Metamodel-based method is a wise reliability analysis technique because it uses the metamodel to substitute the actual limit state function under the predefined accuracy. Adaptive Kriging (AK) is a famous metamodel in reliability analysis for its flexibility and efficiency. AK combined with the importance sampling (IS) method abbreviate as AK–IS can extremely reduce the size of candidate sampling pool in the updating process of Kriging model, which makes the AK-based reliability method more suitable for estimating the small failure probability. In this paper, an error-based stopping criterion of updating the Kriging model in the AK–IS method is constructed and two considerable maximum relative error estimation methods between the failure probability estimated by the current Kriging model and the limit state function are derived. By controlling the maximum relative error, the accuracy of the estimate can be adjusted flexibly. Results in three case studies show that the error-based stopping criterion based AK–IS method can achieve the predefined accuracy level and simultaneously enhance the efficiency of updating the Kriging model.

基于元模型的方法是一种明智的可靠性分析技术，因为它使用元模型替代了预先定义的精度下的实际极限状态函数。自适应克里格（AK）是可靠性分析中著名的元模型，它具有灵活性和效率。AK结合重要性采样（IS）的缩写，因为AK–IS在Kriging模型的更新过程中可以极大地减少候选采样池的大小，这使得基于AK的可靠性方法更适合于估计较小的故障概率。在本文中，构造了一种基于错误的AK-IS方法中更新Kriging模型的停止准则，并得出了当前Kriging模型估计的故障概率与极限状态函数之间的两种相当大的最大相对误差估计方法。通过控制最大相对误差，可以灵活地调整估计的准确性。在三个案例研究中的结果表明，基于错误的基于停止准则的AK-IS方法可以达到预定义的精度水平，同时可以提高更新Kriging模型的效率。