Interval analysis for geometric uncertainty and robust aerodynamic optimization design
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摘要:
不确定性因素会导致飞行器偏离预先设计的气动性能，造成气动性能下降甚至产生严重的后果。针对工程中无法给出准确的几何不确定性概率分布以及跨声速条件下非线性气动问题，对几何不确定性的非概率参数化建模进行了研究，并结合Kriging模型及最优化方法建立了快速非线性区间分析方法。采用该方法对对称翼型进行不确定性分析，获得了气动性能参数的定量变化区间。在区间不确定性分析基础上建立了鲁棒优化设计流程。基于区间序关系及区间可能度转换模型将单目标区间不确定性优化问题转化为多目标确定性优化问题，并采用基于Pareto熵的自适应多目标粒子群算法对优化问题进行寻优。考虑几何不确定性以及升力、力矩、面积约束，以阻力性能为目标对超临界翼型进行了鲁棒优化设计。与确定性优化设计结果对比表明，确定性优化设计在不确定性因素的影响下易失效，而鲁棒设计可得到更安全可靠的结果。
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关键词:
- 几何不确定性 /
- 非线性区间分析 /
- 直接操作自由变形(DFFD) /
- 气动优化设计 /
- 鲁棒优化设计 /
- 自适应多目标粒子群算法 /
- Kriging模型
Abstract:Uncertainties will make aircraft deviate from the designed aerodynamic performance, resulting in the decrease in aerodynamic performance and even destruction. Due to the problem that the probability distribution of geometric uncertainty cannot be given in engineering and nonlinear aerodynamic problem in transonic flows, the non-probabilistic parametric modeling of geometric uncertainty is studied, and the fast nonlinear interval analysis method is established in combination with Kriging model and optimization method. The effects of geometric uncertainties on a symmetric airfoil are analyzed using the above method, and the quantitative variation range of aerodynamic performance is obtained. Based on interval uncertainty analysis, a robust optimization design process is established. The single-objective interval uncertainty optimization problem was transformed into deterministic multi-objective optimization problem based on the order relation and possibility degree model of interval number, and the optimization problem was solved by adaptive multi-objective particle swarm optimization which is based on Pareto entropy. The robust optimization design is implemented for the supercritical airfoil with the drag objective as well as lift, moment and area constraints under geometric uncertainties. The results compared with deterministic optimization design show that deterministic design is prone to failure under the influence of uncertainties, while the robust design is more secure and reliable.
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图 1 FFD方法及DFFD方法控制翼型变形
Figure 1. Airfoil deformations controlled by FFD and DFFD methods
图 2 NACA0012翼型计算与试验压力分布比较
Figure 2. Comparison of pressure distribution between computation and experiment for NACA0012 airfoil
图 4 直接优化、Kriging模型优化与蒙特卡罗方法结果比较
Figure 4. Comparison of results among direct optimization, Kriging model optimization and Monte Carle method
图 5 阻力系数变化区间上下界对应的翼型及压力分布
Figure 5. Airfoils and pressure distribution corresponding to upper and lower bounds of drag coefficient variation interval
图 6 RAE2822翼型计算与试验压力分布比较
Figure 6. Comparison of pressure distribution between computation and experiment for RAE2822 airfoil
图 9 考虑几何不确定性的鲁棒优化设计流程
Figure 9. Robust optimization design process considering geometric uncertainties
图 10 基于Pareto熵的多目标粒子群算法
Figure 10. Multi-objective particle swarm algorithm based on Pareto entropy
图 13 优化所得最优翼型及压力分布比较
Figure 13. Optimized airfoils and pressure distribution comparison
图 14 目标及约束区间上下界对应的翼型及压力分布
Figure 14. Airfoils and pressure distribution corresponding to upper and lower bounds of objective and constraint intervals
图 15 不确定分析采样样本的阻力系数、力矩系数及面积对比
Figure 15. Drag coefficient, moment coefficient and area comparison of samples for uncertainty analysis
表 1 直接操作点x方向位置
Table 1. Position of pilot points in x direction
序号 x/c 1 0 2 0.077 3 0.214 4 0.377 5 0.571 6 0.777 7 1.0 
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表 2 3种方法的分析结果、误差、CFD计算次数、计算时间比较
Table 2. Comparison of analysis results, errors, CFD calculation times and computing time among three methods
方法 最大阻力系数 最大阻力系数相对误差/% 最小阻力系数 最小阻力系数相对误差/% CFD计算次数 并行计算时间/min 直接优化 0.0651303 0.0452392 800 500 Kriging模型1 0.0620658 -4.70 0.0433786 -4.10 20 25 Kriging模型2 0.06480712 -0.49 0.0457063 1.03 27 200
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表 3 RAE2822翼型及优化翼型的计算结果
Table 3. Computing results of RAE2822 and optimized airfoils
翼型 CD α/ (°) CL CM Aa RAE2822 0.02112 2.75377 0.82489 -0.1023 0.07787 优化翼型 0.01354 2.84263 0.82449 -0.0916 0.07804
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表 4 优化翼型与其他文献结果对比
Table 4. Comparison of optimization results between optimized airfoil and other works
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表 5 优化结果比较
Table 5. Optimization result comparison
翼型 CD fC fw CL CM Aa RAE2822翼型 0.021127 0.033261 0.015527 0.824888 -0.102279 0.077873 确定性优化最优翼型 0.013546 0.024063 0.010529 0.824487 -0.091623 0.078044 鲁棒优化最优翼型 0.015634 0.016627 0.002096 0.823707 -0.083295 0.082126
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