The Design Space Root Finding method for efficient risk optimization by simulation

Reliability-Based Design Optimization (RBDO) is computationally expensive due to the nested optimization and reliability loops. Several shortcuts have been proposed in the literature to solve RBDO problems. However, these shortcuts only apply when failure probability is a design constraint. When failure probabilities are incorporated in the objective function, such as in total life-cycle cost or risk optimization, no shortcuts were available to this date, to the best of the authors knowledge. In this paper, a novel method is proposed for the solution of risk optimization problems. Risk optimization allows one to address the apparently conflicting goals of safety and economy in structural design. In the conventional solution of risk optimization by Monte Carlo simulation, information concerning limit state function behavior over the design space is usually disregarded. The method proposed herein consists in finding the roots of the limit state function in the design space, for all Monte Carlo samples of random variables. The proposed method is compared to the usual method in application to one and n-dimensional optimization problems, considering various degrees of limit state and cost function nonlinearities. Results show that the proposed method is almost twenty times more efficient than the usual method, when applied to one-dimensional problems. Efficiency is reduced for higher dimensional problems, but the proposed method is still at least two times more efficient than the usual method for twenty design variables. As the efficiency of the proposed method for higher-dimensional problems is directly related to derivative evaluations, further investigation is necessary to improve its efficiency in application to multi-dimensional problems.