Energy harvesters for mechanical vibrations are electro-mechanical systems designed to capture ambient dispersed kinetic energy, and to convert it into usable electrical power. The random nature of mechanical vibrations, combined with the intrinsic non-linearity of the harvester, implies that long, time domain Monte-Carlo simulations are required to assess the device performance, making the analysis burdensome when a large parameter space must be explored. Therefore a simplified, albeit approximate, semi-analytical analysis technique is of paramount importance. In this work we present a methodology for the analysis and design of nonlinear piezoelectric energy harvesters for random mechanical vibrations. The methodology is based on the combined application of model order reduction, to project the dynamics onto a lower dimensional space, and of stochastic averaging, to calculate the stationary probability density function of the reduced variables. The probability distribution is used to calculate expectations of the most relevant quantities, like output voltage, harvested power and power efficiency. Based on our previous works, we consider an energy harvester with a matching network, interposed between the harvester and the load, that reduces the impedance mismatch between the two stages. The methodology is applied to the optimization of the matching network, allowing to maximize the global harvested power and the conversion efficiency. We show that the proposed methodology gives accurate predictions of the harvester’s performance, and that it can be used to significantly simplify the analysis, design and optimization of the device.

中文翻译：

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用于设计和优化具有多个电自由度的非线性能量采集器的随机平均数学框架


用于机械振动的能量采集器是机电系统，旨在捕获周围分散的动能，并将其转换为可用的电能。机械振动的随机性质与采集器固有的非线性相结合，意味着需要长时间的时域蒙特卡罗模拟来评估设备性能，这使得在必须探索大参数空间时分析变得繁重。因此，简化但近似的半分析分析技术至关重要。在这项工作中，我们提出了一种用于分析和设计随机机械振动的非线性压电能量收集器的方法。该方法基于模型降阶和随机平均的组合应用，以将动态投影到较低维空间，以计算减少变量的平稳概率密度函数。概率分布用于计算最相关量的期望，例如输出电压、收集的功率和功率效率。根据我们之前的工作，我们考虑在能量采集器和负载之间插入一个带有匹配网络的能量采集器，以减少两级之间的阻抗失配。该方法应用于匹配网络的优化，可以最大化全局收集的功率和转换效率。我们表明，所提出的方法可以准确预测收割机的性能，并且可以用来显着简化设备的分析、设计和优化。