This book focuses on fault diagnosis for linear discrete time-varying (LDTV) systems and its applications in modern engineering processes, with more weighting placed on the development of theory and methodologies. A comprehensive and systematic study on fault diagnosis for LDTV systems is provided, covering H∞-optimization-based fault diagnosis, H∞-filtering-based fault diagnosis, parity space-based fault diagnosis, Krein space technique-aided fault detection and fault estimation, and their typical applications in linear/nonlinear processes such as satellite attitude control systems and INS/GPS systems. This book benefits researchers, engineers, and graduate students in the fields of control engineering, electrical and electronic engineering, instrumentation science, and optoelectronic engineering.
Author(s): Maiying Zhong, Ting Xue, Steven X. Ding, Donghua Zhou
Publisher: Springer
Year: 2022
Language: English
Pages: 406
City: Singapore
Preface
Contents
Acronyms
Abbreviations
Mathematical Notations
Part I Introduction and Preliminaries
1 Introduction
1.1 Motivations
1.2 Model-Based Fault Diagnosis
1.2.1 Basic Concepts
1.2.2 Classical Methods
1.2.3 Overview of Fault Diagnosis for LDTV Systems
1.3 Outline of the Contents
References
2 Paradigm of Model-Based Fault Diagnosis
2.1 Basic Tasks and Problems of Fault Diagnosis
2.1.1 Basic Problems of Fault Detection and Estimation
2.1.2 Optimal Fault Detection and Estimation Problems
2.2 Perfect Unknown Input Decoupling
2.3 H2- and Hinfty-Optimal Design of Residual Generator
2.4 Residual Evaluation
2.4.1 Norm-Based Method
2.4.2 Statistical Hypothesis Testing Method
2.5 Conclusion
References
3 LDTV Systems and Fault Detection and Estimation for LDTV Systems
3.1 Introduction
3.2 Mathematical Descriptions of LDTV Systems
3.2.1 Description of Nominal Systems
3.2.2 Modeling of Dynamic Systems with Uncertainties and Faults
3.2.3 Alternative Input-Output Model
3.3 Fault Detection for LDTV Systems
3.3.1 Kalman Filter Method
3.3.2 Unknown Input Observer Method
3.3.3 Fault Detection Filter Method
3.3.4 Parity Space-Based Method
3.4 Fault Estimation for LDTV Systems
3.4.1 Observer-Based State Augmentation Method
3.4.2 Hinfty Fault Estimation
3.5 Conclusion
References
4 Krein Space and Krein Space Based Optimization
4.1 Introduction
4.2 Krein Spaces and Projections in Krein Space
4.2.1 Krein Spaces
4.2.2 Projections in Krein Space
4.3 Minimization Issues in Krein Spaces
4.3.1 Minimization Conditions
4.3.2 Some Remarks and Notes
4.4 Recursive Computation of Krein Space Projections
4.5 Conclusion
References
Part II H2- and Hinfty-Optimization Based Fault Diagnosis for LDTV Systems
5 H2-Optimization-Based Fault Detection for LDTV Systems
5.1 Basic Estimation and Fault Detection Problems
5.1.1 LMS Estimation
5.1.2 A Basic Fault Detection Problem, LMS and CCA
5.1.3 Innovation, Residual and Recursive Residual Generation
5.1.4 Analogous Estimation Problems in Krein Space
5.2 Optimal Detection of Faults in Stochastic Systems
5.2.1 Problem Formulation
5.2.2 Kalman Filter-Based Optimal Solution
5.2.3 An Alternative Interpretation of Kalman Filter-Based Solution
5.3 H2-optimal Detection of Faults in LDTV Systems: A Krein Space Solution
5.3.1 Problem Formulation
5.3.2 An H2-Optimal Observer-Based Residual Generator and Fault Detection Scheme
5.3.3 A Discussion
5.4 Concluding Remarks
References
6 Optimal Fault Detection for LDTV Systems
6.1 Introduction
6.2 Problem Formulation
6.3 Optimal FDFs for Fault Detection
6.4 A Numerical Example
6.5 Conclusion
References
7 A Projection-Based Method of Fault Detection for LDTV Systems
7.1 Introduction
7.2 A Projection Approach to Residual Generation
7.3 Innovation Analysis Aided Optimal Solutions
7.4 Recursive Implementation in State Space
7.5 A Numerical Example
7.6 Conclusion
References
8 An Hi/Hinfty-Optimization Scheme of Fault Detection for LDTV Systems
8.1 Introduction
8.2 Basic Ideas and Problem Formulation
8.3 A Krein Space Based Recursive Solution
8.3.1 Recursive Computation of JN
8.3.2 Analysis of Sensitivity/Robustness Performance
8.4 Applications to Observer-Based Fault Detection
8.5 Conclusion
References
9 An Hi/Hinfty Approach to Event-Triggered Optimal Fault Detection
9.1 Introduction
9.2 Preliminaries of an Event-Triggered FD System
9.3 Event-Triggered Hi/Hinfty-Optimal Fault Detection
9.3.1 Design of an Event-Triggered Hi/Hinfty-FDF
9.3.2 Residual Evaluation
9.4 A Simulation Example
9.5 Conclusion
References
10 Scheme of Optimal Fault Detection for LDTV Systems with Delayed State
10.1 Introduction
10.2 Optimal Fault Detection Under Delayed State
10.3 A Robust Optimal Residual Evaluation Scheme
10.3.1 Design of Evaluation Function JN
10.3.2 Determination of the Threshold
10.4 A Numerical Example
10.5 Conclusion
References
Part III Hinfty-Filtering Based Fault Diagnosis for LDTV Systems
11 A Krein Space Approach to Hinfty Fault Estimation for LDTV Systems
11.1 Introduction
11.2 Problem Statement
11.3 Design of an Hinfty Fault Estimator
11.4 Numerical Examples
11.5 Conclusion
References
12 On Designing Hinfty Fault Detection Filter for LDTV Systems
12.1 Introduction
12.2 Problem Formulation
12.3 Krein Space Based Design of Hinfty-FDF
12.3.1 An Equivalent Problem in Krein Space
12.3.2 The Minimum for JN
12.3.3 Design of an Hinfty-FDF
12.4 Numerical Examples
12.5 Conclusion
References
13 Krein Space Based Hinfty Fault Detection for LDTV Systems with Delayed State
13.1 Introduction
13.2 Problem Formulation
13.3 Design of Hinfty Fault Detection System in Krein Space
13.3.1 The Minimum for JN
13.3.2 Design of an Hinfty-FDF
13.4 Numerical Examples
13.5 Conclusion
References
Part IV Parity Space-Based Fault Diagnosis for LDTV Systems
14 Parity Space-Based Fault Detection for LDTV Systems with Unknown Input
14.1 Introduction
14.2 Problem Formulation
14.3 An Equivalent Optimization Formulation
14.4 A Krein Space Based Recursive Solution
14.4.1 An Equivalent Krein Space Problem
14.4.2 Recursive Computation of Js(k)
14.5 A Numerical Example
14.6 Conclusion
References
15 Parity Space-Based Fault Estimation for LDTV Systems
15.1 Introduction
15.2 Problem Formulation
15.3 Design of a Parity Space-Based Fault Estimator
15.4 Numerical Examples
15.5 Conclusion
References
16 Event-Triggered Parity Space Approach to Fault Detection for LDTV Systems
16.1 Introduction
16.2 Problem Formulation
16.3 Parity Space Based Design of an Event-Triggered FD System
16.3.1 Event-Triggered System Model
16.3.2 Event-Triggered Residual Generation
16.3.3 Residual Evaluation
16.4 Simulation Results
16.5 Conclusion
References
17 Stationary Wavelet Transform Aided Fault Detection for LDTV Systems
17.1 Introduction
17.2 Preliminaries of Wavelet Transform
17.3 Problem Formulation
17.4 SWT Aided Parity Space Approach to Fault Detection
17.4.1 SWT Aided Residual Generators
17.4.2 Design of the SWT Aided Parity Space Vectors
17.4.3 Selection of Wavelet Basis and the Maximal Scale
17.5 A Numerical Example
17.6 Conclusion
References
Part V Applications in Discrete-Time Nonlinear Systems
18 Extended H-/Hinfty-Optimal Fault Detection for a Class of Nonlinear Systems
18.1 Introduction
18.2 Problem Formulation
18.3 Extended H-/Hinfty-Optimal Fault Detection
18.3.1 An EKF Scheme for Stochastic Disturbances
18.3.2 An Extended H-/Hinfty Scheme for Norm-Bounded Disturbances
18.4 A Unified Design Framework for Residual Evaluation
18.5 Threshold Setting and Probabilistic Performance Analyzing
18.5.1 Case I: The PDF of J(x0,dN,vN) is Known
18.5.2 Case II: The PDF of J(x0,dN,vN) is Unknown
18.5.3 Case III: The Norm Bound δ Is Unknown
18.6 Application to a UAV Control System
18.7 Conclusion
References
19 An Hi/Hinfty-Optimal Fault Diagnosis Scheme for Satellite Attitude Control Systems
19.1 Introduction
19.2 System Description
19.3 Extended Hi/Hinfty-Optimal Fault Detection
19.4 Randomized Analysis of FAR
19.5 Contribution Analysis Based Fault Isolation
19.6 Simulation Results
19.7 Conclusion
References
20 Extended Hi/Hinfty-Optimal Fault Detection for INS/GPS Integrated Systems
20.1 Introduction
20.2 System Modeling
20.2.1 Model I
20.2.2 Model II
20.2.3 Model III
20.3 Problem Statement
20.4 Design of an Extended Hi/Hinfty-Optimal FD System
20.4.1 EKF Based FDF
20.4.2 An Extended Hi/Hinfty-FDF
20.5 Experimental Results and Discussion
20.5.1 Experimental Setup
20.5.2 Case I: EKF Based Experimental Results
20.5.3 Case II: Hi/Hinfty-FDF Based Experimental Results
20.6 Conclusion
References
21 Krein Space Based Hinfty Fault Estimation for Discrete-Time Nonlinear Systems
21.1 Introduction
21.2 Problems Formulation
21.2.1 Problem I
21.2.2 Problem II
21.3 Krein Space Based Hinfty Filtering for Nonlinear Systems
21.3.1 The Conditions for a Minimum of JN
21.3.2 Recursive Formulae of Krein Space Nonlinear Filter
21.3.3 The Calculation of H1((k)) and H2((k))
21.4 PMI Observer Based Nonlinear Hinfty Fault Estimation
21.4.1 Krein Space Based Solution
21.4.2 Recursive Realization of PMI Based Fault Estimator
21.5 Experimental Study
21.5.1 Example I
21.5.2 Example II
21.6 Conclusion
References
22 Adaptive In-Flight Alignment of INS/GPS Systems for Aerial Mapping
22.1 Introduction
22.2 Preliminaries and Problem Statement
22.2.1 System Description
22.2.2 A Brief Review of the Existing IFA
22.2.3 Problem Statement
22.3 An Adaptive IFA Method for Aerial Mapping
22.3.1 The Determination of Minimum Window Size
22.3.2 Adaptive Selection of the Window Size
22.3.3 The Strong Tracking Filter
22.3.4 Design of the IFA Method for Aerial Mapping
22.4 Experimental Study
22.4.1 Experimental Setup
22.4.2 Experimental Results
22.5 Conclusion
References
23 On Real-Time Performance Evaluation of the Inertial Sensors in INS/GPS Systems
23.1 Introduction
23.2 Preliminaries and Problem Statement
23.2.1 Kalman Filter Based State Estimation for the INS/GPS System
23.2.2 Existing Evaluation Methods
23.2.3 Problem Statement
23.3 Real-Time Performance Evaluation of the INS/GPS System
23.3.1 Design of the Evaluation Function
23.3.2 Simplification of the Evaluation Function
23.3.3 Evaluation Algorithm for the INS/GPS System
23.4 Experimental Study
23.4.1 Experimental Setup
23.4.2 Example I
23.4.3 Example II
23.5 Conclusion
References
