Robust optimization design under geometric uncertainty based on PCA-HicksHenne method
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摘要:
考虑不确定因素的稳健优化设计在飞行器气动外形设计选型中至关重要。针对环境扰动下稳健优化的研究较多，而对几何不确定性的关注则相对较少。为量化几何不确定性，采用主成分分析(PCA)方法，对RAE2822翼型的参数化过程进行了研究，并揭示了翼型的主要几何变形模态。采用敏感度分析方法，指出厚度变形模态、弯度变形模态及上翼面最大厚度位置的轴向位移模态是主要影响模态，并将其作为扰动模态进行稳健优化研究。结果表明: 不考虑扰动的确定优化翼型的升力变化更加剧烈，标准差增大近200%；考虑几何扰动的优化翼型稳健性更高，在平均性能提升的同时，无论是升力还是阻力的变化都比原始RAE2822翼型更小。
Abstract:The aerodynamic shape design of an aircraft requires a robust optimization approach that takes uncertainty into account. To the knowledge of the authors, research efforts were more paid to the robust optimization considering environmental perturbations, rather than geometric perturbations. For purpose of quantifying the geometric uncertainty, the principal component analysis (PCA) method was utilized to perform research on the parameterization process of the RAE2822 airfoil. The main geometric transformation modes of the airfoil were revealed subsequently. After that, the sensitivity analysis method was applied, and the thickness deformation mode, the camber deformation mode, and the axial displacement mode of the maximum thickness position on the upper surface were indicated as the main influential modes. Those modes were taken as the perturbation modes in the following robust optimization research. The results show that the lift variation of the deterministic optimal airfoil without consideration of perturbation is much huger, with the standard deviation increased by about 200%. However, the optimal airfoil considering geometric perturbation is more robust. The robust airfoil's variability, whether in lift or drag, are lower than those of the original RAE2822 airfoil along with the improvement in mean performance.
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图 2 主要几何变形模态对应模态能量分布
Figure 2. Energy amplitude of main geometric transformation modes
图 3 主要几何变形模态对应累积能量分布
Figure 3. Accumulated energy of main geometric transformation modes
图 5 主要几何变形模态对应参数分布情况
Figure 5. Parameters distribution of main geometric transformation modes
图 10 几何扰动下稳健优化设计流程
Figure 10. Flow chart of robust optimization design under geometric perturbation
图 11 案例2确定优化Pareto前沿面
Figure 11. Pareto frontier of deterministic optimization in Case 2
图 14 RAE2822翼型及扰动翼型的压力分布
Figure 14. Surface pressure distribution of RAE2822 airfoil and its corresponding airfoils under perturbation
图 15 确定优化翼型及扰动翼型的压力分布
Figure 15. Surface pressure distribution of deterministic optimal airfoil and its corresponding airfoils under perturbation
图 16 稳健优化翼型及扰动翼型的压力分布
Figure 16. Surface pressure distribution of robust optimal airfoil and its corresponding airfoils under perturbation
表 1 计算状态
Table 1. Computational condition
参数 马赫数Ma∞ 迎角α/(°) 雷诺数Re∞/m-1 数值 0.734 2.54 6.5×106 
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表 2 不同扰动量下升力系数的不确定度对比
Table 2. Comparisons of lift coefficient uncertainty under different perturbations
扰动量/倍 升力系数 均值 标准差 变异系数 0.2 0.768 0 0.006 57 0.008 6 0.3 0.767 7 0.009 81 0.012 8 0.4 0.766 7 0.012 96 0.016 9
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表 3 不同扰动量下阻力系数的不确定度对比
Table 3. Comparisons of drag coefficient uncertainty under different perturbations
扰动量/倍 阻力系数 均值 标准差 变异系数 0.2 0.016 21 0.000 82 0.050 7 0.3 0.016 27 0.001 21 0.074 7 0.4 0.016 32 0.001 59 0.097 7
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表 4 不同扰动量下翼型厚度的不确定度对比
Table 4. Comparisons of airfoil thickness uncertainty under different perturbations
扰动量/倍 翼型厚度 均值 标准差 变化范围(99.7%) 0.2 0.121 0 0.001 2 ±0.003 6 0.3 0.121 0 0.001 8 ±0.005 4 0.4 0.121 0 0.002 4 ±0.007 2
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表 5 案例1优化结果对比
Table 5. Comparisons of optimal results in Case 1
翼型 μCl σCl/10-2 μθ RAE2822 0.767 7 0.981 2 0.121 0 确定优化外形 0.886 5 1.179 7 0.119 8 稳健优化外形 0.895 9 1.018 3 0.120 8
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表 6 案例2确定优化结果
Table 6. Solutions of deterministic optimization in Case 2
翼型 μCd/10-1 σCd/10-3 μCl σCl/10-2 μθ RAE2822 0.162 7 1.214 5 0.767 7 0.981 2 0.121 0 翼型① 0.124 6 0.449 3 0.731 6 1.459 5 0.120 1 翼型② 0.141 9 0.888 8 0.794 3 1.252 3 0.123 1 翼型③ 0.149 0 0.556 3 0.820 4 2.956 6 0.121 2
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表 7 案例2稳健优化结果
Table 7. Solutions of robust optimization in Case 2
翼型 μCd/10-1 σCd/10-3 μCl σCl/10-2 μθ RAE2822 0.162 7 1.214 5 0.767 7 0.981 2 0.121 0 翼型④ 0.153 7 0.945 3 0.799 9 0.966 0 0.121 0 翼型⑤ 0.149 6 1.035 6 0.832 9 1.026 9 0.122 2 翼型⑥ 0.165 6 1.072 4 0.834 1 0.967 6 0.122 1
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