Assessing small failure probabilities by AK–SS: An active learning method combining Kriging and Subset Simulation

• An active learning method combining Kriging and Subset Simulation (AK–SS) is proposed.
• AK–SS takes advantages of Subset Simulation and the Kriging metamodel.
• The proposed method is applied to several benchmark functions and a tunnel lining structure.
• AK–SS is shown to be more efficient than the other methods in the literature.
• AK–SS can deal with small probability problems with time-consuming function evaluations.

With complex performance functions and time-demanding computation of structural responses, the estimation of small failure probabilities is a challenging problem in engineering. Although Subset Simulation (SS) is a powerful tool for small probabilities, the computation amount is still large for time-consuming numerical procedures. Metamodelling is an important approach to increase the computational efficiency for engineering problems, however, a larger set of sample points is required for higher accuracy. This is a time-consuming task when the performance function needs to be numerically evaluated. To address this issue, AK–SS: an active learning method combining Kriging model and SS is proposed in this paper. The efficiency of this new method relies upon the advantages of SS in evaluating small failure probabilities and the Kriging model with active learning and updating characteristic for approximating the true performance function. The proposed method is applied to several benchmark functions in the literature, and to the reliability analysis of a shield tunnel, which requires finite element analysis. The results demonstrated that as compared to the other approaches in literature, AK–SS can provide accurate solutions more efficiently, making it a promising approach for structural reliability analyses involving small failure probabilities, high-dimensional performance functions, and time-consuming simulation codes in practical engineering.