SpringerLink
Log in

Modal Identification of a Bridge Using the Vibration Response of a Passing Vehicle Combining VMD and TKEO

  • ORIGINAL CONTRIBUTION
  • Published:
Journal of The Institution of Engineers (India): Series A Aims and scope Submit manuscript

Abstract

The majority of the vibration-based structural health monitoring techniques require modal parameter estimation. Recently, modal identification using indirect measurements is being developed and investigated as it avoids elaborate and laborious tasks associated with placing sensors on the structure and data acquisition systems and thereby reducing initial as well as recurring costs. Apart from this, multiple bridges can be scanned using the instrumented vehicle in a shorter time, saving considerable time in the modal parameter estimation of bridges. However, it is extremely challenging to estimate the modal parameters using the vibration responses from the vehicle moving over the bridge. The measured dynamic responses from the instrumented vehicle include components associated with the bridge, vehicle as well as driving frequencies apart from the disturbances associated with the bridge surface roughness. Therefore, isolating the bridge frequencies from the mix of all these frequency components is rather difficult. In this paper, efforts are made to devise a new modal parameter estimation technique using the combination of variational mode decomposition with the Teager–Kaiser energy operator. The vehicle-bridge interaction system employed in the present investigations idealizes the vehicle as a quarter car and the bridge as a beam. Parametric studies have been carried out to test the sensitivity of the proposed algorithm to the measurement noise, vehicle speed, and road surface roughness during signal decomposition as well as modal identification. The studies presented in this paper confirm that the proposed method can identify bridge mode shapes and frequencies with good accuracy by extracting bridge-related components from the instrumented vehicle body responses.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data Availability

Data Available.

Code Availability

Custom Code Available.

References

  1. E.P. Carden, P. Fanning, Vibration based condition monitoring: a review. Struct. Health Monit. 3(4), 355–377 (2004). https://doi.org/10.1177/1475921704047500

    Article  Google Scholar 

  2. Y.B. Yang, C.W. Lin, J.D. Yau, Extracting bridge frequencies from the dynamic response of a passing vehicle. J. Sound Vib. 272(3–5), 471–493 (2004). https://doi.org/10.1016/S0022-460X(03)00378-X

    Article  Google Scholar 

  3. L. Deng, C.S. Cai, Identification of parameters of vehicles moving on bridges. Eng. Struct. 31(10), 2474–2485 (2009). https://doi.org/10.1016/j.engstruct.2009.06.005

    Article  Google Scholar 

  4. E.J. O’Brien, P. McGetrick, A. González, A drive-by inspection system via vehicle moving force identification. Smart Struct. Syst. 13(5), 821–848 (2014). https://doi.org/10.12989/sss.2014.13.5.797

    Article  Google Scholar 

  5. Y. Zhang, L. Wang, Z. **ang, Damage detection by mode shape squares extracted from a passing vehicle. J. Sound Vib. 331(2), 291–307 (2012). https://doi.org/10.1016/j.jsv.2011.09.004

    Article  Google Scholar 

  6. Y. Oshima, K. Yamamoto, K. Sugiura, Damage assessment of a bridge based on mode shapes estimated by responses of passing vehicles. Smart Struct. Syst. 13(5), 731–753 (2014). https://doi.org/10.12989/sss.2014.13.5.731

    Article  Google Scholar 

  7. W.M. Li, Z.H. Jiang, T.L. Wang, H.P. Zhu, Optimization method based on generalized pattern search algorithm to identify bridge parameters indirectly by a passing vehicle. J. Sound Vib. 333(2), 364–380 (2014). https://doi.org/10.1016/j.jsv.2013.08.021

    Article  Google Scholar 

  8. Y.B. Yang, W.F. Chen, Extraction of bridge frequencies from a moving test vehicle by stochastic subspace identification. J. Bridge Eng. 21(3), 04015053 (2016). https://doi.org/10.1061/(ASCE)BE.1943-5592.0000792

    Article  Google Scholar 

  9. X.U.A.N. Kong, C.S. Cai, B. Kong, Numerically extracting bridge modal properties from dynamic responses of moving vehicles. J. Eng. Mech. 142(6), 04016025 (2016). https://doi.org/10.1061/(ASCE)EM.1943-7889.0001033

    Article  Google Scholar 

  10. X. Kong, C.S. Cai, L. Deng, W. Zhang, Using dynamic responses of moving vehicles to extract bridge modal properties of a field bridge. J. Bridge Eng. 22(6), 04017018 (2017). https://doi.org/10.1061/(ASCE)BE.1943-5592.0001038

    Article  Google Scholar 

  11. A. Malekjafarian, E.J. OBrien, Identification of bridge mode shapes using short time-frequency domain decomposition of the responses measured in a passing vehicle. Eng. Struct. 81, 386–397 (2014). https://doi.org/10.1016/j.engstruct.2014.10.007

    Article  Google Scholar 

  12. A. Malekjafarian, E.J. OBrien, On the use of a passing vehicle for the estimation of bridge mode shapes. J. Sound Vib. 397, 77–91 (2017). https://doi.org/10.1016/j.jsv.2017.02.051

    Article  Google Scholar 

  13. C. Tan, N. Uddin, E.J. OBrien, P.J. McGetrick, C.W. Kim, Extraction of bridge modal parameters using passing vehicle response. J. Bridge Eng. 24(9), 04019087 (2019). https://doi.org/10.1061/(ASCE)BE.1943-5592.0001477

    Article  Google Scholar 

  14. Y.B. Yang, J.P. Yang, State-of-the-art review on modal identification and damage detection of bridges by moving test vehicles. Int. J. Struct. Stab. Dyn. 18(02), 1850025 (2018). https://doi.org/10.1142/S0219455418500256

    Article  Google Scholar 

  15. A. Malekjafarian, P.J. McGetrick, E.J. OBrien, A review of indirect bridge monitoring using passing vehicles. Shock. Vib. (2015). https://doi.org/10.1155/2015/286139

    Article  Google Scholar 

  16. X.Q. Zhu, S.S. Law, Structural health monitoring based on vehicle-bridge interaction: accomplishments and challenges. Adv. Struct. Eng. 18(12), 1999–2015 (2015). https://doi.org/10.1260/1369-4332.18.12.1999

    Article  Google Scholar 

  17. S. Chen, F. Cerda, P. Rizzo, J. Bielak, J.H. Garrett, J. Kovačević, Semi-supervised multiresolution classification using adaptive graph filtering with application to indirect bridge structural health monitoring. IEEE Trans. Signal Process. 62(11), 2879–2893 (2014). https://doi.org/10.1109/TSP.2014.2313528

    Article  MathSciNet  Google Scholar 

  18. J. Li, X. Zhu, S.S. Law, B. Samali, Drive-by blind modal identification with singular spectrum analysis. J. Aerosp. Eng. 32(4), 04019050 (2019). https://doi.org/10.1061/(ASCE)AS.1943-5525.0001030

    Article  Google Scholar 

  19. J.D. Sitton, D. Rajan, B.A. Story, Bridge frequency estimation strategies using smartphones. J Civ Struct Health Monit. 10(3), 513–526 (2020). https://doi.org/10.1007/s13349-020-00399-z

    Article  Google Scholar 

  20. S.S. Eshkevari, T.J. Matarazzo, S.N. Pakzad, Bridge modal identification using acceleration measurements within moving vehicles. Mech. Syst. Sig. Process. 141, 106733 (2020). https://doi.org/10.1016/j.ymssp.2020.106733

    Article  Google Scholar 

  21. Q. Mei, N. Shirzad-Ghaleroudkhani, M. Gül, S.F. Ghahari, E. Taciroglu, Bridge mode shape identification using moving vehicles at traffic speeds through non-parametric sparse matrix completion. Struct. Control. Health Monit. 28(7), e2747 (2021). https://doi.org/10.1002/stc.2747

    Article  Google Scholar 

  22. N. **, Y.B. Yang, E.G. Dimitrakopoulos, T.S. Paraskeva, L.S. Katafygiotis, Application of short-time stochastic subspace identification to estimate bridge frequencies from a traversing vehicle. Eng. Struct. 230, 111688 (2021). https://doi.org/10.1016/j.engstruct.2020.111688

    Article  Google Scholar 

  23. J. Li, X. Zhu, J. Guo, Enhanced drive-by bridge modal identification via dual Kalman filter and singular spectrum analysis. Struct. Control. Health Monit. 29(5), e2927 (2022). https://doi.org/10.1002/stc.2927

    Article  Google Scholar 

  24. P. Singh, A. Sadhu, A hybrid time-frequency method for robust drive-by modal identification of bridges. Eng. Struct. 266, 114624 (2022). https://doi.org/10.1016/j.engstruct.2022.114624

    Article  Google Scholar 

  25. D.S. Yang, C.M. Wang, Modal properties identification of damped bridge using improved vehicle scanning method. Eng. Struct. 256, 114060 (2022). https://doi.org/10.1016/j.engstruct.2022.114060

    Article  Google Scholar 

  26. Z. Peng, J. Li, H. Hao, N. Yang, Mobile crowdsensing framework for drive-by-based dense spatial-resolution bridge mode shape identification. Eng. Struct. 292, 116515 (2023). https://doi.org/10.1016/j.engstruct.2023.116515

    Article  Google Scholar 

  27. K. Demirlioglu, S. Gonen, E. Erduran, Efficacy of vehicle scanning methods in estimating the mode shapes of bridges seated on elastic supports. Sensors 23(14), 6335 (2023). https://doi.org/10.3390/s23146335

    Article  Google Scholar 

  28. Y. He, J.P. Yang, Z. Yan, Enhanced identification of bridge modal parameters using contact residuals from three-connected vehicles: theoretical study. Structures 54, 1320–1335 (2023). https://doi.org/10.1016/j.istruc.2023.05.112

    Article  Google Scholar 

  29. Y.B. Yang, Z. Li, Z.L. Wang, Z. Liu, X.Q. Mo, F.Q. Qiu, Closely spaced modes of bridges estimated by a hybrid time-frequency method using a multi-sensor scanning vehicle: theory and practice. Mech. Syst. Signal Process. 192, 110236 (2023). https://doi.org/10.1016/j.ymssp.2023.110236

    Article  Google Scholar 

  30. Z.L. Wang, J.P. Yang, K. Shi, H. Xu, F.Q. Qiu, Y.B. Yang, Recent Advances in Research on Vehicle Scanning Method for Bridges. Int. J. Struct. Stab. Dyn. 22(15), 2230005 (2022). https://doi.org/10.1142/S0219455422300051

    Article  Google Scholar 

  31. P. Singh, S. Mittal, A. Sadhu, Recent Advancements and Future Trends in Indirect Bridge Health Monitoring. Pract. Period. Struct. Des. Constr. 28(1), 03122008 (2023). https://doi.org/10.1061/PPSCFX.SCENG-1259

    Article  Google Scholar 

  32. G. Loprencipe, P. Zoccali, Use of generated artificial road profiles in road roughness evaluation. J. Mod. Transp. 25, 24–33 (2017). https://doi.org/10.1007/s40534-017-0122-1

    Article  Google Scholar 

  33. Y.B. Yang, B. Zhang, Y. Qian, Y. Wu, Contact-point response for modal identification of bridges by a moving test vehicle. Int. J. Struct. Stab. Dyn. 18(05), 1850073 (2018). https://doi.org/10.1142/S0219455418500736

    Article  MathSciNet  Google Scholar 

  34. K. Dragomiretskiy, D. Zosso, Variational mode decomposition. IEEE Trans. Signal Process. 62(3), 531–544 (2013). https://doi.org/10.1109/TSP.2013.2288675

    Article  MathSciNet  Google Scholar 

  35. W. Yang, Z. Peng, K. Wei, P. Shi, W. Tian, Superiorities of variational mode decomposition over empirical mode decomposition particularly in time-frequency feature extraction and wind turbine condition monitoring. IET Renew. Power Gener. 11(4), 443–452 (2017). https://doi.org/10.1049/iet-rpg.2016.0088

    Article  Google Scholar 

  36. H.M. Teager, S.M. Teager, Evidence for nonlinear sound production mechanisms in the vocal tract. Speech production and speech modelling 55, 241–261 (1990). https://doi.org/10.1007/978-94-009-2037-8_10

    Article  Google Scholar 

  37. H. Teager, Some observations on oral airflow during phonation. IEEE Trans. Signal Process. 28(5), 599–601 (1980). https://doi.org/10.1109/TASSP.1980.1163453

    Article  Google Scholar 

  38. J.F. Kaiser, On Teager’s energy algorithm and its generalization to continuous signals. in Proceeding. 4th IEEE digital signal processing workshop. (Mohonk, 1990)

  39. J.F. Kaiser, On a simple algorithm to calculate the ‘energy’ of a signal. in Proceeding IEEE International Conference on Acoustics Speech Signal Processing (IEEE, 1990). pp. 381–384. https://doi.org/10.1109/ICASSP.1990.115702

  40. P. Maragos, J.F. Kaiser, T.F. Quatieri, Energy separation in signal modulations with application to speech analysis. IEEE Trans. Signal Process. 41(10), 3024–3051 (1993). https://doi.org/10.1109/78.277799

    Article  Google Scholar 

  41. X. Diao, J. Jiang, G. Shen, Z. Chi, Z. Wang, L. Ni, Y. Hao, An improved variational mode decomposition method based on particle swarm optimization for leak detection of liquid pipelines. Mech. Syst. Signal Process 143, 106787 (2020). https://doi.org/10.1016/j.ymssp.2020.106787

    Article  Google Scholar 

  42. X. Yan, Y. Liu, W. Zhang, M. Jia, X. Wang, Research on a novel improved adaptive variational mode decomposition method in rotor fault diagnosis. Appl. Sci. 10(5), 1696 (2020). https://doi.org/10.3390/app10051696

    Article  Google Scholar 

  43. S.E. Fang, R. Perera, Power mode shapes for early damage detection in linear structures. J. Sound Vib. 324(1–2), 40–56 (2009). https://doi.org/10.1016/j.jsv.2009.02.002

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support of the Department of Science and Technology, SERB, Government of India, through POWER research grant SERB/F/130/2021-2022 for carrying out this part of the research. The paper is being published with the permission of the Director, CSIR-SERC, Chennai.

Funding

The authors acknowledge the support of the Department of Science and Technology, SERB, Government of India, through POWER research grant SERB/F/130/2021–2022 for carrying out this part of the research.

Author information

Authors and Affiliations

  1. CSIR-Structural Engineering Research Centre, CSIR Campus, Taramani, Chennai, 600113, India

    A. Srinivas & K. Lakshmi

Authors
  1. A. Srinivas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Lakshmi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Lakshmi.

Ethics declarations

Conflict of interest

No conflicts of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Srinivas, A., Lakshmi, K. Modal Identification of a Bridge Using the Vibration Response of a Passing Vehicle Combining VMD and TKEO. J. Inst. Eng. India Ser. A (2024). https://doi.org/10.1007/s40030-024-00818-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40030-024-00818-0

Keywords

Search

Navigation