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

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 2SMART (“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.

► The proposed method aims at assessing small failure probabilities.
► The basic underlying concept is similar to subset simulation.
► A SVM surrogate is adaptively built at each threshold of the limit state function.
► The efficiency of the method is assessed on some challenging examples.