基于无监督学习的飞行器表面网格平滑方法

doi:10.7527/S1000-6893.2025.31172

Abstract

Abstract:

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.

Key words: aircraft design, mesh smoothing, local surface fitting, optimization-based smoothing method, unsupervised learning

CLC Number:

V211.7

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 Aeronautica et Astronautica Sinica, 2025, 46(10): 631172.

Figures/Tables 14

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网格单元大小	网格点数量	网格单元数量
0.10	4 885	4 744
0.25	826	767
0.50	255	224

平滑方法	归一化雅可比
平滑方法	案例1	案例2	案例3
Laplacian平滑方法	0.94	0.97	0.98
基于角度的平滑方法	0.83	0.95	0.97
CVT平滑方法	0.89	0.96	0.97
优化式平滑方法	0.88	0.95	0.97
NN-Smoothing平滑方法	0.89	0.96	0.97
GMSNet3D	0.91	0.97	0.98

方法	N	时间效率
投影方法	25	3.00×10^-4
	100	9.49×10^-4
	400	3.43×10^-3
	10 000	9.44×10^-2
局部曲面坐标变换		2.17×10^-5

平滑方法	计算投影（变换）前坐标	平滑总时间
Laplacian平滑方法	4.87×10^-5	3.48×10^-3
基于角度的平滑方法	3.07×10^-4	3.74×10^-3
CVT平滑方法	5.05×10^-2	5.39×10^-2
优化式平滑方法	4.49×10^-2	4.83×10^-2
NN-Smoothing平滑方法	7.14×10^-5	3.50×10^-3
GMSNet3D	1.60×10^-3	1.62×10^-3

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A surface mesh smoothing method for aircraft based on unsupervised learning

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