基于Lyapunov指数的非线性Lamb波的微裂纹检测

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。

Micro-crack Detection of Nonlinear Lamb Wave Based on Lyapunov Exponent

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.