Model-Based Fault Diagnosis Techniques. Design Schemes, Algorithms and Tools

Description

Model-Based Fault Diagnosis Techniques Series Editors' Foreword Preface Contents Notation Part I: Introduction, Basic Concepts and Preliminaries Chapter 1: Introduction 1.1 Basic Concepts of Fault Diagnosis Technique 1.2 Historical Development and Some Relevant Issues 1.3 Notes and References Chapter 2: Basic Ideas, Major Issues and Tools in the Observer-Based FDI Framework 2.1 On the Observer-Based Residual Generator Framework 2.2 Unknown Input Decoupling and Fault Isolation Issues 2.3 Robustness Issues in the Observer-Based FDI Framework 2.4 On the Parity Space FDI Framework 2.5 Residual Evaluation and Threshold Computation 2.6 FDI System Synthesis and Design 2.7 Notes and References Chapter 3: Modelling of Technical Systems 3.1 Description of Nominal System Behavior 3.2 Coprime Factorization Technique 3.3 Representations of Systems with Disturbances 3.4 Representations of System Models with Model Uncertainties 3.5 Modelling of Faults 3.6 Modelling of Faults in Closed-Loop Feedback Control Systems 3.7 Case Study and Application Examples 3.7.1 Speed Control of a DC Motor Model of DC Motor Models of DC Motor Control System Modelling of Faults 3.7.2 Inverted Pendulum Control System Nonlinear System Model Disturbances Linear Model Discrete-Time Model LCF of the Nominal Model Model Uncertainty Modelling of Faults Closed-Loop Model 3.7.3 Three-Tank System Nonlinear Model Linear Model Model Uncertainty Modelling of Faults Closed-Loop Model 3.7.4 Vehicle Lateral Dynamic System Nominal Model Disturbances Model Uncertainties Modelling of Faults 3.7.5 Continuous Stirred Tank Heater System Dynamics and Nonlinear Model Linear Model Model Uncertainties and Unknown Inputs Modelling of Faults 3.8 Notes and References Chapter 4: Fault Detectability, Isolability and Identifiability 4.1 Fault Detectability 4.2 Excitations and Detection of Multiplicative Faults 4.3 Fault Isolability 4.3.1 Concept of System Fault Isolability 4.3.2 Fault Isolability Conditions 4.4 Fault Identifiability 4.5 Notes and References Part II: Residual Generation Chapter 5: Basic Residual Generation Methods 5.1 Analytical Redundancy 5.2 Residuals and Parameterization of Residual Generators 5.3 Issues Related to Residual Generator Design and Implementation 5.4 Fault Detection Filter 5.5 Diagnostic Observer Scheme 5.5.1 Construction of Diagnostic Observer-Based Residual Generators 5.5.2 Characterization of Solutions 5.5.3 A Numerical Approach 5.5.4 An Algebraic Approach 5.6 Parity Space Approach 5.6.1 Construction of Parity Relation Based Residual Generators 5.6.2 Characterization of Parity Space 5.6.3 Examples 5.7 Interconnections, Comparison and Some Remarks 5.7.1 Parity Space Approach and Diagnostic Observer 5.7.2 Diagnostic Observer and Residual Generator of General Form 5.7.3 Applications of the Interconnections and Some Remarks 5.7.4 Examples 5.8 Notes and References Chapter 6: Perfect Unknown Input Decoupling 6.1 Problem Formulation 6.2 Existence Conditions of PUIDP 6.2.1 A General Existence Condition 6.2.2 A Check Condition via Rosenbrock System Matrix 6.2.3 An Algebraic Check Condition 6.3 A Frequency Domain Approach 6.4 UIFDF Design 6.4.1 The Eigenstructure Assignment Approach 6.4.2 Geometric Approach 6.5 UIDO Design 6.5.1 An Algebraic Approach 6.5.2 Unknown Input Observer Approach 6.5.3 A Matrix Pencil Approach to the UIDO Design 6.5.4 A Numerical Approach to the UIDO Design 6.6 Unknown Input Parity Space Approach 6.7 An Alternative Scheme-Null Matrix Approach 6.8 Discussion 6.9 Minimum Order Residual Generator 6.9.1 Minimum Order Residual Generator Design by Geometric Approach 6.9.2 An Alternative Solution 6.10 Notes and References Chapter 7: Residual Generation with Enhanced Robustness Against Unknown Inputs 7.1 Mathematical and Control Theoretical Preliminaries 7.1.1 Signal Norms L2 ( l2 ) Norm Peak Norm 2 (Euclidean) Norm infty Norm 7.1.2 System Norms Hinfty Norm Peak-to-Peak Gain Generalized H2 Norm H2 Norm Matrix Norm Induced by the 2 Norm for Vectors Frobenius-Norm infty Norm 7.1.3 Computation of H2 and Hinfty Norms 7.1.4 Singular Value Decomposition (SVD) 7.1.5 Co-Inner-Outer Factorization 7.1.6 Model Matching Problem 7.1.7 Essentials of the LMI Technique 7.2 Kalman Filter Based Residual Generation Recursive Computation for Optimal State Estimation Recursive Computation for Kalman Filter Gain 7.3 Robustness, Fault Sensitivity and Performance Indices 7.3.1 Robustness and Sensitivity 7.3.2 Performance Indices: Robustness vs. Sensitivity 7.3.3 Relations Between the Performance Indices 7.4 Optimal Selection of Parity Matrices and Vectors 7.4.1 Sf,+/Rd as Performance Index 7.4.2 Sf,-/Rd as Performance Index 7.4.3 JS-R as Performance Index 7.4.4 Optimization Performance and System Order 7.4.5 Summary and Some Remarks 7.5 Hinfty Optimal Fault Identification Scheme 7.6 H2/H2 Design of Residual Generators 7.7 Relationship Between H2/H2 Design and Optimal Selection of Parity Vectors 7.8 LMI Aided Design of FDF 7.8.1 H2 to H2 Trade-off Design of FDF 7.8.2 On the H- Index 7.8.3 H2 to H- Trade-off Design of FDF 7.8.4 Hinfty to H- Trade-off Design of FDF 7.8.5 Hinfty to H- Trade-off Design of FDF in a Finite Frequency Range 7.8.6 An Alternative Hinfty to H- Trade-off Design of FDF 7.8.7 A Brief Summary and Discussion 7.9 The Unified Solution 7.9.1 Hi/Hinfty Index and Problem Formulation 7.9.2 Hi/Hinfty Optimal Design of FDF: The Standard Form 7.9.3 Discrete-Time Version of the Unified Solution 7.9.4 A Generalized Interpretation 7.10 The General Form of the Unified Solution 7.10.1 Extended CIOF 7.10.2 Generalization of the Unified Solution 7.11 Notes and References Chapter 8: Residual Generation with Enhanced Robustness Against Model Uncertainties 8.1 Preliminaries 8.1.1 LMI Aided Computation for System Bounds 8.1.2 Stability of Stochastically Uncertain Systems 8.2 Transforming Model Uncertainties into Unknown Inputs 8.3 Reference Model Based Strategies 8.3.1 The Basic Idea 8.3.2 A Reference Model Based Solution for Systems with Norm-Bounded Uncertainties 8.4 Residual Generation for Systems with Polytopic Uncertainties 8.4.1 The Reference Model Scheme Based Scheme 8.4.2 H- to Hinfty Design Formulation 8.5 Residual Generation for Stochastically Uncertain Systems 8.5.1 System Dynamics and Statistical Properties 8.5.2 Basic Idea and Problem Formulation 8.5.3 An LMI Solution 8.5.4 An Alternative Approach 8.6 Notes and References Part III: Residual Evaluation and Threshold Computation Chapter 9: Norm-Based Residual Evaluation and Threshold Computation 9.1 Preliminaries 9.2 Basic Concepts 9.3 Some Standard Evaluation Functions Peak Value RMS Value 9.4 Basic Ideas of Threshold Setting and Problem Formulation 9.4.1 Dynamics of the Residual Generator 9.4.2 Definitions of Thresholds and Problem Formulation 9.5 Computation of Jth,RMS,2 9.5.1 Computation of Jth,RMS,2 for the Systems with the Norm-Bounded Uncertainty 9.5.2 Computation of Jth,RMS,2 for the Systems with the Polytopic Uncertainty 9.6 Computation of Jth,peak,peak 9.6.1 Computation of Jth,peak,peak for the Systems with the Norm-Bounded Uncertainty 9.6.2 Computation of Jth,peak,peak for the Systems with the Polytopic Uncertainty 9.7 Computation of Jth,peak,2 9.7.1 Computation of Jth,peak,2 for the Systems with the Norm-Bounded Uncertainty 9.7.2 Computation of Jth,peak,2 for the Systems with the Polytopic Uncertainty 9.8 Threshold Generator 9.9 Notes and References Chapter 10: Statistical Methods Based Residual Evaluation and Threshold Setting 10.1 Introduction 10.2 Elementary Statistical Methods 10.2.1 Basic Hypothesis Test 10.2.2 Likelihood Ratio and Generalized Likelihood Ratio Detection when theta1 (>0) Is Known and theta0=0 Detection when theta1 Is Unknown and theta0=0 10.2.3 Vector-Valued GLR 10.2.4 Detection of Change in Variance Testing with the chi2 Statistic Given by Lapin Testing Using GLR Given by Basseville and Nikiforov 10.2.5 Aspects of On-Line Realization On-Line Implementation with a Fixed Sample Size N On-Line Implementation in a Recursive Manner Setting a Counter 10.3 Criteria for Threshold Computation 10.3.1 The Neyman-Pearson Criterion 10.3.2 Maximum a Posteriori Probability (MAP) Criterion 10.3.3 Bayes' Criterion 10.3.4 Some Remarks 10.4 Application of GLR Testing Methods 10.4.1 Kalman Filter Based Fault Detection 10.4.2 Parity Space Based Fault Detection 10.5 Notes and References Chapter 11: Integration of Norm-Based and Statistical Methods 11.1 Residual Evaluation in Stochastic Systems with Deterministic Disturbances 11.1.1 Residual Generation 11.1.2 Problem Formulation 11.1.3 GLR Solutions 11.1.4 An Example 11.2 Residual Evaluation Scheme for Stochastically Uncertain Systems 11.2.1 Problem Formulation 11.2.2 Solution and Design Algorithms 11.3 Probabilistic Robustness Technique Aided Threshold Computation 11.3.1 Problem Formulation 11.3.2 Outline of the Basic Idea 11.3.3 LMIs Used for the Solutions 11.3.4 Problem Solutions in the Probabilistic Framework 11.3.5 An Application Example The Sample Size N 11.3.6 Concluding Remarks 11.4 Notes and References Part IV: Fault Detection, Isolation and Identification Schemes Chapter 12: Integrated Design of Fault Detection Systems 12.1 FAR and FDR 12.2 Maximization of Fault Detectability by a Given FAR 12.2.1 Problem Formulation Problem of Maximizing SDF Under a Given FAR (PMax-SDF) 12.2.2 Essential Form of the Solution 12.2.3 A General Solution 12.2.4 Interconnections and Comparison Relationship to the PUIDP Relationship to H2/H2 Optimal Design Scheme Relationship to Hinfty/Hinfty and H-/Hinfty Optimal Schemes 12.2.5 Examples 12.3 Minimizing False Alarm Number by a Given FDR 12.3.1 Problem Formulation Problem of Minimizing SDFA Under a Given FDR (PMin-SDFA) 12.3.2 Essential Form of the Solution 12.3.3 The State Space Form 12.3.4 The Extended Form 12.3.5 Interpretation of the Solutions and Discussion 12.3.6 An Example 12.4 On the Application to Stochastic Systems 12.4.1 Application to Maximizing FDR by a Given FAR 12.4.2 Application to Minimizing FAR by a Given FDR 12.4.3 Equivalence Between the Kalman Filter Scheme and the Unified Solution 12.5 Notes and References Chapter 13: Fault Isolation Schemes 13.1 Essentials 13.1.1 Existence Conditions for a Perfect Fault Isolation 13.1.2 PFIs and Unknown Input Decoupling 13.1.3 PFIs with Unknown Input Decoupling (PFIUID) 13.2 Fault Isolation Filter Design 13.2.1 A Design Approach Based on the Duality to Decoupling Control 13.2.2 The Geometric Approach 13.2.3 A Generalized Design Approach 13.3 An Algebraic Approach to Fault Isolation 13.4 Fault Isolation Using a Bank of Residual Generators 13.4.1 The Dedicated Observer Scheme (DOS) 13.4.2 The Generalized Observer Scheme (GOS) 13.5 Notes and References Chapter 14: Fault Identification Schemes 14.1 Fault Identification Filter Schemes and Perfect Fault Identification 14.1.1 Fault Detection Filters and Existence Conditions 14.1.2 FIF Design with Measurement Derivatives 14.2 On the Optimal FIF Design 14.2.1 Problem Formulation and Solution Study 14.2.2 Study on the Role of the Weighting Matrix 14.3 Approaches to the Design of FIF 14.3.1 A General Fault Identification Scheme 14.3.2 An Alternative Scheme 14.3.3 Identification of the Size of a Fault 14.3.4 Fault Identification in a Finite Frequency Range 14.4 Fault Identification Using an Augmented Observer 14.5 An Algebraic Fault Identification Scheme 14.6 Adaptive Observer-Based Fault Identification 14.6.1 Problem Formulation 14.6.2 The Adaptive Observer Scheme Observer Auxiliary Filter Fault Estimator 14.7 Notes and References Chapter 15: Fault Diagnosis in Feedback Control Systems and Fault-Tolerant Architecture 15.1 Plant and Control Loop Models, Controller and Observer Parameterizations 15.1.1 Plant and Control Loop Models 15.1.2 Parameterization of Stabilizing Controllers, Observers, and an Alternative Formulation of Controller Design 15.1.3 Observer and Residual Generator Based Realizations of Youla Parameterization 15.1.4 Residual Generation Based Formulation of Controller Design Problem 15.2 Residual Extraction in the Standard Feedback Control Loop and a Fault Detection Scheme 15.2.1 Signals at the Access Points in the Control Loop 15.2.2 A Fault Detection Scheme Based on Extraction of Residual Signals 15.3 2-DOF Control Structures and Residual Access 15.3.1 The Standard 2-DOF Control Structures 15.3.2 An Alternative 2-DOF Control Structure with Residual Access 15.4 On Residual Access in the IMC and Residual Generator Based Control Structures 15.4.1 An Extended IMC Structure with an Integrated Residual Access 15.4.2 A Residual Generator Based Feedback Control Loop 15.5 Notes and References References Index