Conjugate unscented transformation-based uncertainty analysis of energy harvesters.
Conjugate unscented transformation-based uncertainty analysis of energy harvesters.
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DOI：
10.1177/1045389x18798945
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发表时间：
2018-11
影响因子：
2.7
通讯作者：
Karami, M. Amin
中科院分区：
文献类型：
--
作者：
Nanda, Aditya;Singla, Puneet;Karami, M. Amin
关键词：
本文提出了一种概率方法来研究线性和非线性能量收集系统的平均功率，尖端偏转和尖端速度的参数不确定性的影响。最近开发的共轭无味变换算法用于计算参数具有多维高斯不确定性的输出变量的统计矩。最大熵原理被用来构造的概率密度函数的输出变量的统计矩的知识。平均功率的概率密度函数的形状显着复杂的两个和三个不同的峰值，分别为非线性单稳态和非线性双稳态收割机。采用蒙特-卡罗模拟方法，对单稳态采集器和双稳态采集器分别进行了N = 8 × 104和N = 6.5 × 104样本的概率密度函数验证。它的结论是共轭无迹变换方法提供了一个显着的计算优势，而不影响精度。此外，利用共轭无迹变换方法，我们证明了平均功率对参数（激励频率、激励幅度等）的依赖关系，当存在多维不确定性时，相对于纯确定性趋势，例如，单稳态采集器的确定性趋势和不确定性趋势之间的预测功率差异对于基本频率、基本加速度和磁隙分别达到最大100%、234%和110%。相对于不确定趋势，确定性趋势始终高估了收获的功率。这项工作，因此，可能有应用程序在评估“最坏情况下”的收获功率。所提出的方法相对于现有的能量收集文献中的技术的主要优点是准确和计算有效的多维参数的不确定性的适用性。
This article presents a probabilistic approach to investigate the effect of parametric uncertainties on the mean power, tip deflection, and tip velocity of linear and nonlinear energy harvesting systems. Recently developed conjugate unscented transformation algorithm is used to compute the statistical moments of the output variables with multidimensional Gaussian uncertainty in parameters. The principle of maximum entropy is used to construct the probability density function of output variables from the knowledge of obtained statistical moments. The probability density functions for mean power were significantly complicated in shape with two and three distinct peaks for the nonlinear monostable and nonlinear bistable harvesters, respectively. Monte-Carlo simulations with N = 8 × 104 samples for monostable harvester and N = 6.5 × 104 samples for bistable harvester were used for validating the probability density functions. It is concluded that conjugate unscented transformation methodology affords a significant computational advantage without compromising accuracy. In addition, using conjugate unscented transformation method, we show that the dependence of mean power on parameters (excitation frequency, excitation amplitude, etc.), when multidimensional uncertainties are present, is decidedly different relative to a purely deterministic trend. The discrepancy in predicted power between the deterministic and uncertain trends for the monostable harvester, for instance, reach a maximum of 100%, 234%, and 110% for base frequency, base acceleration, and magnet gap, respectively. The deterministic trend consistently overestimates the harvested power relative to the uncertain trends. This work, therefore, may have applications in evaluating “worst case scenario” for harvested power. The major advantage of the presented methodology relative to extant techniques in energy harvesting literature is the accurate and computationally effective applicability to multidimensional uncertainty in parameters.
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