基于Lyapunov指数的超声导波检测技术

Ultrasonic Guided Wave Inspection Method Based on Lyapunov Exponents

为了提高超声导波的检测灵敏度,提出了一种基于杜芬方程Lyapunov指数特性的超声导波识别方法,该方法利用了杜芬方程对系统参数的敏感性及其对噪声信号的免疫特性。首先,分析了杜芬方程检测导波信号的数学原理;其次,讨论了如何设定检测系统参数,给出了可用于检测导波信号的杜芬系统;最后,通过分析比较噪声和导波信号对Lyapunov指数的不同影响,证明了该方法识别强噪声下弱超声导波的有效性。数值算例表明,通过合理设置杜芬方程参数使系统处于混沌状态,当输入导波信号和混有噪声的导波信号时,系统由混沌状态转变为极限环运动,利用杜芬系统状态改变可实现对强噪声下弱超声导波的识别,该方法可有效延长超声导波的检测范围和提高检测小缺陷的灵敏度。

In order to extend the detection range of the ultrasonic guided wave testing technique and to improve the sensitivity of recognizingsmall defects,a new method of weak signal detection using Lyapunov exponents of the Duffing equation is proposed.Firstly,the mathematical principle of the Duffing equation for guided wave signal detection is analyzed,and the best way to set up the parameters of the inspection system is further researched.Based on studying the phase portraits and Lyapunov exponents of the Duffing system with and without inputting the pure noise and guided wave signal,the feasibility of the proposed method is verified.It is shown that the Duffing system is sensitive to the guided wave and has strong immunity to the noise.Thus,the guided wave signal inspection method based on the Duffing system is a valid inspection method for the weak ultrasonic guided wave.Numerical examples show that the motion states of the Duffing system can transform from strange attractor to limit cycle if the inputting guided wave signal is polluted with strong noise.The proposed method can be used to detect weak guided wave signal with strong noise.It is significant in improving the sensitivity of small defects detection using ultrasonic guided wave nondestructive detection.