A sampling-based approach for probabilistic design with random fields

In this paper, a technique to efficiently include random fields in probabilistic design is presented. The approach is based on the extraction of the main features of a random field using a limited number of experimental observations (snapshots). An approximation of the random field is obtained using proper orthogonal decomposition (POD). For a given failure criterion, an explicit decision function in terms of the coefficients of the POD expansion, separating failure and safe regions, is obtained using a support vector machine (SVM). An adaptive sampling technique is used to generate samples and update the approximated decision function. The coefficients of the orthogonal decomposition are considered as random variables with distributions that are found from the snapshots. This allows an efficient calculation of probabilities of failure based on the explicit decision function. The methodology is demonstrated for the estimation of the probability of failure for two problems. The first example involves the linear buckling of an arch structure, for which the thickness is a random field. The second problem deals with a random field which modifies the planarity of the walls of a tube impacting a rigid wall.