模糊随机可靠性灵敏度分析方法

 依据模糊随机可靠性灵敏度的基本概念,提出了模糊随机可靠性灵敏度分析的通用数字模拟法,推导了模糊随机可靠性灵敏度数字模拟解的方差和变异系数的计算公式。当模糊变量的隶属函数为正态型时,可以将模糊随机可靠性灵敏度转化为随机可靠性灵敏度,并利用复合函数求导法则求解模糊随机失效概率对正态型隶属函数分布参数的灵敏度。对于工程中常用的对称三角型隶属函数,提出了两种近似等价正态化变换基础上的模糊随机可靠性灵敏度分析方法,这两种将对称三角型隶属函数近似等价为正态型的方法分别是“3σ规则”法和“最大最小”法。算例结果表明：由于“最大最小”法比“3σ规则”法所得的等价正态隶属函数能在形状上更好地近似对称三角型隶属函数,因而“最大最小”变换法更适用于对称三角型隶属函数情况下模糊随机可靠性灵敏度的近似计算。

Sensitivity Analysis for Fuzzy Random Reliability

Based on the basic definition of fuzzy random reliability sensitivity, the general numerical simulation method is presented for fuzzy random reliability sensitivity estimation. The variance and the variation coefficient are derived for the numerical estimation of the fuzzy random reliability sensitivity. In case that the fuzzy basic variables possess Gaussian membership functions, the fuzzy random reliability sensitivity can be transformed into the random reliability sensitivity, which can be well solved by the available methods. After the fuzzy random reliability sensitivity is transformed into the random one,the chain rule is employed to obtain the sensitivity of the fuzzy random failure probability with respect to the distribution parameters of the Gaussian membership function.For a symmetric triangle membership,a commonly used function in engineering,two fuzzy random reliability sensitivity methods are constructed on the basis of two equivalent transformations from the symmetric triangle membership to the Gaussian one respectively.One of them is named as "3σ" criterion,the other is named as max.-min.method.Since the shape of the symmetric triangle membership function can be replaced by the max.-min.method more closely than by the "3σ" criterion,the max.-min.method is more applicable to estimate the fuzzy random reliability sensitivity in case of the symmetric triangle membership,which is demonstrated by the given examples.