A sequential surrogate method for reliability analysis based on radial basis function

Abstract

A radial basis function (RBF) based sequential surrogate reliability method (SSRM) is proposed, in which a special optimization problem is solved to update the surrogate model of the limit state function (LSF) iteratively. The objective of the optimization problem is to find a new point to maximize the probability density function (PDF), subject to the constraints that the new point is on the approximated LSF and the minimum distance to the existing points is greater than or equal to a given distance. By updating the surrogate model with the new points, the surrogate model of LSF becomes more and more accurate in the important region with a high failure probability and on the LSF boundary. Moreover, the accuracy of the unimportant region is further improved within the iteration due to the minimum distance constraint. SSRM takes advantage of the information of PDF and LSF to capture the failure features, which decrease the samples of implicit LSF defined by expensive finite element analysis. Several numerical examples show that SSRM improves the accuracy of the surrogate model in the important region around the failure boundary with a small number of samples and has a better adaptability to the nonlinear LSF, hence increases the accuracy and efficiency of the reliability analysis.