电磁超声非线性效应表征的Lyapunov指数分析方法  

Electromagnetic ultrasonic nonlinear effects for the characterization of Lyapunov exponential analytical method

作　　者：蔡智超[1,2,3] 李豪 倪惠发 张磊 Cai Zhichao;Li Hao;Ni Huifa;Zhang Lei(State Key Laboratory of Performance Monitoring Protecting of Rail Transit Infrastructure,East China Jiaotong University,Nanchang 330013,China;School of Electrical and Automation Engineering,East China Jiaotong University,Nanchang 330013,China;Key Laboratory of Nondestructive Testing,Fujian Polytechnic Normal University,Fuqing 350300,China)

机构地区：[1]华东交通大学轨道交通基础设施性能监测与保障国家重点实验室,南昌330013 [2]华东交通大学电气与自动化工程学院,南昌330013 [3]无损检测技术福建省高校重点实验室,福清350300

出　　处：《仪器仪表学报》2022年第10期223-232,共10页Chinese Journal of Scientific Instrument

基　　金：国家自然科学基金青年科学基金(51807065);无损检测技术福建省高校重点实验室(S2-KF2007)项目资助。

摘　　要：针对金属疲劳损伤非线性效应非接触式检测需求及其低信噪比问题,提出电磁超声方案对非线性效应进行信号拾取,并采用Duffing混沌系统实现对金属疲劳程度定量评估,进而依据相轨图和Lyapunov指数表征材料疲劳演变非线性特性。采用有限元方法分析铝合金疲劳损伤演变过程,基于材料Murnaghan模型和微裂纹等效弹簧模型,研究疲劳损伤演变过程中相对非线性系数变化规律;进而探究Duffing混沌系统对于非线性效应特征提取的抗噪能力,当信噪比在20 dB时,相对非线性系数误差为132.12%,而Lyapunov指数误差为8.82%,因而Lyapunov指数较非线性系数而言有显著的抗噪能力;此外,基于对铝合金疲劳检测进行实验研究,验证了电磁超声非线性效应Lyapunov指数表征分析方法的可行性及准确性。研究结果表明,Lyapunov指数能够有效应对电磁超声非线性检测过程中低信噪比问题,从而提升非线性特征拾取的灵敏度和可重复性,进一步增强电磁超声等非接触式超声检测方法在疲劳在线检测演变的工程应用的贡献。Aiming at the non-contact detection needs of nonlinear effects of metal fatigue damage and its low signal-to-noise ratio, an electromagnetic ultrasonic scheme is proposed to collect signals for nonlinear effect. The Duffing chaotic system is used to quantitatively assess the fatigue degree of metal. Then, the nonlinear characteristics of material fatigue evolution are characterized according to the phase trajectory diagram and the Lyapunov index. In this article, the evolution process of fatigue damage of aluminum alloy is analyzed by the finite element method, and the relative nonlinear coefficient change law during the evolution of fatigue damage is studied based on the material Murnaghan model and the micro-crack equivalent spring model. In addition, the noise immunity of the Duffing chaotic system for the extraction of nonlinear effect features is investigated. When the signal-to-noise ratio is 20 dB, the relative nonlinearity coefficient error is 132.12%, while the Lyapunov index error is 8.82%. Therefore, the Lyapunov index has significant noise immunity compared with the nonlinear coefficient. In addition, based on the experimental study of fatigue detection of aluminum alloy, the feasibility and accuracy of the Lyapunov index characterization and analysis method of nonlinear effect of electromagnetic ultrasound are evaluated. Results show that the Lyapunov index can effectively address the problem of low signal-to-noise ratio in the process of electromagnetic ultrasonic nonlinear detection. In this way, the sensitivity and repeatability of nonlinear feature picking are improved, and the contribution of non-contact ultrasonic detection methods is further enhanced, such as electromagnetic ultrasonic in the evolution of fatigue online detection.

关 键 词：非线性电磁超声 LYAPUNOV指数 疲劳损伤 混沌系统 

分 类 号：TH878[机械工程—仪器科学与技术] TB551[机械工程—精密仪器及机械]