Nonlinear system modeling using wavelet networks

Abstract

In this paper we examine modeling of a nonlinear system using wavelet networks. Wavelet networks are similar to neural networks for the structure and the learning approach. But training algorithms for wavelet networks require a smaller number of iterations when compared with neural networks. Also interpretation of the model with neural networks is so hard. Gaussian based mother wavelet function is used as an activation function. Wavelet networks have these parameters; dilation, translation, and weights. Wavelets are rapidly vanishing functions. For this reason heuristic procedure has been used. Selecting initial values of weights are made randomly. Then parameters are optimized during learning. To update parameters, gradient method has been applied by using momentum. Quadratic cost function is used for error minimization. Two test data have been used for the simulations. One of them is a static function and the other one is a second order nonlinear function. © Springer-Verlag Berlin Heidelberg 2005.