Article Article
Tsallis Distribution-Based Fractional Derivative Method for Lamb Wave Signal Recovery

A new fractional derivative method based on the Tsallis distribution function is developed to recover the Lamb wave signals from the noisy Lamb wave signals. After the fractional derivative of the amplitude spectrum of the noisy Lamb signal at different derivative orders, the quartic polynomial function between the peak amplitude and the derivative order as well as that between the peak frequency and the derivative order is proposed based on the Tsallis distribution function. Then, the characteristic parameters of the amplitude spectrum are deduced by using the proposed polynomial relationship. Finally, the noise-free Lamb wave signal is recovered based on the characteristic parameters. Simulated results indicate that the Lamb wave signals can be recovered in the case of the white noise, the transient noise and the sine wave signal. Experimental results confirm the validity of the method. Consequently, the developed method can recover the Lamb wave signals effectively.

  1. X. Chen and M. Wan. Ultrasonics 43:357–364 (2005).
  2. V. Prado, R. Higuti, C. Kitano, O. Martinez-Graullera, and J. Adamowskic. NDT&E Int. 59:86–95 (2013).
  3. A. Leleux, P. Micheau, and M. Castaings. J. Nondestruct. Eval. 32:200–214 (2013).
  4. Y. Lu and L. Ye. J. Comp. Mat. 43:3211–3230 (2009).
  5. K. Xu, D. Ta, B. Hu, P. Laugier, and W. Wang. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 61:997–1005 (2014).
  6. L. Zeng, J. Lin, Y. Lei, and H. Xie. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 60:1025–1029 (2014).
  7. S. Hao, B. Strom, G. Gordon, S. Krishnaswamy, and J. Achenbach. Research in Nondestructive Evaluation 22:208–230 (2011).
  8. X. Chen and J. Li. J. Vibroengineering 15:1157–1165 (2013).
  9. V. Matz, R. Smid, S. Starman, and M. Kreidl. Ultrasonics 49:752–759 (2009).
  10. X. Chen, X. Li, S. Wang, Z. Yang, and B. Chen. IEEE Trans. Instrum. Meas. 62:1354–1363 (2013).
  11. A. Boudraa, J. Cexus, and Z. Saidi. Int. J. Sign. Proc. 1:33–37 (2004).
  12. G. Li, L. Shi, and X. Wang. Acta Metrologica Sinica 27:149–152 (2006).
  13. Z Wu and N. Huang. Adv. in Adapt. Data Anal. 1:1–41 (2009).
  14. H. Zhang, Y. Cao, J. Yu, and X. Chen. Acta Phys. Sin. 60:114301-1 – 114301-9 (2011).
  15. S. Samko, A. Kilbas, and D. Marichev. Fractional Integrals and Derivatives: Theory and Applications. Switzerland: Cordon and Breach Science Publishers (1993).
  16. C. Tsallis. J. Stat. Phys. 52:479–487 (1988).
  17. Y. Li, S. Yu, and G. Zhen. Sci. China, Ser. B: Chem. 50:797–805 (2007).
  18. B. Xu, V. Giugiutiu, and L. Yu. Proc. SPIE. 7292:72920I-1 – 72920I-12 (2009).
  19. X. Chen and K. Xu. Appl. Mech. Mater. 157:987–990 (2012).
  20. X. Chen and H. Wu. Adv. Mater. Res. 458:701–704 (2012).
Usage Shares
Total Views
30 Page Views
Total Shares
0 Tweets
0 PDF Downloads
0 Facebook Shares
Total Usage