模糊可靠度隶属函数求解的迭代线抽样法  

MEMBERSHIP FUNCTION OF FUZZY RELIABILITY ANALYSIS BY ITERATION BASED LINE SAMPLING

作　　者：李璐祎[1] 吕震宙[1] 

机构地区：[1]西北工业大学航空学院,西安710072

出　　处：《工程力学》2011年第5期13-20,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(NSFC10572117;50875213);新世纪优秀人才支持计划项目(NCET-05-0868);航空基础基金项目(2007ZA53012);民口863计划项目(2007AA04Z401)

摘　　要：针对同时存在随机基本变量和模糊基本变量的结构,提出了一种模糊可靠度隶属函数求解的迭代线抽样方法。所提方法首先求得给定隶属度水平下模糊基本变量的取值域。然后通过优化建模和迭代策略,求得使功能函数取最值的模糊基本变量取值点,并求得对应的缩减后的随机变量空间内功能函数的设计点。最后基于功能函数最值对应的模糊基本变量取值点及其相应的设计点,运用线抽样法求得给定隶属水平下可靠度值的上界、下界,进而得到模糊可靠度的隶属函数。对于每个给定隶属度水平对应的模糊变量取值域,所提方法通过寻找功能函数的最值代替寻找可靠度最值的策略,大大降低了计算量。另外,所提方法通过迭代过程保证功能函数最值对应的设计点收敛于可靠度最值对应的设计点,并通过线抽样方法来求解相应的可靠度,可以保证算法具有较高的精度。该文算例将对所提算法的优越性进行验证。For structures with random variables as well as fuzzy variables,a new iteration method based Line Sampling（LS） is presented for obtaining the membership function of fuzzy reliability.The value domain of the fuzzy variables is firstly obtained by means of the given membership level.Then the values of the fuzzy variables which make the performance function take extreme values are obtained by optimization modeling and iterating strategy,and the corresponding design points of the performance function in the reduced random variables space are also obtained at the same time.At last,based on the values of the fuzzy variables and the design points corresponding to the extreme values of the performance function,LS is employed to obtain the bounds of the reliability under the given membership level,and then the membership function of the fuzzy reliability is obtained.For the value domain of the fuzzy variables corresponding to each given membership level,the presented method considerably decreases computational effort by searching the extreme values of performance function instead of those of the reliability.Additionally,the design points corresponding to the extreme values of the performance function are guaranteed to converge to that corresponding to the extreme values of the reliability by the iterative strategy,and the reliability is obtained by LS,which improves the precision of the presented method.Several examples are used to illustrate the advantages of the presented method.

关 键 词：模糊可靠度 模糊基本变量 随机基本变量 隶属函数 线抽样方法 

分 类 号：TB114.3[理学—概率论与数理统计]