高维小失效概率可靠性分析的序列重要抽样法

针对工程实际中大量存在的高维小失效概率问题,提出了基于子集模拟的序列重要抽样法。该方法首先利用子集模拟的基本思路,通过引入合理的中间失效事件将概率空间划分为一系列的子集,然后再依据重要抽样法的思想,逐步构造序列重要抽样函数来求得失效概率的估计。文中给出了序列重要抽样法求解高维小失效概率的基本步骤,并用算例验证了所提方法的效率和可行性。数值算例和工程算例的结果均表明,基于子集模拟的序列重要抽样法不依赖于极限状态方程的形式,且适用于非正态分布随机变量,其可靠性分析结果有很高的计算精度。

A High-Precision and Effective Sequential Importance Sampling Method for Reliability Analysis of Small Failure Probability in High Dimensions

Aim.In our opinion,the existing Markov Chain Monte Carlo(MCMC) method is still deficient in that both its precision and efficiency are not as high as can be.We now present a Sequential Importance Sampling Method(SISM) that is better.In the full paper,we explain our SISM in detail;in the abstract,we just add some pertinent remarks to listing the one topic of explanation:(1) subset simulation based SISM;the subtopics of topic 1 are the numerical simulation of failure probability(subtopic 1.1),the principles of subset simulation(subtopic 1.2),and SISM(subtopic 1.3);although eqs.(5) through(8) in subtopic 1.2 are all taken from the open literature,we feel that it is important to point out that the physical meaning of eq.(5) consists of that the original probability space is replaced by a sequence of subsets by introducing intermediate failure events and that the failure probability is constructed as the product of several conditional failure probabilities;in subtopic 1.3,we construct sequential importance sampling function to estimate the failure probability of structure using the concept of the importance sampling method;also in subtopic 1.3,we derive eq.(9) in the full paper as the formula of failure probability using SISM.Finally,we give two numerical examples,whose results are given in Table 1 in the full paper,and two engineering examples,whose results are given in Table 3 in the full paper.These results show preliminarily that,as compared with traditional Monte-Carlo simulation and MCMC method,our SISM's precision and efficiency are both higher.