Self-organizing Maps for Pareto Optimization of Airfoils

Abstract

This work introduces a new recombination and a new mutation operator for an accelerated evolutionary algorithm in the context of Pareto optimization. Both operators are based on a self-organizing map, which is actively learning from the evolution in order to adapt the mutation step size and improve convergence speed. Standard selection operators can be used in conjunction with these operators.

The new operators are applied to the Pareto optimization of an airfoil for minimizing the aerodynamic profile losses at the design operating point and maximizing the operating range. The profile performance is analyzed with a quasi 3D computational fluid dynamics (Q3D CFD) solver for the design condition and two off-design conditions (one positive and one negative incidence).

The new concept is to define a free scaling factor, which is multiplied to the off-design incidences. The scaling factor is considered as an additional design variable and at the same time as objective function for indexing the operating range, which has to be maximized. We show that 2 off- design incidences are sufficient for the Pareto optimization and that the computation of a complete loss polar is not necessary. In addition, this approach answers the question of how to set the incidence values by defining them as design variables of the optimization.