基于统计复杂度下随机双稳态能量采集系统的随机共振
Stochastic Resonance of a Stochastic Bistable Energy Harvesting System Based on Statistical Complexity
摘要: 针对泊松白噪声和周期信号共同作用下双稳态能量采集系统，运用统计复杂度方法度量了系统的随机共振行为和采能效率。首先，通过数值方法计算了系统的统计复杂度和有效输出功率；其次，深入研究噪声、系统以及信号等参数对系统随机共振现象与采能效率的影响；最后，从信息论的角度解析了随机共振与系统采能效率之间的关系。结果显示，统计复杂度曲线的非单调演化趋势意味着系统产生了随机共振现象；选取合适的噪声强度、耦合系数及阻尼系数等能够增强系统的随机共振行为。此外，均方电压和有效输出功率曲线与统计复杂度曲线具有相同的演化规律，即当系统产生随机共振行为时，采能效率达到最大化。
Abstract: For the bistable energy harvesting system under the combined action of Poisson white noise and periodic signal, the statistical complexity method is used to measure the stochastic resonance behavior and energy recovery efficiency of the system. Firstly, the statistical complexity and effective output power of the system are calculated by numerical methods. Secondly, the influence of noise, system and signal parameters on the stochastic resonance phenomenon and energy recovery efficiency of the system is deeply studied. Finally, from the perspective of information theory, the relationship between stochastic resonance and the energy recovery efficiency of the system is analyzed. The results show that the non-monotonic evolution trend of the statistical complexity curve means that the system produces stochastic resonance. Selecting appropriate noise intensity, coupling coefficient and damping coefficient can enhance the stochastic resonance behavior of the system. In addition, the mean square voltage and effective output power curves have the same evolution law as the statistical complexity curve, that is, when the system produces random resonance behavior, the energy recovery efficiency is maximized.
文章引用：乔艳辉. 基于统计复杂度下随机双稳态能量采集系统的随机共振[J]. 应用数学进展, 2024, 13(3): 1067-1079. https://doi.org/10.12677/aam.2024.133101

参考文献

[1] 王彬. 含分数阶导数电路的振动能量采集系统研究[D]: [硕士学位论文]. 杭州: 中国计量大学, 2022.
[2] Wu, X.P., Zhang, T.S., Liu, J.Y., et al. (2022) A Vibration Energy Harvesting System for Self-Powered Applications in Heavy Railways. Sustainable Energy Technologies and Assessments, 53, Article ID: 102373. [Google Scholar] [CrossRef] 
[3] 黄衡. 面向轨道振动的频率上变换能量采集系统研究[D]: [硕士学位论文]. 成都: 西南交通大学, 2022.
[4] 董博见, 徐鹏, 李海涛. 驰振和基振复合作用下的双稳态能量采集系统动力学分析[J]. 中北大学学报(自然科学版), 2021, 42(1): 26-33.
[5] 高毓璣. 非线性双稳压电悬臂梁振动响应及能量采集研究[D]: [博士学位论文]. 天津: 天津大学, 2017.
[6] 赵泽翔, 王光庆, 谭江平, 等. 双稳态压电振动能量采集器的时频域动力学特性及实验研究[J]. 传感技术学报, 2019, 32(8): 1200-1208.
[7] 王康. 弹性支撑双稳态压电能量采集系统的理论与数值分析[D]: [硕士学位论文]. 天津: 河北工业大学, 2019.
[8] Liu, D., Wu, Y., Xu, Y., et al. (2019) Stochastic Response of Bistable Vibration Energy Harvesting System Subject to Filtered Gaussian White Noise. Mechanical Systems and Signal Processing, 130, 201-212. [Google Scholar] [CrossRef] 
[9] 刘丽兰, 张小静. 白噪声激励下势阱深度对双稳态系统发电性能的影响研究[J]. 机械科学与技术, 2018, 37(9): 1336-1343.
[10] 李小亚. 多稳态振动能量采集系统随机响应分析[D]: [硕士学位论文]. 杭州: 中国计量大学, 2021.
[11] Zhang, X.G., Zhao, W., Guan, J.C., et al. (2023) Development of Bi-Stable Vibration Energy Harvesting System Using Duffing-Type Motion Model. Engineering and Applied Sciences, 8, 5-15. [Google Scholar] [CrossRef] 
[12] Benzi, R., Sutera, A. and Vulpiani, A. (1981) The Mechanism of Stochastic Resonance. Journal of Physics A: Mathematical and General, 14, L453-L457. [Google Scholar] [CrossRef] 
[13] Zhao, W., Wu, Q., Zhao, X.L., et al. (2020) Development of Large-Scale Bistable Motion System for Energy Harvesting by Application of Stochastic Resonance. Journal of Sound and Vibration, 473, Article ID: 115213. [Google Scholar] [CrossRef] 
[14] Guo, L.S., Zhao, W., Gomi, N., et al. (2022) Development of an Opposed Mass-Spring Type Bi-Stable Vibration Energy Harvesting System Using Stochastic Resonance. International Journal of Mechanical Engineering and Applications, 10, Article 899. [Google Scholar] [CrossRef] 
[15] Zhao, W., Zhang, R.C., Yin, X.Y., et al. (2021) An Electromagnetic Energy Harvester of Large-Scale Bistable Motion by Application of Stochastic Resonance. Journal of Vibration and Acoustics, 144, Article ID: 011007. [Google Scholar] [CrossRef] 
[16] 陈仲生, 杨拥民, 骆彦廷. 非线性压电振动能量俘获行为建模及其不同参数影响机理研究[J]. 国防科技大学学报, 2013, 35(2): 154-158.
[17] 肖少敏. 噪声激励下非线性压电俘能器的随机动力学分析[D]: [硕士学位论文]. 北京: 北京理工大学, 2017.
[18] Litak, G., Friswell, M.I. and Sawicki, J.T. (2010) Crack Identification in Rotating Machines with Active Bearings. ISMA, Leuven, 20-22.
[19] 张文明, 赵林川, 邹鸿翔. 振动能量采集与振动控制序[J].力学学报, 2023, 55(10): 2091-2093.
[20] 刘迪, 刘晓婷, 李晶. 基于样本信息的振动能量采集系统的响应预测[J]. 山西大学学报(自然科学版), 2022, 45(3): 591-598.
[21] Grigoriu, M. (1996) Response of Dynamic Systems to Poisson White Noise. Journal of Sound and Vibration, 195, 375-389. [Google Scholar] [CrossRef] 
[22] Lin, B., Wang, Y. and Qian, Y. (2022) Bursting Oscillation Phenomenon and Efficiency Analysis of a Piezoelectric Energy Harvester in Rotational Motion by Low-Frequency Excitation. The European Physical Journal Plus, 137, Article No. 459. [Google Scholar] [CrossRef] 
[23] Lopez-Ruiz, R., Mancini, H.L. and Calbet, X. (1995) A Statistical Measure of Complexity. Physics Letters A, 209, 321-326. [Google Scholar] [CrossRef] 
[24] Shannon, C.E. (1948) A Mathematical Theory of Communication. The Bell System Technical Journal, 27, 379-423. [Google Scholar] [CrossRef] 
[25] Bandt, C. and Pompe, B. (2002) Permutation Entropy: A Natural Complexity Measure for Time Series. Physical Review Letters, 88, Article ID: 174102. [Google Scholar] [CrossRef] 

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