This article addresses the characterization of extreme value statistics of continuous second order random field. More precisely, it focuses on the parametric study of engineering models under uncertainty. Hence, the quantity of interest of this model is defined on both a parametric space and a stochastic space. Moreover, we consider that the model is computationally expensive to evaluate. For this reason it is assumed that uncertainty propagation, at a single point of the parametric space, is achieved by polynomial chaos expansion. The main contribution of the present study is the development of an adaptive approach for the discretization of the random field modeling the quantity of interest. Objective of this new approach is to focus the computational budget over the areas of the parametric space where the minimum or the maximum of the field is likely to be for any realization of the stochastic parameters. To this purpose two original random field representations, based on polynomial chaos expansion and Kriging interpolation, are introduced. Moreover, an original adaptive enrichment scheme based on Kriging is proposed. Advantages of this approach with respect to accuracy and computational cost are demonstrated on several numerical examples. The proposed method is also illustrated on the parametric study of an aircraft wing under uncertainty.
Dubreuil, S., Bartoli, N., Gogu, C., Lefebvre, T., & Colomer, J. M. (2018). Extreme value oriented random field discretization based on an hybrid polynomial chaos expansion — Kriging approach. Computer Methods in Applied Mechanics and Engineering, 332, 540–571. https://doi.org/10.1016/j.cma.2018.01.009