Skip to main content
Skip to article control options
No AccessRegular Articles

Flowfield Reconstruction Method Using Artificial Neural Network

Published Online:https://doi.org/10.2514/1.J057108

Multidimensional aerodynamic database development has become more and more important for the design, control, and guidance of modern aircraft. To relieve the curse of the dimensionality, a novel flowfield reconstruction method based on an artificial neural network is proposed. The idea is to design a simplified problem that is related to the target problem. Then, the map from the simplified problem to the target problem is built using an artificial neural network. Finally, the target problem can be predicted efficiently through solving the simplified problem instead. Examples of the efficiency of this approach include two-dimensional viscous nozzle flows, an inviscid M6 wing flow, a viscous hypersonic flow of a complex configuration, and an unsteady two-dimensional Riemann problem to evaluate the performance of the proposed method. A Gaussian process model is also incorporated for a comparative study. With an artificial neural network of moderate complexity, the solution of the target problem can be generated with good accuracy. Among other observations, it is found that shocks can be predicted well with sharp resolution for steady and unsteady cases. Overall, using a simplified problem that accounts for all the interested parameters as inputs tends to be more reliable than using input parameters.

References

  • [1] Lorente L., Vega J. and Velazquez A., “Generation of Aerodynamic Databases Using High-Order Singular Value Decomposition,” Journal of Aircraft, Vol. 45, No. 5, 2008, pp. 1779–1788. doi:https://doi.org/10.2514/1.35258 LinkGoogle Scholar

  • [2] Eldred M. and Dunlavy D., “Formulations for Surrogate-Based Optimization with Data Fit, Multifidelity, and Reduced-Order Models,” 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2006-7117, Sept. 2006. LinkGoogle Scholar

  • [3] March A. and Willcox K., “Provably Convergent Multifidelity Optimization Algorithm Not Requiring High-Fidelity Derivatives,” AIAA Journal, Vol. 50, No. 5, 2012, pp. 1079–1089. doi:https://doi.org/10.2514/1.J051125 AIAJAH 0001-1452 LinkGoogle Scholar

  • [4] Mifsud M., MacManus D. G. and Shaw S., “A Variable-Fidelity Aerodynamic Model Using Proper Orthogonal Decomposition,” International Journal for Numerical Methods in Fluids, Vol. 82, No. 10, 2016, pp. 646–663. doi:https://doi.org/10.1002/fld.v82.10 IJNFDW 0271-2091 CrossrefGoogle Scholar

  • [5] Hesthaven J. S., Rozza G. and Stamm B., Certified Reduced Basis Methods for Parametrized Partial Differential Equations, Springer, Basel, Switzerland, 2016, pp. 27–43. doi:https://doi.org/10.1007/978-3-319-22470-1 CrossrefGoogle Scholar

  • [6] Liang Y., Lee H., Lim S., Lin W., Lee K. and Wu C., “Proper Orthogonal Decomposition and Its Applications—Part 1: Theory,” Journal of Sound and Vibration, Vol. 252, No. 3, 2002, pp. 527–544. doi:https://doi.org/10.1006/jsvi.2001.4041 JSVIAG 0022-460X CrossrefGoogle Scholar

  • [7] 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: Mathematical Modelling and Numerical Analysis, Vol. 48, No. 1, 2014, pp. 259–283. doi:https://doi.org/10.1051/m2an/2013100 CrossrefGoogle Scholar

  • [8] Shah A., Xing W. and Triantafyllidis V., “Reduced-Order Modelling of Parameter-Dependent, Linear and Nonlinear Dynamic Partial Differential Equation Models,” Proceedings of the Royal Society A, Vol. 473, No. 2200, 2017, Paper 20160809. doi:https://doi.org/10.1098/rspa.2016.0809 CrossrefGoogle Scholar

  • [9] Benner P., Gugercin S. and Willcox K., “A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems,” SIAM Review, Vol. 57, No. 4, 2015, pp. 483–531. doi:https://doi.org/10.1137/130932715 SIREAD 0036-1445 CrossrefGoogle Scholar

  • [10] Barthelmann V., Novak E. and Ritter K., “High Dimensional Polynomial Interpolation on Sparse Grids,” Advances in Computational Mathematics, Vol. 12, No. 4, 2000, pp. 273–288. doi:https://doi.org/10.1023/A:1018977404843 ACMHEX 1019-7168 CrossrefGoogle Scholar

  • [11] Venter G., Haftka R. T. and Starnes J. H., “Construction of Response Surface Approximations for Design Optimization,” AIAA Journal, Vol. 36, No. 12, 1998, pp. 2242–2249. doi:https://doi.org/10.2514/2.333 AIAJAH 0001-1452 LinkGoogle Scholar

  • [12] Rasmussen C. E., “Gaussian Processes in Machine Learning,” Advanced Lectures on Machine Learning, Springer, Berlin, 2004, pp. 63–71. CrossrefGoogle Scholar

  • [13] Wild S. M., Regis R. G. and Shoemaker C. A., “ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions,” SIAM Journal on Scientific Computing, Vol. 30, No. 6, 2008, pp. 3197–3219. doi:https://doi.org/10.1137/070691814 SJOCE3 1064-8275 CrossrefGoogle Scholar

  • [14] 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,” Journal of Physics: Conference Series, Vol. 625, June 2015, pp. 1–10. doi:https://doi.org/10.1088/1742-6596/625/1/012009 CrossrefGoogle Scholar

  • [15] Peherstorfer B. and Willcox K., “Dynamic Data-Driven Reduced-Order Models,” Computer Methods in Applied Mechanics and Engineering, Vol. 291, July 2015, pp. 21–41. doi:https://doi.org/10.1016/j.cma.2015.03.018 CMMECC 0045-7825 CrossrefGoogle Scholar

  • [16] 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:https://doi.org/10.2514/6.2015-1287 LinkGoogle Scholar

  • [17] 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,” Journal of Computational Physics, Vol. 324, Nov. 2016, pp. 115–136. doi:https://doi.org/10.1016/j.jcp.2016.07.038 JCTPAH 0021-9991 CrossrefGoogle Scholar

  • [18] Parish E. J. and Duraisamy K., “A Paradigm for Data-Driven Predictive Modeling Using Field Inversion and Machine Learning,” Journal of Computational Physics, Vol. 305, Jan. 2016, pp. 758–774. doi:https://doi.org/10.1016/j.jcp.2015.11.012 JCTPAH 0021-9991 CrossrefGoogle Scholar

  • [19] Ling J., Kurzawski A. and Templeton J., “Reynolds Averaged Turbulence Modelling Using Deep Neural Networks with Embedded Invariance,” Journal of Fluid Mechanics, Vol. 807, Nov. 2016, pp. 155–166. doi:https://doi.org/10.1017/jfm.2016.615 JFLSA7 0022-1120 CrossrefGoogle Scholar

  • [20] 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:https://doi.org/10.2514/6.2015-1284 LinkGoogle Scholar

  • [21] Lee C., Kim J., Babcock D. and Goodman R., “Application of Neural Networks to Turbulence Control for Drag Reduction,” Physics of Fluids, Vol. 9, No. 6, 1997, pp. 1740–1747. doi:https://doi.org/10.1063/1.869290 CrossrefGoogle Scholar

  • [22] Kurtulus D. F., “Ability to Forecast Unsteady Aerodynamic Forces of Flapping Airfoils by Artificial Neural Network,” Neural Computing and Applications, Vol. 18, No. 4, 2009, p. 359. doi:https://doi.org/10.1007/s00521-008-0186-2 CrossrefGoogle Scholar

  • [23] Bui-Thanh T., Damodaran M. and Willcox K., “Aerodynamic Data Reconstruction and Inverse Design Using Proper Orthogonal Decomposition,” AIAA Journal, Vol. 42, No. 8, 2004, pp. 1505–1516. doi:https://doi.org/10.2514/1.2159 AIAJAH 0001-1452 LinkGoogle Scholar

  • [24] Everson R. and Sirovich L., “Karhunen–Loeve Procedure for Gappy Data,” Journal of the Optical Society of America A, Vol. 12, No. 8, 1995, pp. 1657–1664. doi:https://doi.org/10.1364/JOSAA.12.001657 JOAOD6 0740-3232 CrossrefGoogle Scholar

  • [25] Willcox K., “Unsteady Flow Sensing and Estimation via the Gappy Proper Orthogonal Decomposition,” Computers & Fluids, Vol. 35, No. 2, 2006, pp. 208–226. doi:https://doi.org/10.1016/j.compfluid.2004.11.006 CrossrefGoogle Scholar

  • [26] 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 Engineering Journal, Vol. 55, No. 4, 2016, pp. 3081–3089. doi:https://doi.org/10.1016/j.aej.2016.08.011 AEJAEB CrossrefGoogle Scholar

  • [27] Cybenko G., “Continuous Valued Neural Networks with Two Hidden Layers are Sufficient,” Tufts Univ. TR, Dept. of Computer Science, 1988. Google Scholar

  • [28] Cybenko G., “Approximation by Superpositions of a Sigmoidal Function,” Mathematics of Control, Signals, and Systems (MCSS), Vol. 2, No. 4, 1989, pp. 303–314. doi:https://doi.org/10.1007/BF02551274 CrossrefGoogle Scholar

  • [29] 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 Journal, Vol. 55, No. 12, 2017, pp. 4013–4041. doi:https://doi.org/10.2514/1.J056060 AIAJAH 0001-1452 LinkGoogle Scholar

  • [30] Rowley C. W. and Dawson S. T., “Model Reduction for Flow Analysis and Control,” Annual Review of Fluid Mechanics, Vol. 49, Jan. 2017, pp. 387–417. doi:https://doi.org/10.1146/annurev-fluid-010816-060042 ARVFA3 0066-4189 CrossrefGoogle Scholar

  • [31] Abadi M., Barham P., Chen J., Chen Z., Davis A., Dean J., Devin M., Ghemawat S., Irving G., Isard M. and et al., “TensorFlow: A System for Large-Scale Machine Learning,” OSDI, Vol. 16, Nov. 2016, pp. 265–283. Google Scholar

  • [32] Karlik B. and Olgac A. V., “Performance Analysis of Various Activation Functions in Generalized MLP Architectures of Neural Networks,” International Journal of Artificial Intelligence and Expert Systems, Vol. 1, No. 4, 2011, pp. 111–122. Google Scholar

  • [33] Glorot X., Bordes A. and Bengio Y., “Deep Sparse Rectifier Neural Networks,” Proceedings of the 14th International Conference on Artificial Intelligence and Statistics, Proceedings of Machine Learning Research (PMLR), 2011, pp. 315–323. Google Scholar

  • [34] Kingma D. and Ba J., “Adam: A Method for Stochastic Optimization,” International Conference on Learning Representations (ICLR), Computational and Biological Learning Soc., New York, arXiv preprint arXiv:1412.6980, May 2015. Google Scholar

  • [35] 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 Journal, Vol. 54, No. 3, 2016, pp. 828–846. doi:https://doi.org/10.2514/1.J053813 AIAJAH 0001-1452 LinkGoogle Scholar

  • [36] Alonso D., Vega J. and Velazquez A., “Reduced-Order Model for Viscous Aerodynamic Flow Past an Airfoil,” AIAA Journal, Vol. 48, No. 9, 2010, pp. 1946–1958. doi:https://doi.org/10.2514/1.J050153 AIAJAH 0001-1452 LinkGoogle Scholar

  • [37] Watanabe S., Ishimoto S. and Yamamoto Y., “Aerodynamic Characteristics Evaluation of Hypersonic Flight Experiment Vehicle Based on Flight Data,” Journal of Spacecraft Rockets, Vol. 34, No. 4, 1997, pp. 464–470. doi:https://doi.org/10.2514/2.3259 LinkGoogle Scholar

  • [38] Kurganov A. and Tadmor E., “Solution of Two-Dimensional Riemann Problems for Gas Dynamics Without Riemann Problem Solvers,” Numerical Methods for Partial Differential Equations, Vol. 18, No. 5, 2002, pp. 584–608. doi:https://doi.org/10.1002/(ISSN)1098-2426 NMPDEB 1098-2426 CrossrefGoogle Scholar