ROBUST MODEL-BASED FAULT DIAGNOSIS FOR DYNAMIC SYSTEMS

Transcription

1 ROBUST MODEL-BASED FAULT DIAGNOSIS FOR DYNAMIC SYSTEMS

2 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 FUZZY LOGIC IN DATA MODELING: Semantics, Constraints, and Database Design by Guoqing Chen ISBN

3 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

4 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 ISBN (ebook) DOI / 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, photocopying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+Business Media, LLC. Printed on acid-free paper.

5 Contents List of Figures List of Tables Preface Acknowledgments XI xv xvii 1. INTRODUCTION Background Importance of fault diagnosis Fault diagnosis terminology Fault diagnosis in intelligent fault-tolerant control Model-based fault diagnosis Robustness in model-based fault diagnosis Brief history of model-based fault diagnosis Outline of the Book BASIC PRINCIPLES OF MODEL-BASED FDI I ntrod uction Model-based Fault Diagnosis Methods On-line Fault Diagnosis Modeling of Faulty Systems A General Structure of Residual Generation in Model-based FDI Fault Detectability Fault detectability condition Strong fault detectability condition Fault Isolability Structured residual set Fixed direction residual vector Sensor and actuator faults isolation Residual Generation Techniques Observer-based approaches Parity vector (relation) methods Factorization methods for residual generation Model-based FDI via Parameter Estimation 45 XIX v

6 vi ROBUST MODEL-BASED FAULT DIAGNOSIS FOR DYNAMIC SYSTEMS 2.10 Fault Diagnosis for Stochastic Systems Robust Residual Generation Problems Robustness to disturbances Robustness to modeling errors Discussion on robust FDI Adaptive Thresholds in Robust FDI Applicability of Model-based FDI Methods Observer-based approaches Parity relation approaches Parameter estimation approaches Discussion on applicability Integration of Fault Diagnosis Techniques Fuzzy logic in fault diagnosis Qualitative fault diagnosis Integrated fault diagnosis systems Summary ROBUST RESIDUAL GENERATION VIA UIOS Introduction Theory and Design of Unknown Input Observers Theory of UIOs Design procedure for UIOs Robust Fault Detection and Isolation Schemes based on UIOs Robust fault detection schemes based on UIOs Robust fault isolation schemes based on UIOs Robust actuator FDI example Robust Fault Detection Filters and Robust Directional Residuals Basic principles of fault detection filters Robust fault detection filter and fault isolation Robust isolation of faulty sensors in a jet engine system Filtering and Robust FDI of Uncertain Stochastic Systems Optimal observer for uncertain stochastic systems Robust residual generation and fault detection An illustrative example Summary ROBUST FDI VIA EIGENSTRUCTURE ASSIGNMENT I ntrod uction Residual Generation and Responses General Principle for Disturbance De-coupling Design Disturbance de-coupling design via invariant subspaces Disturbance de-coupling via eigenstructure assignment Disturbance De-coupling by Assigning Left Eigenvectors Robust Design Via Parametric Eigenstructure Assignment Robust FDI via parametric eigenstructure assignment An illustrative example Disturbance De-coupling by Assigning Right Eigenvectors 127

7 Contents vii 4.7 Dead-Beat Design for Robust Residual Generation Two Numerical Examples in Eigenstructure Assignment Conclusion and Discussion DISTURBANCE DISTRIBUTION MATRIX DETERMINATION FOR FDI I ntrod uction Direct Determination of Disturbance Distribution Matrix Noise and additive non-linearity Bilinear systems Model reduction Parameter perturbations Low rank approximation of distribution matrix Bounded uncertainty Estimation of Disturbance and Disturbance Distribution Matrix Disturbance vector estimation via augmented observer Derivation of disturbance distribution matrix Estimation of disturbance vector using de-convolution Optimal Distribution Matrix for Multiple Operating Points Modeling and FDI for a Jet Engine System Background on fault diagnosis for jet engine systems Jet engine system description Application of direct computation and optimization method Application of augmented observer method Conclusion ROBUST FDI VIA MULTI-OBJECTIVE OPTIMIZATION Introduction Residual Generation and Performance Indices Residual generation and responses Performance indices in robust residual generation Remarks on performance indices Parameterization In Observer Design Real eigenvalue case Complex-conjugate eigenvalue case Eigenvalue specifications Multi-Objective Optimization and the Method of Inequalities Multi-objective optimization The method of inequalities Optimization via Genetic Algorithms Introduction to genetic algorithms Steps of a genetic algorithm in optimization Detection of Incipient Sensor Faults in Flight Control Systems Conclusions ROBUST FDI USING OPTIMAL PARITY RELATIONS Introduction Performance Indices for Optimal Parity Relation Design 194

8 viii ROBUST MODEL-BASED FAULT DIAGNOSIS FOR DYNAMIC SYSTEMS 7.3 Optimal Parity Relation Design via Multi-Objective Optimization Solving optimization problems via SVD Solutions for multi-objective optimization A Numerical Illustration Example Discussion on Designing Optimal Parity Relations Robust fault isolation Probability distribution of multiple models Orthogonal parity relations Design of robust parity relations via optimization Closed-loop optimal parity relations Summary FREQUENCY DOMAIN DESIGN AND Hoc OPTIMIZATION FOR FDI Introduction Robust Fault Detection via Factorization Approach Residual generator design using factorization Perfect FDI and disturbance de-coupling Design of optimal residuals Robust FDI Design via Standard Hoc Filtering Formulation Robust residual generation with disturbance attenuation Fault estimation Fault estimation with disturbance attenuation Robustness issues LMI Approach for Robust Residual Generation Problem formulation Analysis of sensitivity norm LMI solution to Hoc control Duality and Hoc estimation Robust fault detection observer design Discussion on LMI robust FDI approach Summary FAULT DIAGNOSIS OF NON-LINEAR DYNAMIC SYSTEMS I ntrod uction Linear and Non-linear Observer-based Approaches Neural Networks in Fault Diagnosis of Non-linear Dynamic Systems Applications of neural networks in non-linear FDI A fault diagnosis scheme based on neural networks Neural network-based FDI for a laboratory system Fuzzy Observers for Non-linear Dynamic Systems Fault Diagnosis Takagi-Sugeno fuzzy model and stability analysis Fuzzy observers and residual generation Induction motor FDI in a rail traction system A Neuro-Fuzzy Approach for Non-linear Systems FDI B-Spline neural networks and fuzzy logic interpretation Residual generation and FDI using B-Spline Networks Fault isolation via B-Spline function networks Fault diagnosis of a two-tanks system 290

9 Contents IX 9.6 Summary Appendices A- Terminology in Model-based Fault Diagnosis 8- Inverted Pendulum Example C- Matrix Rank Decomposition D- Proof of Lemma 3.2 E- Low Rank Matrix Approximation References

10 List of Figures 1.1 Hardware vs analytical redundancy Conceptual structure of model-based fault diagnosis Fault diagnosis and control loop Open-loop system The system dynamics Sensors, output and measured output Actuator, input and actuation Input sensor, actuation and measured actuation Redundant signal structure in residual generation The general structure of a residual generator Faults and the residual Inverted pendulum example (Fault signal) Inverted pendulum example (Fault in sensor 1) Inverted pendulum example (Fault in sensor 2) Inverted pendulum example (Fault in sensor 3) a Structured residual set (Dedicated scheme) b Structured residual set (Generalized scheme) Directional residual vector for fault isolation Residual generation via a generalized Luenberger observer Residual generation via parallel redundancy Residual generation via temporal redundancy Application of an adaptive threshold A FDI system with the threshold adaptor (selector) An integrated knowledge-based system for fault diagnosis The structure of a full-order unknown input observer A robust sensor fault isolation scheme A robust actuator fault isolation scheme UIO residuals when a fault occurs in Ul (t) (without parameter variations) UIO residuals when a fault occurs in U2(t) (without parameter variations) 85 Xl

11 xii ROBUST MODEL-BASED FAULT DIAGNOSIS FOR DYNAMIC SYSTEMS 3.6 UIO residuals when a fault occurs in U3 (t) (without parameter variations) UIO residuals when a fault occurs in Ul(t) (with parameter variations) UIO residuals when a fault occurs in U2(t) (with parameter variations) UIO residuals when a fault occurs in U3 (t) (with parameter variations) Fault isolation based on directional residuals Optimal disturbance de-coupling observer and residual The state estimation error absolute values for 'fly (ODDO: Optimal Disturbance De-coupling Observer; KF: Kalman Filter) The state estimation error absolute values for W Z (ODDO: Optimal Disturbance De-coupling Observer; KF: Kalman Filter) The state estimation error absolute values for 6z (ODDO: Optimal Disturbance De-coupling Observer; KF: Kalman Filter) The fault detection function when a fault occurs in the sensor for 6z The fault detection function when a fault occurs in the actuator Robust observer-based residual generation Disturbance de-coupling via eigenvector assignment Robust residual generation via the 1st-order parity relation Gas turbine jet engine Norm of the output estimation error Absolute value of the fault-free residual The faulty output and residual when a fault occurs in the temperature sensor for T The output estimation error when a fault occurs in the temperature sensor for T Faulty output of the pressure measurement P6 and corresponding residual The disturbance vector d1(k) for the step input case The disturbance vector d1 (k) for the sinusoidal input case The residual (r(k)) norm and the output estimation error (ey(k)) norm Faulty pressure (P6 ) measurement The residual norm and the output estimation error norm for the case a parabolic fault on the spool speed sensor for N H Residual when a fault occurs in the temperature measurement T7 with operating condition changed Robust residual generation via a full-order observer An example of the method of inequalities The "moving-boundaries" process Computational structure of genetic algorithms FDI in flight control systems 189

12 LIST OF FIGURES xiii 6.6 The fault signal shape The faulty and normal measurements for roll rate p The residual norm when a fault occurs in the roll rate sensor Faulty measurement when 'Y = Robust residuals for different operating points Frequency domain residual generator Formulation of disturbance attenuation Standard problem formulation of disturbance attenuation Formulation of fault estimation Standard problem formulation of fault estimation Formulation of filtered fault estimation Standard problem formulation of filtered fault estimation Formulation of filtered fault estimation with disturbance attenuation Standard problem formulation of filtered fault estimation with disturbance attenuation Standard problem formulation of robust fault estimation Formulation of integrated design Standard problem formulation of integrated design Standard problem formulation of integrated design with robustness consideration The neural network model of a non-linear dynamic system A conceptual structure of the integrated fault diagnosis approach Fault detection and isolation scheme using two neural networks Fault detection and isolation scheme using two neural networks Three tanks system Typical shapes of fault signals Alarm signals when an incipient fault occurred in tank Alarm signals when an abrupt fault occurred in tank Alarm signals when an incipient fault occurred in tank Alarm signals when two incipient faults occurred in tank 1 and tank Fuzzy observer Eigenvalue region A rail traction control system Membership grade functions Output estimation error due to initial perturbations Residual response to fault Fault isolation and fault-tolerant control scheme for the traction system Fault diagnostic residuals from real-time simulations Torque error with reconfiguration action Torque error in the presence of phase sensor faults A B-Spine function network with two inputs, 3 basis functions and one output 287

13 XIV ROBUST MODEL-BASED FAULT DIAGNOSIS FOR DYNAMIC SYSTEMS B.l B-Spline functions defined over the normalized input space Network architecture used for fault isolation Two tanks system Residual response Flag 1 response to faults Flag 2 response to faults Flag 3 response to faults The controlled inverted pendulum system

14 List of Tables Unknown input observer (UIO) design procedure Fault isolation using Beard fault detection filter Fault isolation using robust fault detection filter Optimal disturbance de-coupling observer design procedure Robust fault detection design algorithm Performance indices for different designs Training data for fault classifier Qualitative model of the residual generator

15 Preface There is an increasing demand for dynamic systems to become more safe and reliable. This requirement extends beyond the normally accepted safety-critical systems of nuclear reactors and aircraft where safety is paramount important, to systems such as autonomous vehicles and fast railways where the system availability is vital. It is clear that fault diagnosis (including fault detection and isolation, FDI) has been becoming an important subject in modern control theory and practice. For example, the number of papers on FDI presented in many control-related conferences has been increasing steadily. The subject of fault detection and isolation continues to mature to an established field of research in control engineering. A large amount of knowledge on model-based fault diagnosis has been accumulated through the literature since the beginning of the 1970s. However, publications are scattered over many papers and a few edited books. Up to the end of 1997, there is no any book which presents the subject in an unified framework. The consequence of this is the lack of "common language", different researchers use different terminology. This problem has obstructed the progress of model-based FDI techniques and has been causing great concern in research community. Many survey papers have been published to tackle this problem. However, a book which presents the materials in a unified format and provides a comprehensive foundation of model-based FDI is urgently needed. Such a book would promote the subject of model-based FDI and make the techniques more accessible for engineers and research students. This view has been shared by many researchers in this field. Such a book is also possible, because many important definitions have been made and the correspondences between different model-based FDI methods have been established. This new book presents the subject of model-based FDI in a unified framework. It contains many important topics and methods, however perfect coverage and completeness is not the primary concern. The book focuses on fundamental issues such as basic definitions and the importance of robustness in FDI approaches. In this book, FDI concepts and methods are illustrated by either simple academic examples or practical applications. The first two chapters are

16 xviii ROBUST MODEL-BASED FAULT DIAGNOSIS FOR DYNAMIC SYSTEMS of tutorial value and provide a starting point for new comers to this field. The rest of the book presents the state-of-the-art in model-based FDI by discussing many important robust approaches and their applications. This will certainly appeal to experts in this field. The book targets both new comers, who want to get into this subject, and experts, who are concerned with fundamental issues and are also looking for inspiration for future research. The book is useful for both researchers in academia and professional engineers in industry because both theory and applications have been discussed. Although this is a research monograph, it will be an important text for MSc & PhD research students world-wide. The largest market, however will be academics, libraries and practising engineers and scientists throughout the world. DR J. CHEN & PROF. R. J. PATTON

17 Acknowledgments We have been enjoying many fruitful discussions and collaborations with other researchers world-wide. It is impossible to mention all of them. However, we would like to thank Prof. Paul M. Frank of University of Duisburg, Germany and Prof. Janos J. Gertler of George Mason University, USA with whom we had many discussions and debates. We are also grateful to Prof. Peter D. Roberts of City University, UK for his encouragement for starting this book. We have had some help in the writing of this book. Many thanks to Prof. J. Stoustrup of Alborg University, Denmark, Prof. M. Kinnaert of Universite Libre de Bruxelles, Belgium, Prof. X. Ding of FH-Lausitz, Germany, Dr H. Wang of UMIST, UK, Dr D. N. Shields of Coventry University, UK and Prof. M. M. Polycarpou of University of Cincinnati, USA for sending us their recent publications which enable us to include updated information. Special thank goes to Dr Ming Hou of University of Hull, UK who provides us with his new research results in files. We would like to express our sincere gratitude and thanks to our families for their support. Dr Chen is very grateful to his wife Ling Hao and daughter Nancy for their patience and understanding when he devotes many of his evening and weekends to this book. Prof. Patton would like to thank his wife Ann and children Libby, Kirstie and Stephen for their understanding when he carried around the draft manuscript of this book in his weekends and holidays.