Support vectors machines for the estimation of probability of failure: Multifidelity classifiers built from a posteriori discretization error estimators

Abstract

This article proposes two algorithms to compute the probability of failure using Support Vector Machine (SVM) classifiers and Monte Carlo estimator in the context of structural mechanics. The observations used to build the classifiers are obtained from calls to a finite element solver which introduces discretization error. By exploiting guaranteed discretization error estimators, the proposed methodology aims at computing an estimation of the probability of failure not polluted by this discretization error. The first algorithm builds two classifiers in parallel to separate the guaranteed fail population, the guaranteed safe population and the uncertain population. It enables to compute an upper bound and a lower bound of the exact probability of failure. The second algorithm only uses observations whose status (fail or safe) is guaranteed by the error estimators. It results in multi-fidelity SVM-based meta-model as observations computed on different mesh sizes can be used. Those two algorithms are illustrated on two-dimensional mechanical examples for different Monte Carlo populations.