Adaptive Kriging-based probabilistic subset simulation method for structural reliability problems with small failure probabilities

The continuously improving reliability of practical engineering has significantly reduced the failure probability, thereby presenting a challenge for the application of Kriging-based Monte Carlo simulation (MCS). An effective adaptive Kriging-based probabilistic subset simulation (SS) method is proposed in this study. Its core components contain the Kriging-based probabilistic SS, multi-level stopping conditions, and an adaptive parallel learning method. The Kriging-based probabilistic SS makes a more robust exploration of the target failure domain by integrating valuable mean and variance information. Multi-level stopping conditions emphasize the estimation accuracy rather than the good classification of samples. The adaptive parallel learning method can dynamically adjust the number of parallel samples per iteration. Finally, the proposed method is tested through two numerical examples and one engineering example. Compared to representative Kriging-based SS methods, the proposed method exhibits satisfactory accuracy and superior robustness. Even for a complex engineering problem with a minimal failure probability (with P-f < 10(- 5)), the proposed method can effectively reduce the number of iterations and provide accurate results. These findings indicate that this study is significant for the reliability assessment of practical engineering problems with high reliability.