Uncertainties are inherent to real-world systems. Taking them into account is
crucial in industrial design problems and this might be achieved through
reliability-based design optimization (RBDO) techniques. In this paper, we
propose a quantile-based approach to solve RBDO problems. We first transform
the safety constraints usually formulated as admissible probabilities of
failure into constraints on quantiles of the performance criteria. In this
formulation, the quantile level controls the degree of conservatism of the
design. Starting with the premise that industrial applications often involve
high-fidelity and time-consuming computational models, the proposed approach
makes use of Kriging surrogate models (a.k.a. Gaussian process modeling).
Thanks to the Kriging variance (a measure of the local accuracy of the
surrogate), we derive a procedure with two stages of enrichment of the design
of computer experiments (DoE) used to construct the surrogate model. The first
stage globally reduces the Kriging epistemic uncertainty and adds points in the
vicinity of the limit-state surfaces describing the system performance to be
attained. The second stage locally checks, and if necessary, improves the
accuracy of the quantiles estimated along the optimization iterations.
Applications to three analytical examples and to the optimal design of a car
body subsystem (minimal mass under mechanical safety constraints) show the
accuracy and the remarkable efficiency brought by the proposed procedure