基于梯度增强型Kriging模型的气动反设计方法

基于Kriging模型的代理优化算法目前在气动优化设计中得到了广泛应用。但在高维(设计变量大于30个)气动优化中,计算量过大的问题对其进一步发展产生了严重制约。将翼型和机翼气动反设计问题转化为优化问题,采用Adjoint方法进行快速梯度求解,利用基于梯度增强型Kriging(GEK)模型的代理优化算法分别开展了18、36和108个设计变量的气动反设计。首先,通过采用在设计空间局部建立GEK模型的方法成功地将基于代理优化算法的气动反设计问题的维度拓展到了100维以上。其次,研究了梯度计算精度对基于GEK模型的反设计的影响,发现梯度精度越高,反设计的最终效果越好,同时效率相当。最后,通过不同维度的气动反设计算例,比较了改进拟牛顿法(BFGS)、基于GEK模型和Kriging模型的代理气动反设计方法,结果表明基于GEK模型的代理优化算法的效率大幅度高于基于Kriging模型的代理优化算法,并且维度越高,效率优势越明显;同时,基于GEK模型的代理优化算法在优化效果及分析程序调用次数上相比于BFGS方法也略有优势。

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.