基于注意力机制的翼型反设计方法

王超杰; 何磊; 李川; 钱炜祺; 黄友翔

doi:10.13224/j.cnki.jasp.20230106

基于注意力机制的翼型反设计方法

doi: 10.13224/j.cnki.jasp.20230106

王超杰^{1, 2,},
何磊²,
李川^1,*, ,,
钱炜祺²,
黄友翔^{1, 2}

1.
四川大学计算机学院（软件学院），成都 610065
2.
中国空气动力研究与发展中心计算空气动力研究所，四川绵阳 621000

详细信息

作者简介:
王超杰（1998-），男，硕士生，主要从事人工智能应用方面的研究。E-mail：chaojiew@qq.com

通讯作者:
李川（1977-），男，副教授、硕士生导师，博士，主要从事数据挖掘与知识工程、深度学习方面的研究。E-mail：lcharles@scu.edu.cn

中图分类号: V211.3
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- 文章访问数: 670
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- 被引次数: 0
出版历程
- 收稿日期: 2023-02-27
- 网络出版日期: 2024-05-31

Airfoil reverse design method based on self-attention mechanism

WANG Chaojie^{1, 2
,},
HE Lei²,
LI Chuan^{1,*
, ,},
QIAN Weiqi²,
HUANG Youxiang^{1, 2}

1.
School of Computer （School of Software），Sichuan University，Chengdu 610065，China
2.
Computational Aerodynamics Institute，China Aerodynamics Research and Development Center，Mianyang Sichuan 621000，China

摘要

摘要:
为了简化翼型反设计的过程，基于注意力机制设计了一个端到端的，应用于翼型反设计的深度学习模型，该模型可以学习到翼型曲线和压力分布之间的联系，直接输入压力分布图像就可以得到与之对应的翼型图像。生成了6561组样本，其中6000组样本用于训练，561组样本用于验证。实验结果表明：该模型在验证集上的方均根误差为0.0023，平均相对偏差为2.53%，训练耗时743.4 s，验证耗时12.18 s，预测一个翼型曲线平均耗时0.0217 s，由此表明该模型具有较高的精度和效率。
- 翼型反设计 /
- 翼型曲线 /
- 压力分布 /
- 深度学习 /
- 注意力机制
Abstract:
An end-to-end deep learning model for reverse airfoil design based on attention mechanism was proposed to simplify the reverse airfoil design process. The model could learn the relationship between the airfoil curve and the pressure distribution, and the matching airfoil picture could be generated by directly inputting the pressure distribution image. 6561 samples were generated, with 6000 used for training and 561 for validation. The model's root mean square error on the verification set was 0.0023, its average relative deviation was 2.53%, its training and verification time was 743.4 s and 12.18 s, respectively, and its average prediction time for an airfoil curve was 0.0217 s. The results demonstrated the model's high accuracy and efficiency.
- airfoil reverse design /
- airfoil curve /
- pressure distribution /
- deep learning /
- self-attention

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图 1 ViT模型结构

Figure 1. Model structure of ViT

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图 2 缩放点积注意力

Figure 2. Scaled-dot product attention

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图 3 TE层中的多头注意力机制

Figure 3. Multi-head self-attention in TE layer

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图 4 模型结构图

Figure 4. Model architecture

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图 5 翼型图和压力图

Figure 5. Airfoil curve image and pressure distribution image

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图 6 训练loss曲线

Figure 6. Training loss curve

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图 7 验证loss曲线

Figure 7. Validation loss curve

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图 8 模型预测结果

Figure 8. Prediction results of model

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表 1 模型在训练集和验证集上的误差

Table 1. Error on training set and validation set

数据集	E_RMSE	ε/%
训练集	0.001513	1.94
验证集	0.002344	2.53

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表 2 分块大小对模型精度的影响

Table 2. Effect of patch size on accuracy

块大小	E_RMSE	ε/%
10×10	0.146069	97.25
20×20	0.004077	3.88
25×25	0.003782	3.77
50×50	0.003827	3.87
注：加粗数据表示误差最小值。

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表 3 注意力机制对精度的影响

Table 3. Effect of self-attention mechanism on accuracy

块大小	注意力机制	E_RMSE	ε/%
10×10		0.143407	94.76
10×10	√	0.146069	97.25
20×20		0.012391	7.79
20×20	√	0.004077	3.88
25×25		0.011785	7.79
25×25	√	0.003782	3.77
50×50		0.011176	8.19
50×50	√	0.003827	3.87
注：①√表示使用注意力机制；②加粗数据表示最小误差。

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表 4 块嵌入层和全局特征提取层对精度的影响

Table 4. Effect of patch embedding block and global feature extraction block on accuracy

块大小	块嵌入	全局特征提取	E_RMSE	ε/%
10×10	√		0.146069	97.25
10×10	√	√	0.143435	94.78
20×20	√		0.004077	3.88
20×20	√	√	0.003259	3.33
25×25	√		0.003782	3.77
25×25	√	√	0.002344	2.53
50×50	√		0.003827	3.87
50×50	√	√	0.002485	2.61
注：①√表示使用块嵌入层或全局特征提取层；②加粗数据表示误差最小值。

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表 5 多头数目对精度的影响

Table 5. Impact of number of heads on accuracy

块大小	多头数目	E_RMSE	ε/%
25×25	2	0.002344	2.53
25×25	4	0.003255	2.75
25×25	8	0.002434	2.74
25×25	16	0.002403	2.62
25×25	32	0.002328	2.53
25×25	64	0.002427	2.59
注：加粗数据表示误差最小值。

下载: 导出CSV

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