An Airfoil Optimization Method Based on the Convolutional Neural Network Aerodynamic Reduced Order Model
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摘要:
针对非线性大扰动翼型气动力优化问题，提出了基于卷积神经网络气动力降阶模型的优化方法。该方法用不同形状参数下翼型的气动力数据作为训练信号，训练卷积神经网络翼型气动力降阶模型。采用该气动力降阶模型，以最大升阻比为目标，对翼型进行优化，结果表明该方法可用于大扰动下翼型气动力的预测和优化。该文同时还讨论了池化法和径向基法的训练信号数据降维方法对降阶模型精度的影响，结果表明训练信号数据降维能够提高气动力降阶模型的精度。其原因在于训练信号数据降维可以减少神经网络模型的待定参数的个数，在相同数据量下神经网络模型收敛得更好。
Abstract:To solve the nonlinear problem of airfoil shape optimization induced by nonlinear large perturbation, an optimization method was proposed based on the convolutional neural network (CNN) aerodynamic reduced order model (ROM). In the method, the aerodynamic forces on different airfoils were used as the training data for the proposed ROM. For the sake of the maximum lift-drag ratios, the ROM was applied to optimize the airfoil shape. The results show the method applies well to the prediction and optimization of airfoil shape dynamics under large perturbation. The improving effects of the parameter pooling and the radial basis function method based training data method on the accuracy of the dimensionality reduction model, were discussed. The reason for the improvement is that, the training data dimensionality reduction can cut down the number of undetermined parameters in the CNN model and make the CNN model converge better under the same data volume.
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图 3 不同参数翼型的气动力：(a) 压力系数p；(b) 摩擦因数
$ \tau $ Figure 3. Aerodynamics of the airfoils with different parameters: (a) pressure coefficient p; (b) skin friction coefficient
$ \tau $ 
图 5 翼型气动力：(a) 压力系数p；(b) 表面摩擦因数τ
Figure 5. Airfoil aerodynamics: (a) pressure coefficient p; (b) skin friction coefficient τ
图 7 气动力降阶模型的优化结果：(a) 压力系数p；(b) 摩擦因数τ
Figure 7. Aerodynamic ROM optimization results：(a) pressure coefficient p；(b) skin friction coefficient τ
表 1 翼型优化结果
Table 1. Airfoil optimization results
parameter lower bound upper bound optimized upper surface a1
a2
a3
a4
a5
a6
a70
0
0
0
0
0
00.025
0.030
0.030
0.030
0.025
0.020
0.0150.025
0.030
0.030
0.030
0.025
0.020
0.015lower surface b1
b2
b3
b4
b5
b6
b70
0
0
0
0
0
00.025
0.030
0.030
0.030
0.025
0.020
0.0150.025
0.030
0.030
0.030
0.025
0.020
0.015lift-drag ratio $ {C_{\text{l}}}/{C_{\text{d}}} $ – – – 32.41 
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