Deep Learning Method of Flow Time History for Optimizing Position of Vortex Flowmeter Probes

doi:10.3969/j.issn.1004-132X.2026.05.010

Abstract

Abstract:

A vortex flowmeter used the time-varying features of the wake flow around a blunt body to measure flow field. A reasonable probe position might obtain a more robust flow signal， which improved signal processing and measurement accuracy. Based on the deep learning of flow time history data， a probe positioning optimization method was proposed to address the probe location issue in vortex flowmeters. The method was illustrated by using the flow around a triangular prism vortex generator. Feature dimensionality reduction was performed on the flow time history dataset and a comprehensive analysis of the time-varying flow features at the numerous measurement points within the wake was realized. Then， clustering analysis was applied to the low-dimensional representation codes to identify spatial distributions with similar time-varying characteristics. Finally， by analyzing the flow characteristics of different categories， the significant regions of measured variable signals were obtained as the reasonable layout regions for the measuring points of the vortex flowmeters. The results show that the proposed method may provide a finer measurement point layout scheme than that of the traditional methods. And the reasonable sizes of the probes may be obtained according to the sizes of the characteristic areas， providing a new method for the design of vortex flowmeters.

Key words: vortex flowmeter, position of probe, flow time history deep learning, flow feature

摘要：

涡街流量计利用钝体尾流时变特性进行流场测量，合理的探头位置能够测得特征更强的流场数据，有助于信号处理及测量精度的提高。针对涡街流量计探头布设位置问题，提出了基于流场时程信号深度学习的探头位置优化方法。以三棱柱发生体的绕流场为例，对流场时程大数据集开展特征降维，以实现尾流中大量测点的流动时变特征的全面分析；然后对低维表征编码进行聚类，得到具有相似时变特征的位置分布；最后分析不同类别的流动区域特征，得到待测变量信号显著区域作为涡街流量计的测点合理布置区域。研究结果表明，所提出的流场时程信号深度学习方法能够得到比传统经验更精细的测点布置方案，同时能根据特征区域的大小得到探头的合理尺寸，为涡街流量计的设计提供了新的方法。

关键词: 涡街流量计, 探头位置, 流场时程深度学习, 流动特征

CLC Number:

TH814

ZHAN Qingliang, CAO Zihan, WANG Zhiyong, BAI Chunjin, LIU Xin. Deep Learning Method of Flow Time History for Optimizing Position of Vortex Flowmeter Probes[J]. China Mechanical Engineering, 2026, 37(5): 1105-1110.

战庆亮, 曹子涵, 王智勇, 白春锦, 刘鑫. 涡街流量计探头位置优化的流场时程深度学习方法[J]. 中国机械工程, 2026, 37(5): 1105-1110.

Figures/Tables 13

Fig.1 Computational domain and mesh distribution

Fig.2 Arrangement scheme of sampling positions

Fig.3 Time history samples of 6 randomly selected measuring points

Tab.1 Structural parameter of FTH-AE model

网络层	通道数	激活函数	参数量
Input Layer	1		0
Conv1	32	ReLU	640
Conv2	16	ReLU	9744
Conv3	8	ReLU	2440
Flatten	16 000		0
Dense1	10		160 000
Dense2	16 000		160 000
Reshape	8		0
Conv1_T	8	ReLU	1224
Conv2_T	16	ReLU	2448
Conv3_T	32	ReLU	9760
Output Layer	1		609

Fig.4 Loss values of model training

Fig.5 Reconstruction results of time-history samples

Fig.6 Scatter diagram of reconstruction error

Fig.7 Diagram of feature clustering methodology

Fig.8 Results of feature clustering

Fig.9 Features of samples located in different domain

Tab.2 Sample statistics of different clustering regions m/s

区域号	流向速度v_f/10 $- 3$		横向速度v_t/10 $- 3$
区域号	平均值	标准差	平均值	标准差
1	526.48	21.51	0.77	40.60
2	2.65	115.00	$-$ 127.73	64.31
3	304.48	68.90	144.13	65.76
4	341.19	61.32	9.16	215.59
5	482.38	89.39	$-$ 5.82	185.85
6	484.24	89.02	$-$ 1.55	203.01
7	478.72	87.43	$-$ 7.03	202.30
8	461.00	94.48	2.99	207.47
9	478.31	85.54	11.33	200.36

Tab.2 Sample statistics of different clustering regions m/s

区域号	流向速度v_f/10 $- 3$		横向速度v_t/10 $- 3$
区域号	平均值	标准差	平均值	标准差
1	526.48	21.51	0.77	40.60
2	2.65	115.00	$-$ 127.73	64.31
3	304.48	68.90	144.13	65.76
4	341.19	61.32	9.16	215.59
5	482.38	89.39	$-$ 5.82	185.85
6	484.24	89.02	$-$ 1.55	203.01
7	478.72	87.43	$-$ 7.03	202.30
8	461.00	94.48	2.99	207.47
9	478.31	85.54	11.33	200.36

Fig.10 Area distribution with larger speed fluctuation signal values

Fig.11 Overlapping areas with strong signal intensity

References 21

[1]	VENUGOPAL A， AGRAWAL A， PRABHU S V. Review on Vortex Flowmete：Designer Perspective［J］. Sensors and Actuators A： Physical， 2011， 170（1/2）： 8-23.
[2]	PENG J， FU X， CHEN Y. Flow Measurement by a New Type Vortex Flowmeter of Dual Triangulate Bluff Body［J］. Sensors and Actuators A： Physical， 2004， 115（1）： 53-59.
[3]	FU X， YANG H. Study on Hydrodynamic Vibration in Dual Bluff Body Vortex Flowmeter［J］. Chinese Journal of Chemical Engineering， 2001， 20（2）： 123-128.
[4]	CAMBIER P， VANDERMARLIÈRE S， LAVANTE E， et al. Numerical and Experimental Study of Effects of Upstream Disturbance on Accuracy of Vortex-shedding Flow Meter［C］∥19th IMEKO World Congress. Lisbon， 2009：1321-1325.
[5]	REIK M， HÖCKER R， BRUZZESE C， et al. Flow Rate Measurement in a Pipe Flow by Vortex Shedding［J］. Forschung Im Ingenieurwesen， 2010， 74（2）： 77-86.
[6]	CHEN J， LI K， WAN S X， et al. Multi-channel Signal Processing Method for Vortex Flowmeter Based on Parallel Filtering［J］. Flow Measurement and Instrumentation， 2025，106： 103010.
[7]	LI B， WANG C， CHEN J. A Frequency-correcting Method for a Vortex Flow Sensor Signal Based on a Central Tendency［J］. Sensors， 2020， 20（18）： 5379.
[8]	XU Kejun， LUO Qinglin， WANG Gang， et al. Frequency-feature Based Antistrong-disturbance Signal Processing Method and System for Vortex Flowmeter with Single Sensor［J］. Review of Scientific Instruments， 2010， 81（7）： 075104.
[9]	BELLOLI M， GIAPPINO S， MUGGIASCA S， et al. Force and Wake Analysis on a Single Circular Cylinder Subjected to Vortex Induced Vibrations at High Mass Ratio and High Reynolds Number［J］. Journal of Wind Engineering and Industrial Aerodynamics， 2012， 103： 96-106.
[10]	LUO S C， TONG X H， KHOO B C. Transition Phenomena in the Wake of a Square Cylinder［J］. Journal of Fluids and Structures， 2007， 23（2）： 227-248.
[11]	SAHA A K， MURALIDHAR K， BISWAS G. Experimental Study of Flow Past a Square Cylinder at High Reynolds Numbers［J］. Experiments in Fluids， 2000， 29（6）： 553-563.
[12]	ZHOU Y， ANTONIA R A. A Study of Turbulent Vortices in the Near Wake of a Cylinder［J］. Journal of Fluid Mechanics， 1993， 253： 643-661.
[13]	NORBERG C. An Experimental Investigation of the Flow around a Circular Cylinder： Influence of Aspect Ratio［J］. Journal of Fluid Mechanics， 1994， 258： 287-316.
[14]	ROSHKO A. Experiments on the Flow Past a Circular Cylinder at Very High Reynolds Number［J］. Journal of Fluid Mechanics， 1961， 10（3）： 345-356.
[15]	BRUNTON S L， NOACK B R， KOUMOUTSAKOS P. Machine Learning for Fluid Mechanics［J］. Annual Review of Fluid Mechanics， 2020， 52： 477-508.
[16]	战庆亮，刘鑫，白春锦，等. 三维高分辨率流场重构的深度学习方法［J］. 机械工程学报， 2025， 61（16）： 338-346.
	ZHAN Qingliang， LIU Xin， BAI Chunjin， et al. 3D High-resolution Flow Reconstruction Based on Deep Learning［J］. Journal of Mechanical Engineering， 2025， 61（16）： 338-346.
[17]	ZHAN Q， BAI C， LIU X， et al. Reduced-order Representation and Reconstruction of Non-stationary Flow System Using Flow-time-history Deep Learning［J］. Acta Mechanica Sinica， 2023， 39（10）： 322491.
[18]	战庆亮，白春锦，葛耀君. 基于时程深度学习的流场特征分析方法［J］. 力学学报， 2022， 54（3）： 822-828.
	ZHAN Qingliang， BAI Chunjin， GE Yaojun. Fluid Feature Analysis Based on Time History Deep Learning［J］. Chinese Journal of Theoretical and Applied Mechanics， 2022， 54（3）： 822-828.
[19]	战庆亮，刘鑫，白春锦，等. 工程流动模拟中转角附近网格的划分策略比较［J］. 工程力学， 2025， 42（6）： 1-10.
	ZHAN Qingliang， LIU Xin， BAI Chunjin， et al. Comparison of Meshing Strategies at Corners in Engineering Flow Simulation［J］. Engineering Mechanics， 2025， 42（6）： 1-10.
[20]	ZHAN Q， BAI C， GE Y， et al. Flow Time History Representation and Reconstruction Based on Machine Learning［J］. Physics of Fluids， 2023， 35（8）： 087106.
[21]	ZHAN Q， LIU X， BAI C， et al. Flow Time History Deep Learning for Feature Decomposition and Disentanglement［J］. Physica D： Nonlinear Phenomena， 2025， 472： 134470.