基于径向基函数的非线性预测模型

Nonlinear prediction model based on radial basis functions

针对混沌时间序列的预测问题提出一种兼有全局和局部特点的新的预测模型， 通过数值实验探讨这一模型的性能和特点， 并给出对太阳黑子数据较以往文献更好的预测结果．

In this paper,a new nonlinear prediction model of chaotic time series which has both the global and local properties has been given and explained in detail. Firstly, the Kohonen Self Organization Network is used to produce K centers and to cluster the points of the reconstructed attractor using time delay coordinate into K classes; Secondly. a nonlinear model based on radial basis functions is fitted to every class. So the prediction model is composed of K functions which are all defined on the whole attractor and also have the good properties near their correspondent centers, such as the predicting ability can be improved by increasing size of the learning set. Compared with the local prediction model, this new model has an explicit form(only K functions)and avoids the long time searching for the local points as in the previous one. The predicting power and the specific properties are confirmed by the numeric experiments in the paper. Henon data and Lorenz data are used as the examples of chaotic time series and different learning sets and centers are chosen. Another model which has been developed in our previous work is also used at the same time to compare the results.At last, we apply these models to predict the sunspot data and obtain the lower mean square errors than using the connectionist network and some other models in the previous references.