首页|谐和与随机激励共同作用下振动能量采集系统的响应预测

谐和与随机激励共同作用下振动能量采集系统的响应预测

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非线性振动能量采集技术是近年来获得广泛发展且有效的微电子设备供能手段,而各类设备工作的实际环境较为复杂,亟需建立更加贴近其真实服役环境的模型,以便对俘能效率开展准确的预测与分析.周期激励与随机噪声联合激励模型能有效模拟振动能量采集器的真实服役环境,但当前研究常局限于单独的周期激励或随机激励情形.为此,本文利用径向基神经网络方法,分析谐和与高斯白噪声联合激励下振动能量采集系统的瞬态响应.首先,构造由高斯基函数与时变权值系数组成的FPK方程试解;随后,采用有限差分格式离散时间导数项,构造由FPK方程残差和权值系数约束条件组成的损失函数;最后,对损失函数进行最小化,获得最优权值系数矩阵,进而得到系统时变响应概率密度函数的近似解.以单稳态与双稳态系统为算例,验证该求解方案,考察了机电耦合系数及机电时间常数对系统瞬态响应和输出功率的影响,并通过与蒙特卡罗模拟对比验证了理论解析解的正确性.结果表明,系统在所设激励扰动下,其响应概率密度函数的拓扑结构随时间演化有较大改变;调整系统关键参数将会诱导其发生随机跳跃以及随机P-分岔,且关键参数的改变对俘能效率有显著影响.本工作结果对探究能量采集系统的随机动力学演化规律以及优化系统的俘能效率提供了一定理论性参考.
Response prediction of an energy harvesting system under the combined harmonic and random excitation
Adopting nonlinear vibrational-based energy harvesting(VEH)techniques to answer the electrical energy demands of microelectronic devices has become commonplace.Considering the complex service environment of these devices,it is necessary to model VEH systems that closely resemble their real operational conditions.This will facilitate more precise prediction and analysis of the energy harvesting efficiency.The combined periodic and random excitation effectively simulate the real operating environment of VEH systems,but systematic research on VEH systems is usually limited to periodic excitation or random excitation.This paper employs the Radial Basis Function neural networks(RBFNN)method to solve the transient response of a VEH system subjected to combined harmonic and Gaussian white excitations.This technique initially constructs a trial solution composed of Gaussian basis functions and time-varying weight coefficients for the Fokker-Planck-Kolmogorov(FPK)equation.Subsequently,the finite difference method is employed to discretize the time derivative terms,constructing a loss function composed of the residuals of the FPK equation and the constraint conditions of weight coefficients.Lastly,the loss function is minimized to obtain the optimal matrix of weight coefficients,allowing for the determination of the optimal trial solution for the probability density function of the transient response.The mono-stable and bi-stable systems are taken as examples to verify the solution scheme,and the effects of electromechanical coupling coefficients and the ratio between the mechanical and electrical time constants on the transient response and output power of the system are investigated.The semi-analytical solutions are rigorously validated with Monte Carlo simulation.The main conclusions are as follows:under combined periodic and random excitations,the topological structure of the probability density function of system response undergoes significant changes over time.Stochastic jump and stochastic P-bifurcations are induced by changes in critical parameters of the system,and parameter variations have a pronounced impact on the efficiency of energy harvesting.The findings of this work provide theoretical references for exploring the stochastic dynamical evolution of VEH systems and optimizing the efficiency of energy harvesting.

combined harmonic and Gaussian white noisenonlinear energy harvesting systemradial basis function neural networkstransient responses

杨帆、陈林聪、原子

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华侨大学土木工程学院,厦门 361021

福建省智慧基础设施与监测重点实验室,厦门 361021

谐和与高斯白噪声联合激励 能量采集系统 径向基神经网络 瞬态响应

国家自然科学基金国家自然科学基金福建省杰出青年科学基金

12072118123720292021J06024

2024

中国科学(技术科学)
中国科学院

中国科学(技术科学)

CSTPCD北大核心
影响因子:0.752
ISSN:1674-7259
年,卷(期):2024.54(4)
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