Model-based Fault Diagnosis Techniques Design Schemes, Algorithms, and Tools

Transcription

1 Steven X. Ding Model-based Fault Diagnosis Techniques Design Schemes, Algorithms, and Tools Springer

2 Notation XIX Part I Introduction, basic concepts and preliminaries 1 Introduction Basic concepts of fault diagnosis technique Historical development and some relevant issues Notes and references 11 2 Basic ideas, major issues and tools in the observer-based FDI framework On the observer-based residual generator framework Unknown input decoupling and fault isolation issues Robustness issues in the observer-based FDI framework On the parity Space FDI framework Residual evaluation and threshold computation FDI System synthesis and design Notes and references 18 3 Modelling of technical Systems Description of nominal System behavior Coprime factofization technique Representations of disturbed Systems Representations of System modeis with model uncertainties Modelling of faults Modelling of faults in closed loop feedback control Systems Benchmark examples Speed control of a DC motor Inverted pendulum control System Three tank system 38

3 XII Vehicle lateral dynamic system Electrohydraulic Servo-actuator Notes and references 49 4 Structural fault detectability, isolability and identifiability Structural fault detectability Excitations and sufficiently excited Systems Structural fault isolability Concept of structural fault isolability Fault isolability conditions Structural fault identifiability Notes and references 67 Part II Residual generation 5 Basic residual generation methods Analytical redundancy Residuais and parameterization of residual generators Problems related to residual generator design and implementation Fault detection filter Diagnostic observer scheme Construction of diagnostic observer-based residual generators Characterization of Solutions A numerical approach An algebraic approach Parity space approach Construction of parity relation based residual generators Characterization of parity space Examples Interconnections, comparison and some remarks Parity space approach and diagnostic observer Diagnostic observer and residual generator of general form Applications of the interconnections and some remarks Examples Notes and references Perfect unknown input decoupling Problem formulation Existence conditions of PUIDP A general existence condition A check condition via Rosenbrock system matrix 118

4 XIII Algebraic check conditions A frequency domain approach UIFDF design The eigenstructure assignment approach Geometric approach UIDO design An algebraic approach Unknown input observer approach A matrix pencil approach to the UIDO design A numerical approach to the UIDO design Unknown input parity space approach An alternative scheme - null matrix approach Minimum order residual generator Minimum order residual generator design by geometric approach An alternative Solution Notes and references Residual generation with enhanced robustness against unknown inputs Mathematical and control theoretical preliminaries Signal norms System norms Computation of W 2 and Hex, norms Singular value decomposition Co-inner-outer factorization Model matching problem Essentials of the LMI technique Kaiman filter based residual generation Approximation of Ul-distribution matrix Approximation of matrices Ej, Fj Approximation of matrices Hd, s Some remarks Robustness, fault sensitivity and Performance indices Robustness and sensitivity Performance indices: robustness vs. sensitivity Relations between the Performance indices Optimal selection of parity matrices and vectors Sf,+/Rd as Performance index Sf^-fRd as Performance index JS-R as Performance index Optimization Performance and System order Summary and some remarks Hoo optimal fault identification scheme "H-2,I'H.2 design of residual generators 202

5 7.8 Relationship between H2/H2 design and optimal selection of parity vectors LMI aided design of FDF H 2 to H 2 trade-off design of FDF On U- index H 2 to U- trade-off design of FDF Woo to W_ trade-off design of FDF An alternative Hoc to H- trade-off design of FDF A brief summary and discussion The unified Solution Hi/Hoo index and problem formulation Hi/Hoo optimal design of FDF: the Standard form Discrete time version of the unified Solution The general form of the unified Solution Extended CIOF Generalization of the unified Solution Notes and references 244 Residual generation with enhanced robustness against model uncertainties Preliminaries LMI aided computation for system bounds Stability of stochastically uncertain Systems Transforming model uncertainties into unknown inputs Reference model strategies Basic idea A reference model based Solution for Systems with norm bounded uncertainties Residual generation for Systems with polytopic uncertainties The reference model scheme based scheme H to Hoc design formulation Residual generation for stochastically uncertain Systems System dynamics and Statistical properties Basic idea and problem formulation An LMI Solution An alternative approach Notes and references 276

6 XV Part III Residual evaluation and threshold computation 9 Norm based residual evaluation and threshold computation Preliminaries Basic concepts Some Standard evaluation functions Basic ideas of threshold setting and problem formulation Dynamics of the residual generator Definitions of thresholds and problem formulation Computation of Jth,RMs, Computation of Jth,RMS,2 for the Systems with the norm bounded uncertainty Computation of Jth,RMS,2 for the Systems with the polytopic uncertainty Computation of Jth, P eak, P eak Computation of Jth,peak,peak for the Systems with the norm bounded uncertainty Computation of Jth,peak,peak for the Systems with the polytopic uncertainty Computation of Jth,peak, Computation of Jth, P eak,2 for the Systems with the norm bounded uncertainty Computation of Jth,peak,2 f r the Systems with the polytopic uncertainty Threshold generator Notes and references Statistical methods based residual evaluation and threshold setting Introduction Elementary Statistical methods Basic hypothesis test Likelihood ratio and generalized likelihood ratio Vector-valued GLR Detection of change in variance Aspects of on-line realization Criteria for threshold computation The Neyman-Pearson criterion Maximum a posteriori probability (MAP) criterion Bayes' criterion Some remarks Application of GLR testing methods Kaiman filter based fault detection Parity space based fault detection 330

7 XVI 10.5 Notes and references Integration of norm based and Statistical methods Residual evaluation in stochastic Systems with deterministic disturbances Residual generation Problem formulation GLR Solutions Discussion and example Residual evaluation scheme for stochastically uncertain Systems Problem formulation Solution and design algorithms Probabilistic robustness technique aided threshold computation Problem formulation Outline of the basic idea LMIs needed for the Solutions Problem Solutions in the probabilistic framework An application example Concluding remarks Notes and references 364 Part IV Fault detection, isolation and identification schemes 12 Integrated design of fault detection Systems FAR and FDR Maximization of fault detectability by a given FAR Problem formulation Essential form of the Solution A general Solution Interconnections and comparison Examples Minimizing false alarm number by a given FDR Problem formulation Essential form of the Solution The state space form The extended form Interpretation of the Solutions and discussion An example On the application to stochastic Systems Application to maximizing FDR by a given FAR Application to minimizing FAR by a given FDR Notes and references 399

8 XVII 13 Fault isolation schemes Essentials Existence conditions for a perfect fault isolation PFIs and unknown input decoupling PFIs with unknown input decoupling (PFIUID) A frequency domain approach Fault isolation filter design A design approach based on the duality to decoupling control The geometric approach A generalized design approach An algebraic approach to fault isolation Fault isolation using a bank of residual generators The dedicated observer scheme (DOS) The generalized observer scheme (GOS) Notes and references On fault identincation Fault identincation filter and perfect fault identincation FIF design with additional information On the optimal fault identincation problem Study on the role of the weighting matrix Approaches to the design of FIF A general fault identincation scheme An alternative fault detection scheme Identification of the size of a fault Notes and references 460 References 463 Index 471