一种高效求解功能函数累积分布函数的方法  

A Novel Method for Estimating Cumulative Distribution Function of Performance Function

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：《力学季刊》2012年第1期113-120,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(10572117;50875213);航空基础基金(2007ZA53012);863计划课题(2007AA04Z401)

摘　　要：结合贝叶斯公式、最大熵法和条件概率马尔科夫链法,发展了一种高效求解功能函数的累积分布函数(CDF)的方法。该方法首先由贝叶斯公式将功能函数CDF转换为后验分布和全局失效概率的数学表达式,接着由条件概率马尔科夫链法求得全局失效概率,由最大熵法求得后验分布,进而求得功能函数的CDF。与传统方法相比,该方法在先验分布均值附近区域求解精度高,计算代价与概率水平无关,在求解小失效概率附近极限状态的CDF时具有极高的求解效率。Combining the conditional probability markov chain simulation （CPMCS） method with the Bayesian formula and the maximum entropy method, a novel method for estimating cumulative distribu- tion function（CDF） of performance function was developed. In this method, it firstly transforms the CDF of performance function into the expression of a posteriori distribution with an overall failure probability, then estimate the posteriori distribution by using the maximum entropy method and evaluate the overall failure probability by using CPMCS, thus the CDF of performance function was obtained. Compared with traditional method, the proposed method achieves a higher calculation accuracy in the area around the mean value of the prior distribution, and it is independent of the probability level thus has a high efficien- cy when evaluating the CDF of performance function in the area where the failure probability is low.

关 键 词：贝叶斯公式 最大熵法 条件概率 马尔科夫链 鞍点逼近 

分 类 号：TB114.3[理学—概率论与数理统计]