一种新的广义梯形模糊数相似性度量方法及在故障诊断中的应用

A New Similarity Measure Between Generalized Trapezoidal Fuzzy Numbers and Its Application to Fault Diagnosis

当前,研究模糊数(Fuzzy number,FN)或广义模糊数(Generalized fuzzy number,GFN)之间的相似性度量方法,大多用于度量论域在单位区间上的标准模糊数.然而在实际中,非标准模糊数却十分常见,而利用现有的多数方法则须先将其转化为标准模糊数再加以处理.但是,归一化的过程会因引起信息损失致使相似性度量结果不合理.本文提出一种避免归一化过程的广义梯形模糊数(generalized trapezoidal fuzzy numbers,GTFN)相似性度量方法,避免了归一化过程.新的方法结合了广义梯形模糊数的指数距离、周长和面积等因素来计算相似度.同时分析了新度量公式的一些性质.然后,利用12对典型的GFN与现有的主要方法进行比较.结果验证新方法的效能.最后,将所提相似性测度方法应用于基于Dempster-Shafer(DS)证据理论的故障诊断当中,通过实际采集数据来验证本文所提方法的有效性.

At present,some methods have been presented to calculate the degree of similarity between（Fuzzy numbers,FNs） or（Generalized fuzzy numbers,GFNs） Most of them are designed for standardized fuzzy numbers,i.e.,the universe of the discourse of FNs lie in unit interval.In order to deal with the non-standardized fuzzy numbers common in practice,it is necessary to transform it into standardized fuzzy numbers,such that the degree of similarity can be calculated.However,normalization process tends to cause information loss and unreasonable results of similarity measure.This paper presents a new similarity measure between GTFNs avoiding normalization process.The new method combines the concepts of exponential distance,the perimeter and the area of GTFNs for calculating the degree of similarity.Some properties of the proposed similarity measure are also proved.And then 12 typical sets of GFNs are given to compare the proposed method with most of the existing methods.The results show that the new method is more efficient to a certain extent.Finally,a practical example is given to show that the proposed method can provide a useful way to deal with the problem of D-S evidence theory based machinery fault diagnosis.