Abstract: A unified reliability analysis method based on evidence theory was proposed to deal with the reliability problem of structures containing random,fuzzy and interval variables.By using the information entropy method,the membership function of fuzzy variable was converted into probability density function of equivalent random variable.On the basis of interval method of random variable,each variable was separated into discrete intervals,and the Basic Probability Assignment(BPA)was solved by the probability density function of variables.According to the evidence theory,the reliability analysis was carried out to get the belief measure of reliability Bel(R)and the plausibility measure of reliability Pl(R).Two engineering applications were demonstrated to verify the feasibility and effectiveness of the proposed method.

Key words: reliability, information entropy, evidence theory, multi-source uncertainty, basic probability assignment

摘要： 针对同时存在随机、模糊和区间三种输入变量时的可靠性分析问题,提出了一种基于证据理论的统一可靠性分析方法。利用信息熵转化法,将模糊变量的隶属度函数转化为等效随机变量的概率密度函数|基于随机变量的区间化方法,将每个变量离散成有限个小区间,根据变量的概率密度函数求解各小区间的基本概率分配;利用证据理论进行可靠性分析,最终获得可靠度R的置信度Bel(R)和似真度Pl(R)。通过两个工程算例证明了该方法的可行性和有效性。

关键词: 可靠性, 信息熵, 证据理论, 多源不确定性, 基本概率分配