Support vector regress method for determination of failure probability on the basis of weighted linear response surface

For implicit nonlinear limit state function, a support vector regress method (SVRM) is presented in conjunction with weighted linear response surface method (WLRSM) to estimate failure probability. Since the region around design point makes significant contribution to failure probability, the WLRSM is employed to determine the design point at the first step of the presented method. Secondly, the implicit nonlinear limit state function in the vicinity of the design point is approximated by SVRM. The SVRM possesses significant learning capacity at a small amount of information and generalization. By appropriately selecting the training samples required by the SVRM at the important region for the failure probability, the SVRM can approximate the implicit nonlinear limit state function with high precision. In the presented method, the training samples for SVRM are composed of the experimental points from WLRSM and the additional samples selected from complementally sampling strategy. After integrating the WLRSM with the SVRM effectively, the better surrogate of the implicit nonlinear limit state function can be constructed by the SVR around the design point, and the precision of the failure probability, computed by Monte Carlo simulation method or advanced Monte Carlo simulation method such as importance sampling, is improved for the implicit nonlinear limit state function. Examples are carried out to show the wide applicability and benefit of the presented method.