^{1}, and Jean-Luc Hantrais-Gervois

^{2}

^{1}ONERA/DTIS, Université Paris-Saclay, F-91123 Palaiseau, France.

^{2}ONERA/DAAA, Université Paris-Saclay, F-92190 Meudon, France.

In this paper we study aircraft aeroelastic interactions and the propagation of parametric uncertainties in numerical simulations using high-fidelity fluid flow solvers. We more particularly address the influence of variable operational and structural parameters (random inputs) on the drag performance and shape (outputs) of a flexible wing in transonic regime. Polynomial surrogate models based on homogeneous chaos expansions in the random inputs are considered in this respect. The polynomial expansion coefficients are usually constructed by projection using either structured sampling sets of the input parameters, as Gauss quadrature nodes, or unstructured sampling sets, as in Monte-Carlo methods. However, in complex systems such as the advanced aeroelastic test case studied here, the output quantities of interest generally depend only weekly on the multiple cross-interactions between the random inputs. Consequently, only low-order polynomials significantly contribute to their surrogates, which thus have a sparse structure in the underlying polynomial bases. This feature prompts the use of compressed sensing for the construction of the polynomial surrogates by regression. This alternative methodology is nonadapted and considers unstructured sampling sets orders of magnitude smaller than the structured or unstructured sampling sets required in projection methods. It is illustrated in the present work for a moderately to high dimensional parametric space and an aeroelastic test case of industrial relevance.