非高斯过程下混合式能量采集系统的方程识别

Identification of hybrid energy harvesting systems with non-Gaussian process

混合式能量采集系统由于提高采集效率的优点被广泛地应用于许多领域.在实际环境中,许多表现为跳跃、飞行、罕见跃迁以及间歇性特征的现象能够被非高斯Lévy过程所描述.但有时候精确地建立复杂条件下的混合式能量采集系统方程是较为困难的,尤其是由非高斯Lévy噪声驱动的系统.近年来,随着仿真能力和观测技术的发展,大量的噪声测量数据以及仿真数据能够被收集,并且已有许多研究致力于从大量数据中提取控制法则.本文采用数据驱动的方法,从受非高斯Lévy噪声影响的观测数据中提取系统方程.利用Fokker-Planck方程和非局部Kramers-Moyal公式,获得漂移项、扩散项和Lévy参数的近似表达式,并利用稀疏回归方法识别近似表达式中的系数.本文给出了三个算例,验证了该方法的有效性.结果表明,该方法不仅适用于高斯布朗过程下的混合能量收集系统,也适用于非高斯Lévy过程下的混合能量收集系统.此外,还分析了不同时间步长下区间划分参数与指标Ratio的关系.结果表明,该指标可以作为选择合适的划分参数的标准.

Hybrid energy harvesting systems are broadly applied in various fields due to the advantage of improving energy harvesting efficiency.In actual environment,there are many complex phenomena exhibiting jump,flights,rare transition features,and intermittent features,which can be described by systems subjected to non-Gaussian Lévy process.Sometimes,it is difficult to build mathematical models of complex hybrid energy harvesting systems precisely,especially for those driven by non-Gaussian Lévy noise.With the development of simulation capabilities and observing techniques recently,massive noise measurement data or simulating data can be feasibly obtained and there are many existing techniques devoted to discovering governing laws from abundant data.In this paper,we aim to extract the system equations from observed data influenced by non-Gaussian Lévy noise via using a data-driven method.The expressions of drift term,diffusion term and Lévy term can be approximated with the help of Fokker-Planck equation and non-local Kramers-Moyal formulae,and the coefficients of the expressions are learned by utilizing a sparse regression approach in the least square sense.Three examples are given to demonstrate the effectiveness of the method.Results show that the approach can well be applied to not only hybrid energy harvesting systems under Gaussian Brownian process but also the systems subjected to non-Gaussian Lévy process.Additionally,the relations between the demarcation parameter and an indicator denoted as Ratio for different time steps are analyzed,and results demonstrate that the indicator can be regarded as the criterion of selecting the appropriate demarcation parameter.