Shock Wave Intelligent Prediction Method for Hypersonic Vehicle
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摘要: 高超声速飞行器激波位置的准确预测能够有效提升数值模拟的精度和效率。一方面, 对高超声速飞行器激波附近网格进行正交和加密处理, 可有效提升数值计算精度; 另一方面, 使用高超声速飞行器激波位置对计算网格进行修正, 能够加速CFD计算收敛过程。提出了一种基于机器学习的高超声速飞行器激波智能预测方法, 对典型高超声速飞行器外形进行激波位置的高效准确预测。首先, 针对典型高超声速飞行器外形和典型飞行状态, 使用数值模拟方法获得收敛的流场, 并采用基于Mach数等值线的激波提取方法, 从流场中判别激波面并提取构成激波面的关键点位置, 形成训练数据; 然后采用有监督学习算法, 学习关键点位置, 并利用二次曲线沿流向拟合关键点形成初步的激波线族; 最后, 基于剖面压力云图, 构造基于投影压力图像的智能预测神经网络, 对初步形成的激波线族进行修正, 并获得三维激波面。大量的实验结果表明, 激波预测模型能够对高超声速飞行器激波位置做出准确预测, 预测的激波面与CFD数值计算结果中提取的激波面误差在10-4量级。Abstract: Accurate prediction of shock wave position of hypersonic aircrafts can effectively improve the accuracy and efficiency of computational fluid dynamics (CFD) simulation. On the one hand, orthogonalization and densification of the grid near the shock wave of the hypersonic vehicle can effectively improve the numerical accuracy. On the other hand, using the shock wave position of the hypersonic vehicle to correct the computational grid can speed up the CFD convergence process. A shock wave intelligent prediction method for hypersonic vehicles based on machine learning was proposed, which could efficiently and accurately predict the shock position of the typical hypersonic aircraft shape. Firstly, for the typical hypersonic vehicle shape and typical flight state, numerical methods were used to obtain a convergent flow field. Secondly, the shock wave extraction method based on Mach number contour was used to identify the shock wave surface from the flow field and extract the key points that constitute the shock wave to form training data. After that, the supervised learning method was used to predict the positions of these key points and the quadratic curve was used to fit these key points along the flow direction to form a preliminary shock line family. Finally, based on the typical pressure profile, an image-based neural network was constructed to correct the preliminary shock line family and obtain the three-dimensional shock surface. A large number of experimental results show that the shock wave prediction model can effectively predict the shock wave position of the hypersonic vehicle, and the error between the reconstructed shock wave surface and the extracted shock surface from the CFD results is in the order of 10-4.
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Key words:
- numerical simulation /
- CFD /
- shock wave /
- machine learning /
- neural network
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图 1 CFD计算结果中提取的激波线与拟合的二次曲线线对比
Figure 1. Comparison between the shock line extracted from the CFD results and the fitted shock line
图 3 外形投影和对应的压力场投影
Figure 3. Shape projection and corresponding pressure field projection
图 8 像素坐标转实际坐标的原理
Figure 8. Principle of converting pixel coordinates to actual coordinates
图 10 预测的关键点位置与提取的关键点位置的对比
Figure 10. Comparison between the predicted key point locations and the extracted key point locations
图 11 预测的关键点位置与提取的关键点位置的对比
Figure 11. Comparison between the predicted key point locations and the extracted key point locations
图 12 钝锥外形的预测激波面(左)与提取的激波面(右)
Figure 12. Predicted shock wave with blunt cone shape(left), and the compared extracted shock wave (right)
图 13 升力体外形和钝双锥外形的预测激波面(左)与提取的激波面(右)
Figure 13. Predicted shock wave with lifting body shape and double cone shape (left), and the compared extracted shock wave (right)
图 14 不同外形和不同来流条件下CFD计算得到的压力场(上)和预测的压力场(下)
Figure 14. Pressure fields calculated by CFD of different shapes and different inflow conditions (top), and the corresponding predicted pressure fields (bottom)
图 15 双锥外形和升立体锥外形的预测激波面(左)与提取的激波面(右)
Figure 15. Predicted shock wave with double cone shape and lifting body shape (left), and the compared extracted shock wave (right)
图 16 钝锥外形的预测激波面(左)与提取的激波面(右)
Figure 16. Predicted shock wave with blunt cone shape(left), and the compared extracted shock wave (right)
图 17 双椭球外形的预测激波面(左)与提取的激波面(右)
Figure 17. Predicted shock wave with double ellipsoid shape(left), and the compared extracted shock wave (right)
表 1 基于Mach数等值线的激波面提取算法
Table 1. Shock wave extraction algorithm based on Mach number contour
input: u，v，w，ρ，g，xk，yk，Mainput output： xshock，yshock，zshock 1 for any grid point P(i, j, k)do 2 $v_{\mathrm{F}}=\sqrt{u^2+v^2+w^2}$ 3 $v_{\text {sound }}=\sqrt{\gamma \times p / \rho}$ 4 ${Ma}(i, j, k)=\frac{v_{\mathrm{F}}}{v_{\text {sound }}}$ 5 Mashock=Mainput×0.99 6 for any grid point P(i, j, k)do 7 if Ma(i, j, k)≤Mashockand Ma(i, j, k+1)＞Mashock then 8 put P(i, j, k) into set S 9 for Pi, j, k∈S do 10 di, j, k=di, j, k-1+d(Pi, j, k, Pi, j, k-1) 11 dshock=di, j, k+$\frac{d_{i, j, k+1}-d_{i, j, k}}{{Ma}(i, j, k+1)-M a(i, j, k)}$×
(Mashock-Ma(i, j, k))12 xshock=x(i, j, 1)+$\frac{d_{\text {shock }}}{d_{i, j, k}}$×(x(i, j, k)-x(i, j, 1)) 13 yshock=y(i, j, 1)+$\frac{d_{\text {shook }}}{d_{i, j, k}}$×(y(i, j, k)-y(i, j, 1)) 14 zshock=z(i, j, 1)+$\frac{d_{\text {shook }}}{d_{i, j, k}}$×(z(i, j, k)-z(i, j, 1)) 
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表 2 不同外形的MSEave与MAEave
Table 2. MSEave and MAEave of different shapes
shape MSEave MAEave blunt cone 1.482 6×10-4 7.652 7×10-3 double cone 2.184 2×10-4 1.088 1×10-2 lifting body 2.382 8×10-4 1.145 3×10-2
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表 3 浮点运算次数计算结果
Table 3. Calculation results of the number of floating point operations
model FLOPs shape-net 4.0×109 inlet-net 1.54×105 concatenated-net 1.89×109 shock-net 5.89×109
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表 4 预测的压力场与CFD计算得到的压力场误差
Table 4. Error between the predicted pressure field and the pressure field calculated by CFD
shape MSEave MAEave blunt cone 1.655 7×10-10 7.394 2×10-9 double cone 1.724 1×10-10 8.566 4×10-9 double ellipsoid 2.732 8×10-10 1.299 1×10-8 lifting body 1.868 2×10-10 8.711 9×10-9
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表 5 不同外形的MSEave
Table 5. MSEave of different shapes
shape MSEave MAEave blunt cone 1.185 7×10-4 5.815 5×10-3 double cone 1.687 3×10-4 8.622 7×10-3 lifting body 1.778 5×10-4 8.760 5×10-3
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表 6 双椭球外形的MSEave与MAEave
Table 6. MSEave and MAEave of double ellipsoid shape
shape MSEave MAEave double ellipsoid 2.519 1×10-4 1.156 9×10-2
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