Aerodynamic Shape Optimization via Global Extremum Seeking

Optimization of aerodynamic shapes using computational fluid dynamics (CFD) approaches has been successfully demonstrated over a number of years; however, the typical optimization approaches employed utilize gradient algorithms that guarantee only the local optimality of the solution. While numerous global optimization techniques exist, they are usually too time consuming in practice. In this brief, a modified global optimization algorithm (DIRECT-L) is introduced and is utilized in the context of sampled-data global extremum seeking. The theoretical framework and conditions under which the convergence to the steady state of the CFD solver can be interpreted as plant dynamics are stated. This method alleviates the computational burden by reducing sampling and requiring only partial convergence of the CFD solver for each iteration of the optimization design process. The approach is demonstrated on a simple example involving drag minimization on a 2-D aerofoil.