Data mining of Pareto-optimal transonic airfoil shapes using proper orthogonal decomposition

A new approach to extract useful design information from Pareto-optimal solutions of optimization problems is proposed and applied to an aerodynamic transonic airfoil shape optimization. The proposed approach enables an analysis of line, face, or volume data of all Pareto-optimal solutions such as shape and flow field by decomposing the data into principal modes and corresponding base vectors using proper orthogonal decomposition (POD). Analysis of the shape and surface pressure data of the Pareto-optimal solutions of an aerodynamic transonic airfoil shape optimization problem showed that the optimized airfoils can be categorized into two families (low drag designs and high lift designs), where the lift is increased by changing the camber near the trailing edge among the low drag designs while the lift is increased by moving the lower surface upward among the high lift designs.