Genetically Based Wavenets for System Modeling

Abstract

The combination of wavelet theory and neural networks has lead to the development of wavelet networks (wavenets). Wavenets are feed-forward neural networks which used wavelets as activation functions, and the basis used in wavenet has been called wavelons. Wavenets are successfully used in identification problems. The strength of wavenets lies in their capabilities of catching essential features in “frequency-rich” signals. In wavenet, both the translation and the dilation of the wavelets (wavelons) are optimized besides the weights.
The wavenet algorithm consists of two processes: the self-construction of networks and the minimization of errors. In the first process, the network structure is determined by using wavelet analysis. In the second process, the approximation errors are minimized. The wavenets with different types of frame wavelet function are integrated for their simplicity, availability, and capability of constructing unknown nonlinear function. Thus, wavelet can identify the localization of unknown function at any level.