A global–local optimization approach to parameter estimation of RBF-type models

We present a hybrid global–local optimization algorithm for parameter estimation of radial basis function (RBF) networks and the RBF-type autoregressive models without exogenous inputs (RBF-AR) or with exogenous inputs (RBF-ARX). The RBF-AR (X) models are quasi-linear time-varying AR (X) models with Gaussian RBF network-style coefficients, which have been used to effectively model the nonlinear behavior of various complex systems. However, the identification of these models is a difficult optimization problem because of the large number of local minima. A hybrid approach is proposed in this paper to achieve better optimization results for these RBF-type models. The applied hybrid search strategy (EA-SNPOM) is developed by combining an evolutionary algorithm (EA) with a gradient-based algorithm known as the structured nonlinear parameter optimization method (SNPOM). This strategy makes use of the robustness of the EA to cover an entire global search space and the efficiency of the gradient search to converge to a local optimum. Several examples of time series modeling and system identification are presented. The simulation results indicate that the performance of the proposed hybrid approach is better than the performance obtained from using each method (EA or SNPOM) alone. Furthermore, the RBF-AR (X) models estimated by the EA-SNPOM achieve much better modeling accuracy relative to other neural networks or fuzzy models in the simulations.