An efficient method for estimating failure probability of the structure with multiple implicit failure domains by combining Meta-IS with IS-AK

For efficiently estimating the failure probability of the structure with multiple implicit failure domains, a method abbreviated as Meta-IS-AK is proposed by combining the adaptive Kriging Meta model Importance Sampling (Meta-IS) and Importance Sampling based Adaptive Kriging (IS-AK). In the proposed method, the failure probability is equivalently expressed as a product of the augmented failure probability and the correction factor, then two steps are respectively established to solve two terms. In the first step, Meta-IS algorithm is executed to generate IS samples. The augmented failure probability can be estimated as a byproduct in the first step. In the second step, all these IS samples compose a sample pool, in which the AK model is subsequently reconstructed for accurately predicting failure domain indicators instead of the actual implicit limit state function. Then the failure domain indicator at each IS sample and further the correction factor can be efficiently estimated. From the strategy of the proposed method, it can be seen that the proposed Meta-IS-AK possesses both the advantages of the Meta-IS method suitable for multiple failure domains and efficiency of the AK model for accurately predicting the failure domain indicators at all IS samples, which is demonstrated by the numerical and engineering examples.