Abstract
Airfoil shape design is one of the most fundamental elements in aircraft design. Existing airfoil design tools require at least a few minutes to analyze a new shape and hours to perform shape optimization. To drastically reduce the computational time of both analysis and design optimization, we use machine learning to create a model of a wide range of possible airfoils at a range of flight conditions, making it possible to perform airfoil design optimization in a few seconds. The machine learning consists of gradient-enhanced artificial neural networks where the gradient information is phased in gradually. This new gradient-enhanced artificial neural network approach is trained to model the aerodynamic force coefficients of airfoils in both subsonic and transonic regimes. The aerodynamics is modeled with Reynolds-averaged Navier–Stokes (RANS)-based computational fluid dynamics (CFD). The proposed approach outperforms an existing airfoil model that uses a mixture of experts technique combined with a gradient-based kriging surrogate model. The approach yields to similar airfoil shape optimization solutions than high-fidelity CFD optimization solutions with a difference of 0.01 count and 0.12 count for Cd in subsonic and transonic regimes, respectively. Airfoil optimization problems are solved in a few seconds (instead of hours using CFD-based optimization), making the design process much more interactive, as demonstrated in the Webfoil airfoil design optimization tool.
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Funding
This work was partially supported by the Air Force Office of Scientific Research (AFOSR) MURI on “Managing multiple information sources of multi-physics systems,” Program Officer Jean—Luc Cambier, Award Number FA9550-15-1-0038.
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Replication results
The codes needed for reproducing the results in this paper are available online under open-source licenses. After installing TensorFlow, the scripts to generate the results presented in this paper are available on https://data.mendeley.com/datasets/ngpd634smf/1. The Rosenbrock function test results given in Section 2.2 could be reproduced using files available in the repository “Rosenbrock.” The scripts constructing the mSANN and predicting the aerodynamic coefficients given in Section 3.2 are available in the repository “Analysis.” The optimization results given in Section 4 could be reproduced using the script files hosted in the repository “Optimization.” In addition, ADflow is available on https://github.com/mdolab/adflow for reproducing ADflow results.
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Bouhlel, M.A., He, S. & Martins, J.R.R.A. Scalable gradient–enhanced artificial neural networks for airfoil shape design in the subsonic and transonic regimes. Struct Multidisc Optim 61, 1363–1376 (2020). https://doi.org/10.1007/s00158-020-02488-5
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DOI: https://doi.org/10.1007/s00158-020-02488-5