结构可靠度更新的子集模拟自适应延迟拒绝MMH算法

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.