Comparison of Wavenet and Neuralnet for System Modeling

Abstract

This paper presents nonlinear static and dynamic system modeling using wavenet and neuralnet. Wavenet combines wavelet theory and feed-forward neuralnet, so learning approach is similar to neuralnet. The selection of transfer function is crucial for the approximation property and the convergence of the network. The purelin and the tansig functions are used as the transfer functions for neuralnet and the first derivative of a gaussian function is used as the transfer function for wavenet. Wavenet and neuralnet parameters are optimized during learning phase. Selecting all initial values random, but for wavenet, it may be unsuitable for process modeling because wavelets have localization feature. For this reason heuristic procedure has been used for wavenet. In this study gradient methods have been applied for parameters updating with momentum. Error minimization is computed by quadratic cost function for wavenet and neuralnet. Nonlinear static and dynamic functions have been used for the simulations. Recently wavenet has been used as an alternative of the neuralnet because interpretation of the model with neuralnet is so hard. For wavenet learning approach, training algorithms require smaller number of iterations when compared with neuralnet. Consequently, according to the number of training iteration and TMSE, dynamic and static system modeling with wavenet is better as shown in results.