Uncertainty propagation for robust aerodynamic shape optimization

Abstract

Three algorithms for uncertainty propagation and robust aerodynamic optimization are presented in this paper. The perturbation method based on first and second-order Taylor expansion, the asymptotic expansion based on Laplace integrals and the Gauss-Hermite quadrature using sparse grid interpolation are used to compute the mean value and standard deviation of the objective function with respect to the uncertain parameters. The sensitivities of the mean value and standard deviation of the objective function with respect to the shape controlling parameters are computed and drive a gradient-based optimization algorithm towards the robust optimization of the transonic flow around a 2D airfoil for minimum drag-to-lift ratio, incorporating uncertainties of the flow conditions. The optimal design is compared to the one found using deterministic optimization as far as the robustness with respect to the uncertainties is concerned. The three methods are discussed and compared in terms of their computational cost, their effectiveness concerning parallelization issues and complexity related to the level of required sensitivity analysis and intrusiveness.