A Sampling-Based Approach for Probabilistic Design with Random Fields

An original technique to incorporate random fields non-intrusively 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 limit state function (LSF) in terms of the coefficients of the POD expansion is obtained using a support vector machine (SVM). An adaptive sampling technique is used to generate samples and update the approximated LSF. The coefficients of the orthogonal decomposition are considered as random variables with distributions determined from the snapshots. Based on these distributions and the explicit LSF, the approach allows for an efficient assessment of the probabilities of failure. In addition, the construction of explicit LSF has the advantage of handling discontinuous responses. Two test-problems are used to demonstrate the proposed methodology used for the calculation of probabilities of failure. The first example involves the linear buckling of an arch structure for which the thickness is a random field. The second problem concerns the impact of a tube on a rigid wall. The planarity of the walls of the tube is considered as a random field.