机械结构系统模糊可靠性分析的数字计算方法

NUMERICAL ALGORITHM FOR FUZZY RELIABILITY ANALYSIS OF MECHANICAL STRUCTURE SYSTEM

基于模糊可靠性问题向随机可靠性问题的数学转换,提出了应力和强度均为模糊变量时机械结构模糊可靠性分析的数字计算模型,在该模型中与截集水平对应的模糊应力和模糊强度首先被转化为普通的区间,然后在该普通区间上引入合适的概率分布,即可采用随机可靠性模型得到与截集水平对应的模糊失效概率,以此模糊失效概率为被积函数,以模糊应力的截集水平和模糊强度的截集水平为两个积分变量进行二重积分,并以0和1作为两个截集水平的积分限,即可得到机械结构系统的模糊失效概率。在所提方法的基础上,还提出了同时考虑基本变量模糊性和失效/安全域模糊性的失效概率计算公式。所提方法与模糊线性回归相结合,可用于计算具有多个基本模糊变量的机械结构系统的模糊失效概率。

On the basis of the mathematical transition from fuzzy probability to conventional random probability, a numerical algorithm focusing on mechanical structure system with fuzzy stress and fuzzy strength is presented for the fuzzy reliability analysis. In the presented algorithm, the fuzzy stress and fuzzy strength are truncated to the subsets, which are the common sets, corresponding to the truncated level firstly. The appropriate probability distribution is then introduced on the truncated subsets, and the conventional reliability method is used to calculate the fuzzy failure probability, which is called as the truncated fuzzy failure probability. By using the truncated fuzzy failure probability as the integration function, the fuzzy failure probability can be calculated for the structure system, where the truncated levels of the fuzzy stress and the fuzzy strength are utilized as the integration variables. The fuzzy reliability is formulated for the structure system with fuzzy basic variables and fuzzy states as well. The illustrations are used to investigate the effects of the fuzzy distribution parameters and the introduced probability distributions on the fuzzy failure probability. By the conjunction with the fuzzy linear regression, the presented algorithm can be expanded to solve the fuzzy reliability analysis of the complicated structure system with multiple fuzzy basic variables.