Support Vector Machine response surface method based on fast Markov chain simulation

Abstract

The Support Vector Machine (SVM) response surface method (RSM) is proposed on fast Markov chain simulation for the problem with implicit limit state function usually encountered in engineering reliability analysis and design. In the proposed method, Markov chain is used to generate the samples in the important region of the limit state function, and the SVM is employed to construct the response surface by use of these samples. Since Markov chain can adaptively simulate the samples in the important region, and the candidate state but not Markov state is used as the training samples for SVM, the proposed method can well approximate the limit state equation in the zone surrounding the design point, and can make full use of information provided by Markov chain simulation. In addition, the iterative strategy is adopted to improve the convergence speed of the failure probability. Moreover, the proposed method uses the SVM regression method to construct the response surface, which can automatically apply the Structural Risk Minimization (SRM) inductive principle in approximating the limit state equation, thus it can approximate the failure probability with high accuracy. Finally applications in a numerical example and an engineering example indicate that the proposed method owns good performance in calculating efficiency and accuracy.