A random interval coupling-based active learning Kriging with meta-model importance sampling method for hybrid reliability analysis under small failure probability

In this study, a novel active learning method is proposed and combined with Meta-IS-AK for hybrid reliability analysis under small failure probability. Considering the proportion of responses falling into the failure domain, the interval failure degree is introduced to describe the probability of misjudging the state for random samples. The novel active learning method (IAD) is proposed to select valuable samples for updating Kriging model, considering the interval failure degree and the sample clustering. Additionally, a corresponding convergence criterion based on the similarity of the indicator functions in importance sampling samples is proposed to further enhance efficiency. The accuracy and superiority of the proposed method are validated through seven illustrative examples, accompanied by detailed explanations.