Design for reliability: optimization of critical structures using cross-entropy reliability analysis

This article presents an efficient reliability-based optimization method for critical structural design, in which, the probability of failure (Pf) should remain in a small bound. Critical structures should be designed to be optimal and reliable. Despite significant progress in reliability and optimization techniques, their interaction, which is considered in reliability-based optimization (RBDO), is faced with several challenges, especially in reliability analysis of critical constraints (constraints with Pf less than 10-5). To address this issue, in this paper the cross-entropy method is intended for reliability analysis and is combined with Genetic Algorithm in a double-loop framework to implement RBDO. The cross-entropy method is based on Monte Carlo simulation, except that the variance of sampling is reduced, which leads to a faster and more accurate reliability analysis method. The proposed RBDO method is demonstrated on two structural design. The obtained results show a high capability in reliability-based optimization of critical structures. In addition, using the proposed method, in comparison with traditional safety factor method, provides a more substantial manner in reliability improvement.