Analysis of response to thermal noise in electrostatic MEMS bifurcation sensors
Analysis of response to thermal noise in electrostatic MEMS bifurcation sensors
复制标题
静电 MEMS 分叉传感器的热噪声响应分析
DOI：
10.1007/s11071-021-07002-0
复制
发表时间：
2021-11-13
影响因子：
5.6
通讯作者：
Abdel-Rahman, Eihab M.
中科院分区：
文献类型：
--
作者：
Qiao, Yan;Wei, Wei;Abdel-Rahman, Eihab M.
本文提出了一种非线性动力系统随机分析的新方法。它利用这种方法来分析静电MEMS分叉传感器的响应的确定性激励，机械热噪声，和电热噪声的组合。分析方法结合了多尺度和随机平均的方法的振幅，推导出随机伊藤微分方程描述的调制的传感器的振幅和相位差的存在下的热噪声和福克-普朗克-柯尔莫哥洛夫（FPK）方程的随机响应的平稳概率密度函数（PDF）。良好的协议之间的预测派生的调制方程和原来的运动方程。FPK方程适用于噪声激励水平的范围进行了研究。的加性噪声，所产生的机械热和电热噪声，对传感器响应的影响被发现占主导地位的乘性噪声，所产生的电热噪声。响应的PDF被用来研究在激励频率和噪声强度之间的相互作用下，分叉传感器的共存轨道之间的随机切换。我们发现，随机开关被激活时，两个轨道的稳定性的边缘变得可比的噪声驱动的运动的大小。滞后区域内的振幅的均值和方差的变化可以被利用作为随机切换的敏感指标。最后，我们的研究结果表明，实现一种新的高灵敏度的“噪声感知”的分叉传感器，利用随机切换的频率范围内的传感器状态的平均幅度（或RMS）的定量变化，以检测质量变化或气体浓度的可能性。
This paper presents an alternative approach to stochastic analysis of nonlinear dynamic systems. It exploits this approach to analyze the response of electrostatic MEMS bifurcation sensors to a combination of deterministic excitation, mechanical-thermal noise, and electrical-thermal noise. The analytical approach combines the methods of multiple scales and stochastic averaging of the amplitude, to derive the stochastic Itô differential equations describing the modulations of the sensor amplitude and phase difference in the presence of thermal noise and the Fokker–Planck–Kolmogorov (FPK) equation governing the stationary probability density function (PDF) of the stochastic response. Good agreement is found between the predictions of the derived modulation equations and the original equation of motion. The scope of the FPK equation applicability to the noise excitation levels is examined. The impact of the additive noise, arising from mechanical-thermal and electrical-thermal noise, on the sensor response is found to dominate that of the multiplicative noise, arising from the electrical-thermal noise. PDFs of the response are used to investigate the stochastic switching between the co-existing orbits of the bifurcation sensor under the interaction between the excitation frequency and noise intensity. We found that the stochastic switching is activated when the margins of stability of both orbits become comparable to the size of noise-driven motions. Variations in the mean and variance of the amplitude within the hysteretic region can be exploited as sensitive indicators of the stochastic switching. Finally, our results suggest the possibility of implementing a novel highly sensitivity ‘noise-aware’ bifurcation sensor that exploits the quantitative change in the mean amplitude (or RMS) of the sensor states within the frequency range of stochastic switching to detect mass change or gas concentration.