Nonlinear system identification [[electronic resource]] : NARMAX methods in the time, frequency, and spatio-temporal domains / / Stephen A. Billings

• Record Nr.: UNINA9910139042003321
• Autore: Billings S. A
• Pubbl/distr/stampa: Chichester, England, : Wiley, c2013
• ISBN: 1-118-53555-3; 1-118-53556-1; 1-118-53554-5
• Descrizione fisica: 1 online resource (607 p.)
• Disciplina: 003/.75
• Soggetti: Nonlinear systems; Nonlinear theories - Mathematical models; Systems engineering
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
• Nota di contenuto: Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Tempora Domains; Copyright; Contents; Preface; 1 Introduction; 1.1 Introduction to System Identification; 1.1.1 System Models and Simulation; 1.1.2 Systems and Signals; 1.1.3 System Identification; 1.2 Linear System Identification; 1.3 Nonlinear System Identification; 1.4 NARMAX Methods; 1.5 The NARMAX Philosophy; 1.6 What is System Identification For?; 1.7 Frequency Response of Nonlinear Systems; 1.8 Continuous-Time, Severely Nonlinear, and Time-Varying Models and Systems; 1.9 Spatio-temporal Systems; 1.10 Using Nonlinear System Identification in Practice and Case Study ExamplesReferences; 2 Models for Linear and Nonlinear Systems; 2.1 Introduction; 2.2 Linear Models; 2.2.1 Autoregressive Moving Average with Exogenous Input Model; 2.2.1.1 FIR Model; 2.2.1.2 AR Model; 2.2.1.3 MA Model; 2.2.1.4 ARMA Model; 2.2.1.5 ARX Model; 2.2.1.6 ARMAX Model; 2.2.1.7 Box-Jenkins Model; 2.2.2 Parameter Estimation for Linear Models; 2.2.2.1 ARX Model Parameter Estimation - The Least Squares Algorithm; 2.2.2.2 ARMAX Model Parameter Estimation - The Extended Least Squares Algorithm; 2.3 Piecewise Linear Models2.3.1 Spatial Piecewise Linear Models; 2.3.1.1 Operating Regions; 2.3.1.2 Parameter Estimation; 2.3.1.3 Simulation Example; 2.3.2 Models with Signal-Dependent Parameters; 2.3.2.1 Decomposition of Signal-Dependent Models; 2.3.2.2 Parameter Estimation of Signal-Dependent Models; 2.3.2.3 Simulation Example; 2.3.3 Remarks on Piecewise Linear Models; 2.4 Volterra Series Models; 2.5 Block-Structured Models; 2.5.1 Parallel Cascade Models; 2.5.2 Feedback Block-Structured Models; 2.6 NARMAX Models; 2.6.1 Polynomial NARMAX Model; 2.6.2 Rational NARMAX Model; 2.6.2.1 Integral Model2.6.2.2 Recursive Model; 2.6.2.3 Output-affine Model; 2.6.3 The Extended Model Set Representation; 2.7 Generalised Additive Models; 2.8 Neural Networks; 2.8.1 Multi-layer Networks; 2.8.2 Single-Layer Networks; 2.8.2.1 Activation Functions; 2.8.2.2 Radial Basis Function Networks; 2.9 Wavelet Models; 2.9.1 Dynamic Wavelet Models; 2.9.1.1 Random Noise; 2.9.1.2 Coloured Noise; 2.10 State-Space Models; 2.11 Extensions to the MIMO Case; 2.12 Noise Modelling; 2.12.1 Noise-Free; 2.12.2 Additive Random Noise; 2.12.3 Additive Coloured Noise; 2.12.4 General Noise; 2.13 Spatio-temporal ModelsReferences; 3 Model Structure Detection and Parameter Estimation; 3.1 Introduction; 3.2 The Orthogonal Least Squares Estimator and the Error Reduction Ratio; 3.2.1 Linear-in-the-Parameters Representation; 3.2.2 The Matrix Form of the Linear-in-the-Parameters Representation; 3.2.3 The Basic OLS Estimator; 3.2.4 The Matrix Formulation of the OLS Estimator; 3.2.5 The Error Reduction Ratio; 3.2.6 An Illustrative Example of the Basic OLS Estimator; 3.3 The Forward Regression OLS Algorithm; 3.3.1 Forward Regression with OLS; 3.3.1.1 The FROLS Algorithm; 3.3.1.2 Variants of the FROLS Algorithm
• Sommario/riassunto: 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) modelThe orthogonal least squares algorithm that allows models to be built term by