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R. Liang^1,2, W. Liu², Q. Liu¹, C. Li³ and S. Kaewunruen¹

¹Birmingham Centre for Railway Research and Education, University of Birmingham, United Kingdom
²Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, China
³Urban Rail Transit Center, China Academy of Railway Sciences Corporation Limited, Beijing, China

doi:10.4203/ccc.15.18.9

R. Liang, W. Liu, Q. Liu, C. Li, S. Kaewunruen, "Vertical Wheel-Rail Force Identification Using Frequency-Domain Physics-Based Modeling and Data-Driven Priors", in J. Pombo, (Editor), "Proceedings of the Seventh International Conference on Railway Technology: Research, Development and Maintenance ", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 15, Paper 18.9, 2026, doi:10.4203/ccc.15.18.9

Keywords: railway dynamics, wheel-rail force identification, frequency domain analysis, inverse problem, physics guided modelling, deep learning.

Abstract

This paper presents a physics-guided frequency-domain framework for the identification of vertical wheel–rail forces from measured rail acceleration responses. A forward operator is constructed based on an Euler–Bernoulli beam model to capture the dynamic relationship between moving wheel–rail forces and rail responses, including frequency coupling and multi-wheelset phase effects. To address the instability of the inverse problem, a learning-based spectral magnitude prior is introduced to constrain the force distribution without directly modelling the complex spectrum. The identification is formulated as a prior-constrained optimization problem that balances data consistency and prior information across frequencies. Field measurements from a metro tunnel are used to validate the proposed approach. The identified forces produce reconstructed responses that agree well with measured data in both frequency and time domains, demonstrating stable and physically consistent performance under real operating conditions. The proposed framework provides a practical solution for vertical wheel–rail force estimation and offers a general approach for solving ill-posed inverse problems in structural dynamics.

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Front Page Browse CCC CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Conferences ISSN 2753-3239 CCC: 15 PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON RAILWAY TECHNOLOGY: RESEARCH, DEVELOPMENT AND MAINTENANCE Edited by: J. Pombo Paper 18.9 Vertical Wheel-Rail Force Identification Using Frequency-Domain Physics-Based Modeling and Data-Driven Priors R. Liang^1,2, W. Liu², Q. Liu¹, C. Li³ and S. Kaewunruen¹ ¹Birmingham Centre for Railway Research and Education, University of Birmingham, United Kingdom ²Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, China ³Urban Rail Transit Center, China Academy of Railway Sciences Corporation Limited, Beijing, China doi:10.4203/ccc.15.18.9 Full Bibliographic Reference for this paper R. Liang, W. Liu, Q. Liu, C. Li, S. Kaewunruen, "Vertical Wheel-Rail Force Identification Using Frequency-Domain Physics-Based Modeling and Data-Driven Priors", in J. Pombo, (Editor), "Proceedings of the Seventh International Conference on Railway Technology: Research, Development and Maintenance ", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 15, Paper 18.9, 2026, doi:10.4203/ccc.15.18.9 Keywords: railway dynamics, wheel-rail force identification, frequency domain analysis, inverse problem, physics guided modelling, deep learning. Abstract This paper presents a physics-guided frequency-domain framework for the identification of vertical wheel–rail forces from measured rail acceleration responses. A forward operator is constructed based on an Euler–Bernoulli beam model to capture the dynamic relationship between moving wheel–rail forces and rail responses, including frequency coupling and multi-wheelset phase effects. To address the instability of the inverse problem, a learning-based spectral magnitude prior is introduced to constrain the force distribution without directly modelling the complex spectrum. The identification is formulated as a prior-constrained optimization problem that balances data consistency and prior information across frequencies. Field measurements from a metro tunnel are used to validate the proposed approach. The identified forces produce reconstructed responses that agree well with measured data in both frequency and time domains, demonstrating stable and physically consistent performance under real operating conditions. The proposed framework provides a practical solution for vertical wheel–rail force estimation and offers a general approach for solving ill-posed inverse problems in structural dynamics. download the full-text of this paper (PDF, 10 pages, 1107 Kb) go to the previous paper go to the next paper return to the table of contents return to the volume description
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