Uncertainty based robust optimization method for drag minimization problems in aerodynamics

A new robust optimization method is introduced to extend single point design to more realistic problems in aerodynamics taking into account uncertainties. It is well known that single point design techniques produce solutions that perform well for the selected design point but have poor off-design performance. Following ideas of Taguchi’s robust control theory, a design with uncertainties is replaced by an optimization problem with two objectives which are mean performance and variance. Here, this two-objective optimization problem is solved by Pareto and Nash game strategies combined with the adjoint method, in the sense that solutions are less sensitive to uncertainties of input parameters. A constrained Nash strategy is implemented for performing multi-criteria optimization problems with constraints. Starting from a statistical definition of stability, the method simultaneously captures, Pareto and Nash equilibrium solutions ensuring performance and stability.