Abstract

Recently, due to low cost and convenience, the concept of estimating the bridge’s first natural frequency through indirect measurements of a passing vehicle has gained increasing attention—known as drive-by bridge structural health monitoring. As the vehicle acts as a moving mass added to the bridge, this system is nonstationary with time-varying characteristics. Most related studies assume constant bridge and vehicle frequencies of vehicle–bridge interaction (VBI), which is only appropriate when the VBI effect is negligible. When the vehicle mass is significant compared with the bridge mass, often a feature of railway bridges, the interaction effect cannot be ignored. Therefore, this paper presents a nonlinear time–frequency analysis approach to examine the time-varying nature of frequencies in the VBI system using the second-order synchrosqueezing transform. In comparison to the classical linear approaches, such as wavelet transform and short-time Fourier transform, the proposed method can significantly improve the energy concentration of the time–frequency representations, resulting in a clear pattern to show how the frequencies change. In addition, an indicator is proposed to automatically select the parameters with the proposed approach to obtain suitable results. Both numerical simulation and laboratory experiments are carried out to investigate the feasibility of the proposed approach. It is found that due to the time-varying nature of VBI, the frequencies of both vehicles and bridges are time-varying. Therefore, the extracted drive-by bridge frequency should be distinguished from that found using direct (on-bridge free vibration) measurements.

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Acknowledgments

This research was supported by the National Natural Science Foundation of China (52008162), the Key Research and Development Program of Hunan Province (2019SK2172), the Science and Technology Innovation Program of Hunan Province (2020RC2018), the Fellowship of China Postdoctoral Science Foundation (2020M680114), and the Natural Science Foundation of Hunan Province (2022JJ40079).

References

Camarena-Martinez, D., C. A. Perez-Ramirez, M. Valtierra-Rodriguez, J. P. Amezquita-Sanchez, and R. de Jesus Romero-Troncoso. 2016. “Synchrosqueezing transform-based methodology for broken rotor bars detection in induction motors.” Measurement 90: 519–525. https://doi.org/10.1016/j.measurement.2016.05.010.
Cantero, D., P. McGetrick, C. W. Kim, and E. OBrien. 2019. “Experimental monitoring of bridge frequency evolution during the passage of vehicles with different suspension properties.” Eng. Struct. 187: 209–219. https://doi.org/10.1016/j.engstruct.2019.02.065.
Cebon, D. 1999. Handbook of vehicle–road interaction. London: Routledge.
Chang, K., C. W. Kim, and S. Borjigin. 2014. “Variability in bridge frequency induced by a parked vehicle.” Smart Struct. Syst. 13 (5): 755–773. https://doi.org/10.12989/sss.2014.13.5.755.
Daubechies, I., J. Lu, and H.-T. Wu. 2011. “Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool.” Appl. Comput. Harmon. Anal. 30 (2): 243–261. https://doi.org/10.1016/j.acha.2010.08.002.
Deng, L., and C. S. Cai. 2009. “Identification of parameters of vehicles moving on bridges.” Eng. Struct. 31 (10): 2474–2485. https://doi.org/10.1016/j.engstruct.2009.06.005.
Deng, L., Y. Yu, Q. Zou, and C. Cai. 2015. “State-of-the-art review of dynamic impact factors of highway bridges.” J. Bridge Eng. 20 (5): 04014080. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000672.
Elhattab, A., N. Uddin, and E. OBrien. 2018. “Drive-by bridge frequency identification under operational roadway speeds employing frequency independent underdamped pinning stochastic resonance (FI-UPSR).” Sensors (Basel) 18 (12): 4207. https://doi.org/10.3390/s18124207.
Feng, K., A. González, and M. Casero. 2021. “A kNN algorithm for locating and quantifying stiffness loss in a bridge from the forced vibration due to a truck crossing at low speed.” Mech. Syst. Signal Process. 154: 107599. https://doi.org/10.1016/j.ymssp.2020.107599.
Fitzgerald, P. C., A. Malekjafarian, D. Cantero, E. J. OBrien, and L. J. Prendergast. 2019. “Drive-by scour monitoring of railway bridges using a wavelet-based approach.” Eng. Struct. 191: 1–11. https://doi.org/10.1016/j.engstruct.2019.04.046.
Frýba, L., and C. Steele. 1976. “Vibration of solids and structures under moving loads.” J. Appl. Mech. 43 (3): 524. https://doi.org/10.1115/1.3423922.
Herrera, R. H., J. Han, and M. van der Baan. 2014. “Applications of the synchrosqueezing transform in seismic time–frequency analysis.” Geophysics 79 (3): V55–V64. https://doi.org/10.1190/geo2013-0204.1.
ISO. 2016. Mechanical vibration—Road surface profiles—Reporting of measured data. ISO 8608:2016. Geneva: ISO.
Kim, C. W., M. Kawatani, and K. B. Kim. 2005. “Three-dimensional dynamic analysis for bridge–vehicle interaction with roadway roughness.” Comput. Struct. 83 (19–20): 1627–1645. https://doi.org/10.1016/j.compstruc.2004.12.004.
Kim, C.-Y., D.-S. Jung, N.-S. Kim, S.-D. Kwon, and M. Q. Feng. 2003. “Effect of vehicle weight on natural frequencies of bridges measured from traffic-induced vibration.” Earthquake Eng. Eng. Vibr. 2 (1): 109–115. https://doi.org/10.1007/BF02857543.
Law, S., and X. Zhu. 2004. “Dynamic behavior of damaged concrete bridge structures under moving vehicular loads.” Eng. Struct. 26 (9): 1279–1293. https://doi.org/10.1016/j.engstruct.2004.04.007.
Li, C., and M. Liang. 2012. “Time–frequency signal analysis for gearbox fault diagnosis using a generalized synchrosqueezing transform.” Mech. Syst. Signal Process. 26: 205–217. https://doi.org/10.1016/j.ymssp.2011.07.001.
Li, J., M. Su, and L. Fan. 2003. “Natural frequency of railway girder bridges under vehicle loads.” J. Bridge Eng. 8 (4): 199–203. https://doi.org/10.1061/(ASCE)1084-0702(2003)8:4(199).
Li, J., X. Zhu, S.-s. Law, and B. Samali. 2020a. “Time-varying characteristics of bridges under the passage of vehicles using synchroextracting transform.” Mech. Syst. Signal Process. 140: 106727. https://doi.org/10.1016/j.ymssp.2020.106727.
Li, Z., J. Gao, H. Li, Z. Zhang, N. Liu, and X. Zhu. 2020b. “Synchroextracting transform: The theory analysis and comparisons with the synchrosqueezing transform.” Signal Process. 166: 107243. https://doi.org/10.1016/j.sigpro.2019.107243.
Lin, C. W., and Y. B. Yang. 2005. “Use of a passing vehicle to scan the fundamental bridge frequencies: An experimental verification.” Eng. Struct. 27 (13): 1865–1878. https://doi.org/10.1016/j.engstruct.2005.06.016.
Liu, W., S. Cao, Z. Wang, K. Jiang, Q. Zhang, and Y. Chen. 2018. “A novel approach for seismic time–frequency analysis based on high-order synchrosqueezing transform.” IEEE Geosci. Remote Sens. Lett. 15 (8): 1159–1163. https://doi.org/10.1109/LGRS.2018.2829340.
Malekjafarian, A., C.-W. Kim, E. J. OBrien, L. J. Prendergast, P. C. Fitzgerald, and S. Nakajima. 2020. “Experimental demonstration of a mode shape-based scour-monitoring method for multispan bridges with shallow foundations.” J. Bridge Eng. 25 (8): 04020050. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001586.
Matsuoka, K., K. Kaito, and M. Sogabe. 2020. “Bayesian time–frequency analysis of the vehicle–bridge dynamic interaction effect on simple-supported resonant railway bridges.” Mech. Syst. Signal Process. 135: 106373. https://doi.org/10.1016/j.ymssp.2019.106373.
McGetrick, P. J., C. W. Kim, A. Gonzalez, and E. J. O. Brien. 2015. “Experimental validation of a drive-by stiffness identification method for bridge monitoring.” Struct. Health Monit. 14 (4): 317–331. https://doi.org/10.1177/1475921715578314.
Mei, Q. P., and M. Gul. 2019. “A crowdsourcing-based methodology using smartphones for bridge health monitoring.” Struct. Health Monit. 18 (5–6): 1602–1619. https://doi.org/10.1177/1475921718815457.
Mei, Q. P., M. Gul, and M. Boay. 2019. “Indirect health monitoring of bridges using Mel-frequency cepstral coefficients and principal component analysis.” Mech. Syst. Sig. Process. 119: 523–546. https://doi.org/10.1016/j.ymssp.2018.10.006.
Newmark, N. M. 1959. “A method of computation for structural dynamics.” J. Eng. Mech. Div. 85 (3): 67–94. https://doi.org/10.1061/JMCEA3.0000098.
Oberlin, T., S. Meignen, and V. Perrier. 2015. “Second-order synchrosqueezing transform or invertible reassignment? Towards ideal time–frequency representations.” IEEE Trans. Signal Process. 63 (5): 1335–1344. https://doi.org/10.1109/TSP.2015.2391077.
Pham, D.-H., and S. Meignen. 2017. “High-order synchrosqueezing transform for multicomponent signals analysis—With an application to gravitational-wave signal.” IEEE Trans. Signal Process. 65 (12): 3168–3178. https://doi.org/10.1109/TSP.2017.2686355.
Sejdić, E., I. Djurović, and J. Jiang. 2007. “A window width optimized S-transform.” EURASIP J. Adv. Signal Process. 2008 (1): 672941. https://doi.org/10.1155/2008/672941.
Sitton, J. D., D. Rajan, and B. A. Story. 2020. “Bridge frequency estimation strategies using smartphones.” J. Civ. Struct. Health Monit. 10 (3): 513–526. https://doi.org/10.1007/s13349-020-00399-z.
Sony, S., and A. Sadhu. 2020. “Synchrosqueezing transform-based identification of time-varying structural systems using multi-sensor data.” J. Sound Vib. 486: 115576. https://doi.org/10.1016/j.jsv.2020.115576.
Stockwell, R. G. 2007. “A basis for efficient representation of the S-transform.” Digital Signal Process. 17 (1): 371–393. https://doi.org/10.1016/j.dsp.2006.04.006.
Su, C., M. Jiang, J. Liang, A. Tian, L. Sun, L. Zhang, F. Zhang, and Q. Sui. 2020. “Damage assessments of composite under the environment with strong noise based on synchrosqueezing wavelet transform and stack autoencoder algorithm.” Measurement 156: 107587. https://doi.org/10.1016/j.measurement.2020.107587.
Tan, C., A. Elhattab, and N. Uddin. 2017. “‘Drive-by’ bridge frequency-based monitoring utilizing wavelet transform.” J. Civ. Struct. Health Monit. 7 (5): 615–625. https://doi.org/10.1007/s13349-017-0246-3.
Tan, C., and N. Uddin. 2020. “Hilbert transform based approach to improve extraction of ‘drive-by’ bridge frequency.” Smart Struct. Syst. 25 (3): 265–277.
Tan, C., H. Zhao, E. J. OBrien, N. Uddin, P. C. Fitzgerald, P. J. McGetrick, and C.-W. Kim. 2021. “Extracting mode shapes from drive-by measurements to detect global and local damage in bridges.” Struct. Infrastruct. Eng. 17 (11): 1582–1596. https://doi.org/10.1080/15732479.2020.1817105.
Tan, C. J., N. Uddin, E. J. OBrien, P. J. McGetrick, and C. W. Kim. 2019. “Extraction of bridge modal parameters using passing vehicle response.” J. Bridge Eng. 24 (9): 04019087. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001477.
Thakur, G., and H.-T. Wu. 2011. “Synchrosqueezing-based recovery of instantaneous frequency from nonuniform samples.” SIAM J. Math. Anal. 43 (5): 2078–2095. https://doi.org/10.1137/100798818.
Timoshenko, S. 1922. “CV. On the forced vibrations of bridges.” Dublin Philos. Mag. J. Sci. 43 (257): 1018–1019. https://doi.org/10.1080/14786442208633953.
Wang, H. Q., T. Nagayama, J. Nakasuka, B. Y. Zhao, and D. Su. 2018. “Extraction of bridge fundamental frequency from estimated vehicle excitation through a particle filter approach.” J. Sound Vib. 428: 44–58. https://doi.org/10.1016/j.jsv.2018.04.030.
Wang, S., X. Chen, C. Tong, and Z. Zhao. 2016. “Matching synchrosqueezing wavelet transform and application to aeroengine vibration monitoring.” IEEE Trans. Instrum. Meas. 66 (2): 360–372. https://doi.org/10.1109/TIM.2016.2613359.
Xu, H., Y. H. Liu, Z. L. Wang, K. Shi, B. Zhang, and Y. B. Yang. 2022. “General contact response of single-axle two-mass test vehicles for scanning bridge frequencies considering suspension effect.” Eng. Struct. 270: 114880.
Yang, J. N., Y. Lei, S. Lin, and N. Huang. 2004a. “Hilbert–Huang based approach for structural damage detection.” J. Eng. Mech. 130 (1): 85–95. https://doi.org/10.1061/(ASCE)0733-9399(2004)130:1(85).
Yang, Y. B., and K. C. Chang. 2009. “Extraction of bridge frequencies from the dynamic response of a passing vehicle enhanced by the EMD technique.” J. Sound Vib. 322 (4–5): 718–739. https://doi.org/10.1016/j.jsv.2008.11.028.
Yang, Y. B., and C. W. Lin. 2005. “Vehicle–bridge interaction dynamics and potential applications.” J. Sound Vib. 284 (1): 205–226. https://doi.org/10.1016/j.jsv.2004.06.032.
Yang, Y. B., C. W. Lin, and J. D. Yau. 2004b. “Extracting bridge frequencies from the dynamic response of a passing vehicle.” J. Sound Vib. 272 (3–5): 471–493. https://doi.org/10.1016/S0022-460X(03)00378-X.
Yang, Y. B., J. Yau, Z. Yao, and Y. Wu. 2004c. Vehicle–bridge interaction dynamics: With applications to high-speed railways. Singapore: World Scientific.
Yu, G., Z. Wang, and P. Zhao. 2018. “Multisynchrosqueezing transform.” IEEE Trans. Ind. Electron. 66 (7): 5441–5455. https://doi.org/10.1109/TIE.2018.2868296.
Zhang, J., D. Yang, W.-X. Ren, and Y. Yuan. 2021. “Time-varying characteristics analysis of vehicle–bridge interaction system based on modified S-transform reassignment technique.” Mech. Syst. Signal Process. 160: 107807. https://doi.org/10.1016/j.ymssp.2021.107807.
Zhu, L., and A. Malekjafarian. 2019. “On the use of ensemble empirical mode decomposition for the identification of bridge frequency from the responses measured in a passing vehicle.” Infrastructures 4 (2): 32. https://doi.org/10.3390/infrastructures4020032.
Zhu, X., Z. Zhang, J. Gao, B. Li, Z. Li, X. Huang, and G. Wen. 2019. “Synchroextracting chirplet transform for accurate IF estimate and perfect signal reconstruction.” Digital Signal Process. 93: 172–186. https://doi.org/10.1016/j.dsp.2019.07.015.

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Go to Journal of Bridge Engineering
Journal of Bridge Engineering
Volume 28Issue 4April 2023

History

Received: Jul 29, 2022
Accepted: Dec 3, 2022
Published online: Jan 31, 2023
Published in print: Apr 1, 2023
Discussion open until: Jul 1, 2023

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Associate Researcher, Key Laboratory for Wind and Bridge Engineering of Hunan Province, College of Civil Engineering, Hunan Univ., Changsha 410082, China. ORCID: https://orcid.org/0000-0002-1106-7943. Email: [email protected]
Professor, Key Laboratory for Wind and Bridge Engineering of Hunan Province, College of Civil Engineering, Hunan Univ., Changsha 410082, China (corresponding author). Email: [email protected]
Professor, School of Civil Engineering, Univ. College Dublin, Dublin D04 V1W8, Ireland. ORCID: https://orcid.org/0000-0002-6867-1009. Email: [email protected]
Nasim Uddin, F.ASCE [email protected]
Professor, Dept. of Civil Engineering, Univ. of Alabama at Birmingham, Birmingham, AL 35205. Email: [email protected]
Professor, Dept. of Civil and Earth Resources Engineering, Kyoto Univ., Kyoto 606-8501, Japan. ORCID: https://orcid.org/0000-0002-2727-6037. Email: [email protected]

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