响应量分布函数求解的子集模拟方法及其应用  

A Novel and Efficient Subset Simulation(SubSim) Method for Obtaining Cumulative Distribution Function(CDF) of Structural Response and Its Application

作　　者：宋泽舒[1] 吕震宙[1] 周长聪[1] 

机构地区：[1]西北工业大学航空学院,陕西西安710072

出　　处：《西北工业大学学报》2011年第4期542-547,共6页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(10572117;50875213);国家863计划课题(2007AA04Z401)资助

摘　　要：在马尔科夫链Monte Carlo子集模拟法的基础上,提出了响应量分布函数求解的子集模拟方法。所提方法利用子集模拟在计算小失效概率时引入一系列具用较大失效概率的中间失效事件的特点,通过提取引入的每个中间失效事件对应的门槛值和失效概率,求解得到响应量完整的分布函数,并将所求得的分布函数用于基本变量的总效应和主效应分析。在详细给出了响应量分布函数求解子集模拟法的原理和主要步骤后,利用简单数值算例对所提方法的精度和效率进行了验证,结果表明所提方法在效率比Monte Carlo法大大提高的基础上精度也能满足要求。Aim. The introduction of the full paper reviews some papers in the open literature and then proposes what we believe to be a novel and relatively efficient method and its application mentioned in the title. Section 1 explains our method, and section 2 explains our application. The core of section 1 consists of： （1） we brief the Markov Chain Monte Carlo （MCMC） method for computing the CDF; （2） in computing small failure probabilities, we introduce a set of middle failure subsets that have large failure probabilities ; （3） we use the thresholds and the corresponding failure probabilities of the middle failure subsets to calculate the integrated CDF of structural response and to analyze the main effect and total effect of a basic variable. Section 3 presents two numerical examples to verify the precision and efficiency of our SubSim method ; the numerical results, given in Tables 1, 2, 4 and 5 and Figs. 3 and 4, and their analysis show preliminarily that our SubSim method is more efficient for computation than both the MC method and the analytical method while keeping an acceptably high precision.

关 键 词：子集模拟 马尔科夫蒙特卡洛 分布函数 主效应 总效应 

分 类 号：TB114.3[理学—概率论与数理统计]