base of steady states data set. Bootstrap was used for re-sampling the data set and to generate a parameter distribution in order to obtain a marginal interval for each variable. This approach will improve the common methodology of model (Haldane Kinetic Model) fit to average data and will give marginal intervals for identified parameters. All these methodologies are applied to an anaerobic digestion process for wastewater treatment, as an example, but it is extensible to any other kind of chemical and biochemical process.
2. M a t e r i a l s and M e t h o d s 2.1 Experimental setup The anaerobic wastewater treatment pilot plant is composed of a hybrid UASB-UAF reactor of 1 m 3. The measurement devices were: feed and recycling flow meters, pH meter; inflow and reactor Pt100, gas flow meter, infrared gas analyser (CH4 and CO), gas hydrogen analyser and TOC/TIC combustion analyser. The sensors gave a signal every 5 seconds and every 15 minutes a moving average window was saved in the data base. Other parameters were calculated using the measured variables: methane flow rate (Q CH4), hydrogen flow rate (QH2) and organic loading rate (OLR).
2.2 Experimental conditions The reactor was operated at stable conditions for more than a month at an OLR of 5 kg COD/m3.d. Three consecutive increases of the OLR were performed in order to obtain three different steady states (plus the initial steady state). Table 1 present the different conditions for each organic load. The duration of each state was around 5 days, considered enough to achieve steady state because the HRT was around of 0.6 to 1.5 d. For all the calculations, the first period (day 0 to 4) was considered as a normal operation state.
2.3 Multivariate steady state detection algorithm The steady state detection algorithm used was previously presented by Ruiz et al (2004). Principal component analysis (PCA) was applied for reducing the N-dimension space of the multivariate data to two dimensions. By using PCA it is possible to retain the maximum variability (information) of the process with just a few new variables (principal components). Two PCs are usually enough and represent a high level of the total variability of the process. Steady state then is identified using Cao and Rhinehart
1329 (1997) methodology. When both the first and second principal components (PC1 and PC2) are in steady state, the process will be considered at steady state.
Table 1. Experimental conditions applied to the reactor for thejour states State
Duration OLR Feed flowrate (d) (kg COD/m3"d) (Qinf) (L/h)
1: (N.O.)
0-4
5
22
TOC influent (mgC/L) 3000
2: H.O.
4-9
15
66
3000
3: H. O+O. O
9-14
28
66
4500
4: H.O+O.O
14-15.5
32
66
6000
5: (N.O)
15.5-17
5
22
3000
N.O.: Normal operation; H.O. Hydraulic overload; O.O. organic overload
2.4 Bootstrap A parametric bootstrap method is used to estimate the distribution of the kinetic parameters estimators. Lets be y the methane flow rate, x the sustrate concentration, and mo the Haldane kinetic model for methane production. The model can be written as:
y-mo(x)+g
(1)
Where ~ is the noise of the process. The N data are separated by groups and the mean of each group is calculated. Using the mean of each group and the minimun mean squared error criterium, the first estimation of the kinetic parameters is done using simplex algorithm. Each data y, can be expressed as follows. y: - m 0 ( x ) +
~";, 1 _< i _< N
(2)
The residual errors, ~,' will be used to generate the bootstrap samples. The bootstrap sample is obtained from the Haldane model with estimated parameters plus a residue with the same mean and variance of the original error. The expresion of the B bootstrap samples is
Y, */ - m o (x, ) + g ':. Z ,.i, I -,~.z:-:; -'I:::, ..........
.
..f
:,
0.4
Manipulated
:,
0.6
"
"%-0.8 ............ .............. !1
Variable
0.8
:
:
i
. . . .
\ / ........ "7":>->_~. ......... :........... :. . . . . . .
~
]
0.6
0.4
g
i ,
0.2
,
~
I
i
.1
,
0
0.2
0.4
0.6
Scaled Time [-]
0.8
1
0.2
0.4 0.6 Scaled Time [-]
0.8
Fi~m'e 3. Control of the solidi ficatiot7 ratejbr u constant reference.
1344
5. Conclusions The intention of this paper is to develop a fast and simple mechanistic model for the position of the solidification interface. The model is simplified to make it suitable for control purposes, and is used to develop a linear PI-controller in order to control the solidification velocity. For the cases simulated above, the position tracks the reference well. It may be possible to extend the model and control strategy to a gas-liquid transition. Further research will include validation with experimental plant data and comparison with other modeling methods (e.g. the level set method). References
Chun, C.K and Park, S.O., 2000, A Fixed-Grid Finite-Difference Method for Phase-Change Problems, Numerical Heat Transfer Part B 38, 59. Crank, J., 1984, Free and Moving Boundary Problems, Oxford University Press, Walton Street, Oxford OX2 6DP. Franke, D., Steinbach, I., Krumbe, W., Liebermann, J. and Koch, W., 1996, Concept for an Online Material Quality Control by Numerical Simulation of a Silicon Ingot Solidification Process, Proc. 25th IEEE Photovoltaic Specialist Conference, 545. Gibou, F., Fedkiw, R., Caflisch, R. and Osher, S., 2003, A Level Set Approach for the Numerical Simulation of Dendritic Growth, Journal of Scientific Computing 19, 183. Gol'dman, N.L., 1997, Inverse Stefan Problems, Kluwer Academic Publishers, P.O. Box 3300 AA Dordrecht, The Netherlands. Hoffmann, K.H. and Sprekels, J., 1982, Real-Time Control of the Free Boundary in a Two-Phase Stefan Problem, Numerical Functional Analysis and Optimization 5, 47. Hu, H. and Argyropoulos, S.A., 1996, Mathematical modelling of solidification and melting: A review, Modelling Simul. Mater. Sci. Eng. 4, 371. Kou, S., 1996, Transport Phenomena and Materials Processing, John wiley and Sons, Inc. MATLAB, 2004, MATLAB 7, The MathWorks Inc., Natick, MA, USA. Osher, S. and Fedkiw, R., 2003, Level Set Methods and Dynamic Implicit Surfaces, SpringerVerlag New York. Sagues, C., 1982, Simulation and Optimal Control of Free-Boundary Problems, in Workshop on Numerical Treatment on Free Boundary Value Problems 58 Birkhauser, 270. Stefanescu, D.M., 2002, Science and Engineering of Casting Solidification, Kluwer Academic/Plenum Publishers, 233 Spring Street New York NY 10013. Tacke, K.H., 1985, Discretization of the explicit enthalpy method for planar phase change, Int. J. Numer. Meth. Eng. 21,543. Voller, V. and Cross, M., 1981, Accurate Solutions of Moving Boundary Problems Using the Enthalpy Method, Int. J. Heat. Mass Transfer 24, 545. Voller, V. and Cross, M., 1983, An explicit numerical method to track a moving phase front, Int. J. Heat. Mass Transfer 26, 147. Voller, V.R., Swaminatham, C.R. and Thomas, B.G., 1990, Fixed Grid Techniques for Phase Change Problems: A Review, Int. J. Num. Meth. Eng. 30, 875. Zabaras, N., 1990, Inverse Finite Element Techniques for the Analysis of Solidification Processes, Int. J. Num. Meth. Eng. 29, 1569. Zabaras, N., 1999, Inverse Techniques for the Design and Control of Solidification and Forming Processes, Proceedings of the Integration of Material, Process and Product Design, 249. Zabaras, N., Mukherjee, S., and Richmond, O., 1988, An Analysis of Inverse Heat Transfer Problems with Phase Changes Using an Integral Method, Journal of Heat Transfer 110, 554.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1345
h-Techsight: a Knowledge Management Platform for Technology Intensive Industries •
a*
A. Kokossls , R. Bafiares-Alcfintara b, L. Jimdnez c and P. Linke a aDepartment of Chemical and Process Engineering, University of Surrey Guildford, Surrey GU2 7XH, UK bDepartment of Engineering Science, Oxford University Parks Roads, Oxford OX1 3PJ, UK CDepartment of Chemical Engineering and Metallurgy, University of Barcelona Marti i Franqubs 1, Barcelona 08028, Spain
Abstract In knowledge-intensive industries it is of crucial importance to keep an up-to-date knowledge map of their domain in order to take the most appropriate strategic decisions. The main objective of the knowledge management platform (KMP) is to improve the capabilities of chemical process industries to monitor, predict and respond to technological trends and changes. The search, retrieval, analysis, filtering, rating and presentation of information retrieved from the web (or any other type of document) are elucidated through the use of multi-agent systems, dynamic ontologies and learning techniques (conceptually similar documents are clustered and natural language processing techniques are used to retrieve new terms). Discovery of new knowledge leads to recommendations of modifications in the ontology (either classes or instances) by pruning irrelevant sections, refining its granularity and/or testing its consistency. The KMP works using an intelligent, asynchronous and concurrent process to achieve high quality results.
Keywords: knowledge management; knowledge retrieval; web search; ontology. 1. Introduction Decision making in technology intensive industries has to be made based on information that is constantly evolving. New technologies, markets and products emerge and change, and relevant information can be found only if one knows exactly where to look for it. Unfortunately, the amount of information and the various ways in which it can be presented, makes the retrieval of useful information an increasing more difficult and work intensive task. A KMP to monitor, predict and respond to technological, product and market trends has been developed (h-Techsight, 2001; Stollberg et al., 2001), which innovative points are:
Author/s to whom correspondence should be addressed:
[email protected] 1346
•
h-TechSight performs the search based on an initial ontology supplied by the user. An ontology is a conceptualisation of a domain. Ontology-based search is more accurate and complete than traditional keyword-based search (Fensel, 2001). • h-TechSight has the capability to suggest desirable modifications to the initial ontology based on the information retrieved (in the web or the databases). We refer to this capability as dynamic ontologies because it provides a mechanism to update the understanding of a domain with the available, ever-evolving, information. h-TechSight KMP can operate in two different modes: as a generic search or as an application search tool. In the generic search mode the system uses the whole web (or a selected domain in the web) as an information source. Search is performed by a multiagent system and the links retrieved are analysed using text analysis techniques and clustered into new categories. In the application search mode the system searches in domains where the information, while unstructured can be found in documents of similar patterns The smaller number of records and their similar format permit the application of powerful analysis tools (GATE and WebQL). 2. G e n e r i c Search M o d e The generic search mode architecture (Figure 1) is based in four different modules: the ontology editor, the multi-agent search system, the clustering search system and the dynamic ontology update.
2.1. Ontology editor Under the generic search mode, a ontology editor has been integrated in the KMP to facilitate the creation, customisation, browsing and modification of ontologies. Each user of the KMP has a personalised area in which his/her ontologies are stored, thus versions of the same ontology are stored to further analyse their dynamics. Uploading and downloading of ontologies are always performed in RDF format.
2.2. Multi-agent search system This module receives as an input the ontology and uses search engines to perform semantic based search, according to a predefined set of searching parameters. In this way, the Multi Agent Search System (MASH) finds web pages that contain relevant information to each concept in the domain of interest (described by the class path, as each class inherits all instances defined in their ancestors). The retrieval, rating and filtering processes are performed asynchronously, concurrently and in a distributed fashion by the agents with different roles. MASH is described in detail elsewhere (Banares-Alcfintara et al., 2005).
2.3. Clustering search module It is used to perform analysis on the results received from the MASH to propose new categories. For each URL provided by the MASH system, this module finds the URLs that point to it. Let A, B and C be three incoming links of URL D (Figure 2). The module extracts keywords from the incoming links, processes their contents and extracts terms from their hyperlinks to D. Each set of terms that corresponds to a URL D is mapped to a set of concepts of the ontology. WordNet (Wordnet, 2004), an online lexical reference system, in which English nouns, verbs, adjectives and adverbs are
1347
organised into synonym sets, is used for this purpose, and thus, the system is able to process html, pdf, doc or xls documents. The procedure is as follows: • For each term (t~) in the set, a clustering mechanism finds the closest ontology concept (c,i) in WordNet. • Extracted terms are mapped to WordNet (t) is mapped to nodes t~,~, t~,2 and t~,3). • Ontology concepts are mapped to WordNet (c~ is mapped to nodes c~.~ and c~.2). • The distance between every node of t~ and c~ is computed using the Wu and Palmer distance (1994). • The closest pair of nodes (t~,x,c~.>,) defines the distance between term t~ and concept C1.
After this process, each URL is described by a set of terms and a set of ontology concepts. Clustering is performed using the set of concepts of each URL using the D B S C A N (Density Based Spatial Clustering of Applications with Noise) and a similarity measure between URLs (Ester et al, 1996). • For each document D of a cluster the neighbourhood of D has to contain at least a minimum number of documents (MinDoc).
I
~
!
On~otogy e d i t o F (Java iippiet)
f
%,,,
¢
J
-~i
°(
K M P data~ase ::
~Set Vie~ )
recommel~da~ions
J
addi~io~Jdele~iof~
Figm'e 1. Generic search mode architecture. / J ...............\
t2, t 3
~
t3. t4
(
)
Figure 2. (a ) URL relationships, (h) where A, B, C and D are URLs, ti and ti,i are terms and ci and ci,/ are concepts.
:.:
1348 • • •
The neighbours of D are defined to be all the documents whose similarity to D is higher than, or equal to, a minimum similarity threshold (MinSim). DBSCAN is able to detect clusters with strange geometries. The number of clusters is not predefined. The algorithm is repeated for different values of MinDoc and MinSim and the scheme that provides the most compact and discrete clusters is selected.2.4.
Dynamic ontology update Based on the clustering results, the user has the ability to extend/modify the ontology with the newly discovered keywords. In both search modes the systems presents a table to the user where she/he can choose which items should be added to the ontology, and if the recommendation is to add the new terms as new classes or as instances of existing classes. Each time the user saves an ontology, a new version is created and stored in the database. Therefore, a user is able to return to a previous version of the ontology at any point in time. The versioning mechanism allows the user to keep track of the modifications applied to an ontology (as stated in section 2.1).
2.5. Scheduler mechanism The scheduling sub-system of the KMP gives the ability to the users to schedule both search modes of the platform and view the results at a later stage. The scheduled searches are fully configurable (e. g. search parameters of the MASH/Toolbox). This facility opens up the possibility to apply the KMP functionalities not only to snapshots of the web but as it evolves in time.
3. Application Search Mode In the application model the user defines a set of URL sites or database of documents that contain relevant information. The user may wish to automatically extract information, classify documents according to the ontology, assess the "dynamics" of the domain (e.g. site), and monitor changes. The application search mode is illustrated in Figure 3. A number of dedicated Natural Language Processing (NLP) tools are employed. 3.1. GATE GATE is an architecture for NLP, that enables an automatic semantic annotation of web mined documents using the terms of the ontology (entities or relationships). The KMP uses GATE to support the evolution of instances. The findings are stored to perform statistical analysis in order to monitor trends over time. GATE is described in detail elsewhere (Maynard et al., 2004). 3.2. Toolbox This module applyes NLP techniques to assess and validate ontologies. The latter are usually developed in an ad-hoc fashion or are recycled without a prior assessment for relevance and quality. Modules in the toolbox can be applied to enhance ontology relationships, discover new terms, and adjust ontology components according to the application context.
1349
| I
"-. N \ \
I
~i! .....~........... *N~a~bti~°~ ............... ....................... ~::}-~-
\
%.....
\
:;~ta~vgis
.i2005 Elsevier B.V. All rights reserved.
1351
Modelling for Control of Industrial Fermentation Jan Kamyno Rasmussen ~, Henrik Madsen b and Sten Bay Jorgensen ~ ~CAPEC, Department of Chemical engineering, Technical University of Denmark, Building 229, DK-2800 Lyngby, Denmark blnfbrmatics and Mathematical Modelling, Technical University of Denmark, Building 321, DK-2800 Lyngby, Denmark
Abstract This paper presents application of a grey-box stochastic modelling framework for developing continuous time models for dynamic systems based on experimental data. The framework will be used to develop predictive models suited for control purposes. The main idea behind the framework is to combine stochastic modelling with data to obtain information on parameter values and model (in-)validity. In case the initial model is falsified the method can point out specific deficiencies which facilitates further model development. The industrial fermentation case is production of an amylase enzyme by a filamentous fungus.
Keywords: Parameter estimation, industrial fermentation, modelling for control, greybox modelling 1. Introduction Fed-batch processes play a very important role in chemical and biochemical industry. Fermentations are widely used in biochemical industry and are most often carried out as ted-batch processes. Present control schemes do not utilise the full potential of the production facilities and may often fail to achieve uniform product quality and optimal productivity. Application of advanced multivariable control schemes can help solve this problem. The introduction of model based control strategies is considered difficult because suitable models are not readily available and require a significant investment in experimental work tbr their development. First principles engineering models can be used in the controller assuming that they possess satisfactory predictive capabilities. Parameter estimation in a first principles engineering model can be very time consuming and can cause problems when scaling up from laboratory to industrial fermentors. Especially parameters for mass and heat transfer models may change when the volume of the fermentor is changed. These phenomena can not be investigated in laboratory scale equipment which therefore makes large scale experiments necessary. The approach taken in this paper is to combine first principle engineering models with operational data to produce predictive models suited for control purposes. The method described in this paper is grey-box stochastic modelling which consists of a set of stochastic differential equations describing the dynamics of the system in continuous
1352 time and a set of discrete time measurements. An important advantage using this approach compared to using ordinary differential equations type model is that they can account for random variations in data. A framework for this kind of model development has already been developed (Kristensen et al., 2004) and is described in figure 1.
LNonparamet modeling ~~ric Firstprinmodel cipless
engineering
Stati testsstical II
IU/~dr'at~I nen
(re)'oM°du//tioJ\~ /-~~Ex t(? I ara eter J estimation ~
/-~~ ~u nM~sde2 ~ Yes,St°phaS tiCodlale
esidua, I a n a l y s i s ~
Figure 1. Grey-box modelling cycle. One of the key ideas behind the grey-box stochastic modelling framework is to use all prior information for formulation of an initial first principles engineering model. Unknown parameters of the initial model are then estimated from experimental data and a residual analysis is carried out to evaluate the quality of the resulting model. The next step in the modelling cycle is the model falsification or unfalsification which determines if the model is sufficiently accurate to serve its intended purpose. If the model is unfalsified the model development is completed. In case of falsification the modelling cycle must repeated by reformulating the initial model. In this case statistical tests can be used to provide indications of which parts of the model that are deficient. Nonparametric modelling can be applied to estimate which functional relationships are needed to improve the model.
2. Process description The process studied is fermentation of the filamentous fungi Aspergillus oryzae for production of the enzyme amylase. The fermentation is initiated by transferring the contents of a seed tank to the main fermentation tank when a certain transfer criterion has been satisfied. The main fermentation tank contains an initial amount of substrate and the main fermentation process starts immediately after inoculation. The main fermentation is carried out in a batch and fedbatch phase. When the initial substrate has been consumed by the microorganisms the fedbatch phase is initiated. Feed dosing is started at a low level and increased to its final value within a certain time span. The fedbatch phase continues for the rest of the fermentation process. The fermentors are equipped with sensors for online measurements of different variables but some values are only available as offline measurements which makes closed loop control more difficult and requires a more accurate model for predicting the variable values.
1353 The first principles engineering model to be studied here is proposed by Agger et al .(Agger et al., 1998). The model is based on the assumption that the total filamentous biomass can be divided into three distinct regions: • Active region (Xa): Responsible for uptake of substrate and growth of the hyphal element, a-Amylase synthesis occurs in this region. • Extension zone (xe): Building of new cell wall. • Hyphal region (Xh): Contains the degenerated part of the hyphal elements and can be considered as an inactive region. The original model contains 5 states, (The 3 morphological states, substrate concentration (s) and product concentration (p)). During the development of the model Agger et al. has assumed that no oxygen limitation is present. In order to be able to model the behaviour at low dissolved oxygen values and relate the morphological states to off-gas measurements the model has been extended (see Zangirolami, 1998). The oxygen concentration has been introduced as an extra state and as the volume is changing this constitutes an additional state of the system. The formation rate of the three regions is given in equation (1)-(3). C
= q~ - Dx~
(1)
dt (_/
dt ~h
- -
&
= q3 -
q~ -
=
Dx/,
q2
-
q2
-
(2)
Dx
(3)
Substrate, product and oxygen concentration are described by (4)-(6)
dt-
--
dt
q 3 + r , , , - - x +m (xc+x +%) +D s / , - s gv, tl
=
5,x
dco
Dp
(.1
,
(4)
(5)
(6)
dt D -
-
,~'
F
(7)
V The three kinetic expressions are given in equation (8) and (9). It is assumed that the concentration of hyphal elements is above the critical value at all times, meaning that only the second inequality in (8) needs to be considered.
1354
0;
a < Cn
qlk~s
.x
0
>Ix)
,)' q2 -
k2x~ ;
q3 =
(8)
o
k3s
x / c,
axa
S + Ks3 xa / c,, + K 3
Co: ko~ + C~
(9)
In order to account for the decrease of growth rate for the active region under oxygen limiting conditions the last Monod term in equation (9) has been introduced. The specific growth rate and rate of product formation and carbon dioxide and rate of uptake of oxygen is given in equations (9)-(11). ¢t -
q3
(10)
xe + x a + x h kpls
ps
(s+/£,4 )(1+ exp (kp2 (s--S,.ep )))
FC02 ~ Yxc
kl - Y~c
q3 + m~ X e -t-X a nt-x h
;
+k~
ro2 _ Y °
(11)
q3 +m o X e nt-x a -Jr'Xh
(12)
kbran "104
(13)
4 (d. 10-4)2 (1- w ) f p ~-(d. 10- 4 )2 (1- w ) f p
k 3 - ktip,ma x • 10 -4 ~
d - 11.25./~+1.1
;
1
(14)
0_ 4
4~ (l_w)p
(15)
The relations to the off-gas measurements are given in (16). OgR-ro2
(Xe nLXa nt-Xh) ; C E R - r c o
2 (Xe nt-Xa nt-Xh) ; D O T - - -
Zt,
C 02
For more intbrmation on the details of the model please refer to Agger et al., 1998.
(16)
1355
3. Simulation Simulations have been performed to compare the predictions of the model with actual data from an industrial fermentation. The industrial data has been supplied by Novozymes A/S. The parameters for the simulation are provided in table 1. The only input used in the simulation is the feed profile (figure 2) which has been applied to one of the batches from the industrial data set. The figures in the following show characteristic results obtained in the simulation and experiments.
Table 1. Parameters used for the model simulation.
Parameter kbran Ktip...... ke K~I K~3 ins P W f Ysp k~ kpj kp2 Srcp Ks4 Vxc Vxo mc 1110 kLa ko2
Value 1.7"104 49 0.08 3"10 4 6" 10-3 0.01 0.57 1
0.67 0.8 5316 8 32 5000 9.5* 104 6,10 -4 0.01786 0.01563 6.3"10 .5 5.6* 10.7 79 2.25,104
Unit Tip*~am-J*h-1 gin*tip -1. h-I h-I g*L -1 g* L-1 g glucose*g DW-l*h -1 g active DW*g glucose -I kg/L g/g DW FAU*g glucose -1 FAU*g active DW*h -~ FAU*g active DW*h -1 L*g-~ g*L -1 g,L -1 tool CO:*g DW -1 tool O2*g DW -I tool CO2*g DW-l*h -1 mol O2*g DW-l*h -x h-1 mol*L -l
Source Agger et al. Agger et al. Agger et al. Agger et al. Agger et al. Agger et al. Agger et al. Agger et al. Agger et al Agger et al Agger et al Agger et al Agger et al Agger et al Agger et al Agger et al Carlsen et al. Carlsen et al. Carlsen et al. Carlsen et al. Zangirolami Fitted
Figure 3 shows that to some extent the model is able to predict the behaviour of the OUR. During the batch phase the OUR predicted by the model is somewhat lower than actually measured. As the feed dosing is initiated at t=25h a large drop in OUR occurs which is captured by the model. The prediction for the fed-batch phase is somewhat higher than the experimentally observed. Figure 4 shows the evolution of the biomass concentrations with time. It is seen that the concentration of active region and extension zone decreases during the fermentation and the concentration of the hyphal region increases. This behaviour can be explained by the decrease in substrate and oxygen availability occurring after the batch phase. The low concentrations decrease q3 (eq. 9) which reduces the rate of formation of active cells.
1356
0[
0.045[
0,o4[ fi
0.03[ i ii
~ ,150
6O
:.,
',.,.
....
".....,:
iJ
f t..,.( k;"
-i
0'02 t ,i
~100
O 0015~/i
--
101[/i
30
100 Time, h
150
Figure 2:Feedfiow rate used in the simulation.
200
o!
I
_
//
/
I .................
4o
x "1000 I i
:i I
/"
Total
I /;
5'o
....
Simulated
0.005t! 50
-
Time, h
4o
Figure 3:Oxygen Uptake Rate (OUR). Simulated values (dashed line). Experimental values (Continuous line).
0
................................
140 Time, h
150
Figure 4:Extension zone*1000 (dotted line).Active region (dash dotted line). Hyphal region (dashed line). Total biomass (continuous line).
4. Discussion The morphologically structured model presented is able to predict a large part of the behaviour of the industrial fermentation. The model has been developed in laboratory scale equipment where no oxygen limitation has occurred in the experiments. In order to be able to simulate an industrial scale fermentor some of the model parameters need to be reestimated and new functional relationships have to be introduced. It has been shown that the morphology changes drastically under oxygen limitation (Zangirolami, 1998). This runaway phenomenon will also be modelled. During low dissolved oxygen concentration the filamentous fungus changes its filaments which increases viscosity and impairs oxygen transfer. Hence the oxygen concentration becomes even lower. Parameter (re-) estimation and investigation of new functional relationships in the model based on experimental data are carried out in the software program CTSM (Continuous Time Stochastic Modelling) (Kristensen et al., 2004). CTSM provides a graphical user interface which allows the user to specify how the model parameter should be estimated. After specifying which experimental data sets to use, the program determines the parameter estimates and evaluates statistical tests.
References Agger,T., A. B. Spohr, M. Carlsen and J. Nielsen, 1998, Growth and Product Formation of Aspergillus oryzae during Submerged Cultivations: Verification of a Morphologically Structured Model Using Fluorescent Probes, Biotechnol. Bioeng., 57, 321-329. Carlsen, M., Nielsen, J., Villadsen, J., 1996, Growth and Gt-amylase production of by Aspergillus oryzae during continuous cultivations., J. Biotechnol., 45, 81-93. Kristensen, N. R., H. Madsen and S.B. Jorgensen, 2004, A Method for Systematic Improvement of Stochastic Grey-Box Models, Comp. & Chem. Eng., 28/8, 1431-1449 Zangirolami, T. C., 1998 Modeling of Growth and Products Formation in Submerged Cultures of Filamentous Fungi, Ph.D. thesis, Technical University of Denmark, Denmark.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1357
System-Dynamics modelling to improve complex inventory management in a batch-wise plant Zofia Verwater-Lukszo and Tri Susilowati Christina Delft University of Technology, Faculty of Technology, Policy and Management 2600 GA Delft, the Netherlands
Abstract The process industry has to cope with a rigorous competition caused by more short-term dynamics in supply, more unpredictable and turbulent demand patterns, stronger requirements on product variety, delivery lead-time and quality of product. It forces company to spend efforts at improving its competitiveness and productivity. Appropriate strategies or action in the area of inventory management can contribute to survive in these conditions. This paper describes a novel modelling approach aimed at improving complex inventory management of many product grades in a multi-product batch-wise industrial plant. The simulation model of the internal supply-chain addressing the order acceptance and processing constraints- the cornerstone of the proposed approach - is developed according the System Dynamics methodology. The proposed model implemented in a decision support tool assists the decision maker(s) by providing a systematic structure to arrive at potential improvement options for inventory management. The approach is applied in a chemical lnulti-product plant producing a number of grades of resins with different priorities.
Keywords: System Dynamics, internal supply chain, decision support 1. Introduction Inventory holds a crucial but double-sided role in a manufacturing plant. In "rough" situations such as when a plant cannot produce at the desired rate or in moments where suppliers are not reliable, inventory is seen as a saviour, as a survival tool. However, mostly, when everything goes smoothly, inventory is seen as a waste of money, a standing still investment that yields nothing. Inventory management is necessary to create a balance between these two sides. How to manage the inventory to find the right trade-off between both objectives is the basic question addressed in Christina (2004). Inventory decisions are high-risk and high-impact from the perspective of operations. Commitments on inventory and subsequent shipment to a market in anticipation of future sales determine a number of logistics activities. Without the proper inventory, marketing may find that sales are lost and customer satisfaction will decline. Likewise, inventory planning is critical to manufacturing. Raw material shortages can shut down a manufacturing line, which, in turn, introduces goods shortages. Just as shortages can
1358 disrupt planned manufacturing operations, overstocked inventories also create problems. Overstocks increase cost and reduce profitability through added warehousing, working capital requirements, deterioration, taxes, and obsolescence (Bowersox, 1996).
START
1
--)
Investigate the inventory system
Develop an influence diagram
Derive evaluation parameters
I Develop the simulation model to asses evaluations parameters
,
,
Determine plausible tactics and strategies
Choose the most preferred options
,
Deal with uncertainty
ssop -') Figure 1. The framework of the decision support system
Designing an effective inventory policy turns out to be a hard task. In order to properly evaluate the different alternatives, which potentially are intended to improve the inventory management, it is necessary to study the impact of the proposed options on the important performance indicators related to the enterprise goals. Two objectives are considered as the most important indicators: the minimization of the inventory costs and the maximization of the customer satisfaction. Therefore, the problem, which arises here, consists of finding the solution that is the appropriate compromise between expected inventory costs and the customer satisfaction level. By searching for the solutions the uncertainty related to strategies, should be taken into account, too (Verwater-Lukszo, 2004).
2. Decision support: Performance measurement system The approach adopted to attain the goal formulated as improvement of the inventory management of the WIP (Work In Progress) materials was aimed at developing a
1359 decision support tool that is expected to assist decision maker(s) in revealing the performance parameters (inventory level/costs and service level) behaviour under potential tactics and strategies concerning inventory with regards to uncertainties of the system. The approach is decomposed into four phases, as presented in Figure 1. The first phase is to get insights of the inventory conditions in the company and to identify the evaluation parameters, which could measure the influence of potential improvement options on inventory management to the achievement of the company's objectives. This is a creative process supported by an influence diagram representing relations between variables in the internal supply chain with regard to customer orders, materials and production resources; see Figure 2. :< ......
.-
...._ •
.................
" ~ ;"-" / ,,'
_ ..... "--.._---
•'
-
.
O0
I-'- 663 ~ . ,--, 430
.
.
.
.
.
.
.
.
40
80
CO
L
00 ,.&,57.41
} ~
o~- 421
i
~57.2L
A
0
10
time (rain)
20
30
0
20
time (rain)
40
60
Figm'e 5. N M P C simulation results in the presence oflpressure ch'op disturbance (10% decrease at t = 12 min). D![ferent time scales are used to show the detail. .............. , ................................................ ~.........................................................~......................................................
542 . . . . . .
542
..: "-o.
equilibrium point T decrease (5 °C) : ....... T' increase (10 °C) r increase (20 °C) +
i
/
i .t
538
538~
,x/'/
o
C) .~.
S+
...
i---
534
"'"t
""-,... 663.38
663 42
T
(C)
663 46
663.5
I
t •
f
i ,
terminal region projectio
530
terminal region projection
i
534~
i
530
#'
40.4
40.6 W(t°ns)
40.8
Figm'e 6. Frajectoriesfor the system controlled by Q1HNMPC
different control structures tinder different disturbance scenarios. From the simulations performed the best control structure resulted with the three controlled variables: reactor temperature (T,.), regenerator temperature (Treg) and catalyst amount in the reactor (W,.), and three manipulated inputs: openings of the spent and regenerated catalyst circulation pipes between the reactor and regenerator (svsc and svrgc, respectively) and the flow rate of the raw material (/7). This inferential control scheme is able to provide good control performance for the composition in the fractionator (see Figure 5). Figure 6 illustrates the performance of the QIHNMPC for different off-nominal initial conditions. It can be shown that asymptotic stability is achieved in all cases. The very small terminal region (projections of the hyper-ellipsoid on the shown state space) is caused by the strong nonlinearity of the system. Figure 7 illustrates that QIHNMPC achieve better control performance than NMPC. Using QIHNMP the system is stabilized faster.
1368
532.2 ~ 532 531.8 66350
t
0
I-'-
1
' ~
'
½ '
"
~ 6 3 , 4 5 - ~.......... ,.,, ~3663,4 0 ~-408I
40.7 40.6 0
'
8>0.300~ 0.299 0298 0320
3 .... QIHNMPC
--NMPC
~n
>
'
0.31 ~
~ lo
20
'
'
q......... ~ ............................ 20 40 60 80 0'300 "" 1'0 ~ ' ...."............ '_............ ~ 5 7 1 6 r ~ ~57 15~ ........ .. .... i
2
4 time (min~
8
10
30
4'0
50
~
'
,
.......
2'0 -~
3'0 4'0 50 - T - - N-M-PC q L ..... QIHNMPC~
57'.14(~- ...... 1~"....... ~ ........ ~---:7---~--5Z-'~0 time (rain)
Figure 7. Comparison between QIHNMPC and NMPC; variation in time for 20 °C disturbance in Tr (dashed line in Figure 6); Left - controlled outputs; right - manipulated inputs
4. Conclusions The paper presents dynamic simulations for the FCCU aggregate system that includes the main fractionator and a kinetic model for the riser leading to a 2144 th order ODE model. Based on this model an inferential control scheme is proposed that is able to control the product distribution resulted from the fractionator based on easily measurable variables in the regenerator-reactor system. The model was used to simulate the performance of the theoretically founded quasi-infinite-horizon NMPC (QINMPC), to achieve fast stabilization of the closed-loop system. It is shown that using state-ofthe-art optimization approaches based on modern multiple shooting algorithm real-time feasibility can be achieved even in the case of the very high order FCCU model. The results demonstrate that industrial applications of modern NMPC approaches to complex chemical processes can be brought in the realm of possibility.
Aeknowledgelnent This work was supported by the Marie Curie fellowship HPMT-CT-2001-00278.
References Allgoewer F., T.A. Badgwell, J.S. Quin, J.B. Rawlings, and S.J. Wright, 1999, Nonlinear predictive control and moving horizon estimation-An introductory overview, In P.M. Frank (editor), Advances in Control, 391. Chen H and F. Allgoewer, 1998, A Quasy-Infinite Horizon Nonlinear model Predictive Control Scheme with Guaranteed Stability, Automatica, 34, 1205. Diehl M., Real-Time Optimization for Large Scale Nonlinear Processes, 2001, PhD Thesis, University of Heidelberg. Dupain X, E. D. Gamas, R. Madon, C.P. Kelkar, M. Makkee, J.A. Moulijin, 2003, Aromatic gas oil cracking under realistic FCC conditions in a microriser reactor, Fuel, 82, 1559. Qin, S.J., and T. Badgewell, 2003, A Survey of Industrial Model Predictive Control Technology, Control Engineering Practice, 11,733. McFarlane R.C., R.C. Rieneman, J.F. Bartee and C. Georgakis, 1993, Dynamic simulator for a model IV Fluid Catalytic Cracking Unit, Computers Chem. Engng, 17, 275. Nagy Z. K., F. Allgower, R. Franke, A. Frick, B. Mahn, 2004, Efficient tool for nonlinear model predictive control of batch processes, in Proc. of the 12th Mediterranean Conference on Control and Automation (MED'04), Kusadasi, Turkey, on CD.
European Symposium on Computer Aided Process Engineering - 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.
1369
Improving of Wavelets Filtering Approaches Rodollb V. Tona. Antonio Espufia, Lluis Puigjaner Universitat Polit6cnica de Catalunya, Chemical Engineering Department. E.T.S.E.I.B.. Diagonal 647, 08028-Barcelona, Spain.
Abstract In this work, some simple strategies for signals filtering and estimation with wavelets are presented. Firstly, it is studied the adequacy of some type of wavelet for filtering. Then, it is proposed a strategy to determine the best decomposition level and, then, to improve wavelet filtering accuracy. Some known benchmark signals are used to validate the performance of the proposed methods and their comparison with some existing approaches. The results obtained expand the applicability and reliability of existing filtering schemes with wavelets and propose some useful alternative to do it.
Keywords: Data rectification, Wavelets, Depth of Decomposition. 1. Introduction Measured process signals are very important to support a wide number of engineering tasks with a critical impact on the global operation of the plant. Otherwise, these measurements inherently contain noise originating from different sources. Hence, data filtering is a critical step in the operation and control of any chemical plant. Over the last decades, numerous techniques have been proposed for filtering or data rectification. If a process model is available, data reconciliation may be used. If it is not the case, but measurements are redundant, rectification based on an empirical process model derived from data may be proved. However for cases without model or redundancy in measurements the option is the use of univariate filters. These methods are the most widely used in the chemical and process industry (Bakshi, 1997) and include EWMA, median filters and so on. Most recently, because the multiscale nature of process data, wavelets have been proposed for data rectification. In this work, we are focusing on developments for this category of data filtering. Wavelets are families of mathematical functions which are capable of decomposing any signal, y(t), into its contributions in different regions of the time-scale space such as: L
y(') - E uEZ
L
(,) + Z E
(,)
(,
1=1 ueZ
Each term at right of the equation represent a decompose part of the original signal. ¢z,o are the approximation coefficients, d/,o are the detail or wavelets coefficients, ~,~, represents scale [unctions, ~, ,, represents wavelet [unctions, I is the scale [actor, o is the translation [actor and L is the coarsest scale, normally called the decomposition level.
1370 The above decomposition has been shown as very useful for filtering and signal trend estimation (Donoho et al, 1995, Bakhtazad et al, 1999). In these applications, any measured variable signal, y(t), is assumed to be the result of:
y ( t ) = x(t) + e(t)
(2)
Where x(t) is the vector of true process variables and e(t) is the associated measurement error (noise). Then, the basic idea to estimate x(t) (filtering of y(t) and extracting the true trend) with wavelets is as follows (1) Decompose the raw signal by using wavelets (equation 1); (2) Remove wavelets coefficient below a certain threshold value fl (thresholding step); (3) Reconstruct the processed signal using the inverse of the wavelet used. The above procedure (Waveshrink method) was the first method proposed for filtering with wavelets (Donoho and Johnston, 1995). Other methods have also been proposed. In all cases, they are variations or extensions of the Waveshrink method and it remains as the more popular strategy for filtering. A practical difficulty encountered in the application of Waveshrink, consists on how to select the decomposition level L. As it is highlighted by Nounou (1999), thresholding of dl.o under high values of L may result in the elimination of important features of the signal, whereas thresholding under low values of L may not eliminate enough noise. Additionally, wavelets Daubechies (dbN) are commonly adopted for different filtering schemes (Doymaz et al, 2001; Addison, 2002) because their very good capabilities at representing polynomial behaviours within a signal. However, the choice of different dbN can slowly affect the quality of filtering (Nounou, 1999). In general, the choice dbN vary between authors and no rules of what to select exists. In this work, an empirical study of filtering with wavelets is presented. Firstly, it is explored the ability of some popular wavelets for filtering. Then, it is proposed a strategy to determine the best decomposition level. 2. A n a l y s i n g
the performance
of wavelets
for filtering
It was conducted an experiment based on using different dbN and different L values within the Waveshrink scheme. The experiments were organised as follows: - Typical signals from literature were used (Doymaz et al, 2001). They originally contain 1024 observations. In the experiments, they were used in the following intervals: (1) Blocks signal or S1 from 451 to 627; (2) Blocks signal or $2 from 620 to 965; (3) HeaviSine Signal or $3 from 251 to 820; Doppler signal or $4 from 35 to 550. - All signals were contaminated with random errors of N(0,0.5) (see figure 2). - Daubechies from db 1 to db9 were applied for each signal. - Constant L values (from 2 to 9) were used for each dbN and for each Signal. - Each combination (Signal-dbN-L) was applied on-line and according to the On Line rectification (OLMS) and Boundary Corrected Translation Invariant (BCTI) schemes (Nounou et al, 1999) - For the waveshrink, soft thresholding was used and the threshold, fl, was determined by the visushrink rule (Nounou et al, 1999).
1371 Blocks
r
,
- - - _ . . . .
450
.,. : . . -
550
HeaviSine 5
_
-, .:-
]
600
t
Signal-
~
i
r .
'-"
8
~!.='----:
. . . .
.
.
.
.
. . . .
6 4 2 600
650
700
800
Doppler
$3
900
Signal
1000
- $4
1
o,se
[ -
200
Signal-S2
v
10
•
o
-5
12
t
'----
500
Blocks
Signal-S1
i
o
L
400
600
~
A
o
.
. .
.
.
.
.
.
.
.
.
.
-0.5
~
800
1000
_~
0
200
400
600
Figure 2. Reference Signals for experiments.
Mean Square Error (rose) between the filtered signal and the original signal (without noise) is computed on windows of 32 observations length and each time after 16 observations are filtered. This results in 8 consecutive intervals with rose computed for signal S 1, 18 consecutive intervals for signal $2, 32 consecutive intervals for signal $3 and 29 consecutive intervals for signal $4. Then, the frequency of each L value that leads to the low rose in each interval is computed. Similarly, the frequency of each dbN filter that leads to the low rose in each interval is computed. These frequencies are shown in table 1. Table/. Frequency of L values and dbN filters as leadings to the best estimation of different signals. Frequencies for L OLMS L=2 L=3 L=4 L-N L=6 L=7 L=8 L=9
Sl 0 0 1 1 5 0 0 1
$2 5 0 6 0 3 2 0 2
$3 2 2 15 I0 3 0 0 0
Frequencies for dbN
values BCT!
$4 4 10 II 3 0 1 0 0
Si 0 0 1 7 0 0 0 0
$2 5 1 6 4 0 0 0 2
$3 2 9 13 8 0 0 0 0
OLMS $4 4 9 10 5 0 1 0 0
dbl d b2 d b3 d b4 db5 db6 db7 db8 db9
$1 6 0 0 0 0 1 1 0 0
$2 8 5 2 0 0 1 I 0 1
$3 13 1 1 6 1 0 5 1 4
BCT! $4 5 4 5 2 3 0 3 6 1
S1 8 0 0 0 0 0 0 0 0
$2 11 I 0 1 2 2 1 0 0
$3 20 3 0 3 2 2 1 1 0
Sa 2 6 1 4 0 3 4 7 2
Analysing the frequency for dbN it can be noted that dbl is particularly appropriate for signals like S1 in both OLMS and BCTI applications. For signals S2 and S3 dbl is also useful for BCTI. In the OLMS case some other filters are also frequents for $2 (db2) and $3 (db4-db 7). It is noted that these lasts occurrences corresponds to intervals where abrupt changes are at the end of the data window in case of $2 and for intervals with slow trends in case of $3. So, db 1 may be more appropriate for stationary patterns (as in S l) or for dealing with abrupt changes (see discontinuities in signals $2 and $3). In case
1372 of $4 the pattern of the curve is continuously changing through fast and smooth patterns and many filters occurs at different intervals. Only is noted a slow tendency of more occurrences of dbN with even values of N (particularly db2 and db8). So, slow and changing patterns as in $4 may be best treated with db2 or db8 filters. Now, for the frequencies of L values it is shown that every signal tends to be handled around bands of L values (L=2-L-4 for $2, L=4-L-5 for $3 and L=3-L-4 for $4) but a pattern is more difficult to establish than in the case of dbN.
3. Optimal Depth of Wavelet's Decomposition Here, it is explored a simple strategy to deal with L. To do this, consider the curve, y(t), that is shown in figure 3 (labelled as measured). Several approximations, AL, ofy(t) are calculated through equation 3 and varying the scale L from 1 to nL. Then, several powers Pz., between y(t) and each one of the AL are calculated. Also, variations of power, APL, from one scale to another, are computed. Now, by plotting the successive values of APz., one or more minima will be detected (see figure 4). The first minimum is identified and the associated L is labelled as Lm. It is observed that at Lm, the associated AL shows the closest behaviour to the original signal (see figure 3). Therefore, an optimal L can be set as the one corresponding to the first minimum reached in APL. Filtering 69.5
/
,
at
L =
,
i
i
~-"
~
Filtering
1
,
~.o, .
.
.
~
.
~.~
L
68.5
0
10
20
Filtering 695L
,
30
at ,
L
40
~
~
0
10
'
695!
,
20
68
/
Oo_~O
I ~ ~Y~( /
0
~
~
i '
I
10
~ "
i
[
~ Y
I ....... I _
I
[ """"""'
20
,~-
.....
,
' . . . .
30
30
at ,
I 68.5
2
....
~ _; _ 2
-
Filtering o -
L =
~,
= 3
'
at
i .....
L =
40
4
~ . ~ ~
measured filtered _
68
'
I
I
i
40
0
10
20
~rue
I
30
t
I
40
Figure 3. Decomposition of the Jumps signal wit db8. From L--1 to L=4. Mathematically, the different steps required for this optimal depth determination can be set as follows: 1- The, cLo and d/,o at various scales I are obtained with wavelets as in equation (1). 2- The approximations AL, at each scale L is reconstructed through: L
1=1 3 - The power PL, at each scale L (daL), is computed as follows:
(3)
1373 [,
],
Z /='
AI
-
Zl -I /='
(4)
4. The variation of PA is computed as follows:
A P - P/ ( d a ) - P/_, ( d a )
(5)
The optimal scale L,,, that corresponds to the first minimum of JPL is identified. 5. At L,,, a first thresholding, based on setting to zero all the dAo in scales greater than L,,,, is performed. Then, a second thresholding over remaining coefficients is performed through WaveShrink. The first thresholding gives the appropriate L and the second thresholding eliminates coefficients related to noise in scales less or equal than L,,,. 6. The de-noised signal is obtained by taking the inverse of the wavelets used.
o.06 ii -I
....
,'
I 0.02
I
i
0
01015
l 1
I
I 001
0
0
I L
L
I . . . .
J
ILm .....
--
• 2
I
iI
L 3
I 4
.....
~
I
I
I
L_ I m
L
r
I
"-e-
i
i
'
1
i
~
2
3
_
r
_
1
4
I
7
~
w
L _
5 5
J
'
I
_1 0 0 0 5
~ _
i 0
,'
q _ _
I
s
6
Scale
Figure 4. Determination of the optimal level L ....
In the above procedure, computing approximations until nL with values between [10, 12] is sufficient to identify L,,,. The signals used in section 2 are used for testing the above proposed approach. The experiments were organised as follows: - The proposed strategy is applied on-line and for both OLMS and BCTI schemes. MSE between the filtered and the true signal are computed locally (on data windows as in section 2) and globally (over the entire set of each processed signal). Figures 5 shows the best fifteen estimations (expressed as global MSE values) that were obtained with the proposed approach (labelled as LevaShrink) and for the WaveShrink strategy. It is shown that, in general, the proposed approach can compete in estimation accuracy with WaveShrink for both OLMS and BCTI schemes. Only the signal S1 presents considerable differences with traditional WaveShrink but for the first estimation it is comparable in accuracy with WaveShrink. It is also shown some cases where LevaShrink gives best accuracy (lower mse in some plots of figure 5). This is possible because at each time the level tuned is adapted to the current pattern of the trend which is more appropriate than setting a same L tbr all times as it is the case for WaveShrink. Then, the LevaShrink method can be an advantageous alternative use for -
1374 filtering with wavelets. The advantage of use LevaShrink is to avoid the offline analysis of each signal for setting of appropriate values of L. C o m p a r i s o n on S i g n a l S 1
Comparison
0 0.06
I
i. . . . . .
0.04
~d . . . . . . ' W "~21~! • .;YL-' I
Signal
S2
,.... U.I...~2D--i -~
u~---' - - -
-4
i. . . . . .
H
I I
I_L
2:~--~ _ _ ~. . . . . . . ~. . . . . . . . . . ~r. . . . " , - " O < > : ~ : : i , ~ : ~ O - ~ r ~ ' = " ~ = : f ~ : :
0.02
,"'
/
0.16 O. 14
-
m~-m
0.12
~" _
_[;:.:i"":-"
~..:::~.-=,ll
Comparison O. 1
10
on
Signal
15
S3
I
~ ~:~
L~..-L.j/~"
I
I
/
......
:. . . . . . .
:. . . . . .
......... ~ ................
:
0
5
OLMSLEvAShrink
/ -
~..~2~-
~:~;~l.:l~---
-
I
_1 . . . . . . .
,~---,t I
I-
:
10
-~
15
.............. i l l .............. O L M S w a v e S h r i n k
-t -
-
-
---'-°°
l /
I
~ 10
on
I
~.
,.... _.._C~_...C;,.---(~;
I _ , . . : S " ) O _ , ~ - - O_ --~
i 15
Signal
S4
I
I
1
I
o.o~
_
Comparison
t
[~3
o.oo
.m-~..~
l 5
0
i
I. . . . . . .
~......._~.j--CI~F-4,.~~Y"
......
:~
0.08
5
i
. . . . . .
O. 1 0
>,
on
0.18 I
t
0 -0---
5 BCTILEvAShrink
10 ..............e ..............
15 BCTIwaveShrink
[
Figure 5. Comparison of LevaShrink with traditional WaveShrink.
4. Conclusions Wavelet filtering schemes have been studied. By the way of experiments it has been show the adequacy of dbl for signals with stationary and/or abrupt change patterns, particularly under BCTI schemes. By other hand, wavelets like db2-db8 may be more appropriate for dealing with signals with smooth changing patterns. It has also been show that appropriate level values can be very variables from one type of signal pattern to another. Then, the proposed approach can deal with this issue by identifying at each time the required level. Finally, further improvements and extended comparisons with other existing approaches and for different case studies will be made in future works.
References Addison, P. S., 2002, The Illustrated Wavelet Transform Handbook: Applications in Science, Engineering, Medicine and Finance. Institute of Physics Publishing, Bristol. Donoho, D.L., and I.M. Johnstone, 1995, J. Am. Star. Assoc., 90, 1200. Doymaz, F., A. Bakhtazad, J. Romagnoli, and A. Palazoglu, 2001, Comp. Chem. Eng., 25, 1549. Nounou, M. N., B. R. Bakshi, 1999, AIChE J., 45(5), 1041. Bakshi, B. R., P., Bansal, M.N. Nounou, 1997, Comp. Chem. Eng., 21(Supplement), s1167. Bakhtazad, A., and A. Palazoglu, J.A. Romagnoli, 1999, Intelligent Data Analysis, 3,267.
Acknowledgements Financial support received from the "Generalitat de Catalunya" (a FI research grant to Tona, R. V.), from "Ministerio de Ciencia y Tecnologia" (project DPI2002-00856), and from the European Community (projects GIRD-CT-2000-00318) are fully appreciated.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) (¢2,)2005 Elsevier B.V. All rights reserved.
1375
Supply chain monitoring" a statistical approach Fernando D. Mele, Estanislao Musulin and Luis Puigjaner* Chemical Engineering Department, ETSEIB, Universitat Politbcnica de Catalunya Av. Diagonal 647, E-08028, Barcelona, Spain
Abstract Although the nodes of a supply chain (SC) network generate a huge amount of data along their operation, extracting useful information from them is not straightforward. Within the Supply Chain Management (SCM) scope, monitoring reveals as a key task that is currently waiting for further study. It is necessary to minimize risks of undesired situations and administrative efforts to manage material flows. Supply Chain Monitoring (SCMo) techniques should support manager decisions warning of the abnormal situation telling what have gone wrong and suggesting solutions. Additionally, they should be able to store the causes and consequences in order to help in the decision making onto future similar situations. This work presents an extension of multivariate statistical methods to SCMo that consists in a wavelet based multi-scale Principal Component Analysis (PCA) technique accounting for time delays. The proposed approach has been tested using data generated through an event discrete simulation model running in several scenarios. Results have revealed that statistical multivariate techniques are very useful for SCMo.
Keywords: SCM, SCMo, PCA.
1. Introduction A company's supply chain (SC) comprises both geographically dispersed facilities where raw materials, intermediate products, or finished products are acquired, transformed, stored, or sold, and transportation links that connect these facilities among them (Simchi-kevi et al. 2000). Within a SC there is an actual agreement among the different partners so as to award the general coordination task to a central entity. The central entity has a global view and tries to equilibrate the stresses that each SC nodes creates. In this point, Supply Chain Monitoring (SCMo) plays its essential role offering the information in a suitable way to the central entity's disposal. It is as the halfway between the transactional and analytical tools on which Supply Chain Management (SCM) is often supported. In recent years, astonishing gains in personal computer speed, e-commerce, and the power and flexibility of data management software have promoted a range of applications. Widespread implementation of transactional tools or backend-systems as Enterprise Resource Planning (ERP), Material Requirement Planning (MRP) or Distribution Resource Planning (DRP) systems offer the promise of homogeneous, Author/s to whom correspondence should be addressed:
[email protected].
1376 transactional databases that will facilitate integration of SC activities. In many companies, however, the scope and flexibility of these systems have been less than expected or desired, and their contribution to integrated SCM has yet to be fully realised. Moreover, competitive advantage in SCM is not gained simply through faster and cheaper communication of data. Companies are seeking to utilise systems that automatically analyse their corporate databases to identify plans for redesigning their SCs and operating them more efficiently. Nevertheless, extracting useful information from data is not straightforward. These data are disparate in nature and, additionally they are collected at different frequency and even saved occasionally. Thus, within the SCM scope, monitoring reveals as a key task that has received little attention up to now and it is currently waiting for further study. In this work, monitoring is proposed as an intermediate technique that provides an initial analysis over the large amount of data saved in the aforementioned databases, which enables to characterise the normal operation of the system. This is very useful in order to visualise the operation of the SC to control whether it is kept between the normality boundaries. Otherwise the traditional fault detection for chemical processes, in SCM it is not necessary to detect the occurrence of a fault but to obtain a pattern indicating how this event, whose occurrence is known, affects the value of the measured variables in the system, e.g. inventory levels. The idea is to store in a database a model that could give notion about the variations or changes in the variables when the event is repeated in such a way to be able to study and anticipate corrective actions. This work is based on multivariate statistical methods usually applied to process monitoring.
2. Monitoring Methodology 2.1 Principal components analysis PCA (MacGregor et al. 1995) is a statistical method for process monitoring based on data correlation. Consider a matrix X (of dimension m x n) containing data corresponding to m samples of n variables. Each column of X is supposed to follow a normal probability distribution and is normalized with zero mean and unit variance. Let R be its corresponding correlation matrix. Then, performing singular value decomposition on R, a diagonal matrix D~ = diag()~l, )L2,..., ~n) where ~i are the eigenvalues of R sorted in decreasing order )~1 > )g2 > . . . > )gn, is obtained. The corresponding eigenvectors Pi are the principal components (PCs) and form an orthonormal base in R n. It is possible to divide the PCs in two orthogonal sets, P = [Pl, Pz,..., PA] and P = [PA+I, PA+~,..., P.]. The first containing most of the common cause variation and the second describing the variation due to the noise (called the residual subspace). A reduction of dimensionality is made by projecting every normalized sample vector x' in the subspace generated by P, obtaining t = PVx', which is called the principal score vector. Then, the state of the process can be monitored using two statistics, the Hotelling's statistic (7 e) and the Squared Prediction Error statistic (SPE). The first describing common cause deviations and the second describing deviations in the residual subspace.
2.2 Genetic algorithm-based delay adjusted PCA (DAPCA)
1377 One main drawback of PCA is that it does not account for time-delays present in data. Those delays can cause that the percentage of variance contained in the first few PCs is low and the difference between the variance contained in the last significant PC ()~A) and the next one ()~A+,) is not accentuated. Therefore, there exists a trade-off between the number of linear relations considered (A) and the embedded errors that is introduced in the model, causing an inefficient reduction of dimension and a bad performance to filter the noise and to detect disturbances and changes in the process correlation (faults). If one want to deal with all the complete adjustment problem, without additional assumptions, (dmax)n singular value decompositions have to be evaluated (Wachs and Lewin, 1999), where d,,,ax is the maximum delay considered. In this work, a Genetic Algorithm (GA) has been developed to solve this high combinatorial optimization problem. In this approach, each chromosome represents a backward shift vector (DV = [d~, d2.... , dn_~], with dj in the range 0 < dj < dma~ for j = 1, 2,..., n - 1) and contains the delays present in the process signals with respect to a reference signal. This reference signal can be in general any input. The optimization is performed in two loops. The first one, find DV that minimize the number of PCs that are selected by a parallel analysis (Himes et al. 1994). The fitness function is simply (I)~ = -A. The second loop searches DV that maximize the variance contained in the first A PCs (selected in the loop 1) (i.e. @~:~i' 2 ), which is considered as the true system variation. As a consequence, )~A results greater than )~A+,, making easier the distinction between spurious and system variance. Additionally, the model explains the most of the true process variance in the smallest number of PCs.
2.3. Multiscale DAPCA (MS-DAPCA): The capacity of PCA to eliminate the noise heavily relies on the assumption of the normality of data. Therefore, sometimes measurement and process noise can difficult the detection of small faults and disturbances. MS-DAPCA aims to join the properties of DAPCA to those of Multi-scale PCA (MSPCA, Bakshi, 1998). MSPCA is an approach that handles multi-scale data by using wavelets. PCA is then applied to generate independent latent variables at each scale. In addition, wavelets act as a multiscale filter by thresholding the coefficient of the more detailed scales. MSDAPCA performs similar to MSPCA, but DAPCA is applied instead of PCA, at each scale of the wavelet decomposition. One main advantage of this method is that two stages of dimension reduction are performed. First the MSPCA decomposition reduce the length of the coefficient matrixes from tn to m/(21), and the maximum delay considered results d,naxl : dmax/(2l) were l is the decomposition level. This situation reduces the computation time of DAPCA several times, especially in the approximation scale, sometimes allowing the use of exhaustive delay adjustment. Finally, delays can be estimated and compensated independently at different scales. The Matlab® genetic algorithm Toolbox developed by the University of Sheffield has been used in the following case study, which has been solved using an AMD XP2500 processor with 512MB RAM.
4. Case Study
1378 An event-driven simulation model has been constructed using two toolboxes of Matlab®: Stateflow and Simulink. The case study is a SC network involving six entities: one raw material supplier (S), a manufacturing plant (P), two distribution centres (DA, DB), and two retailers (RA, RB) (Figure 1). The row material that enters P is designed by W and the products manufactured by the plant are A and B. In this case, customer orders for A and B arrive to RA and RB, respectively, which, in turns, send orders to DA and De. The plant P supplies the distribution centres whilst S provides the raw material to the plant. Furthermore, the study is addressed to variables belonging to the operational and tactical level.
0
.li
Figure 1" Supply Chain case study.
The nineteen monitored variables are of two kinds: flows that involve material (inputs and outputs of materials at each node) and information (inputs and outputs of orders at each node), and cumulated variables that also involve material (inventory level at each location) and information (cumulated orders level at each node). Two different abnormal situations have been programmed. The first one is related to a machine breakdown in the production line of product B at the factory P. This causes a delay in the production response. The second one is due to a transport fault between P and DB. Then, during a certain time period De cannot replenish its inventory.
5. Results Firstly, a standard PCA model has been built using simulated data from normal operation condition. Seven PCs has been selected using parallel analysis (A - 7). The variance contained in each PC is presented in Table 1. Note that X7 ~ Xs, making difficult the distinction between the common cause and residual subspaces. 500
500
400
.oo
uJ 300 200 O0
O0
'
2000
.:
"
'
'.
4000Time6000
"
8000
a
Time
b
Figure 2. PCA results. SPE statistic for: a) Event I at t=3000 b) Event II at t=3500. The dashed line represents the detection limit of 99%
With this model, Event II is easily detected. However, Event I cannot be detected (see Fig 2). In addition several false alarms (3 consecutive points out of limit) occur.
1379
Table 1 Variance percentage contained in the.first ten PC dimensions. Gray cells correspond to lhe selected PCs in each case. kl
X,
;L~
X4
k~
k~,
k7
k~
k,~
k 1~,
CPU time
PCA DAPCA aSPCA MS-DAPCA aS-DAPCA •
5.51 i~!!~!ii~i i ~ i i i i iii~ii~i ~ i ~ ! i i i!iiii~i~i!!!ii! ! ~!ii!!~!!!!:':::~:'7':.'85 ::)i~!~::::::~::]9::.94.......... ........ 13.93
5.24 5.76 5:1~5']..................5.08 9.62 6.67
5.09 5.27 4.94 . .
5.36 5.00 4.69 4.27 . .
5.21 4.79 4.19 3.71
4.96 4.66 3.92 3.53
836s 32s 5s
Therefore, DAPCA has been implemented to reduce the model dimension and to look for a better detection of Event I. In this case only three PCs has been selected (A = 3) and XA results significantly greater than XA.~(see Table 1). However, the detection performance has not improved (Fig. 3a). Then, to improve the monitoring performance the MSPCA has been applied. Five PCs are chosen. Results corresponding to the approximation scale of MSPCA are presented in Figure 3. The Event i is clearly detected without false alarms. 5O0
80
Norma{ ............ Event I
400 ~0 w
300
] I
O0
I
200
~40
I
~
!
i,
I
1
,
:
o.._ax.-, 0
i
2000
,
r
4000 6000 Time
8O
8000
Q
~o
I -~,.
,,~o
4o
! !
20
60
80
I: 00
i 20
140
t20
140
b
il1
a40
40
t00
N orma/ .......... E v e m !
6o
~0
so
80
........... Norma! Event 1
t
80
I
C
~,0
{
4o
l
! ~ 4i"
60
8o
~00 t20 ~40 d
Figm'e 3. SPE statistic.for Event I. a)DAPCA h)MSPCA c)MS-DAPCA d)MS-DAPCA using only inventom' signals. The dashed line represents the detection limit of 99%
Applying MS-DAPCA similar results are obtained, but using only three PCs (Figure 3c). Finally, MS-DAPCA has been applied but only on the six inventory signals because they are variables that are registered in an almost continuous manner. Then, data processing is easier than in case that the register is eventual, such as material flows transported by the lorries or the orders sent out by the customers. Now, only one PC is enough to describe the system variance contained in data. Figure 3d shows that the detection limit can be placed lower leading to a faster and more reliable detection. Once the deviation is detected, the causes and consequences of the abnormal events can be investigated. Figure 4 shows the statistics conesponding to Event I using the last implemented DA-MSPCA model. One can observe that the SPE is first deviated,
1380 showing a broke in the system correlation, and then the T2 statistic. Figure 5a shows that the D B is the inventories that cause the deviation in SPE, and then the disturbance in P due to accumulation of orders (Figure 5b). 15
20
40
60
ill & co
60
.
.
80 .
.
1 O0
120
.
40-
20,
o
Figure 4: MS-DAPCA using only inventory signals: T2 and SP£ statistic for Event [
5 Conclusions Several statistical techniques usually applied in Chemical Engineering for process monitoring has been tested in a new environment, the SCM network. Results so far obtained are very promising. This study reveals that the standard PCA algorithm is not able to deal with the noise and non-gaussianity featuring of this kind of signals. Nevertheless, multiscale and the novel delay adjusted techniques can strongly improve the monitoring performance. Research tasks in this direction will continue.
~i~4
........
i
2 2,m_ ¢
. mm, - - ~ ,
......
a
b
Figure 5: MS-DAPCA. Inventory contributions to the statistics deviations a) absolute contribution to the SPE in the 64 rh coefficient b) absolute contribution to T2 in the 86 th coefficient
Acknowledgements
Financial support received from the Generalitat de Catalunya (FI programs) and from GICASA-D (I0353) project is fully appreciated. References
(1) Simchi-Levi, D., P. Kamisky and E. Simchi-Levi., 2000, Designing and managing the Supply Chain. Concepts, strategies and case studies. (2) Himes, D. M.; Storer, R H.; Georgakis, C. Determination of the number of principal components for disturbance detection and isolation. In Proc. of the ACC; IEEE Press: NJ, 1994. (3) MacGregor, J. F.; Kourti, T. Statistical process control of multivariate processes. Control Eng. Practice 1995, 3,403-414. (4) Wachs,A., Lewin, R. 1999, Improved PCA methods for process disturbance and failure identification. AIChE J. 1999,45 (8), 1688-1700Copyright © 1999 (5) Bakshi, B. Multi scale PCA with application to multivariate statistical process monitoring. AIChE Journal 1998, 44, 1596-1610.
European Symposiumon ComputerAided Process Engineering- 15 L. PuigAanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1381
Closing the Information Loop in Recipe-Based Batch Production Estanislao Musulin, Maria J. Arbiza, Anna Bonfill, and Luis Puigjaner 1 Chemical Engineering Department, Universitat Polit&nica de Catalunya, Av. Diagonal 67, 08028-Barcelona, Spain. Rasmus Olsson and Karl-Erik Arz6n Department of Automatic Control, Lund University, Box 118, SE-221 00 Lund, Sweden.
Abstract In addition to the basic regulatory functions, a batch control system must support production planning and scheduling, recipe management, resource allocation, batch report generation, unit supervision and exception handling. A closed-loop framework is presented in this work that integrates decision support tools required at the different levels of a decision-making hierarchical batch control system. Specifically, the proposed framework consists of a reactive batch scheduler (MOPP) and a fault diagnosis system (ExSit-M) developed by the Universitat Politacnica de Catalunya, and a S88-recipe-based coordinator (JGrafchart) developed by the Lund University. These tools need to exchange information to obtain optimal utilization of the production plant. The complete integrated system is built using a general recipe description and other guidelines from ISA $88 standard (ANSI/ISA 1995).
Keywords" Batch, Integration, Reactive Scheduling, Fault Diagnosis, Recipe
1. Introduction in a production plant environment the presence of unpredictable events not only related to external market factors but also to the operational level, e.g., equipment breakdowns and variable operation times, is usually unavoidable. Despite the uncertainty in the production scenario, the scheduler has to make some decisions both to start production and to face abnormal events. The need to increase the reliability of any decision-making process, thus reducing the gap between theory and practice, makes necessary to take this uncertainty into account. Research in scheduling under uncertainty has mostly been focused either on rescheduling algorithms, which are implemented once the uncertainty is disclosed, or stochastic approaches that incorporate the uncertain information at the decision level prior to scheduling. On one hand, the execution of deterministic optimal schedules based on nominal parameter values and the implementation of rescheduling strategies to tackle the problem once the uncertainty is revealed can result cumbersome or unrealistic without previous consideration of the uncertainty. If the uncertainty can be characterised at the time of scheduling, it should be advantageous to take possible future events into consideration before they happen in order to minimise the negative i Author to whom correspondence should be addressed:
[email protected] 1382 outcomes. On the other hand, the future cannot be perfectly forecasted so, despite considering the uncertainty a priori, deviations from the predicted schedule can always occur once the uncertainty is realised. Therefore, it is required to adapt the schedule to the new scenario if a good performance of the system is pursued. The integration of a Fault Diagnosis System (FDS) aims to timely provide the process state information to the different levels in the decision-making hierarchical structure, thus reducing the risk of accidents and improving the efficiency of the reactive scheduling in the most effective way. To handle unit supervision, exception handling, and recipe execution a coordinator is implemented in JGrafchart. The unit supervision is based on modelling the state of each equipment object and procedural element using finite state machines. A closed-loop framework for on-line scheduling of batch chemical plants integrating, robustness considerations, fault diagnosis, recipe coordination, and exception handling is proposed in this work. This on-line integration leads to a fast execution of the recovery procedures and the rescheduling.
2. Scheduling and reactive scheduling The developed scheduler uses the Event Operation Network (Cant6n 2003) to model the system and has a library of different dispatching rules to determine a feasible schedule. The dispatching rules available can be classified into three sets: priority rules that determine a list of recipes to be sequenced and assigned to specific units, assignment rules that determine which equipment should be used for each stage of each batch, and sequencing rules that determine the sequence of batches and the sequence of operations for each unit. It also has a library containing a variety of heuristic and rigorous optimization algorithms to determine an initial optimum schedule. Furthermore, the objective function used by the optimization algorithms can be customized to optimize the use of resources, cost of changeovers, profit, makespan, etc. Once generated, the optimum schedule is sent to the coordinator to be executed in the process. Unexpected events or disruptions can change the system status and affect its performance. Therefore, during the on-line execution the scheduler receives from the process coordinator information about the actual executed schedule. Deviations from the original schedule and information about equipment breakdowns coming from the FDS will trigger a rescheduling (Arbiza et al. 2003 and Bonfill et al. 2004). The new generated schedule will be optimum according to the new plant situation. If some modification is made, the new schedule is sent to the process coordinator. The rescheduling algorithm (Arbiza et al. 2003b) is presented in Table 1. Table 1" Rescheduling algorithm 1 2 3 4 5
-
C r e a t e a master schedule. Send schedule to the process coordinator. Receives the actual executed schedule f r o m the process coordinator. Generate new optimal schedule. I f the new schedule differs f r o m the implemented one go to 2, else go to 3.
The rescheduling system is completely configurable and customizable considering the manager objectives. It allows selecting different dispatching rules, optimizers and objective functions according to the process knowledge. The alternative rescheduling
1383 techniques (recalculate a new robust schedule, recalculate considerations, actualize operation times, reassignment, system selects the best suited ones according to the Optimization algorithms may be included depending on maker and the required reaction time.
schedule without robustness etc.) are evaluated and the objective function adopted. the interest of the decision
3. Fault Diagnosis The FDS is designed based on artificial neural networks (ANN) and fuzzy logic, with a modular structure based on process decomposition following the ISA $88 standard. It was developed using G2 ...., and operates in collaboration with the coordinator and the scheduler sending complete information with regard to the process state (equipment breakdowns, lime of unavailability, etc.). Furthermore, it incorporates a complete decision-support system for the process operator based on the information obtained from a HAZOP analysis and a user friendly graphical interface. Normal operation conditions modelling is a central issue in batch process monitoring. To improve and simplify the modelling a step-wise model of the process is built. Each unit is represented by a set of ANN models that model the behaviour of each unit during a specific operation. In processes with complex dynamics this step-wise modelling can be extended to model the equipment at the phase level. Then, during the on-line operation, a model-manager activates and deactivates the models depending on the active process operations that are being executed into the process; information that c o m e s f r o m the coordinator. Phase/Operation residuals alarms
d
,,,
Pfw}t~t~ 2 l~.~ur~|s
a)
ANN model
Fuzzy System
t
Process variables
b)
Figure 4." Fault Diagnosis system, a). Resid.al bounds and membelwhipjimctions de/hfition in the intersection o./t~'o c'ontro/ phases, h). Partial eqtfipmertt model with its diagnosis stage.
The model predictions are compared with historical data to obtain limits for the normal operation conditions. Residuals corresponding to one variable from 20 operation runs are presented in Figure 4a. The area between the inner limits is considered as the normal behaviour region. Outer limits are calculated by multiplying the inner bounds by a factor. The factor depends on the trade-off between incipient fault diagnosis and robustness (no false alarm generation). Note that the limits depend on the process variability along the operation/phase time, and using the phase-time instead of the operation-time the limits can be set tighter especially around the change of phases. Finally, the methodology presented in (Ruiz et al. 2001) has been extended to obtain rules from a HAZOP analysis. Rules are introduced into a fuzzy system to relate the deviated residuals with taults. The membership functions change during the operation in such a way that residual values in the inner limits are considered normal, values located between the two limits lie in two fuzzy sets (High and Normal or Low and Normal), and finally, values located outside the external limits are considered to lie either in the Low or High set (Figure 4a). For each control operation the system shown in Figure 4b is applied.
1384
4. Coordinator The coordinator is implemented in JGrafchart, a Java implementation of Grafchart (A~rz6n 1994). The coordination involves management of scheduled batches, recipe execution, unit supervision, alarm propagation, and exception handling. The plant is divided into units according to $88. Each unit consists of equipment and control modules such as agitators, valves, and pumps. The units also contain the equipment control. The recipe/equipment control separation is on the operation level in $88, i.e., the recipe makes a procedure call from a procedure step representing a recipe operation to a procedure representing the corresponding equipment operation. Within the coordinator each batch is represented by a control recipe expressed using Sequential Function Chart (SFC) formalisms. Since the control recipe is carrying all the information about the development of the batch a report can be sent back to the scheduler every time a new phase is started. If an exception occurs and a batch has to be aborted this information is also sent back to the scheduler. The unit supervision is based on finite state machine models of the state of each equipment object and procedural element (Olsson 2002). The equipment state machine serves two purposes. The first is to be able to check that all the equipment objects are in a consistent state when an operation is invoked. The second purpose is to provide a structure for organizing the safety and supervision logic at the equipment control level. if a fault occurs, the safety logic causes a state transition from a normal state to a fault state. The state of an equipment/control module will propagate up to the unit level. Most of the functionality is associated with equipment operations. Each equipment operation object contains a procedure (i.e. the sequential control) and a state machine monitoring the state of the procedure. The procedure of an equipment operation holds not only the equipment sequential control, but also contains several checks, which need to be performed when a procedure is called from a recipe. It checks if the procedure itself is in the Idle state and, if so, changes the state to Running. The check if the unit is in a consistent state at the start of the operation is also checked using state machines. The separation between the normal recipe execution and the exception handling can be made in different ways. In Procel most of the exception handling is operation specific. When a procedure containing the operation is called the associated exception handling is enabled. The exception handling logic of an operation involves both the recipe level and the equipment level. Exception handling logic that must be active also for an idle equipment unit is contained in the unit exception handling object. Exception handling is also needed at the recipe level. For example, an exception that has occurred must be fed back to the control recipe, recorded in the batch report and sent to the scheduler, and appropriate actions must be taken to deal with the exception. An important consideration is how to separate the recipe information from the exception handling logic and operations. The actions that are taken in the recipe depend on the type of exception. In a few special cases it might be possible to "undo" an operation and rollback the execution of the recipe to a safe execution point, and from there continue the execution using, e.g., a new unit. However, due to the nature of chemical batch processes a rollback is in most cases not a viable alternative. Also in the more common case where the batch cannot be produced as intended there are several alternatives. In certain situations it might be possible to still make use of the batch to produce a product of a different quality. In other situations it is possible to recirculate the batch ingredients for later reuse.
1385
5. Integration Methodology and Technology The proposed integrated framework along with the flow of information through the different modules is depicted in Figure 1. There exists a central agent (DTM) that manages the information flows. ~
1.sched__J_"~ ~rS..executed I 12.scheduleschedule alarms 2.schedul.e [- ~ 7.8~'$c°u~tj21::ht,)dnu~eI [ 8...... 2ed,schedale 11.SChl~U21earalm~i/ msDTM I 6.pro~:s~lasr~2t'----~ ' 6"Pr°c5e:rSo::tsas data~~n trolactions
Figure 1. hTtegration diagram The scheduler generates an initial schedule that is then translated into control actions and executed into the process by the Process Coordinator. When an abnormal event is detected by the fault diagnosis system (FDS), it sends an alarm to the scheduler through the Process Coordinator, which executes some pre-specified recovery procedure, depending on the alarm. The scheduler receives the alarm and generates a new optimum schedule. All the information is stored in an ISA $88 compliant database. The developed software toolboxes have been integrated in a common infrastructure, named the CHEM Communications Manager (CCOM) (CHEM 2003) that allows communication through the exchange of XML messages. It is based on public domain Message Oriented Middleware (MOM) software that provides Publish/Subscribe and Point to Point message communication. CCOM acts as a server that clients can connect to. Moreover, a client API has been developed on top of the MOM interface to provide additional functionality and hide the aspects of transport protocols to the clients.
6. Case study The proposed integration architecture has been successfully tested on PROCEL, a pilot plant located at UPC (Fig. 5a). It consists of three tank reactors, three heat exchangers, sensors, and the necessary pumps and valves to connect the equipment. Tests of the performance of the FDS, and the reaction of both the coordinator and the scheduler in case of abnormal events have been performed. A test starts with the generation of an initial schedule and its execution into the plant. During the execution of the schedule a fault is introduced. The FDS isolates the fault and informs the coordinator about the equipment unavailability. The coordinator starts an exceptionhandling procedure to abort the batch and sends a schedule alarm to the scheduler. A new schedule considering the actual plant situation is generated and sent to the coordinator for its execution. Once the fault is corrected, the loop is repeated to find a new optimum schedule considering the repaired equipment. In Figure 5b, the main GUI interface of the scheduling package is presented. It summarizes the execution of the test. The upper left of the screen shows a Gantt-chart of the initial schedule. The down left part shows the actual executed schedule. There is a dotted batch that represents a faulty batch. Finally, at the upper right is presented the new schedule.
1386
/ .....
...
i
i
a)
!
i
_ ! I
....i
i
~
5J
i
:........i
i:
o.!
~
[:i~':
lt
i
~
i
~
!
i/
i|
~ ~ ....
~:,i~,:~;~:!::
:::::i:ii i:~I;~:~>~'.:.:.:'...~...
!i~!i)i:.............................. ~:~'~'=~b)
Figure 5. Case Study." a) Flexible chemical plant (PROCEL)flowsheet, b) Interface of the scheduler showing the original scheduler; the actual schedule and the rescheduling proposed.
7. Conclusions The applicability and effectiveness of the proposed on-line integrated framework is illustrated with its implementation into a batch chemical plant. The integrated system has shown the ability of detecting and reacting to abnormal process events under uncertainty. A structured FDS approach has been presented that leads to simpler, robust and faster to train models, which allow tighter detection limits leading to an incipient and robust detection of faults. Knowledge from a HAZOP analysis is introduced as rules to isolate the faults and to support operator decisions. The simplicity and adaptability of the FDS for its application in complex plants is presented. An open and flexible system for rescheduling has also been presented which takes advantage of user's process knowledge. The efficiency of the rescheduling system to adapt the schedule to the current situation in the plant has been successfully tested.
Acknowledgement Financial support from the E.C, (Project G 1RD-CT-2001-00466) is gratefully appreciated. References
ANSI/ISA, 88.01 Batch Control, Part 1: Models and Terminology, 1995. Arbiza M.J, Cant6n J., Espufia A., Puigjaner, L. Flexible rescheduling tool for short-term plan updating, AIChE 03', San Francisco, USA, 16-21 November 2003. Arbiza, M.J., Cant6n, J. Espufia, A. and Puigjaner, L. Objective based schedule selector: a rescheduling toolfor short-term plan updating, [CD-ROM]. ESCAPE 14, Lisboa, 2003b ]krzdn, K.E. Grafcet for intelligent supervisory control applications. Automatica, Volume 30, Issue 10, October 1994, Pages 1513-1525. Bonfill A., Arbiza M.J., Musulin E., Espufia A., Puigjaner, L. Integrating robustness and fault diagnosis in on-line scheduling of batch chemical plants. In: Proceedings of IMS International Forum 2004, Milano, Italy, pp. 515 - 522. Cant6n J., 2003, Integrated support system for planning and scheduling of batch chemical plants, PhD Thesis, Universitat Polit6cnica de Catalunya, Espafia. CHEM, Advanced Decision Support System for Chemical~Petrochemical Manufacturing Processes. fOrt-line][Accessed 2003] Available on: < http://www.chem-dss.org/>. Olsson, R. Exception handling in recipe-based batch control, Licentiate thesis, Department of Automatic Control, Lund Institute of Technology, 2002, Sweden. Ruiz, D., Nouguds, J.M., Puigjaner, L. Fault diagnosis support system for complex chemical plants. Computers & Chemical Engineering, 25, pp. 151-160 (2001).
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1387
Agent-based intelligent system development for decision support in chemical process industry Ying Gao, Antonis C. Kokossis* Chemical Process Engineering, University of Surrey Guildford, Surrey, GU2 7XH UK
Abstract This paper experiments with an agent-based system designed to support decisions in chemical process industry. Chemical engineering technology, artificial intelligent and information technology are integrated to automate decisions on-line. A multi-agent system is employed to coordinate tasks and information stored in heterogeneous resources. The system architecture is first discussed in this paper. The implementation of the system provides an environment to coordinate manufacturing and integrate rules, optimization and simulation models.
Keywords: Multi-agent system, artificial intelligence, coordinate manufacturing and decision support.
information
integration,
1. Introduction Data and information resources are important assets of the chemical process industry. Their effective management and sharing are vital to maintain sustainable operations. Available assets include several software applications, models, reports (text, design results, software solutions etc) that are largely unstructured making it difficult for search, management procedures and computer environments to register and support management. The development of agent-based tools enables flexible infrastructures that support integration, manufacturing management, information sharing, and decisionsupport. In contrast to traditional software programs, software agents facilitate collaboration and integration of software as well as access to in-hourse resources (Bradshaw, et al., 1997). Agent-based systems have capabilities to function in networked distributed environment and cope with system changes (Nwana, 1996). Agents can further incorporate legacy programs by building wrappers around the program that manage interactions with other systems (Genesereth and Ketchpel, 1994, p. 48) and require only minor modification as programs change or replaced. *To whom the correspondence should be addressed:
[email protected] 1388 In this paper, we explain the prototype of an agent-based system with a focus on on-line operations and negotiations. The paper is organized as the follows. Its first section, introduces basic concept. The system architecture is described next with an emphasis on the decision-support tools to use in the chemical process industry. Implementation issues are last discussed with an example of an operational scenario.
2. Multi-agent system and agent communication
2.1 Multi-agent system Multi-agent systems (MAS) have their origin in distributed artificial intelligence and object-oriented distributed systems. An agent is a computational process that implements the autonomous, communicating functionality of an application (FIPA00023, 2000). The intelligent agents have capabilities to acquire information from its environment and make decisions. Agents are relatively independent pieces of software interacting with each other through a message-based communication. Two or more agents acting together form a multi-agent system. Unlike those stand-alone agents, agents in a multi-agent system collaborate with each other to achieve common goals. These agents share information, knowledge, and tasks among themselves. Cooperation and coordination between agents is the most important feature of a multi-agent system. Major advantages in utilizing agent-based techniques are that: •
• •
Multi-agent systems have capabilities to incorporate legacy programs using wrappers that one could build around them so that the legacy programs can be accessed and exploited. Systems can be incorporated into wider cooperating agent systems and rewriting of application programs can be avoided. Multi-agent system can provide efficient solutions when information sources and expertise is distributed in the chemical manufacturing process. Application of agent-based systems help to enhance system performance in the aspects of computational efficiency, reliability, extensibility, maintainability, flexibility and reusability (Sycara, 1998). System development, integration and maintenance are easier and less costly. It is easy to add new agents into the multiagent system, and the modification can be done without much change in the system structure.
2.2 Agent communication Cooperation and coordination of agents in a multi-agent system requires that the agents be able to understand each other and communicate effectively. The infrastructure that supports the agent cooperation includes the following key components: a common agent communication language (ACL), and a shared ontology (Wooldridge, 2002).
1389
Agents typically communicate by exchanging messages represented in a standard format and using a standard agent communication language (ACL). A number of ACLs have been proposed, in which Knowledge Query and Manipulation Language (KQML) (Finin, et al., 1997, p. 291) and FIPA's agent communication language (FIPA ACL) (FIPA00023, 2000) are used most frequently. If two agents are to communicate about a specific domain, then it is necessary for them to agree on the terminology that they use to describe the domain. In the terminology of the agent community, agents must share a common ontology. Ontology is defined as specification schemes for describing concepts and their relationships in a domain (Gruber, 1993, p. 199). Once interacting agents have committed to a common ontology, it is expected that they will use this ontology to interpret communication interactions, thereby leading to mutual understanding and predictable behaviors. With a common communication language, and a shared ontology, agents can communicate with each other in the same manner, in the same syntax, and with the same understanding of the domain.
3. Agent-based information system architecture for decision support in chemical process industry Figure 1 presents the system architecture. The integrated components include process simulation, rules that comprise a decision support system, and black box regression tools in the form of artificial intelligent components and neural network (ANNs) for process analysis, data processing, process monitoring and diagnosis, process performance prediction and operation suggestion. The system comprises a knowledge base with access to software agents, and a user interface. A system knowledge base comprises process models, heuristics, as well as process data. Process models may include models for process simulation, optimization, scheduling, forecasting, and manufacturing planning and can be developed utilizing different computing languages and software. Forecasting applies to the history data and real-time data of plant operation and management. Heuristic rules provide for on-line decisions that may or may not use optimization models. Information on expert knowledge and technical resources related to the chemical manufacturing process are also provided in the knowledge base. The agents can be specialized around specific expertise and tasks to assemble and process relevant intbrmation and knowledge utilizing the available resources in the knowledge base. They could also negotiate and cooperate with each other to achieve timely decisions in dealing with different operational scenarios. Scenarios can involve negotiations with trading points and other agents. Agents are organized in a layered, distributed system, which comprises user agents, a coordinator and task agents. User agents process jobs triggered by users and managed by the coordinator that ushers jobs and regulates communication. The task agents are
1390
UserAgents
Taskagents Process P monitoring& I Optimization I Dataanalysis ati°Kng Production process
Knowledge~
Utility system
~
Information and Management system
~
~
Figure 1. Agent-based information system architecture assigned to different processes that monitor performance, forecast trends, apply optimization, support scheduling and planning decisions and develop scenarios for negotiation. Monitoring agents review performance and may release warnings about abnormal operations. Forecasting agents develop trends applying artificial neural network. Data management agents collect data, and apply mining and clustering. A separate set of agents is devoted to analyze text from documents following h-techsight technology (Banares et al., 2003). These agents employ Natural Language Processing analysis to retrieve text from reports, populate ontologies with relevant resources, correlate resources and update ontologies, and apply background search. The system infrastructure supports communication between previously established application software and programs for process simulation, optimization, scheduling and forecasting. Agents can run on the same or different computers, and information sources can be stored in distributed locations. This enables applications in networks of CPU's as these exist in industrial R&D environments. The cooperation and coordination is exemplified in negotiation examples of open markets, as this can be the case of utility networks that can trade steam and power in changeful environments. Utility systems have to compete with main grids, mini-grids, and local suppliers and service regular (process operations) and unplanned customers, as they become available during peak demand periods.
1391
4. System implementation JADE (Java Agent DEvelopment Framework) is used as a standard to develop the different agents described above. A user interface is constructed to account for a functional access to tasks, services and data. The agents communicate in FIPA, use ACL for security and control in the communication, and employ machine interpretable ontologies in RDFS. With the common communication language and shared ontologies, agents can launch experiments in negotiation, and integrate decision stages with models, rules and operational data. A simple illustration case is next presented to demonstrate the application of agents on a process operation case. Benzene-toluene separation process is selected as a process with an objective to monitor process operation condition and adjust process operation parameters in the case of abnormal situation. Agents are used to: (i) monitor operational data and compare data with acceptable profiles (ii) calculate the abnormal error and optimize the maintenance schedule (iii) warn and alarm about operational failures and under-performance (iv) communicate with users for authorization and decisions (v) forecast operational changes and economic impact Figure 2 illustrates the user interface of the agent-based system for process performance prediction. A simple ontology is developed to model the basic knowledge behind the process and allocate the different agents and models employed in the experiment. -
-
Agents in (i) apply a rule based system that calculates deviations from design profiles. Flags for acceptable or unacceptable performance are set by the agent to the user. Agents in (ii) and (v) apply models that make use of artificial neural networks trained from history data of 30,000 points that represent operation of a past year. ANN's apply back-propagation to tune parameters.
'{ " #iu ~ii_,k,;j~nLi3y~i~r;i ............................... ~- F'erforrnarlc e_Pr edictlOrl e,. Inforrr~atiorl Retlie',,,'ing o- Pro(:e,_=:s_k~o nitorir~g
M;iiii~,~enLs~st~i~ ................................................................................... o- Perl-orman ce_Predictlon Information_Retrieving Process_Monitoring
"~,
OH
:
~
:.~.tq: I~SSa~
~i!iiiii!!iiiiiiii~i~i:i
,
........
l
. ~ , ~ ~J
Response from " Separ ation Benezene I ecoveW. 9.769316 I~ml )luene recover,/:. 1.998984 Kmol~tlr
.....
Figm'e 2. User intel:'face.for process pepformance prediction
OK
1392 Agents in (iii) apply simple rules with the flags noted earlier. Agents in (iv) launch communication windows such as the ones shown in Figure 2. Forecasting models are programmed in C and wrapped by JAVA Native Interface (JNI). The coordination of monitoring agent and prediction agents operate at regular time intervals.
5. Conclusion and future work In this paper we presented an agent-based system capable of supporting information integration and decision-making for the chemical process industries. The system architecture is discussed first. Knowledge management is applied with the use of ontologies to integrate regression, simulation and optimization models, heuristic rules, and data management tools. The Java Agent Development Framework (JADE) has been deployed as the basis. With a common communication language and shared ontologies, agents cooperate to exchange and share information, and achieve timely decisions in dealing with various enterprise scenarios. The system has also been tested in a variety of negotiation problems that involve utility networks and trade energy and power. Agents take up negotiations, trigger optimization studies and determine prices dynamically. The paper illustrates a maintenance problem that requires the monitoring of data, comparisons with design solutions, and optimization. Agents manage information on-line, process tasks and communicate recommendations to users who authorize decisions. The work illustrates the potential of the technology to change the shape of process engineering practices and upgrade the quality of the environments currently in use. References
Bradshaw, J. M., Dutfield, S., Benoit, P., Woolley, J.D., 1997, Software Agent, MIT Press. Finin,T., Labrou, Y., Mayfield, J., 1997, Software agents, MIT Press. FIPA00023, 2000, FIPA agent management specification, Foundation for Intelligent Physical Agents, http://www.fipa.org/specs/fipa00023/ Genesereth, M.R., Ketchpel, S.P., 1994, Communications of the ACM 37, 7. Gruber, T. R., 1993, Knowledge Acquisition, 5. Nwana, H., 1996, The Knowledge Engineering Review 11, 3. Sycara, K. P., 1998, Artificial Intelligence Magazine 19, 2. Wooldridge, M., 2002, An Introduction to Multi-agent Systems, John Wiley and Sons Limited. Bafiares-Alcfintara, R., AC Kokossis and P. Linke, 2003, Applications: Building the Knowledge Economy: Issues, Applications, Case Studies, P. Cunningham, M. Cunningham, P. Fatelnig (Editors), pp 892-897
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1393
Enhanced Modeling of an Industrial Fermentation Process through Data Fusion Techniques Sophia Triadaphillou, Elaine Martin, Gary Montague l, Paul Jeffkins ~, Sarah Stimpson ~, Alison Nordon 2 Centre for Process Analytics and Control Technology University of Newcastle, Newcastle upon Tyne, NE 1 7RU, England ~GlaxoSmithKline, Worthing, England 2~Centre for Process Analytics and Control Technology University of Strathclyde, Glasgow, G1 1XN Scotland
Abstract A novel strategy for the analysis and interpretation of spectral data from a fermentation process is considered. The interpretation is challenging as a consequence of the large number of correlated spectral measurements recorded from the process in which a complex series of biochemical reactions occur. A full spectral analysis using PLS is the standard interpretation strategy. However, within this paper an alternative method, Spectral Window Selection (SWS), is proposed, and compared with that of genetic algorithms. SWS is shown to provide a more robust calibration model. Furthermore its performance is hypothesised to be enhanced by multiple model bagging. This claim is investigated and proven. Finally an overall calibration model is compared with a local modelling approach. The methodologies are applied and compared on an industrial NIR data-set from an antibiotic production process.
Keywords: Data Fusion; Modelling; Fermentation Process; Industrial Application
1. Introduction The large scale manufacture of pharmaceutical products is a highly competitive industry in which technological improvements can maintain fine business margins in the face of competition from those with lower manufacturing overheads. Processes in which pharmaceuticals are produced are particularly susceptible to large variability due to limited monitoring and control options. Previous research has demonstrated that the infrared spectral analysis of fermentation broth can provide on-line measurements of key concentrations throughout the duration of a batch but signal interpretation remains a challenge. Relating the spectra to the analyte of interest requires the construction of a robust calibration model. The traditional strategy is to apply projection to latent structures, PLS (Tosi et. al., 2003) utilising the full spectrum or else implement wavelength selection through genetic algorithms, GAs (Abrahamsson et. al., 2003) for example. An alternative approach is reported in this paper where a search strategy identifies a limited number of spectral windows (SWS) that are most descriptive of the concentrations of interest. The methodology is demonstrated by application to NIR spectral data generated from the routine operation of an industrial antibiotic production process. NIR spectroscopy was used as a result of recent successes in the determination of individual component concentrations in fermentation broth (Tamburini, et. al., 2003). J Author to whom correspondence should be addressed:
[email protected] 1394
2. Wavelength Selection and Model Bagging When developing a linear model for quantitative analysis of spectral data, prediction results can be affected by wavelengths that do not offer predictive information about the analyte of interest. Also absorbance ranges of different functional groups may overlap and many substances contained in the complex samples may contribute to signals across the complete spectral wavelength range. Wavelength selection is one approach to eliminating wavelengths where descriptive information is not present. Typical wavelength-selection approaches have focused on selecting individual wavelengths using methods such as genetic algorithms. GAs' are a global search method that mimic biological evolution. GA's apply the principle of survival of the fittest to produce better approximations to the solution. Each member of the population is made up of a binary string which in this case serves to indicate whether a wavelength is selected or not. It is an iterative procedure and at each generation a portion of the population of solutions are selected with consideration of their fitness. The fitness is assessed through an objective function that characterises the performance of an individual member of the population. Once the individuals are chosen from the population, genetic operators are applied and the population is updated to produce the next generation. Further details of the GA methodology can be found in Goldberg (1989). Many significant drawbacks have been reported in the literature (McShane et al 1999): GAs tend to be slow to converge, they present a configuration challenge because of the adjustable factors (e.g. initial population, number of generations) that influence their outcome, and finally they can be biased by including wavelengths with a spurious correlation to the prediction property and the chosen wavelength subset may therefore not be appropriate for predicting future samples. In this paper, a spectral window selection (SWS) algorithm is proposed where windows of wavelengths are chosen. The algorithm is based on that described in Hinchliffe et al. (2003). By constraining the spectra selection to a limited number of windows rather than allowing multiple individual wavelengths to be selected potentially improves the calibration model performance by preventing it becoming too specific to the training information. The steps in the algorithm are summarised in Figure 1. 'Bagging' has been proposed in the literature to improve the accuracy of models. It has proven to be successful mainly in classification and pattern recognition problems. It was originally introduced by Breiman (1996). The bagged prediction is generated as a weighted combination of the predictions from n individual models. Two methods were investigated for the calculation of the weights, mean and PLS for both the results from the GAs and SWS. For average bagging, each individual model is equally weighted and the mean of the predictions for each time point is calculated. For PLS bagging, linear PLS is used to attain a weighted average.
3. Data and Spectral Measurements The data considered is from an industrial pilot-plant scale fermentation process, which involves two stages, the seed and final stage. Biomass is grown in the seed stage and is then transferred to the final stage for the production of the desired product. The final stage is a fed batch process and lasts approximately 140 hours. Seven fermentations were carried out and NIR measurements were collected on-line from the final stage of the process. Product concentration in the broth was considered to be critical to the monitoring of the batch and in this paper is the analyte of interest. A further approach investigated to improve model robustness was local modelling as suggested by Arnold et. al (2001) to achieve an improvement in overall performance compared with a global
1395 model. The local modelling approach was considered for this data set, with three regions of operation identified using mechanistic process knowledge. Algorithm initialization r-
- -
i
Select the traming and validation b a t c h e s for m o d e l ~ construction
[
........
|
t
I Randomly generate centers and w i d t h s for e a c h one of the spectral w i n d o w s
,-~ i
Initial m o d e l construction
-i
j '
i
S p e c i f y the n u m b e r of spectral w i n d o w s to be u s e d within t h e m o d e l a n d the algorithm search parameters
....
j
,k
[
-~
T a k e d e r i v a t i v e s of the spectral d a t a and m e a n center
L_ ~ - I
~_ •,--
Generate a PLS model b e t w e e n t h e input d a t a and analyte concentrations. Determine the model RMS error
Build input data m a t r i x from the spectral w i n d o w s and eliminate replicated d a t a
I
---
S e a r c h for i m p r o v e d m o d e l s r
--q
l I G e n e r a t e zero m e a n r a n d o m ' i n c r e m e n t s for e a c h of the
l
i ...........
]
d i d t l Ss . . . . . . . . . .
~
] l [
No
A p p l y the r a n d o m i n c r e m e n t s ] to the spectral w i n d o w s ~ c e n t e r s a n d widths
/
__
Build a n e w m o d e l i n p u t m a l r i x f r o m tile u p d a t e d spectral w i n d o w s , g e n e r a t e a
.......
i
!c
Revert to the previous centers and widths. D e t e r m i n e w h e t h e r the m a x i m u m n u m b e r of iterations for m o d e l c o n s t r u c t i o n has b e e n exceeded
]
/
Yes
. . . . . 2/aTe PtLS 2ew°dRIIv~sde . . . .
]
~~--
iI
....
"~
[
~e;r'2%aWshgtehc%at ~; 2 MS I~
c o m p a r e d to the odginal spectral w~ndows
No
1
|
Yes
! ]
S a v e the m o d e l g e n e r a t e d
Final model construction
D e t e r m m e w h e t h e r all t h e models have been constructed
Yes
Apply the bagging procedure to g e n e r a t e the c o m b i n e d model. A s s e s s its p e r f o r m a n c e on validation d a t a prior to implementation
J
No
Re-initialize the m o d e l g e n e r a t i o n algorithm
tqgm'e 1. F/o~t' diagram o/the spectral window selection (SWS) algorithm
4.
Application of the Methodology
Calibration model training was carried out utilising two thirds of the data with the remaining one-third being used to test the models. Several pre-treatments steps were required. The raw spectroscopic data for a batch can be seen in Figure 2. For this application, first derivatives were taken (Figure 3). The derivatives were calculated using Savitsky-Golay smoothing (Gory, 1990) for l l points and a second order polynomial. For the fitness function of the GA algorithm, the RMS prediction error was used in order to be consistent with the SWS method. The reproduction was performed with a single point crossover with probability 0.7 followed by mutation. A population of 100 individuals was used. 100 generations were performed with a generation gap of 0.5.
1396
o 12
~:
2
008 --~
006
~ oo4
12!
J
~ 0 o2
1
1100
1200
1300 1400 Wart lef g:bi~ m
1500
%?~,,
//"
o
j/
..
OO4
1600
1000
Figure 2." Raw NIR spectra
1050
1100
W120 aveOle ngt12 h/Sn0m
1150
1350
1300
1400
1450
Figure 3." First derivative spectra
5. Results and Discussion The results from the various approaches for the prediction of the product concentration are summarised in Table 1 and Table 2. Table 1 summarises the RMS errors for global modelling both without SWS, i.e. applying PLS to the complete spectra, and through the application of SWS and Average and PLS bagging. The results indicate that if a global modelling approach is implemented there are some benefits to be gained from the wavelength selection algorithm when average bagging is applied. PLS bagging tends to produce better fits to the training data but the models become too specific and consequently does not perform as well on the test data set. Table 1. Results for global modelling of the product concentration
Without SWS
With SWS Average Bag
PLS Bag
Linear PLS for Training
0.056
0.068
0.045
Linear PLS for Testing
0.092
0.059
0.096
Table 2 reports the performance of the local models constructed following the application of SWS and GAs to the test data set The training data results are not presented due to space limitation. The enhanced performance of the local model approach in terms of the RMS error is a consequence of limiting the range over which the calibration model is constructed. The local model strategy (SWS with average bagging) outperforms both global modelling and strategy involving GAs followed by PLS in all but the first time interval where the results are comparable. Table 2. RMS for the quality variable from the NIR spectra for the testing data set Time Interval 1 Time Interval 2 Time Interval 3
PLS Bag Average Bag PLS Bag Average Bag PLS Bag AverageBag SWS with Linear PLS 0.045 0.049 0.059 0.048 0.095 0.058 GAs with Linear PLS PLS (without wavelength selection)
0.045
0.043 0.042
0.067
0.069 0.059
0.177
0.139 0.084
The importance of bagging can be observed in Figure 4 where the results of the thirty individual model errors are presented. Most notably, the RMS error for the bagged model (presented in Table 1) is lower than that for the individual model errors justifying the bagging strategy.
1397
Figure 4. Errors /br the 30 models.for the first time interva/.[br the standard batches for the ¢:rperimental and the testing &ira set, ..... RMS error qflter PLS Bagging 'r
T
T
/
i
/
i]
:iJi
/, :/
/
/
/
,L
Figure 5a. Erperimental results./br 4 hatches.
Figm'e 5b. Testing data resu/ts./br 3 batches. Frequency of Appearances
30[-25
t
20
=
15 I
"5 E 2 5
0
10
20
30
40
50
60
wavelengths
Figure 6. f)'equenc.~, distribution O/the wavelengths selected by the SWS (left) and GA (right).
As an example of typical model behaviour in Table 2, Figure 5 shows the results from Time Interval I from a SWS PLS bagged model. Thirty models were used to generate the final model. Multiple batches are concatenated and the large falls in product concentrations are the breaks between batches. It can be observed that an off-set exists which is most significant for the second validation batch. The issue of offset removal is discussed in the conclusions. Figure 6 shows the frequency distribution of the wavelengths selected by the SWS algorithm and the GA. The wavelengths in the region 30 to 40 were selected the most frequently. This range aligns closely with those identified by analytical chemistry specialists. The GA did not indicate any special critical regions and the important wavelengths were not selected preferentially.
6.
Conclusions and Future W o r k
NIR spectroscopic techniques can potentially be used to measure and predict within a few minutes a number of critical components concentrations in an unprocessed
1398 fermentation broth sample. This paper has demonstrated that the selection of informative spectral regions can improve the results by reducing the contribution of overall noise from those regions not containing relevant information on the analyte concentrations. In this paper a new method, SWS, in combination with bagging has been developed and compared with the traditional approach of GAs. A local modelling strategy was used to improve the accuracy of the prediction. Offsets in predictions based solely on spectral analysis still occur, particularly if the calibration region is large. The inclusion of other process measurements in a hybrid calibration model structure can potentially deliver more robust models and reduce the offsets. For example, the residuals of the calibration model can be related to other process information to 'explain' the model deviations and 'corrections' to spectral prediction can be made. This is an ongoing area of research (Triadaphillou et al., 2004).
References Abrahamsson C., Johansson, J, Spardn A. and Lindgren, F. 2003. Comparison of different variable selection methods conducted on NIR transmission measurements on intact tablets, Chemometrics and Intelligent Laboratory Systems, 69, 1-2, 28: 3. Arnold, A.S., Matheson, L, Harvey, L M., McNeil, B. 2001. Temporally segmented modelling: a route to improved bioprocess monitoring Using near infrared spectroscopy?, Biotechnology Letters, 23:143. Breiman L. 1996. Bagging Predictors. Machine Learning Journal. 24(2): 123-140. Goldberg D.E. 1989. Genetic algorithms in search, optimization and machine learning, Addison Wesley. Gory, P.A. 1990. General least-squares smoothing and differentiation by the convolution (Savitzky-Golay) method. Anal. Chem. 62:570. Hinchliffe M, Montague GA, Willis M, Burke A. 2003. Correlating polymer resin and end-use properties to molecular-weight distribution. AIChE Journal. 49:2609. Kornmann, H, Rhiel, M, Cannizzaro, C, Marison, I, von Stockar, U. 2003. Methodology for realtime, multianalyte monitoring of fermentations using an in-situ mid-infrared sensor. Biotechnology and Bioengineering, 82 (6): 702. McShane M.J., Cameron, B.D., Cote, G.L., Motamedi, M., Spiegelman, C.H. 1999. A novel peakhopping stepwise feature selection method with application to Raman spectroscopy. Analytica Chimica Acta 388:$251. Tamburini E, Vaccari G, Tosi S, Trilli A. 2003. Near-Infrared Spectroscopy: A tool for monitoring submerged fermentation processes using an immersion optical-fiber probe. Applied Spectroscopy. 57(2). Tosi, S., Rossi, M., Tamburini, E., Vaccari, G., Amaretti, A., Matteuzzi, D. 2003. Assessment of In-Line Near-Infrared Spectroscopy for Continuous Monitoring of Fermentation Processes', Biotechnology Progress, 19(6):1816. Triadaphillou, S., Martin, E., Montague, G., Jeffkins, P., Stimpson, S., Nordon, A. 2004. Monitoring of a fermentation process through on-line spectroscopic data and the conjunction of spectroscopic and process data. Presented in BatchPro Symposium, Poros, Greece.
Acknowledgements ST would like to acknowledge the EPSRC award, KNOWHOW and the EU project BATCHPRO for financial support. CPACT acknowledges the vendor company Clairet Scientific for the loan of spectroscopic instrumentation.
European Symposium on Computer Aided Process Engineering- 15 I,. Puigjaner and A. Espufia(Editors) d co
/
2~
/
c~
/
/
iI ~ It ~ - ~ jI
I -
'
I 5O0
'
I
'
, fl
' o OOE+OOO
I
I000 1500 E XTRAC TI ON TIM E (s I
2 OOE-O03 ~
200O
'
2500 -)
Figure/.Solid residual oil at the extractor exit.
I 500
'
I
'
I
1000 1500 EXTRACTION TIME (s)
'
I 2000
' 25O0
Figure ~..Solvent oil content at the extractor exit as a.function o f extraction time.
1444
4. Parameter Sensitivity Analysis The objective of this section is to understand how the variables affect the residual oil content in the solids (time dependent) at the extractor exit. The variables analyzed were" mean solvent velocity (U); oil mass fraction of the solid material (N); oil mass fraction of the solvent at the extractor entrance (Y0), and mean solid particle diameter (dp). The values of the variables related to the extraction process in a standard condition are" U=5.0E-4 m/s; ~= 0.144; Y0 = 0.0 and dp=2.7 E-4 m. Figure 3 shows the main effects as a function of the extraction time. It can be seen that, in the initial extraction time (limited by convection), only the effect of the initial oil content of the solid particles is not null. In the extraction front region, however, all the variables have significant effects. The effects of the solvent velocity and of the initial oil content in the solids have positive effects on the residual oil, while the solvent velocity has a negative effect. The mean solid particle diameter shows an inversion in the signal of the main effect, in the region of the front of extraction. Firstly, the signal is negative, indicating that the residual oil in the extractor exit is lower for greater particles. After, the signal becomes strongly positive, signifying that as bigger the particles, greater will be the residual oil content in the solids. In the period of extraction rates limited by diffusion inside the solid particles, the particle mean diameter is the unique variable with important effect on the residual oil in the solids. The analysis made above indicates that the solvent velocity may be manipulated to control the residual oil concentration at the extractor exit, after disturbances in the solid and inlet solvent initial oil contents. The analysis of the impact of changes in the particle mean diameter is also useful, since although it may not be controlled during the extraction, an appropriated treatment in the particles before the extraction will be an effective procedure for high performance process operation t 20,-T ...........................................................................................................................................................................................................................
XO /
....!
/
..............
i
LI3 I I--
/
/"
~:: t' since nothing is said about the interval t ' a t which run i begins.
1456
3.3 Delivery due-date constraints In the formulation of Cafaro and Cerdfi (2004), the variable qmp,/i) denotes the amount of product p transferred from depot j to the local market during the injection of a new run i ~I "ew , i.e. over the interval [Ci-1, Ci]. If vmpj stands for the maximum discharge rate of product p at terminal j, then: q m (i)p,y ui~/2 -J+~~ - a k/ , u n c • {a~, a kj+l } are missing ~
)
- u n c , (a ' k+l ,~ ' Hj+I ~[-k/2~ -
/+~~ - u n c aFk/2
¢'l~k/2~-J=+lm i s s i n g ,
O, urtc(dik/2~)]+l
a kJ , ,4/+1 ~'Fk/21 = 0,urtc~,.,Fk/27)
: O;
- 0;
a~k/27J+' ) - missing;
u n c [[
d S k/27 ' = missing,unc(dF~)~21
) -
missing.
From the rules above, we can see that when no missing data is present, the procedure consists of applying the Haar wavelet with uncertainty propagation. When we have missing data, it can also happen that it remains present at coarser scales (see the fourth rule). This can be instrumental when analysing the information content at different scales, and enables the development of tools for scale selection.
3. Guidelines on the Use of Uncertainty-Based M R D Frameworks Methods 1 and 2 differ deeply on how they implement the incorporation of uncertainty information. In this section we provide a general guideline about which of the two approaches to use and when. Let us consider an artificial piecewise constant signal, where the values are held constant in windows of 24 - 16 successive a), to which proportional noise with uncertainty assumedly known is noisy signal (Figure l-b), it is possible to calculate its approximations ( j = 1, 2,... ) using the two types of approaches and then to see which
values (Figure ladded. Using the for coarser scales method performs
better in the task of approximating the true signal when projected at the same scale, j. Our performance index is the mean square error between the approximation at scale j, calculated for the noisy signal, and that for the true signal, MSE(]). Figure 1-c summarizes the results obtained from 100 simulations. These results illustrate the general guideline according to which, from the strict stand point of the approximation ability at coarser scales, Method 1 is more adequate then Method 2 for constant signals and for piecewise constant signals until we reach the scale where the true values begin to vary from observation to observation, i.e., for which the piecewise constant behaviour stops. As the original signal has constant values along windows of 16 values, the piecewise constant pattern breaks down after scale j - 4. This occurs because Method 1 is based on the MVUE estimator of an underlying constant mean for two successive values, thus leading to improved results when this assumption holds, at least
1505 approximately as in the case of piecewise constant signals, being overtaken by Method 2 when such an assumption is no longer valid. True signal I
a~ 0
r~
~L !
~
~[~ •
±
7'i
-o.2
~._i q
J
-0.6 Noisy signal
"-~-0.8 F i
-lc
L
-1.2, -1.4
J
c~
-1.6i, i
2
3
4
5
6
Scale index (j)
Figure 1. (a) true signal used in the simulation; (b) a realization of the noisy signal and (c) box plots for the d(fference in MSE at each scale (j) obtained for the two methods 1O0 simulations).
4. An Uncertainty-Based De-Noising Application Wavelets found great success in the task of "cleaning signals" from undesirable components of stochastic nature, called noise, if we are in such a position that we do know the main noise features, namely measurement uncertainties, then we can use this additional piece of information to come up with simple but effective de-noising schemes. As an illustration, consider a smoothed version of a NIR spectrum as the "true" signal, to which heteroscedastic proportional noise is added. The standard denoising procedure was then applied to the noisy signal, according to the following sequence of steps: 1. Decomposition of the signal into its wavelet coefficients; 2. Application of a thresholding technique to the calculated coefficients; 3. Reconstruction of the signal using processed coefficients. This procedure is tested for the classic Haar wavelet with the threshold suggested by Donoho and Johnstone (1992), T-6-x/21n(N ) , where 6- is a robust estimator of the noise (constant) standard deviation, along with a "Translation Invariant" extension of it, based on Coifman's "Cycle Spinning" concept (Coifman and Donoho, 1995): "Average[Shift- De-noiseUnshifl]", where all possible shifts were used. We will call this alternative as "TI Haar". These methods are to be compared with their counterpart procedures that have the ability of using explicitly the available uncertainty information: "Haar + uncertainty propagation", "TI Haar + uncertainty propagation" (only 10 rotations were used in this method). All the tested methods used the same wavelet (Haar), threshold constant
1506 (~21n(N)) and thresholding policy ("Hard Threshold"). Figure 2 presents results for the MSE scores of the reconstructed signal (scale j - - 0 ) relatively to the tree one, obtained for 100 realizations of the additive noise. A clear improvement in MSE is found for the uncertainty-based methods, relatively to their classic counterparts.
2.5 ..................l.................
........ i ................................t
+
............... j i
1.5
0.5
Haar
Haar+unc.
prop.
TI H a a r
TI H a a r + u n c .
prop.
Figure 2. De-noising results associated with the four alternative methodologies ("Haar" "Haar+uncertainty propagation . . . . TI Haar" and "TI Haar+uncertain~ propagation ").for 1O0 noise realizations.
5. Conclusions In this paper, we propose two methods for handling the issues of missing data and data uncertainty in MRD. Both Methods 1 and 2 are not extensions of the wavelet transform in a strict sense, as some of their fundamental properties do not always hold, such as the energy conservation property (in the sense of the Plancherel formula; Mallat, 1998). However, they can lead to improved results by effectively incorporating uncertainty information and allow one to extend the wavelet MRD to contexts where it could not be directly applied, namely when we have missing data, as well as provide new tools for addressing other types of problems in data analysis, such as the one of selecting a proper scale for data analysis.
References Alsberg, B.K., A.M. Woodward, D.B. Kell, 1997, Chemometrics Intell. Lab. Syst. 37, p. 215-239. ISO, 1993, Guide to the Expression of Uncertainty. Geneva, Switzerland. Lira, I., 2002, Evaluating the Measurement Uncertainty, NJ: Institute of Physics Publishing. Mallat, S., 1989, IEEE Trans. on Pattern Analysis and Machine Intell. 11, 7, p. 674-693. Mallat, S., 1998, A Wavelet Tour of Signal Processing. San Diego [etc.]: Academic Press.
Acknowledgements The authors would like to acknowledge Portuguese FCT for financial support through research project POCTI/EQU/47638/2002.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1507
Integrated Process and Product Design Optimization" a Cosmetic Emulsion Application Fernando P. Bernardo* and Pedro M. Saraiva GEPSI-PSE Group, Department of Chemical Engineering, University of Coimbra, P61o II - Pinhal de Marrocos, 3030-290 Coimbra, Portugal
Abstract A simultaneous approach to address optimal product and process design is presented and applied to a cosmetic lotion case study. The problem formulation integrates product quality, as assessed by customers, a model predicting lotion viscosity as a function of its composition and a process model linking process design and operation with lotion composition and microstructure. The solution of such a problem identifies the optimal lotion composition together with the interrelated process optimal specifications. This integrated design approach is shown lo provide better solutions than the ones obtained when product and process design problems are solved separately.
Keywords: Process and Product Design, Optimization, Cosmetic Emulsions.
1. Introduction Integrated chemical product and process design may be understood as the specification of a chemical-based product together with the design of the correspondent manufacturing process. The product/process specification should take into account product functionalities and attributes valued by customers, as well as feasibility and profitability of production at a commercial scale. Generic methodologies to guide the solution of such an integrated problem along the way from customer needs to product manufacturing have started to be developed (Cussler and Moggridge, 2001; Wibowo and Ng, 2001, 2002). The basic idea under these methodologies is to drive decisions by product quality factors related to customer satisfaction, that once identified are then translated to a product/process technical specification. |n a previous work (Bernardo and Saraiva, 2004), and accordingly to the above qualitydriven perspective, we have proposed an optimal design formulation that integrates a product quality function together with product and process models. Based on this optimization problem, and handling its associated uncertainties, we have then presented a method to analyse the value of obtaining additional knowledge regarding a particular problem level. A cosmetic lotion case study was used to illustrate the application of our approach dealing with uncertainties in the prediction of product viscosity, which is correlated with customer satisfaction, but at that stage the interconnected manufacturing process design was not considered. Corresponding author, e-mail address:
[email protected] 1508 In this paper, we focus on the simultaneous optimization of product and process design and its application to our previous cosmetic lotion case study, now enlarged with an approximate model of the manufacturing process. Our main objective here is thus to illustrate how both product and process design decisions may interact with each other and therefore verify to what extent an overall formulation that accounts for product quality, as well as process costs, may lead to improved solutions over the common sequential approach, where product and process design are handled separately.
2. Optimal Product/Process Design Formulation Although it may be further generalised, our design formulation is primarily dedicated to consumer formulated products, such as pharmaceutical, cosmetic, and cleansing products. Usually, such products comprise a mixture of several ingredients, combined in a structured system, such as an emulsion, suspension, foam or gel. Table 1 presents a set of variables and parameters relevant to the design of these products. Table 1. Product~process design variables and parameters.
QF y p
Xl
Z2
02 03
Description Product quality factors valued by customers Quality variables: product properties p or states x related to quality factors Product physicochemical properties or effects during usage Product design variables (process independent): ingredients used and their proportion Product state variables (process dependent): product structure Product operating variables: external conditions during product usage Process design variables: flowsheet configuration and equipment dimensions Process operating variables: operating procedure (recipe) and equipment operating conditions Process parameters: physicochemical properties and kinetic/equilibrium parameters Additional parameters, such as economic coefficients or market indicators
Cosmetic Lotion Example Skin feeling Lotion viscosity Lotion viscosity Oil-in-water emulsion (water, thickener, oil, emulsifier, etc) Droplet size distribution of the oilphase Shear rate of lotion application on skin Mixing equipment dimensions Impeller speed Heat transfer coefficient in mixing/heating tank Quality loss coefficient, electricity cost
Our design methodology is therefore based on three main groups of relationships: 1. The quality function, relating quality factors QF with product quality variables y; 2. The product function, which predicts product properties as a function of its related variables: p= fl(dl,Xl,Zl) ;
(1)
3. The process function, linking product and process variables: f2 (dl, d2, z2,02, Xl ) = 0 .
(2)
Regarding quality functions, we will assume here that, for each y variable, there is an optimal y* value, from the customer point of view, and that the quality loss L associated with a deviation ( y - y*) is well quantified by a Taguchi loss function:
1509 (3)
L = k ( y - y*)2,
where k is a quality loss coefficient to be estimated based on customer satisfaction surveys and panels. Other quality function definitions may be used as an alternative and are easily incorporated in the proposed methodology. Given the above mappings, leading all the way from customer perceptions to process operating conditions, our integrated product/process design problem can then be formulated as follows: max P(dl,Xj,zl,p,d,,z,,02,03)_ _ ~11,d2 ,:2
(4)
s.t. p - . f l (dl ,xl ,zl) A gl (dl ,Xl ,zl, P) C 3- + C [ . The reaction network on the catalytic sites is displayed in table 1.. Table 1 Reaction ;Tetwork on lhe catalytic sites
1. n -
C*;;' 4,~, ~-~ i s o - (~.H' "~ 4.~,
2. 2 n •
C 4,o *;;~
C*;; ~ *n' S.o +
,
c,tt'
'
4. C;,~
-I-- H - C415 --~ 3C3, o + 2 *'v'
5 C£,~H, + * ' ; •
~
.
--> 2iso - c * " ' "'-
NII~
NI21
N~3~
N~4~
NI5,
1
o
o
o
0
(1)
0
1
1
I
1
(2)
o
o
o
1
1
(3)
0
0
0
0
1
(4)
0
1
0
0
0
(5)
o
o
1
o
o
(6)
o
o
o
-1
-1
(7)
1
2
1
2
3
(8)
-1
-2
-1
0
0
(9)
0
0
0
-1
0
10
4.o
6.
C s,o *;;+ + *;;' ---> i s o - - C 4.o *;;+ + n - - C4,o *" A. C3," + B.
*H +
+
/'/--84o
*H*
E C3, , . H + ,..,
~
n-C4,
.H + °
c. i s o - C 4 ,, + * " - E i s o - C *;;+ ,
D. C5, o +
*H ~
' 4,0
*H ~
E C~.~,
On the right hand side of the equations (1)-(10) above, the stoichiometric numbers (N) the of steps along independent routes are presented. Model A corresponds to monomolecular isobutane formation and included route N (~ as the sole path to isobutane. Routes N ~4~ and N ~5~ describe byproduct formation. In model B isobutane is formed bimolecularly (N ~3.) and the monomolecular path for isobutane formation is neglected. The valid routes are NI3LN ~5~. Model C includes routes N t~t, Nt3LN 15~. Thus, in model C isobutane can be formed either monomolecularly or bimolecularly. The rate equations of Langmuir-Hinshelwood type were derived using the assumption that ratelimiting steps are the surface reactions on the catalyst
k~ ( K , , : . .
, P ( ~ - K i c;.H +P i c: K , ' )
r4=
Z3
k 2 K c 2~, H + P~c2
r(=
Z2
(2)
1534
where Z
-1+
Z K i , H + P i +O'c2,H+ i,ole/in i¢C~
and
Oc2,H, -
0c~ H÷ ~ OV
(3)
The rate constants and their temperature dependencies were modelled with the Arrhenius equation, modified in order to improve simultaneous estimation of preexponential factor and activation energy. Since catalyst deactivation is a profound feature, it was included in a general way in the model. The rate of the reactions are given by equation below, where r0.i is the initial reaction rate for reaction i, and a denotes the relative activity: r i = ro,ia
(4)
where the activity factor is calculated from p a-
[
1
1 + (a -1)k'c e,0 ~-'
a - e x p ( - ilk'cp,o~-I t)
a~l t
(5)
a -1
(6)
Reaction and deactivation were assumed to be uniform throughout the reactor bed and the catalyst particles. The component mass balance is written as (p-partial pressure).
dpj dr
= m~trja
j - C 3, C 4,i - C 4 , C s
(7)
where r is the space time of the fixed bed. The overall generation rates of alkanes are determined by the isomerization of olefins on acid sites giving generation rates rc~ - r3 + 3 r 4
(propane)
l/'i-C 4 =]el "of-]e6
(isobutane)
]eC4 -- --]el
-2r3 - r 4
-r6
rcs =r3 - r 4
(n-butane) (pentane)
ru~ -- rc~,, - %; - rc; = . . . = 0 The reactor model equations were solved numerically by a stiff ODE-solver during the parameter estimation which was carried out by a Levenberg-Marquardt algorithm implemented in the software Modest (Haario 2001). Examples of the fit of the model to the experimental data are provided by Figs 2-3. The figures reveal that the description of the conversion a l o n e - including the catalyst deactivation- is not enough, but a detailed analysis of the product distribution is needed, as revealed by the selectivity analysis (Fig. 3). The detailed kinetic modeling
1535 enables us to judge, which mechanism is prevailing under specified conditions (pressure, temperature). The model, which enabled bimolecular reaction path for isobutane formation, had a good fit on the selectivity to isobutane at high reactant pressures but was incapable to predict the increase in selectivity to isobutane with decreasing n-butane pressures. At the same time, the above mentioned tendency was very well predicted by the models enabling monomolecular mechanism for isobutane formation. The kinetic modelling also supported the proposal that excess of propane compared to pentanes is due to consecutive codimerization of formed C f with C 4 to C~- followed by cracking to three C 3 species. 30
673 K, n-butane:H 2 40"60 25Z 6 ©
20
=- 15O
.,.-,
0o ;>
\
10-
7 ~ i Model
eel
0 _
0
i
I
50
0
100
i
I
150 TOS/min
I
200
250
Figure 2. Examples o/convetwion as a./imction of time on stream at 673 K by the kinetic models compared to the experimental values.
9O 6
80
O
d +...,
=
A
~;~
70-
--o-- Model ~+- Model QModel
,½
60-
©
•©-~ 50+..a
>' 40-
.+..a
;>
. ,..-~ .,..a
¢)
3020 0.0
673 K l
0.1
l
I
[
I
0.2 0.3 0.4 0.5 n-Butane partial
l
0.6
0.7
Figure 3. Selectivity to isobutane at TOS = 10 min as a function of n-butane partial pressure at 673 K by the kinetic models compared to the experimental values.
1536
3. Conclusions The approach applied is briefy summarized in the flowsheet sketched below. Successful modelling of catalytic reactors requires a strongly integrated approach. Due to the progress of applied quantum chemistry it is possible to get ideas and inspiration for mechanistic hypothesis, which are brought to kinetic equations including catalyst deactivation. Furthermore, models for heat and mass transfer as well as flow models are incorporated. Efficient and robust numerical algorithms are used to solve the kinetic and reactor models. The approach should not have a single missing link, since the final goal is a reliable design tool for chemical reactors integrated to surrounding process units. Construction of stoichiometric scheme
Quantum J chemical calculations
,4
-
~- Check of overall thermodynamics
l fypoth esis o n reaction mechanism
Derivation of rate 4 equatiolls
Kinetic experiments
4 Model for test reactor Estimation of kinetic parameters v Mass and heat transfer correlations and experimentation
Kinetic model Mass and heat transfer i,. model
4, REACTOR P" MODEL
-
Experimental verification offlowcond ifion s
Flow ¢, model
References Sie, S. T. Handbook of Heterogeneous Catalysis, eds. Ertl, G.; Kn6zinger, H.; Weitkamp, J. VCH/Wiley, 1997, p. 1998. Guillaume, D.; Surla, K.; Galtier, P. From single events theory to molecular kinetics-application to industrial modelling. Chem. Eng. Sci. 2003, 58, 4861. Nieminen, V.; Kumar, N.; Salmi T.; Murzin, D. Yu. n-Butane isomerization over Pt-H-MCM-41. Catal. Comm. 2004, 5, 15. Haario, H. Modest Users's Guide 6.0, ProfMath Oy, Helsinki, 2001. Hou~vi~ka, J.; Ponec, V. Skeletal isomerization ofn-butene. Catal. Rev.-Sci. Eng. 1997, 39, 319 Ono, Y. A survey of the mechanism in catalytic isomerization of alkanes. Catal. Today 2003, 81, 3.
Acknowledgements This work is part of the activities at the Abo Akademi Process Chemistry Centre within the Finnish Centre of Excellence Programme (2000-2005) by the Academy of Finland
European Symposiumon ComputerAided Process Engineering 15 L. PuiNaner and A. Espufia(Editors) ¢~)2005 Elsevier B.V. All rights reserved.
1537
An MILP Model for Optimal Design of Purification Tags and Synthesis of Downstream Processing Evangelos Simeonidis a, Jose M. Pinto b and Lazaros G. Papageorgiou a'* aCentre for Process Systems Engineering, Department of Chemical Engineering UCL (University College London), Torrington Place, London WC 1E 7JE, U.K. UDepartment of Chemical and Biological Sciences and Engineering Polytechnic University, Six Metrotech Center, Brooklyn NY 11201, U.S.A.
Abstract Downstream protein processing in biochemical production plants can be improved significantly with the use of peptide purification tags: comparatively short sequences of amino acids fused onto the product protein, which modify the physical properties of the desired product in a way that enhances its separation from contaminants. A two-step MINLP framework that integrates the selection of optimal peptide tags with the synthesis of downstream processing has previously been developed by the authors. The objective of this work is to transform this framework to a simpler MILP model. The methodology is validated by an illustrative example based on experimental data.
Keywords: protein purification processes, peptide tags, mixed integer linear programming
1. Introduction Recent advances in biotechnology have given immense impetus to the introduction of biopharmaceutical and biotechnological products. Downstream processing is typically among the most difficult and complex stages and the source of a large portion of the manufacturing and investment costs in a biochemical production plant. The quality of the product is predominantly determined at the purification level, which may therefore be regarded as the most important production stage. Early systematic methods for the synthesis of downstream protein processing made use of expert knowledge systems for selecting operations (Lienqueo el al., 1996). Vasquez-Alvarez and Pinto (2004) presented a mixed integer linear programming (MILP) framework, in which mathematical models for each chromatographic technique rely on physicochemical data on the protein mixture that contains the desired product, and provide information on its potential purification. Considerable improvement of downstream protein purification processes can be achieved with the use of peptide purification tags (Steffens et al., 2000, Simeonidis et al., 2004). Peptide tags are comparatively short sequences of amino acids, genetically fused on the protein product, in order to modify its physicochemical properties in a way that will enhance the separation, thus simplifying the purification flowsheet. The Author to whom correspondence should be addressed: l.
papageorgiou@ucl,
ac. uk
1538 development of a framework for the optimal design of case-specific peptide tags that alter the properties of a particular protein product in the most beneficial way, and the concurrent synthesis of downstream protein processing has been previously presented by the authors (Simeonidis et al., 2004); a methodology based on a two-step, mixed integer non-linear programming (MINLP) framework has been developed. In this work, the above model is reformulated as a mixed integer linear programming (MILP) model through piecewise linear approximations of the nonconvex, nonlinear functions. The new model utilises physicochemical property data to specify the amino acid composition of the shortest and most advantageous peptide tag configuration, and concurrently select operations among a set of candidate chromatographic techniques in order to achieve a specified purity level. The applicability of the model is demonstrated by an example that relies on experimental data.
2. Problem Statement Overall, the problem of simultaneous optimal tag design and synthesis of downstream protein processing can be stated as follows:
Given" • a mixture of proteins (p: 1,...,P) with known physicochemical properties; • a set of available chromatographic techniques (i: 1,...,/) each performing a separation task by exploiting a specific physicochemical property; • the properties of the twenty amino acids (k: 1.... ,20); and • a minimum purity level for the desired product (dp). Determine: • the amino acid composition of the shortest and most advantageous peptide tag; • the physicochemical properties of the tagged protein (desired product + tag); and • the flowsheet of the high-resolution purification process. So as to optimise a suitable performance criterion.
3. Mathematical Formulation Next, the main components of the proposed mathematical framework are briefly described. The resulting MILP representation, designed for the synthesis of purification bioprocesses, so as to consider the optimal design of purification tags, extends an earlier MINLP formulation (Simeonidis et al., 2004).
3.1 Physicochemical property constraints The tagged protein's net charge (Qdp) is predicted based on the methodology suggested by Mosher et al. (1993). Q,.~,~-
~)~.+ + ~ keBA
nk K k_~_ 1
II4+L
-
~
nk
keAA ___-[H+]J ~ 1
x~
(1)
1539 where BA and AA are the acidic and basic amino acid groups respectively; R) is the ionisation constant; 17x is the integer number of amino acids k in the tag and Q,.+ is the initial product charge. The tagged protein's hydrophobicity (H,o,) is estimated using the work by Lienqueo et al. (2002). The calculation is based on the relative contribution of each amino acid to the surface properties of the product protein and the knowledge of its 3D structure. 3.2 D i m e n s i o n l e s s r e t e n t i o n t i m e s
Dimensionless retention times KD]], are defined as a function of net charge Qo, or hydrophobicity H,. For ion exchange chromatography, retention times for the tagged protein product are estimated based on approximations of the chromatograms by isosceles triangles and on physicochemical property data for the product and contaminants (Vasquez-Alvarez eta/., 2001). The methodology presented by Lienqueo et al. (2002) is used to estimate the dimensionless retention times for hydrophobic interaction (KDm.],). Both relationships between retention t i m e - physicochemical property are nonlinear; therefore piecewise linear approximations are used for their linearisation, as presented in Figure 1. --
~
7~
KD
-
A
£
-
110 ]K D .....
-
0.8
i
0.3
KD c6
!
." . ' ' ' ' "
0.6
".11
-3.0
-2.0
-t0
~'"
0.0 O ,op
1.0
2.0
I
0.4
!
O.2
I 3.0 I
i0.0
i ,F i
o.17
0.22
0.27
0.32
Hop
:
Figure 1. Piecewise linear approximations of retention times for ion exchanq, e chromatogt'aphy (AE." anion c
< l i s : p h y s i c a l _ o b j e c t r d f : I D : " T I C 01"> Temperature Controller
TIC-01
<xsd:float rdf:value="800.0"/>
1548 < / r d f :D e s c r i p t i o n > < /t e m p e r a t u r e _ s e t p o i n t < / I i s :p h y s i c a l _ o b j ect >
>
Figure 5. 0 WL Code illustrating the definition of physical quantities. We can also specify temporal boundings (beginning and ending) to temporal_part_of_TIC_01_at_800K to indicate the time interval in which the setpoint of TIC-01 was at 800K.
6. C o n c l u s i o n s Industries around the world recognize that some of the keys to compete in the everincreasing global markets, as well as to meet increasingly tighter safety and environmental constraints lie in improved work flow processes and in the integration of information systems. However, many current information systems can be integrated only at great cost because of their incompatible proprietary representations of information. One approach to integration of information systems is by means of shared ontologies. In particular, upper ontologies define top-level concepts such as physical objects, activities, mereological and topological relations from which more specific classes and relations can be defined. We have provided a brief overview of an upper ontology based on ISO 15926-2:2003 which has been implemented in OWL. The ontology is being used as an approach to represent and query knowledge generated during Hazards and Operability Studies, and it is also the upper ontology for defining and searching modeling services. It would be of great benefit to the process engineering community to explore the integration with other efforts such as the OntoCAPE ontology. The upper ontology in OWL format can be downloaded from: http://www.ompek.org/
References Bayer, B., 2003, Conceptual information modeling for computer aided support of chemical process design. VDI Verlag GmbH, Daseldorf. ISBN 3-18-378703-2 Gangemi A., N. Guarino, C. Masolo, A. Oltramari, L. Schneider, 2000, Sweetening Ontologies with DOLCE. Proceedings of EKAW 2002. Siguenza, Spain ISO 10303-11, 1994, Industrial automation systems and integration - Product data representation and exchange - Part 11: Description methods: The EXPRESS language reference manual ISO 15926-2, 2003, ISO-15926:2003 Integration of lifecycle data for process plant including oil and gas production facilities: Part 2 - Data model Niles, I. and A. Pease, 2001, Towards a Standard Upper Ontology. 2nd International Conference on Formal Ontology in Information Systems (FOIS), Ogunquit, Maine, October 17-19 Sowa, J., 2000, Knowledge Representation: logical, philosophical, and computational foundations. Brooks/Cole Uschold, M. and M. Gruninger, 1996, Ontologies: Principles, Methods and Applications Engineering Review 11 No. 2 (1996) 93-113 West, M., 2003, Replaceable Parts: A Four Dimensional Analaysis Proceedings of the Conference on Spatial Information Theory (COSIT), Ittingen, Switzerland, September 24-28 W3C, 2004, OWL Web Ontology Language Overview, W3C Recommendation, [Online] Available: http ://www.w3.org/TR/owl-features/ Yang, A. and W. Marquardt, 2004, An Ontology-based Approach to Conceptual Process Modelling. Proceedings of ESCAPE-14, Portugal.
European Symposiumon ComputcrAided Process Engineering 15 L. Puigjaner and A. Espufia (Editors) g~ 2005 Elsevier B.V. All rights reserved.
1549
Multi-Agent Systems for Ontology-Based Information Retrieval R. Bafiares-Alcantara ~ , L. Jimdnez b and A. Aldea c ~Department of Engineering Science, Oxtbrd University Parks Roads, Oxford OXI 3PJ, UK bDepartment of Chemical Engineering and Metallurgy, University of Barcelona Marti i Franqu~s 1, Barcelona 08028, Spain CDepartment of Computing, Oxford Brookes University Wheatley Campus, Wheatley, Oxford OX33, UK
Abstract The Web offers a huge amount of valuable intbnnation, but it is very hard and time consuming to retrieve thousands of web pages related to a concept, filter the relevant ones, analyse this intbrmation and integrate it in a knowledge repository. This paper describes one component of a knowledge management platform (h-TechSight project) that performs these tasks, the multi-agent search module (MASH). MASH employs a domain ontology to search for web pages thai contain relevant information to each concept in the domain of interest. The search is then constrained to a specific domain to avoid as much as possible the analysis of irrelevant information.
Keywords: ontology; multi-agent system; knowledge retrieval.
1. Introduction A good use of knowledge management practices can greatly benefit knowledge intensive industries, such as chemical process industries. Maintaining an up-to-date knowledge of the domain is of capital importance for those industries. The WWW offers a huge amount of information, but it is impossible for a person to retrieve thousands of web pages related to a concept, filter the relevant ones, analyse their content and integrate it in the company knowledge repositories [Batres et al., 2002]. Knowledge management tools can help by providing tools that automatically update technological domains, and monitor and assess how products, services, and technologies evolve, emerge, mature or decline. Furthermore, engineers typically identify the evolution of their disciplines by reading journals, attending conferences or by hearsay. All this information can be found nowadays on the web, but it is weakly structured, scattered, distributed and impossible to analyse manually. Traditional search engines allow users to retrieve information by combining keywords. This type of search can cause several problems: the number of
Author to whom correspondence should be addressed:
[email protected] 1550 pages retrieved may not be manageable; some of the retrieved documents are irrelevant while some of the relevant documents may have not been retrieved. Fensel (2001) argued that the performance of a search engine could be improved by using ontologies. In its conventional form, an ontology can be seen as a representation of the concepts which are relevant to a particular domain. Ontologies provide a semantic view that helps to sort out web pages with relevant information about a concept from web pages that contain data with just syntactic similarities to the concept. The aim of the EU research project h-TechSight (h-TechSight, 2001) is the construction of a knowledge management platform (KMP) (Stollberg et al., 2004; Kokossis et al, 2005), which can be used by knowledge-intensive industries to keep a dynamically updated knowledge map of their domain. This paper describes in detail one of the main components of the KMP, the MASH search module, which main task is to find web pages with relevant information about a predefined field represented by a domain ontology (Aldea et al., 2003).
2. The Multi-Agent Search Engine (MASH) The search engine requires a domain ontology to perform the search, so the user must generate that ontology or use an existing one to start the procedure. The implementation of the search module is based on the agent technology (Wooldridge, 2002) where several software agents work together in an asynchronous, concurrent and intelligent way that can be distributed among several computers.
2.1. Domain ontology The search is driven by the domain ontology which is represented by a hierarchical taxonomy of concepts. Every concept (class) is connected to a parent concept (superclass) and thus a class and all its ancestors define a class path (for example, in Figure 1: Biosensor\Application\Environment\Air analysis). Every class (e.g.. air analysis ) contains a set of slots which represent the properties and characteristics that are important for this specific class in the general domain of interest (e.g. biosensors). Every class also inherits all slots defined in its ancestors (Fensel, 2001). Figure 1 depicts a part of one domain ontology (biosensor ontology) used in this work. For instance, the concept biosensor application in health care is represented by the subclass "health-care" within this class, the user decided to include two slots "researcher-field" and "re searc h-top ic". During the search process, the difference between classes and properties is that classes define the search domain, while properties are used to evaluate to what extend the retrieved pages have the sort of information required by the user. The use of synonyms in the definition of classes and slots extends the domain ontology with the possibilities of having alternative terms as, for example, "domain" and "field", acronyms as "computer fluid dynamics" and "CFD", chemical formulas as "sodium sulphate" and "NazSO4" or language differences as "generalisation" and "generalization".
1551 •[ ~ Biosen sot .
.
.
.
(!~
Application
(~!!:!;E:!n~;:v iron ment z :::x ~:~;;~,:A i r analysis @
De.,,/ice app
Web Client Other Client
UDDIRegister]~ (;enter
"-~
2005 Elsevier B.V. All rights reserved.
1609
Process Integration and Optimization of Logistical Fuels Processing for Hydrogen Production Fadwa T. Eljack ~, Rose M. Cummings ~, Ahmed F. Abdelhady, Mario R. Eden ~* and Bruce J. Tatarchuk h :'Department of Chemical Engineering, Auburn University 230 Ross Hall, Auburn, AL 36849-5127, USA ~Center for Microfibrous Materials Manufacturing (CM 3) 337 Ross Hall, Auburn, AL 36849-5127, USA
Abstract In this work, the preliminary results of a process integration analysis of a logistical fuels processing plant is presented. A simulation model of a bench scale test bed was developed using a commercial simulator (Pro/II) and used to generate the necessary data for performing a thermal pinch analysis. The analysis shows that considerable savings can be obtained through increased thermal integration of the system. The specific application of the fuel processing system is to power a portable radar system, thus reductions in energy requirements translates into equally important reductions in equipment size. To further increase the integration potential the use of heat pipe technology has been investigated. Heat pipes allow for near isothermal heat transfer and thus significantly reduce the required temperature driving force. A simple, systematic method for identification of optimum heat pipe usage in heat exchange networks is presented in this work.
Keywords: Fuels processing, process integration
1. Introduction Fuel cells are emerging as an important component of a renewable energy future for many utility and mobile applications. Proton exchange membrane (PEM) fuel cells are capable of achieving much higher energy efficiency levels since a fuel cell is not limited by the traditional Carnot cycle found in combustion engines. A very promising technique is to obtain the required hydrogen by reforming a liquid hydrocarbon fuel, which has a significantly higher energy density than gaseous hydrogen. Recent efforts are focused on reforming existing logistical fuels, e.g. diesel or JP-8 for use in fuel cell systems (Amphlett et al., 1998). This is particularly important for military applications, as it would allow for the US armed forces to move towards using one single logistical fuel. Since the overall energy efficiency of a fuel cell system is approximately three times higher than a combustion engine based generator, it would provide substantial savings for the US Army if alternative means of power production could be developed.
Author to whom correspondence should be addressed:
[email protected] 1610 To meet these ends the Center for Microfibrous Materials Manufacturing (CM 3) at Auburn University has developed a bench scale test bed for investigating running a portable radar system of a Ballard Nexa TM PEM fuel cell stack by producing high purity hydrogen from reforming JP-8. The PEM fuel cell system consists of the fuel processing section and the fuel cell itself, with the former being the reformer and postcombustion cleanup steps. Such systems inherently possess tremendous integration potential, not just limited to recycling unused material, but also in terms of energy recovery (Godat and Marechal, 2003). The objective of this work is to develop a process simulation model of the fuel processing test bed and use it to generate the data required for subsequently performing a thermal pinch analysis in order to identify the potential energy savings attainable. As this system is targeted for mobile applications reductions in utility requirements will automatically result in reductions in the system size.
2. Process Description and Model Development A schematic of the fuel processing test bed is given in fgure 1. A central theme for the test bed is the use of microfibrous entrapped catalysts and sorbents. These microfibrous materials provide high contacting efficiency through a high surface area to volume ratio. This enhanced heat and mass transfer capability presents an opportunity for miniaturization of the processing units compared to conventional catalyst supports, such as packed beds. In figure 2, 500 lam water gas shift catalysts particles are entrapped in 10-50 ~tm Nickel fibres. Similarly 150 ~m particles of a precious metal catalyst on alumina support are depicted in figure 3 (Karanjikar et al., 2004). The simulation model was developed using a commercially available process simulator Pro/II (Simulation Sciences, 2004) augmented with a customized model for the fuel cell. It should be noted, that the simulation model is specified to match the experimental data. JP-8 ''"""''~t H~.O ~
Two Stage Reforming
Preformer (900~'C) Postformer (700:;C)
.................. ~-
HzS Removal !
.................... ~,~ i
(370:C ]
J
I Pure water
,~"......... ....--.. ~,~ ................ "~v-"....
! l
PEM Fuel Cell
{
} [_.
Water Gas Shift I PR OX HTS (300="C) ...................... ~ (~2~ )'::~C) LTS (200':C)
L ............................................................. : .................
Fuel Filter
h,,
(25C)
{-"
CO~ Removal (25 c)
Figure 1. Fuel processing test bed schematic
Figure 2. WGS catalyst in Nickel fibres
Figure 3. PROX catalyst on Al:03 support
1611 2.1 Reforming section There is no standard formula for jet fuels such as JP-8. The exact composition depends on the crude oil from which they were refined. Variability in fuel composition occurs because of differences in the original crude oil and in the individual additives. As a result of this variability, little information exists on the exact chemical and physical properties of jet fuels (Custance et al., 1992). JP-8 consist of a variety of hydrocarbons ranging from C7 to C~,, however the bulk of the fuel (over 80%) is made up by decane, dodecane, tetradecane and hexadecane (US Air Force, 1991). The steam-to-carbon ratio in the feed is 2.4, which has been reported as being the optimal choice (Zalc and L/Sft'ler, 2002). The mixture of steam and fuel is heated to 900°C and fed to the first reactor, which performs the majority of the reforming according to equations (1)-(3), while the second reactor reduces the methane content fi'om approximately 15% to 1%. Chromatographic analysis of the effluents for the preformer and postformer is presented in figures 4 and 5, respectively and the reactor models are specified to match the performance of the experimental test bed. CnHm + nH_~O ---> nCO + (n + 0.5m)H_~
(1)
CH 4 + HeO ---->nCO + 3H 2
(2)
CO + H,O --> CO,_ + H,_ _
(3) 25O
25O: 1 225 :
C02
_,_,5
CO 2
CO 2 = 20%
CO = 11.3%
CO~ = 20% zIM~i
z,,
C O - I O%
i !
C H 4 - ,5%
175
Is°i
60ppm
175
H~S
H 2 = Bulk
C2H 6 = 1%
.~,
6 0 p p m H2S
~ " 150
n~ u ~
CO
CH a = 1.57%
.~ ~125 ".~
.I~ 12~
":~
ii~ j
~. 75
C2H6
75
CH,
50:
,.
C2H 4 O' 0
O.S
1.5
CH a
_,s .I
25
2
2.5
Retention
3
3.5
4
4.5
5
5.5
Time (mint
Figure 4. Analysis of pr~:/'ormer e[]luent
¢,
0
o.5
i
1.5
2
2.5
Retention
3
Time
3.5
4
4.5
5
5.5
~.
(mint
Figure 5. Analysis of postformer effluent
2.2 Reformate cleanup The purpose of the next sequence of units is solely to purify the hydrogen by removing or converting the reforming by-products. Analogous to the reformer models, the model specifications are based on experimental data. First step is removal of hydrogen sulphide as it serves as a catalyst poison. The removal is performed by a microfibrous entrapped ZnO/SiO2 catalyst. The removal rate is greater than 99%, thus reducing the H2S content to less than 1 ppm. Next are two water gas shift reactors, which convert carbon monoxide (which poisons the PEM fuel cell) into carbon dioxide as described by equation (3). The CO content after the shift reactors is reduced from 15% to less than 0.75%. The remaining CO is converted to CO2 through preferential oxidation (PROX), which reduces the CO content to less than 10 ppm. The selectivity of the PROX catalyst
1612 (Pt-M/A1203) is 60% towards the oxidation of CO, while the remaining 40% reacts with hydrogen to form water. The CO2 is then removed by adsorption on a microfibrous entrapped alkaline sorbent. The last unit before the hydrogen rich gas enters the fuel cell is an inline fuel filter, which is a series of microfibrous entrapped sorbents that can remove traces of HzS, NH3, CO and CO2 (Karanjikar et al., 2004).
2.3 PEM fuel cell The high purity hydrogen stream is sent to the PEM fuel cell along with a feed of atmospheric air. The fuel cell produces electrical power and heat along with pure water, some of which is then recycled back to the steam production section. For the specific application envisioned by the military, i.e. power supply for a portable radar system, this presents an additional benefit. Since there is a net production of water (on a molar basis roughly 6 times the water supplied for the steam reforming) in the system, the on board fuel processor is capable of providing drinking water for the personnel.
3. Process Integration Analysis Once the simulation model had been developed based on the experimental data obtained from the fuel processing test bed, a process integration study was performed to identify the potential energy recovery. By employing pinch analysis methods the global flow of energy in the system was mapped and analyzed. Assuming a 20°C minimum allowable temperature driving force, the pinch analysis showed that by extensive integration the external heating duty could be reduced by 58%, while the external cooling duty could be reduced 54%. These are quite significant savings when keeping in mind that these reductions in energy can be translated to reductions in equipment size as well. Furthermore, the fresh water requirement for steam production has been completely eliminated due to the fact that there is a net production of water in the system. Further investigations include dynamic simulation of the system, which may reveal that the hold-ups in the system require the water the recycle to be increased in order to run the system continuously. However it is still anticipated that a considerable amount of the fresh water produced can be used as drinking water.
4. Enhancing HEN Performance using Heat Pipes Implementation of heat pipe technology has the potential of significantly increasing the attainable integration potential for process systems as the required driving force is decreased (Gaugler, 1944; Chi, 1976). A heat pipe is a heat transport device that utilizes evaporation and condensation to transport high rates of heat almost isothermally. Figure 6 outlines the structure of a generic heat pipe, where the heat transport is realized by evaporating a liquid contained in the wick in the heat inlet region and then subsequently condensing the vapour in the heat rejection region. Closed circulation of the heat transfer fluid is maintained by capillary and/or bulk forces. Heat is transferred radially through the casing and into the wick causing the liquid to evaporate and thus transferring mass from the wick to the vapour core. This increases the pressure in the vapour core at the evaporator end of the pipe, thus allowing vapour to flow to the condenser end of the pipe. Heat is removed through a suitable heat sink attached to the pipe casing at the condenser end. The condensing vapour replaces previously
1613
evaporated liquid mass to the wick and capillary forces feeds the liquid back to the evaporation section (Harris et al., 2001). Besides the inherent benefits associated with nearly isothermal heat transport, an additional advantage of using heat pipes rather than conventional heat exchangers is that the pipe and the heat transfer liquid provides additional separation between the two streams exchanging heat. This ability reduces the dangers associated with transferring energy between incompatible materials, thus relaxing some of the conventional constraints encountered when designing heat exchanger networks (Harell, 2004). 4.1 Identification of optimal heat pipe placement Since heat pipes are an emerging technology available to the processing industry and thus still quite costly, it is imperative to use them efficiently. For a conventional heat exchanger network the minimum allowable temperature difference (ATtain) is usually between 10 and 20°C. Hence, for a given heat exchanger network the pinch analysis is first performed with ATtar,, equal to e.g. 20°C. Next, the utility targets for a heat pipe only network are identified by performing a pinch analysis with a significantly lower value of ATmio, e.g. 2°C. Now, an iterative procedure as outlined in figure 7 is employed to identify the placement and minimum number of heat pipes required to achieve these targets. The rationale behind the developed iterative approach is that in a standard heat exchanger network the thermal pinch point is the bottleneck, which must be overcome in order to transfer additional energy. Therefore the pinch location is the ideal point to implement a heat pipe. Once the first heat pipe has been implemented, the pinch analysis is redone and the utility targets evaluated. If another pinch point is identified, then a second heat pipe is added to remove this bottleneck. This procedure is continued until the utility targets identified from the 2°C pinch analysis have been matched, and thus no benefits will be obtained by adding additional heat pipes. HEATEXCHANGERNETWORK Thermal Pinch Analysis for AT,:,
F¸
/i~|'~::-
i
:
F | HEATPIPEONLYNETWORK [ ThermalPinchAnalysisfor
20:C
AT ......
Minimum Utility Requirements Heating: E×~ HU ..... Cooling: E×,-CU ......
Minimum Utility Requirements H e a t i n g : H P _ H U .... Cooling: HP_CU ....
Pinch k)cation
:
~ K
2:C
: ......
N~ DESIGNNETWORKWITHHEAT I X .,NO .SONL
IMPLEMENTHEATPIPEAT I PINCHPOINT H Y B R I D NETWORK ThermalPinchAnalysisfor AT ......
20cC and 2~C.
Minimum Utility Requirements
Healing:E X : 1-HU CoolingEX, ,-CU ......
v,~ P O ~ ......
.....
New pinch location
wK~
'
__
" l:: ................................... " MINIMUMHEATPIPES
Fi,~ure 6. Calfillao'.force heat pipe
Fi~llre 7. lterati~,e procedure.for heal pipe placemenl
1614 The iterative procedure outlined in figure 7 ensures that wherever possiblethe bulk heat transfer requirements are carried out using conventional heat exchangers and the more expensive heat pipes are only implemented, where a lower temperature difference is required in order to achieve the desired utility targets.
5. Conclusions and Future Work Using commercial process simulation software a model of a logistical fuel processing system for mobile applications has been developed based on data from an experimental test bed. A process integration analysis showed that energy savings in excess of 50% are achievable through thermal integration of the system. A systematic method for evaluating the effect of using heat pipes in heat exchange networks has also been presented. The method is a simple extension to conventional pinch analysis methods. The presented method utilizes an iterative procedure where heat pipes are implemented at the pinch locations to overcome the thermodynamic bottlenecks. The implementation of heat pipes in the fuel processing system was found to potentially reduce the external heating and cooling demands by an additional 5% as well as providing a technology for reducing the physical size of the system. Future efforts will be focused on further developments of the simulation model including the use of alternative fuels, e.g. diesel, and different reforming schemes, i.e. partial oxidation and auto-thermal reforming. Furthermore, the design changes suggested by the thermal pinch analysis will be implemented on the test bed and the performance validated. Finally, the presented methodology for augmenting heat exchange networks with heat pipes will be extended from the current targeting approach to include actual network design. References Amphlett, J.C., R.F. Mann, B.A. Peppley, P.R. Roberge, A. Rodrigues, J.P. Salvador, 1998, Journal of Power Sources, 7 l, 179-184. Custance, S.R., P.A. McCaw, and A.C. Kopf, 1992, Journal of Soil Contamination 1(4), 379. Chi, S.W., 1976, Heat Pipe Theory and Practice, Hemisphere Publishing Corporation. Gaugler, R., 1944, Heat Transfer Device, US Patent 2350348. Godat, J. and F. Marechal, 2003, Journal of Power Sources, 118, 411-423. Harell, D.A., 2004, Ph.D. Thesis, Texas A&M University. Harris, D.K, D.R. Cahela and B.J. Tatarchuk, 2001. Composites - Part A: Applied Science and Manufacturing 32(8), 1117-1126. Karanjikar, M., B.K. Chang, Y. Lu, and B.J. Tatarchuk, 2004, Pre-prints of Fuel Chemistry Division, ACS Annual Meeting Philadelphia August 2004, 49(2), 910. Simulation Sciences, 2004, Pro/II User Guide. US Air Force, 1991, Supercritical fluid fractionation of JP-8. Aero Propulsion and Power Directorate, Wright Research and Development Center, Air Force Systems Command, WrightPatterson Air Force Base, OH. NTIS Publication no. AD-A247-835. Zalc, J.M. and D.G. LOffier, 2002, Journal of Power Sources, 111, 58-64.
Acknowledgements This work was performed under a U.S. Army contract at Auburn University (DASG 6000-C-0070) administered through the U.S. Army Space & Missile Defense Command (SMDC). This financial support along with support from the Auburn University Undergraduate Research Fellowship Program (AU-URF) is highly appreciated.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1615
A Systematic Approach for Synthesis of Optimal Polymer Films for Radioactive Decontamination and Waste Reduction Tracey L. Mole a*, Mario R. Eden a, Thomas E. Burch a, A. Ray Tarrer a and Jordan Johnston b a
Auburn Engineering Technical Assistance Program (AETAP) Auburn University, AL 36849 b Orex Technologies 1850-E Beaver Ridge Circle, Norcross, GA 30071
Abstract In this work, an effective and systematic modelling technique is devised to generate optimal formulations for explicit polymer film engineering applications. These methods aim at developing quantitative values for not only intrinsic properties, but qualitative characteristics are developed in order to simultaneously optimize the formulation subject to the product specifications. The predictive modelling framework developed is comprised of material and energy balances, constraint parameters, constitutive equations, design/optimization variables and possible polymer synthesis techniques. A set of user defined design constraints produces a subset of different optimization formulations comprised of different polymer blends, molecular weights, hydrolyzation extents, solvents, and additives. This contribution illustrates a novel way to evaluate a wide range of polymeric fihn compounds and mixtures with fewer testing iterations.
Keywords: Formulation synthesis, material development
1. Introduction Formulation of new products and improvement of existing merchandise is practiced in many different industries including paints and dyes, polymers and plastics, foods, personal care, detergents, pharmaceuticals and specialty chemical development. Current trends in the engineering design community have moved towards the development of quantitative integrated solution strategies for simultaneous consideration of multiple product characteristics. The optimization variables are most often determined by qualitative attributes, stochastic variables, visual observations and/or design experience. The effectiveness of these approaches is limited by available data, bias towards specific solutions, reproducibility, and experimental error. Model insight is required for development of fast, reliable and systematic screening methods capable of identifying optimal formulations and reducing the number of subsequent laboratory trials. Author to whom correspondence should be addressed:
[email protected] 1616
2. Model Development Methodology In order for the product to exhibit the desired performance, a combination of discrete constraints must be fulfilled. Identification of an optimal formulation that is suitable for the desired system requires integration of all the interlacing behaviours of the product constituents. These characteristics include the constituents used for construction as well as their inherent properties. This is accomplished by using a combination of novel modelling techniques. 2.1 Property integration This method consists of tracking functionalities instead of chemical species in order to represent the synthesis problem from a properties perspective. The conventional approach to product formulation development is selecting constituents that exhibit desired produced properties and optimizing the mixing ratios. In order to model the product characteristics, these pre-determined candidate components are required as inputs to the design algorithm. These inputs are based on qualitative process knowledge and/or design experience, which can exclude solutions involving other possible raw material sources. In this work, the concept of property integration for process development introduced by E1-Halwagi et al. (2004) is applied to product synthesis. This modelling approach allows for solution of many different engineering problems to be conducted on a property only basis. This method allows for identifying optimized solutions to specified chemical engineering problems by determining the desired output and solving backwards for the constituents and compositions. In the case study to be described in the next section, these techniques are used in conjunction with a model decomposition technique to allow for formulation of reverse property prediction problems.
Conventional Model Structure
~
Decoupled Model Structure
I Balance and Constraint Equations ] Mixing Rules & Formula Concentrations) ]
Balance and ConstraintEquations (Mixing Rules & Formula Concentrations)
Property and Constitutive Equations~" I (Phenomena Models & Intensive | Properties) ~]
REVERSE SIMULATION
Design Parameters and Limitations We" (Desired Behaviors & Attributes)
DESIGN TARGETS (Constitutive Variables) gp
(a~
REVERSE PROPERTY REDICTION
Design Parametersand Limitations (Desired Behaviors & Attributes)
(b] Figure 1. Decoupling of constitutive equations for reverse problem formulation
1617
2.2 Model decomposition and reverse property prediction These modelling techniques are useful tools to reduce the complexity involved when trying to simultaneously optimize balance and constraint equations with constitutive and property models. The development of these novel techniques has been described by Eden et al (2004). Although these procedures were created for process development, minor changes allow for application to product design. The main objective of the method is to separate the balance and constraint equations from the often complex and non-linear constitutive property relations. Figure 1 illustrates this decomposition principle by showing how the overall model (a) is divided into two separate models by defining target property variables (b). These target variables are a set of solutions to both the formula balance model and the constitutive property design model. Each mathematical system is solved independent of the other until valid sets of solutions are found that satisfies both networks. This technique is illustrated in the following case study.
3. Case S t u d y - Polymer Film for Nuclear Applications The desire to decontaminate surfaces inside nuclear power plants has been addressed with a number of different products. The implementation of latex-based pealable films has been used for many years. The coating serves to initially "fix" the contaminants in place for containment and ultimate removal. However, power plants have discontinued the use of these products because of their long drying times and expensive disposal costs, in the place of these products, protocol has turned to the use of steam jets to remove the radioactive particles and clean the exposed surface. This method has proven to be ineffective due to a build up of contaminants that, through molecular transport, become airborne and contaminate larger areas. The purpose of this work is to develop an effective and systematic model to synthesize a formulation of a water soluble polymer film coating for radioactive decontamination and waste reduction. This material development involves the use of a polymer matrix that is applied to surfaces as part of the decontamination system in place of the past latex products. Upon mechanical entrapment and removal, the polymer coating containing the radioactive isotopes can be dissolved in a solvent processor, where separation of the radioactive metallic particles occurs. Ultimately, only the collection of filtered solids must be disposed of as nuclear waste. The ability to identify such a product creates an attractive alternative to direct land filling or incineration. In order for the polymeric film to be a viable candidate, it must exhibit the desired performance that previous coatings are unable to. These characteristics include, drying time, storage constraints, decontamination ability, removal behaviour, application technique, coating strength and dissolvability processes.
3.1 Property integration of polymer coating model Identification of an optimized formulation that is suitable for this entire decontamination system requires integration of all the interlacing characteristics of the coating composition that affect the film behaviour. In order to accomplish this, an accurate representation of the system must be developed in order to solve the design parameters in terms of properties only. The representation of the design parameters along with the interactions between them and the overall formula behaviour is given in
1618 figure 2. This model could be solved as a reverse simulation problem using the final coating characteristics as input variables and the final polymer, solvent, and additive selections established as output solutions. The intricacy here is producing an accurate model, as the inherent non-linearity of the property relationships in conjunction with the complex formulation balance equations makes acquiring viable solutions difficult. In order to overcome these obstacles, model decomposition is employed. .............
......
[ |PQ[~ I~'/~S ~'~iO[~ [j
/ , . .....................,,T..................
.......... ............
,r ........................,,(..............
Formula Constraint Equations
/
of Add~ve~
[
0fSc~l'¢~'~t~ ....... i
Pro:due Formulation
%:
Se:k~t:~on Homc, g e a m y
L ~
Target Property Variables
....'i
VT:':
m ~
Design
BIIPParameters & Limits Figure 2. Schematic representation for polymer film design & model decomposition
3.2 Decomposition of polymer film design problem The problem schematic shown in figure 2 is decomposed into three separate parts in order to reduce the complexity of the solution procedure. These subparts are comprised of formula equations, design parameters, and target property values. 3.2.1 Formula constraint equations The formula balance equations are separated into a reverse simulation problem that includes polymer, additive and solvent choices. Among these selections are available synthesis variables that affect polymeric properties such as molecular weight and extent of hydrolysis. With this information included in the model, not only can different polymer chains be compared, but also different variations of the same polymer and polymer blends. The ability to optimize the polymer synthesis as well as the film composition increases the possible formula combinations and improves the chances of acquiring an acceptable optimized formula. The additive options include components that enhance the desired film properties in order to fulfil the necessary constraints from
1619 the target property variables. This assortment of compounds contains wetting agents, surface tension reducers, biocides, cross-linking agents, elastomers, resin hardeners, dyes, pigments and dispersants. The choice of solvents is limited not only by the polymer selection, but also by the application. The list and amounts of volatile solvents allowed to be used on a nuclear power plant floor is extremely limited. The initial concentration of solvent present in the coating is the primary driving tbrce involved with drying time. It is imperative for this part of the overall model to simultaneously optimize the formulation so that target properties are exhibited and the overall film behaviour is superior to current competitor products.
3.2.2 Design parameters The design parameters and limitations represent a compilation of attributes that the final product must exhibit. Because this formulation is intended to fulfil a market niche that already exists, the final formula characteristics are well known. The primary design parameters are the decontamination ability, drying time and redissolvability. The ability for the film to remove contaminates is measured by the ratio of radiation detected divided by the radiation present before the film removal. This numeric value is known as the decontamination factor and is a major selling point that must be equivalent or better than other possible decontamination products and processes. Another parameter where the new formulation must out perform the competing processes is drying time. Nuclear power plant outages are very costly and the schedule is optimized to minimize profit losses. By producing an optimized formula with the customer's major objectives in mind increases the marketability of the product and improves possible sales. The issue of redissolvability mostly pertains to the manner in which the film is disposed of. The current operations in nuclear plants involve the use of many different polymer based products that are sent to processing stations for redissolving and filtering. It is desired that the film can be disposed of by utilizing these same processing procedures. Other constraints include a simple and effective means to apply the coating to the walls and surfaces inside the plant as well as removal techniques. The model's main objective is to determine what intrinsic properties govern the desired performance variables and develop a dynamic set of target properties. 3.2.3 Target property variables The development of a set of target properties allows this model to utilize reverse property prediction to identify the design alternatives. This is accomplished thru experimentation to determine what property ranges equate to final film behaviour. In order to illustrate the modelling techniques presented in section 2, we can simplify the system by assuming that the only major target property in figure 2 is viscosity. This seemingly simple model is decoupled into two separate systems, which is illustrated by figure 1; the chemical makeup equations that produce a given viscosity and the behavioural models which predict how the viscosity affects the design parameters and limitations. By conducting laboratory tests and simulation studies, the optimum fluid viscosity that produces adequate application behaviour can be determined to be a given value, 4000 centipoises for example. This value becomes the viscosity design target of the qualitative prediction model. By implementing the reverse simulation of mixing rules and formula concentration models, a set of viable product formulations that meet the 4000cps design target are determined. These techniques seem unnecessary when
1620 considering only one target property, but when numerous targets are set, these simplification processes are extremely advantageous.
4. Results The ultimate result of this model aided in the development of a product that increases the removal rate of radioactive contaminates by 69% while attaining a 33% reduction in drying time over the current marketed competitors. The finalized product formula will be available through the Orex Technologies Catalogue in Fall of 2005.
............ .
i~
!iiiiii i~iiiiiiiiiii::iii
::::: : ::~ ....
i : ::: :
!i!i;:.~i!ii!ii iiiiii i!i!ii!il!~i
:. . . . .
..i?: ....iili.... ii:il/~ /
..............?
....
i!!!!!i!i!!!!!ii!!!!i!!
! !! !i!!
Figure 4. Carbonparticle encapsulated in the final polymer film formula
5. Conclusions By employing novel model development techniques such as property integration and model decomposition; a complex product formulation development process has been simplified. In this work, these methods were illustrated by addressing a problematic phenomenon in the nuclear power industry. The utilization of these modelling techniques took an industrial idea to full scale testing and production in under 18 months by reducing the number of subsequent laboratory trials.
References E1-Halwagi, M.M., I.M. Glasgow, M.R. Eden and X. Qin, AIChE Journal, Vol 50(8), 2004. Eden, M.R., S.B. Jorgensen, R. Gani and M.M. E1-Halwagi, Chemical Engineering and Processing, 43, 2004. Eden, M.R., S.B. Jorgensen, R. Gani and M.M. E1-Halwagi, Computer Aided Chemical Engineering, 15B, 2003 Finch, C.A. 1992, Polyvinyl Alcohol Developments, Wiley & Sons, Chichester
Acknowledgements The authors would like to acknowledge the support of the National Science Foundation for their support of the Auburn Engineering Technical Assistance Program and Orex Technologies for this opportunity and the financial support to conduct this research.
European Symposiumon ComputerAided Process Engineering- 15 L. PuiNaner and A. Espufia(Editors) © 2005 Elsevier B.V. All rights reserved.
1621
Integration of Planning and Scheduling in Multi-site Plants" Application to Paper Manufacturing Munawar, S.A. a, Mangesh D. Kapadi b, Patwardhan, S.C. a, Madhavan, K.P. a, Pragathieswaran, S. b, Lingathurai, p.b and Ravindra D. Gudi a* aDepartment of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai- 400 076, India. bHoneywell Technology Solution Laboratory, Banerghatta Road, Bangalore- 560076, lndia.
Abstract In this paper, a general multi-level decomposition based framework has been proposed for integration of planning and scheduling in a multi-site, multi-product plant, with applications to paper manufacturing. The problem involves complex issues relating to large-scale production in a hybrid flowshop configuration, decisions relating to minimizing trim losses, while maintaining on-time delivery of orders. Due to these complexities, the overall problem of integrated planning and scheduling is logically partitioned into several levels, depending on the problem size. As followed in other decomposition-based approaches, the upper level models are equipped with appropriate abstractions of the lower level constraints. Also from a reactive scheduling point of view, some pro-active measures are embedded into the multi-level structure. The proposed multi-level decomposition scheme is demonstrated on a representative planning and scheduling problem.
Keywords: Planning, Scheduling, Integration, Decomposition 1. Introduction Integration of planning and scheduling in the process industries has received significant attention in the recent years by practitioners and academicians because of the high economic incentives and the challenges involved. Most of the large-scale multienterprise facilities currently employ some heuristics for this integration and are generally dissatisfied with the resulting inconsistencies in decision-making (Shobrys and White, 2000). Over the last few years, though some progress has been made in this direction tbr development of more superior frameworks for such integration problems, there is a large scope for additional improvements. In the literature there are several works on planning and scheduling. Shah (1998) gives a detailed review and current status on single and multi-site planning and scheduling. However, there has not been much work done in the literature towards the integration of planning and scheduling in the paper industries. Pinar et al. (2002) proposed an agent Author to whom correspondence should be addressed:
[email protected] 1622 based decision support system termed as Asynchronous Team (A-Team) framework for central planning and scheduling of gross root paper industries based on heuristics. The challenges are in terms of the complex issues relating to handling large-scale advanced planning and scheduling problems leading to combinatorial explosion of the problem sizes for centralized decision-making. Moreover, the horizons of interest are broadly different in planning and scheduling models. Hence, decomposition based approaches have been increasingly gaining attention in the recent years. Additionally, in the decomposition based approach, the models at the upper levels must reflect accurate abstractions of the lower levels and should be revised as infrequently as possible when compared to the lower levels. The planning models must be consistent with lower level scheduling models, and the scheduling models must again be consistent with the plant level operation thus achieving the vertical integration. Traditionally, the decisions in an enterprise flow in a top-down manner leaving less degree of freedom at lower levels fbr rescheduling, leading to frequent revision of targets set by the top levels. Embedding contingency measures for integration of rescheduling has been ignored in most of the works published. With this motivation, in this paper an integrated multi-level decomposition based framework has been proposed for efficient integration of planning and scheduling for a multi-site, multi-product plant with applications to paper manufacturing. Productionplanning and scheduling for paper manufacturing in real world environment involves intricate issues related to large-scale production in a hybrid flowshop configuration. Issues related to minimizing trim loss while maintaining on-time delivery of orders need to be addressed. Typical real world problems have about 1000-5000 orders to be manufactured across 5-10 paper machines from 3-6 mills in 1-3 months time (Pinar et al., 2002). The resulting formulation involves solution of mixed integer linear/nonlinear problems with very large number of variables and constraints. Despite the significant progress in the computational resources in the recent years, such large models cannot be solved with the capabilities of the existing solvers. Hence a decomposition based solution approach is necessitated. In this work, we consider a mathematical programming based multi-level framework with minimal heuristics for the above integrated planning and scheduling problem. This is an extension of the earlier work (Munawar et al., 2003; Munawar and Gudi, 2004) but oriented for multi-site plants. This paper is organized as follows. In the next section, we discuss a general multi-level decomposition based framework. Later in section 3, the proposed framework is illustrated for solving the integrated planning and scheduling problem in a paper manufacturing industry, along with a representative case study.
2. Multi-level Decomposition based Framework Consider a general multi-site, multi-product planning and scheduling problem with several plants located in different geographic locations with product demands specified over a multi-period operation. Each product has different site dependent manufacturing/production cost, and depending on the customer location there is also an additional transportation cost involved from the manufacturing location. Furthermore, each site has some inventory cost for products produced earlier than their due date, and a tardiness penalty for products produced later than their corresponding due date. At
1623 each site, a generic hybrid flowshop configuration of various machines is assumed that can be easily simplified to any problem specific topology of series and/or parallel configuration of different stages. The global objectives are minimizing the overall costs discussed above and timely satisfaction of customer orders with minimal impact of the disruptions if any (machine breakdowns etc.), on the plant operation. The latter objective is achieved implicitly through the proposed proactive measures for local attenuation of the plant disruptions leading to infrequent revision of the commitments made to the customers. Based on the inherent, functional decomposition of the global objectives, the overall problem can be traditionally decomposed into two major levels, a primary level for strategic (or longterm) planning over a multi-period operation across multiple sites and a secondary level for tactical (or mid-term) planning and scheduling at each site in each time period. The primary level has multi-period demands over a longer horizon (say 1 year) and has an abstraction of each plant in terms of the average production and inventory capacities. Accordingly, based on minimization of the overall cost mentioned above, the abstract model at this level sets production targets for each plant. Additionally at this level we consider an abstraction of the other production losses that may possibly occur at the lower levels. The production losses could be either the trimming losses in cutting stock problems or the slopping losses during grade changeovers in refinery problems (Munawar and Gudi, 2004). The primary level is revised on a less frequent basis (say monthly/quarterly) to avoid frequent revision of the commitments made to customers. At the secondary level, for mid-term planning and scheduling at each site/plant with detailed plant constraints, the horizon of interest is smaller (1-3 months) catering to less number of customers, and the model here may be revised/updated on a frequent (say weekly/monthly) basis but without violating the global objectives. The lower levels have detailed constraints to account for the production losses mentioned above. Depending on the complexity of the problem these levels may further need to be decomposed as discussed later in section 3.2. From a reactive scheduling point of view, some pro-active measures are embedded into the multi-level structure; such as assuming higher production losses at the top levels; and appropriate relative penalties to some of the cost terms in the objective function. This is motivated towards better flexibility at later stages for reacting to unforeseen plant disruptions.
3. Application to Paper Manufacturing The major decisions in paper manufacturing are order allocation across multiple sites, run formation and order sequencing in each paper machine, trim schedule for minimum wastage of paper and a load schedule for order distribution to various destinations. In this work, we consider decision support for only the first three processes and propose ways of solving the integrated production planning and scheduling problem.
3.1 Paper Manufacturing as a Hybrid Flowshop Facility The superstructure of all the alternate products at any site can be viewed as paper machines for producing different disjunctive mode; i.e. only one paper
production routes for producing different paper a hybrid flowshop facility. For a site with two grades of paper, the paper machine operates in a grade can be produced at a time, and involves
1624 transition time for grade changeovers which might be sequence and machine dependent. Orders of smaller roll dimensions may often need to be further cut on common rewinders (parallel lines) before they are wrapped and packaged for dispatch. 3.2 M u l t i - l e v e l D e c o m p o s i t i o n
The proposed multi-level framework is shown in Figure 1. For small-size problems with fewer customer orders, a two-level decomposition may be adequate as shown in Figure 1(a), while for medium to large-scale problems a four level decomposition, as shown in Figure 1(b), is found to be necessary for obtaining the solution in real time.
Level-1
Z T Level-2
Simultaneous order allocation and sequencing at multiple sites
Simultaneous Trim loss minimization & pattern sequencing
(a) two-levelframework for small-size problems
rI ,
Level-la ,, Order allocation across , multiple-sites
r ,
Level-lb
' Detailed scheduling at each , site (including sequencing) Ak
I
~ Level-2a
', Trim loss minimization
i.
I
r ,, Level-2b
, Optimal sequencing of ', cutting patterns
(b) four levelframework for medium to large-scaleproblems
Figure 1. Proposed multi-levelframework for multi-sitepaper manufacturing In Level-1 problem of Figure l(a), a MINLP formulation has been proposed for simultaneous order allocation and grade sequencing across multiple sites with assumed trim losses, which is later linearized to an MILP after removing the bilinearities. For addressing the complex issues related to large-scale production in a hybrid flowshop configuration at the upper levels, some simplifying assumptions have been made. Generally the production rates in a paper machine are much lower compared to processing in other downstream units. Hence, the order allocation problem is generally assumed to be based on the aggregate properties of the paper machine alone rather than based on the entire production route in the hybrid flowshop. For medium to large-size problems as shown in Figure l(b), the objective at the top sub-level (Level-la) is primarily order allocation (without sequencing) across multiple sites with assumed production losses; while at the next sub-level (Level-lb) the objective is sequencing of grades for each paper machine individually, with penalties for violation of due dates. Before going into the details of the lower level problem (Level-2) we first present the results of the upper levels for a representative problem.
Case Study on Small-size Planning and Scheduling Problem." Consider 4 paper machines at 3 paper mills located in distinct locations for meeting 21 orders placed from 5 different customers. All the MILP models in this work are solved using CPLEX solver on ILOG OPL STUDIO, while the MINLP model is solved using SBB solver on GAMS. When we applied the simple two-level decomposition shown in Figure 1(a), the MINLP problem at Level-1 takes long computational time (more than 1 hr). When the four-level decomposition shown in Figure 1(b) was applied, both the sublevels at Level-
1625 1 together are solved relatively faster to find the order-machine allocation and grade sequencing (for all 4 machines). On each paper machine, for the set of orders assigned to each time slot, the problem at Level-2 involves trim loss minimization and sequencing of optimal cutting patterns. In the literature, typically, the trim loss problems (Level-2a) and the sequencing of the optimal cutting patterns (Level-2b) are solved sequentially (Westerlund et al., 1998; Westerlund and Isaksson, 1998). Due to the current computational limitations, the traditional sequential approach (Level-2a followed by Level-2b) needs to be used for large-scale problems. In this work, it is demonstrated that for small to medium-size problems, the proposed novel approach (aggregate Level-2) shown in Figure l(a) for simultaneous trim loss minimization and sequencing of cutting patterns has more flexibility leading to better customer satisfaction and lower overall costs.
3.3 Simultaneous Trim loss Minimization and Sequencing of Optimal Cutting Patterns Consider the one-dimensional trim loss problem with fixed deckle size of the paper machine that allows variation only in the length of the cutting patterns. Given the problem parameters of the paper machine and winder, along with the data related to the customer orders, the total number of feasible cutting patterns can be enumerated using the explicit procedure listed in Westurlund et al. (1998). The link between the trim loss minimization problem and the pattern sequencing problem is through the use of the common decision variables for selection of optimal patterns and their corresponding optimal lengths. The resulting MILP problem formulation is not presented here due to space limitations. We assume as many time slots as the total number of feasible cutting patterns. Since all the cutting patterns may not be selected at the optimal solution some slots would be empty. (When the number of feasible cutting patterns is large it may lead to combinatorial problems and hence the proposed simultaneous approach is applicable to small to medium size problems, otherwise the sequential approach is recommended). We enforce unique allotment of a pattern to a time slot with the provision for some slots being empty. All the empty slots are pulled towards the beginning of the horizon and the corresponding decision variables are assigned to zero for these slots. The objective function includes penalties for tardiness and under production, in addition to the costs resulting from trim loss and knife changes (due to the transition between patterns).
Case Study." For illustrating the proposed model, consider a set of 7 orders of the same grade assigned to a single slot. For the given problem data, the total number of feasible patterns are enumerated to be 22. Using the trim minimization problem, 7 optimal set of patterns are selected (p5, p9, p14, p17, p 1S, p19 and p22) and the total cost is $20504. Then the pattern sequencing problem for these 7 optimal patterns yields a total tardiness cost of $2438. The overall results for the traditional sequential approach are: % Trim loss : 1.0312 Trim cost : S9899 Under production cost : $9906 Knife change cost : $700 Tardiness cost : $2438 The total cost : $22943 The optimal sequence is: p 17 --) p9 ---)p5 --) p 18 --) p 19 --) p22 --) p 14
1626 When we solve the proposed simultaneous trim minimization problem and pattern sequencing problem, the following output is obtained. 10 optimal patterns are selected. % Trim loss : 1.0313 Trim cost : $9901 Under production cost : $9907 Knife change cost : $1000 Tardiness cost : $1015 The total cost : $21823 The optimal sequence is: p17-) p12 --) p9 ---)p5 --) p21--) p19 --) p22-) pl 8--) p14 --) p7 A comparison of the above results reveals that, though there is an increase in the knife change cost for the 10 optimal patterns selected by the simultaneous approach, there is a drastic reduction in the tardiness costs for the same trim loss and underproduction costs and hence the overall costs for the simultaneous approach are relatively lower. Conclusions
In this paper, the integration of planning and scheduling in a multi-site, multi-product plant is discussed with applications to paper manufacturing. At the lower level a novel simultaneous approach is proposed for the combined trim loss minimization and pattern sequencing problem. Realistically (large) sized industrial problems would bring in further complexities (constraints) and challenges that require novel approaches for decomposition and global solution; this is an aspect of future research. References
Munawar, S.A. and R.D. Gudi, 2004, A multi-level, control-theoretic framework for integration of planning, scheduling and rescheduling, In: 7th International Symposium on Dynamics and Control of Process Systems (DYCOPS-7), July 5-7, 2004, Massachusetts, USA. Munawar, S.A., Bhushan, M., Gudi, R.D. and Belliappa, A.M., 2003, A multi-level, control-theoretic approach to reactive scheduling in continuous plants, In: 4 th Conf. on Foundations Of Computer Aided Process Operations (FOCAPO), 397. Pinar, K., Wu Frederick, R. Goodwin, S. Murthy, R. Akkiraju, S. Kumaran and A. Derebail, 2002, Scheduling solutions for the paper industry, Oper. Res., 50(2), 249. Shah, N., 1998, Single and multisite planning and scheduling: current status and future challenges, AIChE Symp. Ser., 94 (320), 75. Shobrys, D. E. and D. C. White, 2000, Planning, scheduling and control systems: why can they not work together, Comp. Chem. Eng., 24, 163. Westurlund, T., J. Isaksson and I. Harjunkoski, 1998, Solving a two-dimensional trimloss problem with MILP, Euro. J. Oper. Res., 104, 572. Westurlund, T. and J. Isaksson, 1998, Some efficient formulations for the simultaneous solution of trim-loss and scheduling problems in the paper-converting industry, Trans. IChemE., 76 Part A, 677.
European Symposiumon ComputerAided Process Engineering- 15 L. Puigjanerand A. Espufia(Editors) (©2005 Elsevier B.V. All rights reserved.
1627
Review of optimization models in the pollution prevention and control Emilia Kondili a, a Assistant Professor Dept. of Mechanical Engineering, Technological Educational Institute of Piraeus, Greece
Abstract The objective of the present work is to investigate the extent and effectiveness of the implementation of optimization methods for the solution of environmental problems. In order to fulfill its objective, the present work reviews a significant number of scientific / research papers dealing with the application of optimization approaches for the solution of environmental problems, in the areas of air pollution, solid, liquid and industrial waste management, and production integrated pollution control. The review focuses its attention to the identification of the basic problem parameters, the type of the optimization model for each particular problem category and the results obtained. Amongst its various other conclusions, the present work exhibits the contribution of the optimization modeling to the identification of all the characteristics of the environmental problems and their integrated approach.
Keywords: Optimization, Modeling, Pollution Prevention, Mathematical Programming 1. Introduction In many cases the solution of problems related to the environment require decisionmaking and selection between a number of alternatives that need to satisfy a number of technical and regulation constraints. Therefore, in parallel to various other efforts for the solution of the environmental problems, a significant number of scientific works have appeared in the literature, approaching the environmental issues through the development of optimization models and their implementation in practical cases. The objective of the present work is to investigate the extent and effectiveness of the implementation of optimization methods for the solution of environmental problems. In order to fulfill its objective, the present work reviews a significant number of scientific / research papers dealing with the application of optimization approaches for the solution of environmental problems. The review focuses its attention to the identification of the basic problem parameters, the development of the optimization model, i.e. the identification of the optimization criteria that drive the problem solution, the various different constraints that need to be taken into account in each specific type of problem, the algorithms being used for the solution of the optimization models and the results obtained.
1628
2. Optimisation methods and tools Optimisation methods and algorithms have lately become very valuable tools for the solution of a wide variety of complex engineering problems. Two recent excellent review papers of Biegler and Grossmann (2004) and Grossmann and Biegler (2004) analyse and classify the current situation and future prospects of optimisation methods and tools, as well as their applicability to the solution of various practical problems. Mathematical programming and optimization in general have also found extensive use in various types of environmental problems. The reason is that, in these problems, there is very often a need for decision making under conflicting objectives, since there is a number of alternative solutions and the optimal one needs to be chosen. Therefore, a list of mathematical and decision support techniques have been deployed in the past years to aid in forming policies or solving various environment-related design, operation, planning, scheduling and routing problems. The optimization techniques being implemented in the reviewed literature are deterministic and stochastic programming models. The deterministic optimization models range from simple Linear Programming, Mixed Integer Linear Programming, Non-Linear Programming, Dynamic Programming models, as well as multi-objective optimization models, depending on the specific characteristics of the problem under consideration. For problems including uncertainty stochastic programming models, such as Fuzzy linear programming, fuzzy integer programming, Interval linear Programming, are used. The use of multicriteria decision methods in a number of real environmental problems is described by Ladhema et. al (2000). The authors describe the methodology for approaching environmental problems with multicriteria analysis, supporting the view that this formulation provides a comprehensive framework for storing all relevant problem information, makes the requirement for new information explicit and thus supports the most efficient allocation of resources.
3. Optimisation methods in various environmental problems 3.1 General considerations A wide spectrum of environmental problems is solved with optimization methods, such as the environmental process synthesis and design, waste management and minimization, water resources management, energy management with environmental considerations. However, the present work only deals with a rather limited area of environmental problems, focusing its attention to the problems with most interest for the CAPE community (Table 1). Table 1. Environmental problems included in the present work
Air pollution Waste minimisation Environmental synthesis and design Facility location Supply chain with environmental considerations Solid waste management
1629 3.2 Air pollution Mathematical programming models are extensively used in air pollution management literature. Generally, the objective of these models is to optimise the cost of policy decisions with the great majority oriented to minimising the cost of control and removal methods. The main possibilities are the minimisation of the pollutants, the minimisation of the pollutants reduction cost and the minimisation of the pollutants concentration in the most sensitive receptors. The constraints being developed express the conformity to pollution standards. A very comprehensive survey of mathematical programming models in air pollution management is presented by Cooper et al (1996). However, since then, various papers have appeared in the literature, dealing with a number of interesting aspects of air pollution management. For example, Shaban, Elkamel and Gharbi (1996) have developed a Mixed Integer Linear Programming model for the selection of the best pollution control strategy to achieve a given pollution reduction level. The objective of the model is to minimise the total control cost, consisting of operating and investment costs. Various constraints are imposed on the model, including a prescribed pollution reduction level and maximum budget available for investment. The model gives the optimum set of control options along with their optimum set-up times. 3.3 Waste minimisation Wu and Chang (2003) have developed a method and procedure for the optimisation of a textile dyeing manufacturing process in response to the designated waste minimisation alternatives, the new environmental regulations and the limitations of production resources. They use a nonlinear integer optimisation framework. The objective function is the profit maximisation, including benefits from product sales as well as the emission/effluent charge and water resources fees required by new environmental regulations. The constraint set includes capital and labour limitations, equipment availability, demand requirements, water balances and capacity limitations. The optimisation method that is used is based on the Genetic Algorithm and uncertainties are dealt with via an interval analysis. Chakraborty et. al. (2003) introduce a systematic planning methodology for obtaining a long-term waste management strategies for entire batch manufacturing sites. Their work introduces a dynamic view of designing optimal waste management strategies for a planning horizon of 5-10 years. The objective function minimises the net present cost that includes the operating cost, the annualised capital investment and the maintenance costs. The operating cost is obtained as the probabilistic average of the operating cost in the individual waste forecast scenarios. This term takes into account penalties for capacity constraint violations. The problem constraints include corporate-wide budget limitations, special permit constraints, emission trading opportunities, emission limitations. The resulting model is an MILP model. Alidi (1996) proposes a multiobjective optimisation model based on the goal programming approach to assist in the proper management of hazardous waste generated by the petrochemical industry. The analytic hierarchy process (AHP), a decision making approach, incorporating qualitative and quantitative aspects of a problem is incorporated in the problem to prioritise the conflicting goals usually
1630 encountered when addressing the waste management problems of the petrochemical industry.
3.4 Environmental Synthesis and Design Brett et al (2000) believe that the incorporation of environmental sensitivity into process models has not been very satisfactory, mainly because of the difficulty in translating process information to environmental objectives. In their work they propose a methodology according to which the Life Cycle Analysis (LCA) assists in the development of environmental objectives in process design and they use a multiobjective formulation of the process that combines economic objectives with the LCA environmental objectives. A case study of a nitric acid plat has been undertaken to demonstrate their approach. The process is modelled in Hysys to obtain mass and energy information. Goal programming, a multiobjective optimisation technique, has been used to solve the problem. In conclusion, they believe that LCA linked to rigorous process analysis tools allow for explicit considerations to the design decisions. Linninger and Chakraborty (1999) proposed a hybrid methodology for the synthesis of waste treatment flowsheets through a search based superstructure generation step using a linear planning algorithm. Next, a rigorous plant specific policy optimisation is carried out, with a desired performance function, such as treatment cost, and a set of site specific environmental capacity and logistics constraints. 3.5 Facility location Rakas et al. (2004) have developed a model for determining locations of undesirable facilities. It is formulated as multiobjective model, since the problem of locating undesirable facilities faces many conflicting criteria. Mathematical models for the location of undesirable facilities are designed to address key questions, such as how many facilities should be located and how large each facility should be. In general, such problems are multiobjective. The objective functions of the optimisation model express the total cost minimisation and the minimisation of the population opposition to the construction of the landfill in their area. This paper also proposes another way to treat uncertainties in locating undesirable facilities, which is based on Fuzzy Mathematical Programming. Chang and Wei (2000) illustrate a new approach with a view to optimising siting and routing aspects using a fuzzy multiobjective nonlinear integer programming model as a means that is particularly solved by a genetic algorithm. The effective planning of solid waste recycling programs is a very important challenge in many solid waste management systems. One of such efforts is how to effectively allocate the recycling drop-off stations with appropriate size in the solid waste collection network to maximise the recycling achievement with minimum expense. 3.6 Supply chain with environmental considerations Hu et al (2002) present a cost-minimisation model for a multi-step, multi-type hazardous waste reverse logistics system. They develop a discrete-time linear analytical model that minimises total reverse logistics operating costs subject to constraints that take into account such internal and external factors as business operating strategies and environmental regulations. The model that is developed consists of four critical activities: collection, storage, treatment and distribution. The objective of the proposed
1631 model is to maximise the total reverse logistics cost for a given multi-step period, including total collection cost, total storage, treatment, transportation cost for reusing processed wastes and total transportation costs tbr disposing processed wastes. Turkay et al (2003) address the multicompany collaborative supply chain management problem. Fhe proposed approach consists of modelling process units using fundamentals of thermodynamics, conservation of mass and energy and process data, development of an MILP model for the supply chain integration of different process systems and comparative analysis of the results. The problem is solved using ILOG system.
3.7 Solid Waste Management Various deterministic mathematical programming models have been used for planning solid waste management systems. Nema and Gupta (1999) have dealt with the planning and design of a regional hazardous waste management system that involves the selection of treatment and disposal facilities, allocation of hazardous wastes and waste residues from generator to treatment and disposal sites and selection of the transportation routes. They present an improved formulation based upon multi-objective integer programming approach to arrive at the optimal configuration. The objectives addressed are the minimisation of the total cost, which includes treatment and disposal costs and transportation cost, minimisation of the total risk, which includes waste treatment and disposal risk as well as risk involved in waste transportation. The problem constraints are mass balances of wastes, allowable capacities for treatment and disposal technologies, waste-treatment technology compatibility constraints and waste-waste compatibility constraints. The resulting model is an MILP problem. Costi et. al (2003) have developed a Decision Support System (DSS) designed to help decision makers of a municipality in the development of incineration, disposal, treatment and recycling integrated programs. The main goal of the proposed DSS is to plan the MSW management, defining the refuse flows that have to be sent to recycling or to different treatment or disposal plants and suggesting the optimal number, the kinds and the localisation of the plants that have to be active. The DSS is based on a decision model that requires the solution of a constrained non-linear optimisation model where some variables are binary and other ones are continuous. The objective function takes into account all possible economic costs, whereas constraints arise from technical, normative and environmental issues. Huang et. al (2001) have applied an integrated solid waste management system based on inexact fuzzy stochastic mixed integer linear programming to the long term planning of waste management activities in the city of Regina. Their model can effectively reflect dynamic, interactive and uncertain characteristics of the solid waste management system in the city. Their approach is able to answer questions like the appropriate reduction goals, the waste flow allocation pattern, level of reliability and ways to handle rapid increase of waste generation.
4. Summary and conclusions The need for effective optimisation methods that incorporate concepts of efficient resource use and environmental concern is becoming more and more urgent as the
1632 environmental situation deteriorates. This paper offers a review on optimisation methods that have been used for the solution of environmental problems and reviews a number of papers in specific environmental problems. Depending on the characteristics of the treated problem, different optimization models and optimization algorithms are used. Critical success factors are the problem size and the reliability of various process models that are used. In any case, one of the most significant contributions of the optimization modeling is the identification of all the characteristics of the environmental problems and their integrated approach. References Alidi Abdulaziz S., 1996, A multiobjective optimization model for the waste management of the petrochemical industry, Appl. Math. Modelling, Vol. 20 Biegler, L. T., Grossmann, I. E., 2004, Retrospective on Optimisation, Computers and Chemical Engineering 28, 1169-1192 Brett A., Barton G., Petrie J., Romagnoli J., 2000, Process synthesis and optimisation tools for environmental design: methodology and structure, Comp. and Chemical Engng 24, 1195-1200 Chakraborty A., A.Malcolm, R. D. Colberg, A. Linninger, 2003, Optimal waste reduction and investment planning under uncertainty, Computers and Chemical Engineering 2003 Chang N-Bin, Y.L. Wei, 2000, Siting recycling drop-off stations in urban area by genetic algorithm-based fuzzy multiobjective nonlinear integer programming modelling, Fuzzy Sets and Systems 114, 133-149 Cheng S., C.W. Chan, G.H. Huang, 2003, An integrated multi-criteria decision analysis and inexact mixed integer linear programming approach for solid waste management, Engineering Applications of Artificial Intelligence 16, 543-554 Cooper, W.W., Hemphill, H., Huang, S.L., Lelas, V., Sullivan D.W., 1997, Survey of Mathematical Programming models in air pollution management, 96, 1, 1-35. Costi P., Minciardi, R., Robba, M., Rovatti, M., Sacile R., 2003, An environmentally sustainable decision model for urban solid waste management, Waste Management 24, Issue 3,277-295 Grossmann, I. E., Biegler, L. T., 2004, Part II. Future Perspective on Optimisation, Computers and Chemical Engineering 28, 1193-1218 Hu Tung-Lai, Jiuh-Biing Sheu, Kuan-Hsiung Huang, 2002, A reverse logistics cost minimization model for the treatment of hazardous wastes, Transportation Research, Part E, 38 457-473 Huang G.H., N. Sae-Lim, Z. Chen and L. Liu, 2001, Long-term planning of waste management system in the City of Regina- An integrated inexact optimisation approach, Environmental Modelling and Assessment 6, 285-296 Ladhema R., Salminen P., Hokkanen J., 2000, Using Multicriteria Methods in Environmental Planning and Management, Environmental Management, 26, 595-605 Linninger A. A., Aninda Chakraborty, 1999, Synthesis and optimisation of waste treatment flowsheets, Computers and Chemical Engineering 23, 1415-1425 Nema Arvind K, S.K. Gupta, 1999, Optimization of regional hazardous waste management systems: an improved formulation, Waste Management 19, 441-451 Rakas J., Theodorovic D., Kim, T., 2004, Multi-objective modeling for determining location of undesirable facilities, Transportation Research Part D 9, 125-138 Shaban H. I., A. Elkamel, R. Gharbi, 1997, An optimization model for air pollution control decision making, Environmental Modeling & Software, Vol. 12, No. 1, pp. 51-58 TOrkay Metin, Cihan Orug, Kaoru Fujita, Tatsuyuki Asakura, 2003, Multi-company collaborative supply chain management with economical and environmental considerations, Comp. and Chemical Engineering Wu C.C., N.B. Chang, 2003, Global strategy for optimising textile dyeing manufacturing process via GA-based grey nonlinear integer programming, Comp.and Chemical Engng 27, 833-854
European Symposiumon ComputerAided Process Engineering- 15 I,. Puigjaner and A. Espufia (Editors) :CI:,2005 Elsevier B.V. All rights reserved.
1633
Models for integrated resource and operation scheduling Alain Ha~'ta*, Martin Tr~panier b and Pierre Baptiste b a Institut National Polytechnique de Toulouse, E N S I A C E T - LGC 118 route de Narbonne 31078 Toulouse cedex 4, France b Ecole Polytechnique de Montrdal C.P. 5079 Succ. Centre-Ville, Montrdal (Qudbec), Canada H3C3A7
Abstract This paper deals with energy and human resource constraints in scheduling models, it outlines the influence of these resources, and the necessity to account for them in scheduling models. A parallel view of these resources is presented, and their characteristics are illustrated in the case study of a tubing plant.
Keywords: scheduling, energy, human resources, integrated models.
1. Introduction As a part of production management, scheduling has been widely addressed in the process engineering literature (Pinto and Grossmann, 1998). According to Pinedo (Pinedo, 2002), "scheduling deals with the allocation of scarce resources to tasks over time. It is a decision-making process with the goal of optimizing one or more objectives." Most scheduling research deals with sequencing problems, assuming that processing times are constant and known. Many authors noticed that, unfortunately, those theoretical results are hardly applied in real situations. Sometimes processing times can be variable, due to the scheduling itself. This happens when a resource is shared between some processing stages: operator working simultaneously on several machines, limited power provided to several energyconsuming equipments, etc. Processing times then depend on the operator (availability, efficiency, priority choices), the energy provided, and so on. Consequently, processing times and scheduling decisions are embedded, due to "secondary" resources essential to know the processing behaviour. These resources, generally considered at a real-time control level, have a significant influence on the scheduling objective.
2. Scheduling with secondary resources Introducing secondary resources in scheduling models means that these resources have specific constraints (e.g. a limited capacity) and/or influence on the objective function (e.g. cost). In these cases, scheduling is not restricted to task sequencing.
Author/s to whom correspondence should be addressed:
[email protected] 1634 The Resource Constrained Project Scheduling Problem (RCPSP) can be view as a general frame for these problems. A limited amount of renewable resources is shared between the operations. Each operation needs a fixed amount of each resource to be performed. Operation start and end times are then necessary to determine the cumulative resource needs at any time. Precedence constraints represent the sequence of operations. Solving approaches take advantage of problems specificities: few precedence constraints (project scheduling), disjunctive resources (job shop scheduling). However, the problem remains complex. Another solution is to separate operation and secondary resource scheduling in two steps (Boukas, Haurie and Soumis, 1990). When operations can be performed with a variable amount of resource, processing times are a function of this amount. Resource assignment decisions set the amount of resource for each operation at any time. Integrated scheduling must then solve simultaneously three problems: sequencing, start/end times determination and secondary resource assignment over time (Daniels and Mazzola, 1994).
3. Energy in scheduling models Energy may be an important part of production costs in the process industry. However, it has been often considered as an uncompressible cost, or hidden in a global bill without seeking for the origin of the consumption. Recently, some research in sustainable development addressed this problem, for strategic and tactic decisions: energy exchange between plants (korhonen, 2002), long-term maintenance scheduling for better energy utilization (Cheung and Hui, 2004). Some years earlier, Kondily et al. (Kondily, Shah and Pantelides, 1991) presented an algorithm for the planning of multiproduct energy intensive continuous operations. For short-term decision, Corominas et al. (Corominas, Espufia and Puigjaner, 1994) studied energy-saving by heat exchange between operations.
3.1 Processing time In scheduling problems, energy is treated as a renewable resource, shared by the process units. Capacity constraints represent the amount of energy available at any time (e.g. maximal power). Processing times may depend on the amount of resource provided. Continuous models (linear or not) describe processing time evolution, according to the equipment unit, the product and the operation. In (Corominas, Espufia and Puigjaner, 1994), the authors notice an energy-time trade off. Cycle time variations are due to decisions on operation start times, taken to optimize heat exchanges by operation synchronization. When processing time depends on the energy provided, another type of decision appears: assignment decisions.
3.2 Energy assignment Energy delivered to the units varies over time according to operation needs and assignment decisions. Scheduling aims at determining the assignment, along with operations start/end times and operation sequence, which give the best objective. Assignment models rely on the energy evolution: evolution on the time axis (when does the energy value change?) and on the values axis (how does it change?). For time evolution three policies are possible: • Free change: the energy provided to the units can change continuously;
1635 • Periodic change: energy delivery is re-evaluated at each period; • Event change: for example, the configuration changes after the end of an operation. These policies may be combined to fit with the process behavior, but this induces more complex models. A periodic approach with sufficiently small periods can be a satisfying way to represent in a same model the three policies. Energy value evolution also obeys to different constraints, according to equipment characteristics. For example, overall energy provided to the process may not increase too rapidly. Similarly, for a single unit, energy increase may be bounded, involving a continuous shape to the energy evolution curve.
4. H u m a n resources in s c h e d u l i n g m o d e l s Even though human resources (HR) are more important in manufacturing, they can have a significant action in the process industry. Due to variations of the demand, flexible organizations induce both more complex tasks and more important HR costs. Some research present scheduling approaches, integrating human resources, for parallel machines (Chen, 2004, Daniels, Hoopes and Mazzola, 1996), and flow shops (Daniels and Mazzola, 1994, Daniels Mazzola and Shi, 2004), where processing times vary according to the number of operators allocated to the tasks.
4.1 Processing time HR are renewable resources, but the capacity is not constant: operator availability varies with shifts, breaks and days-off. We identify three situations where processing times vary due to HR: • When an operator can run several machines. His work is shared between these machines and consequently productivity decreases on each machine. Various operating modes can be defined, to improve the productivity of one machine or another. • When work posts need several operators to run. The number of operators assigned to a work post determines the productivity of this post. • When productivity varies with skill or experience (or learning, etc.). Then individual assignment has an influence on processing time. Except for fatigue and learning, discrete models represent processing time variations, according to assignment and operating mode choices.
4.2 HR assignment In theory, the three change policies presented for energy are applicable. However, periodic change (at rest or lunch breaks) and event change (end of operation) are more realistic. These changes affect the number of operators at each work post, or the number of machines assigned to an operator (the workshop configuration), and the individual assignment, according to skill, experience, etc. Finally, they affect the operating modes.
4.3 Personnel scheduling HR are subject to legal constraints and specific agreements on the work duration, schedule, rest, etc. These constraints introduce interruptions, delays in some operations. Many research deals with this topic, but few approaches integrate it into scheduling
1636 (Mercier, Cordeau and Soumis, 2003). These approaches generally consider a discrete time horizon, and use column generation to deal with these problems.
5. Case study The case study is a tubing plant in the Montreal area. The plant is divided in three main departments: • Foundry: native and recycled metal is melted in induction melting furnace. Then, it is cast in individual billets and stored for further processing. • Drawing mill: billets are heated and drawn into bars. • Pipe-tubing: billets are heated and extruded to make pipes of different sizes, shapes and lengths. These melting and heating processes use a huge quantity of energy: electricity, natural gas and steam. Electricity expenses account for more than half the annual energy costs for the plant. Non regular power consumption peaks occur and cause high electricity bills. The subscription is 10 700 kW, while the average consumption power is about 65% of subscription. However, consumption along the day is highly irregular, leading to overspendings. Figure 1 shows the number of overspendings during the day. There are evident cuts at shift changes (7h00, 15h00 and 23h00) and break periods.
,4] 12
10 8 6 4 2 0
0 h O0
6 h O0
12 h O0
18 h O0
0 h O0
Figure 1. Number of overspendings (mean values between 01-01-2002 and 29-03-2003) Our goal is to limit these overspendings. A better synchronization of the furnaces would bring more regular electricity consumption and less power peaks, resulting in lower electricity costs. The following linear model minimises the electricity bill for the foundry. It is based on a formulation of the RCPSP (G61inas, 2004). There are m furnaces to perform n fusion operations. We assume that operation assignment to the furnaces and sequence on each furnace are known. Job j is composed of three consecutive operations: loading (duration aj), fusion (duration function of the power provided to the furnace) and unloading (duration bj). When fusion is completed, a minimal power Pwait is provided to the furnace until unloading. Loading and unloading are performed by an operator. The number of operators is limited to R. Energy consumption and overspendings are estimated by the supplier every 15 minutes. The horizon is divided in U periods of 15 min. Each period u is subdivided in N steps, so that the horizon is also divided in N. U steps. Period u starts at time t, = N . u .
1637 Nomenclature
Due date of job j Release date o f j o b j .
4
r/ X .t
.I
yj
t
Ai l!
e~
~f jl l
(l'c[l'n]).
= 1 if the loading operation of job j begins at time t or before.
ewi
=1 if the unloading operation of j o b j begins at time t or before. Set of jobs assigned to filmace i. Precedence links of Ii jobs. Ai = {(/l,j:) jl precedesje in i}. Energy necessary to complete operation j at time t,,. Energy necessary for job j.
ii
Pnlitl~
Pmax
Energy assigned to furnace i for the fusion of job j E li during period u. Energy spent in furnace i during period u, waiting for unloading job j. Mirdmax power in furnace i. Power in furnace i waiting for unloading. Energy consumption during period u. Overspending during period u.
Pwait
OVu
Power subscription
Constraints
Vt c [O ,'4- bj- @-2] v t ~ [,:;+~; • 4 - b,.-2] Vt _< t) -1 V t >- di--b/ . . - a; V t < t)+aj-1 . , Vt _> di-b/
(1)
x/+ / > - - x' ,]
(2)
.,V1/ + / > F/
(3) (4) (5) (6) (7)•
x.'1 = 0 r.'- 1 -.i y/- 0 .,v - ' = l xJ .('-"j) ->- .v.J
W, v t e [r/+a, • 4 - bj-/]
(8)
x / sp,,-1,1.P or,, > 0 Xj.I e F. l
{0,1 } .~ E {0,1}
el'>_ 0
Vu e [O,U- 1] Vue[O,U-1] vj, v t ~ V; ; 4 - b / - , j - / ] vj, v t ~ [,~;+a; • 4 - bj-/]
e.ff'>_ 0 ew/'_> 0
vj, v u E [ 0 ; U-l] Vj, Vu c [ 0 ; U-l] Vj, Vu c [ 0 ; U-l]
sp,, >_ 0
Vue[O,U-1]
Energy consumption during period u. Overspending during period u. Binary variables Continuous variables.
1638
We wish to minimise the energy bill, function of subscription P, consumption overspendings or,,: min(f.P
sp, and
+ f2.~. sp. + f3.~-'~ ov.) II
It
This basic model can be modified: operator availability could vary with time (lunch, rest), subscription P could be variable so the model would choose the best subscription to minimise the bill, etc. A Constraint Programming formulation could be used for the cumulative constraints (15), replacing the numerous variables x/and y / b y the loading and unloading operation start times.
Conclusion This paper outlines the importance of secondary resources in scheduling. Energy and human resources are influent on processing times and production costs. Their assignment may change during processing, in order to provide the resources to the operating units. Accounting for these resources in scheduling is still a challenging problem. References Baptiste, P., M. Trepanier, S. Piraux, S. Quessy, 2004, Vers une int6gration de la gestion des ressources dans le pilotage des op6rations. Boukas, E.K., A. Haurie, F.Soumis 1990, Hierarchical approach to steel production scheduling under a global energy constraint, Annals of Operations Research, 26, 289-311. Chen, Z.-L., 2004, Simultaneous job scheduling and resource allocation on parallel machines, Annals of Operations Research, 129, 135-153. Cheung, K.-Y., and C.-W. Hui, 2004, Total-site scheduling for better energy utilization, Journal of Cleaner Production, 12, 171-184. Corominas, J., A. Espufia and L. Puigjaner, 1994, Method to incorporate energy integration considerations in multiproduct batch processes, Computers and Chemical Engineering, 18 (11/12), 1043-1055. Daniels, R.L., B.J. Hoopes and J.B. Mazzola, 1996, Scheduling parallel manufacturing cells with resource flexibility, Management science, 42 (9), 1260-1276. Daniels, R.L., and J.B. Mazzola, 1994, Flow shop scheduling with resource flexibility, Operations Research, 42 (3), 504-522. Daniels, R.L., J.B. Mazzola and D. Shi, 2004, Flow shop scheduling with partial resource flexibility, Management Science, 50 (5), 658-669. G61inas, S., 2004, Probl6mes d'ordonnancement, Ph.D. thesis, Ecole Polytechnique de Montr6al. Kondily, E., N. Shah and C.C. Pantelides, 1991, Production planning for the rational use of energy in multiproduct continuous plants, European Symposium on computer Aided Process Engineering, ESCAPE-2. Korhonen, J., 2002, A material and energy flow for co-production of heat and power, Journal of Cleaner Production, 10, 537-544. Mercier, A., J.-F. Cordeau and F. Soumis, 2003, A computational study of Benders decomposition for the integrated aircraft routing and crew scheduling problem, Tech. report G2003-48, Les cahiers du GERAD. Pinedo, M., 2002, Scheduling. Theory, algorithms and Systems, Prentice Hall. Pinto, J.M. and I.E. Grossmann, 1998, Assignment and sequencing models for the scheduling of process systems, Annals of Operations Research, 81,433-466.
European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espufia (Editors) © 2005 Elsevier B.V. All rights reserved.
1639
Automated Process Design Using Web-Service based Parameterised Constructors Timo Seuranen I *, Tommi Karhela 2, Markku Hurme 1 1Helsinki University of Technology Laboratory of Chemical Engineering and Plant Design P.O. Box 6100, FIN-02015 HUT, Finland 2VTT Industrial Systems P.O. Box 1301, FIN-02044 VTT
Abstract This paper introduces a web-service based approach in conceptual process design, parameterised constructors, which are able to construct process and initial data for control system configuration. Constructors use unit process or larger sub-process templates readily available in a plant model library. The templates consist of upper level process structures, control descriptions and detailed process structures. Thus, the preliminary process design can be defined in a more general level and as the design process proceeds, more accurate models ('e.g. PI and automation diagrams, simulation models) are composed and used. Definitions of a common data model are also discussed.
Keywords: Conceptual
process design, fiamework, plant model, process life-cycle
parameterised
constructor,
web-service
I. Introduction Open extensibility for value-added services is becoming an essential issue in information management during all phases of process life cycle, from process design to demolition. The progress in information technologies offers possibilities for new kind of integration of process design systems, simulation tools and different value-added services such as dimensioning tools and intelligent constructors. The new value-added services are implemented as web services. A common data model, manipulated through web service interfaces, links and reflects the different requirements of the process and automation design, delivery project and plant operation and maintenance. The objective of this paper is to introduce a value-added service applicable to construct a process and a control system configuration. In practice, the processes consists of almost alike structures. However, template based reuse does not solve the whole design problem because the modifications may be laborious. Thus more intelligent software components, parameterised constructors, are needed.
*Corresponding author:
[email protected] 1640
2. Design support systems for conceptual process design In recent years, numerous approaches have been developed to support the activities in chemical process design. In this chapter, a few new methods are presented. Rodriguez-Martinez et al. (2004) have represented a proposal of a multi-model knowledge representation to be used within a retrofit methodology for chemical processes. The retrofit methodology consists of four steps: data extraction, analysis, modification and evaluation. The use of structural, behavioural, functional and teleological models of process equipment/devices allows the designer to work with a combination of detailed and abstract information depending on the retrofit step. Marquardt and Nagl (2004) have studied the early phases of the chemical process design lifecycle, the conceptual design and front-end engineering. The research issues were development of an integrated information model of the design process, a number of innovative functionalities to support collaborative design, and a-posterior integration of existing software tools to an integrated design support environment. Efficient networking emphasises the need to have a common data model. In different process design phases of the process life cycle, several interest groups interact and need to exchange information between each other. Global CAPE-OPEN is a project for standardising communication between components in process engineering, leading to the availability of software components offered by leading vendors, research institutes and specialised suppliers. This will enable the process industries to reach new quality and productivity levels in designing and operating their plants (CO-LaN, 2005). Open issues of information modelling are also discussed by Schneider and Marquardt (2002) and Bayer and Marquardt (2004). They have developed a conceptual model framework CliP, which holds solution approaches for the integrated representation of information and work processes, the description of documents as carriers of data, and the integration of existing data models. Clip can also serve as an integration basis for existing information models. Because design processes are highly creative, many design alternatives are explored, and both unexpected and planned feedback occurs frequently. Therefore, it is difficult to manage the workflows in design processes. One approach to manage design processes is the web-service framework, which also supports the progress of a new kind of design practice (Kondelin et. al., 2004).
3. Web-service framework In order to achieve tool integration for the whole process plant life cycle, a domain specific framework specification is needed. The specification takes into account the software architectural aspects and the variety of existing production related information systems that end users have. Compared to the use of separate systems, the proposed service framework provides • a common user interface and knowledge presentation • a common way to extend the existing systems with new value-added services The framework also enables discovering and binding of the services by service requestors. It thus makes it viable to construct, compose and consume software component based web services, which will add domain specific value.
1641 Life cycle information management is a common concern in research and development activities today. The issue is addressed from different viewpoints in several national and international projects. All these activities support the need of a generic framework for information management. The framework can be divided into core services, framework services and value added services. The interfaces of core services and framework services are defined in the framework specification while the interfaces of value added services are not fixed beforehand. Core services represent legacy systems in the architecture such as process design systems, simulators or control systems. The most important core service from the viewpoint of the case of this paper is the plant model core service. The plant model service contains information that is accumulated in design time, updated and specified in operational phase, and used by various services of the framework during various life cycle phases (Kondelin et. al., 2004). 3.1 Common data model of the web-service framework
A common data model (a plant model) offers possibility for transformations between different application software attached to the framework. For example different management, design and simulation tools are used at different stages of the process life cycle and many of them are incompatible. The plant model is actually a domain specific meta-model that describes how object types are defined. Object types are created by defining plant object types, property types, and relation types according to the meta-model. In addition, relation rules that restrict relations between objects and properties are defined. Object types describe the common taxonomy for plant object instances. In the framework, instances are represented and transferred as XML fragments that conform to the plant data model, which is defined by utilizing XML Schema type definitions (Kondelin et. al., 2004). In the case described in this paper, there are four different object types depicted in Figure 1. The Conceptual function type represents upper level functions of some kind, such as pressure change. The Constructional function type represents more specific functions analogous with objects in a PI-chart. Conceptual functions may contain several constructional functions. Base object type :
Represents:
I
Conceptual function
I
Broader requirement specifications i.e. requirements for pressure change
I
Constructional function
I
Design knowledge An object in a PI -chart i.e. requirements for pumping
Product
I
Product specific information i.e. pump model A from supplier B and its properties
I
Individual
Information related to individuals i.e. pump C in operation at plant D
Figure 1. Base object O~pes
1642 The Product type realizes the functionality of the Constructional function type i.e. an equipment type. The Individual type represent equipment individual (e.g. pump A in plant X).
3.2 Parameterised constructors Parameterised constructors can be applied to construct process and produce initial data for configuration. They use unit process templates and larger sub-process readily available in a plant model library. The templates consist of upper level process structures, control descriptions and detailed process structures. Parameterised constructors are used to: • Generate process structures and/or parts of the processes. • Intensify routine process design tasks. • Generate operational descriptions. Based on the loop type descriptions detailed initial data is generated for control engineers for design purposes, operation information for operators is also given. • Integrate operability and flexibility considerations into the process synthesis procedures. The benefit of using constructors is that the preliminary process design can be at first defined in a more general level. As the design proceeds, more accurate models (e.g. PI and automation diagrams, simulation models) are used. Unit processes and equipment models are defined to the plant model library and based on the user selections the plant model is dynamically created. The constructors also generate control scheme according to the user's selections and include it into the plant model. As a result, detailed operational descriptions are generated and are readily available to the control system supplier for configuration.
3.3 Process templates Similar process structures are often used in the design of processes. Existing design knowledge, like upper level process structures, automation diagrams and detailed process structures, is stored in the templates. They are defined to whole plant models, unit process models and equipment models, and stored in the plant model library. Different templates can be defined for the same process structure. Templates can also be differently equipped depending on the purpose of the design task. The templates in the plant |brary are updated when new design concepts, like new and better technical solutions or process improvements, are developed.
4. Case study: Fibre Refining Process The fibre refining process is a part of a stock preparation department in the paper plant. Typically, stock preparation consists of several refining lines, which produce different stock to the paper machine. Refining is one of the most important stages in raw material affecting the running of paper machine and especially the paper properties. Typically, there are two or three refiners in a series in a production line supplying one paper machine. Possible process design tasks are the following: 1. Utilize existing similar design concepts (old design documents) 2. Create new design concept 3. Equipment delivery
1643 4. Control system delivery 5. Define service and maintenance routines 4.1 Definition of plant object types
Before an engineering project, a set of object types is defined. In many cases, previous, well-established types can be re-used. The object types of the plant model are described in Section 3.1. The initial data and parameters for the conceptual model are derived from basis of design i.e. requirement specifications (raw materials, products, capacity, consistency, power demand, etc.). Conceptual models o f processes or sub-processes are also generalised in three sections: pre-treatment (raw material purification, initial feed), primary treatment (reaction, refining) and post treatment (product separation, recycle, discharge). Application-wide conceptual functions are derived from those generalized functions. An example of conceptual object type, Short Fibre Line, in which the essential properties (e.g. capacity, furnish, consistency) of the fibre line are defined, is presented in Table 1. The Short Fibre Line object type also includes information about unit processes it is composed of. The constructional, product and individual object types are defined in the similar way depending of accuracy of design. Fable 1. Short Fibre Line object type. i
Short Fibre Line property Raw materials (conceptual Products function Capacity type) Consistency Initial Feed Feed Refining Recycling Discharge
|
type enuln enum double double boolean boolean boolean boolean boolean
i
property set description design list of raw materials design list of products design admt/d, bdkg/min. design percentage of solids design feed from pulper design pre-processing design primary processing design post processing design feed blending chest
4.2 Use case: Design a new process concept
The fibre line design process begins with definition of functions in the conceptual level. First, the initial data of the refining process is defined. The initial data includes definition of stock to be produced, capacity of the refining line, specific refining energy, number of refiners, and connections of refiners (parallel/series). At this stage the upper level templates, from which the refining line is composed, are chosen. The upper level templates are e.g. Feed, Refining and Recycle. Depending on user's input and selections, the conceptual model is further composed by the constructor. The user can define what type of control loops (e.g. liquid level control, flow rate control)these functions are equipped with. When the conceptual plant model is sufficiently defined, the constructor begins to compose the constructional plant model based on user's selections. Constructional and control system hierarchies and their component type instances are dynamically composed and the suitable unit process templates are chosen from the plant model library. Unit process templates contain P I - a n d automation diagrams in SVG graphic-format. The constructional model can be disaggregated in very detailed level, e.g. every single pipeline component can be modelled.
1644 Operational description definitions i.e. loop type description of commonly used control systems are readily defined in the plant model library. The user selects and checks initial information for control system design, e.g. which kind of control structures is used. The constructor ensures that the operational description e.g. of liquid level control of the pulp tower is transformed to an automation schema, which is used by the automation system supplier. When the constructional plant model is defined, the user can transform the plant model to simulation service. Equipment selections and dimensioning, different operation value studies and mass and energy balance calculations are made in the simulator. After simulation the plant model is updated.
4.3 Hierarchies of the plant model During an engineering project, object types are instantiated and the plant model is constructed in different hierarchies. From web-service framework viewpoint, each hierarchy is a different view to the plant model. The constructors ensure that hierarchies, objects and their relations remain consistent. The fibre line upper level conceptual model hierarchy is formed based on the user selections when defining the requirement specifications for the process. After the conceptual modelling is finished, i.e. the process designer continues to the next design step, the constructional model hierarchy is derived by the constructor. The structure of the constructional hierarchy is based on the user's selections in the conceptual design phase. Product hierarchy is formed based on ~luipment models. Individual hierarchy consists of e.g. equipment operating in the plant. Conclusion In practice, processes are often designed based on previous solutions and using almost similar unit process structures. Routine process and control system design can be intensified using process templates readily defined in a plant model library and parameterised constructors. This approach also supports chance of design practice so that one designer will be responsible for all the design tasks of a certain sub-process. The web-service framework, which is able to manage all the information during process life cycle, and the common plant model give an opportunity for the integration of process and control system design, simulation, operation and maintenance and plant concept modelling. This means that any plant-modelling task is not a separate duty but an integrated part of information management in a plant delivery project.
References Bayer, B., W. Marquardt, 2004, Towards integrated information models for data and documents, Comp. Chem. Eng., 28, 1249. CO-LaN, 2005, The CAPE-OPEN laboratories network. Available online at http://www.colan.org/. Kondelin, K., T. Karhela, P. Laakso, 2004. Service Framework Specification for Process Plant Lifecycle, VTT Research Notes 2277. Marquardt, W., M. Nagl, 2004, Workflow and information centered support of design processes the IMPROVE perspective, Comp. Chem. Eng., 29, 65. Rodriguez-Martinez, A., I. Ldpez-Ar6valo, R. Bafiares-Alcfintara and A. Aldea, 2004, Multimodel knowledge representation in the retrofit of processes, Comp. Chem. Eng., 28, 781. Schneider, R., W. Marquardt, 2002, Information technology support in the chemical process design lifecycle. Chem. Eng. Sci., 57, 1763.
European Symposiumon ComputerAided Process Engineering- 15 L. PuiNanerand A. Espufia(Editors) ~')2005 Elsevier B.V. All rights reserved.
1645
Integrated Design of Optimal Processes and Molecules: A Framework for Solvent- Based Separation and ReactiveSeparation Systems Athanasios I. Papadopoulos and Patrick Linke* Centre for Process and Information Systems Engineering School of Engineering, University of Surrey GU2 7XH, Guildford, Surrey, U.K.
Abstract The presented work addresses the integrated design of solvent molecules with separation and reactive-separation process systems. The proposed design philosophy relies on extensive structural optimization both at the solvent and process synthesis stage and allows the identification of solvent molecules based on process performance criteria, it employs multi-objective optimization technology in order to capture the manifold trends and trade-offs characterizing the solvent design space, while avoiding the introduction of unnecessary biases or user defined assumptions. The obtained solvent design information is effectively incorporated into the process synthesis stage through the use of data mining techniques in the form of clustering. The process synthesis framework is sufficiently flexible to accommodate for separation or reactiveseparation superstructures of the most general type. The presented method is illustrated through examples on the design of solvents for liquid-liquid extraction, gas-absorption, extractive distillation and extractive fermentation processes.
Keywords" Solvent synthesis, Reaction- separation process synthesis, Multiobjective optimization, clustering
1. Introduction The design philosophy generally followed in computer aided molecular design (CAMD) solvent synthesis involves screening for solvent molecules based on pre-specified thermodynamic property objectives and constraints that are expected to have a positive impact in process performance (Marcoulaki and Kokossis, 2000a). Clearly, following this approach the synthesis drives involved in process synthesis are misrepresented and the results are prematurely biased towards presumably optimal options. In contrast, methods that facilitate the integrated CAMD solvent and process synthesis by accounting for process and solvent design interactions have also been proposed (Stefanis and Pistikopoulos, 1998; Hostrup et al., 1999). The design philosophy followed by these methods involves screening for solvent molecules based on prespecified property targets. The molecules meeting these targets are further screened with regards to their process performance either by participating in process simulation or Author to whom correspondence should be addressed:
[email protected] 1646 process optimization, in these cases sub-systems of the overall system are targeted, thus the results are liable to assumptions regarding the size of the solvent-process design space. On the other hand, some methods (Marcoulaki and Kokossis, 2000b; Wang and Achenie, 2002; Linke and Kokossis, 2002) propose the simultaneous optimization of the formulated solvent-process superstructure which may involve separation and reactive separation processes. The enormous amount of solvent-process design options and the complexities caused by the non-convexities of the employed models introduce low confidence with regards to the optimality of the obtained results. This work addresses the previously presented limitations through a generic and systematic methodology that will robustly determine performance targets for integrated solvent and separation/reaction-separation process systems. Based on our previously presented work (Papadopoulos and Linke, 2004) multi-objective optimization is used at the solvent design stage in order to identify optimum solvent candidates without a priori excluding options that will potentially be useful at the process design stage. The obtained solvent design information is systematically introduced into the process synthesis stage through the efficient exploitation of this information using a data mining technique in the form of clustering. This work focuses on the development of an effective clustering strategy as well as on the exemplification of the proposed framework through extensive solvent-separation and solvent-reaction-separation synthesis cases.
2. Synthesis of solvent-separation processes
and solvent-reaction-separation
2.1 Multi-objective CAMD solvent synthesis-Overview In the proposed unified framework for solvent and process design CAMD solvent synthesis is performed using multiple objective optimization (M.O.O.) technology (Papadopoulos and Linke, 2004a). This formulation of the optimization problem allows unnecessarily premature assumptions about the process requirements to become redundant as each objective is treated independently, freed of artificial constraints. While the interactions among a variety of objectives are thoroughly explored, the optimization results in a comprehensive set of solvents that represents molecules with a broad range of structural, physical and economic characteristics regardless of the process task in which they will be utilized. This design philosophy allows all the underlying trends and trade-offs amongst the properties of the candidate optimal molecules, as well as the structure- property relations to be revealed. The design information included in the obtained solvent set can then be systematically exploited in the process synthesis stage so that the computational requirements remain largely unaffected.
2.2 Efficient exploitation of solvent design information in process synthesis The obtained solvent set from the M.O.O. CAMD solvent synthesis contains all the important solvent design information that must be incorporated into the process synthesis stage. We propose the formation of molecular clusters according to physical properties so that all the molecules in each cluster are similar to each other and as different as possible to the molecules in other clusters. The properties of the molecule
1647 that lies closest to the cluster centre can be considered to be approximately representative of the properties of the other molecules within the cluster and a representative molecule from each cluster can be introduced into the process synthesis. The result of the process pertFbrmance of each representative molecule ~br each cluster will reveal the cluster that includes the molecules that are ideally suited for the process, thus rejecting the molecules that belong to other clusters. An iterative application of this procedure will result into a tree-like representation tbr the optimization problem. In each iteration the various branches of the representation will focus the search on a decreased solvent solution space and the size of the problem will decrease without discarding important solvent infonnation. The appropriate directions for the development of the branches involved in the proposed representation are selected based on a set of decision criteria. In summary four major criteria have been identified: the number of clusters, the distances between the cluster centres and within each cluster, the number of data points in each cluster and the process performance of the molecule closest to the cluster centre. These criteria describe the clusters both in terms of statistical partitioning information and of cost of solvent/process configuration ~br each cluster. Each individual criterion provides a sense of quantity of what it describes, but, as the criteria operate independently from each other, they only identify the overall trends and directions of the clustering paths in a qualitative manner. A function is required in order to unite and quantify the proposed criteria under a single index. This function will suggest new clustering paths that are likely to lead to optimal clusters. We therefore define the chtstering heuristic probabiliO, as follows: P - exp[-(E,,cw
- Emm ) / ( a . T~j )]
a = 1- SSB/(SSB + SSW)
(1) (2)
Although the clustering heuristic probability P follows the Simulated Annealing (SA) probability function, the aim of this approach is to model the uncertainties involved in the clustering decisions and not to perform a SA search. This approach capitalizes on the knowledge regarding the physical characteristics of the clusters in order to identify clusters that are likely to include a molecule that can produce a solvent/process configuration with a cost lower than the best existing one. In this context the numerator of the probability fraction compares the cost of a cluster centre E,,e~,. with the best existing cost E,,,;,,. In the present case, the annealing temperature T can be appropriately reduced by a quantity a, that is a function of the available clustering information. The term a (Eq.4) is the R-Squared (RS) clustering index (Halkidi et al., 2002) ranging between 0 and 1 and represents a measure of between clusters difference (SSB) and within clusters homogeneity (SSW). For each cluster the annealing temperature is reset to an initial value (T~,/j) which is selected based on the discussion found in Aarts and van Laarhoven (1985). The advantage of using the clustering heuristic probability is that it allows the decision maker to quickly assess the problem and adjust the followed clustering policies. However, the understanding of the conditions of the overall problem at hand through the decision criteria previously discussed should always supplement the decisions made with the clustering probability.
1648
2.3 Process synthesis The process synthesis framework utilises stochastic optimization in combination with generic superstructures which have proved beneficial for the synthesis and optimization of separation (Papadopoulos and Linke, 2004b) and reaction/separation (Linke and Kokossis, 2003) processes. The process models incorporated in the superstructures represent reaction, reactive separation and separation options in generic reaction mass/exchange (RMX) units. An RMX unit can provide a conceptual or rigorous representation of all possible reaction or mass exchange phenomena taking place during process synthesis. Separation task units supplement the RMX units by offering a conceptual representation of separation options based on emerging separation paths, while leaving the rigorous representation of separation processes to RMX units 3. Illustrative e x a m p l e s 3.1 Design of solvents for separation processes The proposed method is illustrated with three applications on the integrated design of solvents and liquid-liquid extraction/recovery (P j), gas-absorption/recovery (P2) and extractive distillation (P3). The mixtures that are being separated are n-butanol-water for P1, air-acetone for P2 and cyclohexane-benzene for P3. An example of generation of new clustering paths based on the methodology analyzed in section 2 is shown in Figure 2 for P2. Each table shows the number of clusters (C1), the objective function value (OF), the number of points in each cluster (Nm) and the probability (P). Clusters 1 and 4 of iteration 1 present higher probabilities of including a molecule that benefits the process because of low OF values in combination with a large Nm. The information regarding OF and Nm as well as the rest of the decision criteria analyzed in section 2 are transparently represented by the reported probability values. On the other hand, the certainty that clusters 2 and 3 do not include beneficial molecules is high and this is also reflected in the probability values. Therefore, clusters 1 and 4 are further developed into the sub-clusters of iteration 2. Iteration 1
Iteration 2
(1) ~ C1 1 2 3 4
OF(k$/yr) 1971.7 3155.2
Nm 34 2
P 0.83 0.17
3190.1 1278.3
6 69
0.50 0.89
J
"•• (4)
C1 1 2 3 4
OF(kS/yr) 1712.3 1925.9 2030.9 2510.8
Nm 4 21 8 1
C1 1 2 3
OF(k$/yr) 1424.3 1640.9 1457.8
Nm 22 38 1
P 0.86 0.87
8
0.75
4
1383.0
0.41 0.56 0.46 -
0
Figure 1. Clustering decisions for (P2)
Following the presented clustering methodology it is possible to significantly reduce the computational time required for the identification of the cluster with the optimal solvent-process configuration. The number of molecules screened with regards to their
1649 process performance in cases P~, P2 and P3 are 18%, 15% and 25% of the initially obtained solvent set, respectively. These results represent a level of reduction from the initial solvent set that can be achieved following an approach that involves a low risk of missing the optimum molecule. Depending on the requirements of the problem, the method allows the user to set the threshold of the probability value below which clusters are rejected. Table 1 shows the optimum molecules identified for each case using the proposed methodology. For P~ the best molecule designed using M.O.O. is better in terms of process cost (OF) than the molecules designed using single objective optimization (S.O.O.). Furthermore, it is shown that by changing the objectives in the S.O.O. cases from solvent selectivity (S~) to solvent distribution coefficient (M) the process performance of the obtained molecules deteriorates. The same happens for case P2 as well when instead of using vapour pressure (Pvp) as the objective in S.O.O. we use solute solubility (Sb). Finally, in case P3 the process performance of the proposed molecule overcomes the process performance of industrial solvents or solvents reported in published literature. Table 1. Designed molecules and comparisons
Ca,~e P1
Method M.O.O. S.O.O. ( S ~ )
Malecllle CH~-CH~-CH(CH~)-CH~(C=O )-CH,-CN CH~-C(CH3)2-CH2(C=O)-CH2-CN
OF(k$/yr) 153.8 169.2 S.O.O. (M) CH2=CH-C(CH3)2-(CH2)2-(CH3)C(H(C=O))2 183.1 p-) M.O.O. CH~-O-CH(Br)CH(Br)C1 486.0 S.O.O.(Pvp) FCH20-C(Br)2-CH2C1 613.3 S.O.O.(Sb) CH2=C(-OCH3)-CH2-C1 657.7 M.O.O. FCH,-O-C-(HC=O)~ 317.2 P3 industrial a Aniline 711.8 Literature a n-meth~l-2-p~rrolidone 913.8 Results presented by van Dyk and Nieouwoudt (2000)
3.2 Design of solvents for reactive separation The second example involves the design of solvents for the extractive fermentation of ethanol. Details regarding the implementation of this example can be found in Linke and Kokossis (2002). Table 2. Molecules.fi)r the design of extractive fermentation processes
ID
Molecule
SI
CH3-O-CH2-C(CH=CH2)2 (OH)C(CH3)-CH=CH2 Dodecanol Large aromatic Octane Isopropyl-propionate
S~ $3 $4 $5
EF
S~:F(kg/hr )
EFN
S/zEFN(kg/hr)
1630.2
768
8100
400
6.46
1396
960 3135
2326 2000
13.91 15.77
1061 1321
A desired solvent-process superstructure must facilitate the complete conversion of glucose in the aqueous phase and the complete extraction of ethanol, whilst utilizing a minimum amount of solvent flow that dissolves as little glucose as possible. The
1650 employed objective function is a dimensionless equation incorporating these trends. The clustered solvent molecules are first screened with regards to their process performance in the synthesis of a well-mixed extractive fermentor (EF). Molecules with high process performance in EF synthesis are introduced in generic extraction fermentation network synthesis (EFN). Molecule S~ of Table 2 is designed using the presented method and molecule $2 has been proposed by Fournier (1986) as an ideal solvent. Molecule $3 has been proposed by Linke and Kokossis (2002) and is not shown for space economy. Finally, molecules $4 and $5 have been proposed by Wang and Achenie (2002). The results show that the already high performance of the EF structure can be significantly improved by EFN synthesis. The structure of the EFN allows the use of almost half of the solvent quantity
(S~rx) required in
EF (S~F). The proposed
molecule S~ performs better than all the molecules presented in literature and has lower toxicity than dodecanol, which is very important for extractive fermentation processes. Furthermore, molecules $3, $4 and $5 have been reported to be locally optimal, whereas following the proposed methodology we are confident that molecule $1 is a globally optimal solution.
4. Conclusions This presented work proposes a new technology for the integrated design of solvent and process synthesis. Molecules are designed for simultaneous optimality in a set of desired objectives using M.O.O. The obtained set of molecules is effectively introduced into the process synthesis through a clustering strategy that is especially designed to exploit the solvent design information, whilst reducing the amount of required computations. The methodology is exemplified through extensive examples in separation and reactive separation process synthesis. In all cases the obtained molecules outperform molecules designed using previously presented approaches. Overall, the proposed methodology demonstrates the systematic selection of solvents based on process performance criteria. This allows the introduction of confidence in the obtained solvent structures even in the most complex cases of the design of extractive fermentation networks.
References Fournier, R.L., 1986, Biotech. & Bioeng., 28, 1206 Halkidi, M., Batistakis, Y., Vazirgiannis, M., 2002, SIGMOD Record, 31 (3) Hostrup M, Harper P.M., Gani, R., 1999, Comp. & Chem. Eng., 23, 1395 Linke P., Kokossis, A.C, 2003, Comp. & Chem. Eng., 27(5), 733 Linke, P., Kokossis, A., 2002, In proceedings of ESCAPE-12, Elsevier Marcoulaki E.C., Kokossis, A.C., 2000a, Chem. Eng. Sci., 55(13), 2529 Marcoulaki, E.C., Kokossis, A.C, 2000b, Chem. Eng. Sci., 55(13), 2547 Papadopoulos A., Linke, P., 2004a, In proceedings of ESCAPE-14, Elsevier Papadopoulos A., Linke, P., 2004b, Comp. & Chem. Eng., 28, 2391 Stefanis, S.K., Pistikopou!os, E N., 1998, Comp. & Chem. Eng., 22(6), 717 Van Dyk, B, Nieuwoudt, I., 2000, Ind. Eng. Chem. Res., 39(5), 1423 Wang, Y., Achenie, L.E.K., 2002, Fluid Phase Equilibria, 201, 1
European Symposiumon Computer Aided Process Engineering- 15 I,. Puigjaner and A. Espufia(Editors) 4:, 2005 Elsevier B.V. All rights reserved.
1651
A computer-aided methodology for optimal solvent design for reactions with experimental verification Milica Folid, Claire S. Adjiman* and Efstratios. N. Pistikopoulos Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
Abstract An extension of a hybrid experimental/computer-aided methodology for the design of solvents for reactions is presented. Previous work (Folid et al., 2004a,b) was based on the use of reaction rate measurements to build a reaction model, followed by the formulation and solution of an optimal computer-aided molecular design problem (CAMD). In this work~ feedback is introduced in the methodology to verify the suitability of the solvent candidates identified in the CAMD step via experimentation and to assess the reliability of the model used in the CAMD step. When the reliability of the model is found to be insufficient, experimental data for the candidate solvents are added to the original data set to create an updated reaction model which can be used to find new candidate solvents. This methodology is illustrated through application to a solvolysis reaction and to a Menschutkin reaction.
Keywords: solvent design, optimisation, solvatochromic equation, group contribution methods, reaction rate 1. Introduction Solvents are widely used as a reaction medium in the fine chemicals industry, where they serve to bring solid reactants together by dissolving them, to control temperature, and to enhance reaction rate. The effect of solvent choice on reaction rate can be dramatic. Reichardt (1988) reports that the solvolysis of 2-chloro-2-methylpropane is 335,000 times faster in water than in ethanol, while the reaction between trimethylamine and trymethylsulfonium ion is 119 times faster in nitromethane than in water. In spite of the importance of solvent choice on productivity, there has been little work on systematic approaches to the selection of solvents for reactions. Thus, industry currently relies mostly on experience and intuition to guide its choice during the development of new processes. This situation is in striking contrast with the selection of solvents for separation, where several computer-aided design approaches have been proposed in the last two decades. Several of these methods are described in Achenie el al. (2003). These have been successfully applied to a variety of solvent-based separation problems, allowing a much larger number of solvent molecules to be considered during separation system design
Author to whom correspondence should be adressed :
[email protected] 1652 than is possible by experimentation alone. Based on these considerations, the goal of this work is develop a systematic approach to solvent design for reactions. The basic idea behind the methodology presented here is that, in the context of reactions, it is especially important to rely on a combination of experiments and computer-aided molecular design (CAMD). The computations serve as a guide to the experiments, focussing the search on promising solvents, and the experiments allow a verification of the models used. Furthermore, the methodology is developed with a view to plant-wide solvent selection, where it is important to focus on overall performance rather than the performance of single process units. This motivates the use of an optimisation-based approach to CAMD, where trade-offs between different aspects of the process can be accounted for explicitly. The methodology is described in section 2, and is applied to two reactions in section 3.
2. Methodology The overall methodology proposed in this work is illustrated in Figure 1. For a given reaction, eight initial solvents are chosen. These solvents should be selected to be
Choose 8 solvents
1
1
"1"1Obtain rate constant data I
1
I Build reaction model (
1
I Identify optimal solvent candidates I
1
I VerificatiOn, ]
YES
NO
Stop
)
Figure 1. Overview of the solvent design methodology diverse in terms of the types of interactions they can have with the species involved in the reaction. In general, the ETN solvent polarity scale (Reichardt and Harbusch-G0rnert, 1983). In addition, solvents with different functional groups are typically chosen. Wherever possible, literature data should be used at this stage to minimise experimental costs. Experimental reaction rate constants for these eight solvents are obtained. This information is then used to build a reaction model that predicts the reaction rate constant in other solvents based solely on their molecular structure. Next, a computer-aided solvent design problem (CAMD) is formulated and solved. Here, the objective is to find candidate solvents which give high values of the reaction rate constant. In the verification step, the predicted rate constants for the best candidate solvents identified are compared to experimental rate constants, to determine whether the reaction model needs improvement. If so, the experimental rate constants for the candidate solvents are
1653 added to set of initial solvents to build an updated reaction model. This procedure is repeated until the model reliability is sufficient. The computer-aided design step thus serves two purposes: it identifies promising solvents and it guides experiments. The model building and CAMD steps are briefly discussed in the next sections. 2.1 Building the reaction model The reaction model, as illustrated in Figure 2, consists of a set of property estimation methods which relate solvent molecular structure to solvent properties, and a solvatochromic equation (Abraham et al., 1987) which relates solvent properties to reaction rate constant for a given reaction.
Building
Group contribution techniques & correlations
t~b
Solvent properties
Solvatochromic
A, B, S, ~ ~1~
equation
Reaction rate constant k
blocks
Figure 2. Schematic of the reaction model
Atom groups such as CH2 and OH are used as building blocks. The solvent properties needed in the solvatochromic equation are the so-called solvatochromic parameters, A, B and S, a polarisability correction term, 6, and the cohesive energy density, which is the square of the Hildebrand solubility parameter, dH. The polarisability correction term can be calculated exactly based on molecular structure. The cohesive energy density is estimated through its relation with the molar volume, Vm, and the heat of vaporisation, Hv, as discussed in Sheldon et al. (2004). Vm and Hv are estimated using the first-order versions of the group contribution techniques of Constantinou and Gani (1994) and Marrero and Gani (2001) respectively. The group contribution techniques proposed in Sheldon et al. (2004) for the hydrogen-bond acidity A and the hydrogen-bond basicity B and the technique discussed in Folid et al. (2004a, b) for the dipolarity/polarisability S have been extended in this work. Group contribution coefficients are available for 43 groups, allowing a wider variety of solvent molecules to be represented. The regression has been based on a solvent database, which contains 350 solvents, giving increased confidence in the prediction techniques. The average absolute percentage error for each of the methods is reported in Table 1. Table 1. Average absolute percentage error (AAPE) for the proper~ estimation methods used to predict solvent properties.
Property AAPE
A
B
S
d,
0.017
0.043
0.065
1.13
The solvent properties are used in the solvatochromic equation: Iogk = Iogk. + s ( S + dd) + aA + bB + h d H I 100
(1)
where k is the reaction rate constant, and ko, s, el, a, b and h are reaction-specific parameters. The values of these reaction parameters are obtained via linear regression, based on measurements of the rate constant in a number of different solvents. Here,
1654 eight solvents are used to build the initial reaction model. Since the overall reaction model is based on predictions of the solvent properties, the predicted values of A, B, S and ~SHfor the eight solvents are used in the regression.
2.2 The computer-aided molecular design problem Once the reaction model has been developed, it is embedded within a CAMD optimisation problem. This is based on an MINLP formulation of the following form: max Iogk lt,y
s.t. logk =logk o +s(S+d6)+aA+bB+h6~ / I00 property estimation techniques for A, B, S, 6, Vm, H,,, Tm, t~4 melting point constraint molecular complexity constraints definition of n based on binary variables y
(2)
The constraint on the melting point 7,, ensures the solvent designed is liquid at room temperature. The group contribution technique of Constantinou and Gani (1994) is used to estimate E,,. The molecular complexity constraints consist of the octet rule (Odele and Macchietto, 1993), the bonding rule (as modified by Buxton et al., 1999), limits on the combinations of functional groups that may appear in the final molecule, and limits on the total number of groups in the molecule. Finally, the continuous variables n~ which define the number of groups of type i in the optimal molecule are related to binary variables to make sure that they only take on integer values. Nonlinearities arise in the above formulation from the estimation of the cohesive energy density. As a result, this problem is an MINLP which is linear in the binary variables. It can be solved locally with the outer-approximation algorithm (Viswanathan and Grossmann, 1990).
3. Case studies The case studies reported here are based on two reactions for which relatively large amounts of data are available in the literature. In such a case, it is desirable to complete the first iterations of the methodology using available data, in order to reduce process development time and cost. Such a procedure can then guide the choice of solvents in which to perform new measurements. 3.1 Soivolysis of t-butyl chloride Reaction rate constant data for the solvolysis of t-butyl chloride (CH3CCI --> (CH3)3C÷C1- --> (CH3)3C+ISolvlCI---~ Products) is available in 41 solvents (Abraham, 1972, Abraham et al., 1981, Abraham et al., 1987, Gon~alves et al., 1992, Dvorko et al., 2002). The reaction rate constants reported vary by 11 orders of magnitude and the best experimemal solvent is glycerol. The eight diverse solvents selected to build the reaction model are shown in Table 2 with their experimental ranking, where rank 1 denotes the solvent with the largest rate constant. A wide range of polarities and functional groups results in a set which contains both good and poor solvents. Good statistics are obtained for the solvatochromic equation regression: R 2 is 0.93 and the standard error is 1.9. The average absolute percentage error for all 41 solvents is 17%. A
1655 comparison of solvent rankings using experimental data and predictions (Table 3), shows good overall agreement. Table 2. Soh, ents /or the solvolysis case study, with experimental rank.
Solvent
Rank
Solvent
Rank
Solvent
Rank
Solvent
Rank
1,2ethanediol Dimethyl acetamide
2
2-methyl-2propanol Chlorobenzene
4
Diethylene glycol Benzene
6
Acetic acid Pentane
14
29
36
38
4l
Table 3- Comparison of solvenl rankings. experiments and predictions.
Solvent Glycerol Phenol Propane- 1,2-diol Butane-1,4-diol Butane- 1,2-diol
Exp
Pred
1 3 5 7 9
1 10 6 7 8
Solvent 1,2-ethanediol Propane- 1,3-diol Diethylene glycol Triethylene glycol Aniline
Exp
Pred
2 4 6 8 10
3 5 4 2 15
The CAMD MINLP identifies glycerol as the best solvent, with a reaction rate constant three times larger than that of 1.2-ethanediol, the best solvent used in the regression. Verification against literature data shows that the rate constant in glycerol has been measured and that it is the best solvent known to date. Given the consistency between the computational and experimental results, the search is stopped. 3.2 A Menschutkin reaction
In this case study, the Menschutkin reaction between methyl iodide and tripropylamine is considered: (n-CsHT)N + CH31 -+ (CH3)(n-C3H7)3N+-I -. Reaction rate constant measurements in 59 different solvents can be found in Lassau and Jungers (1968). The range of rate constants reported covers five orders of magnitude and the best ranked solvent is benzyl cyanide. A set of eight diverse solvents for which experimental data are available is chosen: it consists of a cyanide, an alkyltetrahalide, a nitrate, a halosubstituted aromatic, an aromatic, an alcohol, an oxide and an alkane. The solvatochromic reaction parameters are regressed based on these data, giving an R 2 value of 0.85 and a standard error of 1.2. When the predictions for all 59 solvents are compared with the experimental data, the average absolute percentage error is found to be only 19%. A comparison of the experimental and predicted solvent rankings shows that 7 out of the top 10 experimental solvent are predicted in the top 10 and that 17 out of the top 20 experimental solvents are predicted in the top 20. The CAMD MINLP identifies chiorobenzylcyanide as the best solvent. Integer cuts are added to find the second and third best solvents, chlorobenzylnitrate and 1,7-heptanediol. The verification step is then performed. Although no experimental data are available for any of the candidate solvents, data are available for benzylcyanide and chlorobenzene, which have functional groups and structures similar to the top two solvent candidates. Benzylcyanide is already included in the set of eight solvents used to build the reaction model, but the error between prediction and measurement is large, indicating that the
1656 model reliability could be improved. Since none of the eight initial solvents contains a chlorine group, the chlorobenzene data is added to the data set. A new reaction model is regressed based on these nine solvents. The overall statistics are similar to those obtained with eight solvents, but the qualitative ranking is slightly improved, with 8 of the top 10 experimental solvents predicted in the top 10. The CAMD MINLP is solved with the new reaction model and once again yields chlorobenzylcyanide as the top candidate. There is no further data in the data set which may be used to verify this prediction and the measurement of the rate of reaction in chlorobenzylcyanide is now needed.
4. Concluding remarks A methodology for the systematic design of solvents for reactions has been proposed. It is based on an iterative approach which alternates between experiments and computeraided molecular design. The reaction model at the core of the CAMD problem is based on the empirical solvatochromic equation, in which the solvent properties are obtained by group contribution techniques and the reaction parameters are regressed from experimental data. The CAMD results are verified against experimental data, and an improved reaction model is generated if needed. This is then used in an updated CAMD problem. The approach has been applied to a solvolysis reaction, in which only one reaction model was used, and to a Menschutkin reaction, in which two reaction models were used. Further verification of the results via experimentation is underway.
References Abraham, M.H., 1972, J. Chem. Soc.- Perkin Trans. 2, 1343. Abraham, M.H., R.W. Taft and M.J. Kamlet, 1981, J. Org. Chem. 46, 3053. Abraham M.H., R.M. Doherty, M.J. Kamlet., J.M. Harris and R.W. Taft, 1987, J. Chem. Soc., Perkin Trans. 2, 913. Achenie L.E.K., R. Gani and V. Venkatasubramanian, Eds., 2003, Computer Aided Molecular Design: Theory and Practice, Elsevier, Amsterdam. Buxton A., A.G. Livingston and E.N. Pistikopoulos, 1999, AIChE J. 45, 817. Constantinou L. and R. Gani, 1994, AIChE J. 40, 1697. Dvorko, G.F., V.V. Zaliznyi and N.E. Ponomarev, 2002, Russian J. General Chemistry 72, 1549. Foli6 M., C.S. Adjiman, E.N. Pistikopoulos, 2004a, Proceedings of ESCAPE-14, Elsevier. Foli6 M., C.S. Adjiman, E.N. Pistikopoulos, 2004b, Proceedings of FOCAPD, in press. Gon~:alves R.M.C., A.N.M. Sim6es, R.A.S.E Leitfio and L.M.P.C. Albuquerque, 1992, J. Chem. Research (S), 330. Lassau C. and J.C. Jungers, 1968, Bull. Soc. Chim. Fr. 7, 2678. Marrero J. and R. Gani, 2001, Fluid Phase Eq. 183-184, 183. Odele O. and S. Macchietto, 1993, Fluid Phase Eq. 82, 47. Reichardt C., 1988, Solvents and Solvent Effects in Organic Chemistry, VCM Publishers, UK. Reichardt C. and E. Harbusch-G6rnert, 1983, Liebigs. Ann. Chem., 721. Sheldon T., C.S. Adjiman and J.L. Cordiner, 2004, Fluid Phase Eq. accepted for publication. Viswanathan, J. and I.E. Grossmann, 1990, Computers chem. Engng. 14, 769.
Acknowledgements Financial support from the ORS scheme and CPSE is gratefully acknowledged.
European Symposium on Computer Aided Process Engineering- 15 L. Puigjaner and A. Espuna (Editors) g) 2005 Elsevier B.V. All rights reserved.
1657
Development of Information System for Extrusion Forming Process of Catalyst Pastes Andrey V. Jensa, Anatoliy A. Pohmin, Vyacheslav V. Kostutchenko, Igor A. Petropavlovskiy, Eleonora M. Koltsova Department of Cybernetics of Chemical Engineering, D. Mendeleev University of Chemical Technology of Russia 125047, Miusskaya pl. 9, Moscow, Russia, Tel. +7 (095) 978 65 89, E-mail:
[email protected] Abstract Evolution of theoretical basis of extrusion paste forming processes will raise the solution of several problems in the technology of catalysts, which are used in different branches of chemical, automobile (block ceramic overburning catalysts) and petrochemical industries. Taking into account the importance of this problem on the department of cybernetics of chemical technological processes we developed the information system which allow us to find initial concentrations of catalyst paste components for obtaining target product with predefined properties (mechanical strength and porosity). User of this system can specify desired values of target product specifications (such as mechanical strength, porosity of catalyst) or intermediate ones without dealing with experiments., i.e. specify the values of rheological parameters of catalyst pastes (viscosity, plastic strength, elasticity) on the catalysts preparation stage. As a result of interaction with this system end-user will receive a set of recipes (component mass compositions) for catalyst paste preparation and the ram extruder which can be used tbr production of catalyst with user defined properties.
Keywords: [extrusion, catalyst pastes, information system] 1. Introduction By means of extrusion forming it is possible to obtain various materials: catalysts with different form (from cylinder to figured grains and honeycomb blocks), ceramic materials, food materials (noodles, candies, etc.). Obtaining of materials, based on ot-Fe203 is considered in this work. Following stages are contained in the process of wide class materials obtaining (including new ones): synthesis, mixing, flowing through an extruder, drying and firing. The obtained materials should have a series of the given properties: appearance, durability, porosity, water absorption, etc. Extrusion is one of the processes, where the process of paste's particles agglomeration is unwelcome, as it leads to turn for the worse of the paste's properties. Therefore, this paper is devoted to investigation and mathematical simulation of catalyst pastes
1658 preparation with taking into account formation of solvate films, which prevent the agglomeration of particles. At this stage, the solid carrier (ot-Fe203) is being mixed with the water solutions of surfactants (in or case, these are solutions of PVA and MC). Addition of these substances makes the forming paste plastic. The substances keep the dispersed phase in a bounded condition, counteracting the factors, which disintegrate the structure. The most important problem at preparation of catalyst pastes is a problem of evaluation and prediction of their forming properties with help of their rheological properties, where the plastic strength and viscosity are two general ones. The properties of pastes start getting their properties at the preparation stage. According to representations of physical chemical mechanics, plastic forming pastes present themselves a system of rigid particles, surrounded by the solvate films. Cross-linking of such dispersed systems happens in the result of molecular coupling of dispersed phase particles by the most lyophobic areas of surface, which are the least protected by the solvate films of media. Thickness of solvate films significantly determines the system's technological parameters, including its formability.
2. Experimental A series o experiments were carried out, where the pastes with different composition were being prepared by varying the concentration of continuous phase (PVA and MC) and the content of a solid phase (table 1). Each paste was being prepared in a mixer for about 30 minutes, then it was being matured for 24 hours. Plastic strength was being determined after 30 minutes and after 24 hours by means of Rebinder's conic plastometer by the cone penetration method under action of a constant weight [1]. Viscosity was being determined after 24 hours by means of capillary viscosimeter at the shear strain, equal to 10 s-1. Table 1. Experimental values of rheological characteristics of catalyst pastes.
N exp. 1 2 3 4 5 6 7 8 9 10 11 12 13 14
0,502 0,460 0,500 0,458 0,501 0,459 0,499 0,457 0,492 0,476 0,477 0,454 0,484 0,462
awhen jt =10s -1. b After 30 minutes. After 24 hours.
a
co
co
q
0,012 0,012 0,012 0,012 0,0012 0,0012 0,0012 0,0012 0,0075 0,0075 0,00375 0,00375 0,01125 0,01125
0,06 0,06 0,018 0,018 0,06 0,06 0,018 0,018 0,04 0,04 0,06 0,06 0,02 0,02
41,20 0,78 6,61 0,36 15,85 1,12 0,31 0,24 19,01 14,79 5,75 0,66 4,68 0,56
pmb
PITI c
2059 84 566 25 3031 74 173 32 727 507 496 105 289 63
3658 298 1304 82 3536 192 318 65 1755 1221 875 180 742 186
1659 Experimental values of plastic strength and viscosity are presented in the table 1. Behaviour plastic strength in time was observed for some experiments. The graph of plastic strength in time comes out to plateau (see figure 1), what means the system's stabilization. Only two limiting values of plastic strength are presented in table 1: after 30 minutes and after 24 hours. But even these two values are enough to get convinced in importance of taking into account the maturing stage. For 24 hours plastic strength doubles for almost all the experiments, and for the experiment 3 it even quadruples. Structurization of the system happens for this time, the paste becomes more dense and rigid. Pro,
kPa
1400 1200
1000 800 600 400
200 ,
0
2
4
6
8
:
10
12
14
16
18
20
22
24 t, hours
Figure 1. Experimental dependeno' of plastic strength fi'om time for the experiment 3.
3. Results 3.1 Obtaining of functional dependencies The mathematical model for the stage of catalyst paste mixing was built on a base of application of heterogeneous media mechanics apparatus and colloid chemistry. This model allows calculation of c~-Fe~O3 particle-size distribution density at any moment of time on solvate films thicknesses. Multicomponent two-phase system is considered at the stage of paste preparation in a mixing apparatus. First phase is continuous, the second one consists of solid ~-Fe203 particles. Components of continuous phase are: water, PVA and MC. We consider that in the process of mixing, particles of a-Fe203 get covered by the solvate film. Properties of this film depend on composition of continuous phase. The mathematical model of a catalyst pastes mixing stage is constructed on a base of application of heterogeneous media mechanics and methods of colloid chemistry. The model allows to calculate a distribution density of Fe203 particles number for any moment of time on solvate films thickness and includes the following equations:
1660 - b a l a n c e equation of ~-Fe203 particles number, predicting the number of particles in any moment of mixing and storing, having solvate film; predicting the medium size of solvate film:
-0f- + 0f~ =0; c~t
(1)
c~r
dependency for the solvate film growth rate:
-
dr _ 4zc/2 [K1C1C3 + K 2 C 2 C2+ K3C 3 ]; - -~-
(2)
mass change at the expense of solutions' components income of continuous
-particles
phase:
V - - dm ~ _ 47t/2 [Pl 1K1C1C3 + Pl2K2C2C~ + P13K3C3 ]; -
equation of liquid phase density changing: dPl dt
-
(3)
=-
Rm Ifaltdr; 0
(4)
equation of components concentrations changes for liquid phase: dC i
Pl ~
dt
Rm
Rm
= - fPliflai dr + Ci f f g tdr , 0
(5)
0
where la1 - 4zff2K1C1C3, ~t2 - 4FI2K2C2C~, ~t3 - 4~12K3C3 . Volume content of a solid phase is determined on a base of these equations (1-5): Rm
¢z2 - (xO + ~rfdr 0
(6)
Unknown kinetic constants of the mathematical model (1-6) are K1, 1£2, 1£3. For the definition of kinetic constants we took the data, represented in a paper of Yu. Mosin [2]. Following values of kinetic constants were found in the result of this search: K1 = 10,5.10 -1° (m s-l), 1£2 - 0,66.10 -1° (m s-l), 1£3 = 0,2.10 -1° (m s-l).
Following functional dependencies were obtained by comparing data, obtained with help of the mathematical model (for example, volume content of catalyst, taking into account the presence of a solvate film; average values of solvate films thicknesses) with the experimental data on plastic and rheological properties of pastes: - dependencies for the plastic strength: Pm - 103 exp(- 14,792 + 1,77.106h +8,1.1012h 2 + +15,207et 2 + 61,113(z 2 -2,547.10 7 h(x21 ; - dependencies for viscosity of catalyst paste:
(7)
1661
q 1 q°exp(98°t2 - - 36'8)(45'12"10-7h
-3,7
(8)
3.2 Informationsystems The Information System (IS) allows user to find paste composition for specified input parameters. Search results consist of a set of pastes, so user need to choose one of them. At the moment the IS applicable only to catalytic paste based on ferric oxide ~-Fe203 and consists of four modules. First module represents a database of theological, deformation properties of catalyst pastes and target product parameters. This database was built using the mathematical model of the mixing stage within the catalyst preparation process. This model takes into account formation and growth of adsorption solvate shells on solid phase particle. Rheological and deformation properties of catalyst pastes were generated by equations for plastic strength (7) and viscosity (8). Target product parameters were put into database from equations tbr mechanical durability and porosity of target product. This module allows one to choose automatically the composition of catalyst paste, which satisfy user demands (fig. 2). Second module is the database of ram extruder parameters, including unit geometry, manufacturer's name and address (at the moment the system contain information about ram extruder, but it is possible to put other types of extruders there). In the third module system calculates extruder load for chosen catalyst paste forming. Calculations are based on mathematical model for catalyst paste flow in extruder. Fourth module of information system allows us to choose ram extruder from industrial units database depending on calculated in the second module extruder load. By using the assurance factor when choosing the unit we can expand search range for the system. ' Resull o! Seleclio
,~Composition of Paste ................................................... Weicjht of iron oxide (g): 1667 Weight of sotution MC(g)(%wg):
157 (:3 :-',8I)
Weight of sotu~i:onPVA(g)(%wg):
183 (10.75)
Composition of Paste: 17
.......................................
Rheologicei property of Paste
Properly of Product .............................................
Plastic strength(kPet): ii :31-15.:377 Humidity(%):
aechetnice]
strength(MPet): ii..075
ti 5..',~6',_~ Porosity:
Vi sco s i~(Pe* s): ]:30 G4. !38
.................... Weightof
6
667
lweighto,so,
IPlestic
jHumidily(%)
I
Viscosity(Pet's)
Porosty
1 !',07.!--t42
15.868
8-1 r] n 75I
I :',FF,::177
1 ~ I~F,',:', :-1064.98 1 .L-17g . . . . . . . . . . . . .
n £2
8
11U '.i',-',:_:I . :!',:3)
1 2':~6..052
1 5..',3E,',:',
!',0 'E;.25'J
,
-
1..075
I
57 (14 92) , -
:!;063.76
IMechanice,
7 !~i67.................................... 157 i":-i-11-11 ......... =................................................ :. , ,
6G7
',-_-;:", (2!;5)
lweight ofsol.
11:J..5 .';"
11152
:!',069..28:-',
1..11175
0..52
9
800
11 0 11.78'~
57 (1 4.92)
1 0G4.:324
1 E;
:3659.2FI
1 lIE :i
0..519
1:0
813111
'8:?, (2..:35)
',-;:!',(10.75)
106:!1.879
16
:3659.425
1.0871
0.519
1t
8 I-II-I
57 1:I3.~J'l-',',l
11 Ill '~8 I :-I !i:3)
10E;1 !97
1 E;
:365'.:I.!322
1i 1383
0.51 II9
Figure 2. The results after we chosen the paste.
_...j
~
]
1662 Work sequence for this system include several stages: • Query definition for calculation of paste composition • Database preparation for rheological properties dependency on paste composition • Calculation of extrusion process parameters for ram extruder • Extrusion equipment vendor selection from database • Equipment selection from unit database basing on calculation results In order to determine paste composition in is necessary to specify following parameters: • catalyst powder nature, type and its dispersity • temporary technological linkage information (quantity and type of technological linkage used) • rheological and deformation properties of paste (plastic strength, humidity and viscosity) • target product parameters (mechanical strength and porosity) Data is input by ranges. For the plastic strength it is needed to specify more exact value. From the data obtained the program automatically choose appropriate catalyst paste compositions from database, from which user can select one item satisfying his demands. Then user chooses extruder type for this selected paste composition. Extrusion pressure calculations are performed using user specified ram extruder parameters. If extruder load does not suit user needs, it is possible to get back to previous stage and choose another paste composition. Then the same procedure executed for the new paste. As a result, user selects one of computer-proposed paste compositions, which satisfies not only demanded rheological and deformation properties, but also extruder load wanted. After this stage program look for suitable equipment for the selected paste in the database. In order to run this user should input geometry parameters of the unit and assurance factor. Additionally, you can use this module apart from others, but in that case you need to specify manually all unit parameters for database search. At the last stage you can print the report for all stages of calculation with this system. This report can be saved in a file or printed.
References M.S. Akutin, N.N. Tikhonov, Laboratory works on rheology of polymers, Mendeleyev University of Chemical Technology, 1983 (in Russian). Yu.M. Mosin, A.F. Krivoshepov, G.G. Shikhieva, A.V. Bulinko, Formation of interphase bound oxide-solution of high-molecular compound, Glass and Ceramics (1997), No 9, pp. 27-30 (in Russian).
Acknowledgements This work was supported by grants RFBR No 02-03-32215, ~o 03-01-00567, RFBRNSFC grant No 02-03-39003 and Ministration of Education Russian Federation T 0209.4-2936.
European Symposium on Computer Aided Process Engineering - 15 I,. Puigjaner and A. Espufia (Editors) (C: 2005 Elsevier B.V. All rights reserved.
1663
Integrating short-term budgeting into multi-site scheduling Gonzalo Guilldn, Mariana Badell, Antonio Espufia and Luis Puigjaner Universitat Politbcnica de Catalunya, Chemical Engineering Department, E.T.S.E.I.B., Diagonal 647, E-08028, Barcelona, Spain
Abstract In this work a novel approach is applied with the aim to improve the operation of supply chains with embedded multi-purpose batch chemical plants. The major contribution of this work with respect to previous approaches is that it includes a corporate financial planning model within the mathematical tbrmulation applied for optimizing scheduling/planning decisions variables regarding the supply chain management. Such model maximizes the change in equity of the company and provides the budgetary guidelines for the planned period. This consideration exhibits two main advantages compared to the existing methodologies. In first place, it allows to check the feasibility of the resulting planning decisions from the financial viewpoint thus ensuring that the production and distribution activities to be carried out through the different nodes of the network do not spend more cash than the available one. In second place, it leads to better overall economic performance than in previous methodologies since the model properly evaluates the impact of financial expenses and earnings derived from the SC operation thus integrating production and financial corporate decisions. Such integration also makes the difference when considering the opportunity of investing the idle cash.
Keywords" agents, multi-site scheduling, financial, uncertainty. 1. Introduction The concept of Supply Chain Management (SCM), which appeared in the early 90s, has recently raised a lot of interest since the opportunity of an integrated management of the SC can reduce the propagation of unexpected/undesirable events through the network and can influence decisively the profitability of all the members. A lot of attempts have been made to model and optimise the SC behaviour, currently existing a big amount of deterministic and stochastic derived approaches. Most of the works reported in the literature address the SCM problem from a strategic or tactical point of view. They identify the placement of production facilities or distribution centres, the flow of materials and the inventory levels optimizing a certain performance measure, commonly cost or profit. From an operational perspective, and due to the complexity associated to the interdependencies between the production and distribution tasks of the network, the detailed scheduling of the various processes of the SC has been left to be decided locally. In this sense, Applequist et al. (1993) highlight the importance of the coordination of the activities of the different entities and specifically at the enterprise level, which requires integration of the logistics and manufacturing aspects with strategic business and financial decisions. Grossmann
1664 (2004) highlights also that major challenges in enterprise and supply chain optimization include development of models for strategic and tactical planning for process networks which must be eventually integrated with scheduling models. The author suggests that while very significant progress has been made, these models still lack sufficient generality despite significant advances made in this area. A topical review of historical guidelines and approaches in integration of operative planning/scheduling and cash management modelling must take into account that budgeting models for financial control emerged earlier than operation schedules. The initial sequential approach, which focused on individual financing decisions, was later developed towards the simultaneous consideration of financial decisions. These included cash flow synchronization, financing distribution and the investment of the excess cash in marketable securities. On the operative side, a huge number of models, especially in the last 25 years, have been developed to perform short term scheduling and longer term planning. Most of these works address scheduling/planning activities by optimizing quality or cost-related performance measures. However, very limited works were reported on the joint financial and operative modelling. Shapiro et al. (2001) recognizes that optimization models offer an appealing framework for analyzing corporate financial decisions and constraints as well as for integrating them with supply chain decisions and constraints. Unfortunately, he also admits that relatively few corporate financial models of this type have been so far developed in the literature. If in practice the financial matters are not still integrated with operations management to support decision making, is mainly because until today scheduling/planning and budgeting modelling have been treated as separate problems and were implemented in independent environments.
2. Multi-site planning/scheduling In the chemical-processing context, production planning and scheduling refers to the routine of allocating resources and equipment over time in order to execute the processing tasks required for satisfying a specific product demand and quality while fulfilling some predefined optimization criteria. Production planning implies allocation decisions over longer time scales (months), while scheduling focuses on the shorter time scale allocation thus considering those sequencing decisions that satisfy the production requirements imposed by the former. When talking about a SC, it is important to extend the decision variables related to the plant activity to the whole network. This consideration gives rise to a muti-site scheduling/planning problem where it is necessary to decide not only the production rates of the plants and the flows of materials between sites but also the way in which such amounts of materials are manufactured (partial schedules), stored and transported through the nodes of the network.
3. Mathematical formulation The proposed model divides the planning and scheduling horizon H into intervals of length H1 where production is planned using known as well as estimated demands
1665 which are provided by a forecasting tool. Moreover, the first planning period is divided into intervals of lower length H2 where production is scheduled as depicted in Figure 1. The model is to be rerun every H1 period as forecasts become real orders. Therefore, the results of the planning horizon beyond the first period H1 will never reach execution. However, they are important to be considered when solving the scheduling horizon, because one could schedule in such period the production of materials needed in periods beyond it and keep them as inventory. At the financial side, the reschedule carried out each H1 period provides a reliable forward-looking scenario aiding the synchronized financial/operative decision making.
3.1 First stage" detailed scheduling In this first stage, production demands and raw materials and final product stocks are known. Here, the detailed schedules of the different sites of the SC as well as the transport decisions to be implemented through the nodes are computed. The first time period H1 is divided into t intervals of length H2. The scheduling constraints are based on the discrete STN formulation of Shah et al. (1993), although other either continuous or discrete time scheduling formulations could be easily applied. It should be also mentioned at this point, that it is necessary to slightly modify the mass balance constraints proposed by the author for properly modelling the transport of materials through the nodes of the SC. !
......~ ,i~,
:
ilil ~i2i!: ii~i~!iiiiii!i~i~ii~i~i~!~!!!~!~i~Jiiiii~iii~ii~!ii~iiiii~i~iiiiii~iii!i~Ji~Ji~ii!iiiiiii~i~i~iiii~iiiiiiiiiiiiiiiiiii~ii~iiiiiiiiiiiiii~i~Jii!Jiiiii~iiiiiii~iiiiii~i~iiiii~ii;iiiiiii!i~iiii~ii~i~i~iiiiiiiiiiiii~i~ii{~ii
i . . . . . . . .... . . . . . .IME . . . H o R , z o NI..............
4
...~ . . . < ,.~' ~' )i~ ...... •, ......~g~':: ~...-.-:
•
:) "~: ~~ ~
'
.
,, ...~
...............
~
!...2
Figure 1. Structure qf the model
Figure 2. Case Stud3,
3.2 Second stage: production planning Here, nor the exact sequence of batches produced neither the initial and finishing times of the involved tasks are computed within every period, apart from the first one, but estimated by means of an aggregated STN representation based on the work of Maravelias and Grossmann (2004). For each task i, it is defined a maximum number of copies, i.e. an upper bound on the number of batches of task i that can be carried out in any feasible solution. Constraint (1) is a relaxed assignment constraint which enforces that the sum of the durations of the tasks assigned to a unit does not exceed the length of each planning interval (H1). Here, !/ represents the set of tasks that can be assigned to unitj. In this case, it has been assumed constant processing times. The capacity limits for equipments are expressed by equation (2). ZZPti.Wi,
