Quantile-based optimization under uncertainties using adaptive Kriging surrogate models

TL;DR

This paper introduces a quantile-based method for reliability-based design optimization that leverages adaptive Kriging surrogate models to efficiently handle uncertainties in complex engineering problems.

Contribution

It proposes a novel quantile-based formulation combined with adaptive Kriging surrogates and a two-stage enrichment process for efficient RBDO under high-fidelity model constraints.

Findings

Accurate quantile estimation with fewer model evaluations.

Enhanced efficiency in solving complex RBDO problems.

Successful application to automotive design demonstrates practical benefits.

Abstract

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.