一种基于小波的模糊建模方法

Wavelet-based approach to fuzzy modelling

为克服一般Takagi-Sugeno模糊模型的局限性,提出了一种新的用于复杂系统建模的模糊模型．理论分析表明该模型可表示任何一个紧集上的连续函数．该模型的一个显著特点是,模糊模型的输入输出关系与使用特殊母波函数的小波变换的形式相同．基于该性质,可方便地运用小波变换理论确定模糊模型的结构并初始化模型参数．本文详细地介绍了辨识该模糊模型的算法．通过对一个复杂非线性系统的建模并与以前的结果进行比较,验证了本文方法的有效性．

A new fuzzy model for complex systems is presented to overcome the limitation of the general Takagi-Sugeno fuzzy models. Theoretical analysis is given to show that the proposed fuzzy model can represent any continuous function over a compact set. The distinguished feature of the fuzzy model is that the input-output representation of the fuzzy model is the same as that of wavelet transforms of using special mother wavelet function. Based on the property, wavelet transforms can thus be conviently used to determine the proper structure and initial parameters. An algorithm for identifying the proposed fuzzy model is then described in detail. Finally, an example is given to show the feasibility of the proposed fuzzy model by comparing it with existing research.