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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。
Agent optimization algorithm based on Kriging model has been widely used in aerodynamic optimization design. However, in the high-dimensional (more than 30 design variables) of aerodynamic optimization, the problem of over-calculation greatly restricts its further development. The aerodynamic inverse design of the airfoil and the wing is converted into an optimization problem, and the Adjoint method is used to solve the fast gradient. Aerodynamic parameters of 18, 36 and 108 design variables are respectively calculated by a proxy optimization algorithm based on the gradient-enhanced Kriging (GEK) model. Anti-design. First of all, by using the method of establishing the GEK model locally in the design space, the dimensions of the aerodynamic inverse design problem based on the agent optimization algorithm are successfully extended to more than 100 dimensions. Secondly, the effect of gradient calculation accuracy on the inverse design based on GEK model is studied. It is found that the higher the gradient accuracy, the better the final effect of anti-design and the same efficiency. Finally, the aerodynamic inverse design method based on improved quasi-Newton method (BFGS), GEK model and Kriging model is compared through numerical examples of aerodynamic inverse design. The results show that the efficiency of the proxy optimization algorithm based on GEK model is significantly higher than The Kriging model-based agent optimization algorithm, and the higher the dimension, the more obvious the advantage of efficiency. Meanwhile, the agent optimization algorithm based on the GEK model has a slight advantage over the BFGS method in terms of the optimization effect and the number of analysis program calls.