Aerodynamic inverse design method based on gradient-enhanced Kriging model

Up to date, the surrogate-based optimization methods using Kriging model are widely used in the aerodynamic optimization design. However, the huge time costs seriously restrict the in-depth development of Kriging model when it comes to cases with dimension course (more than 30 design variables). Inverse design problems of airfoils and wings are formulated as optimization problems. Surrogate-based optimization using gradient-enhanced Kriging (GEK) model is adopted to conduct aerodynamic inverse design of 18, 36 and 108 variables, and gradient is solved via the efficient adjoint method. It is worth mentioning that the dimension of aerodynamic inverse design using surrogate-based optimization is successfully expanded to more than 100 by constructing GEK model in part of the design space. Besides, the influence of gradient accuracy on surrogate-based optimization using GEK model is studied. The results show that the effect of optimization is improved with more accurate gradients. BFGS (Broyden, Fletcher, Goldfarb and Shanno) and surrogate-based optimizations using GEK and Kriging models are compared through aerodynamic inverse design of different dimensions. The results show that surrogate-based optimization using GEK model has significantly higher efficiency, and the advantage of efficiency is more obvious with higher dimension of design. At the same time, surrogate-based optimization using GEK model has better optimization effect and less number of calls of analysis programs than the BFGS method.