A Fast and Robust Adaptive Methodology for Airfoil Design Under Uncertainties based on Game Theory and Self- Organising-Map Theory

Robust Design Optimization is the most appropriate approach to face problems characterized by uncertainties in the operating conditions, that represent a crucial point of aeronautical research activities. The Robust Design methodology illustrated in this paper is based on the multi-objective approach: applying the statistical definition of stability, the method finds, at the same time, optimised solutions for performances and stability. Game Theory is an innovative and efficient numerical methodology that can be applied to solve this kind of multi-objective optimization problems. A Competitive Game Strategy is applied in this paper by linking a mono-objective algorithm, like Downhill Simplex, with a statistical analysis methodology, based on t-Student or on the correlation matrix, that allow to find the optimal variables decomposition between the players (objectives) in the course of the optimization. An alternative to this statistical procedure is given by the innovative Self-OrganisingMaps (SOM) theory, used to find correlations between input or output variables and based on non-linear ordered regression for topology data mapping. The test case used to compare the different methodologies, after a preliminary test on mathematical functions, is the optimization of a symmetric airfoil in transonic and Eulerian flow field with uncertainties in the free stream Mach Number; once the most efficient algorithm is chosen, it is applied to the most demanding optimization of a RAE2822 airfoil in transonic and viscous flow field with uncertainties in the free stream Mach Number and in the angle of attack. In these optimization cases, an adaptive Response Surface Methodology, called DACE, has been used in order to reduce the number of computations required.