Nonlinear system identification. NARMAX methods in the time, frequency, and spatio-temporal domains (Q2847892)

The book is a comprehensive overview of huge and manifold work of Stephen A. Billings and his co-workers in the area of nonlinear system identification with the use of NARMAX methodology, introduced in 1981 and developed for over 30 years by these researchers. Applicability, implementation and efficiency of NARMAX methods is presented for various kinds of nonlinear dynamical systems including time-invariant, time-varying, weakly nonlinear, severely nonlinear, as well as spatio-temporal systems including cellular automata in both time and frequency domain. In each case under investigation construction of the adequate parametric system model, proper identification/estimation routine of unknown model parameters and suitable model validation tests are provided yielding complete identification schemes. The considerations are illustrated by numerous examples and case studies.NEWLINENEWLINE Chapter 1 has an introductory character and presents the context in which the NARMAX methods were developed. In Chapter 2, different classes of dynamic models, and in particular NARMAX models, are presented. Model structure detection and parameter estimation with the use of orthogonal least squares are discussed in Chapter 3. In turn, feature selection and extraction based on principal components analysis is described in Chapter 4, and Chapter 5 discusses model validation issue, including detection of nonlinearity, model predictions, correlation tests and qualitative validation of nonlinear dynamical models. In Chapter 6, the identification and analysis of nonlinear systems in the frequency domain is considered, and the concepts of generalized frequency response functions, nonlinear output frequency response functions, and output frequency response functions of nonlinear systems, along with their evaluation, are presented. Chapter 7 is devoted to the design of nonlinear systems in the frequency domain, and in particular - based on the results from Chapter 6 - to the design of a class of energy transfer and energy focus filters, and nonlinear damping devices.NEWLINENEWLINE In Chapter 8, neural radial basis function and wavelet networks are considered as tools for nonlinear system identification, with particular emphasis put on the multiresolution wavelet models and networks. These models are, in turn, exploited in Chapter 9 to deal with severely nonlinear system identification with the help of wavelet multiresolution NARMAX models. Systems that exhibit sub-harmonics and chaos are considered there, and a modeling framework as well as generalized frequency response functions are formulated.NEWLINENEWLINE Chapter 10, in contrast to former parts of the book, is focused on the identification of continuous-time nonlinear systems. The kernel invariance method for model structure determination, and implementation of generalized frequency response functions for step-wise reconstruction of linear, quadratic and higher-order terms of nonlinear integro-differential model are presented.NEWLINENEWLINE In Chapter 11 nonlinear time-varying system identification problems are considered, and it is explained in which way rapid changes can be identified and tracked in both time and frequency domains. In particular, tracking rapid parameter variations with the use of wavelets and time-varying, first and second-order, frequency response functions is demonstrated.NEWLINENEWLINE Chapter 12 describes identification of spatio-temporal systems with finite number of states - namely cellular automata and n-state systems, and Chapter 13 deals with the analysis, system identification problems and frequency response methods for spatio-temporal systems with continuous state. Spatio-temporal patterns of continuous-state systems, identification of coupled map lattice models and partial differential equation models are presented. Also proper nonlinear frequency response functions for spatio-temporal systems are introduced there.NEWLINENEWLINE Final Chapter 14 presents many various case studies where NARMAX methodology is successfuly applied. These include, among others, characterization of robot behavior, detecting and tracking time-varying causality for EEG data, identification of hysteresis effect in metal-rubber damping devices, or forecasting high tides in the Venice lagoon.NEWLINENEWLINE All chapters are completed with extensive list of references.NEWLINENEWLINE The book is addressed to researchers and practitioners from various fields interested in nonlinear model building.