结构可靠度更新的子集模拟自适应延迟拒绝MMH算法

An adaptive MMH algorithm with delayed rejection in subset simulation for structural reliability updating

文章着重研究结构可靠度更新的子集模拟改进抽样算法。首先,阐述观测信息条件下结构可靠度更新的基本理论,构建事件概率计算的通用子集模拟方法实现结构可靠度更新;进一步提出适用于子集模拟条件样本生成的自适应延迟拒绝MMH(Modified Metropolis-Hastings)算法,采用正态分布作为建议分布,以当前时刻样本作为建议分布的均值,以全部马尔可夫链生成的条件样本估计建议分布的标准差,使建议分布的标准差与目标分布标准差较为接近,达到提高备选样本接受率、减少样本序列重复样本的目的;最后通过刚架和导管架海洋平台结构体系可靠度更新计算实例验证子集模拟自适应延迟拒绝MMH算法的适用性。研究表明:等式观测信息事件域边界的对数变换可以调节中间事件域范围,提高数值计算稳定性,满足中间事件全部条件样本估计的似然函数最大值可用于计算等式观测信息事件的概率;自适应延迟拒绝MMH算法根据全部马尔可夫链生成的条件样本实现建议分布标准差的动态调节,能够提高子集模拟失效概率更新的精度并降低其变异性。

In this work,the structural reliability updating with subset simulation(SS)and the corresponding improved sampling algorithm are studied.Firstly,the fundamental theories for the reliability updating of structural systems based on the observation information are elaborated.To update the reliability of structural systems,a generalized SS method for the probability calculation is established.Furthermore,an adaptive modified Metropolis-Hastings with delayed rejection(AMMHDR)algorithm is proposed for the generation of conditional samples in SS,in which the normal distribution is used as the proposal distribution.For the proposal distribution,the current sample is used as its mean value and all the conditional samples generated in Markov chains are used to estimate its standard deviation,so that the standard deviation of the proposal distribution approaches to that of the target distribution,which can improve the acceptance rate of the candidates and reduce repeated samples in the sample sequence.Finally,three examples of plane frames and a jacket offshore platform for the reliability updating of structural systems are employed to verify the applicability of AMMHDR,considering the inequality and equality observation information.The results show that the domain for the equality observation information is invariable by using logarithmic transformation of its boundary,which can regulate the ranges of the internal domains and improve the stability for numerical calculation.The maximum value of the likelihood function for the equality observation information can be estimated by using all the conditional samples satisfying the internal domains,which can be used to calculate the probability of the equality observation information.The standard deviation of the proposal distribution for the AMMHDR can be adjusted dynamically according to the candidates generated by all Markov chains,which can improve the accuracy of the updated failure probability and reduce its variability in SS.