Reliability assessment using probabilistic support vector machines (PSVMs)

This article presents a new probability of failure measure based on the notion of probabilistic support vector machines (PSVMs). A PSVM allows one to quantify the probability of having an error in the approximation of the failure boundary using a support vector machine (SVM). SVM can define explicitly the boundaries of disjoint and non-convex failure domains. The approximation of the failure boundary can be refined using an adaptive sampling scheme with a limited number of samples. However, the calculation of the probability of failure might still be inaccurate despite the adaptive sampling. In order to refine the probability estimate, the "quality" of the approximated boundary is quantified through the probability of misclassification of a sample by the SVM. A new measure of probability is then calculated using Monte-Carlo simulations that include the probability of misclassification. The proposed measure of probability of failure is such that it is always larger (i.e., more conservative) than the one obtained using a deterministic SVM. Several analytical examples are presented, including a case with two failure modes.