Fast pressure distribution prediction of airfoils using deep learning

Abstract In the aerodynamic design, optimization of the pressure distribution of airfoils is crucial for the aerodynamic components. Conventionally, the pressure distribution is solved by computational fluid dynamics, which is a time-consuming task. Surrogate modeling can leverage such expense to some extent, but it needs careful shape parameterization schemes for airfoils. As an alternative, deep learning approximates inputs-outputs mapping without solving the efficiency-expensive physical equations and avoids the limitations of particular parameterization methods. Therefore, this paper presents a data-driven approach for predicting the pressure distribution over airfoils based on Convolutional Neural Network (CNN). Given the airfoil geometry, a supervised learning problem is presented for predicting aerodynamic performance. Furthermore, we utilize a universal and flexible parametrization method called Signed Distance Function to improve the performances of CNN. Given the unseen airfoils from the validation dataset to the trained model, our model achieves predicting the pressure coefficient in seconds, with a less than 2% mean square error.

[1]  Jinlong Wu,et al.  Physics-informed machine learning approach for augmenting turbulence models: A comprehensive framework , 2018, Physical Review Fluids.

[2]  José C. Páscoa,et al.  ANN assisted flow modeling and analysis for a cyclorotor in ground effect , 2019 .

[3]  Nateri K. Madavan,et al.  AERODYNAMIC DESIGN USING NEURAL NETWORKS , 2000 .

[4]  Yoshua Bengio,et al.  Deep Sparse Rectifier Neural Networks , 2011, AISTATS.

[5]  J. Templeton Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty , 2015 .

[6]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1989, Math. Control. Signals Syst..

[7]  Slawomir Koziel,et al.  Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction , 2010, J. Comput. Sci..

[8]  K. Duraisamy,et al.  Using field inversion to quantify functional errors in turbulence closures , 2016 .

[9]  Prakash Vedula,et al.  Data-driven deconvolution for large eddy simulations of Kraichnan turbulence , 2018, Physics of Fluids.

[10]  Nando de Freitas,et al.  Taking the Human Out of the Loop: A Review of Bayesian Optimization , 2016, Proceedings of the IEEE.

[11]  Gang Sun,et al.  Artificial neural network based inverse design: Airfoils and wings , 2015 .

[12]  Zhonghua Han,et al.  Surrogate-based aerodynamic shape optimization of hypersonic flows considering transonic performance , 2019, Aerospace Science and Technology.

[13]  Gang Sun,et al.  Application of deep learning based multi-fidelity surrogate model to robust aerodynamic design optimization , 2019, Aerospace Science and Technology.

[14]  Karthik Duraisamy,et al.  Turbulence Modeling in the Age of Data , 2018, Annual Review of Fluid Mechanics.

[15]  Oliver Hennigh,et al.  Lat-Net: Compressing Lattice Boltzmann Flow Simulations using Deep Neural Networks , 2017, 1705.09036.

[16]  Ken Perlin,et al.  Accelerating Eulerian Fluid Simulation With Convolutional Networks , 2016, ICML.

[17]  T. P. Miyanawala,et al.  An Efficient Deep Learning Technique for the Navier-Stokes Equations: Application to Unsteady Wake Flow Dynamics , 2017, 1710.09099.

[18]  A. Kharal,et al.  Neural networks based airfoil generation for a given Cp using Bezier–PARSEC parameterization , 2012 .

[19]  Paolo Mantegazza,et al.  Nonlinear aerodynamic reduced order modeling by discrete time recurrent neural networks , 2015 .

[20]  Sergey Ioffe,et al.  Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift , 2015, ICML.

[21]  Arthur Rizzi,et al.  Reynolds Stress Transport Modeling of Transonic Flow Around the RAE2822 Airfoil , 1994 .

[22]  Thomas J. Santner,et al.  Design and analysis of computer experiments , 1998 .

[23]  Vincenzo Pesce,et al.  Radial basis function neural network aided adaptive extended Kalman filter for spacecraft relative navigation , 2020, Aerospace Science and Technology.

[24]  G. Matheron Principles of geostatistics , 1963 .

[25]  X. Liu,et al.  Modeling Multiresponse Surfaces for Airfoil Design with Multiple-Output-Gaussian-Process Regression , 2014 .

[26]  Karthik Duraisamy,et al.  Prediction of aerodynamic flow fields using convolutional neural networks , 2019, Computational Mechanics.

[27]  Sabine Coquillart,et al.  Extended free-form deformation: a sculpturing tool for 3D geometric modeling , 1990, SIGGRAPH.

[28]  Karthik Duraisamy,et al.  Status, Emerging Ideas and Future Directions of Turbulence Modeling Research in Aeronautics , 2017 .

[29]  Yao Zhang,et al.  Application of Convolutional Neural Network to Predict Airfoil Lift Coefficient , 2017, ArXiv.

[30]  Boo Cheong Khoo,et al.  Fast flow field prediction over airfoils using deep learning approach , 2019, Physics of Fluids.

[31]  Xun Huan,et al.  Towards Real-Time In-Flight Ice Detection Systems via Computational Aeroacoustics and Machine Learning , 2019, AIAA Aviation 2019 Forum.

[32]  Raphael David Aquilino Bacchi,et al.  The use of the Reynolds force vector in a physics informed machine learning approach for predictive turbulence modeling , 2019, Computers & Fluids.

[33]  Joseph Morlier,et al.  Gaussian Process for Aerodynamic Pressures Prediction in Fast Fluid Structure Interaction Simulations , 2017 .

[34]  G. Tryggvason,et al.  Using statistical learning to close two-fluid multiphase flow equations for a simple bubbly system , 2015 .

[35]  Pierre Sagaut,et al.  A surrogate-model based multidisciplinary shape optimization method with application to a 2D subsonic airfoil , 2007 .

[36]  Gang Wang,et al.  Convolutional recurrent neural networks: Learning spatial dependencies for image representation , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW).

[37]  Linyang Zhu,et al.  Machine learning methods for turbulence modeling in subsonic flows around airfoils , 2018, Physics of Fluids.

[38]  Aleksander Madry,et al.  How Does Batch Normalization Help Optimization? (No, It Is Not About Internal Covariate Shift) , 2018, NeurIPS.

[39]  Jimmy Ba,et al.  Adam: A Method for Stochastic Optimization , 2014, ICLR.

[40]  M. Stein Large sample properties of simulations using latin hypercube sampling , 1987 .

[41]  Mengqi Zhang,et al.  Inverse Design of Airfoil Using a Deep Convolutional Neural Network , 2019, AIAA Journal.

[42]  Masakazu Matsugu,et al.  Subject independent facial expression recognition with robust face detection using a convolutional neural network , 2003, Neural Networks.

[43]  W. Haase EUROVAL : an European initiative on validation of CFD codes : results of the EC/BRITE-EURAM project EUROVAL, 1990-1992 , 1993 .

[44]  Hong Liu,et al.  Deep learning based short-term air traffic flow prediction considering temporal–spatial correlation , 2019, Aerospace Science and Technology.

[45]  Xiangyang Wang,et al.  Aerodynamic shape optimization using a novel optimizer based on machine learning techniques , 2019, Aerospace Science and Technology.

[46]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[47]  Wei Li,et al.  Convolutional Neural Networks for Steady Flow Approximation , 2016, KDD.

[48]  Stuart S. Ochs,et al.  CFD calculations of S809 aerodynamic characteristics , 1997 .

[49]  Brian J. German,et al.  A Convolutional Neural Network Approach to Training Predictors for Airfoil Performance , 2017 .

[50]  L Krist Sherrie,et al.  CFL3D User''s Manual (Version 5.0) , 1998 .

[51]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[52]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[53]  Hui Li,et al.  Prediction model of velocity field around circular cylinder over various Reynolds numbers by fusion convolutional neural networks based on pressure on the cylinder , 2018 .