Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-22T11:44:52.280Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow field reconstruction method based on array neural network

Part of: Smart Aircraft International Symposium on Smart Aircraft 2019 Collection

Published online by Cambridge University Press:  02 October 2020

W. Yuqi Open the ORCID record for W. Yuqi [Opens in a new window] ,
Y. Wu ,
L. Shan ,
Z. Jian ,
R. Huiying ,
Y. Tiechui  and
K. Menghai
W. Yuqi
Affiliation:
Renmin University of ChinaBeijing 100872 China
Y. Wu*
Affiliation:
Computer Network Information Center Chinese Academy of Sciences Beijing 100190 China
L. Shan
Affiliation:
Computer Network Information Center Chinese Academy of Sciences Beijing 100190 China
Z. Jian
Affiliation:
Computer Network Information Center Chinese Academy of Sciences Beijing 100190 China
R. Huiying
Affiliation:
Computer Network Information Center Chinese Academy of Sciences Beijing 100190 China University of Chinese Academy of SciencesBeijing 100049 China
Y. Tiechui
Affiliation:
Computer Network Information Center Chinese Academy of Sciences Beijing 100190 China University of Chinese Academy of SciencesBeijing 100049 China
K. Menghai
Affiliation:
China Unicom Software Research InstituteBeijing 100176 China
*
[email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Multi-dimensional aerodynamic database technology is widely used, but its model often has the curse of dimensionality. In order to solve this problem, we need projection to reduce the dimension. In addition, due to the lack of traditional method, we have improved the traditional flow field reconstruction method based on artificial neural networks, and we proposed an array neural network method.

In this paper, a set of flow field data for the target problem of the fixed Mach number is obtained by the existing CFD method. Then we arrange all the sampled flow field data into a matrix and use proper orthogonal decomposition (POD) to reduce the dimension, whose size is determined by the first few modals of energy. Therefore, significantly reduced data are obtained. Then we use an arrayed neural network to map the flow field data of simplified target problem and the flow field characteristics. Finally, the unknown flow field data can be effectively predicted through the flow field characteristic and the trained array neural network.

At the end of this paper, the effectiveness of the method is verified by airfoil flow fields. The calculation results show that the array neural network can reconstruct the flow field of the target problem more accurately than the traditional method, and its convergence speed is significantly faster. In addition, for the case of high angle flow field, the array neural network also performs well. There are no obvious jumps, and huge errors are found in results. In general, the proposed method is better than the traditional method.

Keywords

neural networkflow field reconstructionproper orthogonal decompositionmachine learning
Type
Research Article
Information
The Aeronautical Journal , Volume 125 , Issue 1283 , January 2021 , pp. 223 - 243
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Royal Aeronautical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Lorente, L., Vega, J., and Velazquez, A. Generation of aerodynamic databases using high-order singular value decomposition, J. Aircr., 2008, 45, (5), pp 1779–1788. doi: 10.2514/1.35258 CrossRefGoogle Scholar
Hesthaven, J.S., Rozza, G., and Stamm, B., Certified Reduced Basis Methods for Parametrized Partial Differential Equations, Springer, 2016. doi: 10.1007/978-3-319-22470-1 CrossRefGoogle Scholar
Liang, Y., Lee, H., Lim, S., Lin, W., Lee, K., and Wu, C. Proper orthogonal decomposition and its applications—Part 1: theory, J. Sound Vibr., 2002, 252, (3), pp 527–544. doi: 10.1006/jsvi.2001.4041 CrossRefGoogle Scholar
Hesthaven, J.S., Stamm, B., and Zhang, S. Efficient greedy algorithms for high-dimensional parameter spaces with applications to empirical interpolation and reduced basis methods, ESAIM-Math. Model. Num., 2014, 48, (1), pp 259–283. doi: 10.1051/m2an/2013100 CrossRefGoogle Scholar
Shah, A., Xing, W. and Triantafyllidis, V. Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models, Proc. Royal Soc. A, 2017, 473, (2200), Paper 20160809. doi: 10.1098/rspa.2016.0809 CrossRefGoogle ScholarPubMed
Benner, P., Gugercin, S. and Willcox, K. A survey of projection-based model reduction methods for parametric dynamical systems, SIAM Rev., 2015, 57, (4), pp 483–531. doi: 10.1137/130932715 CrossRefGoogle Scholar
Jie, L., Yanhui, D. and Jinsheng, C. A quick method of flow field prediction based on proper orthogonal decomposition. Adv. Aeronaut. Eng., 2014, 5, (3), pp 350–357.Google Scholar
Yasong, Q., Junqiang, B. and Jun, H. Flow field estimation method based on proper orthogonal decomposition and surrogate model. Hangkong Xuebao/Acta Aeronautica et Astronautica Sinica, 2013, 34, (6), pp 1249–1260.Google Scholar
Zhi, H., Peng-yin, L., Xiao-cheng, Z. and Zhao-hui, D. DMD analysis of airfoil’s flow field under different degrees of dynamic stall. J. Eng. Thermal Energ. Power, 2017, 32, (7), pp 52–57.Google Scholar
Yu, J. and Hesthaven, J.S. Flowfield reconstruction method using artificial neural network. AIAA J., 2019, 57, (2), pp 482–498.CrossRefGoogle Scholar
Iungo, G.V., Santoni-Ortiz, C., Abkar, M., Porté-Agel, F., Rotea, M.A. and Leonardi, S. Data-driven reduced order model for prediction of wind turbine wakes, J. Phy. Conf. Ser., 2015, 625, Paper 012009. doi: 10.1088/1742-6596/625/1/012009 CrossRefGoogle Scholar
Peherstorfer, B. and Willcox, K. Dynamic data-driven reduced-order models, Comput. Methods Appl. Mech. Eng., 2015, 291, pp 21–41. doi: 10.1016/j.cma.2015.03.018 CrossRefGoogle Scholar
Tracey, B.D., Duraisamy, K. and Alonso, J.J. A Machine Learning Strategy to Assist Turbulence Model Development, 53rd AIAA Aerospace Sciences Meeting, AIAA Paper 2015-1287, 2015. doi: 10.2514/6.2015-1287 CrossRefGoogle Scholar
Xiao, H.,Wu, J.-L.,Wang, J.-X., Sun, R. and Roy, C. Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier–Stokes simulations: a data-driven, physics-informed Bayesian approach, J. Comput. Phy., 2016, 324, pp 115–136. doi: 10.1016/j.jcp.2016.07.038 CrossRefGoogle Scholar
Parish, E.J. and Duraisamy, K. A paradigm for data-driven predictive modeling using field inversion and machine learning, J. Comput. Phy., 2016, 305, pp 758–774. doi: 10.1016/j.jcp.2015.11.012 CrossRefGoogle Scholar
Ling, J., Kurzawski, A. and Templeton, J. Reynolds averaged turbulence modelling using deep neural networks with embedded invariance, J. Fluid Mech., 2016, 807, pp 155–166. doi: 10.1017/jfm.2016.615 CrossRefGoogle Scholar
Duraisamy, K., Zhang, Z.J. and Singh, A.P. New Approaches in Turbulence and Transition Modeling Using Data-Driven Techniques, 53rd AIAA Aerospace Sciences Meeting, AIAA Paper 2015-1284, 2015. doi: 10.2514/6.2015-1284 CrossRefGoogle Scholar
Lee, C., Kim, J., Babcock, D. and Goodman, R. Application of neural networks to turbulence control for drag reduction, Phy. Fluids, 1997, 9, (6), pp 1740–1747. doi: 10.1063/1.869290 CrossRefGoogle Scholar
Kurtulus, D.F. Ability to forecast unsteady aerodynamic forces of flapping airfoils by artificial neural network, Neural Comput. Appl., 2009, 18, (4), p 359. doi: 10.1007/s00521-008-0186-2 CrossRefGoogle Scholar
Bui-Thanh, T., Damodaran, M. and Willcox, K. Aerodynamic data reconstruction and inverse design using proper orthogonal decomposition, AIAA J., 2004, 42, (8), pp 1505–1516. doi: 10.2514/1.2159 CrossRefGoogle Scholar
Everson, R. and Sirovich, L. Karhunen–Loeve procedure for Gappy data, J. Opt. Soc. Am., 1995, 12, (8), pp 1657–1664. doi: 10.1364/JOSAA.12.001657 CrossRefGoogle Scholar
Willcox, K. Unsteady flow sensing and estimation via the Gappy proper orthogonal decomposition, Comput. Fluids, 2006, 35, (2), pp 208–226. doi: 10.1016/j.compfluid.2004.11.006 CrossRefGoogle Scholar
Tosun, E., Aydin, K. and Bilgili, M. Comparison of linear regression and artificial neural network model of a diesel engine fueled with biodiesel-alcohol mixtures, Alexandria Eng. J., 2016, 55, (4), pp 3081–3089. doi: 10.1016/j.aej.2016.08.011 CrossRefGoogle Scholar
Cybenko, G. Continuous Valued Neural Networks with Two Hidden Layers are Sufficient, TR, 1988.Google Scholar
Cybenko, G. Approximation by superpositions of a sigmoidal function, Math. Control Signal Syst., 1989, 2, (4), pp 303–314. doi: 10.1007/BF02551274 CrossRefGoogle Scholar
Shojaeefard, M.H., Khorampanahi, A. and Mirzaei, M. Numerical investigation of oscillation frequency and amplitude effects on the hydrodynamic coefficients of a body with NACA0012 hydrofoil section. J. Mech. Sci. Tech., 2017, 31, (5), pp 2251–2260.CrossRefGoogle Scholar
Taira, K., Brunton, S.L., Dawson, S.T., Rowley, C.W., Colonius, T., McKeon, B.J., Schmidt, O.T., Gordeyev, S., Theofilis, V. and Ukeiley, L.S. Modal analysis of fluid flows: an overview, AIAA J., 2017, 55, (12), pp 4013–4041. doi: 10.2514/1.J056060 CrossRefGoogle Scholar
Rowley, C.W. and Dawson, S.T. Model reduction for flow analysis and control, Ann. Rev. Fluid Mech., 2017, 49, pp. 387–417. doi: 10.1146/annurev-fluid-010816-060042 CrossRefGoogle Scholar
Abadi, M., Barham, P., Chen, J., Chen, Z., Davis, A., Dean, J., Devin, M., Ghemawat, S., Irving, G., Isard, M., Kudlur, M., Levenberg, J., Monga, R., Moore, S., Murray, D.G., Steiner, B., Tucker, P., Vasudevan, V., Warden, P., Wicke, M., Yu, Y. and Zheng, X. Tensor flow: a system for large-scale machine learning, OSDI, 2016, 16, pp 265–283.Google Scholar
Karlik, B. and Olgac, A.V. Performance analysis of various activation functions in generalized MLP architectures of neural networks, Int. J. Artif. Intell. Expert Syst., 2011, 1, (4), pp 111–122.Google Scholar
Glorot, X., Bordes, A. and Bengio, Y. Deep Sparse Rectifier Neural Networks, Proceedings of the 14th International Conf. on Artificial Intelligence and Statistics, 2011, pp 315–323.Google Scholar
Kingma, D. and Ba, J. Adam:AMethod for Stochastic Optimization, arXiv preprint , 2014.Google Scholar
Economon, T.D., Palacios, F., Copeland, S.R., Lukaczyk, T.W. and Alonso, J.J. SU2: an open-source suite for multiphysics simulation and design, AIAA J., 2016, 54, (3), pp. 828–846. doi: 10.2514/1.J053813 CrossRefGoogle Scholar
Alonso, D., Vega, J. and Velazquez, A. Reduced-order model for viscous aerodynamic flow past an airfoil, AIAA J., 2010, 48, (9), pp 1946–1958. doi: 10.2514/1.J050153 CrossRefGoogle Scholar
Watanabe, S., Ishimoto, S. and Yamamoto, Y. Aerodynamic characteristics evaluation of hypersonic flight experiment vehicle based on flight data, J Spacecraft Rockets, 1997, 34, (4), pp 464–470. doi: 10.2514/2.3259 CrossRefGoogle Scholar
Kurganov, A. and Tadmor, E. Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers, Numer. Methods Part. Different. Equations, 2002, 18, (5), pp 584–608. doi: 10.1002/(ISSN)1098-2426 CrossRefGoogle Scholar
Hansen, P.C. The truncated SVD as a method for regularization, Bit Numer. Math., 1987, 27, (4), pp 534–553.CrossRefGoogle Scholar
Shnayderman, A., Gusev, A. and Eskicioglu, A.M. An SVD-based grayscale image quality measure for local and global assessment, IEEE Trans. Image Process., 2006, 15, (2), pp 422–429.CrossRefGoogle ScholarPubMed
Drma, Z and Veseli, K. New fast and accurate Jacobi SVD algorithm. SIAM J. Matrix Anal. Appl., 2008, 29, (4), pp 1322–1342.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. and Lumley, J.L. The proper orthogonal decomposition in the analysis of turbulent flows. Ann. Rev. Fluid Mech., 1993, 25, (1), pp 539–575.CrossRefGoogle Scholar
Rowley, C.W. Model reduction for fluids, using balanced proper orthogonal decomposition. Int. J. Bifurcat. Chaos, 2011, 15, (3), pp 997–1013.CrossRefGoogle Scholar
Volkwein, K.K. Galerkin proper orthogonal decomposition methods for a general equation in fluid dynamics. SIAM J Numer. Anal., 2003, 40, (2), pp 492–515.Google Scholar
Liang, Y.C., Lee, H.P. and Lim, S.P., et al. Proper orthogonal decomposition and its applications—Part I: Theory. J. Sound Vibr., 2002, 252, (3), pp 527–544.CrossRefGoogle Scholar