基于随机集的不完整信息可靠性分析方法  

Analysis of Reliability with Imperfect Information in the Unified Framework of Random Set Theory

作　　者：郭惠昕[1] 戴娟[1] 唐蒲华[1] 陈蕾[1] 庞小兵[1] 

机构地区：[1]长沙大学机电工程系,长沙410003

出　　处：《机械科学与技术》2011年第2期290-296,共7页Mechanical Science and Technology for Aerospace Engineering

基　　金：湖南省自然科学基金项目(09JJ3091);湖南省教育厅科学研究项目(09A009);长沙大学科研基金项目(SF070201)资助

摘　　要：提出一种基于随机集的混合不完整信息可靠性分析方法。将各类不完整信息用随机集表示,在随机集理论框架下建立了混合不完整信息的可靠性分析统一模型。用基于随机集的函数扩张原理,得到极限状态函数的随机集表示,然后求出可靠度的极限累积分布函数。在此基础上,求出可靠度的上下界,得到可靠度的区间估计。给出了基于随机集的可靠性分析实施方法与步骤,并给出了一个组合拉杆的可靠性分析实例。A method for analyzing the reliability of a structure affected by heterogeneous variables with imperfect information is proposed based on the random set theory.The heterogeneous variables are transformed and expressed in the random set formalism,and then a unified mathematical model for reliability analysis is established in the framework of random set theory.The limit-state function（LSF） of the structure is mapped into an image in the random set formalism by using the extension principle of random set,and the limit cumulative distribution functions（CDF） of the LSF are calculated.According to the upper and the lower CDF of LSF,the bounds of reliability are calculated and considered as the interval estimation of the reliability of a structure.The implementing steps of the proposed method are presented and demonstrated with a reliability analysis example of a two-component rod under tensile load.

关 键 词：可靠性 不完整信息 随机集理论 分析方法 

分 类 号：TB114.3[理学—概率论与数理统计]