Wavelet Network-Based Narmax Model for Nonlinear System Identification

Wavelet Networks, which combine the properties of wavelet decomposition with the characteristics of neural networks, have been successfully applied in model structure for nonlinear system identification in recent years. One the basic challenges of such wavelet network-based models is the identification of high-dimensional systems with a small number of variables to solve the problem known as the cruse of dimensionality. In this paper B-spline-wavelet network-based NARMAX model are developed for the identification of nonlinear systems. By adopting the analysis of variance (ANOVA) expansion and using truncated wavelet decompositions, the multivariate nonlinear wavelet networks are converted into linear-in-the-parameter equations, which can be solved by least square methods. Significant model term selection is improved by combing the Orthogonal Forward Regression (OFR) selection method with the Bayesian information criterion (BIC). Simulations are carried out by Matlab and standard errors on the estimated model coefficients are calculated. One of the simulation examples illustrated in this work considers SIMO system model of gas exhaust operation during the warm-up period of an ignition engine. The results show that the introduction of wavelet networks improves the prediction ability of the model when compared with wavelets with the same number of regressors.