Abstract
Machine learning models are recently adopted to generate airfoil shapes. A typical task is to obtain airfoil shapes that satisfy the required lift coefficient. These inverse design problems can be solved by generative adversarial networks (GAN). However, the shapes obtained from ordinal GAN models are not smooth; hence, flow analysis cannot be conducted. Therefore, Bézier curves or smoothing methods are required. This study employed conditional Wasserstein GAN with gradient penalty (cWGAN-gp) to generate smooth airfoil shapes without any smoothing method. In the proposed method, the cWGAN-gp model outputs a shape that indicates the specified lift coefficient. Then, the results obtained from the proposed model are compared with those of ordinal GANs and variational autoencoders; in addition, the proposed method outputs the smoothest shape owing to the earth mover's distance used in cWGAN-gp. By adopting the proposed method, no additional smoothing method is required to conduct flow analysis.
Similar content being viewed by others
References
Abbot I.. von Doenhoff AE, Stivers Jr L (1945) Summary of airfoil data. United States
Achour G, Sung WJ, Pinon-Fischer OJ, Mavris DN (2020) Development of a conditional generative adversarial network for airfoil shape optimization. p 2261
Arjovsky M, Bottou L (2017) Towards principled methods for training generative adversarial networks
Arjovsky M, Chintala S, Bottou L (2017) Wasserstein generative adversarial networks
Barrett TR, Bressloff NW, Keane AJ (2006) Airfoil shape design and optimization using multifidelity analysis and embedded inverse design. AIAA J 44(9):2051–2060
Bidgoli A, Veloso P (2019) Deepcloud. The application of a data-driven, generative model in design. 1904.01083
Brown NC, Mueller CT (2019) Design variable analysis and generation for performance-based parametric modeling in architecture. Int J Archit Comput 17(1):36–52
Bui-Thanh T, Damodaran M, Willcox K (2004) Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition. AIAA J 42(8):1505–1516
Chen W, Chiu K, Fuge MD (2020) Airfoil design parameterization and optimization using Bézier generative adversarial networks. AIAA J 58(11):4723–4735
Chen W, Ramamurthy A (2021) Deep generative model for efficient 3D airfoil parameterization and generation
Drela M (1989) Xfoil: An analysis and design system for low Reynolds number airfoils. In: M TJ (Ed) Low reynolds number aerodynamics, Lecture Notes in Engineering. vol 54, Berlin, Heidelberg, pp 1–12
Du X, He P, Martins JRRA (2020) A B-Spline-based generative adversarial network model for fast interactive airfoil aerodynamic optimization
Fainekos GE, Giannakoglou KC (2003) Inverse design of airfoils based on a novel formulation of the ant colony optimization method. Inverse Probl Eng 11(1):21–38
Filippone A (1995) Airfoil inverse design and optimization by means of viscous-inviscid techniques. J Wind Eng Ind Aerodyn 56(2):123–136
Gaggero S, Vernengo G, Villa D, Bonfiglio L (2020) A reduced order approach for optimal design of efficient marine propellers. Ships Offshore Struct 15(2):200–214
Goodfellow I (2017) NIPS 2016 tutorial: generative adversarial networks
Goodfellow IJ, Pouget-Abadie J, Mirza M, Xu B, Warde-Farley D, Ozair S, Courville A, Bengio Y (2014) Generative adversarial nets. In: Proceedings of the 27th International Conference on Neural Information Processing Systems - Volume 2, NIPS’14, MIT Press, Cambridge, MA, USA pp 2672–2680
Gulrajani I, Ahmed F, Arjovsky M, Dumoulin V, Courville AC (2017) Improved training of Wasserstein GANs
Jahangirian A, Shahrokhi A (2009) Inverse design of transonic airfoils using genetic algorithm and a new parametric shape method. Inverse prob Sci Eng 17(5):681–699
Jameson A (1995) Optimum aerodynamic design using CFD and control theory pp 926–949
Li J, Zhang M (2021) On deep-learning-based geometric filtering in aerodynamic shape optimization. Aerosp Sci Technol 112:106603
Nash C, Williams CKI (2017) The shape variational autoencoder: a deep generative model of part-segmented 3D objects. Comput Graphics Forum 36(5):1–12
Obayashi S, Takanashi S (1996) Genetic optimization of target pressure distributions for inverse design methods. AIAA J 34(5):881–886
Oh S, Jung Y, Kim S, Lee I, Kang N (2019) Deep generative design: integration of topology optimization and generative models. J Mech Design 141(11)
Paszke A, Gross S, Chintala S, Chanan G, Yang E, DeVito Z, Lin Z, Desmaison A, Antiga L, Lerer A (2017) Automatic differentiation in pytorch
Press WH, Teukolsky SA (1990) Savitzky-Golay smoothing filters. Comput Phys 4(6):669–672
Sekar V, Zhang M, Shu C, Khoo BC (2019) Inverse design of airfoil using a deep convolutional neural network. AIAA J 57(3):993–1003
Shelton ML, Gregory BA, Lamson SH, Moses HL, Doughty RL, Kiss T (1993) Optimization of a transonic turbine airfoil using artificial intelligence, CFD and cascade testing. Turbo expo: power for land, sea, and air 3A: General
Sun G, Sun Y, Wang S (2015) Artificial neural network based inverse design: Airfoils and wings. Aerosp Sci Technol 42:415–428
Vicini A, Quagliarella D (1997) Inverse and direct airfoil design using a multiobjective genetic algorithm. AIAA J 35(9):1499–1505
Villani C (2009) Optimal transport: old and new. Springer, Berlin, Heidelberg
Volkan Pehlivanoglu Y (2019) Efficient accelerators for PSO in an inverse design of multi-element airfoils. Aerosp Sci Technol 91:110–121
Wang Y, Shimada K, Farimani AB (2021) Airfoil GAN: encoding and synthesizing airfoils for aerodynamic-aware shape optimization. arXiv. 2101.04757
Weng L (2019) From GAN to WGAN. arXiv. 1904.08994
Yilmaz E, German B. A deep learning approach to an airfoil inverse design problem. 2018 Multidisciplinary Analysis and Optimization Conference
Yonekura K, Suzuki K (2021) Data-driven design exploration method using conditional variational autoencoder for airfoil design. Struct Multidisc Optim 64:613–624
Yonekura K, Wada K, Suzuki K (2022) Generating various airfoils with required lift coefficients by combining NACA and Joukowski airfoils using conditional variational autoencoders. Eng Appl Artif Intell 108:104560
Yonekura K, Watanabe O (2014) A shape parameterization method using principal component analysis in application to shape optimization. J Mech Des 136:121401
Acknowledgments
This work was partially supported by JSPS KAKENHI Grant Number 21K14064.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The first author works part-time for IHI Corporation and MJOLNIR SPACEWORKS.
Replication of result
The source code and data are available on github (https://github.com/miyamotononno/generate_airfoil).
Additional information
Responsible Editor: Yoojeong Noh
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Topical Collection: 14th World Congress of Structural and Multidisciplinary Optimization.
Guest Editors: Y Noh, E Acar, J Carstensen, J Guest, J Norato, P Ramu.
Rights and permissions
About this article
Cite this article
Yonekura, K., Miyamoto, N. & Suzuki, K. Inverse airfoil design method for generating varieties of smooth airfoils using conditional WGAN-gp. Struct Multidisc Optim 65, 173 (2022). https://doi.org/10.1007/s00158-022-03253-6
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00158-022-03253-6