Sparse generalized polynomial chaos expansion for non-intrusive uncertainty quantification in aerodynamic computations
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hdl:2117/334003
Tipus de documentText en actes de congrés
Data publicació2015
EditorCIMNE
Condicions d'accésAccés obert
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Abstract
Because of the high complexity of steady-state or transient fluid flow solvers, non-intrusiveuncertainty propagation techniques have been developed in aerodynamic simulations for theconsideration of random inputs such as the operational conditions or some geometrical data of theprofile. Polynomial surrogate models based on dedicated collocation sets or generalized polynomialchaos (gPC) have usually been implemented [1,2], though kriging-based or radial basis functionsurrogates may also be envisaged [3]. Polynomial representations suffer from the so-called curse ofdimensionality when the number of inputs increases since the evaluation of the expansioncoefficients becomes intractable in this situation. Sparse quadrature rules may be achieved using thealgorithm proposed by Smolyak (seee.g. [1] and references therein), but we envisage in this work touse the sparsity of the output signal, or quantity of interest, in trying to circumvent the dimensionalityconcern.Indeed, sparsity in the gPC basis expansion is expected to be enhanced in higherdimensions, where it is commonly observed that many cross-interactions between the inputparameters are actually negligible. This yields only a small fraction of the polynomial coefficients tobe significant, hence a sparse signal. In this context the number of samples needed for the synthesis istypically less than the one anticipated by the Shannon sampling theorem. We therefore expect toachieve a successful signal recovery by the techniques known under the terminology of compressedsensing [4], which are reported to be highly efficient for such sparse signals using incoherent randomprojections for their reconstruction. The procedure shall be illustrated on some basic examples offlow simulations about uncertain profiles, or fluid-structure interaction test cases with uncertainstructural parameters.
CitacióSavin, É.; Resmini, A.; Peter, J. Sparse generalized polynomial chaos expansion for non-intrusive uncertainty quantification in aerodynamic computations. A: ADMOS 2015. CIMNE, 2015, p. 818-81.
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