Research on Morlet Wavelet Based Lamb Wave Spatial Sampling Signal Optimization Method

  • Bin Liu (刘彬)
  • Tingzhang Liu (刘廷章)Email author
  • Fanqin Meng (孟凡芹)


In recent years, Lamb wave and piezoelectric transducers (PZTs) array based wavenumber filtering technique for damage estimation has been gradually studied. Compared with the time domain and frequency domain analysis of the Lamb wave signals, the wavenumber domain analysis is an effective approach to distinguish wave propagating direction and wave modes. However, the spatial resolution sampled by the PZTs is lower than that sampled by scanning laser Doppler vibrometer. As for the diameter of the PZT, it cannot be very small. In this paper, a new Lamb wave spatial sampling signal optimization method based on Morlet wavelet is proposed. Firstly, the frequency band parameter of the Morlet mother wavelet function is calculated by the Lamb wave excitation signal. Then, the sum of squared errors between the Lamb wave spatial sampling signal and the Morlet wavelet function fitting waveform at each scale factor and time factor is calculated. Finally, the scale factor and time factor corresponding to the least sum of squared errors can be judged to be the best match scale factor and time factor respectively, and the Morlet wavelet function fitting waveform in that scale factor and time factor can be seen as the optimized Lamb wave spatial sampling signal. The validation experiment performed on a glass fiber epoxy composite plate shows that the proposed method can improve the spatial resolution and length of the Lamb wave spatial sampling signal, and the sum of squared errors of this method is no more than 0.2.

Key words

structural health monitoring Lamb wave spatial sampling Morlet wavelet 

CLC number

TN 911 

Document code


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



The authors thank to YUAN Shenfang and QIU Lei for their help in the experiment.


  1. [1]
    FARRAR C R, WORDEN K. An introduction to structural health monitoring [J]. Philosophical Transactions of The Royal Society A, 2007, 365(1851): 303–315.CrossRefGoogle Scholar
  2. [2]
    POHL J, WILLBERG C, GABBERT U, et al. Experimental and theoretical analysis of Lamb wave generation by piezoceramic actuators for structural health monitoring [J]. Experimental Mechanics, 2012, 52(4): 429–438.CrossRefGoogle Scholar
  3. [3]
    GE L Y, WANG X W, JIN C H. Numerical modeling of PZT-induced Lamb wave-based crack detection in plate-like structures [J]. Wave Motion, 2014, 51(6): 867–885.MathSciNetCrossRefGoogle Scholar
  4. [4]
    ZHU R, HUANG G L, YUAN F G. Fast damage imaging using the time-reversal technique in the frequencywavenumber domain [J]. Smart Materials and Structures, 2013, 22(7): 075028.CrossRefGoogle Scholar
  5. [5]
    CAI J, YUAN S F, QING X P, et al. Linearly dispersive signal construction of Lamb waves with measured relative wavenumber curves [J]. Sensors and Actuators A: Physical, 2015, 221: 41–52.CrossRefGoogle Scholar
  6. [6]
    SOHN H, DUTTA D, YANG J Y, et al. Automated detection of delamination and disbond from wavefield images obtained using a scanning laser vibrometer [J]. Smart Materials and Structures, 2011, 20(4): 045017.CrossRefGoogle Scholar
  7. [7]
    MICHAELS T E, MICHAELS J E, RUZZENE M. Frequency-wavenumber domain analysis of guided wavefields [J]. Ultrasonics, 2011, 51(4): 452–466.CrossRefGoogle Scholar
  8. [8]
    ROGGE M D, LECKEY C A C. Characterization of impact damage in composite laminates using guided wavefield imaging and local wavenumber domain analysis [J]. Ultrasonics, 2013, 53(7): 1217–1226.CrossRefGoogle Scholar
  9. [9]
    TIAN Z H, YU L Y. Lamb wave frequencywavenumber analysis and decomposition [J]. Journal of Intelligent Material Systems and Structures, 2014, 25(9): 1107–1123.CrossRefGoogle Scholar
  10. [10]
    FLYNN E B, CHONG S Y, JARMER G J, et al. Structural imaging through local wavenumber estimation of guided waves [J]. NDT & E International, 2013, 59: 1–10.CrossRefGoogle Scholar
  11. [11]
    KUDELA P, RADZIENŃSKI M, OSTACHOWICZ W. Identification of cracks in thin-walled structures by means of wavenumber filtering [J]. Mechanical Systems and Signal Processing, 2015, 50/51: 456–466.CrossRefGoogle Scholar
  12. [12]
    PUREKAR A S, PINES D J, SUNDARARAMAN S, et al. Directional piezoelectric phased array filters for detecting damage in isotropic plates [J]. Smart Materials and Structures, 2004, 13(4): 838–850.CrossRefGoogle Scholar
  13. [13]
    PUREKAR A S, PINES D J. Damage detection in thin composite laminates using piezoelectric phased sensor arrays and guided lamb wave interrogation [J]. Journal of Intelligent Material Systems and Structures, 2010, 21(10): 995–1010.CrossRefGoogle Scholar
  14. [14]
    WANG Y, YUAN S F, QIU L. Improved wavelet-based spatial filter of damage imaging method on composite structures [J]. Chinese Journal of Aeronautics, 2011, 24(5): 665–672.CrossRefGoogle Scholar
  15. [15]
    QIU L, LIU B, YUAN S F, et al. A spatial filter and two linear PZT arrays based composite structure imaging method [J]. Journal of Vibroengineering, 2015, 17(3): 1218–1231.Google Scholar
  16. [16]
    QIU L, LIU B, YUAN S F, et al. Impact imaging of aircraft composite structure based on a modelindependent spatial-wavenumber filter [J]. Ultrasonics, 2016, 64: 10–24.CrossRefGoogle Scholar
  17. [17]
    QIU L, LIU B, YUAN S F, et al. A scanning spatialwavenumber filter and PZT 2-D cruciform array based on-line damage imaging method of composite structure [J]. Sensors and Actuators A, 2016, 248: 62–72.CrossRefGoogle Scholar
  18. [18]
    QIU L, YUAN S F, ZHANG X Y, et al. A time reversal focusing based impact imaging method and its evaluation on complex composite structures [J]. Smart Materials and Structures, 2011, 20(10): 105014.CrossRefGoogle Scholar
  19. [19]
    QIU L, YUAN S F, CHANG F K, et al. On-line updating Gaussian mixture model for aircraft wing spar damage evaluation under time-varying boundary condition [J]. Smart Materials and Structures, 2014, 23(12): 125001.CrossRefGoogle Scholar

Copyright information

© Shanghai Jiaotong University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Bin Liu (刘彬)
    • 1
    • 2
  • Tingzhang Liu (刘廷章)
    • 1
    Email author
  • Fanqin Meng (孟凡芹)
    • 2
  1. 1.School of Mechatronic Engineering and AutomationShanghai UniversityShanghaiChina
  2. 2.Department of Military Supply and FuelAir Force Logistics CollegeXuzhou, JiangsuChina

Personalised recommendations