Electrical Response Estimation of Vibratory Energy Harvesters via Hilbert Transform Based Stochastic Averaging

K. R. D. dos Santos
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Abstract

Converting mechanical vibrations into electrical power with vibratory energy harvesters can ensure the portability, efficiency, and sustainability of electronic devices and batteries. Vibratory energy harvesters are typically modeled as nonlinear oscillators subject to random excitation, and their design requires a complete characterization of their probabilistic responses. However, simulation techniques such as Monte Carlo are computationally prohibitive when the accurate estimation of the response probability distribution is needed. Alternatively, approximate methods such as stochastic averaging can estimate the probabilistic response of such systems at a reduced computational cost. In this paper, the Hilbert transform based stochastic averaging is used to model the output voltage amplitude as a Markovian stochastic process with dynamics governed by a stochastic differential equation with nonlinear drift and diffusion terms. Moreover, the voltage amplitude dependent damping and stiffness terms are determined via an appropriate equivalent linearization, and the stationary probability distribution of the output voltage amplitude is obtained analytically by solving the corresponding Fokker–Plank equation. Two examples are used to demonstrate the accuracy of the obtained analytical probability distributions via comparisons with Monte Carlo simulation data.
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基于希尔伯特变换的随机平均振动能量采集器电响应估计
用振动能量采集器将机械振动转化为电能,可以确保电子设备和电池的便携性、效率和可持续性。振动能量采集器通常被建模为受随机激励的非线性振荡器,其设计需要对其概率响应进行完整的表征。然而,当需要准确估计响应概率分布时,蒙特卡罗等模拟技术在计算上是禁止的。或者,近似的方法,如随机平均,可以估计这样的系统的概率响应在一个减少的计算成本。本文采用基于Hilbert变换的随机平均方法,将输出电压幅值建模为具有非线性漂移和扩散项的随机微分方程所控制的动态马尔可夫随机过程。通过适当的等效线性化,确定了电压幅值相关的阻尼项和刚度项,并通过求解相应的Fokker-Plank方程解析得到输出电压幅值的平稳概率分布。通过与蒙特卡罗模拟数据的比较,用两个例子证明了所得解析概率分布的准确性。
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CiteScore
5.20
自引率
13.60%
发文量
34
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