  The aim of the present paper is to develop a strategy for solving
reliability-based design optimization (RBDO) problems that remains applicable
when the performance models are expensive to evaluate. Starting with the
premise that simulation-based approaches are not affordable for such problems,
and that the most-probable-failure-point-based approaches do not permit to
quantify the error on the estimation of the failure probability, an approach
based on both metamodels and advanced simulation techniques is explored. The
kriging metamodeling technique is chosen in order to surrogate the performance
functions because it allows one to genuinely quantify the surrogate error. The
surrogate error onto the limit-state surfaces is propagated to the failure
probabilities estimates in order to provide an empirical error measure. This
error is then sequentially reduced by means of a population-based adaptive
refinement technique until the kriging surrogates are accurate enough for
reliability analysis. This original refinement strategy makes it possible to
add several observations in the design of experiments at the same time.
Reliability and reliability sensitivity analyses are performed by means of the
subset simulation technique for the sake of numerical efficiency. The adaptive
surrogate-based strategy for reliability estimation is finally involved into a
classical gradient-based optimization algorithm in order to solve the RBDO
problem. The kriging surrogates are built in a so-called augmented reliability
space thus making them reusable from one nested RBDO iteration to the other.
The strategy is compared to other approaches available in the literature on
three academic examples in the field of structural mechanics.
