可靠性灵敏度函数及其特征指标的条件概率模拟求解方法  

Reliability sensitivity measure based on reliability sensitivity function and its solution by conditional probability simulation method

作　　者：袁修开[1] 吕震宙[1] 吕媛波[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》2011年第3期444-451,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(50875213);航空基础基金(2007ZA53012);863计划课题(2007AA04Z401)资助项目

摘　　要：可靠性分析中基本变量分布参数为区间均匀变量时,失效概率为分布参数的函数。基于条件概率马尔科夫链模拟,提出了一种可靠性灵敏度函数的求解方法,并提出了一种新的可靠性灵敏度度量指标,它为参数可靠性灵敏度函数在参数空间上的期望。文中推导了线性极限状态正态变量下全局灵敏度函数及新指标的计算式,并提出了高效的基于条件概率马尔科夫链模拟的可靠性灵敏度函数求解法,该方法基于贝叶斯公式,得到可靠性灵敏度函数的表达式,并采用马尔科夫链算法直接模拟失效域中的样本来进行求解,且采用三阶最大熵法拟合参数的条件概率密度函数,最终得到可靠性灵敏度函数的解。文中结合数值算例和工程算例的比较探讨了所提方法的精度、效率和适用性,结果表明所提基于失效概率函数的灵敏度函数求解方法在保证精度的情况下具有极高的效率,可用于工程上的基于可靠性的优化设计。In case that distribution parameters of the basic random variables are uniformly distributed interval variables in reliability analysis,the reliability sensitivity is a function of the distribution parameters.The conditional probability Markov chain simulation method is proposed to obtain the reliability sensitivity function and a new sensitivity measure,which is the statistics characteristic value of the reliability sensitivity function in the space of the distribution parameters.The formulas of the reliability sensitivity function and the sensitivity measure for a linear limit state function with normally distributed variables are derived.The proposed method obtains the formulas of the reliability sensitivity function by the Bayes rule,and Markov chain algorithm is adopted to directly simulate the samples of the failure regions.The third order maximum entropy method is implemented to estimate the conditional probability distributional function and finally the reliability sensitivity function is obtained.The accuracy,efficiency and applicability of the proposed method are demonstrated by several examples.The results show that the proposed method can efficiently estimate the reliability sensitivity function with high accuracy.The proposed method should be valuable for reliability-based optimization.

关 键 词：可靠性 灵敏度 最大熵法 马尔可夫链 

分 类 号：TB114.3[理学—概率论与数理统计] O213.2[理学—数学]