Technical Papers
Dec 5, 2023

Joint Identification of Cable Force and Bending Stiffness Using Vehicle-Induced Cable–Beam Vibration Responses

Publication: Journal of Bridge Engineering
Volume 29, Issue 2

Abstract

Cables play an important role in the structure of cable-stayed bridges. The cable force is an important indicator for the construction control, health monitoring, and performance evaluation of cable-stayed bridges. In practice, the boundary conditions of the cable are complex and changeable, and most of the existing formulas for cable force identification are derived from the assumption of some ideal boundary conditions. The boundaries of the cable are disturbed due to vehicle-induced beam vibration during the operation of bridges. The purpose of this study is to establish the cable–beam transmissibility function (CBTF) from the vehicle-induced vibration response of the main beam and cable and propose a new joint identification method for cable force and bending stiffness considering boundary disturbances. First, a theoretical model of the cable considering boundary disturbances is established. Then, the response transfer relationship between the anchorage of the beam end of the cable and a point on the cable is derived, as is the CBTF. Next, a parametric study is carried out to verify that the CBTF can characterize the inherent properties of cables under boundary disturbances. Then, the joint identification algorithm for determining cable force and bending stiffness is proposed. Finally, the feasibility of the proposed CBTF for identifying cable force and bending stiffness is verified by numerical simulations of a single cable and a cable-stayed bridge. The proposed method is suitable for studying the excitation of random vehicles during bridge operations, which is very significant for the safe service and timely maintenance of bridge cables.

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Data Availability Statement

All data, models, or codes generated or used during the study are available from the corresponding author by request.

Acknowledgments

This research work was jointly supported by the National Natural Science Foundation of China (Grant Nos. 52250011 and 12002224).

References

Casas, J. R. 1994. “A combined method for measuring cable forces: The cable-stayed Alamillo Bridge, Spain.” Struct. Eng. Int. 4: 235–240. https://doi.org/10.2749/101686694780601700.
Chen, C.-C., W.-H. Wu, Y.-T. Liu, and G. Lai. 2022. “A convenient cable tension estimation method simply based on local vibration measurements to fit partial mode shapes.” Eng. Struct. 272 (10): 115008. https://doi.org/10.1016/j.engstruct.2022.115008.
Cong, Y., H. Kang, T. Guo, and X. Su. 2022. “One-to-one internal resonance of a cable-beam structure subjected to a concentrated load.” J. Sound Vib. 529: 116915. https://doi.org/10.1016/j.jsv.2022.116915.
Dan, D., Y. Chen, and B. Xu. 2015. “A PSO driven intelligent model updating and parameter identification scheme for cable-damper system.” Shock Vib. 2015 (1626): 423898. https://doi.org/10.1155/2015/423898.
Du, Y.-L., T.-H. Yi, X.-J. Li, X.-L. Rong, L.-J. Dong, D.-W. Wang, Y. Gao, and Z. Leng. 2023. “Advances in intellectualization of transportation infrastructures.” Engineering 24 (4): 239. https://doi.org/10.1016/j.eng.2023.01.011.
Foti, F., M. Geuzaine, and V. Denoël. 2021. “On the identification of the axial force and bending stiffness of stay cables anchored to flexible supports.” Appl. Math. Modell. 92: 798–828. https://doi.org/10.1016/j.apm.2020.11.043.
He, W.-Y., F.-C. Meng, and W.-X. Ren. 2021. “Cable force estimation of cables with small sag considering inclination angle effect.” Adv. Bridge Eng. 2 (1): 127. https://doi.org/10.1186/s43251-021-00037-8.
Irvine, H. M., and T. K. Caughey. 1974. “The linear theory of free vibrations of a suspended cable.” Proc. R. Soc. London, Ser. A 341 (1626): 299–315. https://doi.org/10.1098/rspa.1974.0189.
Li, D.-L., D.-H. Yang, T.-H. Yi, S.-H. Zhang, W.-J. Li, and C. Li. 2023a. “Anomaly diagnosis of stay cables based on vehicle-induced cable force sums.” Eng. Struct. 289: 116239. https://doi.org/10.1016/j.engstruct.2023.116239.
Li, J.-X., T.-H. Yi, C.-X. Qu, H.-N. Li, and H. Liu. 2023b. “Early warning for abnormal cable forces of cable-stayed bridges considering structural temperature changes.” J. Bridge Eng. 28 (2): 04022137. https://doi.org/10.1061/JBENF2.BEENG-5797.
Lin, S.-W., Y.-L. Du, T.-H. Yi, and D.-H. Yang. 2022. “Model updating using bridge influence lines based on an adaptive metamodel global optimization method.” J. Bridge Eng. 27 (3): 04022003. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001839.
Liu, M.-Y., D. Zuo, and N. P. Jones. 2013. “Analytical and numerical study of deck-stay interaction in a cable-stayed bridge in the context of field observations.” J. Eng. Mech. 139 (11): 1636–1652. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000596.
Luo, L.-Y., Y.-L. Du, T.-H. Yi, C.-X. Qu, S.-H. Zhang, and T.-S. Geng. 2023. “Piecewise-fitted formula for cable force identification considering bending stiffness, sag, and inclination.” J. Bridge Eng. 28 (7): 04023038. https://doi.org/10.1061/JBENF2.BEENG-6143.
Luongo, A., and D. Zulli. 2012. “Dynamic instability of inclined cables under combined wind flow and support motion.” Nonlinear Dyn. 67 (1): 71–87. https://doi.org/10.1007/s11071-011-9958-9.
Ma, L. 2017. “A highly precise frequency-based method for estimating the tension of an inclined cable with unknown boundary conditions.” J. Sound Vib. 409 (1626): 65–80. https://doi.org/10.1016/j.jsv.2017.07.043.
Macdonald, J. H. G. 2016. “Multi-modal vibration amplitudes of taut inclined cables due to direct and/or parametric excitation.” J. Sound Vib. 363 (6): 473–494. https://doi.org/10.1016/j.jsv.2015.11.012.
Qu, C.-X., T.-H. Yi, and H.-N. Li. 2019. “Mode identification by eigensystem realization algorithm through virtual frequency response function.” Struct. Control Health Monit. 26 (10): 743. https://doi.org/10.1002/stc.2429.
Ren, W.-X., G. Chen, and W.-H. Hu. 2005. “Empirical formulas to estimate cable tension by cable fundamental frequency.” Struct. Eng. Mech. 20 (3): 363–380. https://doi.org/10.12989/sem.2005.20.3.363.
Spak, K., G. Agnes, and D. Inman. 2014. “Parameters for modeling stranded cables as structural beams.” Exp. Mech. 54 (9): 1613–1626. https://doi.org/10.1007/s11340-014-9941-8.
Wu, G.-M., T.-H. Yi, D.-H. Yang, and H.-N. Li. 2021. “Damage detection of tension pendulums in cable-stayed bridges using structural frequency variance.” J. Perform. Constr. Facil. 35: 04020126. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001540.
Yan, B., W. Chen, J. Yu, and X. Jiang. 2019. “Mode shape-aided tension force estimation of cable with arbitrary boundary conditions.” J. Sound Vib. 440 (2001): 315–331. https://doi.org/10.1016/j.jsv.2018.10.018.
Yan, B., J. Yu, and M. Soliman. 2015. “Estimation of cable tension force independent of complex boundary conditions.” J. Eng. Mech. 141 (1): 06014015. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000836.
Yang, D.-H., Z.-X. Guan, T.-H. Yi, H.-N. Li, and Y.-S. Ni. 2022. “Fatigue evaluation of bridges based on strain influence line loaded by elaborate stochastic traffic flow.” J. Bridge Eng. 27 (9): 04022082. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001929.
Zhang, H., Y. Zhou, Z. Huang, R. Shen, and Y. Wu. 2023. “Multiparameter identification of bridge cables using XGBoost algorithm.” J. Bridge Eng. 28 (5): 04023016. https://doi.org/10.1061/JBENF2.BEENG-6021.
Zhang, L., G. Qiu, and Z. Chen. 2021. “Structural health monitoring methods of cables in cable-stayed bridge: A review.” Measurement 168 (4): 108343. https://doi.org/10.1016/j.measurement.2020.108343.
Zhang, S., R. Shen, K. Dai, L. Wang, G. De Roeck, and G. Lombaert. 2019. “A methodology for cable damage identification based on wave decomposition.” J. Sound Vib. 442 (3): 527–551. https://doi.org/10.1016/j.jsv.2018.11.018.
Zhang, S., R. Shen, Y. Wang, G. De Roeck, G. Lombaert, and K. Dai. 2020. “A two-step methodology for cable force identification.” J. Sound Vib. 472: 115201. https://doi.org/10.1016/j.jsv.2020.115201.
Zhang, T., Y. Zhang, and H. Zhang. 2022. “A three-stage criterion method for extracting local vibration modes of tensioned cables in beam string structures.” Front. Mater. 589 (9): 1055635. https://doi.org/10.3389/fmats.2022.1055635.
Zui, H., T. Shinke, and Y. Namita. 1996. “Practical formulas for estimation of cable tension by vibration method.” J. Struct. Eng. 122 (6): 651–656. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:6(651).

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Go to Journal of Bridge Engineering
Journal of Bridge Engineering
Volume 29Issue 2February 2024

History

Received: Jul 5, 2023
Accepted: Oct 10, 2023
Published online: Dec 5, 2023
Published in print: Feb 1, 2024
Discussion open until: May 5, 2024

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Authors

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Lan-Ying Luo, S.M.ASCE [email protected]
Ph.D. Candidate, School of Civil Engineering, Dalian Univ. of Technology, Dalian 116023, China. Email: [email protected]
Yan-Liang Du, Ph.D. [email protected]
Professor, College of Civil and Transportation Engineering, Shenzhen Univ., Shenzhen 518061, China. Email: [email protected]
Professor, School of Civil Engineering, Dalian Univ. of Technology, Dalian 116023, China (corresponding author). Email: [email protected]
Song-Han Zhang, Ph.D. [email protected]
Associate Professor, School of Civil Engineering, Dalian Univ. of Technology, Dalian 116023, China. Email: [email protected]

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