A Regularized SNPOM for Stable Parameter Estimation of RBF-AR(X) Model

Recently, the radial basis function (RBF) network-style coefficients AutoRegressive (with exogenous inputs) [RBF-AR(X)] model identified by the structured nonlinear parameter optimization method (SNPOM) has attracted considerable interest because of its significant performance in nonlinear system modeling. However, this promising technique may occasionally confront the problem that the parameters are divergent in the optimization process, which may be a potential issue ignored by most researchers. In this paper, a regularized SNPOM, together with the regularization parameter detection technique, is presented to estimate the parameters of RBF-AR(X) models. This approach first separates the parameters of an RBF-AR(X) model into a linear parameters set and a nonlinear parameters set, and then combines a gradient-based nonlinear optimization algorithm for estimating the nonlinear parameters and the regularized least squares method for estimating the linear parameters. Several examples demonstrate that the proposed approach is effective to cope with the potential unstable problem in the parameters search process, and may also yield better or similar multistep forecasting accuracy and better robustness than the previous method.