Reliability-based design optimization using Kriging and support vector machines

This article presents a novel approach for Reliability-Based Design Optimization (RBDO) using Kriging and Support Vector Machines (SVMs). The proposed algorithm is based on a sequential two level scheme. The first stage consists of solving an approximated probabilistic optimization problem. The objective function and the failure domains are approximated by Kriging and SVMs respectively. The probability of failure and its sensitivity are estimated using subset simulation. The availability of the sensitivity allows one to solve the subproblem using a gradient-based method. The second level deals with the local refinement of the failure domains approximations around the first stage subproblem solution. In the second stage, a key contribution of this work is the use of a novel probabilistic "max-min" sample that refines the failure boundary based on the random variable distributions as well as the locations of the samples. The proposed scheme is applied to three test cases including an analytical example featuring a failure domain defined by 100 dummy failure modes and a crash-worthiness analysis featuring 11 dimensions and 10 failure domains.