Wavelet Neural Networks and Its Applications in Chaotic Systems Identification

Abstract

The combination of wavelets with neural networks can hopefully remedy each others weaknesses, resulting in wavelet based neural network capable of handling system identification problems of a moderately large dimension. A wavelet based neural network is a nonlinear regression structure that represents nonlinear mappings as the superposition of dilated and translated versions of a function, which is found both in the space and frequency domains. In this paper, a wavelet-based neural network is introduced for the nonlinear identification of dynamic systems with chaotic behavior (chaotic time series). The structure of the wavelet based neural network is similar to that of radial basis function neural networks, except that here the activation function of the hidden nodes is replaced by wavelet functions. The proposed wavelet-based neural network is evaluated on two case studies: (i) the Henon map, and (ii) the Rossler system. Simulation results demonstrate the accuracy and the reliability of the proposed identification methodology based on a wavelet based neural network.