Abstract: In order to improve the efficiency and accuracy of the numerical calculation for the aerodynamic design of winglets, an optimization method based on multi-level response surfaces is proposed. After the establishment of the initial parameterized model of a wing with a blended winglet for an amphibious aircraft, the Plackett-Burman design is used to screen the design parameters and divide them into three grades according to their respective effect on the objective function: the significant factors, sub-significant factors, and non-significant factors. Subsequently the steepest ascent method is applied to obtain the design center point of the significant factors above the 95% probability level. Finally the optimum design parameters are obtained by the multi-level response surface method. The method is based on the computational fluid dynamics （CFD） results. Eight design parameters are selected and sixty-eight experiments are performed. The maximum lift-drag ratio of the optimization design is 20.680 56, and that of the direct numerical experiment is 20.680 31. The relative deviation is 0.001%, which confirms the effectiveness of the optimization model. After the installation of the winglets, the maximum lift-drag ratio is increased by 5.62% with an accompanying decrease of 4.13% in total resistance and an increase of 2.88% in wing-root bending moment.

Key words: winglet, aerodynamic optimization, response surface method, Plackett-Burman design, steepest ascent method, Box-Behnken design