Learning Mappings from Iced Airfoils to Aerodynamic Coefficients Using a Deep Operator Network
Publication: Journal of Aerospace Engineering
Volume 36, Issue 5
Abstract
This study abstracted the prediction of the aerodynamic coefficients of an iced airfoil as a mapping from the iced airfoil space to the aerodynamic coefficient space. Thus, a deep network called Airfoils2AeroNet that can learn this mapping was established based on Deep Operator Network (DeepONet). The deep network consists of a branch network for encoding the iced airfoil images and a trunk network that learns a nonlinear mapping from the one-dimensional aerodynamic coefficient function input to -dimensional outputs. The branch network consists of deep convolutional neural networks (CNNs), and the trunk network consists of fully connected neural networks (FNNs). Then the network was trained and tested on iced airfoils based on NACA 0012 airfoils. Comparing the prediction results of Airfoils2AeroNet with those of the conventional direct CNN network, the network proposed in this paper has a strong advantage for generalization. Unlike the traditional CNN, which can only predict the aerodynamic coefficients at fixed flow conditions consistent with the training data, the network can flexibly predict the aerodynamic coefficients at different flow conditions. Finally, the influence of the structure of the branch network and trunk network on the prediction results was analyzed.
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References
Balla, K., R. Sevilla, O. Hassan, and K. Morgan. 2021. “An application of neural networks to the prediction of aerodynamic coefficients of aerofoils and wings.” Appl. Math. Modell. 96 (4): 456–479. https://doi.org/10.1016/j.apm.2021.03.019.
Bragg, M., T. Hutchison, and J. Merret. 2000. “Effect of ice accretion on aircraft flight dynamics.” In Proc., 38th Aerospace Sciences Meeting and Exhibit. Reston, VA: American Institute of Aeronautics and Astronautics.
Chen, H., L. He, W. Qian, and S. Wang. 2020. “Multiple aerodynamic coefficient prediction of airfoils using a convolutional neural network.” Symmetry 12 (4): 544. https://doi.org/10.3390/sym12040544.
Chen, J. 2014. “The effects of turbulence model corrections on drag prediction of NASA common research model.” In Proc., 32nd AIAA Applied Aerodynamics Conf. Reston, VA: American Institute of Aeronautics and Astronautics.
Chen, J., J. Zhang, J. Tang, and Y. Zhang. 2018. “Numerical investigations of the jaxa high-lift configuration standard model with mflow solver.” In Numerical simulation of the aerodynamics of high-lift configurations, 45–65. Berlin: Springer.
Chen, J., Y. Zhang, N. Zhou, and Y. Deng. 2015. “Numerical investigations of the high-lift configuration with mflow solver.” J. Aircr. 52 (4): 1051–1062. https://doi.org/10.2514/1.C033143.
Chen, T., and H. Chen. 1993. “Approximations of continuous functionals by neural networks with application to dynamic systems.” IEEE Trans. Neural Networks 4 (6): 910–918. https://doi.org/10.1109/72.286886.
Gray, V. H. 1958. Aerodynamic effects caused by icing of an unswept NACA 65A004 airfoil. Washington, DC: National Aeronautics and Space Administration.
Kim, H., and M. Bragg. 1999. “Effects of leading-edge ice accretion geometry on airfoil performance.” In Proc., 17th Applied Aerodynamics Conf. Reston, VA: American Institute of Aeronautics and Astronautics.
Lang, X., and X. Liu. 2015. “Numerical simulation of icing airfoil and analysis of aerodynamic characteristics.” Aeronaut. Comput. Tech. 45 (5): 82–85.
Lanthaler, S., S. Mishra, and G. E. Karniadakis. 2022. “Error estimates for DeepONets: A deep learning framework in infinite dimensions.” Trans. Math. Appl. 6 (1): tnac001.
Lin, C., Z. Li, L. Lu, S. Cai, M. Maxey, and G. E. Karniadakis. 2021. “Operator learning for predicting multiscale bubble growth dynamics.” J. Chem. Phys. 154 (10): 104118. https://doi.org/10.1063/5.0041203.
Lu, L., P. Jin, G. Pang, Z. Zhang, and G. E. Karniadakis. 2021. “Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators.” Nat. Mach. Intell. 3 (3): 218–229. https://doi.org/10.1038/s42256-021-00302-5.
Lynch, F. T., and A. Khodadoust. 2001. “Effects of ice accretions on aircraft aerodynamics.” Prog. Aerosp. Sci. 37 (8): 669–767. https://doi.org/10.1016/S0376-0421(01)00018-5.
Mao, Z., L. Lu, O. Marxen, T. A. Zaki, and G. E. Karniadakis. 2021. “DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators.” J. Comput. Phys. 447 (Dec): 110698. https://doi.org/10.1016/j.jcp.2021.110698.
Ollivier-Gooch, C. 2010. Grummp version 0.5. 0 user’s guide. Endowment Lands, Canada: Univ. of British Columbia.
Pokhariyal, D., M. Bragg, T. Hutchison, and J. Merret. 2001. “Aircraft flight dynamics with simulated ice accretion.” In Proc., 39th Aerospace Sciences Meeting and Exhibit. Reston, VA: American Institute of Aeronautics and Astronautics.
Raissi, M., A. Yazdani, and G. E. Karniadakis. 2020. “Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations.” Science 367 (6481): 1026–1030. https://doi.org/10.1126/science.aaw4741.
Rajkumar, T., C. Aragon, J. Bardina, and R. Britten. 2002. “Prediction of aerodynamic coefficients for wind tunnel data using a genetic algorithm optimised neural network.” In WIT transactions on information and communication technologies. Ashurst, UK: WIT Press.
Rajkumar, T., and J. E. Bardina. 2002. “Prediction of aerodynamic coefficients using neural networks for sparse data.” In Proc., 15th Int. Florida Artificial Intelligence Research Society Conf., edited by S. M. Haller and G. Simmons, 242–246. Washington, DC: Association for the Advancement of Artificial Intelligence Press.
Santos, M., B. Mattos, and R. Girardi. 2008. “Aerodynamic coefficient prediction of airfoils using neural networks.” In Proc., 46th AIAA Aerospace Sciences Meeting and Exhibit. Reston, VA: American Institute of Aeronautics and Astronautics.
Suresh, S., S. N. Omkar, V. Mani, and T. N. G. Prakash. 2003. “Lift coefficient prediction at high angle of attack using recurrent neural network.” Aerosp. Sci. Technol. 7 (Sep): 595–602. https://doi.org/10.1016/S1270-9638(03)00053-1.
Wallach, R., B. S. Mattos, M. Girardi, and M. Curvo. 2006. “Aerodynamic coefficient prediction of a general transport aircraft using neural network.” In Proc., 25th Int. Congress of the Aeronautical Sciences, 1–18. Hamburg, Germany: ICAS.
Wu, Q., H. Xu, Y. Wei, B. Pei, and Y. Xue. 2022. “Research on aerodynamics/flight dynamics coupling characteristics of aircraft under icing conditions.” Acta Aeronaut. Astronaut. Sin. 43 (8): 125566. https://doi.org/10.7527/S1000-6893.2021.25566.
Yi, X., Y. Gui, G. Zhu, and Y. Du. 2011. “Experimental and computational investigation into ice accretion on airfoil of a transport aircraft.” [In Chinese.] J. Aerosp. Power 26 (Jun): 808–813.
Yi, X., G. Zhu, K. Wang, and S. Li. 2002. “Numerically simulating of ice accretion on airfoil.” [In Chinese.] Acta Aerodynamica Sin. 20 (4): 428–433.
Yuan, K., and Y. Cao. 2007. “Simulation of ice effect on aircraft flight dynamics.” J. Syst. Simul. 19 (9): 1929–1932.
Yuan, K., and Y. Cao. 2008. “Effect of ice geometry to airfoil performance using neural networks prediction.” [In Chinese.] J. Beijing Univ. Aeronaut. Astronaut. 34 (8): 900–903.
Yuan, Z., Y. Wang, Y. Qiu, J. Bai, and G. Chen. 2019. “Aerodynamic coefficient prediction of airfoils with convolutional neural network.” In Proc., 2018 Asia-Pacific Int. Symp. on Aerospace Technology. Berlin: Springer.
Zhang, Y., W. J. Sung, and D. N. Mavris. 2018. “Application of convolutional neural network to predict airfoil lift coefficient.” In Proc., 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conf. Reston, VA: American Institute of Aeronautics and Astronautics.
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Received: Feb 22, 2022
Accepted: Jan 5, 2023
Published online: May 19, 2023
Published in print: Sep 1, 2023
Discussion open until: Oct 19, 2023
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