A new efficient hybrid intelligent method for nonlinear dynamical systems identification: The Wavelet Kernel Fuzzy Neural Network

• We propose a hybrid intelligent method for system identification.
• Parameterization of FWNN has great effect on identification results, therefore it must be done correctly.
• Wavelets are used as time–scale decomposition and as kernel functions.
• The method is applied successfully with delayed systems and chaotic times series.
• An extensive benchmarking is presented and discussed.

In this paper a hybrid computational intelligent approach of combining kernel methods with wavelet Multi-resolution Analysis (MRA) is presented for fuzzy wavelet network construction and initialization. Mother wavelets are used as activation functions for the neural network structure, and as kernel functions in the machine learning process. By choosing precise values of scale parameters based on the windowed scalogram representation of the Continuous Wavelet Transform (CWT), a set of kernel parameters is taken to construct the proposed Wavelet Kernel based Fuzzy Neural Network (WK-FNN) with an efficient initialization technique based on the use of wavelet kernels in Support Vector Machine for Regression (SVMR). Simulation examples are given to test usability and effectiveness of the proposed hybrid intelligent method in the system identification of dynamic plants and in the prediction of a chaotic time series. It is seen that the proposed WK-FNN achieves higher accuracy and has good performance as compared to other methods.