A New Adaptive Structural Reliability Analysis Method for Rare Failure Probability

Currently, the Kriging‐based adaptive structural reliability analysis method has emerged as an effective approach for estimating the probability of failure. Despite utilizing the Kriging surrogate model as a replacement for the structure performance function, the computational resources necessary for conducting numerical analysis of large‐scale Monte Carlo simulation (MCS) remain prohibitively excessive. Therefore, a new adaptive structural reliability analysis method for rare failure probability is proposed in this study. The proposed method, which combines Markov Chain Monte Carlo (MCMC) and importance sampling, effectively evaluates the convergence condition even under the condition of rare failure probability, through the construction of an appropriate importance sampling function and the utilization of its normalization factor. Once the Kriging surrogate model satisfying the required accuracy has been acquired, the subset simulation (SS) method is subsequently employed to derive the ultimate failure probability estimation. The efficacy of the proposed method has been validated through a range of benchmark examples as well as the practical application in ship engineering. In comparison to other similar studies, the results demonstrate that the proposed method can deal with the reliability analysis problems of rare failure probability with greater efficiency, while maintaining accuracy.