基于Lyapunov指数的非线性Lamb波的微裂纹检测
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摘要
为了提高在背景噪声干扰下非线性Lamb对于结构微裂纹的检测精度,提出了利用Duffing振子和Lya-punov指数对噪声干扰下的非线性Lamb波特征进行增强与量化分析的方法。首先,采用了庞加莱图确定Duffing系统外策动力参数;其次,将周期延拓滤波后的非线性Lamb波输入调整好的Duffing系统中,对系统输出时间序列进行相空间重构,计算出相应的最大Lyapunov指数。通过多个模型数据的仿真分析结果表明,即使在噪声干扰情况下,Lyapunov指数与裂纹大小也存在着良好的线性关系。该方法对噪声干扰下的微裂纹缺陷识别具有明显的优势,对提高非线性Lamb波的检测灵敏度具有重要意义。
In order to improve the detection accuracy of nonlinear Lamb for structural micro-cracks under background noise interference,the Duffing system and Lyapunov exponent are used to enhance and quantify the nonlinear Lamb characteristics under noise interference.Firstly,the Poincare diagram is used to determine the dynamic parameters of the Duffing system,and then the Lamb waves nonlinearly extended are input into the adjusted Duffing system.Lastly,the method uses the phase space reconstruction of the system output time series to obtain the corresponding Lyapunov exponent.Simulation results of several model data show that there is a good linear relationship between the Lyapunov exponent and the crack size even in the case of noise.This method has an obvious advantage for the identification of microcracks defects under noise interference,which is very important to improve the detection sensitivity of nonlinear Lamb wave.
In order to improve the detection accuracy of nonlinear Lamb for structural micro-cracks under background noise interference,the Duffing system and Lyapunov exponent are used to enhance and quantify the nonlinear Lamb characteristics under noise interference.Firstly,the Poincare diagram is used to determine the dynamic parameters of the Duffing system,and then the Lamb waves nonlinearly extended are input into the adjusted Duffing system.Lastly,the method uses the phase space reconstruction of the system output time series to obtain the corresponding Lyapunov exponent.Simulation results of several model data show that there is a good linear relationship between the Lyapunov exponent and the crack size even in the case of noise.This method has an obvious advantage for the identification of microcracks defects under noise interference,which is very important to improve the detection sensitivity of nonlinear Lamb wave.
引文
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[7]Matlack K H,Kim J Y,Jacobs L J,et al.Experimental characterization of efficient second harmonic generation of Lamb wave modes in a nonlinear elastic isotropic plate[J].Journal of Applied Physics,2011,109(1):014905.
[8]Bermes C,Kim J Y,Qu J,et al.Nonlinear Lamb waves for the detection of material nonlinearity[J].Mechanical Systems&Signal Processing,2008,22(3):638-646.
[9]Wan Xiang,Zhang Qing,Xu Guanghua,et al.Numerical simulation of nonlinear Lamb waves used in a thin plate for detecting buried micro-cracks[J].Sensors,2014,14(5):8528-8546.
[10]Dubrovski A D.The nature of chaos in conservative and dissipative systems of the Duffing-Holmes oscillator[J].Differential Equations,2010,46(11):1653-1657.
[11]Xie Zhongyu,Wang Kejun,Zhang Li.Improved algorithm for calculating Lyapunov exponent and distinguishing chaos from noise[J].Journal of Harbin Institute of Technology,2010,17(1):101-104.
[2]Li Weibin,Cho Y.Thermal fatigue damage assessment in an isotropic pipe using nonlinear ultrasonic guided waves[J].Experimental Mechanics,2014,54(8):1309-1318.
[3]Deng Ming,Xiang Yanxun,Liu Liangbing.Time-domain analysis and experimental examination of cumulative second-harmonic generation by primary Lamb wave propagation[J].Journal of Applied Physics,2011,109(11):1829-1836.
[4]Li Weibin,Cho Y,Ju T,et al.Evaluation of material degradation of composite laminates using nonlinear Lamb wave[M].Netherlands:Springer,2013:593-598.
[5]武静,张伟伟,马宏伟.利用Lyapunov指数实现超声导波检测的实验研究[J].振动与冲击,2014,33(24):82-87.Wu Jing,Zhang Weiwei,Ma Hongwei.Tests for ultrasonic guided wave inspection using Lyapunov exponents[J].Journal of Vibration&Shock,2014,33(24):82-87.(in Chinese)
[6]Yang Fei,Jing Lin,Zhang Weiwei,et al.Experimental and numerical studies of the oblique defects in the pipes using a chaotic oscillator based on ultrasonic guided waves[J].Journal of Sound&Vibration,2015,347:218-231.
[7]Matlack K H,Kim J Y,Jacobs L J,et al.Experimental characterization of efficient second harmonic generation of Lamb wave modes in a nonlinear elastic isotropic plate[J].Journal of Applied Physics,2011,109(1):014905.
[8]Bermes C,Kim J Y,Qu J,et al.Nonlinear Lamb waves for the detection of material nonlinearity[J].Mechanical Systems&Signal Processing,2008,22(3):638-646.
[9]Wan Xiang,Zhang Qing,Xu Guanghua,et al.Numerical simulation of nonlinear Lamb waves used in a thin plate for detecting buried micro-cracks[J].Sensors,2014,14(5):8528-8546.
[10]Dubrovski A D.The nature of chaos in conservative and dissipative systems of the Duffing-Holmes oscillator[J].Differential Equations,2010,46(11):1653-1657.
[11]Xie Zhongyu,Wang Kejun,Zhang Li.Improved algorithm for calculating Lyapunov exponent and distinguishing chaos from noise[J].Journal of Harbin Institute of Technology,2010,17(1):101-104.