ACTA AERONAUTICAET ASTRONAUTICA SINICA >
A surface mesh smoothing method for aircraft based on unsupervised learning
Received date: 2024-09-09
Revised date: 2024-12-10
Accepted date: 2025-01-09
Online published: 2025-02-06
Supported by
National Natural Science Foundation of China(12402349);Natural Science Foundation of Hunan Province(2024JJ6468);Youth Foundation of the National University of Defense Technology(ZK2023-11);National Key Research and Development Program of China(2021YFB0300101)
In numerical simulations for aircraft design， mesh smoothing methods are crucial for enhancing mesh quality in the preprocessing stage and reducing simulation errors. Traditional optimization-based smoothing methods are limited by complex iterative solving processes， leading to high memory consumption and low computational efficiency. To address these issues， existing intelligent smoothing methods use neural networks to learn the smoothing process， achieving a balance between smoothing efficiency and quality. However， when applied to three-dimensional surface meshes， these methods often rely on projection operations or supervised learning to ensure mesh node conformity， which introduces additional computation or data generation overhead. This study develops an intelligent smoothing surrogate model， GMSNet3D， specifically designed for aircraft surface meshes， based on unsupervised learning techniques and local surface fitting. The model uses an unsupervised loss function tailored for surface mesh smoothing， enabling intelligent training without the need for high-quality supervised data. Furthermore， the model innovatively introduces local surface coordinate transformation to ensure the conformity of smoothed mesh nodes. Experimental results demonstrate that the local surface coordinate transformation method used in the GMSNet3D model achieves a speedup of 13.82 times compared to projection operations in existing methods. Additionally， while maintaining mesh smoothing quality， GMSNet3D achieves a 29.81-fold improvement in optimization efficiency compared to traditional optimization-based smoothing methods.
Zhichao WANG , Xinhai CHEN , Liang DENG , Yang LIU , Yufei PANG , Jie LIU . A surface mesh smoothing method for aircraft based on unsupervised learning[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2025 , 46(10) : 631172 -631172 . DOI: 10.7527/S1000-6893.2025.31172
| 1 | GU X Y， CIAMPA P D， NAGEL B. An automated CFD analysis workflow in overall aircraft design applications［J］. CEAS Aeronautical Journal， 2018， 9（1）： 3-13. |
| 2 | MCCORMICK D J. An analysis of using CFD in conceptual aircraft design［D］. Blacksburg： Virginia Polytechnic Institute and State University， 2002. |
| 3 | RAJ P. Aircraft design in the 21st century-Implications for design methods?［C］?∥29th AIAA， Fluid Dynamics Conference. Reston： AIAA， 1998. |
| 4 | VIVIANI A， APROVITOLA A， PEZZELLA G， et al. CFD design capabilities for next generation high-speed aircraft［J］. Acta Astronautica， 2021， 178： 143-158. |
| 5 | KNUPP P M. Algebraic mesh quality metrics for unstructured initial meshes?［J］. Finite Elements in Analysis and Design， 2003， 39（3）： 217-241. |
| 6 | KNUPP P M. Algebraic mesh quality metrics［J］. SIAM Journal on Scientific Computing， 2001， 23（1）： 193-218. |
| 7 | KNUPP P. Remarks on mesh quality?［R］. Albuquerque： Sandia National Lab.， 2007. |
| 8 | PRASAD T. A comparative study of mesh smoothing methods with flipping in 2D and 3D［D］. Camden： Rutgers University-Camden Graduate School， 2018. |
| 9 | FIELD D A. Laplacian smoothing and delaunay triangulations?［J］. Communications in Applied Numerical Methods， 1988， 4（6）： 709-712. |
| 10 | ZHOU T X， SHIMADA K. An angle-based approach to two-dimensional mesh smoothing?［C］?∥International Meshing Roundtable Conference， 2000. Albuquerque： Sandia National Laboratories， 2000： 373-384. |
| 11 | VARTZIOTIS D， PAPADRAKAKIS M. Improved GETMe by adaptive mesh smoothing［J］. Computer Assisted Methods in Engineering and Science， 2017， 20（1）： 55-71. |
| 12 | SCOTT A CANANN S A SA， TRISTANO J J R， STATEN M M L. An approach to combined Laplacian and optimization-based smoothing for triangular， quadrilateral， and quad-dominant meshes［J］. 7th International Meshing Roundtable， 1998： 479-494. |
| 13 | WANG J， YU Z Y. Quality mesh smoothing via local surface fitting and optimum projection?［J］. Graphical Models， 2011， 73（4）： 127-139. |
| 14 | PARTHASARATHY V N， KODIYALAM S. A constrained optimization approach to finite element mesh smoothing?［J］. Finite Elements in Analysis and Design， 1991， 9（4）： 309-320. |
| 15 | GUO Y F， WANG C R， MA Z， et al. A new mesh smoothing method based on a neural network［J］. Computational Mechanics， 2022， 69（2）： 425-438. |
| 16 | WANG Z C， CHEN X H， YAN J J， et al. Proposing an intelligent mesh smoothing method with graph neural networks［DB/OL］. arXiv Preprint： 2311.12815， 2023. |
| 17 | WANG N H， ZHANG L P， DENG X G. Unstructured surface mesh smoothing method based on deep reinforcement learning?［J］. Computational Mechanics， 2024， 73（2）： 341-364. |
| 18 | DU Q， GUNZBURGER M. Grid generation and optimization based on centroidal Voronoi tessellations?［J］. Applied Mathematics and Computation， 2002， 133（2-3）： 591-607. |
| 19 | DU Q， WANG D S. Tetrahedral mesh generation and optimization based on centroidal Voronoi tessellations［J］. International Journal for Numerical Methods in Engineering， 2003， 56（9）： 1355-1373. |
| 20 | CHEN X H， LIU J， GONG C Y， et al. MVE-net： an automatic 3-D structured mesh validity evaluation framework using deep neural networks?［J］. Computer-Aided Design， 2021， 141： 103104. |
| 21 | CHEN X H， LI T J， WAN Q， et al. MGNet： a novel differential mesh generation method based on unsupervised neural networks?［J］. Engineering with Computers， 2022， 38（5）： 4409-4421. |
| 22 | ZHANG Z Y， JIMACK P K， WANG H. MeshingNet3D： Efficient generation of adapted tetrahedral meshes for computational mechanics［J］. Advances in Engineering Software， 2021， 157： 103021. |
| 23 | WANG Z C， CHEN X H， LI T J， et al. Evaluating mesh quality with graph neural networks［J］. Engineering with Computers， 2022， 38（5）： 4663-4673. |
| 24 | ALLIEGRO A， SIDDIQUI Y， TOMMASI T， et al. PolyDiff： Generating 3D polygonal meshes with diffusion models［DB/OL］. arXiv preprint： 2312.11417， 2023. |
| 25 | CROITORU F A， HONDRU V， IONESCU R T， et al. Diffusion models in vision： A survey［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence， 2023， 45（9）： 10850-10869. |
| 26 | SIDDIQUI Y， ALLIEGRO A， ARTEMOV A， et al. MeshGPT： Generating triangle meshes with decoder-only transformers?［DB/OL］. arXiv preprint： 2311.15475， 2023. |
| 27 | YUE H J， LI Z Y， XU K R， et al. Three-dimensional hyperbolic mesh generation method based on the neural network［J］. Applied Sciences， 2024， 14（24）： 11931. |
| 28 | SONG W B， ZHANG M R， WALLWORK J G， et al. M2N： Mesh movement networks for PDE solvers［DB/OL］. arXiv preprint： 2204.11188， 2022. |
| 29 | DURKAN C， BEKASOV A， MURRAY I， et al. Neural spline flows［DB/OL］. arXiv preprint： 1906.04032， 2019. |
| 30 | VELI?KOVI? P， CUCURULL G， CASANOVA A， et al. Graph attention networks?［DB/OL］. arXiv preprint： 1710.10903， 2017. |
| 31 | ZHANG M R， WANG C Y， KRAMER S， et al. Towards universal mesh movement networks?［DB/OL］. arXiv preprint： 2407.00382， 2024. |
| 32 | WIERING M， VAN OTTERLO M. Reinforcement learning： State-of-the-art： Issue 12［M］. Berlin， Heidelberg： Springer， 2012. |
| 33 | MARSCHNER S， SHIRLEY P. Fundamentals of Computer Graphics?［J］. 4th ed. Boca Raton： A K Peters/CRC Press， 2018. |
| 34 | WU Z H， PAN S R， CHEN F W， et al. A comprehensive survey on graph neural networks［J］. IEEE Transactions on Neural Networks and Learning Systems， 2021， 32（1）： 4-24. |
| 35 | DIKE H U， ZHOU Y， DEVEERASETTY K K， et al. Unsupervised learning based on artificial neural network： A review?［C］?∥2018 IEEE International Conference on Cyborg and Bionic Systems （CBS）. Piscataway： IEEE Press， 2018： 322-327. |
| 36 | GORDON W J， RIESENFELD R F. B-spline curves and surfaces?［M］?∥Computer Aided Geometric Design. Amsterdam： Elsevier， 1974： 95-126. |
| 37 | RAMPá?EK L， GALKIN M， DWIVEDI V P， et al. Recipe for a general， powerful， scalable graph transformer［DB/OL］. arXiv preprint： 2205.12454， 2022. |
| 38 | SHI Y S， HUANG Z J， FENG S K， et al. Masked label prediction： unified message passing model for semi-supervised classification?［DB/OL］. arXiv preprint： 2009.03509， 2020. |
| 39 | SORGENTE T， BIASOTTI S， MANZINI G， et al. A survey of indicators for mesh quality assessment?［J］. Computer Graphics Forum， 2023， 42（2）： 461-483. |
| 40 | DOZAT T. Incorporating nesterov momentum into adam［C］?∥Proceedings of the 4th International Conference on Learning Representations （ICLR）. 2016. |
/
| 〈 |
|
〉 |
CJA