Optimal Aerodynamic Design under Uncertainty

Volker Schulz and Claudia Schillings

Abstract. 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 non­negligible 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 MEGADESIGN[3] [4], 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-Loeve 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.

1 Introduction

Uncertainties pose problems for the reliability of numerical computations and their results in all technical contexts one can think of. They have the potential to render worthless even highly sophisticated numerical approaches, since their conclusions do not realize in practice due to unavoidable variations in problem data. The proper treatment of these uncertainties within a numerical context is a very important chal­lenge. This paper is devoted to the enhancement of highly efficient optimal design techniques developed in the framework of MEGADESIGN by a robustness com­ponent, which tries to make the optimal design generated a still good design, if the setting of a specific design point is varied.