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

doi:10.3901/JME.2020.13.050

Abstract

Abstract: 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 0.000 1 and 0.001, the relative error detected is controlled within 0.005 2%. 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.

Key words: Duffing oscillator system, weak signal detection, resonant microcantilever sensor, improved RHR algorithm, maximum Lyapunov exponent

CLC Number:

TG156

DAI Rong, YU Haitao, WANG Quan. Weak Resonant Signal Detection of Resonant Microcantilever Sensors Based on Duffing System[J]. Journal of Mechanical Engineering, 2020, 56(13): 50-59.

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