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为降低噪声对超声兰姆波检测信号的影响，提高信噪比和增加特征提取的精度，提出了一种赛利斯模型下分数阶微分方法用于超声兰姆波信号去噪. 该方法对含噪声的兰姆波信号幅值谱进行各阶分数微分，用赛利斯分布作为待处幅值谱的模型，提出了幅值谱分数阶微分最大值和过零点与微分阶数的拟合三次关系式，建立了幅值谱特征参数的计算式来提取特征参数和重建原始信号的幅值谱，并结合相位谱重构去噪后的兰姆波信号. 仿真结果表明，该方法可以有效地提高兰姆波信号甚至微弱兰姆波信号的信噪比，同时降低均方误差和平滑度. 实验结果显示，与小波去噪和集合经验模态去噪方法相比，该方法在没有信号先验知识的情况下，可以更有效地去除兰姆波信号的噪声，同时更好地保留主信号的细节特征. 因此，本文提出的方法可以有效地去除兰姆波检测信号中混入的噪声.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 60 104303]
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[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 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 61 196301]
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[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 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 62 164501]
[22] Hu J B, Zhao L D 2013 Acta Phys. Sin. 62 240504(in Chinese)[胡建兵, 赵灵冬 2013 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 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 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 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 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 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 62 164501]
[22] Hu J B, Zhao L D 2013 Acta Phys. Sin. 62 240504(in Chinese)[胡建兵, 赵灵冬 2013 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 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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