Support vector machine-based importance sampling for rare event estimation

Structural reliability analysis aims at computing failure probability with respect to prescribed performance function. To efficiently estimate the structural failure probability, a novel two-stage meta-model importance sampling based on the support vector machine (SVM) is proposed. Firstly, a quasi-optimal importance sampling density function is approximated by SVM. To construct the SVM model, a multi-point enrichment algorithm allowing adding several training points in each iteration is employed. Then, the augmented failure probability and quasi-optimal importance sampling samples can be obtained by the trained SVM model. Secondly, the current SVM model is further polished by selecting informative training points from the quasi-optimal importance sampling samples until it can accurately recognize the states of samples, and the correction factor is estimated by the well-trained SVM model. Finally, the failure probability is obtained by the product of augmented failure probability and correction factor. The proposed method provides an algorithm to efficiently deal with multiple failure regions and rare events. Several examples are performed to illustrate the feasibility of the proposed method.