Optimal Aerodynamic Design under Uncertainty

Recently, optimization has become an integral part of the aerodynamic design process chain. However, because of uncertainties with respect to the flight conditions and geometry uncertainties, a design optimized by a traditional design optimization method seeking only optimality may not achieve its expected performance. Robust optimization deals with optimal designs, which are robust with respect to small (or even large) perturbations of the optimization setpoint conditions. That means, the optimal designs computed should still be good designs, even if the input parameters for the optimization problem formulation are changed by a non-negligible amount. Thus even more experimental or numerical effort can be saved. In this paper, we aim at an improvement of existing simulation and optimization technology, developed in the German collaborative effort MEGADESIGN1, so that numerical uncertainties are identified, quantized and included in the overall optimization procedure, thus making robust design in this sense possible. We introduce two robust formulations of the aerodynamic optimization problem which we numerically compare in a 2d testcase under uncertain flight conditions. Beside the scalar valued uncertainties we consider the shape itself as an uncertainty source and apply a Karhunen-Loève expansion to approximate the infinite-dimensional probability space. To overcome the curse of dimensionality an adaptively refined sparse grid is used in order to compute statistics of the solution