Metamodel-Based Directional Importance Sampling for Structural Reliability Analysis

For reliability analysis of complex structures with time-consuming implicit performance functions, the computational cost required by direct sampling methods is usually unaffordable for engineering applications. However, the adaptive metamodel embedded in sampling methods can significantly improve reliability analysis efficiency. Therefore, a new metamodel-based directional importance sampling method (Meta-DIS-AK) is proposed for reliability analysis in this article. The main novelty of Meta-DIS-AK is constructing the quasi-optimal DIS density (DIS-D) by the Kriging model and giving a simple rejection sampling algorithm for accurately extracting DIS-D samples. By the constructed quasi-optimal DIS-D, the failure probability is transformed into a two-step estimation of augmented failure probability and a correction item. The updating of the first step is designed to ensure that the constructed DIS-D is well approaching to theoretical optimal DIS-D and obtain augmented failure probability estimation, and the second step updating can guarantee the accuracy of correction item estimation. Meta-DIS-AK not only overcomes the difficulties of constructing DIS-D and extracting importance direction vector samples in the existing DIS but also inherits the advantages of DIS in dealing with high-dimensional and small failure probability problems. Compared with the existing efficient sampling methods combined with AK, the results of the examples fully verify the accuracy and efficiency of the proposed Meta-DIS-AK.