Nanda Aditya, Singla Puneet, Karami M Amin
Department of Mechanical and Aerospace Engineering, University at Buffalo, Buffalo, NY, USA.
Department Aerospace Engineering, Pennsylvania State University, University Park, PA, USA.
J Intell Mater Syst Struct. 2018 Nov;29(18):3614-3633. doi: 10.1177/1045389x18798945. Epub 2018 Sep 21.
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 = 8 × 10 samples for monostable harvester and = 6.5 × 10 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.
本文提出了一种概率方法，用于研究参数不确定性对线性和非线性能量收集系统的平均功率、尖端挠度和尖端速度的影响。最近开发的共轭无迹变换算法用于计算参数具有多维高斯不确定性时输出变量的统计矩。最大熵原理用于根据获得的统计矩知识构建输出变量的概率密度函数。对于非线性单稳态和非线性双稳态能量收集器，平均功率的概率密度函数形状明显复杂，分别有两个和三个不同的峰值。使用单稳态能量收集器的(8×10)个样本和双稳态能量收集器的(6.5×10)个样本进行蒙特卡罗模拟，以验证概率密度函数。得出的结论是，共轭无迹变换方法在不影响准确性的情况下具有显著的计算优势。此外，使用共轭无迹变换方法，我们表明，当存在多维不确定性时，平均功率对参数（激励频率、激励幅度等）的依赖性相对于纯确定性趋势有明显不同。例如，对于单稳态能量收集器，确定性趋势和不确定性趋势之间预测功率的差异在基频、基加速度和磁隙方面分别达到最大值(100%)、(234%)和(110%)。相对于不确定性趋势，确定性趋势始终高估了收集到的功率。因此，这项工作可能在评估收集功率的“最坏情况”中具有应用价值。相对于能量收集文献中的现有技术，所提出方法的主要优点是对参数的多维不确定性具有准确且计算有效的适用性。
