Hybrid adaptive wavelet-neuro-fuzzy system for chaotic time series identification

In the paper a five-layers architecture of hybrid wavelet-neuro-fuzzy system which is using the adaptive W-neurons as the nodes is proposed. W-neuron is a neuron which structure is similar to a radial basis functions network, but instead of conventional radial basis functions we used multidimensional adaptive wavelet activation–membership functions. The distinctive feature of the proposed system is usage of the wavelets as membership functions in the antecedent layer, and the adaptive multidimensional wavelets as activation functions in the consequent layer that can tune not only the dilation and translation parameters but also its own form during the learning process. The learning algorithms for all antecedent and consequent functions’ parameters that have both following and filtering properties are proposed. The experimental results have shown that this wavelet-neuro-fuzzy system has improved approximation properties and has a higher learning rate in comparison with usual wavelet-neuro-fuzzy networks. The proposed hybrid wavelet-neuro-fuzzy system can be used to solve tasks of diagnosis, forecasting, emulation, and identification of nonlinear chaotic and stochastic non-stationary processes.