Abstract
This study presents an effective procedure for extracting the first few bridge frequencies using the data collected by a moving test vehicle. Previously, the effectiveness of the vehicle scanning method for bridge frequencies was hampered by factors such as vehicle frequency and road surface roughness. To this end, the contact-point response of the vehicle with the bridge that is free of the vehicle frequency is adopted in the analysis. To enhance the visibility of the first few bridge frequencies for extraction, the variational mode decomposition with band-pass filter (VMD-BPF) is proposed herein. The VMD is neater and more elegant than the empirical mode decomposition (EMD) in that less decompositions are needed, while there exists no mode-coupling problem, and the BPF serves to remove the undesired roughness frequencies. To verify the feasibility of the proposed procedure, both the vehicle and contact-point responses generated either numerically or by the field test are analyzed. It is demonstrated that the VMD-BPF is an effective method for extracting the bridge frequencies using the contact-point response for the scenarios considered.
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References
Doebling, S.W., Farrar, C.R., Prime, M.B.: A summary review of vibration-based damage identification methods. Shock Vib. Dig. 30, 91–105 (1998)
Carden, E.P., Fanning, P.: Vibration based condition monitoring: a review. Struct. Health Monit. 3, 355–377 (2004)
Yang, Y.B., Yang, J.P., Zhang, B., Wu, Y.T.: Vehicle Scanning Method for Bridges. Wiley, London (2020)
Yang, Y.B., Lin, C.W., Yau, J.D.: Extracting bridge frequencies from the dynamic response of a passing vehicle. J. Sound Vib. 272, 471–493 (2004)
Yin, S.H., Tang, C.Y.: Identifying cable tension loss and deck damage in a cable-stayed bridge using a moving vehicle. J. Vib. Acoust. 133, 021007 (2011)
Yang, Y.B., Wang, Z.L., Wang, B.Q., Xu, H.: Track modulus detection by vehicle scanning method. Acta Mech. 231(7), 2955–2978 (2020)
Malekjafarian, A., McGetrick, P.J., Obrien, E.J.: A review of indirect bridge monitoring using passing vehicles. Shock Vib. 2015, 286139 (2015)
Yang, Y.B., Yang, J.P.: State-of-the-art review on modal identification and damage detection of bridges by moving test vehicles. Int. J. Struct. Stab. Dyn. 18, 1850025 (2018)
Cooly, J.W., Tukey, J.W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965)
Duhamel, P.: Fast fourier transforms: a tutorial review and a state of the art. Signal process. 19, 259–299 (1990)
Gabor, D.: Theory of communication. IEEE J. Inst. Electr. Eng. 93, 429–441 (1946)
Wang, L., McCullough, M., Kareem, A.: Modeling and simulation of nonstationay processes utilizing Wavelet and Hilbert transforms. ASCE J. Eng. Mech. 140, 345–360 (2014)
Zhou, Z., Adeli, H.: Wavelet energy spectrum for time-frequency localization of earthquake energy. Int. J. Imaging Syst. Technol. 13, 133–140 (2003)
Kim, H., Adeli, H.: Hybrid control of smart structures using a novel wavelet-based algorithm. Comput. Aided Civ. Infrastruct. Eng. 20, 7–22 (2005)
Laflamme, S., Slotine, J., Connor, J.: Wavelet network for semiactive control. ASCE J. Eng. Mech. 137, 462–474 (2011)
Zhu, X.Q., Law, S.S.: Wavelet-based crack identification of bridge beam from operational deflection time history. Int. J. Solids Struct. 43, 2299–2317 (2006)
Tan, C., Elhattab, A., Uddin, N.: “Drive-by” bridge frequency-based monitoring utilizing wavelet transform. J. Civil Struct. Health Monit. 615, 615–625 (2017)
Huang, N.E., Shen, Z., Long, S.R., Wu, M.C., Shih, H.H., Zheng, Q., Yeh, N.C., Tung, C.C., Liu, H.H.: The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A. 454, 903–995 (1998)
Chen, C.H., Wang, C.H., Lui, J.Y., Lui, C., Liang, W.T., Yen, H.Y., Yeh, Y.H., Chia, Y.P., Wang, Y.: Identification of earthquakes signals from groundwater level records using the HHT method. Geophys. J. Int. 180, 1231–1241 (2010)
He, X.H., Hua, X.G., Chen, Z.Q., Huang, F.L.: EMD-based random decrement technique for modal parameter identification of an existing railway bridge. Eng. Struct. 33, 1348–1356 (2011)
Zhang, R.R., King, R., Olson, L., Xu, Y.L.: Dynamic response of the Trinity River Relief Bridge to controlled pile damage: modeling and experimental data analysis comparing Fourier and Hilbert-Huang techniques. J. Sound Vib. 285, 1049–1070 (2005)
Yang, Y.B., Chang, K.C.: Extraction of bridge frequencies from the dynamic response of a passing vehicle enhanced by the EMD technique. J. Sound Vib. 322, 718–739 (2009)
Obrien, E.J., Malekjafarian, A., Gonzalez, A.: Application of empirical mode 711 decomposition to drive-by bridge damage detection. Eur. J. Mech. A-Solid. 61, 151–163 (2017)
Yang, J.P., Lee, W.C.: Damping effect of a passing vehicle for indirectly measuring bridge frequencies by EMD technique. Int. J. Struct. Stab. Dyn. 18, 1850008 (2018)
Wu, Z., Huang, N.E.: Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv. Adapt. Data Anal. 01, 1–41 (2009)
Yeh, J.R., Shieh, J.S., Huang, N.E.: Complementary ensemble empirical mode decomposition: a novel noise enhanced data analysis method. Advan. Adapt. Data Analy. 2, 135–156 (2010)
Aied, H., González, A., Cantero, D.: Identification of sudden stiffness changes in the acceleration response of a bridge to moving loads using ensemble empirical mode decomposition. Mech. Syst. Signal Process. 66–67, 314–338 (2016)
Zhu, L., Malekjafarian, A.: On the use of ensemble empirical mode decomposition for the identification of bridge frequency from the responses measured in a passing vehicle. Infrastruct. 4, 32 (2019)
Tributsch, A., Adam, C.: A multi-step approach for identification of structural modifications based on operational modal analysis. Int. J. Struct. Stab. Dyn. 14(05), 1440004 (2014)
Tributsch, A., Adam, C.: An enhanced energy vibration-based approach for damage detection and localization. Struct. Control Health. 25(1), e2047 (2017)
Dragomiretskiy, K., Zosso, D.: Variational mode decomposition. IEEE Trans. Signal Process. 62, 531–544 (2014)
Bagheri, A., Ozbulut, O.E., Harris, D.K.: Structural system identification based on variational mode decomposition. J. Sound Vib. 417, 182–197 (2018)
Yi, C., Lv, Y., Dang, Z.: A fault diagnosis scheme for rolling bearing based on particle swarm optimization in variational mode decomposition. Shock Vib. 2016, 1–10 (2016)
Moschas, F., Stiros, S.: Measurement of the dynamic displacements and of the modal frequencies of a short-span pedestrian bridge using GPS and an accelerometer. Eng. Struct. 33, 10–17 (2011)
Wallin, J., Leander, J., Karoumi, R.: Strengthening of a steel railway bridge and its impact on the dynamic response to passing trains. Eng. Struct. 33, 635–646 (2011)
Yang, Y.B., Chang, K.C., Li, Y.C.: Filtering techniques for extracting bridge frequencies from a test vehicle moving over the bridge. Eng. Struct. 48, 353–362 (2013)
Yang, Y.B., Li, Y.C., Chang, K.C.: Effect of road surface roughness on the response of a moving vehicle for identification of bridge frequencies. Interact. Multiscale Mech. 5, 347–368 (2012)
Yang, Y.B., Li, Y.C., Chang, K.C.: Using two connected vehicles to measure the frequencies of bridges with rough surface: a theoretical study. Acta Mech. 223, 1851–1861 (2012)
Lin, C.W., Yang, Y.B.: Use of a passing vehicle to scan the bridge frequencies: an experimental verification. Eng. Struct. 27, 1865–1878 (2005)
Yang, Y.B., Xu, H., Zhang, B., Xiong, F., Wang, Z.L.: Measuring bridge frequencies by a test vehicle in non-moving and moving states. Eng. Struct. 203, 109859 (2020)
Yang, Y.B., Zhang, B., Qian, Y., Wu, Y.T.: Contact-point response for modal identification of bridges by a moving test vehicle. Int. J. Struct. Stab. Dyn. 18, 1850073 (2018)
Yang, Y.B., Yau, J.D.: Vehicle-bridge interaction element for dynamic analysis. ASCE J. Struct. Eng. 123, 1512–1518 (1997)
Yang, Y.B., Yau, J.D., Wu, W.S.: Vehicle-Bridge Interaction Dynamics: With Applications to High-Speed Railways. World Scientific, Singapore (2004)
Fryba, L.: Vibration of solids and structures under moving loads. Noordhoff International Publishing, Prague (1972)
Yang, Y.B., Lin, C.W.: Vehicle-bridge interaction dynamics and potential applications. J. Sound Vib. 284, 205–226 (2005)
Biggs, J.M.: Introduction to Structural Dynamics. McGraw-Hill, New York (1964)
Clough, R.W., Penzien, J.: Dynamics of Structures, 2nd edn. McGraw-Hill Book Co., Singapore (1993)
ISO 8608, Mechanical Vibration-road Surface Profiles-reporting of Measured Data. International Organization for Standardization, Geneva (1995)
Lyons, R.G.: Understanding Digital Signal Processing, 3rd edn. Prentice-Hall, Boston (2011)
Chang, K.C., Wu, F.B., Yang, Y.B.: Disk model for wheels moving over highway bridges with rough surfaces. J. Sound Vib. 330, 4930–4944 (2011)
Acknowledgements
The senior author likes to thank The Fengtay Foundation for endowment of the Fengtay Chair Professorship. This research reported herein is sponsored by the following agencies: National Natural Science Foundation of China (Grant No. 51678091) and Chongqing Science and Technology Commission (Grant No. cstc2017zdcy-yszxX0006).
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Yang, Y.B., Xu, H., Mo, X.Q. et al. An effective procedure for extracting the first few bridge frequencies from a test vehicle. Acta Mech 232, 1227–1251 (2021). https://doi.org/10.1007/s00707-020-02870-w
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DOI: https://doi.org/10.1007/s00707-020-02870-w