Block-oriented Nonlinear System Identification (Lecture Notes in Control and Information Sciences, 404)

✍ Scribed by Fouad Giri (editor), Er-Wei Bai (editor)

• Publisher: Springer
• Year: 2010
• Tongue: English
• Leaves: 425
• Edition: 2010
• Category: Library

✦ Synopsis

Block-oriented Nonlinear System Identification deals with an area of research that has been very active since the turn of the millennium. The book makes a pedagogical and cohesive presentation of the methods developed in that time. These include: iterative and over-parameterization techniques; stochastic and frequency approaches; support-vector-machine, subspace, and separable-least-squares methods; blind identification method; bounded-error method; and decoupling inputs approach. The identification methods are presented by authors who have either invented them or contributed significantly to their development. All the important issues e.g., input design, persistent excitation, and consistency analysis, are discussed. The practical relevance of block-oriented models is illustrated through biomedical/physiological system modelling. The book will be of major interest to all those who are concerned with nonlinear system identification whatever their activity areas. This is particularly the case for educators in electrical, mechanical, chemical and biomedical engineering and for practising engineers in process, aeronautic, aerospace, robotics and vehicles control. Block-oriented Nonlinear System Identification serves as a reference for active researchers, new comers, industrial and education practitioners and graduate students alike.

✦ Table of Contents

Title
Preface
Contents
Part I Block-oriented Nonlinear Models
Introduction to Block-oriented Nonlinear Systems
Block-oriented Nonlinear Systems
About This Book
Book Topics
Who Can Use This Book
References
Nonlinear System Modelling and Analysis fromthe Volterra and Wiener Perspective
Introduction
General System Considerations
The Volterra Series
Applications of the Volterra Series
The Wiener Theory
The Wiener G-functionals
System Modelling with the G-functionals
General Wiener Model
The Gate Function Model
An Optimum System Calculator
References
Part II Iterative and Overparameterization Methods
An Optimal Two-stage Identification Algorithm for Hammerstein–Wiener Nonlinear Systems
Introduction
Optimal Two-stage Algorithm
Concluding Remarks
References
Compound Operator Decomposition and Its Application to Hammerstein andWiener Systems
Introduction
Decomposition
Serial Application
Parallel Application
Decomposition of Block-oriented Nonlinear Systems
Hammerstein System
Wiener System
Identification of Hammerstein–Wiener Systems
Hammerstein–Wiener Systems
Piecewise-linear Characteristics
Algorithm
Example
Conclusions
References
Iterative Identification of Hammerstein Systems
Introduction
Hammerstein System with IIR Linear Part
Non-smooth Nonlinearities
Examples
Conclusion
References
Part III Stochastic Methods
Recursive Identification for Stochastic Hammerstein Systems
Introduction
Nonparametric f (·)
Identification of A(z)
Identification of B(z)
Identification of f (u)
Piecewise Linear f (·)
Parameterized Nonlinearity
Concluding Remarks
Appendix
References
Wiener System Identification Using the Maximum Likelihood Method
Introduction
An Output-error Approach
The Maximum Likelihood Method
Likelihood Function for White Disturbances
Likelihood Function for Coloured Process Noise
Maximum Likelihood Algorithms
Direct Gradient-based Search Approach
Expectation Maximisation Approach
Simulation Examples
Example 1: White Process and Measurement Noise
Example 2: Coloured Process Noise
Example 3: Blind Estimation
Conclusion
References
Parametric Versus Nonparametric Approach to Wiener Systems Identification
Introduction toWiener Systems
Nonlinear Least Squares Method
Nonparametric Identification Tools
Inverse Regression Approach
Cross-correlation Analysis
A Censored Sample Mean Approach
Combined Parametric-nonparametric Approach
Kernel Method with the Correlation-based Internal Signal Estimation
Identification of IIR Wiener Systems with Non-Gaussian Input
Recent Ideas
Conclusion
References
Identification of Block-oriented Systems: Nonparametric and Semiparametric Inference
Introduction
Nonparametric and Semiparametric Inference
Semiparametric Block-oriented Systems
Semiparametric Hammerstein Systems
Semiparametric Parallel Systems
Concluding Remarks
References
Identification of Block-oriented Systems Using the Invariance Property
Introduction
Preliminaries
The Invariance Property and Separable Processes
Block-oriented Systems
Discussion
References
Part IV Frequency Methods
Frequency Domain Identification of Hammerstein Models
Introduction
Problem Statement and Point Estimation
Continuous Time Frequency Response
Point Estimation of $G(j\omega)$ Based on $Y_T$ and $U_T$
Implementation Using Sampled Data
Identification of G(s)
Finite-order Rational Transfer Function G(s)
Non-parametric G(s)
Identification of the Nonlinear Part f (u)
Unknown Nonlinearity Structure
Polynomial Nonlinearities
Simulation
Concluding Remarks
References
Frequency Identification of Nonparametric Wiener Systems
Introduction
Identification Problem Statement
Frequency Behaviour Geometric Interpretations
Characterisation of the Loci (xn(t),w(t)) and (x−n (t),w(t))
Estimation of the Loci C$_Psi$ (U,$omega$)
Wiener System Identification Method
Phase Estimation (PE)
Nonlinearity Estimation (NLE)
Frequency Gain Modulus Estimation
Simulation Results
Further Expressions
Geometric Area
Signal Spread
Conclusion
References
Identification of Wiener–Hammerstein Systems Using the Best Linear Approximation
Introduction
Block-oriented versus Black-box Models
Identification Issues
The Best Linear Approximation
Definition
Class of Excitations
Nonlinear Block Structure Selection Method
Two-stage Nonparametric Approach
Some Nonlinear Block Structures
Theoretical Results
Experimental Results
Concluding Remarks
Initial Estimates forWiener–Hammerstein Models
Set-up
Initialisation Procedure
Experimental Results
Concluding Remarks
Conclusions
References
Part V SVM, Subspace and Separable Least-squares
Subspace Identification of Hammerstein–Wiener Systems Operating in Closed-loop
Introduction
Problem Formulation
Problem Formulation
Concept of Basis Functions
Assumptions and Notation
Hammerstein–Wiener Predictor-based Subspace Identification
Predictors
Extended Observability Times Controllability Matrix
Estimation of the Wiener Nonlinearity
Recovery of the System Matrices
Estimation of the Hammerstein Nonlinearity
Example
Conclusions
References
NARX Identification of Hammerstein Systems Using Least-Squares Support Vector Machines
Introduction
Hammerstein Identification Using an Overparametrisation Approach
Implementation of Overparametrisation
Potential Problems in Overparametrisation
Function Approximation Using Least Squares Support Vector Machines
NARX Hammerstein Identification as a Componentwise LS-SVM
SISO Systems
Identification of Hammerstein MIMO Systems
Example
Extensions
Outlook
References
Identification of Linear Systems with Hard Input Nonlinearities of Known Structure
Problem Statement
Deterministic Approach
Identification Algorithm
Consistency Analysis and Computational Issues
Correlation Analysis Method
Concluding Remarks
References
Part VI Blind Methods
Blind Maximum-likelihood Identification of Wiener and Hammerstein Nonlinear Block Structures
Introduction: Blind Nonlinear Modelling
Nonlinear Sensor Calibration
Outline
Introduction of Models and Related Assumptions
Class of Discrete-time Wiener and Hammerstein Systems Considered
Parametrisation
Stochastic Framework
Identifiability
The Gaussian Maximum-likelihood Estimator (MLE)
The Negative Log-likelihood (NLL) Function
The Simplified MLE Cost Function
Asymptotic Properties
Loss of Consistency in the Case of a Non-Gaussian Input
Non-white Gaussian Inputs
Generation of Initial Estimates
Subproblem 1: Monotonically Increasing Static Nonlinearity Driven by Gaussian Noise
Subproblem 2: LTI Driven by White Input Noise
Minimisation of the Cost Function
The Cram´er-Rao Lower Bound
Impact of Output Noise
Simulation Results
Setup: Presentation of the Example
Graphical Presentation of the Results
Monte Carlo Analysis Showing the Impact of Output Noise
Laboratory Experiment
Conclusion
References
A Blind Approach to Identification of Hammerstein Systems
Introduction
Problem Description
Estimation of n$_a$, $\tau$ and A(q)
Estimation of x(t)
Numerical Examples
Experimental Example
Hammerstein Model of MR Dampers
Experiment Setup
Experiment Result
Conclusion
References
A Blind Approach to the Hammerstein-Wiener Model Identification
Introduction
Problem Statement and Preliminaries
Identification of the Hammerstein-Wiener Model
Output Nonlinearity Estimation
Linear Transfer Function Estimation
Input Nonlinearity Estimation
Algorithm and Simulations
Discussions
Concluding Remarks
References
Part VII Decoupling Inputs and Bounded Error Methods
Decoupling the Linear and Nonlinear Parts in Hammerstein Model Identification
Problem Statement
Nonlinearity with the PRBS Inputs
Linear Part Identification
Non-parametric Identification
Parametric Identification
Nonlinear Part Identification
Concluding Remarks
References
Hammerstein System Identification in Presence of Hard Memory Nonlinearities
Introduction
Identification Problem Formulation
Linear Subsystem Identification
Model Reforming
Model Centring and Linear Subsystem Parameter Estimation
A Class of Exciting Input Signal
Consistency of Linear Subsystem Parameter Estimates
Simulation
Nonlinear Element Estimation
Estimation of m$_1$
Estimation of (h1,h2)
Simulation
Conclusion
References
Bounded Error Identification of Hammerstein Systems with Backlash
Introduction
Problem Formulation
Assessment of Tight Bounds on the Nonlinear Static Block Parameters
Definitions and Preliminary Results
Exact Description of D$^l_γ$
Tight Orthotope Description of D$^l_γ$
Bounding the Parameters of the Linear Dynamic Model
A Simulated Example
Conclusion
References
Part VIII Application of Block-oriented Models
Block Structured Modelling in the Study of the Stretch Reflex
Introduction
Preliminaries
Initial Applications
Hard Nonlinearities
The Parallel Cascade Stiffness Model
Iterative, Correlation based Approach
Separable Least Squares Optimisation
Conclusions
References
Application of Block-oriented System Identification to Modelling Paralysed Muscle Under Electrical Stimulation
Introduction
Problem Statement
The Wiener–Hammerstein Fatigue Model
Identification of theWiener–Hammerstein System
Identification of the Wiener–Hammerstein Non-fatigue Model (Single Train Stimulation Model)
Identification of the Wiener–Hammerstein Fatigue Model
Collection of SCI Patient Data
Results
Discussion and Conclusions
References
Index