Classification approach for reliability analysis with stochastic finite-element modeling

The assessment of the reliability of structural systems is increasingly being estimated with regard to the spatial fluctuation of the mechanical properties as well as loads. This leads to a detailed probabilistic modeling known as stochastic finite elements (SFE). In this paper an approach that departs from the main stream of methods for the reliability analysis of SFE models is proposed. The difference lies in that the reliability problem is treated as a classification task and not as the computation of an integral. To this purpose use is made of a kernel method for classification, which is the object of intensive research in pattern recognition, image analysis, and other fields. A greedy sequential procedure requiring a minimal number of limit state evaluations is developed. The algorithm is based on the key concept of support vectors, which guarantee that only the points closest to the decision rule need to be evaluated. The numerical examples show that this algorithm allows obtaining a highly accurate approximation of the failure probability of SFE models with a minimal number of calls of the finite element solver and also a fast computation.