Robust Design Measures for Airfoil Shape Optimization

Two kinds of robustness measures are introduced and applied to design optimization of the UMRIDA BC-02 transonic airfoil test case under uncertainty. Robust design optimization (RDO) aims at minimizing the mean and standard deviation of the drag coefficient. Reliability-based design optimization (RBDO) targets minimizing the maximum drag coefficient. Both robustness measures are efficiently evaluated by using efficient sampling techniques assisted by a gradient-enhanced Kriging model. The airfoil is parameterized with 10 deterministic design variables, which are optimized by a gradient-free Subplex algorithm. The nominal airfoil geometry is assumed to be perturbed by a Gaussian random field which is parameterized by 10 independent variables through a truncated Karhunen–Loève expansion. Two operational parameters are also considered uncertain. The airfoil obtained by optimizing the two robustness measures has similar geometrical features and shows better performance in terms of the robustness measures than the initial and the deterministically designed airfoils. The strength and location of the shock wave of the robustly designed airfoils are shown to be less sensitive to random geometrical perturbations than the initial and deterministically designed airfoils.