A Mathematical Method for Predicting Tunnel Pressure Waves Based on Train Wave Signature and Graph Theory

Previous research has demonstrated that the Train Wave Signature (TWS) method enables rapid calculation of pressure waves in straight tunnels. However, its application to subway tunnels with complex structural features remains insufficiently explored. This study proposes a generalized mathematical m...

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Main Authors: Xu Zhang, Haiquan Bi, Honglin Wang, Yuanlong Zhou, Nanyang Yu, Jizhong Yang, Yao Jiang
Format: Article
Language:English
Published: MDPI AG 2025-07-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/13/15/2360
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author Xu Zhang
Haiquan Bi
Honglin Wang
Yuanlong Zhou
Nanyang Yu
Jizhong Yang
Yao Jiang
author_facet Xu Zhang
Haiquan Bi
Honglin Wang
Yuanlong Zhou
Nanyang Yu
Jizhong Yang
Yao Jiang
author_sort Xu Zhang
collection DOAJ
description Previous research has demonstrated that the Train Wave Signature (TWS) method enables rapid calculation of pressure waves in straight tunnels. However, its application to subway tunnels with complex structural features remains insufficiently explored. This study proposes a generalized mathematical method integrating TWS with graph theory for the simulation of pressure wave generation, propagation, and reflection in complex tunnel systems. A computational program is implemented using this method for efficient simulation. The proposed method achieves high-accuracy prediction of pressure waves in tunnels with complex geometries compared with field measurements conducted in a high-speed subway tunnel with two shafts. We discuss the impact of iteration time intervals on the results and clarify the minimum time interval required for the calculation. Moreover, the sin-type definition of TWSs enhances the precision of pressure gradient prediction, and omitting low-amplitude pressure and reflected waves from the train can improve computational efficiency without compromising accuracy. This study advances the application of TWSs in tunnels with complex structures and provides a practical solution for aerodynamic analysis in high-speed subway tunnels, balancing accuracy with computational efficiency.
format Article
id doaj-art-81313f245b06478bbb40da0897a5cd8b
institution DOAJ
issn 2227-7390
language English
publishDate 2025-07-01
publisher MDPI AG
record_format Article
series Mathematics
spelling doaj-art-81313f245b06478bbb40da0897a5cd8b2025-08-20T03:02:58ZengMDPI AGMathematics2227-73902025-07-011315236010.3390/math13152360A Mathematical Method for Predicting Tunnel Pressure Waves Based on Train Wave Signature and Graph TheoryXu Zhang0Haiquan Bi1Honglin Wang2Yuanlong Zhou3Nanyang Yu4Jizhong Yang5Yao Jiang6School of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, ChinaSchool of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, ChinaSchool of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, ChinaSchool of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, ChinaSchool of Mechanical Engineering, Southwest Jiaotong University, Chengdu 610031, ChinaChina Railway Eryuan Engineering Group Co., Ltd., Chengdu 610031, ChinaChina Railway Eryuan Engineering Group Co., Ltd., Chengdu 610031, ChinaPrevious research has demonstrated that the Train Wave Signature (TWS) method enables rapid calculation of pressure waves in straight tunnels. However, its application to subway tunnels with complex structural features remains insufficiently explored. This study proposes a generalized mathematical method integrating TWS with graph theory for the simulation of pressure wave generation, propagation, and reflection in complex tunnel systems. A computational program is implemented using this method for efficient simulation. The proposed method achieves high-accuracy prediction of pressure waves in tunnels with complex geometries compared with field measurements conducted in a high-speed subway tunnel with two shafts. We discuss the impact of iteration time intervals on the results and clarify the minimum time interval required for the calculation. Moreover, the sin-type definition of TWSs enhances the precision of pressure gradient prediction, and omitting low-amplitude pressure and reflected waves from the train can improve computational efficiency without compromising accuracy. This study advances the application of TWSs in tunnels with complex structures and provides a practical solution for aerodynamic analysis in high-speed subway tunnels, balancing accuracy with computational efficiency.https://www.mdpi.com/2227-7390/13/15/2360tunnel pressure wavetrain wave signaturewave modelingtunnel modelingmathematical method validation
spellingShingle Xu Zhang
Haiquan Bi
Honglin Wang
Yuanlong Zhou
Nanyang Yu
Jizhong Yang
Yao Jiang
A Mathematical Method for Predicting Tunnel Pressure Waves Based on Train Wave Signature and Graph Theory
Mathematics
tunnel pressure wave
train wave signature
wave modeling
tunnel modeling
mathematical method validation
title A Mathematical Method for Predicting Tunnel Pressure Waves Based on Train Wave Signature and Graph Theory
title_full A Mathematical Method for Predicting Tunnel Pressure Waves Based on Train Wave Signature and Graph Theory
title_fullStr A Mathematical Method for Predicting Tunnel Pressure Waves Based on Train Wave Signature and Graph Theory
title_full_unstemmed A Mathematical Method for Predicting Tunnel Pressure Waves Based on Train Wave Signature and Graph Theory
title_short A Mathematical Method for Predicting Tunnel Pressure Waves Based on Train Wave Signature and Graph Theory
title_sort mathematical method for predicting tunnel pressure waves based on train wave signature and graph theory
topic tunnel pressure wave
train wave signature
wave modeling
tunnel modeling
mathematical method validation
url https://www.mdpi.com/2227-7390/13/15/2360
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