Hybrid reliability analysis based on an active learning method considering the coupling effects of random-interval uncertainty

Hybrid reliability analysis (HRA) is used to assess the safety of engineering containing mixed uncertain variables with different levels of information, which is computation intensive. Active learning Kriging is employed to replace expensive black-box functions and reduce computational costs. However, whether samples fail in HRA is affected by the coupling effect of hybrid uncertainty, which needs to be considered in active learning Kriging. This study introduces the interval failure degree to quantify the probability of misjudging the state for the random samples by calculating the ratio of response intervals falling into the safety domain to the failure domain. Based on that, an active learning Kriging is constructed and the failure probability upper bound (FPUB) is estimated. Furthermore, the key samples coverage, defined using Euclidean distance, is proposed to describe how closely newly added training samples align with key samples prone to misjudgment, providing reasonable explanations for the improvement of the modelling efficiency and convergence speed. The rationality and efficiency of the proposed method are verified by seven examples. Results illustrate that proposed method accelerate the convergence of failure probability upper bound while reducing the number of performance function evaluations.