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