Reliability Assessment with Correlated Variables using Support Vector Machines

This paper presents an approach to estimate probabilities of failure in cases where the random variables are correlated. An explicit limit state function is constructed in the uncorrelated standard normal space using the Nataf transformation and a support vector machine (SVM). The method of explicitly constructing the limit state function is referred to as explicit design space decomposition (EDSD), which also includes an adaptive sampling strategy to build an accurate SVM approximation. Several analytical examples with various distributions and also multiple failure modes are presented.