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The wavelet-NARMAX representation : a hybrid model structure combining polynomial models with multiresolution wavelet decompositions

Billings, S.A. and Wei, H.L. (2005) The wavelet-NARMAX representation : a hybrid model structure combining polynomial models with multiresolution wavelet decompositions. International Journal of Systems Science, 36 (3). pp. 137-152. ISSN 1464-5319

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A new hybrid model structure combing polynomial models with multiresolution wavelet decompositions is introduced for nonlinear system identification. Polynomial models play an important role in approximation theory, and have been extensively used in linear and nonlinear system identification. Wavelet decompositions, in which the basis functions have the property of localization in both time and frequency, outperform many other approximation schemes and offer a flexible solution for approximating arbitrary functions. Although wavelet representations can approximate even severe nonlinearities in a given signal very well, the advantage of these representations can be lost when wavelets are used to capture linear or low-order nonlinear behaviour in a signal. In order to sufficiently utilise the global property of polynomials and the local property of wavelet representations simultaneously, in this study polynomial models and wavelet decompositions are combined together in a parallel structure to represent nonlinear input-output systems. As a special form of the NARMAX model, this hybrid model structure will be referred to as the WAvelet-NARMAX model, or simply WANARMAX. Generally, such a WANARMAX representation for an input-output system might involve a large number of basis functions and therefore a great number of model terms. Experience reveals that only a small number of these model terms are significant to the system output. A new fast orthogonal least squares algorithm, called the matching pursuit orthogonal least squares (MPOLS) algorithm, is also introduced in this study to determine which terms should be included in the final model.

Item Type: Article
Copyright, Publisher and Additional Information: © 2005 Taylor & Francis Group Ltd. This is an author produced version of a paper subsequently published in 'International Journal of Systems Science'.
Keywords: nonlinear system identification, 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: 06 Jun 2014 06:32
Published Version: http://dx.doi.org/10.1080/00207720512331338120
Status: Published
Publisher: Taylor and Francis
Refereed: Yes
Identification Number: 10.1080/00207720512331338120
URI: http://eprints.whiterose.ac.uk/id/eprint/1972

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