基于重要抽样马尔可夫链模拟的可靠性参数灵敏度分析方法

针对重要抽样法求解失效概率的问题,提出了一种基于重要抽样马尔可夫链模拟的快速可靠性参数灵敏度分析方法。该方法首先采用Metropolis准则和马尔可夫链模拟,将重要抽样法抽取的落入失效域中的样本点转化为条件样本点,这些条件样本点是落在失效域中的基本变量的实现,它们服从失效域条件下基本变量的概率分布,利用这些样本点替代Monte Carlo法抽取的条件样本点,可以通过加权回归分析快速得到隐式极限状态方程的近似,进而得到可靠性灵敏度。所提方法的显著优点是效率高,它只要在重要抽样法计算失效概率的结果中增加非常小的工作量,即可以快速得到可靠性参数灵敏度,算例结果充分说明所提方法的效率和合理性。

Making Importance Sampling (IS) Method Suitable for Sensitivity Analysis of Reliability Parameter Sensitivity

IS method is known to be fast for sensitivity analysis of reliability parameters but unfortunately it cannot be used for such analysis because it does not satisfy a necessary condition required by such analysis.We propose combining IS method with Markov chain simulation in such a way that IS-Markov method can be used for sensitivity analysis of reliability parameters.In the full paper, we explain our IS-Markov method in detail;in this abstract,we just add some pertinent remarks to listing the three topics of explanation:(1) the basic line of thinking of reliability sensitivity analysis,(2) the method of transforming importance sampling conditional samples into conditional samples,(3) obtaining approximate limit state function by weighted linear regression analysis;under topic 1,we point out that the reliability parameter sensitivities can be obtained with eqs.(4) and(5) in the full paper taken from the open literature;under topic 2,we explain how to combine Markov chain simulation with IS method;also under topic 2,we list the four steps given by S.K.Au in Ref.5 for transforming importance sampling conditional samples into conditional samples;under topic 3,we use the conditional samples obtained in topic 2 to obtain by weighted linear regression analysis the approximate limit state function,which is needed in calculating sensitivities with eqs.(4) and(5).To illustrate our IS-Markov method,we give three numerical examples,whose sensitivity results calculated by several different methods,including IS-Markov method,are summarized respectively in Tables 1,2,and 4 in the full paper.These results show preliminarily that,by comparison,IS-Markov method is remarkably high in efficiency.