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Application of multisynchrosqueezing transform for structural modal parameter identification


The accurate identification of modal parameters is a critical issue in the determination of features of civil structures. In this paper, a novel method based on the multisynchrosqueezing transform (MSST) is proposed to identify modal parameters, including natural frequencies, damping ratios and mode shapes of civil structures. The MSST consists of multiple operations of a synchrosqueezing transform so that the time-frequency representation of an analyzed signal becomes more concentrated, which allows more accurate decomposition of the signal. To identify modal parameters based on the MSST, first, the natural extraction technique is used to obtain a free vibration response from a measured ambient vibration response. Second, the free vibration response is decomposed into several modes by using the MSST, and mode shape vectors can be obtained from the decomposed modes for all measurements. Then, instantaneous phases and instantaneous amplitudes of the modes are obtained by using the Hilbert transform. Finally, a least-squares curve fitting technique is performed on the instantaneous phases and instantaneous amplitudes to extract natural frequencies and damping ratios. Two numerical examples, a 3-degree-of-freedom free vibration response signal and a four-story frame steel structure subjected to environmental vibration, are used to demonstrate the applicability of the MSST-based method. In addition, an experimental validation based on a pedestrian overpass, located in Tufts University, United States, is conducted. Case analyses indicate that the MSST-based method can easily identify high-quality natural frequencies and damping ratios from measurements of structures.

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  1. 1.


  1. 1.

    Amezquita-Sanchez JP, Park HS, Adeli H (2017) A novel methodology for modal parameters identification of large smart structures using music, empirical wavelet transform, and hilbert transform. Eng Struct 147:148–159

    Article  Google Scholar 

  2. 2.

    Bagheri A, Ozbulut OE, Harris DK (2018) Structural system identification based on variational mode decomposition. J Sound Vib 417:182–197

    Article  Google Scholar 

  3. 3.

    Behmanesh Iman, Moaveni Babak (2016) Accounting for environmental variability, modeling errors, and parameter estimation uncertainties in structural identification. J Sound Vib 374:92–110

    Article  Google Scholar 

  4. 4.

    Caicedo JM, Dyke SJ, Johnson EA (2004) Natural excitation technique and eigensystem realization algorithm for phase I of the IASC-ASCE benchmark problem: simulated data. J Eng Mech 130(1):49–60

    Article  Google Scholar 

  5. 5.

    Daubechies I, Jianfeng L, Hau-Tieng W (2011) Synchrosqueezed wavelet transforms: an empirical mode decomposition-like tool. Appl Comput Harmonic Anal 30(2):243–261

    MathSciNet  Article  Google Scholar 

  6. 6.

    Dragomiretskiy K, Zosso D (2013) Variational mode decomposition. IEEE Trans Signal Process 62(3):531–544

    MathSciNet  Article  Google Scholar 

  7. 7.

    Johnson EA, Lam HF, Katafygiotis LS, Beck JL (2004) Phase I IASC-ASCE structural health monitoring benchmark problem using simulated data. J Eng Mech 130(1):3–15

    Article  Google Scholar 

  8. 8.

    Feldman M (2014) Hilbert transform methods for nonparametric identification of nonlinear time varying vibration systems. Mech Syst Signal Proces 47(1–2):66–77

    Article  Google Scholar 

  9. 9.

    Gilles J (2013) Empirical wavelet transform. IEEE Trans Signal Process 61(16):3999–4010

    MathSciNet  Article  Google Scholar 

  10. 10.

    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 

  11. 11.

    Hermans L, Van der Auweraer H (1999) Modal testing and analysis of structures under operational conditions: industrial applications. Mech Syst Signal Process 13(2):193–216

    Article  Google Scholar 

  12. 12.

    Hilbert D (1912) Begründung der kinetischen gastheorie. Math Ann 72(4):562–577

    MathSciNet  Article  Google Scholar 

  13. 13.

    James GH, Carne TG, Lauffer JP et al (1995) The natural excitation technique (next) for modal parameter extraction from operating structures. Modal Anal Int J Anal Exp Modal Anal 10(4):260

    Google Scholar 

  14. 14.

    Jin H, Lin J, Chen X, Yi C (2019) Modal parameters identification method based on symplectic geometry model decomposition. Shock Vib 2019(12):1–26

    Google Scholar 

  15. 15.

    Keyhani A, Mohammadi S (2018) Structural modal parameter identification using local mean decomposition. Meas Sci Technol 29(2):025003

    Article  Google Scholar 

  16. 16.

    Lazhari M, Sadhu A (2019) Decentralized modal identification of structures using an adaptive empirical mode decomposition method. J Sound Vib 447:20–41

    Article  Google Scholar 

  17. 17.

    Li H, Li Z, Mo W (2017) A time varying filter approach for empirical mode decomposition. Signal Process 138:146–158

    Article  Google Scholar 

  18. 18.

    Luo Z, Liu T, Yan S, Qian M (2018) Revised empirical wavelet transform based on auto-regressive power spectrum and its application to the mode decomposition of deployable structure. J Sound Vib 431:70–87

    Article  Google Scholar 

  19. 19.

    McNeill SI (2016) Decomposing a signal into short-time narrow-banded modes. J Sound Vib 373:325–339

    Article  Google Scholar 

  20. 20.

    Moaveni B, Behmanesh I (2012) Effects of changing ambient temperature on finite element model updating of the Dowling Hall footbridge. Eng Struct 43:58–68

    Article  Google Scholar 

  21. 21.

    Pan H, Yang Y, Li X, Zheng J, Cheng J (2019) Symplectic geometry mode decomposition and its application to rotating machinery compound fault diagnosis. Mech Syst Signal Process 114:189–211

    Article  Google Scholar 

  22. 22.

    Perez-Ramirez CA, Amezquita-Sanchez JP, Adeli H, Valtierra-Rodriguez M, Camarena-Martinez D, Romero-Troncoso RJ (2016) New methodology for modal parameters identification of smart civil structures using ambient vibrations and synchrosqueezed wavelet transform. Eng Appl Artif Intell 48:1–12

    Article  Google Scholar 

  23. 23.

    Rainieri C, Gargaro D, Fabbrocino G, Maddaloni G, Di Sarno L, Prota A, Manfredi G (2018) Shaking table tests for the experimental verification of the effectiveness of an automated modal parameter monitoring system for existing bridges in seismic areas. Struct Control Health Monit 25(7):e2165

    Article  Google Scholar 

  24. 24.

    Xin Yu, Hao H, Li J (2019) Operational modal identification of structures based on improved empirical wavelet transform. Struct Control Health Monit 26(3):e2323

    Article  Google Scholar 

  25. 25.

    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 

  26. 26.

    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 

  27. 27.

    Yang JN, Lei Y, Pan S, Huang N (2003) System identification of linear structures based on Hilbert-Huang spectral analysis. Part 2: Complex modes. Earthq Eng Struct Dyn 32(10):1533–1554

    Article  Google Scholar 

  28. 28.

    Yang J, Li P, Yang Y, Dian X (2018) An improved EMD method for modal identification and a combined static-dynamic method for damage detection. J Sound Vib 420:242–260

    Article  Google Scholar 

  29. 29.

    Gang Yu, Wang Z, Zhao P (2018) Multisynchrosqueezing transform. IEEE Trans Ind Electron 66(7):5441–5455

    Google Scholar 

  30. 30.

    Zhou W, Feng Z, Liu D, Wang X, Chen B (2020) Modal parameter identification of structures based on short-time narrow-banded mode decomposition. Adv Struct Eng 23(14):3062–3074

    Article  Google Scholar 

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The authors are grateful for the financial support from the National Natural Science Foundation of China through Grant no. 51868045 and from Shaanxi Institute of Technology through Grant no. Gfy20-03.

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Correspondence to Hu Sun.

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Sun, H., Di, S., Du, Z. et al. Application of multisynchrosqueezing transform for structural modal parameter identification. J Civil Struct Health Monit 11, 1175–1188 (2021).

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  • Signal decomposition
  • Modal parameter identification
  • Multisynchrosqueezing transform
  • Civil structures