基于模糊模型支持向量机的混沌时间序列预测  

Prediction of the chaotic time series using support vector machines for fuzzy rule-based modeling

作　　者：崔万照[1] 朱长纯[1] 保文星[1] 刘君华[1] 

机构地区：[1]西安交通大学电子与信息工程学院,西安710049

出　　处：《物理学报》2005年第7期3009-3018,共10页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:60176020和60276037);教育部博士点基金(批准号:20020698014)资助的课题.~~

摘　　要：基于支持向量机强大的非线性映射能力和模糊逻辑易于将先验的系统知识结合到模糊规则的特性,根据混沌动力系统的相空间重构理论,提出了一种混沌时间序列的模糊模型的支持向量机预测模型,并采用适用于大规模问题求解的最小二乘法来训练预测模型,利用该模型分别对模型的整体预测性能与嵌入维数及延迟时间的关系进行了探讨.最后利用Mackey Glass时间序列和典型的Lorenz系统生成的时间序列对该模型进行了验证,结果表明该预测模型不仅能够自动的从学习数据中获取知识产生模糊规则,提取能够代表混沌时间序列内在规律的支持向量,大大减少支持向量的数目,精确地预测未来的混沌时间序列,而且在混沌时间序列的嵌入维数未知和延迟时间不能合理选择的情况下,也能取得比较好的预测效果.这一结论预示着基于模糊模型的支持向量机是一种研究混沌时间序列的有效方法.Based on the powerful nonlinear mapping ability of support vector machines and the characteristics of fuzzy logic which can combine a prior knowledge into fuzzy rules, the forecasting model of the support vector machine for fuzzy rules-based model in combination with Takens' delay coordinate phase reconstruction of chaotic time series has been established; and the least squares method for large-scale problems is used to train this model. Moreover, based on this model, relationships among the prediction performances of this model, the embedding dimension and the delay time are discussed. Finally, the Mackey-Glass equation and the time series that Lorenz systems generate are applied to test this model, respectively, and the results show that the support vector machine for fuzzy rule-based modeling can not only acquire knowledge and generate fuzzy rules from the given data, reduce the number of support vectors greatly, but also predict chaotic time series accurately, and even if the embedding dimension is unknown and the delay time is appropriately selected, the predicted results are satisfactory. These results imply the support vector machine for fuzzy rule-based modeling is a good tool to study chaotic time series in practice.

关 键 词：支持向量机 混沌时间序列预测 模糊模型 非线性映射能力 相空间重构理论 混沌动力系统 预测模型 模糊规则 延迟时间 嵌入维数 最小二乘法 系统知识 模糊逻辑 问题求解 系统生成 预测性能 内在规律 有效方法 预测效果 序列对 

分 类 号：O211.61[理学—概率论与数理统计]