Nonlinear System Identification 2 Nonlinear System Structure Identification

This is the second part of a two-volume handbook presenting a comprehensive overview of nonlinear dynamic system identification. The books include many aspects of nonlinear processes such as modelling, parameter estimation, structure search, nonlinearity and model validity tests.

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.

This book provides engineers and scientists in academia and industry with a thorough understanding of the underlying principles of nonlinear system identification. It equips them to apply the models and methods discussed to real problems with confidence, while also making them aware of potential difficulties that may arise in practice. Moreover, the book is self-contained, requiring only a basic grasp of matrix algebra, signals and systems, and statistics. Accordingly, it can also serve as an introduction to linear system identification, and provides a practical overview of the major optimization methods used in engineering. The focus is on gaining an intuitive understanding of the subject and the practical application of the techniques discussed. The book is not written in a theorem/proof style; instead, the mathematics is kept to a minimum, and the ideas covered are illustrated with numerous figures, examples, and real-world applications. In the past, nonlinear system identification was a field characterized by a variety of ad-hoc approaches, each applicable only to a very limited class of systems. With the advent of neural networks, fuzzy models, Gaussian process models, and modern structure optimization techniques, a much broader class of systems can now be handled. Although one major aspect of nonlinear systems is that virtually every one is unique, tools have since been developed that allow each approach to be applied to a wide variety of systems.

Written from an engineering point of view, this book covers the most common and important approaches for the identification of nonlinear static and dynamic systems. The book also provides the reader with the necessary background on optimization techniques, making it fully self-contained. The new edition includes exercises.

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.

System identification plays a significant role in engineering design process, since it helps in correlating numerical or mathematical models with the actual real-life structures. Once the virtual representation of a mechanical system is found, it can be further used in: (i) predicting the structure's motion or (ii) redesigning or optimizing the structure. Many system identification methods are available which have found success in identifying certain linear and/or nonlinear systems. However, there are many nonlinear cases where the algorithms are still not successful in identifying an accurate model from measurements. Much work is still needed in this field to develop a toolbox of methods that can give adequate results when applied to any system, just as linear system identification can handle almost any linear system. Nonlinear Normal Modes (NNMs) are a common way to express the dynamics of a nonlinear structure over a range of amplitudes since they are independent of the forcing applied to the system. NNMs can be estimated experimentally and further used to correlate, validate, and update the mathematical or numerical representations of the system. Naturally, there are different kinds of methods that can be used to extract the NNM curve from measurements. Each of these nonlinear system identification techniques tries to handle the problem in its own original way. Hence, they can be classified into different categories based on the domain they operate in, or models they use. The primary contribution of this work is the development and demonstration of two new techniques for nonlinear system identification. The first one utilizes near-resonant steady-state harmonically excited vibration measurements to estimate the Nonlinear Normal Mode backbones. The algorithm can be classified as a modal method since it is based on the previously proposed Single Nonlinear Resonant Mode (SNRM) formula and uses it in a new and more effective way. Namely, it can estimate one point on the nonlinear mode from only one steady-state measurement collected near the resonance. Compared to some of the existing methods of similar type, the proposed technique can reduce the time required to obtain measurements and avoids difficulties due to e.g. the premature jump phenomenon. The other technique operates in the frequency domain and tries to fit a differential equation to the transient measurements to estimate the terms in the nonlinear equation of motion (EOM). Nonlinear terms are added to the linear EOM in the form of polynomials, and the proposed algorithm seeks to estimate the polynomial coefficients. This method requires the user to postulate a form for the nonlinearity. However, this work also presents an extension that revealed an interesting black-box identification capability. The algorithms are first evaluated numerically using benchmark case studies, such as the Duffing equation or reduced models of clamped-clamped flat and curved beams. Then the methods are employed experimentally to estimate the NNM backbones of beams that were manufactured from polylactide using a 3D printer and experience significant eigen-frequency shifts when the motion amplitude increases. The results are validated against measurements collected using the traditional phase resonance testing or swept-sine approaches.

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.

The subject of the book is to present the modeling, parameter estimation and other aspects of the identification of nonlinear dynamic systems. The treatment is restricted to the input-output modeling approach. Because of the widespread usage of digital computers discrete time methods are preferred. Time domain parameter estimation methods are dealt with in detail, frequency domain and power spectrum procedures are described shortly. The theory is presented from the engineering point of view, and a large number of examples of case studies on the modeling and identifications of real processes illustrate the methods. Almost all processes are nonlinear if they are considered not merely in a small vicinity of the working point. To exploit industrial equipment as much as possible, mathematical models are needed which describe the global nonlinear behavior of the process. If the process is unknown, or if the describing equations are too complex, the structure and the parameters can be determined experimentally, which is the task of identification. The book is divided into seven chapters dealing with the following topics: 1. Nonlinear dynamic process models 2. Test signals for identification 3. Parameter estimation methods 4. Nonlinearity test methods 5. Structure identification 6. Model validity tests 7. Case studies on identification of real processes Chapter I summarizes the different model descriptions of nonlinear dynamical systems.

Many types of engineering structures exhibit nonlinear behavior under real operating conditions. Sometimes the unpredicted nonlinear behavior of a system results in catastrophic failure. In civil engineering, grandstands at sporting events and concerts may be prone to nonlinear oscillations due to looseness of joints, friction, and crowd movements.