Journal of Mechanical Science and Technology

The Korean Society of Mechanical Engineers (대한기계학회)
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Dispersion-Based Continuous Wavelet Transform for the Analysis of Elastic Waves

  • Sun, Kyung-Ho (School of Mechanical and Aerospace Engineering and National Creative Research Initiatives Center for Multiscale Design, Seoul National University) ;
  • Hong, Jin-Chul (Test Team 5, Test Center, Research and Development Division for Hyundai Motor Company and Kia Motors Corporation) ;
  • Kim, Yoon-Young (School of Mechanical and Aerospace Engineering and National Creative Research Initiatives Center for Multiscale Design, Seoul National University)
  • Published : 2006.12.01
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Abstract

The continuous wavelet transform (CWT) has a frequency-adaptive time-frequency tiling property, which makes it popular for the analysis of dispersive elastic wave signals. However, because the time-frequency tiling of CWT is not signal-dependent, it still has some limitations in the analysis of elastic waves with spectral components that are dispersed rapidly in time. The objective of this paper is to introduce an advanced time-frequency analysis method, called the dispersion-based continuous wavelet transform (D-CWT) whose time-frequency tiling is adaptively varied according to the dispersion relation of the waves to be analyzed. In the D-CWT method, time-frequency tiling can have frequency-adaptive characteristics like CWT and adaptively rotate in the time-frequency plane depending on the local wave dispersion. Therefore, D-CWT provides higher time-frequency localization than the conventional CWT. In this work, D-CWT method is applied to the analysis of dispersive elastic waves measured in waveguide experiments and an efficient procedure to extract information on the dispersion relation hidden in a wave signal is presented. In addition, the ridge property of the present transform is investigated theoretically to show its effectiveness in analyzing highly time-varying signals. Numerical simulations and experimental results are presented to show the effectiveness of the present method.

Keywords

References

  1. ？Angrisani, L. and D'Arco, M., 2002, 'A Measurement Method Based on a Modified Version of the Chirp let Transform for Instantaneous Frequency Estimation,' IEEE Transactions on Instrumentation and Measurement, Vol. 51, pp. 704-711 https://doi.org/10.1109/TIM.2002.803295
  2. Auger, F. and Flandrin, P., 1995, 'Improving the Readability of Time-Frequency and TimeScale Representations by the Reassignment Method,' IEEE Transactions on Signal Processing, Vol. 43, pp. 1068-1089 https://doi.org/10.1109/78.382394
  3. Baraniuk, R. G. and Jones, D. L., 1996, 'Wigner-Based Formulation of the Chirplet Transform,' IEEE Transactions on Signal Processing, Vol. 44, pp.3129-3135 https://doi.org/10.1109/78.553486
  4. Cho, S. H., Sun, K. H., Lee, J. S. and Kim, Y. Y., 2004, 'The Measurement of Elastic Waves in a Nonferromagnetic Plate by a Patch-Type Magnetostrictive sensor,' Proceedings of the SPIE, Vol. 5384, pp. 120-130 https://doi.org/10.1117/12.539641
  5. Daubechies, I., 1992, Ten Lectures on Wavelets, Philadelphia: SIAM
  6. Delprat, N. et al., 1992, 'Asymptotic Wavelet and Gabor Analysis: Extraction of Instantaneous Frequencies,' IEEE Transactions on Information Theory, Vol. 38, pp. 644-665 https://doi.org/10.1109/18.119728
  7. Gabor, D., 1946, 'Theory of Communication,' Proceedings of the Institute of Electrical Engineers, Vol. 93, pp. 429-457
  8. Graff, K. F., 1975, Wave Motion in Elastic Solids, Ohio State Univ. Press. : Columbus
  9. Hong, J. -C. and Kim, Y. Y., 2004, 'The De？termination of the Optimal Gabor Wavelet Shape for the best Time-Frequency Localization Using the Entropy Concept,' Experimental Mechanics, Vol. 44, pp. 387 - 395 https://doi.org/10.1007/BF02428092
  10. Hong, J. -C., Sun, K. H. and Kim, Y. Y., 2005, 'Dispersion-Based Short-Time Fourier Transform Applied to Dispersive Wave Analysis,' Journal of Acoustical Society of America, Vol. 117, pp. 2949-2960 https://doi.org/10.1121/1.1893265
  11. Jones, D. L. and Park, T. W., 1990, 'A High Resolution Data- Adaptive Time- Frequency Representation,' IEEE Transactions on Acoustic, Speech, and Signal Processing, Vol. 38, pp.2127-2135 https://doi.org/10.1109/29.61539
  12. Jones, G. and Boashash, B., 1992, 'Window Matching in the Time-Frequency Plane and the Adaptive Spectrogram,' Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, pp. 87-90
  13. Kim, Y. Y. and Kim, E. H., 2001, 'Effectiveness of the Continuous Wavelet Transform in the Analysis of Some Dispersive Elastic Waves,' Journal of Acoustical Society of America, Vol. 110, pp.86-94 https://doi.org/10.1121/1.1378348
  14. Lanza di Scalea, F. and McNamara, J., 2004, 'Measuring High-Frequency Wave Propagation in Railroad Tracks by Joint Time-Frequency Analysis,' Journal of Sound and Vibration, Vol. 273, pp.637-651 https://doi.org/10.1016/S0022-460X(03)00563-7
  15. Lemistre, M. and Balageas, D., 2001, 'Structural Health Monitoring System Based on Diffracted Lamb Wave Analysis by Multiresolution ？Processing,' Smart Materials and Structures, Vol. 10, pp. 504-511 https://doi.org/10.1088/0964-1726/10/3/312
  16. Mallat, S. and Zhang, Z., 1993, 'Matching Pursuits with Time-Frequency Dictionaries,' IEEE Transactions on Signal Processing, Vol. 41, pp. 3397-3415 https://doi.org/10.1109/78.258082
  17. Mallat, S., 1998, A Wavelet Tour of Signal Processing, Academic Press: London
  18. Mann, S. and Haykin, S., 1995, 'The Chirp1et Transform: Physical Considerations,' IEEE Transactions on Signal Processing, Vol. 43, pp.2745-2761 https://doi.org/10.1109/78.482123
  19. Miklowitz, J., 1978, Elastic Waves and Waveguides, North-Holland: New York
  20. Niethammer, M., Jacobs, L. J., Qu, J. and Jarzynski, J., 2001, 'Time-Frequency Representations of Lamb Waves,' Journal of Acoustical Society of America, Vol. 109, pp. 1841-1847 https://doi.org/10.1121/1.1357813
  21. Onsay, T. and Haddow, A. G., 1994, 'Wavelet Transform Analysis of Transient Wave Propagation in a Dispersive Medium,' Journal of Acoustical Society of America, Vol. 95, pp.1441-1449 https://doi.org/10.1121/1.408586
  22. Sun, X. and Baa, Z., 1996, 'Adaptive Spectrogram for Time-Frequency Signal Analysis,' Proceedings of 8th IEEE Signal Processing Workshop on Statistical Signal and Array Processing, pp.460-463 https://doi.org/10.1109/SSAP.1996.534915
  23. Wigner, E. P., 1932, 'On the Quantum Correction for Thermodynamic Equilibrium,' Physics Review, Vol. 40, pp. 749-759 https://doi.org/10.1103/PhysRev.40.749