Robust optimization for a wing at drag divergence Mach number based on an improved PSO algorithm

In this study, an improved PSO (particle swarm optimization) algorithm is proposed and applied to the robust optimization of a wing at drag divergence Mach number. In order to reduce the number of design variables, a six-order CST (class/shape function transformation) method is employed for airfoil parameterization. For the purpose of improving the optimization efficiency, Delaunay graph mapping method is adopted for mesh deformation in each iteration of the airfoil optimization, and NURBS (non-uniform rational B-splines)-FFD (free-form deformation) method is employed for mesh deformation in each iteration of the wing optimization. For improving the standard PSO algorithm, CVTs (centroidal Voronoi tessellations) method is introduced to generate original positions of the particles more dispersedly, a second-order oscillating scheme is used and an FDR (fitness distance ratio) item is added for updating velocities and positions of the particles. By virtue of the improved PSO algorithm, single point optimization and robust optimization are conducted for both airfoil and wing. The results indicate that, comparing with the single point optimizations, the robust optimizations not only reduce drag coefficients of the airfoil and the wing at cruise Mach numbers, but also attenuate the drag increments as the Mach number increases up to drag divergence Mach numbers. (C) 2019 Elsevier Masson SAS. All rights reserved.