Chin. Phys. B, 2022, Vol. 31(12): 120203    DOI: 10.1088/1674-1056/ac9cbf
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# Sparse identification method of extracting hybrid energy harvesting system from observed data

Ya-Hui Sun(孙亚辉)1,2, Yuan-Hui Zeng(曾远辉)1, and Yong-Ge Yang(杨勇歌)1,†
1 School of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, China;
2 State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi'an Jiaotong University, Xi'an 710049, China
Abstract  Hybrid energy harvesters under external excitation have complex dynamical behavior and the superiority of promoting energy harvesting efficiency. Sometimes, it is difficult to model the governing equations of the hybrid energy harvesting system precisely, especially under external excitation. Accompanied with machine learning, data-driven methods play an important role in discovering the governing equations from massive datasets. Recently, there are many studies of data-driven models done in aspect of ordinary differential equations and stochastic differential equations (SDEs). However, few studies discover the governing equations for the hybrid energy harvesting system under harmonic excitation and Gaussian white noise (GWN). Thus, in this paper, a data-driven approach, with least square and sparse constraint, is devised to discover the governing equations of the systems from observed data. Firstly, the algorithm processing and pseudo code are given. Then, the effectiveness and accuracy of the method are verified by taking two examples with harmonic excitation and GWN, respectively. For harmonic excitation, all coefficients of the system can be simultaneously learned. For GWN, we approximate the drift term and diffusion term by using the Kramers-Moyal formulas, and separately learn the coefficients of the drift term and diffusion term. Cross-validation (CV) and mean-square error (MSE) are utilized to obtain the optimal number of iterations. Finally, the comparisons between true values and learned values are depicted to demonstrate that the approach is well utilized to obtain the governing equations for the hybrid energy harvester under harmonic excitation and GWN.
Keywords:  data-driven      hybrid energy harvester      harmonic excitation      Gaussian white noise
Received:  15 August 2022      Revised:  13 October 2022      Accepted manuscript online:  21 October 2022
 PACS: 02.50.-r (Probability theory, stochastic processes, and statistics) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion) 05.40.Ca (Noise)
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12002089 and 11902081) and Project of Science and Technology of Guangzhou (Grant No. 202201010326).
Corresponding Authors:  Yong-Ge Yang     E-mail:  yonggeyang@163.com