Skip to main content
SpringerLink
Log in

Combined wavelet–Hilbert transform-based modal identification of road bridge using vehicular excitation

  • Original Paper
  • Published:
Journal of Civil Structural Health Monitoring Aims and scope Submit manuscript

Abstract

In this paper, continuous wavelet transform (CWT)-based filtering strategy is utilized along with Hilbert transform (HT) for modal identification of reinforced concrete road bridge. Although, wavelet-based pre-filtering prior to Hilbert–Huang transform is published in the literature, the advantage and uniqueness of the proposed method over traditional HHT or WT-HHT lies in its ability to bypass the time-consuming evaluation of intrinsic mode functions (IMFs) that often produces spurious modes and mode-mixing. This is achieved using a modified form of Littlewood–Paley basis function whose compact support in frequency domain helps to filter the signal in leakage-free frequency bands. It is followed by HT for modal parameter estimation. The proposed identification algorithm is first tested with synthetic records having closely spaced strong and weak modes to validate its efficiency and accuracy. Then, a full-scale reinforced concrete road bridge is considered for experimental validation. Results presented in this work clearly show that it can effectively evaluate significant number of modes which are helpful in finite element model updating of large structures. Finally, the advantage of the proposed method is demonstrated by comparing its performance with other methods available in the literature.

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
Fig. 13

Similar content being viewed by others

References

  1. Li H, Ou J (2015) The state of the art in structural health monitoring of cable-stayed bridges. J Civ Struct Health Monit 1–25

  2. Ko JM, Ni YQ (2005) Technology developments in structural health monitoring of large-scale bridges. Eng Struct 27(12):1715–1725

    Article  Google Scholar 

  3. Catbas FN, Susoy M, Frangopol DM (2008) Structural health monitoring and reliability estimation: long span truss bridge application with environmental monitoring data. Eng Struct 30(9):2347–2359

    Article  Google Scholar 

  4. Nishikawa T, Yoshida J, Sugiyama T, Fujino Y (2012) Concrete crack detection by multiple sequential image filtering. Comput Aided Civ Infrastruct Eng 27(1):29–47

    Article  Google Scholar 

  5. Park SW, Park HS, Kim JH, Adeli H (2015) 3D displacement measurement model for health monitoring of structures using a motion capture system. Measurement 59:352–362

    Article  Google Scholar 

  6. Han Q, Xu J, Carpinteri A, Lacidogna G (2015) Localization of acoustic emission sources in structural health monitoring of masonry bridge. Struct Control Health Monit 22(2):314–329

    Article  Google Scholar 

  7. Doebling SW, Farrar CR, Prime MB (1998) A summary review of vibration-based damage identification methods. Shock Vib Dig 30(2):91–105

    Article  Google Scholar 

  8. Das S, Saha P, Patro SK. Vibration-based damage detection techniques used for health monitoring of structures: a review. J Civ Struct Health Monit 1–31

  9. Reynders E (2012) System identification methods for (operational) modal analysis: review and comparison. Arch Comput Methods Eng 19(1):51–124

    Article  MathSciNet  MATH  Google Scholar 

  10. Peeters B, De Roeck G (2001) Stochastic system identification for operational modal analysis: a review. J Dyn Syst Meas Control 123(4):659–667

    Article  Google Scholar 

  11. Cimellaro GP, Piantà S, De Stefano A (2011) Output-only modal identification of ancient L’Aquila city hall and civic tower. J Struct Eng 138(4):481–491

    Article  Google Scholar 

  12. Brownjohn JMW, Magalhaes F, Caetano E, Cunha A (2010) Ambient vibration re-testing and operational modal analysis of the Humber Bridge. Eng Struct 32(8):2003–2018

    Article  Google Scholar 

  13. Andersen P, Brincker R, Kirkegaard PH (1995) Theory of covariance equivalent ARMAV models of civil engineering structures. Technical report, Dept. of Building Technology and Structural Engineering, Aalborg University

  14. Ubertini F, Gentile C, Materazzi AL (2013) Automated modal identification in operational conditions and its application to bridges. Eng Struct 46:264–278

    Article  Google Scholar 

  15. Siringoringo DM, Fujino Y (2008) System identification of suspension bridge from ambient vibration response. Eng Struct 30(2):462–477

    Article  Google Scholar 

  16. Yang Y, Nagarajaiah S (2012) Time-frequency blind source separation using independent component analysis for output-only modal identification of highly damped structures. J Struct Eng 139(10):1780–1793

    Article  Google Scholar 

  17. Yang Y, Nagarajaiah S (2013) Blind modal identification of output-only structures in time-domain based on complexity pursuit. Earthq Eng Struct Dyn 42(13):1885–1905

    Article  Google Scholar 

  18. Yang Y, Nagarajaiah S (2013) Output-only modal identification with limited sensors using sparse component analysis. J Sound Vib 332(19):4741–4765

    Article  Google Scholar 

  19. Yang Y, Nagarajaiah S (2014) Blind identification of damage in time-varying systems using independent component analysis with wavelet transform. Mech Syst Signal Process 47(1):3–20

    Article  Google Scholar 

  20. Magalhães F, Cunha Á, Caetano E, Brincker R (2010) Damping estimation using free decays and ambient vibration tests. Mech Syst Signal Process 24(5):1274–1290

    Article  Google Scholar 

  21. Huffman JT, Xiao F, Chen G, Hulsey JL (2015) Detection of soil-abutment interaction by monitoring bridge response using vehicle excitation. J Civ Struct Health Monit 5(4):389–395

    Article  Google Scholar 

  22. Benedettini F, Dilena M, Morassi A (2015) Vibration analysis and structural identification of a curved multi-span viaduct. Mech Syst Signal Process 54:84–107

    Article  Google Scholar 

  23. Nagarajaiah S, Varadarajan N (2005) Short time Fourier transform algorithm for wind response control of buildings with variable stiffness {TMD}. Eng Struct 27(3):431–441

    Article  Google Scholar 

  24. Narasimhan S, Nagarajaiah S (2005) A STFT semiactive controller for base isolated buildings with variable stiffness isolation systems. Eng Struct 27(4):514–523

    Article  Google Scholar 

  25. Staszewski WJ (1997) Identification of damping in MDOF systems using time-scale decomposition. J Sound Vib 203(2):283–305

    Article  Google Scholar 

  26. Kijewski T, Kareem A (2003) Wavelet transforms for system identification in civil engineering. Comput Aided Civ Infrastruct Eng 18(5):339–355

    Article  Google Scholar 

  27. Chakraborty A, Basu B (2008) Nonstationary response analysis of long span bridges under spatially varying differential support motions using continuous wavelet transform. J Eng Mech 134(2):155–162

    Article  Google Scholar 

  28. Feldman M (2011) Hilbert transform applications in mechanical vibration. Wiley, New York

    Book  Google Scholar 

  29. Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu H (1998) The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis. Proc R Soc Lond A Math Phys Eng Sci 454(1971):903–995

    Article  MathSciNet  MATH  Google Scholar 

  30. Wu Z, Huang NE (2009) Ensemble empirical mode decomposition: a noise-assisted data analysis method. Adv Adapt Data Anal 1(01):1–41

    Article  Google Scholar 

  31. Peng ZK, Tse PW, Chu FL (2005) A comparison study of improved Hilbert-Huang transform and wavelet transform: application to fault diagnosis for rolling bearing. Mech Syst Signal Process 19(5):974–988

    Article  Google Scholar 

  32. Yang JN, Lei Y, Pan S, Huang N (2003) System identification of linear structures based on Hilbert–Huang spectral analysis. Part 1: normal modes. Earthq Eng Struct Dyn 32(9):1443–1467

    Article  Google Scholar 

  33. Chen J, Xu YL, Zhang RC (2004) Modal parameter identification of Tsing Ma suspension bridge under Typhoon Victor: EMD-HT method. J Wind Eng Ind Aerodyn 92(10):805–827

    Article  Google Scholar 

  34. He XH, Hua XG, Chen ZQ, Huang FL (2011) Emd-based random decrement technique for modal parameter identification of an existing railway bridge. Eng Struct 33(4):1348–1356

    Article  Google Scholar 

  35. Yu DJ, Ren WX (2005) EMD-based stochastic subspace identification of structures from operational vibration measurements. Eng Struct 27(12):1741–1751

    Article  Google Scholar 

  36. Yan B, Miyamoto A (2006) A comparative study of modal parameter identification based on wavelet and Hilbert-Huang transforms. Comput Aided Civ Infrastruct Eng 21(1):9–23

    Article  Google Scholar 

  37. Mahato S, Teja MV, Chakraborty A (2015) Adaptive HHT (AHHT) based modal parameter estimation from limited measurements of an RC-framed building under multi-component earthquake excitations. Struct Control Health Monit 22(7):984–1001

    Article  Google Scholar 

  38. Chopra AK (2013) Dynamics of structures–theory and application to earthquake engineering, 3rd edn. Pearson, London

    Google Scholar 

  39. Bendat JS, Piersol AG (2010) Random data: analysis and measurements procedures, 4th edn. Willey, New York

    Book  MATH  Google Scholar 

  40. Peng ZK, Tse PW, Chu FL (2005) An improved Hilbert–Huang transform and its application in vibration signal analysis. J Sound Vib 286(1):187–205

    Article  Google Scholar 

  41. Wang T, Zhang M, Yu Q, Zhang H (2012) Comparing the applications of EMD and EEMD on time-frequency analysis of seismic signal. J Appl Geophys 83:29–34

    Article  Google Scholar 

  42. Deering R, Kaiser JF (2005) The use of a masking signal to improve empirical mode decomposition. In: International conference on acoustics, speech, and signal processing, proceedings (ICASSP’05), IEEE, vol 4, pp 485–488

  43. Chen G, Wang Z (2012) A signal decomposition theorem with Hilbert transform and its application to narrowband time series with closely spaced frequency components. Mech Syst Signal Process 28:258–279

    Article  Google Scholar 

  44. Shen WC, Chen YH, Wu AYA (2014) Low-complexity sinusoidal-assisted EMD (SAEMD) algorithms for solving mode-mixing problems in HHT. Digit Signal Process 24:170–186

    Article  Google Scholar 

  45. Debnath L, Shah FA (2002) Wavelet transforms and their applications. Springer, Berlin

    Book  MATH  Google Scholar 

  46. Basu B, Gupta VK (1998) Seismic response of SDOF systems by wavelet modeling of nonstationary processes. J Eng Mech 124(10):1142–1150

    Article  Google Scholar 

  47. Chakraborty A, Basu B, Mitra M (2006) Identification of modal parameters of a mdof system by modified L-P wavelet packets. J Sound Vib 295(3):827–837

    Article  Google Scholar 

  48. Vandiver JK, Dunwoody AB, Campbell RB, Cook MF (1982) A mathematical basis for the random decrement vibration signature analysis technique. J Mech Des 104:307–313

    Article  Google Scholar 

  49. Asmussen JC (1997) Modal analysis based on the random decrement technique—application to civil engineering structures. Ph.D. thesis, Aalborg University, Department of Building Technology and Structural Engineering

  50. Friswell MI, Mottershead JE (1995) Finite element model updating in structural dynamics, vol 38. Springer, Berlin

    MATH  Google Scholar 

  51. Marwala T (2010) Finite-element-model updating using computational intelligence techniques. Springer, Berlin

    Book  MATH  Google Scholar 

  52. Allemang RJ, Brown DL (1982) A correlation coefficient for modal vector analysis. In: Proc. of the 1st international modal analysis conference. SEM, Orlando, USA, vol 1, pp 110–116

  53. Allemang RJ (2003) The modal assurance criterion-twenty years of use and abuse. J Sound Vib 37(8):14–23

    Google Scholar 

  54. Tarinejad R, Damadipour M (2014) Modal identification of structures by a novel approach based on FDD-wavelet method. J Sound Vib 333(3):1024–1045

    Article  Google Scholar 

  55. SMIT (2014) Structural modal identification toolsuite. http://smit.atlss.lehigh.edu/. Accessed 01 Mar 2014

Download references

Acknowledgements

First author acknowledges Ministry of Human Resource and Development, Govt. of India, for financial support during this study. The authors also acknowledge Prof. S. Talukdar for his help and valuable suggestions to carry out the bridge experiment.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Swarup Mahato & Arunasis Chakraborty

  2. Department of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, 30318, USA

    Meda Vinay Teja

Authors
  1. Swarup Mahato
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Meda Vinay Teja
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Arunasis Chakraborty
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Arunasis Chakraborty.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mahato, S., Teja, M.V. & Chakraborty, A. Combined wavelet–Hilbert transform-based modal identification of road bridge using vehicular excitation. J Civil Struct Health Monit 7, 29–44 (2017). https://doi.org/10.1007/s13349-017-0206-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13349-017-0206-y

Keywords

Search

Navigation