Identification of physical systems applications to condition monitoring fault diagnosis softsensor and controller design 1st Edition by Rajamani Doraiswami, Maryhelen Stevenson, Chris Diduch ISBN B00MBTQ9EY 978-1118536490
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ISBN 10: B00MBTQ9EY
ISBN 13: 978-1118536490
Author: Rajamani Doraiswami, Maryhelen Stevenson, Chris Diduch
Identification of a physical system deals with the problem of identifying its mathematical model using the measured input and output data. As the physical system is generally complex, nonlinear, and its input–output data is corrupted noise, there are fundamental theoretical and practical issues that need to be considered.
Identification of Physical Systems addresses this need, presenting a systematic, unified approach to the problem of physical system identification and its practical applications. Starting with a least-squares method, the authors develop various schemes to address the issues of accuracy, variation in the operating regimes, closed loop, and interconnected subsystems. Also presented is a non-parametric signal or data-based scheme to identify a means to provide a quick macroscopic picture of the system to complement the precise microscopic picture given by the parametric model-based scheme. Finally, a sequential integration of totally different schemes, such as non-parametric, Kalman filter, and parametric model, is developed to meet the speed and accuracy requirement of mission-critical systems.
Identification of physical systems applications to condition monitoring fault diagnosis softsensor and controller design 1st Table of contents:
1 Modeling of Signals and Systems
1.1 Introduction
1.2 Classification of Signals
1.3 Model of Systems and Signals
1.4 Equivalence of Input–Output and State-Space Models
1.5 Deterministic Signals
1.6 Introduction to Random Signals
1.7 Model of Random Signals
1.8 Model of a System with Disturbance and Measurement Noise
1.9 Summary
References
Further Readings
2 Characterization of Signals: Correlation and Spectral Density
2.1 Introduction
2.2 Definitions of Auto- and Cross-Correlation (and Covariance)
2.3 Spectral Density: Correlation in the Frequency Domain
2.4 Coherence Spectrum
2.5 Illustrative Examples in Correlation and Spectral Density
2.6 Input–Output Correlation and Spectral Density
2.7 Illustrative Examples: Modeling and Identification
2.8 Summary
2.9 Appendix
References
3 Estimation Theory
3.1 Overview
3.2 Map Relating Measurement and the Parameter
3.3 Properties of Estimators
3.4 Cramér–Rao Inequality
3.5 Maximum Likelihood Estimation
3.6 Summary
3.7 Appendix: Cauchy–Schwarz Inequality
3.8 Appendix: Cramér–Rao Lower Bound
3.9 Appendix: Fisher Information: Cauchy PDF
3.10 Appendix: Fisher Information for i.i.d. PDF
3.11 Appendix: Projection Operator
3.12 Appendix: Fisher Information: Part Gauss-Part Laplace
Problem
References
Further Readings
4 Estimation of Random Parameter
4.1 Overview
4.2 Minimum Mean-Squares Estimator (MMSE): Scalar Case
4.3 MMSE Estimator: Vector Case
4.4 Expression for Conditional Mean
4.5 Summary
4.6 Appendix: Non-Gaussian Measurement PDF
References
Further Readings
5 Linear Least-Squares Estimation
5.1 Overview
5.2 Linear Least-Squares Approach
5.3 Performance of the Least-Squares Estimator
5.4 Illustrative Examples
5.5 Cramér–Rao Lower Bound
5.6 Maximum Likelihood Estimation
5.7 Least-Squares Solution of Under-Determined System
5.8 Singular Value Decomposition
5.9 Summary
5.10 Appendix: Properties of the Pseudo-Inverse and the Projection Operator
5.11 Appendix: Positive Definite Matrices
5.12 Appendix: Singular Value Decomposition of a Matrix
5.13 Appendix: Least-Squares Solution for Under-Determined System
5.14 Appendix: Computation of Least-Squares Estimate Using the SVD
References
Further Readings
6 Kalman Filter
6.1 Overview
6.2 Mathematical Model of the System
6.3 Internal Model Principle
6.4 Duality Between Controller and an Estimator Design
6.5 Observer: Estimator for the States of a System
6.6 Kalman Filter: Estimator of the States of a Stochastic System
6.7 The Residual of the Kalman Filter with Model Mismatch and Non-Optimal Gain
6.8 Summary
6.9 Appendix: Estimation Error Covariance and the Kalman Gain
6.10 Appendix: The Role of the Ratio of Plant and the Measurement Noise Variances
6.11 Appendix: Orthogonal Properties of the Kalman Filter
6.12 Appendix: Kalman Filter Residual with Model Mismatch
References
7 System Identification
7.1 Overview
7.2 System Model
7.3 Kalman Filter-Based Identification Model Structure
7.4 Least-Squares Method
7.5 High-Order Least-Squares Method
7.6 The Prediction Error Method
7.7 Comparison of High-Order Least-Squares and the Prediction Error Methods
7.8 Subspace Identification Method
7.9 Summary
7.10 Appendix: Performance of the Least-Squares Approach
7.11 Appendix: Frequency-Weighted Model Order Reduction
References
8 Closed Loop Identification
8.1 Overview
8.2 Closed-Loop System
8.3 Model of the Single Input Multi-Output System
8.4 Kalman Filter-Based Identification Model
8.5 Closed-Loop Identification Schemes
8.6 Second Stage of the Two-Stage Identification
8.7 Evaluation on a Simulated Closed-Loop Sensor Net
8.8 Summary
References
9 Fault Diagnosis
9.1 Overview
9.2 Mathematical Model of the System
9.3 Model of the Kalman Filter
9.4 Modeling of Faults
9.5 Diagnostic Parameters and the Feature Vector
9.6 Illustrative Example
9.7 Residual of the Kalman Filter
9.8 Fault Diagnosis
9.9 Fault Detection: Bayes Decision Strategy
9.10 Evaluation of Detection Strategy on Simulated System
9.11 Formulation of Fault Isolation Problem
9.12 Estimation of the Influence Vectors and Additive Fault
9.13 Fault Isolation Scheme
9.14 Isolation of a Single Fault
9.15 Emulators for Offline Identification
9.16 Illustrative Example
9.17 Overview of Fault Diagnosis Scheme
9.18 Evaluation on a Simulated Example
9.19 Summary
9.20 Appendix: Bayesian Multiple Composite Hypotheses Testing Problem
9.21 Appendix: Discriminant Function for Fault Isolation
9.22 Appendix: Log-likelihood Ratio for a Sinusoid and a Constant
References
10 Modeling and Identification of Physical Systems
10.1 Overview
10.2 Magnetic Levitation System
10.3 Two-Tank Process Control System
10.4 Position Control System
10.5 Summary
References
11 Fault Diagnosis of Physical Systems
11.1 Overview
11.2 Two-Tank Physical Process Control System
11.3 Position Control System
11.4 Summary
References
12 Fault Diagnosis of a Sensor Network
12.1 Overview
12.2 Problem Formulation
12.3 Fault Diagnosis Using a Bank of Kalman Filters
12.4 Kalman Filter for Pairs of Measurements
12.5 Kalman Filter for the Reference Input-Measurement Pair
12.6 Kalman Filter Residual: A Model Mismatch Indicator
12.7 Bayes Decision Strategy
12.8 Truth Table of Binary Decisions
12.9 Illustrative Example
12.10 Evaluation on a Physical Process Control System
12.11 Fault Detection and Isolation
12.12 Summary
12.13 Appendix
References
13 Soft Sensor
13.1 Review
13.2 Mathematical Formulation
13.3 Identification of the System
13.4 Model of the Kalman Filter
13.5 Robust Controller Design
13.6 High Performance and Fault Tolerant Control System
13.7 Evaluation on a Simulated System: Soft Sensor
13.8 Evaluation on a Physical Velocity Control System
13.9 Conclusions
13.10 Summary
References
Index
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Tags: Rajamani Doraiswami, Maryhelen Stevenson, Chris Diduch, physical systems, fault diagnosis