Rare-event probability estimation with adaptive support vector regression surrogates

• Adaptive SVR surrogates are used for assessing low failure probabilities.
• Accurate SVR are constructed by minimizing a LOO error estimate with the CE method.
• MCMC training samples are generated to quickly explore the safe domain.
• The method finally focuses on the limit-state surface for an enhanced accuracy.
• The efficiency of the proposed method is assessed on three challenging examples.

Assessing rare event probabilities still suffers from its computational cost despite some available methods widely accepted by researchers and engineers. For low to moderately high dimensional problems and under the assumption of a smooth limit-state function, adaptive strategies based on surrogate models represent interesting alternative solutions. This paper presents such an adaptive method based on support vector machine surrogates used in regression. The key idea is to iteratively construct surrogates which quickly explore the safe domain and focus on the limit-state surface in its final stage. Highly accurate surrogates are constructed at each iteration by minimizing an estimation of the leave-one-out error with the cross-entropy method. Additional training points are generated with the Metropolis–Hastings algorithm modified by Au and Beck and a local kernel regression is made over a subset of the known data. The efficiency of the method is tested on examples featuring various challenges: a highly curved limit-state surface at a single most probable failure point, a smooth high-dimensional limit-state surface and a parallel system.