基于马尔科夫链与鞍点逼近的模糊随机可靠性分析方法  

Methods for the fuzzy and random probability analysis problem based on Markov Chain and Saddle-point Approximation

作　　者：魏鹏飞[1] 吕震宙[1] 袁修开[1] 

机构地区：[1]西北工业大学航空学院,西安710072

出　　处：《计算力学学报》2012年第2期184-189,204,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(51175425);航空基础基金(2007ZA53012);863计划课题(2007AA04Z401)资助项目

摘　　要：针对同时存在随机不确定性和模糊不确定性的可靠性分析问题,提出了两种高效解决方法。一种是迭代马尔科夫链鞍点逼近法,该方法的基本思想是给定隶属水平下由迭代马尔科夫链和一次鞍点逼近法求得可靠度上下限,不同的隶属水平对应不同的可靠度上下限,遍历隶属水平的取值区间[0,1]即可求得可靠度隶属函数,与传统的两相Monte Carlo数字模拟法和迭代一次二阶矩法相比,该方法具有效率高和对非正态基本随机变量不需要进行正态转换的优点;第二种方法是迭代条件概率马尔科夫链模拟法,该方法在求解给定隶属度水平下的可靠度上下限时,由条件概率公式引入一个非线性修正因子,该因子的引入大大提高了功能函数为非线性的可靠性问题的求解精度。本文算例验证了所提方法的优越性。Two novel methods are developed to solve the mixed probability analysis problem with both random and f uzzy uncertainties.The first one is Iterative Markov Chain Simulation First Order Saddle-point Approximation（IMCSFOSA） whose key idea is to get the upper limit and lower limit of the reliability for a given membership level with Markov Chain and First Order Saddle-point Approximation,and throughout the whole value domain of membership level by this process,the membership function of reliability can be obtained.Compared with the traditional methods,such as double-loop Monte Carlo simulation and iterative first order and second moment method,the IMCSFOSA is more efficient due to less simulation and more effective due to no transformation from the non-normal distribution to the normal one.The second method is Iterative Conditional Probability Markov Chain Simulation（ICPMCS）,in which a nonlinear modification factor is introduced by Conditional Probability formula in solving the upper limit and lower limit of the reliability for a given membership level.The introduction of this factor highly improves the calculation accuracy for the highly nonlinear performance function.Several examples are introduced to illustrate the advantages of the presented methods.

关 键 词：随机变量 模糊变量 马尔科夫链 鞍点逼近 条件概率 

分 类 号：O213.2[理学—概率论与数理统计] O324[理学—数学]