Airfoil Aerodynamic Optimization Design Using Ensemble Learning Surrogate Model
Publication: Journal of Aerospace Engineering
Volume 37, Issue 6
Abstract
The conventional manual design process and data acquisition for aerodynamic parameters can be time-consuming. Consequently, this study proposes a solution to address this issue. The main contributions of this study are as follows. (1) A surrogate model based on ensemble learning (Ensemble) is proposed, which utilizes a two-layer learner combining the Cokriging model (Cokriging) with the neural network model based on transfer learning (TL). A numerical example is conducted to evaluate its performance, comparing it with single-surrogate methods. (2) A criterion—the mp-cvvor hybrid sampling strategy—is proposed for application to any surrogate model. The efficiency of the mp-cvvor method compared to that of other sampling strategies is validated by a synthetic benchmark. (3) The aerodynamic optimization framework is applied to the RAE2822 airfoil. Our method reduces average computation fluid dynamics (CFD) calls by more than 48.2% than do the nondominated sorting genetic algorithm-II (NSGA-II) and particle swarm optimization (PSO), and the lift-drag ratio increases by 3.087% compared to the increase from the single-surrogate-based Cokriging approach.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This work was supported by Key Laboratory of Computational Aerodynamics, AVIC Aerodynamics Research Institute, and the Fundamental Research Funds for the Central Universities (N2404015).
References
Aurenhammer, F. 1991. “Voronoi diagrams—A survey of a fundamental geometric data structure.” ACM Comput. Surv. 23 (3): 345–405. https://doi.org/10.1145/116873.116880.
Cook, P. H., M. A. McDonald, and M. C. P. Firmin. 1979. Aerofoil RAE 2822: Pressure distributions, and boundary layer and wake measurements. AGARD report ar 138, 47. Neuilly sur Seine, France: AGARD.
Deb, K., A. Pratap, S. Agarwal, and T. Meyarivan. 2002. “A fast and elitist multiobjective genetic algorithm: NSGA-II.” IEEE Trans. Evol. Comput. 6 (2): 182–197. https://doi.org/10.1109/4235.996017.
Della Vecchia, P., E. Daniele, and E. D’Amato. 2014. “An airfoil shape optimization technique coupling PARSEC parameterization and evolutionary algorithm.” Aerosp. Sci. Technol. 32 (1): 103–110. https://doi.org/10.1016/j.ast.2013.11.006.
Derksen, R., and T. Rogalsky. 2010. “Bezier-PARSEC: An optimized aerofoil parameterization for design.” Adv. Eng. Software 41 (7–8): 923–930. https://doi.org/10.1016/j.advengsoft.2010.05.002.
Fang, K.-T., D. K. Lin, P. Winker, and Y. Zhang. 2000. “Uniform design: Theory and application.” Technometrics 42 (3): 237–248.
Fuhg, J. N., A. Fau, and U. Nackenhorst. 2021. “State-of-the-art and comparative review of adaptive sampling methods for kriging.” Arch. Comput. Methods Eng. 28 (Aug): 2689–2747. https://doi.org/10.1007/s11831-020-09474-6.
Gardner, B., and M. Selig. 2003. “Airfoil design using a genetic algorithm and an inverse method.” In Proc., 41st Aerospace Sciences Meeting and Exhibit. Reston, VA: American Institute of Aeronautics and Astronautics.
Giunta, A., S. Wojtkiewicz, and M. Eldred. 2003. “Overview of modern design of experiments methods for computational simulations (invited).” In Proc., 41st Aerospace Sciences Meeting and Exhibit. Reston, VA: American Institute of Aeronautics and Astronautics.
Han, Z.-H., S. Görtz, and R. Zimmermann. 2013. “Improving variable-fidelity surrogate modeling via gradient-enhanced kriging and a generalized hybrid bridge function.” Aerosp. Sci. Technol. 25 (1): 177–189. https://doi.org/10.1016/j.ast.2012.01.006.
Han, Z.-H., Z. Zimmermann, and S. Görtz. 2012. “Alternative Cokriging method for variable-fidelity surrogate modeling.” AIAA J. 50 (5): 1205–1210. https://doi.org/10.2514/1.J051243.
Jeong, S., M. Murayama, and K. Yamamoto. 2005. “Efficient optimization design method using kriging model.” J. Aircr. 42 (2): 413–420. https://doi.org/10.2514/1.6386.
Johnson, M., L. Moore, and D. Ylvisaker. 1990. “Minimax and maximin distance designs.” J. Stat. Plann. Inference 26 (2): 131–148. https://doi.org/10.1016/0378-3758(90)90122-B.
Kim, S., I. Kim, and D. You. 2022. “Multi-condition multi-objective optimization using deep reinforcement learning.” J. Comput. Phys. 462 (Aug): 111263. https://doi.org/10.1016/j.jcp.2022.111263.
Kingma, D. P., and J. Ba. 2014. “Adam: A method for stochastic optimization.” Preprint, submitted December 22, 2016. https://arxiv.org/abs/1412.6980.
Kitson, R., and C. E. Cesnik. 2017. “High speed vehicle fluid-structure-jet interaction analysis and modeling.” In Proc., 58th AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conf. Reston, VA: American Institute of Aeronautics and Astronautics.
Kulfan, B. M. 2008. “Universal parametric geometry representation method.” J. Aircr. 45 (1): 142–158. https://doi.org/10.2514/1.29958.
Kurtulus, D. F. 2009. “Ability to forecast unsteady aerodynamic forces of flapping airfoils by artificial neural network.” Neural Comput. Appl. 18 (Apr): 359–368. https://doi.org/10.1007/s00521-008-0186-2.
LeCun, Y., Y. Bengio, and G. Hinton. 2015. “Deep learning.” Nature 521 (7553): 436–444. https://doi.org/10.1038/nature14539.
Li, K., J. Kou, and W. Zhang. 2022. “Deep learning for multifidelity aerodynamic distribution modeling from experimental and simulation data.” AIAA J. 60 (7): 4413–4427. https://doi.org/10.2514/1.J061330.
Li, R., Y. Zhang, and H. Chen. 2021. “Learning the aerodynamic design of supercritical airfoils through deep reinforcement learning.” AIAA J. 59 (10): 3988–4001. https://doi.org/10.2514/1.J060189.
Liu, J., Z. Han, and W. Song. 2012. “Efficient kriging-based aerodynamic design of transonic airfoils: Some key issues.” In Proc., 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Reston, VA: American Institute of Aeronautics and Astronautics.
Liu, Y., and X. Yao. 1999. “Ensemble learning via negative correlation.” Neural Networks 12 (10): 1399–1404. https://doi.org/10.1016/S0893-6080(99)00073-8.
Martins, J. R. R. A., C. Mader, and J. Alonso. 2006. “ADjoint: An approach for rapid development of discrete adjoint solvers.” In Proc., 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conf. Reston, VA: American Institute of Aeronautics and Astronautics.
Martins, J. R. R. A., P. Sturdza, and J. J. Alonso. 2003. “The complex-step derivative approximation.” ACM Trans. Math. Software 29 (3): 245–262. https://doi.org/10.1145/838250.838251.
Massaoudi, M., S. S. Refaat, I. Chihi, M. Trabelsi, F. S. Oueslati, and H. Abu-Rub. 2021. “A novel stacked generalization ensemble-based hybrid LGBM-XGB-MLP model for Short-Term Load Forecasting.” Energy 214 (Jan): 118874. https://doi.org/10.1016/j.energy.2020.118874.
Samareh, J. 2004. “Aerodynamic shape optimization based on free-form deformation.” In Proc., 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conf. Reston, VA: American Institute of Aeronautics and Astronautics.
Slowik, A., and H. Kwasnicka. 2020. “Evolutionary algorithms and their applications to engineering problems.” Neural Comput. Appl. 32 (Mar): 12363–12379. https://doi.org/10.1007/s00521-020-04832-8.
Sripawadkul, V., M. Padulo, and M. Guenov. 2010. “A comparison of airfoil shape parameterization techniques for early design optimization.” In Proc., 13th AIAA/ISSMO Multidisciplinary Analysis Optimization Conf. Reston, VA: American Institute of Aeronautics and Astronautics.
Stein, M. 1987. “Large sample properties of simulations using Latin hypercube sampling.” Technometrics 29 (2): 143–151.
Wang, Q., W. Qian, and K. He. 2015. “Unsteady aerodynamic modeling at high angles of attack using support vector machines.” Chin. J. Aeronaut. 28 (3): 659–668. https://doi.org/10.1016/j.cja.2015.03.010.
Wu, P., W. Yuan, L. Ji, L. Zhou, Z. Zhou, W. Feng, and Y. Guo. 2022. “Missile aerodynamic shape optimization design using deep neural networks.” Aerosp. Sci. Technol. 126 (Jul): 107640. https://doi.org/10.1016/j.ast.2022.107640.
Xia, C.-C., T.-T. Jiang, and W.-F. Chen. 2016. “Particle swarm optimization of aerodynamic shapes with nonuniform shape parameter–based radial basis function.” J. Aerosp. Eng. 30 (3): 04016089. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000686.
Xu, S., H. Liu, X. Wang, and X. Jiang. 2014. “A robust error-pursuing sequential sampling approach for global metamodeling based on voronoi diagram and cross validation.” J. Mech. Des. 136 (7): 071009. https://doi.org/10.1115/1.4027161.
Yan, X., J. Zhu, M. Kuang, and X. Wang. 2019. “Aerodynamic shape optimization using a novel optimizer based on machine learning techniques.” Aerosp. Sci. Technol. 86 (Mar): 826–835. https://doi.org/10.1016/j.ast.2019.02.003.
Yilmaz, E., and B. German. 2020. “Conditional generative adversarial network framework for airfoil inverse design.” In Proc., AIAA Aviation 2020 Forum, Virtual Event. Reston, VA: American Institute of Aeronautics and Astronautics.
Zhang, X., F. Xie, T. Ji, Z. Zhu, and Y. Zheng. 2021. “Multi-fidelity deep neural network surrogate model for aerodynamic shape optimization.” Comput. Methods Appl. Mech. Eng. 373 (Jan): 113485. https://doi.org/10.1016/j.cma.2020.113485.
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Published In
Journal of Aerospace Engineering
Volume 37 • Issue 6 • November 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Aug 4, 2023
Accepted: Jun 14, 2024
Published online: Sep 10, 2024
Published in print: Nov 1, 2024
Discussion open until: Feb 10, 2025
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