基于expectation maximization算法的Mamdani-Larsen模糊系统及其在时间序列预测中的应用  

Mamdani-Larsen fuzzy system based on expectation maximization algorithm and its applications to time series prediction

作　　者：张钦礼[1,2] 王士同[1] 

机构地区：[1]江南大学信息工程学院,无锡214122 [2]北华航天工业学院,廊坊065000

出　　处：《物理学报》2009年第1期107-112,共6页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:60773206/F020106, 60704047/F030304);国家高技术研究发展计划(863)项目(批准号: 2007AA1Z158,2006AA10Z313)资助的课题~~

摘　　要：Epanechnikov混合模型和Mamdani-Larsen模糊系统之间的对应关系被建立:任何一个Epanechnikov混合模型都唯一对应着一个Mamdani-Larsen模糊系统,在一定条件下,Epanechnikov混合模型的条件均值和Mamdani-Larsen模糊模型的输出是等价的。一个设计模糊系统的新方法被提出,即利用expectation maximization算法设计模糊系统。将设计的模糊系统应用于时间序列预测,仿真结果表明:利用EM算法设计的模糊系统比其他模糊系统精度更高,抗噪性更强。This work explores how Epanechnikov mixture model can be translated to Mamdani-Larsen fuzzy model.The mathematical equivalence between the conditional mean of an Epanechnikov mixture model and the defuzzified output of a Mamdani-Larsen fuzzy model is proved.The result provides a new perspective of studying the Mamdani-Larsen fuzzy model by interpreting a fuzzy system from a probabilistic viewpoint.Instead of estimating the parameters of the fuzzy rules directly,the parameters of an Epanechnikov mixture model can be firstly estimated using any popular density estimation algorithm,such as expectation maximization.Mamdani-Larsen fuzzy model trained in the new way has higher accuracy and stronger anti-noise capability.After comparing the simulation results with the ones obtained from other fuzzy system modeling tools,it can be claimed that the results are successful.

关 键 词：EXPECTATION maximization(EM)算法 Mamdani-Larsen模糊系统 Epanechnikov混合模型 混沌时间序列 

分 类 号：O159[理学—数学]