An efficient and robust adaptive Kriging for structural reliability analysis

Even though extensive efforts have been made, structural reliability analysis method with both efficiency and robustness is still infrequent in engineering especially when time-consuming numerical models are involved. To address the issue, this paper develops multi-ring-based important sampling (MRIS) and incorporates it into the Kriging-based reliability analysis method authors previously proposed. MRIS can uniformly fill the region of importance with an acceptable number of random points regardless of the number of most probable points and failure sub-domains of investigated structure. As MRIS does not need to evaluate Kriging model during sampling random points, its efficiency does not decrease with increasing the training points of Kriging model, which is a substantial advantage. Therefore, it is used as an optimization method to search for the best next point so as to adaptively increase the accuracy of Kriging model. Additionally, the failure probability predicted by Kriging model and its corresponding accuracy measure are roughly calculated with MRIS. Both of them are essential to judge whether Kriging model meets with a prescribed requirement. Four benchmark examples verify the accuracy, efficiency, and robustness of the proposed reliability analysis method.