Fine reconstruction method of airfoil surface pressure based on multi-source data fusion
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摘要: 在风洞试验模型表面布置测压孔是获得表面压力分布的重要手段，但受限于空间位置和试验成本，通常难以在复杂模型表面布置足量的测压孔获得完整的表面压力分布信息，直接积分获得的升力和力矩精度不足，因此提出了一种融合稀疏的风洞试验数据和数值计算（CFD）数据的方法，通过较少的风洞测压试验数据获得高精度的压力分布。首先通过本征正交分解技术提取数值计算数据的压力分布低维特征（POD基函数），然后利用稀疏的试验测压数据，通过压缩感知算法获得基函数的坐标，最后将坐标转化到物理空间重构出压力分布。利用定常固定翼型变状态以及变几何变来流状态算例验证该方法的精度，重构结果均能精确匹配试验结果。该重构方法可在一定程度上解决空间受限稀疏观测条件下的分布载荷精细化重构难题。Abstract: Laying out pressure taps on the surface of the wind tunnel test model is an important means to obtain the surface pressure distribution. However, due to the limited space location and experimental cost, it is usually difficult to arrange enough pressure taps on the complex model surface to obtain complete surface pressure distribution information. Hence, the accuracy of the lift and moment calculated by the direct integration may fail to meet expectations. In this paper, to obtain the high-precision pressure distribution through less pressure test data, a method of combining the sparse wind tunnel test data and the numerical simulation data is proposed. Firstly, the proper orthogonal decomposition （POD） technique is used to extract the low-dimensional feature of the pressure distribution of the numerical simulation data, which is called the POD basis. Then, by applying the compressed sensing algorithm, the coordinates of the basis function are obtained with the sparse wind tunnel pressure measurement data, and finally transformed into the physical space to reconstruct the pressure distribution. The accuracy of the method is verified by the steady fixed airfoil variable state or with variable geometry in conjunction with variable flow state examples, and the reconstructed results can accurately match the experimental results. The developed reconstruction method largely solves the problem of fine reconstruction of distributed load under the condition of limited space and sparse observation.
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图 6 稀疏重构与插值重构结果对比
Figure 6. Comparison of sparse reconstruction and interpolation reconstruction
图 10 变几何变来流状态重构结果
Figure 10. Reconstruction of variable geometry with variable flow state
表 1 重构误差
Table 1. Reconstruction error
${C_{{l} } }$ ${C_{{m} } }$ 实验 0.3910 0.0030 重构 0.3862 0.0017 Absolute error 0.0048 0.0013 Relative error 0.0122 0.4333 
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表 2 误差区间
Table 2. Error interval
上限 下限 $C_{l\_{\rm{error}}}$ 0.0050 0.0010 $C_{m\_{\rm{error}}}$ 0.0035 0.0010
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表 3 重构误差
Table 3. Reconstruction error
（a） （b） ${C_{l，{\rm{CFD}}} }$ 0.7650 0.6730 ${C_{l，{\rm{exp}}} }$ 0.7040 0.6130 ${C_{l，{\rm{r}}} }$ 0.7058 0.6143 $C_{l\_{\rm{error} } }$ 0.0018 0.0013 Relative error（Cl） 0.0026 0.0021 RMSE 0.0705 0.0655
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表 4 重构误差
Table 4. Reconstruction error
（a） （b） （c） ${C_{l，{\rm{exp}}} }$ 0.5330 0.4080 0.1270 ${C_{l，{\rm{r} } } }$ 0.5292 0.4047 0.1269 $C_{l\_{\rm{error} } }$ 0.0038 0.0033 0.0001 Relative error（$ {C_{{l}}} $） 0.0071 0.0069 0.0001 ${C_{m，{\rm{exp}}} }$ 0.0015 0.0043 0.0036 ${C_{m，{\rm{r}}} }$ 0.0074 0.0089 0.0050 $C_{m\_{\rm{error} } }$ 0.0059 0.0046 0.0014 Relative error（$ {C_m} $） 3.9333 1.0698 0.3888 RMSE 0.0578 0.0380 0.0318
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表 5 误差区间
Table 5. Error interval
上限 下限 $C_{l\_{\rm{error} } }$ 0.005 0.001 $C_{m\_{\rm{error} } }$ 0.006 0.001
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表 6 重构误差
Table 6. Reconstruction error
（a） （b） （c） ${C_{l，{\rm{exp}}} }$ 1.0240 0.2580 0.5660 ${C_{l，{\rm{r}}} }$ 1.0242 0.2628 0.5627 $C_{l\_{\rm{error} } }$ 0.0002 0.0048 0.0033 Relative error（${C_{{l} } }$） 0.0002 0.0186 0.0058 ${C_{m，{\rm{exp}}} }$ –0.0405 0.0055 –0.082 ${C_{m，{\rm{r}}} }$ –0.0400 0.0035 –0.0795 $C_{m\_{\rm{error} } }$ 0.0005 0.002 0.0025 Relative error（${C_{{m} } }$） 0.0123 0.3636 0.0305
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表 7 误差区间
Table 7. Error interval
上限 下限 $C_{l\_{\rm{error} } }$ 0.005 0.001 $C_{m\_{\rm{error} } }$ 0.005 0.001
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