对称抛物型模糊变量下的可靠性及灵敏度分析

Reliability and Reliability Sensitivity Analysis Including Fuzzy Variables with Symmetric Parabolic Membership Functions

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及可靠性灵敏度转化为随机可靠性及可靠性灵敏度,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。对于对称抛物型隶属函数,文中提出了"改进最大最小"法和"改进等面积"法两种近似等价正态化方法,从而将模糊随机可靠性问题转换为随机可靠性问题,并利用线抽样方法分析之。算例结果表明,由于"改进最大最小"法所得的等价正态型隶属函数能在函数图形尾部更好地近似对称抛物型隶属函数,因而"改进最大最小"法更适用于模糊变量的隶属函数为对称抛物型分布时模糊随机可靠性及可靠性灵敏度的近似计算。

In the case of the fuzzy variables possess Gaussian membership functions, the fuzzy random failure probability and reliability sensitivity can be transformed into the random ones. After that the chain rule was employed to obtain the sensitivity of the fuzzy random failure probability with respect to the distribution parameters of Gaussian membership function. For the symmetric parabolic membership function, the improved max-min method and the improved equivalent-area method were presented to transform the symmetric parabolic membership function to Gaussian one equivalently. The fuzzy random reliability problem can be transformed into the random one, which can be analyzed by the line sampling method. Since the symmetric parabolic membership function can be well approximated by equivalent Gaussian one based on the improved max-min method at the tail of the membership function graph, which is illustrated by the examples. Hence the improved max-rain method is more suitable for the estimation of the fuzzy random failure probability and reliability sensitivity, where the fuzzy variables possess the symmetric parabolic membership functions.