Sparse polynomial surrogates for non-intrusive, high-dimensional uncertainty quantification of aeroelastic computations

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This paper is concerned with aircraft aeroelastic interactions and the propagation of parametric uncertainties in numerical simulations using high-fidelity fluid flow solvers. More specifically, the influence of variable operational and structural parameters (random inputs) on the drag performance and deformation (outputs) of a flexible wing in transonic regime, is assessed. Because of the complexity of fluid flow solvers, non-intrusive uncertainty quantification techniques are favored. Polynomial surrogate models based on homogeneous chaos expansions in the random inputs are commonly considered in this respect. The polynomial expansion coefficients are constructed using either structured sampling sets of the input parameters, as Gauss quadrature nodes, or unstructured sampling sets, as in Monte-Carlo methods. In complex systems such as the advanced aeroelastic test case studied here, the output quantities of interest generally depend only weakly 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 to use compressed sensing, or compressive sampling theory for the construction of the polynomial surrogates. The proposed methodology is non-adapted and considers unstructured sampling sets orders of magnitude smaller than the ones required by the usual techniques with structured sampling sets. It is illustrated in the present work for a moderately to high dimensional parametric space.