Error-based stopping criterion for the combined adaptive Kriging and importance sampling method for reliability analysis

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.