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Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains, by Stephen A. Billings
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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 included
to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems
NARMAX 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.
- Sales Rank: #2472466 in Books
- Published on: 2013-09-23
- Original language: English
- Number of items: 1
- Dimensions: 9.95" h x 1.40" w x 7.00" l, 2.41 pounds
- Binding: Hardcover
- 574 pages
From the Back Cover
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 EGG data are all included
to demonstrate how easily the methods can be applied in practice and to show the insight that the algorithms reveal even for complex systems
NARMAX 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.
About the Author
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.
Most helpful customer reviews
3 of 3 people found the following review helpful.
A comprehensive and algorithmic approach to nonlinear system identification
By Luigi Fatori
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.
1 of 1 people found the following review helpful.
A Useful Text for System Identification, particularly NARMAX
By Walter W. Olson, Ph.D, P.E.
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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