An aerodynamic optimization method based on virtual Nash equilibrium for global and local parameter decoupling

The parameterization of aerodynamic shape in the aircraft design optimization usually includes both global and local configuration features. The global parameters determine the wing span, aspect ratio, angle of attack, twist angle, and sweep angle. Meanwhile, the local parameters define the geometric shape of the wing section, including thickness and camber, etc. The changes in different types of parameters during the optimization process will lead to perturbations in the corresponding wavelength of the geometric shape, which in turn will cause different spatial frequency responses in the flow field. Generally, local parameter changes will generate highfrequency perturbations in the flow field and propagate only near the disturbance source; While global parameter changes will cause low-frequency perturbations in the flow field and propagate throughout the entire flow field. If these two different types of parameters are optimized at all once, it will lead to significant mutual interference, thereby reducing optimization efficiency. Therefore, this paper proposes an efficient optimization algorithm NashGL based on the concept of virtual Nash equilibrium. It decouples global and local variables and optimizes them simultaneously on different populations, effectively isolating interference between these two types of design variables. On the other hand, due to the small number of global variables, their rapid convergence can guide local variables towards the optimal solution. Through two aerodynamic optimization cases of NACA0012 airfoil and wing body aircraft, it is shown that compared with the method of simultaneously optimizing global and local parameters, the NashGL algorithm in this paper has the highest optimization efficiency, with an improvement of about 30% and 60%, respectively.