Assessing small failure probabilities by combined subset simulation and Support Vector Machines

Abstract Estimating small probabilities of failure remains quite a challenging task in structural reliability when models are computationally demanding. FORM/SORM are very suitable solutions when applicable but, due to their inherent assumptions, they sometimes lead to incorrect results for problems involving for instance multiple design points and/or nonsmooth failure domains. Recourse to simulation methods could therefore be the only viable solution for these kinds of problems. However, a major shortcoming of simulation methods is that they require a large number of calls to the structural model, which may be prohibitive for industrial applications. This paper presents a new approach for estimating small failure probabilities by considering subset simulation proposed by S.-K. Au and J. Beck from the point of view of Support Vector Machine (SVM) classification. This approach referred as 2 SMART (“ Two SMART ”) is detailed and its efficiency, accuracy and robustness are assessed on three representative examples. A specific attention is paid to series system reliability and problems involving moderately large numbers of random variables.