Iterative projection on critical states for reliability-based design optimization

Reliability-Based Design Optimization (RBDO) has been developed to design structures that reach the best compromise between cost reduction and reliability by considering uncertainties. This is achieved by reformulating the initial optimization problem in order to introduce probabilistic constraints. Numerical evaluation of these constraints by direct approaches turns out to be difficult: estimation of probability of failure implies calculation of multidimensional integrals. The integrals often rely on complex models whose evaluation is time-consuming. In this article, the RBDO framework is used to propose a new approach. For this purpose, a method to project a deterministic optimal solution onto a reliable domain is provided. This is achieved by a two-step iterative scheme. A sensitivity analysis identifies a critical situation. The latter leads to an adapted reliable safety domain. This new area is used to define a reliable design through a Newton-like process. Corresponding safety margins can be easily interpreted as partial safety factors. Finally, numerical applications in engineering are discussed to show the efficiency and the interest of the proposed algorithm.