Reliability assessment of offshore structures using subset simulation with adaptive standard deviation for MMH algorithm with two-stage delayed rejection

This paper explores modified strategies for the Modified Metropolis-Hastings (MMH) algorithm in the subset simulation (SS) for structural reliability assessment in ocean engineering. To improve sampling efficiency in complex distributions comprising correlated or non-normal variables, this study proposes a modified approach involving a two-stage delayed rejection and an adaptive standard deviation (STD) for the proposal distribution based on MMH. The acceptance rate of candidate samples in two-stage delayed rejection approach is derived based on the reversibility condition of Markov chain to reduce the repeated samples. Additionally, the STD for all accepted samples is used as the STD for the normal proposal, which dominates the sampling scale and increases the acceptance rate. The Neal's normal distribution, the Banana-shaped bivariate distribution, and the correlated joint distribution for wind and wave are adopted to study the sampling efficiency and ergodicity for the MMH with delayed rejection (MMHDR), the adaptive STD for MMH with delayed rejection (AMMHDR), and the adaptive STD for MMH with two-stage delayed rejection (AMMHDDR). Furthermore, three sampling algorithms are employed to generate conditional samples for estimating the probabilities of base shear failure and system failure in jacket platforms. The results indicate that the AMMHDDR can enhance sampling efficiency, especially for complex distributions with correlated variables. Also, the AMMHDDR can be used in SS to improve the accuracy and reduce the variation when estimating failure probabilities of offshore structures.