Abstract Structural reliability analysis aims to estimate the failure probability of a structure with respect to the performance function. This estimation may be a difficult task when the computation of a structural response requires large computational efforts. Although simulation-based methods can be used directly, they may require a large number of calls to the performance function for small failure probabilities. Metamodels (such as Kriging) that can replace the original performance function can be applied to address the computational costs. Among these methods, the active learning reliability method combining Kriging and Monte Carlo simulation (AK-MCS) is efficient, except for small failure probabilities and system reliability analysis. In this paper, a modified algorithm that combines the AK-MCS and the modified subset simulation (MSS) is proposed to estimate small failure probabilities. The strategy replaces the initial population with a large population that is generated by the MSS. No prior knowledge about the probability level is needed, and the sample size will adaptively change according to the estimation that is obtained in the last iteration and the target coefficient of variation. Therefore, the limit state can be covered by the new population, which is important for refining the Kriging model. The efficiency and accuracy of the proposed algorithm are illustrated using several examples.

中文翻译：

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AK-MSS：针对小故障概率的 AK-MCS 方法的改编

摘要 结构可靠性分析旨在估计结构相对于性能函数的失效概率。当结构响应的计算需要大量计算工作时，这种估计可能是一项艰巨的任务。尽管可以直接使用基于仿真的方法，但它们可能需要对性能函数进行大量调用以实现较小的故障概率。可以应用可以替代原始性能函数的元模型（如克里金法）来解决计算成本。在这些方法中，除了小故障概率和系统可靠性分析之外，结合克里金法和蒙特卡罗模拟（AK-MCS）的主动学习可靠性方法是有效的。在本文中，提出了一种结合 AK-MCS 和改进的子集模拟 (MSS) 的改进算法来估计小故障概率。该策略用 MSS 生成的大量种群替换初始种群。不需要关于概率水平的先验知识，样本量将根据上次迭代中获得的估计和目标变异系数自适应变化。因此，极限状态可以被新的种群覆盖，这对于完善克里金模型很重要。通过几个例子说明了所提出算法的效率和准确性。不需要关于概率水平的先验知识，样本量将根据上次迭代中获得的估计和目标变异系数自适应变化。因此，极限状态可以被新的种群覆盖，这对于完善克里金模型很重要。通过几个例子说明了所提出算法的效率和准确性。不需要关于概率水平的先验知识，样本量将根据上次迭代中获得的估计和目标变异系数自适应变化。因此，极限状态可以被新的种群覆盖，这对于完善克里金模型很重要。通过几个例子说明了所提出算法的效率和准确性。