Support vector machine method for reliability analysis based on weighted linear response surface

To estimate failure probability of nonlinear implicit limit state function, a support vector machine (SVM) method is presented in conjunction with weighted linear response surface method (WLRSM). The design point which is the most likely in failure region is determined exactly by the WLRSM at the first step of the presented method. Secondly, the experimental points selected by WLRSM and some additional samples located in the vicinity of the design point selected from complemental sampling strategy are used as the training samples for SVM, which possesses significant learning capacity at a small amount of information and generalization. Since the samples in the vicinity of the design point are selected as the training samples for SVM, a better surrogate of the nonlinear implicit limit state function around the design point can be constructed by the SVM, and the precision of the failure probability is improved for the nonlinear implicit limit state function. Examples are carried out to show the wide applicability and benefit of the presented method.