Fast Predictions of Aircraft Aerodynamics Using Deep-Learning Techniques
Abstract
The numerical analysis of aerodynamic components based on the Reynolds–averaged Navier–Stokes equations has become critical for the design of transport aircraft but still entails large computational cost. Simulating a multitude of different flow conditions with high-fidelity methods as required for loads analysis or aerodynamic shape optimization is still prohibitive. Within the past few years, the application of machine learning methods has been proposed as a potential way to overcome these shortcomings. This is leading toward a new data-driven paradigm for the modeling of physical problems. The objective of this paper is the development of a deep-learning methodology for the prediction of aircraft surface pressure distributions and the rigorous comparison with existing state-of-the-art nonintrusive reduced-order models. Bayesian optimization techniques are employed to efficiently determine optimal hyperparameters for all deep neural networks. Three data-driven methods which are Gaussian processes, proper orthogonal decomposition combined with an interpolation technique, and deep learning are investigated. The results are compared for a two-dimensional airfoil case and the NASA Common Research Model transport aircraft as a relevant three-dimensional case. Results show that all methods are able to properly predict the surface pressure distribution at subsonic conditions. In transonic flow, when shock waves and separation lead to nonlinearities, deep-learning methods outperform the others by also capturing the shock wave location and strength accurately.
References
[1] , “Reduced-Order Modeling: New Approaches for Computational Physics,” Progress in Aerospace Sciences, Vol. 40, Nos. 1–2, 2004, pp. 51–117. https://doi.org/10.1016/j.paerosci.2003.12.001
[2] , “Rapid Gust Response Simulation of Large Civil Aircraft Using Computational Fluid Dynamics,” Aeronautical Journal, Vol. 121, No. 1246, 2017, pp. 1795–1807. https://doi.org/10.1017/aer.2017.104
[3] , “Nonlinear Model Reduction via Discrete Empirical Interpolation,” SIAM Journal on Scientific Computing, Vol. 32, No. 5, 2010, pp. 2737–2764. https://doi.org/10.1137/090766498
[4] , “Reduced-Order, Trajectory Piecewise-Linear Models for Nonlinear Computational Fluid Dynamics,” 34th AIAA Fluid Dynamics Conference and Exhibit, AIAA Paper 2004-2329, 2004.
[5] , “Reduced Order Unsteady Aerodynamic Model of a Rigid Aerofoil in Gust Encounters,” Aerospace Science and Technology, Vol. 63, 2017, pp. 203–213. https://doi.org/10.1016/j.ast.2016.12.029
[6] , “Nonlinear Unsteady Reduced Order Models Based on Computational Fluid Dynamics for Gust Loads Predictions,” AIAA Journal, Vol. 57, No. 5, 2019, pp. 1839–1850. https://doi.org/10.2514/1.J057804
[7] , “Proper Orthogonal Decomposition Extensions for Parametric Applications in Compressible Aerodynamics,” 21st AIAA Applied Aerodynamics Conference, AIAA Paper 2003-4213, 2003.
[8] , “Proper Orthogonal Decomposition, Surrogate Modelling and Evolutionary Optimization in Aerodynamic Design,” Computers and Fluids, Vol. 84, Sept. 2013, pp. 327–350, https://www.sciencedirect.com/science/article/pii/S0045793013002223. https://doi.org/10.1016/j.compfluid.2013.06.007
[9] , “Interpolation-Based Reduced-Order Modeling for Steady Transonic Flows via Manifold Learning,” International Journal of Computational Fluid Dynamics, Vol. 28, Nos. 3–4, 2014, pp. 106–121.
[10] , “Evaluation of Aerodynamic Loads via Reduced-Order Methodology,” AIAA Journal, Vol. 53, No. 8, 2015, pp. 2389–2405. https://doi.org/10.2514/1.J053755
[11] , “Reduced Order Models for Aerodynamic Applications, Loads and MDO,” CEAS Aeronautical Journal, Vol. 9, No. 1, 2018, pp. 171–193. https://doi.org/10.1007/s13272-018-0283-6
[12] , “Recent Advances in Surrogate-Based Optimization,” Progress in Aerospace Sciences, Vol. 45, Nos. 1–3, 2009, pp. 50–79. https://doi.org/10.1016/j.paerosci.2008.11.001
[13] , “Learning Deep Architectures for AI,” Foundations and Trends® in Machine Learning, Vol. 2, No. 1, 2009, pp. 1–127. https://doi.org/10.1561/2200000006
[14] , “Aerodynamic Coefficient Prediction of Airfoils Using Neural Networks,” 46th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2008-0887, 2008. https://doi.org/10.2514/6.2008-887
[15] , “A Convolutional Neural Network Approach to Training Predictors for Airfoil Performance,” 18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2017-3660, 2017. https://doi.org/10.2514/6.2017-3660
[16] , “Layered Reduced-Order Models for Nonlinear Aerodynamics and Aeroelasticity,” Journal of Fluids and Structures, Vol. 68, Jan. 2017, pp. 174–193, https://www.sciencedirect.com/science/article/pii/S0889974616301852. https://doi.org/10.1016/j.jfluidstructs.2016.10.011
[17] , “Data-Driven Prediction of Unsteady Pressure Distributions Based on Deep Learning,” Journal of Fluids and Structures, Vol. 104, July 2021, Paper 103316, https://www.sciencedirect.com/science/article/pii/S0889974621000992. https://doi.org/10.1016/j.jfluidstructs.2021.103316
[18] , “Convolutional Neural Networks for Steady Flow Approximation,” Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Assoc. for Computing Machinery, New York, 2016, pp. 481–490. https://doi.org/10.1145/2939672.2939738
[19] , “Prediction Model of Velocity Field Around Circular Cylinder over Various Reynolds Numbers by Fusion Convolutional Neural Networks Based on Pressure on the Cylinder,” Physics of Fluids, Vol. 30, No. 4, 2018, Paper 047105. https://doi.org/10.1063/1.5024595
[20] , “Fast Flow Field Prediction over Airfoils Using Deep Learning Approach,” Physics of Fluids, Vol. 31, No. 5, 2019, Paper 057103. https://doi.org/10.1063/1.5094943
[21] , “Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks,” Computational Mechanics, Vol. 64, 2019, pp. 525–545. https://doi.org/10.1007/s00466-019-01740-0
[22] , “Deep Learning Methods for Reynolds-Averaged Navier–Stokes Simulations of Airfoil Flows,” AIAA Journal, Vol. 58, No. 1, 2020, pp. 25–36. https://doi.org/10.2514/1.J058291
[23] , “A Deep Learning Approach for Efficiently and Accurately Evaluating the Flow Field of Supercritical Airfoils,” Computers and Fluids, Vol. 198, 2020, Paper 104393. https://doi.org/10.1016/j.compfluid.2019.104393
[24] , “A Taxonomy of Global Optimization Methods Based on Response Surfaces,” Journal of Global Optimization, Vol. 21, No. 4, 2001, pp. 345–383. https://doi.org/10.1023/A:1012771025575
[25] , “Design and Analysis of Computer Experiments,” Statistical Science, Vol. 4, No. 4, 1989, pp. 409–423. https://doi.org/10.1214/ss/1177012413
[26] , “Asymptotic Behavior of the Likelihood Function of Covariance Matrices of Spatial Gaussian Processes,” Journal of Applied Mathematics, Vol. 2010, 13 Jan. 2011, Paper 494070. https://doi.org/10.1155/2010/494070
[27] , “Turbulence and the Dynamics of Coherent Structures, Part I: Coherent Structures,” Quarterly of Applied Mathematics, Vol. 45, Oct. 1987, pp. 561–571. https://doi.org/10.1090/qam/910462
[28] , “Interpolation des Fonctions de deux Variables Suivant le Principe de la Flexion des Plaques Minces,” ESAIM: Mathematical Modelling and Numerical Analysis—Modélisation Mathématique et Analyse Numérique, Vol. 10, No. R3, 1976, pp. 5–12, http://www.numdam.org/item/M2AN_1976__10_3_5_0.
[29] , “Frank Rosenblatt: Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms,” Brain Theory, edited by Palm G. and Aertsen A., Springer, Berlin, 1986, pp. 245–248.
[30] , “On the Distribution of Points in a Cube and the Approximate Evaluation of Integrals,” USSR Computational Mathematics and Mathematical Physics, Vol. 7, No. 4, 1967, pp. 86–112. https://doi.org/10.1016/0041-5553(67)90144-9
[31] , “The DLR TAU-Code: Recent Applications in Research and Industry,” European Conference on Computational Fluid Dynamics, ECCOMAS CFD, TU Delft, Delft, Netherlands, 2006.
[32] , “The FlowSimulator—A Software Framework for CFD-Related Multidisciplinary Simulations,” European NAFEMS Conference Computational Fluid Dynamics (CFD)—Beyond the Solve, NAFEMS, Glasgow, U.K., 2015.
[33] , “Modifications and Clarifications for the Implementation of the Spalart-Allmaras Turbulence Model,” Seventh International Conference on Computational Fluid Dynamics (ICCFD7), ICCFD, Big Island, HI, 2012, pp. 1–11.
[34] , “Computational Aeroelastic Investigation of a Transonic Limit-Cycle-Oscillation Experiment at a Transport Aircraft Wing Model,” Journal of Fluids and Structures, Vol. 49, 2014, pp. 223–241. https://doi.org/10.1016/j.jfluidstructs.2014.04.014
[35] , “Gust Response: Simulation of an Aeroelastic Experiment by a Fluid–Structure Interaction Method,” Journal of Fluids and Structures, Vol. 38, 2013, pp. 290–302. https://doi.org/10.1016/j.jfluidstructs.2012.12.007
[36] , “Non-Linear Reduced Order Models for Steady Aerodynamics,” Procedia Computer Science, Vol. 1, No. 1, 2010, pp. 165–174. https://doi.org/10.1016/j.procs.2010.04.019
[37] , “Algorithm 247: Radical-Inverse Quasi-Random Point Sequence,” Communications of the ACM, Vol. 7, No. 12, 1964, pp. 701–702. https://doi.org/10.1145/355588.365104
[38] , “Summary of Data from the Sixth AIAA CFD Drag Prediction Workshop: Case 5 (Coupled Aero-Structural Simulation),” AIAA Science and Technology Forum and Exhibition (SciTech), AIAA Paper 2017-1207, 2017.
[39] , “DLR Results of the Sixth AIAA Computational Fluid Dynamics Drag Prediction Workshop,” AIAA Aviation and Aeronautics Forum and Exposition (AVIATION), AIAA Paper 2017-4232, 2017.
[40] , “Validation and Assessment of Turbulence Model Impact for Fluid-Structure Coupled Computations of the NASA CRM,” CEAS Aeronautical Journal: 5th CEAS Air and Space Conference, Council of European Aerospace Societies (CEAS) Paper 103, 2015.
