Efficient subset simulation for rare-event integrating point-evolution kernel density and adaptive polynomial chaos kriging

Rare-event probability estimation has a wide range of applications, including the design and manufacture of precision equipment, aerospace systems, and critical industrial and civil structures. However, traditional simulation-based reliability calculation methods, such as brute Monte Carlo simulation (MCS) and subset simulation (SS), face challenges in efficiently evaluating small-failure probabilities due to the need for a large number of simulations, especially for non-linear and complex scenarios. Thus, to efficiently assess the probability of rare failure events in structural engineering, this paper develops a novel method for assessing the small-failure probability by integrating the point-evolution kernel density (PKDE), SS, and polynomial chaos kriging (PCK). The proposed PKDE-Adaptive PCK-based SS (PAPS) method aims to reduce the implementation of the original performance function by PCK and enrich the training set using an adaptive strategy. Moreover, the initial cumulative distribution function (CDF) of the performance function estimated by PKDE is modified gradually to facilitate the estimation of small-failure probability. Four numerical examples of small-failure probability estimation involving classical analytical cases, time-variant cases, and non-linear stochastic structures are used to illustrate the accuracy and efficiency of the proposed method. The computational results show that the proposed method can provide accurate computational results with a smaller computational burden than traditional methods (e.g., MCS, SS, LHS-PCK-SS).