基于模糊树模型的混沌时间序列预测  

Chaotic time series prediction based on fuzzy tree

作　　者：毛剑琴[1] 姚健[1] 丁海山[2] 

机构地区：[1]北京航空航天大学自动化科学与电气工程学院,北京100191 [2]中国空空导弹研究院,洛阳471009

出　　处：《物理学报》2009年第4期2220-2230,共11页Acta Physica Sinica

基　　金：国家重点基础研究(973)计划(批准号:2002cb312205);国家自然科学基金(批准号:60534020);北京市重点学科基金(批准号:XK100060526);高等学校博士学科点专项科研基金(批准号:20070006060)资助的课题~~

摘　　要：应用模糊树模型,对混沌时间序列进行建模和预测.该方法可以根据建模数据在空间中的分布信息,基于二叉树结构自适应划分输入空间,得到模糊子空间,在与叶节点对应的子空间上建立线性函数作为模糊规则的后件,用隶属度函数将各分片线性函数光滑连接,最后得到一个精度比较高的非线性映射.通过对Mackey-Glass、Lorenz和Henon混沌时间序列的建模和预测研究,仿真结果表明,该方法具有建模精度高、运行速度快、泛化能力强、预测步数多、适用范围广等优点.In this paper,an adaptive-tree-structure-based fuzzy model is applied to predict chaotic time series.The fuzzy partition of input data set is adaptive to the pattern of data distribution to optimize the number of the subsets automatically by binary-tree model.A fuzzy area around every discriminant edge is set up by the membership functions corresponding to every subset of input data.A complex nonlinear function is obtained by piecewise linear approximation and smoothing the discontinuous at the discriminant edges of subsets to reduce the error of approximation.The fuzzy tree model is evaluated using prediction of the Mackey-Glass,Lorenz and Henon chaotic time series.In comparison with some existing methods,it is shown that the FT is also of less computation and high accuracy.

关 键 词：模糊树模型 混沌时间序列 预测 

分 类 号：O415.5[理学—理论物理]