基于Duffing系统的谐振式微悬臂梁传感器微弱谐振信号检测  

Weak Resonant Signal Detection of Resonant Microcantilever Sensors Based on Duffing System

作　　者：戴荣 于海涛[2] 王权[1] DAI Rong;YU Haitao;WANG Quan(School of Mechanical Engineering,Jiangsu University,Zhenjiang 212013;State Key Laboratory of Transducer Technology,Shanghai Institute of Microsystem and Information Technology,Chinese Academy of Sciences,Shanghai 200050)

机构地区：[1]江苏大学机械工程学院,镇江212013 [2]中国科学院上海微系统与信息技术研究所传感技术国家重点实验室,上海200050

出　　处：《机械工程学报》2020年第13期50-59,共10页Journal of Mechanical Engineering

基　　金：国家自然科学基金资助项目(51675246,91750112)。

摘　　要：研究了基于Duffing振子系统的微弱信号检测在谐振式微悬臂梁传感器中的应用。根据待测信号频率的不同,通过时间尺度变换建立了任意频率下的Duffing振子数学模型。利用RHR改进算法求解最大Lyapunov指数,并确定系统相变临界阈值,通过监测最大Lyapunov指数符号的变化来检测微弱谐振信号。详细介绍了两种幅值检测算法,通过试验验证了减法算法比加法算法更具优越性,不受大范围幅值的影响。评价了Duffing振子系统在不同噪声水平下检测微弱谐振信号的能力,添加噪声方差0.0001和0.001后,检测相对误差控制在0.0052%以内;当添加噪声方差到0.01时,原有Duffing方程模型无法检测到最大Lyapunov指数符号的变化,检测失效。最后,通过改变原有Duffing方程非线性恢复力项系数,在添加噪声方差到0.5时,依然能够通过求取所测信号频率的平均值准确提取微弱谐振信号。The application of weak signal detection based on Duffing oscillator system is studied in resonant microcantilever sensors.According to the frequency of the detected signal,the mathematical model of Duffing oscillator at any frequency is established by transforming the time domain scale.An improved RHR algorithm is used to solve the maximum Lyapunov exponent,and the critical threshold of the phase transition in the system is determined.The weak resonant signal is detected by monitoring the change of the maximum Lyapunov exponent sign.Two amplitude detection algorithms are introduced in detail.Experiments show that the minus algorithm is superior to the plus algorithm and is not affected by the large amplitude range.The performance of the Duffing oscillator system for detecting weak resonant signals at different noise levels is evaluated.After increasing the noise variance of 0.0001 and 0.001,the relative error detected is controlled within 0.0052%.When the noise variance is increased to 0.01,the Duffing equation model cannot detect the transition of the largest Lyapunov exponent sign,and the detection is invalid.Finally,the nonlinear restoring force coefficient of Duffing equation is changed.When the noise variance is increased to 0.5,the weak resonant signal can still be accurately detected by calculating the average value of the measured signal frequencies.

关 键 词：Duffing振子系统 微弱信号检测 谐振式微悬臂梁传感器 RHR改进算法 最大LYAPUNOV指数 

分 类 号：TG156[金属学及工艺—热处理]