Abstract: The early surrogate-based reliability analysis could not quantify the error on account of the substitution,and the existing variance reduction techniques remained time-consuming when the performance function involved the output of an expensive-to-evaluate black box function.For these problems,an approach of importance sampling based on Kriging metamodel to compute the failure probability was proposed.An initial surrogate for the performance function was established and then updated to specified precision based on active learning function.An augmented probability of failure was calculated,and a quasi-optimal importance sampling density function was devised.Thus,the samples used to estimate the correction term were acquired through Markov Chain Monte Carlo (MCMC).Eventually the probability of failure was obtained as an augmented probability of failure and correction term.The applications in various reliability problems showed that the proposed approach was efficient,robust and accurate.

Key words: failure probability, Kriging metamodel, importance sampling, augmented failure probability, correction term

摘要： 针对早期基于替代模型的结构可靠性方法无法度量因替代而导致的误差,现存的方差减少技术在面对功能函数复杂的计算模型时依然效率不高,提出基于Kriging模型的重要性抽样方法计算单个构件或系统的失效率。首先建立功能函数的初始替代模型,然后使用基于主动学习函数的准则对模型更新至精确,计算出一个增大的失效率,并得到一个次最优重要性抽样密度函数,进而由Markov链蒙特卡洛方法产生样本,计算出修正项的估计量,最后将失效率表示成增大的失效率与修正项的乘积。将所提方法应用到各类可靠性问题中,结果表明该方法是高效、稳健和精确的。

关键词: 失效率, Kriging模型, 重要性抽样, 增大失效率, 修正项