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To suppress the noise and increase the accuracy of feature extraction for ultrasonic Lamb wave signals, we present a new method based on the Tsallis mode and the fractional-order differential in this paper. Firstly, the fractional-order differentials of the amplitude spectrum of the noisy Lamb signal at different orders are obtained by using the fractional differential theory. Then, the cubic polynomial between the peak amplitude and the derivative order, and that between the peak frequency and the derivative order are proposed based on the Tsallis mode. The characteristic parameters of the amplitude spectrum are extracted with the developed equations. Finally, the Lamb signal without the noise is restored by combining the amplitude spectrum with the phase spectrum. Simulated and experimental results show that the proposed method can improve the performance parameters such as mean square error, r, and signal-to-noise ratio. Consequently, the new method based on the Tsallis mode and the fractional-order differential has the effective noise suppression performance for Lamb wave signals.
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Keywords:
- Lamb wave /
- fractional-order differential /
- Tsallis mode /
- noise suppression
[1] Hong K, Yuan L, Shen Z H, Ni X W 2011 Acta Phys. Sin. 60 104303(in Chinese)[洪轲, 袁玲, 沈中华, 倪晓武 2011 物理学报 60 104303]
[2] Pavlopoulou S, Soutis C, Manson G 2012 Plastics, Rubber Compos. 41 61
[3] Zhang H Y, Cao Y P, Yu J B, Chen X H 2011 Acta Phys. Sin. 60 114301(in Chinese)[张海燕, 曹亚萍, 于建波, 陈先华 2011 物理学报 60 114301]
[4] Ding H X, Shen Z H, Li J, Zhu X F, Ni X W 2012 Acta Phys. Sin. 61 196301(in Chinese)[丁红星, 沈中华, 李加, 祝雪丰, 倪晓武 2012 物理学报 61 196301]
[5] Zhang H Y, Yu J B 2011 Chin. Phys. B 20 094301
[6] Deng M X, Xiang Y X 2010 Chin. Phys. B 19 115202
[7] Zhang H Y, Yao J C, Ma S W 2014 Chin. Phys. Lett. 31 034301
[8] Beard M D, Lowe M J S 2003 Rock Mech. Mining Sci. 40 527
[9] Laguerre L, Treyssede F 2011 Eur. J. Environ. Civil Eng. 15 487
[10] Prado V T, Higuti R T 2013 NDT&E International 59 86
[11] Cawley P, Lowe M J S, Alleyne D N, Pavlakovic B N, Wilcox P 2003 Mater. Eval. 61 66
[12] Chen X, Wan M 2005 Ultrasonics 43 357
[13] Lu Y, Ye L 2009 J. Compos. Mater. 43 26
[14] Liu Z Q, Zhang H Y, Ma X S 2003 Acta Phys. Sin. 52 2492(in Chinese)[刘镇清, 张海燕, 马小松 2003 物理学报 52 2492]
[15] Abbate A, Koay J 1997 IEEE Trans. Ultrason. Ferroelect. Freq. Contr.44 14
[16] Pardo E, Emeterio J, Rodriguez M, Ramos A 2006 Ultrasonics 44 1063
[17] Boudraa A O, Cexus J C, Saidi Z 2004 Int. J. Signal Process. 1 1
[18] Wu Z H, Huang N E 2009 Adv. Adapt. Data Anal. 1 1
[19] Chen X, Li J 2013 J. Vibroengineer. 15 1157
[20] Zhang X P 2001 IEEE Trans. Neural Networks 12 567
[21] Zhang Y 2013 Acta Phys. Sin. 62 164501(in Chinese)[张毅 2013 物理学报 62 164501]
[22] Hu J B, Zhao L D 2013 Acta Phys. Sin. 62 240504(in Chinese)[胡建兵, 赵灵冬 2013 物理学报 62 240504]
[23] Xin B G, Chen T, Liu Y Q 2011 Acta Phys. Sin. 60 048901(in Chinese)[辛宝贵, 陈通, 刘艳芹 2011 物理学报 60 048901]
[24] Podlubny I 1999 IEEE Trans. Automatic Control 44 208
[25] Pu Y F, Wang W X 2008 Sci. China F: Inform. Sci. 51 1319
[26] Samko S C, kilbas A A, Marichev D I 1993 Fractional Integrals and Derivatives: Theory and Applications (Switzerland: Cordon and Breach Science Publishers) p21
[27] Tsallis C 1988 J. Statist. Phys. 52 479
[28] Li Y L, Yu S L 2007 Sci. China B: Chemistry 50 797
[29] Xu B, Giurgiutiu V, Yu L 2009 SPIE 7292 72920I
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[1] Hong K, Yuan L, Shen Z H, Ni X W 2011 Acta Phys. Sin. 60 104303(in Chinese)[洪轲, 袁玲, 沈中华, 倪晓武 2011 物理学报 60 104303]
[2] Pavlopoulou S, Soutis C, Manson G 2012 Plastics, Rubber Compos. 41 61
[3] Zhang H Y, Cao Y P, Yu J B, Chen X H 2011 Acta Phys. Sin. 60 114301(in Chinese)[张海燕, 曹亚萍, 于建波, 陈先华 2011 物理学报 60 114301]
[4] Ding H X, Shen Z H, Li J, Zhu X F, Ni X W 2012 Acta Phys. Sin. 61 196301(in Chinese)[丁红星, 沈中华, 李加, 祝雪丰, 倪晓武 2012 物理学报 61 196301]
[5] Zhang H Y, Yu J B 2011 Chin. Phys. B 20 094301
[6] Deng M X, Xiang Y X 2010 Chin. Phys. B 19 115202
[7] Zhang H Y, Yao J C, Ma S W 2014 Chin. Phys. Lett. 31 034301
[8] Beard M D, Lowe M J S 2003 Rock Mech. Mining Sci. 40 527
[9] Laguerre L, Treyssede F 2011 Eur. J. Environ. Civil Eng. 15 487
[10] Prado V T, Higuti R T 2013 NDT&E International 59 86
[11] Cawley P, Lowe M J S, Alleyne D N, Pavlakovic B N, Wilcox P 2003 Mater. Eval. 61 66
[12] Chen X, Wan M 2005 Ultrasonics 43 357
[13] Lu Y, Ye L 2009 J. Compos. Mater. 43 26
[14] Liu Z Q, Zhang H Y, Ma X S 2003 Acta Phys. Sin. 52 2492(in Chinese)[刘镇清, 张海燕, 马小松 2003 物理学报 52 2492]
[15] Abbate A, Koay J 1997 IEEE Trans. Ultrason. Ferroelect. Freq. Contr.44 14
[16] Pardo E, Emeterio J, Rodriguez M, Ramos A 2006 Ultrasonics 44 1063
[17] Boudraa A O, Cexus J C, Saidi Z 2004 Int. J. Signal Process. 1 1
[18] Wu Z H, Huang N E 2009 Adv. Adapt. Data Anal. 1 1
[19] Chen X, Li J 2013 J. Vibroengineer. 15 1157
[20] Zhang X P 2001 IEEE Trans. Neural Networks 12 567
[21] Zhang Y 2013 Acta Phys. Sin. 62 164501(in Chinese)[张毅 2013 物理学报 62 164501]
[22] Hu J B, Zhao L D 2013 Acta Phys. Sin. 62 240504(in Chinese)[胡建兵, 赵灵冬 2013 物理学报 62 240504]
[23] Xin B G, Chen T, Liu Y Q 2011 Acta Phys. Sin. 60 048901(in Chinese)[辛宝贵, 陈通, 刘艳芹 2011 物理学报 60 048901]
[24] Podlubny I 1999 IEEE Trans. Automatic Control 44 208
[25] Pu Y F, Wang W X 2008 Sci. China F: Inform. Sci. 51 1319
[26] Samko S C, kilbas A A, Marichev D I 1993 Fractional Integrals and Derivatives: Theory and Applications (Switzerland: Cordon and Breach Science Publishers) p21
[27] Tsallis C 1988 J. Statist. Phys. 52 479
[28] Li Y L, Yu S L 2007 Sci. China B: Chemistry 50 797
[29] Xu B, Giurgiutiu V, Yu L 2009 SPIE 7292 72920I
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