模糊变量与随机变量组合时模糊可靠度计算方法研究  

CALCULATION METHOD OF FUZZY RELIABILITY IN COMBINATION OF FUZZY VARIABLES AND RANDOM VARIABLES

作　　者：周建方[1,2] 郑鼎聪 高冉 冷伟 ZHOU Jian-fang;ZHENG Ding-cong;GAO Ran;LENG Wei(Hohai University,College of Mechanical and Electrical Engineering,Changzhou 213022,China;Hohai University,College of Mechanics and Material,Nanjing 211100,China;Sichuan Water Resources and Hydroelectric Investigation&Design Institute,Chengdu 610072,China)

机构地区：[1]河海大学机电工程学院,常州213022 [2]河海大学力学与材料学院,南京211100 [3]四川省水利水电勘测设计研究院,成都610072

出　　处：《工程力学》2021年第10期12-23,共12页Engineering Mechanics

基　　金：国家自然科学基金项目(51679075);国家重点研发计划项目(2017YFC1502603)。

摘　　要：对现有的随机应力、模糊强度可靠度计算方法进行了系统的分析研究,将其分成模糊变量直接转化为随机变量、由模糊强度的隶属函数直接构造模糊失效事件的隶属函数、可能度法和实用计算法四类,根据模糊失效概率的属性又可分成定量计算法和模糊计算法两类;得到了在定量计算方法中,广义密度函数法与面积法等价,当量密度函数法与截集法等价,真正独立的主要方法为广义密度函数法、当量密度函数法和直接转化法三种等结果;对强度模糊隶属函数为线性、正态分布情况推导了有关公式;通过算例给出了各主要方法的计算结果,其值相差较大,因此,哪种方法更合理还必须作进一步研究。The existing reliability calculation methods of random stress and fuzzy strength have been systematically studied,and divided into four categories:method of directly transforming fuzzy variables into random variables,method of directly constructing membership functions of fuzzy failure events from that of fuzzy strength,possibility method and practical calculation method.Moreover,they can also be simply classified as quantitative calculation methods and fuzzy calculation methods due to the attribute of fuzzy failure probability.As for the quantitative calculation methods,the generalized density function method and equivalent density function method are,respectively,equivalent to the area method and cut set method.Under such circumstances,it can be concluded that the really independent methods for the quantitative calculation methods only include the generalized density function method,the equivalent density function method and the direct transformation method.Relevant formulas are derived for the cases where the fuzzy membership function of strength follows linear or normal distribution.The numerical results of common methods are comparatively studied,where the significant differences between each other indicate that the most reasonable method need to be further studied.

关 键 词：模糊变量 随机变量 模糊可靠度 模糊失效概率 计算方法 

分 类 号：TV314[水利工程—水工结构工程]