Modeling And Prediction Of Multivariate Chaotic Time Series Based On Neural Network

In this paper, RBF neural network is used for modeling and prediction on multivariate chaotic time series. Because the selection of hidden layer cluster centers has a very significant impact on RBF network performance, also, for multivariate time series, the large number data samples which contain too much redundant information may disturb the network training process. This paper improves the RBF network from two aspects: the optimization of samples and the selection of hidden layer cluster centers.Firstly, a linear correlation function and a nonlinear correlation function are respectively used to detect the linear correlations and the nonlinear correlations in the multivariate states. And a small data set which includes effective information of the system is defined. Then, K-means clustering algorithm is used to choose hidden layer’s clustering centers of RBF neural network, and a local search procedure is introduced to optimize the clustering centers. Finally, the pseudo inverse method of orthogonal least-squares is used to determine network weights.This algorithm is used to simulate single-step prediction for x, y, z three-variable time series from typical Lorenz chaotic equations and two variables time series from temperature and rainfall of Dalian with chaotic characteristics. Compared with the conventional nearest neighbor clustering algorithm under the same conditions, simulation results show that the RBF network model which established by improved method has less hidden layer nodes, more compact, and better predictive accuracy.