Adaptive learning for reliability analysis using Support Vector Machines

Abstract

A novel algorithm is presented for adaptive learning of an unknown function that separates two regions of a domain. In the context of reliability analysis these two regions represent the failure domain, where a set of constraints or requirements are violated, and a safe domain where they are satisfied. The Limit State Function (LSF) separates these two regions. Evaluating the constraints for a given parameter point requires the evaluation of a computational model that may well be expensive. For this reason we wish to construct a meta-model that can estimate the LSF as accurately as possible, using only a limited amount of training data. This work presents an adaptive strategy employing a Support Vector Machine (SVM) as a meta-model to provide a semi-algebraic approximation of the LSF. We describe an optimization process that is used to select informative parameter points to add to training data at each iteration to improve the accuracy of this approximation. A formulation is introduced for bounding the predictions of the meta-model; in this way we seek to incorporate this aspect of Gaussian Process Models (GPMs) within a SVM meta-model. Finally, we apply our algorithm to two benchmark test cases, demonstrating performance that is comparable with, if not superior, to a standard technique for reliability analysis that employs GPMs.