高斯白噪声下非对称单稳态能量采集系统的随机响应分析  

Stochastic Response Analysis of Asymmetric Monostable Energy Harvesting System Driven by Gaussian White Noise

作　　者：刘迪 胡美 LIU Di;HU Mei(School of Mathematical Sciences,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2022年第4期947-953,共7页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(11972019)。

摘　　要：能量采集系统可以将周围环境中废弃的动能转化为电能,因此吸引了越来越多的关注。文章研究了高斯白噪声作用下非对称单稳态能量采集系统的概率响应。通过引入坐标变换,将非对称单稳态机电耦合系统等价为一个包含系统频率的单自由度系统。在Markov近似下得到总能量的Fokker-Plank-Kolmogorov(FPK)方程,进而获得了其稳态响应的概率密度函数(PDF)的解析表达式,由此获得衡量系统能量采集效率的均方电压(MSOV)。通过实例验证了所提出的方法的有效性,并分析了噪声强度、阻尼系数、非线性系数和耦合系数等系统物理量对均方电压的影响。研究结果表明:噪声强度和非对称度有利于提高均方电压的输出,从而提高了系统的能量采集效率;而阻尼系数和三次非线性系数的增加会引发一个与之相悖的结果。Energy harvesting system can convert the wasted kinetic energy of the surrounding environment into electric energy,so it attracts more and more attention.The probabilistic response of asymmetric monostable energy harvesting system driven by Gaussian white noise is studied.The asymmetric monostable electromechanical coupling system is equivalent to a single degree of freedom system by a transformation,which contains system frequency.The Fokker-Plank-Kolmogorov(FPK)equation of the total energy is obtained based on the Markov approximation,and then the analytical expression of probability density function(PDF)of stationary response is derived.Thus,the mean-square output voltage(MSOV)can also be obtained,which is an effective amount to measure the efficiency of the energy harvesting of the system.The effectiveness of the proposed method is verified by an example,and the effects of the physical parameters of the system including the excitation intensity,damping coefficient,nonlinear coefficients,and coupling parameter on MSOV are analyzed in detail.The results show that the increase of the noise intensity and asymmetry parameter is beneficial to the output of mean square voltage,and can improve the energy harvesting efficiency.However,the increase of damping coefficient and the cubic nonlinear coefficient can lead to an opposite result.

关 键 词：能量采集 非对称 单稳态 随机响应 高斯白噪声 

分 类 号：O175[理学—数学]