Aerodynamic Force Calculation and Inverse Design for Airfoil Based on Neural Network
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摘要: 开展了机器学习在翼型气动力计算和反设计方法中的应用研究，实现了在更大翼型空间范围内，人工神经网络的训练和优化，建立了翼型气动力计算模型，和给定目标压力分布的翼型反设计优化模型.作为机器学习领域兴起的研究热点，人工神经网络的研究工作不断深入，有研究者尝试将其应用于流体力学的学科范畴内.文章实现人工神经网络在翼型计算领域中应用的方法如下：首先通过Parsec参数化方法，围绕基准翼型构造了一定翼型空间范围的翼型库，利用XFOIL进行数值模拟，搭建了和翼型库具有一一映射关系的流场信息库.通过训练和优化神经网络，实现了基于此模型的快速、高可信度的翼型气动力预测，以及新型的翼型优化设计方法.通过自动化编程实现样本库的批量生成，实现了不同翼型空间的样本量下，神经网络的训练和优化过程.实验结果表明，在机器学习领域中，基于神经网络的翼型反设计模型的精确性高度依赖于训练样本量的大小和覆盖范围.Abstract: The application of machine learning in airfoil aerodynamic calculation and inverse design methods was studied in this paper, with the training and optimization of artificial neural networks in the larger airfoil space realized. The airfoil aerodynamic calculation model was constructed, and an airfoil inverse design optimization model with targeted pressure distribution was established, which gives rise to the potential usage in the engineering field. As a research hotspot in the field of machine learning, the research work of artificial neural network has gained increasingly interests, and some researchers have tried to apply it to the subject of fluid mechanics. In this paper, the application of artificial neural network in the field of airfoil calculation was studied as follows. Firstly, the airfoil library with a certain airfoil space range was constructed around a reference airfoil by Parsec parameterization method. Secondly, the numerical simulation was performed using XFOIL, generating a CFD library, which is mapped to the airfoil library one-by-one. Lastly, through training and optimization of neural networks, a fast and highly reliable airfoil aerodynamic prediction method was realized, and a new airfoil optimization design method was introduced. Through the automated programming, the generations of different sample-size databases were easily constructed, and the training and optimization process of the neural network under different sample-size of the airfoil space was investigated. Experimental results show that in the field of machine learning, the accuracy of the airfoil inverse design model based on neural network is highly dependent on the size and coverage of samples.
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图 1 基于PARSEC参数化生成的部分翼型库范围
Figure 1. Partial airfoil library ranges based on PARSEC parameterization
图 2 XFOIL计算结果和实验结果对比
Figure 2. Comparisons between XFOIL calculation and experiment result
图 3 原翼型的压力分布和预测翼型的计算压力分布对比图
Figure 3. Comparisons of Cp distributions between the original airfoil and the predicted airfoil
图 4 针对压力分布系数和翼型几何坐标, 原翼型和预测翼型的偏移大小
Figure 4. Deviation of Cp distribution and airfoil geometry
表 1 翼型气动力计算工况
Table 1. Working conditions over the calculation of airfoil aerodynamic parameters
aerodynamic parameters Re Ma α/(°) CL 3×105 0.2 0~8 CD 3×105 0.2 0~8 Cp 3×105 0.2 2 
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表 2 神经网络结构
Table 2. BP neural network structure
input output sample size airfoil geometry aerodynamic parameters 4 000
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表 3 不同训练和传递函数的计算结果
Table 3. Results based on different training and activation functions
time/s training functions activation functions maximum absolute error Δ 337 trainlm [tansig, tansig] 0.024 12 traingdx [tansig, tansig] 0.025 17 traingdx [tansig, purelin] 0.032 23 traingdx [purelin, purelin] 0.056
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表 4 翼型反设计的输出误差分布
Table 4. Output error distributions of airfoil inverse design
PARSEC parameters definitions geometric parameters relevant error ΔA P1 leading edge radius of upper surface rle 0.14% P2 maximum thickness po-sition of upper surface Xup -0.039% P3 maximum thickness of upper surface Zup 0.095% P4 maximum thickness curvature of upper surface ZXXup 0.019% P5 maximum thickness po-sition of lower surface Xlo -0.079% P6 maximum thickness of lower surface Zlo 0.049% P7 maximum thickness cur-vature of lower surface ZXXlo 0.026% P8 trailing edge thickness ZTE 3.16% P9 trailing edge offset ΔZTE 0 P10 trailing edge angle αTE 0.92% P11 trailing edge wedge angle βTE 0.26%
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表 5 本文和Waqas组的计算结果对照
Table 5. Comparisons of the results with Waqas results
BP neural network mse≤1×10-5 mse≥1×10-5 count percentage count percentage known(present) 1 968 98.4% 32 1.6% known(Waqas) 273 54.6% 227 45.4% unknown(present) 191 95.5% 9 4.5% unknown(Waqas) 113 56.5% 87 43.4%
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