AERODYNAMIC MODELING METHOD INCORPORATING PRESSURE DISTRIBUTION INFORMATION
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摘要: 气动外形优化设计与飞行器性能分析中, 直接运用数值模拟或风洞实验获取气动力的成本高, 构建代理模型是提高外形优化和性能分析效率的重要途径. 然而, 构建模型的过程中, 研究者只关注积分后的气动力和力矩信息. 本文通过充分利用采样过程中所产生的压力分布信息, 来提高建模的精度和泛化性, 进而降低样本获取的成本. 提出了一种小样本框架下融入压力分布信息的气动力建模方法, 首先通过数值模拟或风洞试验获得不同流动参数状态下翼型表面的压力分布信息和气动系数, 其次通过本征正交分解技术对压力分布信息进行特征提取, 获取不同输入参数状态下压力分布信息对应的POD系数, 之后结合输入参数通过Kriging算法对压力分布信息进行建模, 将压力分布信息积分得到低精度气动系数的预测模型, 最后低精度气动系数结合输入参数通过Kriging算法构造高精度的气动系数预测模型. 通过同状态变翼型算例以及CAS350翼型变状态算例进行验证, 该方法相比于传统的克里金模型直接预测气动力, 有效提高了气动力的预测精度和模型的鲁棒性, 同时缩小了学习样本的数据量.Abstract: In aerodynamic shape optimization design and aircraft performance analysis, the cost of directly using numerical simulation or wind tunnel experiments to obtain aerodynamic forces is high. Building surrogate model is an important way to improve the efficiency of shape optimization and performance analysis. However, in the process of building the model, researchers only focus on the aerodynamic force and moment information after integration. In this paper, the accuracy and generalization of modeling are improved by making full use of the pressure distribution information generated in the sampling process, thereby reducing the cost of sample acquisition. In this paper, an aerodynamic modeling method integrating pressure distribution information under the framework of small sample is proposed. Firstly, the pressure distribution information and aerodynamic coefficients of airfoil surface under different flow parameters are obtained by numerical simulation or wind tunnel experiments. Secondly, the pressure distribution information is extracted by proper orthogonal decomposition technology to obtain the POD coefficients corresponding to the distribution information under different input parameters. Then, the pressure distribution information is modeled by Kriging algorithm combined with input parameters. The pressure distribution information is integrated to obtain the prediction model of low precision aerodynamic coefficients. Finally, the low precision aerodynamic coefficients are combined with the input parameters to construct a high precision aerodynamic prediction model by Kriging algorithm. The method is verified by the same-state variable airfoil example and the CAS350 airfoil variable-state example. Compared with the traditional Kriging model, this method can effectively improve the prediction accuracy of aerodynamic force and the robustness of the model, and reduce the data amount of learning samples.
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图 5 训练样本数=30 前三阶压力分布基函数
Figure 5. Training number=30 The first three-order pressure distribution basis function
图 6 训练样本数=30 测试集中POD反算得到的压力分布与CFD仿真对比
Figure 6. Training number=30 Comparison of pressure distribution obtained by POD inverse calculation and CFD simulation
图 7 直接建模同间接建模误差对比
Figure 7. Comparison of error between direct modeling and indirect modeling
图 11 CAS350翼型部分压力分布曲线
Figure 11. Partial pressure distribution curve of CAS350 airfoil
图 12 直接建模同间接建模误差对比
Figure 12. Comparison of error between direct modeling and indirect modeling
表 1 气动系数预测误差
Table 1. Prediction error of aerodynamic coefficient
30 50 70 Absolute error Direct_CL 0.0096 0.0084 0.0070 Indirect_CL 0.0071 0.00059 0.0054 Direct_CM 0.00086 0.00073 0.00064 Indirect_CM 0.00084 0.00071 0.00063 Percentage CL 26.04% 29.76% 22.56% CM 2.32% 2.74% 1.56% Relative error Direct_CL 0.0233 0.0198 0.0192 Indirect_CL 0.0176 0.0154 0.0149 Direct_CM 0.0767 0.0662 0.0612 Indirect_CM 0.0761 0.0652 0.0593 
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表 2 气动系数预测误差
Table 2. Prediction error of aerodynamic coefficient
40 80 116 Absolute error Direct_CL 0.0588 0.0411 0.0376 Indirect_CL 0.0553 0.0310 0.0268 Direct_CM 0.00660 0.00425 0.00365 Indirect_CM 0.00650 0.00423 0.00329 Percentage CL 5.95% 24.57% 28.82% CM 1.51% 0.47% 9.86% Relative error Direct_CL 0.1872 0.1527 0.1139 Indirect_CL 0.1714 0.1243 0.0826 Direct_CM 0.5679 0.3416 0.2053 Indirect_CM 0.5603 0.3305 0.2045
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[1] Kumar K, Bhattacharya S. Artificial neural network vs linear discriminant analysis in credit ratings forecast: A comparative study of prediction performances. Review of Accounting and Finance, 2009, 5(3): 216-227 [2] Yang B, Jian KH, Si CZ. Stock Market Prediction Using Artificial Neural Networks. Information Technology for Manufacturing Systems III, 2012, 6-7: 1055-1060 [3] Kim K J, Lee WB. Stock market prediction using artificial neural networks with optimal feature transformation. Neural Computing and Applications, 2004, 13(3): 255-260 doi: 10.1007/s00521-004-0428-x [4] Yamashita T, Hirasawa K, Hu J. Application of multi-branch neural networks to stock market prediction// IEEE International Joint Conference on Neural Networks. IEEE, 2005 [5] Jeong S, Murayama M, Yamamoto K. Efficient Optimization Design Method Using Kriging Model. Journal of Aircraft, 2005, 42(2): 413-420 doi: 10.2514/1.6386 [6] Kanazaki M, Tanaka K, Jeong S, et al. Multi-objective aerodynamic exploration of elements' setting for high-lift airfoil using Kriging model. Journal of the Japan Society for Aeronautical & Spaceences, 2007, 54(3): 419-426 [7] Kumano T, Jeong S, Obayashi S, et al. Multidisciplinary design optimization of wing shape for a small jet aircraft using kriging model// In: 44th AIAA Aerospace Sciences Meeting and Exhibit. 2006 [8] Liu J, Han Z, Song W. Efficient Kriging-based aerodynamic design of transonic airfoils: some key issues//50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. 2012 [9] Kuya Y, Takeda K, Zhang X, et al. Multi-fidelity surrogate modeling of experimental and computational aerodynamic data sets. AIAA Journal, 2011, 49(2): 289-298 doi: 10.2514/1.J050384 [10] Han ZH, Ralf Z, Stefan G. A new cokriging method for variable-fidelity surrogate modeling of aerodynamic data// In: 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. 2010 [11] Toal T, David J, Andy JK. Efficient multipoint aerodynamic design optimization via cokriging. Journal of Aircraft, 2011, 48(5): 1685-1695 doi: 10.2514/1.C031342 [12] Rumpfkeil MP. Optimizations under uncertainty using gradients, Hessians, and surrogate models. AIAA Journal, 2012, 51(2): 444-451 [13] Palar PS, Koji S. Multi-fidelity uncertainty analysis in CFD using hierarchical kriging. In: 35th AIAA Applied Aerodynamics Conference. 2017 [14] Schmit LA, Farshi B. Some Approximation Concepts for Structural Synthesis. AIAA Journal, 1974 [15] Zhang KS, Han ZH, Li WJ, et al. Bilevel adaptive weighted sum method for multidisciplinary multi-objective optimization. AIAA Journal, 2008 [16] Xiong JT, Qiao ZD, Han ZH. Aerodynamic shape optimization of transonic airfoil and wing using response surface methodology// 25 th Congress of the International Council of the Aeronautical Sciences. 2006 [17] Secco NR, Bento SM. Artificial neural networks to predict aerodynamic coefficients of transport airplanes. Aircraft Engineering and Aerospace Technology, 2017, 89(2): 211-230 doi: 10.1108/AEAT-05-2014-0069 [18] Luo C, Hu Z, Zhang SL, et al. Adaptive space transformation: An invariant based method for predicting aerodynamic coefficients of hypersonic vehicles. Engineering Applications of Artificial Intelligence, 2015, 46: 93-103 doi: 10.1016/j.engappai.2015.09.001 [19] Yuan Z, Wang Y, Qiu Y, et al. Aerodynamic coefficient prediction of airfoils with convolutional neural network//Asia-Pacific International Symposium on Aerospace Technology, 2018 [20] Peng W, Zhang Y, Desmarais M. Spatial convolution neural network for efficient prediction of aerodynamic coefficients// AIAA Scitech 2021 Forum. 2021 [21] 何磊, 张显才, 钱炜祺等. 基于长短时记忆神经网络的非定常气动力建模方法. 飞行力学, 2021, 39(5): 8-12 (He Lei, Zhang Xiancai, Qian Weiqi, et al. Unsteady aerodynamics modeling method based on long short-term memory neural network. Flight Dynamics, 2021, 39(5): 8-12 (in Chinese)He Lei, Zhang Xiancai, Qian Weiqi, et al. Unsteady aerodynamics modeling method based on long short-term memory neural network, Flight Dynamics, 2021, 39(05): 8-12 (in Chinese) [22] Andres-Perez E, Paulete-Perianez C. On the application of surrogate regression models for aerodynamic coefficient prediction. Complex & Intelligent Systems, 2021, 7(4): 1991-2021 [23] Huang JH, Su HL, Zhao X. Aerodynamic coefficient prediction of airfoil using BP neural network. Advances in Aeronautical Science and Engineering, 2010, 1: 36-39 [24] Liu X. Simulation of airfoil plunging aerodynamic parameter prediction based on neural network. Computer Simulation, 2015, 32(12): 67-71 [25] Wallach R, Mattos BS, Girardi R, et al. Aerodynamic coefficient prediction of a general transport aircraft using neural network// 25 th Congress of the International Council of the Aeronautical Sciences. 2006 [26] Santos M, Mattos BD, Girardi R. Aerodynamic coefficient prediction of airfoils using neural networks// In Proceedings of the 46 th AIAA Aerospace Sciences Meeting and Exhibit. 2008 [27] Liu H, Ong YS, Cai J, et al. Cope with diverse data structures in multi-fidelity modeling: A Gaussian process method. Engineering Applications of Artificial Intelligence, 2018, 67: 211-225 doi: 10.1016/j.engappai.2017.10.008 [28] Yan C, Yin Z, Shen X, et al. Surrogate-based optimization with improved support vector regression for non-circular vent hole on aero-engine turbine disk. Aerospace Science and Technology, 2020, 96: 105332 doi: 10.1016/j.ast.2019.105332 [29] Raj LP, Yee K, Myong R, Sensitivity of ice accretion and aerodynamic performance degradation to critical physical and modeling parameters affecting airfoil icing. Aerospace Science and Technology, 2020, 98: 105659 [30] 陈健, 王东东, 刘宇翔等. 无网格动力分析的循环卷积神经网络代理模型. 力学学报, 2022, 54(3): 1-14 (Chen Jian, Wang Dongdong, Liu Yuxiang, et al. A recurrent convolutional neural network surrogate model for dynamic meshfree analysis. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 1-14 (in Chinese) doi: 10.6052/0459-1879-17-020Chen Jian, Wang Dongdong, Liu Yuxiang, et al. A recurrent convolutional neural network surrogate model for dynamic meshfree analysis. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(3): 1-14 (in Chinese) doi: 10.6052/0459-1879-17-020 [31] Li K, Kou J, Zhang W. Deep Learning for multi-fidelity aerodynamic distribution modeling from experimental and simulation data. AIAA Journal, 2022: 1-15 [32] 王旭, 宁晨伽, 王文正等. 面向飞行试验的多源气动数据智能融合方法. 空气动力学学报: 2022: 1-8Wang Xu, Ning Chenjia, Wang Wenzheng, et al. Intelligent fusion method of multi-source aerodynamic data for flight tests. Acta Aerodynamic Sinca, 2022: 1-8 (in Chinese) [33] 寇家庆, 张伟伟, 高传强. 基于POD和DMD方法的跨声速抖振模态分析. 航空学报, 2016, 37(9): 2679-2689 (Kou Jiaqing, Zhang Weiwei, Gao Chuangqiang. Modal analysis of transonic buffet based on POD and DMD techniques. Acta Aeronautica et Astronautica Sinica, 2016, 37(9): 2679-2689 (in Chinese) doi: 10.7527/S1000-6893.2016.0003Kou Jiaqing, Zhang Weiwei, Gao Chuangqiang. Modal Analysis of Transonic Buffet Based on POD and DMD Techniques. Acta Aeronautica et Astronautica Sinica, 2016, 37(009): 2679-2689 (in Chinese) doi: 10.7527/S1000-6893.2016.0003 [34] 雷玉昌, 张登成, 张艳华. 环量控制翼型非定常气动力建模. 北京航空航天大学学报, 2021, 47(10): 2138-2148Lei Yuchang, Zhang Dengcheng, Zhang Yanhau. Unsteady aerodynamic modeling of circulation control airfoil, Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(10): 2138-2148 (in Chinese) [35] 韩忠华. Kriging模型及代理优化算法研究进展. 航空学报, 2016, 37(11): 3197-3225 ((Han Zhonghua. Kriging surrogate model and its application to design optimization: A review of recent progress. Acta Aeronautica et Astronautica Sinica, 2016, 37(11): 3197-3225 (in Chinese)Han Zhonghua. Kriging surrogate model and its application to design optimization: A review of recent progress. Acta Aeronautica et Astronautica Sinica, 2016, 37(11): 3197-3225 (in Chinese [36] Kulfan BM. Universal parametric geometry representation method. Journal of Aircraft, 2008, 45(1): 142-158 doi: 10.2514/1.29958 -
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