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Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains |  |
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Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains | |
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains describes a comprehensive framework for the identification and analysis of nonlinear dynamic systems in the time, frequency, and spatio-temporal domains. This book is written with an emphasis on making the algorithms accessible so that they can be applied and used in practice.
Includes coverage of:
The NARMAX (nonlinear autoregressive moving average with exogenous inputs) model The orthogonal least squares algorithm that allows models to be built term by term where the error reduction ratio reveals the percentage contribution of each model term Statistical and qualitative model validation methods that can be applied to any model class Generalised frequency response functions which provide significant insight into nonlinear behaviours A completely new class of filters that can move, split, spread, and focus energy The response spectrum map and the study of sub harmonic and severely nonlinear systems Algorithms that can track rapid time variation in both linear and nonlinear systems The important class of spatio-temporal systems that evolve over both space and time Many case study examples from modelling space weather, through identification of a model of the visual processing system of fruit flies, to tracking causality in EEG data are all includedNARMAX algorithms provide a fundamentally different approach to nonlinear system identification and signal processing for nonlinear systems. NARMAX methods provide models that are transparent, which can easily be analysed, and which can be used to solve real problems.
This book is intended for graduates, postgraduates and researchers in the sciences and engineering, and also for users from other fields who have collected data and who wish to identify models to help to understand the dynamics of their systems.
作者简介Stephen A. Billings is Professor of Signal Processing and Complex Systems, and Director of the Signal Processing and Complex Systems Research Group, in the Department of Automatic Control and Systems Engineering at the University of Sheffield, He is counted as "highly cited" by the ISI Web of Knowledge with 250 publications to his name.
目录Preface xv
1 Introduction 1
1.1 Introduction to System Identification 1
1.2 Linear System Identification 3
1.3 Nonlinear System Identification 5
1.4 NARMAX Methods 7
1.5 The NARMAX Philosophy 8
1.6 What is System Identification For? 9
1.7 Frequency Response of Nonlinear Systems 11
1.8 Continuous-Time, Severely Nonlinear, and Time-Varying Models and Systems 12
1.9 Spatio-temporal Systems 13
1.10 Using Nonlinear System Identification in Practice and Case Study Examples 13
References 14
2 Models for Linear and Nonlinear Systems 17
2.1 Introduction 17
2.2 Linear Models 18
2.3 Piecewise Linear Models 22
2.4 Volterra Series Models 30
2.5 Block-Structured Models 31
2.6 NARMAX Models 33
2.7 Generalised Additive Models 40
2.8 Neural Networks 41
2.9 Wavelet Models 45
2.10 State-Space Models 48
2.11 Extensions to the MIMO Case 49
2.12 Noise Modelling 49
2.13 Spatio-temporal Models 52
References 53
3 Model Structure Detection and Parameter Estimation 61
3.1 Introduction 61
3.2 The Orthogonal Least Squares Estimator and the Error Reduction Ratio 64
Representation 65
3.3 The Forward Regression OLS Algorithm 70
3.4 Term and Variable Selection 79
3.5 OLS and Sum of Error Reduction Ratios 80
3.6 Noise Model Identification 84
3.7 An Example of Variable and Term Selection for a Real Data Set 87
3.8 ERR is Not Affected by Noise 94
3.9 Common Structured Models to Accommodate Different Parameters 95
3.10 Model Parameters as a Function of Another Variable 98
3.11 OLS and Model Reduction 100
3.12 Recursive Versions of OLS 102
References 102
4 Feature Selection and Ranking 105
4.1 Introduction 105
4.2 Feature Selection and Feature Extraction 106
4.3 Principal Components Analysis 107
4.4 A Forward Orthogonal Search Algorithm 108
4.5 A Basis Ranking Algorithm Based on PCA 113
References 117
5 Model Validation 119
5.1 Introduction 119
5.2 Detection of Nonlinearity 121
5.3 Estimation and Test Data Sets 123
5.4 Model Predictions 124
5.5 Statistical Validation 127
5.6 Term Clustering 135
5.7 Qualitative Validation of Nonlinear Dynamic Models 137
References 145
6 The Identification and Analysis of Nonlinear Systems in the Frequency Domain 149
6.1 Introduction 149
6.2 Generalised Frequency Response Functions 151
6.3 Output Frequencies of Nonlinear Systems 184
6.4 Nonlinear Output Frequency Response Functions 191
6.5 Output Frequency Response Function of Nonlinear Systems 202
References 213
7 Design of Nonlinear Systems in the Frequency Domain – Energy Transfer Filters and Nonlinear Damping 217
7.1 Introduction 217
7.2 Energy Transfer Filters 218
7.3 Energy Focus Filters 240
7.4 OFRF-Based Approach for the Design of Nonlinear Systems in the Frequency Domain 249
References 259
8 Neural Networks for Nonlinear System Identification 261
8.1 Introduction 261
8.2 The Multi-layered Perceptron 263
8.3 Radial Basis Function Networks 264
8.4 Wavelet Networks 270
8.5 Multi-resolution Wavelet Models and Networks 277
References 284
9 Severely Nonlinear Systems 289
9.1 Introduction 289
9.2 Wavelet NARMAX Models 291
9.3 Systems that Exhibit Sub-harmonics and Chaos 301
9.4 The Response Spectrum Map 305
9.5 A Modelling Framework for Sub-harmonic and Severely Nonlinear Systems 313
9.6 Frequency Response Functions for Sub-harmonic Systems 320
9.7 Analysis of Sub-harmonic Systems and the Cascade to Chaos 326
References 334
10 Identification of Continuous-Time Nonlinear Models 337
10.1 Introduction 337
10.2 The Kernel Invariance Method 338
10.3 Using the GFRFs to Reconstruct Nonlinear Integro-differential Equation Models Without Differentiation 352
References 367
11 Time-Varying and Nonlinear System Identification 371
11.1 Introduction 371
11.2 Adaptive Parameter Estimation Algorithms 372
11.3 Tracking Rapid Parameter Variations Using Wavelets 376
11.4 Time-Dependent Spectral Characterisation 378
11.5 Nonlinear Time-Varying Model Estimation 380
11.6 Mapping and Tracking in the Frequency Domain 381
11.7 A Sliding Window Approach 388
References 389
12 Identification of Cellular Automata and N -State Models of Spatio-temporal Systems 391
12.1 Introduction 391
12.2 Cellular Automata 393
12.3 Identification of Cellular Automata 402
12.4 N -State Systems 414
References 427
13 Identification of Coupled Map Lattice and Partial Differential Equations of Spatio-temporal Systems 431
13.1 Introduction 431
13.2 Spatio-temporal Patterns and Continuous-State Models 432
13.3 Identification of Coupled Map Lattice Models 437
13.4 Identification of Partial Differential Equation Models 458
13.5 Nonlinear Frequency Response Functions for Spatio-temporal Systems 466
References 471
14 Case Studies 473
14.1 Introduction 473
14.2 Practical System Identification 474
14.3 Characterisation of Robot Behaviour 478
14.4 System Identification for Space Weather and the Magnetosphere 484
14.5 Detecting and Tracking Iceberg Calving in Greenland 493
14.6 Detecting and Tracking Time-Varying Causality for EEG Data 498
14.7 The Identification and Analysis of Fly Photoreceptors 505
14.8 Real-Time Diffuse Optical Tomography Using RBF Reduced-Order Models of the Propagation of Light for Monitoring Brain Haemodynamics 514
14.9 Identification of Hysteresis Effects in Metal Rubber Damping Devices 522
14.10 Identification of the Belousov–Zhabotinsky Reaction 528
14.11 Dynamic Modelling of Synthetic Bioparts 534
14.12 Forecasting High Tides in the Venice Lagoon 539
References 543
Index
网友对Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains的评论
This book is truly comprehensive in many different aspects: it covers most of the model classes currently used in black-box nonlinear system identification (an exception to this is fuzzy-logic models), it discusses time-domain and frequency-domain techniques for nonlinear systems, it deals with temporal (lumped-parameter) and spatio-temporal (distributed-parameter) models. Although most of the final models in the time domain are discrete-time, the author also addresses continuous-time models. Although it is hard to find all this for linear systems in a single book, the reader will find all such topics covered (with varying degrees of detail) in this book in the context of nonlinear systems! Two features stand out: i) an easy-to-uderstand overview of the specific problem at the beginning of each chapter and ii) an algorithmic approach to the problem of black-box system identification. In other words, the author provides step-by-step procedures for implementing the methods discussed in the book. On the other hand, the book does not provide fundamental system theory and some fundamental discussions are quite superficial, which is not surprising given the breath of the book. Therefore if you plan to implement and try some methods on your own, this is the book to go for, but it would be hard to teach a course following this book.
The author of this book has contributed much to the field of Nonlinear System Identification. While the book seems short on theoretical development, it does provide a number of good algorithms for both linear and nonlinear system identification. Therefore, it has value to the reader who wishes to apply a method for developing a NARMAX model. The methods are well described with supporting examples. However, I wished the author had discussed over sampling further and methods to resample as needed for a NARMAX model. I have personally used algorithms similar to these described in Chapters 3 and 6 and have performed validations similar to the methods of Chapter 5. I am not a fan of Principal Component Analysis discussed in Chapter 4 as it tends to obfuscate and hide the key variables of a model when it then becomes necessary to apply the model in an attempt to control the system.
The development of Generalized Frequency Response Functions discussed in Chapter 6 for performing frequency domain analysis is intriguing. I have not encountered some of the technique used before but I look forward to exploring the subject further. While I was generally disappointed with attempting to used a Volterra approach a few years ago for this, the parametric method described deserves further examination. Unfortunately for the controls community, insufficient work has been performed in analyzing frequency response of nonlinear models. This is one of the few authors that has performed some exploration in this area.
Then the author gets into areas that could better, in my personal opinion, be omitted from the book. These include his discussion of Neural Nets and Automata Theory. The author's treatment of this is cursory and generally not useful in the vein of attempting to identify models for further control system work. However, if one is attempting to perform model identification for purposes other than control system development, there may good reasons and arguments for considering these chapters.
I would advise reading Chapter 14, Case Studies, in depth, as there is good information contained within. In my first reading, I more or less skimmed this chapter to my detriment. However, a later reference to it caused me to revisit this chapter. I wished the author had put some of the information contained therein in earlier chapters where, I believe, it belongs.
In my opinion, the book is overly referenced. Since the author has performed seminal work in this area and documented such in archival journals, he makes liberal use of this work and references it as such. It is my belief that the author does not need to make these references in the text of the chapters as the people to whom this book should be of interest already have awareness of the author and his work. Listing these papers in the Reference Sections of the chapters should be sufficient in most cases. In part, this is why I haven't rated the book as high as possible.
I could recommend this book to a practicing controls engineer. It is readable and the algorithms are generally clear and executable. I would not recommend this as a text for a graduate course. However, clearly, parts of the book could be used as references for a course in System Identification.
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