Nonlinear System Identification Based on a Novel Adaptive Fuzzy Wavelet Neural Network

In this paper, an optimized adaptive Fuzzy Wavelet Neural Network (FWNN) is proposed for identification of nonlinear systems. The network combines Takagi-Sugeno-Kang fuzzy neural networks with the advantages of adaptive wavelet functions. Therefore, it provides an effective nonlinear mapping which can approximate the local as well as the global behaviour of nonlinear complex systems. Furthermore, an optimized constructive learning algorithm is proposed. In this regard, all network parameters including center and variance of membership functions, dilation and translation of wavelets, and weights are assumed to be adjustable which make the network structure quite flexible. In this method, the orthogonal projection pursuit (OPP) algorithm is invoked in the structure learning phase which can generate the fuzzy rules automatically. Then, the parameters of each rule are optimized based on a nonlinear global optimization method, here, the genetic algorithm (GA). To increase the performance of the optimization scheme, a nonlinear local optimization algorithm, the Levenberg-Marquardt (LM), is also applied with the initial point from the GA. This hybrid combination produces a more accurate optimal solution which provides better performance with a fewer number of required fuzzy rules. As some advantages of this approach, the proposed network is self-implemented, and there is no need to initialize the parameters or pre-determine the number of fuzzy rules. Finally, a nonlinear case study is provided which shows the efficiency of the proposed identification approach.