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Flow analysis and low-dimensional representation model is of great significance in studying the complex flow mechanism. However, the turbulent flow field has complex and unstable spatiotemporal evolution feature, and it is difficult to establish the low-dimensional representation model for the flow big data. A low-dimensional representation model of complex flow is proposed and verified based on the flow time-history deep learning method. One-dimensional linear convolution, nonlinear full connection and nonlinear convolution autoencoding methods are established to reduce the dimension of unsteady flow time history data. The decoding mapping from low-dimensional space to time domain is obtained to build the representation model for turbulence. The proposed method is verified by using flow around the square clyinder with Re = 2.2×104. The results show that the flow time-history deep learning method can be used to effectively realize the low-dimensional representation of the flow and is suitable for solving the complex turbulent flow problems; the nonlinear one-dimensional convolutional autoencoder is superior to the full connection and linear convolution methods in representing the complex flow features. The method in this work is an unsupervised training method, which can be widely used in single-point-based sensor data processing, and is a new method to study the characteristics of turbulence and complex flow problems.
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Keywords:
- time-history deep learning /
- dimensionality reduction of flow data /
- convolution neural network /
- turbulent flow field /
- flow representation
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图 1 数据示意图
Figure 1. Data type for modeling.
图 2 整体计算域及平面网格划分 (a) 整体计算域; (b) 局部网格
Figure 2. Global computational domain and plane grid settings: (a) Global computing domain; (b) local mesh.
图 3 数值模拟结果 (a) 升力与阻力系数; (b) z = 0切面瞬时速度矢量图; (c) y = 0切面瞬时速度矢量图; (d) x = 2切面瞬时速度矢量图
Figure 3. Partial results of simulation: (a) Lift and drag coefficient; (b) sectional instantaneous velocity vector diagram at z = 0; (c) sectional instantaneous velocity vector diagram at y = 0; (d) sectional instantaneous velocity vector diagram at x = 2.
图 4 测点分布及时程结果 (a) 测点布置位置; (b) 部分测点的流向速度结果
Figure 4. Distributions of monitoring points and time history results: (a) Layout position of measure points; (b) flow velocity of some measure points.
图 5 表征模型的原理
Figure 5. Methodology of the representation model.
图 6 训练集的模型损失值 (a) 流向速度; (b) 横向速度; (c) 展向速度; (d) 速度绝对值
Figure 6. Loss function of different models on training set: (a) Flow velocity; (b) lateral velocity; (c) spanwise velocity; (d) absolute value of velocity.
图 7 线性卷积模型的误差分布 (a) 流向速度; (b) 横向速度; (c) 展向速度; (d) 速度绝对值
Figure 7. Distributions of relatively error using LCN-AE: (a) Flow velocity; (b) lateral velocity; (c) spanwise velocity; (d) absolute value of velocity.
图 8 全连接模型的误差分布 (a) 流向速度; (b) 横向速度; (c) 展向速度; (d) 速度绝对值
Figure 8. Distribution of relatively error using MLP-AE: (a) Flow velocity; (b) lateral velocity; (c) spanwise velocity; (d) absolute value of velocity.
图 9 非线性卷积模型的误差分布 (a) 流向速度; (b) 横向速度; (c) 展向速度; (d) 速度绝对值
Figure 9. Distributions of relatively error using NCN-AE: (a) Flow velocity; (b) lateral velocity; (c) spanwise velocity; (d) absolute value of velocity.
图 10 不同模型的误差散点图均值
Figure 10. Mean relatively error of different models.
图 11 原始时程与重构时程的比较 (a) 流向速度; (b) 横向速度; (c) 展向速度; (d) 速度绝对值; (e) 流向速度的局部视图; (f) 横向速度的局部视图; (g) 展向速度的局部视图; (h) 速度绝对值的局部视图
Figure 11. Comparision of original and reconstructed flow time history samples: (a) Flow velocity; (b) lateral velocity; (c) spanwise velocity; (d) absolute value of velocity; (e) partial view of flow velocity; (f) partial view of lateral velocity; (g) partial view of spanwise velocity; (h) partial view of absolute value of velocity.
表 1 非线性卷积自动编码模型参数
Table 1. NCN-AE model parameters.
名称 滤波器个数 非线性激活方法 Input — — Conv 1 64 ReLU Conv 2 32 ReLU Conv 3 20 ReLU Flatten layer — — Dense layer 20 ReLU Code layer 20 ReLU Dense layer2 20000 Reshape layer — — Conv_T 1 20 ReLU Conv_T 2 32 ReLU Conv_T 3 64 ReLU Output 1 ReLU 
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表 2 全连接自动编码模型参数
Table 2. MLP-AE model parameters.
名称 神经元数 非线性激活方法 Input — — Dense 1 64 ReLU Dense 2 32 ReLU Dense 3 20 ReLU Flatten layer — — Dense layer 20 ReLU Code layer 20 ReLU Dense layer2 20000 Reshape layer — — Dense 1 20 ReLU Dense 2 32 ReLU Dense 3 64 ReLU Output 1 ReLU
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表 3 不同模型的误差散点图均值
Table 3. Mean relatively error of different models.
流场参数 LCN-AE MLP-AE NCN-AE 流向速度 0.0554 0.0306 0.0104 横向速度 0.0532 0.0192 0.0076 展向速度 0.0621 0.0199 0.0039 速度绝对值 0.0585 0.0310 0.0122
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[1] Berkooz G, Holmes P, Lumley J L 1993 Annu. Rev. Fluid Mech. 25 539
Google Scholar
[2] Sirovich L 1987 Q. Appl. Math. 45 561
Google Scholar
[3] Schmid P J, Sesterhenn J 2010 J. Fluid Mech. 656 5
Google Scholar
[4] Clarence W R, Igor M, Shervin B, Philipp S, Dan S H 2009 J. Fluid Mech. 641 115
Google Scholar
[5] 金晓威, 赖马树金, 李惠 2021 力学学报 53 2616
Google Scholar
Jin X W, Lai M S J, Li H 2021 Chin. J. Theor. Appl. Mech. 53 2616
Google Scholar
[6] Ling J, Kurzawski A, Templeton J 2016 J. Fluid Mech. 807 155
Google Scholar
[7] Li B, Yang Z, Zhang X, He G, Shen L 2020 J. Fluid Mech. 905 A10
Google Scholar
[8] Raissi M, Karniadakis G E 2018 J. Comput. Phys. 357 125
Google Scholar
[9] Kim H, Kim J, Won S, Lee C 2021 J. Fluid Mech. 910 A29
Google Scholar
[10] Murata T, Fukami K, Fukagata K 2020 J. Fluid Mech. 882 A13
Google Scholar
[11] Omata N, Shirayama S 2019 AIP Adv. 9 015006
Google Scholar
[12] Fukami K, Fukagata K, Taira K 2021 J. Fluid Mech. 909 A9
Google Scholar
[13] Liu B, Tang J, Huang H B, Lu X Y 2020 Phys. Fluids 32 025105
Google Scholar
[14] Callaham J, Maeda K, Brunton S L 2019 Phys. Rev. Fluids 4 103907
Google Scholar
[15] Fukami K, Maulik R, Ramachandra N, Fukagata K, Taira K 2021 Nat. Mach. Intell. 3 945
Google Scholar
[16] Erichson N B, Mathelin L, Yao Z W, Brunton S L, Maboney M W, Kutz J N 2020 Proc. R. Soc. A: Math. Phys. Eng. Sci. 476 20200097
Google Scholar
[17] Deng Z W, Chen Y J, Liu Y Z, Kim K C 2019 Phys. Fluids 31 075108
Google Scholar
[18] Han R K, Wang Y X, Zhang Y, Chen C 2019 Phys. Fluids 31 127101
Google Scholar
[19] Fukami K, Fukagata K, Taira K 2020 Theor. Comput. Fluid Dyn. 34 497
Google Scholar
[20] 战庆亮, 白春锦, 葛耀君 2022 力学学报 54 822
Google Scholar
Zhan Q L, Bai C J, Ge Y J 2022 Chin. J. Theor. Appl. Mech. 54 822
Google Scholar
[21] 战庆亮, 白春锦, 张宁, 葛耀君 2022 航空学报 43 126531
Google Scholar
Zhan Q L, Bai C J, Zhang N, Ge Y J 2022 Acta Aeronaut. Astronaut. Sin. 43 126531
Google Scholar
[22] 战庆亮, 葛耀君, 白春锦 2022 71 074701
Google Scholar
Zhan Q L, Ge Y J, Bai C J 2022 Acta Phys. Sin. 71 074701
Google Scholar
[23] 战庆亮, 周志勇, 葛耀君 2015 哈尔滨工业大学学报 47 75
Google Scholar
Zhan Q L, Zhou Z Y, Ge Y J 2015 J. Harbin Inst. Technol. 47 75
Google Scholar
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