Multi Attribute Design of Airfoil under Uncertainties by Combining Game Theory and Mcdm Methods

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, optimized 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. When a Pareto approach is used, a Multi Criteria Decision Method needs for selecting the final optimal solution. The design method is tested on an aeronautic case: the design of an airfoil in transonic case with uncertainties in free Mach number and angle of attack. The final solution is compared with a well known airfoil, and the new design performs the original in every objective, especially for the lift and drag stability.