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由于兰姆波的多模和频散特性，实际检测时在同一激发频率下存在多种模式的混合信号，而各模式信号有不同的频散特性，使得在时频混叠的情况下兰姆波的检测变得十分复杂.本文在频散补偿的基础上，通过时延函数建模，依靠不同模式频散趋势的差异性，将时频混叠信号的分离问题转化为部分模式混叠信号的分离问题.基于分数阶微分的理论，用信号幅值谱分数阶微分极大值和对应频率分别与微分阶次拟合多项式实现特征参数的提取并依靠特征参数重建幅值谱.结合相位谱重构时域信号以实现部分混叠信号中频散补偿后的模式的分离.最后恢复频散获得分离后的兰姆波信号.仿真和实验结果表明，本文方法不仅可以实现时频混叠多模式兰姆波信号的分离，更能保证分离精度，有助于复杂多模式频散信号的分离与处理的进一步研究.With the rapid development of material science and industrial technology, the application of ultrasonic Lamb wave to the industrial nondestructive testing has received considerable attention due to its advantages of rapidness, high efficiency, high accuracy, and low cost. However, the multimode and dispersion problem of Lamb waves are still challenging. Multimode mixed Lamb wave signals are often present at the same excitation frequency in the actual detection. To separate dispersive multimode Lamb waves overlapped in time and frequency domains, a separation method based on dispersion compensation and fractional differential is presented. The multimode Lamb waves overlapped in time and frequency domains are first compensated by using the dispersion characteristic. Based on the dispersion compensation, the time-delay function is modeled. The function is used as a transfer function. Its inverse is considered as a dispersion compensation function. Then, the amplitude spectra of Lamb waves are divided into fractional order differentials. The parameters of each mode are extracted by using the fitting polynomial between the maximum amplitude and the differential order and that between the peak frequency and the differential order. Its amplitude spectrum is extracted based on its parameters. By combining with its phase spectrum, the individual mode is constructed after the dispersion has been recovered. Simulation and experiments are performed on a 1 mm-thick stainless steel plate. The oblique transducers with the angle of 26 and the central frequency of 3 MHz are used to excite the S1 and A1 mode overlapped Lamb wave signal in the plate. The transducers are coupled with the stainless steel plate by using the ultrasonic couplant. Simulation and experimental analysis show that the present method can not only achieve the separation of time-frequency overlapped multimode Lamb waves, but also guarantee the separation precision. The main advantage of the presented method is the combination of the dispersion compensation and the fractional differential, which solves the problem of mixing with other mode signals after the single mode dispersion has been compensated, and improves the extraction precision of each mode. Therefore, this method can be used for separating the time-frequency overlapped multimode Lamb waves. It is conducible to the signal processing of multi-mode Lamb wave dispersion.
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Keywords:
- Lamb wave /
- dispersion compensation /
- fractional differential /
- multimode separation
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[1] Gao G J, Geng M X 2012 Appl. Acoust. 31 42 (in Chinese)[高广健, 邓明晰 2012 应用声学 31 42]
[2] 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]
[3] Zhai G, Jiang T, Kang L, Wang S 2010 IEEE Trans. Ultrason. Ferr. 57 2725
[4] Yu Y L, Zhang H Y, Feng G R, Ma S W 2013 Acta Acustica 38 576 (in Chinese)[于勇凌, 张海燕, 冯国瑞, 马世伟 2013 声学学报 38 576]
[5] Zhang H Y, Yao J C, Wang R, Ma S W 2014 Chin. Phys. Lett. 31 084301
[6] Wang D, Mao G J, Huang H 2012 Nondestruct. Test. 34 22 (in Chinese)[王杜, 毛国均, 黄辉 2012 无损检测 34 22]
[7] Xu B C, Wang M L, Jia Q 2014 Appl. Mech. Mater. 490 1698
[8] Fan S X, Zhang H Y, Lv D H 2007 Tech. Acoust. 26 628 (in Chinese)[樊仕轩, 张海燕, 吕东辉 2007 声学技术 26 628]
[9] Liu Z Q, Ta D A 2000 Tech. Acoust. 19 212 (in Chinese)[刘镇清, 他得安 2000 声学技术 19 212]
[10] Wang Z G, Liu D, Ta D A 2015 Appl. Acoust. 34 189 (in Chinese)[张正罡, 刘丹, 他得安 2015 应用声学 34 189]
[11] Zhang Y, Tang B P, Deng L 2014 J. Mech. Eng. 50 1 (in Chinese)[张焱, 汤宝平, 邓蕾 2014 机械工程学报 50 1]
[12] Chen X, Gao Y, Bao L 2014 J. Vibroeng. 16 464
[13] Sicard R, Goyette J, Zellouf D 2002 Ultrasonics 40 727
[14] Xu K, Ta D, Moilanen P, Wang W 2012 J. Acoust. Soc. Am. 131 2714
[15] Xu K L, Tan Z, Ta D A, Wang W Q 2014 Acta Acustica 39 99 (in Chinese)[许凯亮, 谈钊, 他得安, 王威琪 2014 声学学报 39 99]
[16] Wang J, Wang Q 2015 Inform. Res. 41 16 (in Chinese)[王晶, 王强 2015 信息化研究 41 16]
[17] Chen L, Wang Y M, Geng H Q, Ye W, Deng W L 2016 China Measurement Test 42 132 (in Chinese)[陈乐, 王悦民, 耿海泉, 叶伟, 邓文力 2016 中国测试 42 132]
[18] Samko S G, Kilbas A A, Marichev O I 1993 Fractional Integrals and Derivatives: Theory and Applications (Switzerland: Cordon and Breach Science Publishers) p21
[19] Li Y L, Yu S L, Zhen G 2007 Science in China Series B: Chemistry 37 361 (in Chinese)[李远禄, 于盛林, 郑罡 2007 中国科学B辑 化学 37 361]
[20] Chen X, Wang C L 2014 Acta Phys. Sin. 63 184301 (in Chinese)[陈晓, 汪陈龙 2014 物理学报 63 184301]
[21] Chen X, Gao Y, Wang C 2015 J. Vibroeng 17 4211
[22] Chen X, Wang C L 2015 Res. Nondestruc. Eval. 26 174
[23] Chen X, Wang C L 2014 J. Vibroeng. 16 2676.
[24] Yang Z Z, Zhou J L, Lang F N 2014 J. Image. Graph. 19 1418 (in Chinese)[杨柱中, 周激流, 郎方年 2014 中国图象图形学报 19 1418]
[25] Zhang Y, Huang S, Zhao W, Wang K 2015 Electr. Meas. Instrum. 52 19 (in Chinese)[张宇, 黄松岭, 赵伟, 王珅 2015 电测与仪表 52 19]
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