A New Class of Wavelet Networks for Nonlinear System Identification

A new class of wavelet networks (WN's) is proposed for nonlinear system identification. In the new networks, the model structure for a high dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated waveket decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least- squares type methods. An efficient model term detection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study.