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A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

Wei, H.L. and Billings, S.A. (2004) A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure. International Journal of Control, 77 (4). pp. 351-366. ISSN 1366-5820

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A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems.

Item Type: Article
Copyright, Publisher and Additional Information: © 2004 Taylor and Francis Ltd. This is an author produced version of a paper subsequently published in 'International Journal of Control'.
Keywords: nonlinear system identification, NARX and NARMAX models, wavelets, orthogonal least squares
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield)
Depositing User: Repository Officer
Date Deposited: 20 Feb 2007
Last Modified: 12 Jun 2014 20:24
Published Version: http://dx.doi.org/10.1080/0020717042000197622
Status: Published
Publisher: Taylor and Francis
Refereed: Yes
Identification Number: 10.1080/0020717042000197622
URI: http://eprints.whiterose.ac.uk/id/eprint/1974

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