Reliability-based design optimization using kriging surrogates and subset simulation

摘要

The aim of the present paper is to develop a strategy for solvingreliability-based design optimization (RBDO) problems that remains applicablewhen the performance models are expensive to evaluate. Starting with thepremise that simulation-based approaches are not affordable for such problems,and that the most-probable-failure-point-based approaches do not permit toquantify the error on the estimation of the failure probability, an approachbased on both metamodels and advanced simulation techniques is explored. Thekriging metamodeling technique is chosen in order to surrogate the performancefunctions because it allows one to genuinely quantify the surrogate error. Thesurrogate error onto the limit-state surfaces is propagated to the failureprobabilities estimates in order to provide an empirical error measure. Thiserror is then sequentially reduced by means of a population-based adaptiverefinement technique until the kriging surrogates are accurate enough forreliability analysis. This original refinement strategy makes it possible toadd several observations in the design of experiments at the same time.Reliability and reliability sensitivity analyses are performed by means of thesubset simulation technique for the sake of numerical efficiency. The adaptivesurrogate-based strategy for reliability estimation is finally involved into aclassical gradient-based optimization algorithm in order to solve the RBDOproblem. The kriging surrogates are built in a so-called augmented reliabilityspace thus making them reusable from one nested RBDO iteration to the other.The strategy is compared to other approaches available in the literature onthree academic examples in the field of structural mechanics.