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.
Metamodeling techniques have been widely used as substitutes of high-fidelity and timeconsuming models in various engineering applications. Examples include polynomial chaos expansions, neural networks, Kriging or support vector regression. This papers attempts to compare the latter two in different case studies so as to assess their relative efficiency on simulation-based analyses. Similarities are drawn between these two metamodels types leading to the use of anisotropy for SVR. Such a feature is not commonly used in the SVR related literature. A special care is given to a proper automatic calibration of the model hyperparameters by using an efficient global search algorithm, namely the covariance matrix adaptation-evolution scheme (CMA-ES). Variants of these two metamodels, associated with various kernel or auto-correlation functions, are first compared on analytical functions and then on finite-element-based models. From the comprehensive comparison, it is concluded that anisotropy in the two metamodels clearly improves their accuracy. In general, anisotropic L 2-SVR with the Matérn kernels is shown to be the most effective metamodel.
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