Robust Model-Based Fault Diagnosis for Dynamic Systems

369 Pages·1999·10.475 MB·English

by  Jie Chen, Ron J. Patton (auth.)

ROBUST MODEL-BASED
FAULT DIAGNOSIS FOR
DYNAMIC SYSTEMS
The Kluwer International Series on
ASIAN STUDIES IN COMPUTER
AND INFORMATION SCIENCE
Series Editor
Kai-Yuan Cai
Beijing University of Aeronautics
Beijing, CHINA
Also in the Series:
SOFTWARE DEFECT AND OPERATIONAL PROFILE
MODELING
by Kai-Yuan Cai
ISBN 978-1-4613-7344-5
FUZZY LOGIC IN DATA MODELING: Semantics, Constraints,
and Database Design
by Guoqing Chen
ISBN 978-1-4613-7344-5
ROBUST MODEL-BASED
FAULT DIAGNOSIS FOR
DYNAMIC SYSTEMS
by
Jie Chen
Brunei University, Uxbridge, UK
Ron J. Patton
University of Hull, Hull, UK
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Library of Congress Cataloging-in-Publication Data
A CLP. Catalogue record for this book is available
from the Library of Congress.
Copyright © 1999 by Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 1999
Softcover reprint of the hardcover 1st edition 1999
ISBN 978-1-4613-7344-5 ISBN 978-1-4615-5149-2 (eBook)
DOI 10.1007/978-1-4615-5149-2
All rights reserved. No part of this publication may be reproduced, stored in a
retrieval system or transmitted in any form or by any means, mechanical, photo
copying, recording, or otherwise, without the prior written permission of the
publisher, Springer Science+Business Media, LLC.
Printed on acid-free paper.
Contents
List of Figures XI
List of Tables xv
Preface xvii
Acknowledgments XIX
1. INTRODUCTION 1
1.1 Background 1
1.1.1 Importance of fault diagnosis 1
1.1.2 Fault diagnosis terminology 2
1.1.3 Fault diagnosis in intelligent fault-tolerant control 3
1.1.4 Model-based fault diagnosis 3
1.1.5 Robustness in model-based fault diagnosis 5
1.2 Brief history of model-based fault diagnosis 7
1.3 Outline of the Book 14
2. BASIC PRINCIPLES OF MODEL-BASED FDI 19
2.1 In trod uction 19
2.2 Model-based Fault Diagnosis Methods 20
2.3 On-line Fault Diagnosis 21
2.4 Modeling of Faulty Systems 22
2.5 A General Structure of Residual Generation in Model-based FDI 26
2.6 Fault Detectability 28
2.6.1 Fault detectability condition 28
2.6.2 Strong fault detectability condition 30
2.7 Fault Isolability 31
2.7.1 Structured residual set 31
2.7.2 Fixed direction residual vector 32
2.7.3 Sensor and actuator faults isolation 33
2.8 Residual Generation Techniques 35
2.8.1 Observer-based approaches 35
2.8.2 Parity vector (relation) methods 38
2.8.3 Factorization methods for residual generation 44
2.9 Model-based FDI via Parameter Estimation 45
v
vi ROBUST MODEL-BASED FAULT DIAGNOSIS FOR DYNAMIC SYSTEMS
2.10 Fault Diagnosis for Stochastic Systems 46
2.11 Robust Residual Generation Problems 48
2.11.1 Robustness to disturbances 49
2.11.2 Robustness to modeling errors 50
2.11.3 Discussion on robust FDI 51
2.12 Adaptive Thresholds in Robust FDI 51
2.13 Applicability of Model-based FDI Methods 54
2.13.1 Observer-based approaches 55
2.13.2 Parity relation approaches 56
2.13.3 Parameter estimation approaches 57
2.13.4 Discussion on applicability 58
2.14 Integration of Fault Diagnosis Techniques 59
2.14.1 Fuzzy logic in fault diagnosis 59
2.14.2 Qualitative fault diagnosis 60
2.14.3 Integrated fault diagnosis systems 62
2.15 Summary 63
3. ROBUST RESIDUAL GENERATION VIA UIOS 65
3.1 Introduction 65
3.2 Theory and Design of Unknown Input Observers 68
3.2.1 Theory of UIOs 71
3.2.2 Design procedure for UIOs 76
3.3 Robust Fault Detection and Isolation Schemes based on UIOs 78
3.3.1 Robust fault detection schemes based on UIOs 78
3.3.2 Robust fault isolation schemes based on UIOs 79
3.3.3 Robust actuator FDI example 82
3.4 Robust Fault Detection Filters and Robust Directional Residuals 87
3.4.1 Basic principles of fault detection filters 88
3.4.2 Robust fault detection filter and fault isolation 90
3.4.3 Robust isolation of faulty sensors in a jet engine system 94
3.5 Filtering and Robust FDI of Uncertain Stochastic Systems 98
3.5.1 Optimal observer for uncertain stochastic systems 100
3.5.2 Robust residual generation and fault detection 104
3.5.3 An illustrative example 105
3.6 Summary 108
4. ROBUST FDI VIA EIGENSTRUCTURE ASSIGNMENT 109
4.1 In trod uction 109
4.2 Residual Generation and Responses 111
4.3 General Principle for Disturbance De-coupling Design 112
4.3.1 Disturbance de-coupling design via invariant subspaces 113
4.3.2 Disturbance de-coupling via eigenstructure assignment 113
4.4 Disturbance De-coupling by Assigning Left Eigenvectors 116
4.5 Robust Design Via Parametric Eigenstructure Assignment 120
4.5.1 Robust FDI via parametric eigenstructure assignment 122
4.5.2 An illustrative example 123
4.6 Disturbance De-coupling by Assigning Right Eigenvectors 127
Contents vii
4.7 Dead-Beat Design for Robust Residual Generation 130
4.8 Two Numerical Examples in Eigenstructure Assignment 133
4.9 Conclusion and Discussion 135
5. DISTURBANCE DISTRIBUTION MATRIX DETERMINATION FOR FDI 137
5.1 In trod uction 137
5.2 Direct Determination of Disturbance Distribution Matrix 139
5.2.1 Noise and additive non-linearity 140
5.2.2 Bilinear systems 140
5.2.3 Model reduction 141
5.2.4 Parameter perturbations 141
5.2.5 Low rank approximation of distribution matrix 142
5.2.6 Bounded uncertainty 145
5.3 Estimation of Disturbance and Disturbance Distribution Matrix 146
5.3.1 Disturbance vector estimation via augmented observer 146
5.3.2 Derivation of disturbance distribution matrix 147
5.3.3 Estimation of disturbance vector using de-convolution 149
5.4 Optimal Distribution Matrix for Multiple Operating Points 152
5.5 Modeling and FDI for a Jet Engine System 153
5.5.1 Background on fault diagnosis for jet engine systems 154
5.5.2 Jet engine system description 155
5.5.3 Application of direct computation and optimization method 157
5.5.4 Application of augmented observer method 159
5.6 Conclusion 166
6. ROBUST FDI VIA MULTI-OBJECTIVE OPTIMIZATION 167
6.1 Introduction 167
6.2 Residual Generation and Performance Indices 169
6.2.1 Residual generation and responses 169
6.2.2 Performance indices in robust residual generation 171
6.2.3 Remarks on performance indices 172
6.3 Parameterization In Observer Design 174
6.3.1 Real eigenvalue case 175
6.3.2 Complex-conjugate eigenvalue case 175
6.3.3 Eigenvalue specifications 176
6.4 Multi-Objective Optimization and the Method of Inequalities 177
6.4.1 Multi-objective optimization 177
6.4.2 The method of inequalities 178
6.5 Optimization via Genetic Algorithms 182
6.5.1 Introduction to genetic algorithms 182
6.5.2 Steps of a genetic algorithm in optimization 186
6.6 Detection of Incipient Sensor Faults in Flight Control Systems 188
6.7 Conclusions 191
7. ROBUST FDI USING OPTIMAL PARITY RELATIONS 193
7.1 Introduction 193
7.2 Performance Indices for Optimal Parity Relation Design 194
viii ROBUST MODEL-BASED FAULT DIAGNOSIS FOR DYNAMIC SYSTEMS
7.3 Optimal Parity Relation Design via Multi-Objective Optimization 197
7.3.1 Solving optimization problems via SVD 198
7.3.2 Solutions for multi-objective optimization 199
7.4 A Numerical Illustration Example 202
7.5 Discussion on Designing Optimal Parity Relations 203
7.5.1 Robust fault isolation 203
7.5.2 Probability distribution of multiple models 204
7.5.3 Orthogonal parity relations 205
7.5.4 Design of robust parity relations via optimization 206
7.5.5 Closed-loop optimal parity relations 207
7.6 Summary 208
8. FREQUENCY DOMAIN DESIGN AND Hoc OPTIMIZATION FOR FDI 209
8.1 Introduction 209
8.2 Robust Fault Detection via Factorization Approach 212
8.2.1 Residual generator design using factorization 212
8.2.2 Perfect FDI and disturbance de-coupling 216
8.2.3 Design of optimal residuals 222
8.3 Robust FDI Design via Standard Hoc Filtering Formulation 228
8.3.1 Robust residual generation with disturbance attenuation 228
8.3.2 Fault estimation 231
8.3.3 Fault estimation with disturbance attenuation 234
8.3.4 Robustness issues 236
8.4 LMI Approach for Robust Residual Generation 239
8.4.1 Problem formulation 239
8.4.2 Analysis of sensitivity norm 241
8.4.3 LMI solution to Hoc control 244
8.4.4 Duality and Hoc estimation 245
8.4.5 Robust fault detection observer design 247
8.4.6 Discussion on LMI robust FDI approach 248
8.5 Summary 249
9. FAULT DIAGNOSIS OF NON-LINEAR DYNAMIC SYSTEMS 251
9.1 In trod uction 251
9.2 Linear and Non-linear Observer-based Approaches 254
9.3 Neural Networks in Fault Diagnosis of Non-linear Dynamic Systems 262
9.3.1 Applications of neural networks in non-linear FDI 263
9.3.2 A fault diagnosis scheme based on neural networks 266
9.3.3 Neural network-based FDI for a laboratory system 267
9.4 Fuzzy Observers for Non-linear Dynamic Systems Fault Diagnosis 272
9.4.1 Takagi-Sugeno fuzzy model and stability analysis 273
9.4.2 Fuzzy observers and residual generation 275
9.4.3 Induction motor FDI in a rail traction system 279
9.5 A Neuro-Fuzzy Approach for Non-linear Systems FDI 286
9.5.1 B-Spline neural networks and fuzzy logic interpretation 286
9.5.2 Residual generation and FDI using B-Spline Networks 288
9.5.3 Fault isolation via B-Spline function networks 290
9.5.4 Fault diagnosis of a two-tanks system 290
Contents IX
9.6 Summary 294
Appendices
A- Terminology in Model-based Fault Diagnosis 297
8- Inverted Pendulum Example 299
C- Matrix Rank Decomposition 301
D- Proof of Lemma 3.2 303
E- Low Rank Matrix Approximation 305
References 307
List of Figures
1.1 Hardware vs analytical redundancy 5
2.1 Conceptual structure of model-based fault diagnosis 21
2.2 Fault diagnosis and control loop 22
2.3 Open-loop system 23
2.4 The system dynamics 23
2.5 Sensors, output and measured output 24
2.6 Actuator, input and actuation 24
2.7 Input sensor, actuation and measured actuation 25
2.8 Redundant signal structure in residual generation 26
2.9 The general structure of a residual generator 27
2.10 Faults and the residual 29
2.11 Inverted pendulum example (Fault signal) 29
2.12 Inverted pendulum example (Fault in sensor 1) 29
2.13 Inverted pendulum example (Fault in sensor 2) 30
2.14 Inverted pendulum example (Fault in sensor 3) 30
2.15a Structured residual set (Dedicated scheme) 33
2.15b Structured residual set (Generalized scheme) 33
2.16 Directional residual vector for fault isolation 33
2.17 Residual generation via a generalized Luenberger observer 37
2.18 Residual generation via parallel redundancy 39
2.19 Residual generation via temporal redundancy 43
2.20 Application of an adaptive threshold 53
2.21 A FDI system with the threshold adaptor (selector) 54
2.22 An integrated knowledge-based system for fault diagnosis 63
3.1 The structure of a full-order unknown input observer 71
3.2 A robust sensor fault isolation scheme 80
3.3 A robust actuator fault isolation scheme 81
3.4 UIO residuals when a fault occurs in Ul (t) (without parameter
variations) 85
3.5 UIO residuals when a fault occurs in U2(t) (without parameter
variations) 85
Xl