Model-based Fault Diagnosis Techniques (eBook)

Preface 6
Contents 9
Notation 16
Part I Introduction, basic concepts and preliminaries 18
1 Introduction 19
1.1 Basic concepts of fault diagnosis technique 20
1.2 Historical development and some relevant issues 24
1.3 Notes and references 27
2 Basic ideas, major issues and tools in the observer-based FDI framework 28
2.1 On the observer-based residual generator framework 28
2.2 Unknown input decoupling and fault isolation issues 29
2.3 Robustness issues in the observer-based FDI framework 30
2.4 On the parity space FDI framework 32
2.5 Residual evaluation and threshold computation 32
2.6 FDI system synthesis and design 33
2.7 Notes and references 33
3 Modelling of technical systems 35
3.1 Description of nominal system behavior 36
3.2 Coprime factorization technique 37
3.4 Representations of system models with model uncertainties 39
3.5 Modelling of faults 41
3.6 Modelling of faults in closed loop feedback control systems 44
3.7 Benchmark examples 45
3.8 Notes and references 63
4 Structural fault detectability, isolability and identi.ability 65
4.1 Structural fault detectability 65
4.2 Excitations and su ciently excited systems 70
4.3 Structural fault isolability 71
4.4 Structural fault identi.ability 79
4.5 Notes and references 81
Part II Residual generation 83
5 Basic residual generation methods 84
5.1 Analytical redundancy 85
5.2 Residuals and parameterization of residual generators 88
5.3 Problems related to residual generator design and implementation 91
5.4 Fault detection .lter 93
5.5 Diagnostic observer scheme 94
5.6 Parity space approach 110
5.7 Interconnections, comparison and some remarks 116
5.8 Notes and references 127
6 Perfect unknown input decoupling 128
6.1 Problem formulation 128
6.2 Existence conditions of PUIDP 130
6.3 A frequency domain approach 138
6.4 UIFDF design 141
6.5 UIDO design 152
6.6 Unknown input parity space approach 166
6.7 An alternative scheme - null matrix approach 166
6.8 Minimum order residual generator 167
6.9 Notes and references 172
7 Residual generation with enhanced robustness against unknown inputs 174
7.1 Mathematical and control theoretical preliminaries 175
7.2 Kalman .lter based residual generation 187
7.3 Approximation of UI-distribution matrix 191
7.4 Robustness, fault sensitivity and performance indices 197
7.5 Optimal selection of parity matrices and vectors 200
7.6 H optimal fault identi.cation scheme 214
7.7 H2/H2 design of residual generators 215
7.8 Relationship between H2/H2 design and optimal selection of parity vectors 219
7.9 LMI aided design of FDF 224
7.10 The uni.ed solution 245
7.11 The general form of the uni.ed solution 251
7.12 Notes and references 257
8 Residual generation with enhanced robustness against model uncertainties 260
8.1 Preliminaries 261
8.2 Transforming model uncertainties into unknown inputs 263
8.3 Reference model strategies 265
8.4 Residual generation for systems with polytopic uncertainties 272
8.5 Residual generation for stochastically uncertain systems 278
8.6 Notes and references 289
Part III Residual evaluation and threshold computation 291
9 Norm based residual evaluation and threshold computation 292
9.1 Preliminaries 293
9.2 Basic concepts 295
9.3 Some standard evaluation functions 296
9.4 Basic ideas of threshold setting and problem formulation 298
9.5 Computation of J 2 302
9.6 Computation of J 308
9.7 Computation of J 2 313
9.8 Threshold generator 318
9.9 Notes and references 321
10 Statistical methods based residual evaluation and threshold setting 322
10.1 Introduction 322
10.2 Elementary statistical methods 323
10.3 Criteria for threshold computation 331
10.4 Application of GLR testing methods 335
10.5 Notes and references 344
11 Integration of norm based and statistical methods 345
11.1 Residual evaluation in stochastic systems with deterministic disturbances 345
11.2 Residual evaluation scheme for stochastically uncertain systems 353
11.3 Probabilistic robustness technique aided threshold computation 366
11.4 Notes and references 374
Part IV Fault detection, isolation and identi.cation schemes 376
12 Integrated design of fault detection systems 377
12.1 FAR and FDR 378
12.2 Maximization of fault detectability by a given FAR 381
12.3 Minimizing false alarm number by a given FDR 394
12.4 On the application to stochastic systems 406
12.5 Notes and references 407
13 Fault isolation schemes 410
13.1 Essentials 411
13.2 A frequency domain approach 417
13.3 Fault isolation .lter design 419
13.4 An algebraic approach to fault isolation 433
13.5 Fault isolation using a bank of residual generators 438
13.6 Notes and references 445
14 On fault identi.cation 448
14.1 Fault identi.cation .lter and perfect fault identi.cation 449
14.2 FIF design with additional information 452
14.3 On the optimal fault identi.cation problem 455
14.4 Study on the role of the weighting matrix 457
14.5 Approaches to the design of FIF 463
14.6 Notes and references 467
References 469
Index 477