Monte Carlo simulation in reliability-based optimization using approximation concepts

A reliability-based optimization (RBO) methodology, that uses Monte Carlo simulation (MCS) techniques, is presented. An initial design is obtained from an RBO based on first order reliability method (FORM). Limit state approximations are constructed that are used in an approximate RBO during each iteration of the RBO methodology. A symmetric rank-1 (SR1) variable metric algorithm is used to construct and update quadratic limit state approximations during each iteration of the RBO methodology. An axis orthogonal simulation technique is used in the approximate RBO. The methodology was implemented for an analytic test problem and a control augmented structure test problem. The results indicate that the SR1 algorithm was able to give highly accurate limit state approximations for most of the cases. The methodology was able to give the exact solution for the problems considered and was shown to be very computationally efficient for the second problem.