DATA-DRIVEN MODELING AND APPLICATION OF VIBRATION ENERGY HARVESTER WITH DOUBLE FILM
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摘要:随着工程研究对象日益复杂化、系统化, 单纯依赖先验知识的力学建模手段难以满足日渐复杂的系统建模需求. 相比而言, 数据驱动通过大数据处理方法得到准确反映系统当前运动状态的数学模型, 体现了数据科学融入基础与应用科学领域的发展趋势. 特别是稀疏非线性动力系统辨识算法(SINDy)的出现, 解决了直接构建非线性数学模型的难点问题, 实现了由实验数据到非线性控制方程的直接过渡. 然而, 受制于噪声数据的影响显著以及奇异矩阵难以准确分析等因素, SINDy在实际应用中的可靠性仍有待加强. 有鉴于此, 文章在已有SINDy算法基础上提出增强型稀疏筛选辨识算法(ESINDy), 改进了数据滤波模块以强化其对于含噪信号的处理能力, 并且改变了原有算法的循环函数体, 以提高其对于奇异问题的识别能力, 使之更适于分析工程信号中常见的强噪声、高奇异性等问题. 作为应用, 研究了一类双层薄膜结构电磁式振动能量采集器(EMH), 利用理论建模与ESINDy方法相结合的手段建立了采集器动力学方程, 并通过实验和仿真对理论结果进行验证. 结果表明: 相比于SINDy算法, ESINDy算法能够更加准确地识别该动力学系统的信息, 刻画系统蕴含的复杂振动行为. 理论、实验和仿真结果较好的一致性体现了改进算法对于提高实际非线性系统识别精度的有效性, 强化了数据驱动建模方法的工程应用价值, 为实际工程问题中的信号处理提供了一种可行的分析方法.Abstract:With the increasing complexity and systematization of engineering research objects, it is difficult for mechanical modeling methods that rely solely on prior knowledge to meet the increasingly complex system modeling needs. In contrast, the data-driven system obtains a mathematical model that accurately reflects the current motion state of the system through big data processing methods, which reflects the development trend of data science integrating into the fields of basic and applied science. In particular, the emergence of sparse identification of nonlinear dynamical systems (SINDy) has solved the difficult problem of directly constructing nonlinear mathematical model and realized the direct transition from experimental data to nonlinear control equations. However, due to the significant influence of noise data and the difficulty of accurate analysis of singular matrix, the reliability of SINDy in practical application still needs to be strengthened. In view of this, based on the existing SINDy algorithm, this paper puts forward the enhanced sparse identification of nonlinear dynamical systems (ESindy) algorithm, improves the data filtering module to strengthen its processing ability for noisy signals, and changes the cyclic function body of the original algorithm to improve its ability to identify singular problems, making it more suitable for analyzing the common problems such as strong noise and high singularity in engineering signals. As an application, a kind of electromagnetic vibration energy harvester (EMH) with double-layer membrane structure is studied. The dynamic equation of the harvester is established by combining theoretical modeling with ESINDy method, and the theoretical results are verified by experiments and simulations. The results show that compared with SINDy algorithm, ESINDy algorithm can identify the information of the dynamic system more accurately and describe the complex vibration behavior contained in the system. The good consistency of theoretical, experimental and simulation results reflects the effectiveness of the improved algorithm in improving the identification accuracy of actual nonlinear systems, strengthens the engineering application value of data-driven modeling method, and provides a feasible analysis method for signal processing in practical engineering problems.
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Key words:
- data driving/
- data filtering/
- energy harvester
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图 4磁力及弹力参数测量装置 (1. 测力计, 2. 手轮, 3. 磁铁, 4. EMH)
Figure 4.Magnetic force and elastic force parameters measuring device (1. dynamometer, 2. rocker, 3. magnet, 4. EMH)
图 5磁力的实验、仿真与理论结果
Figure 5.Experimental, simulation and theoretical results of magnetic force
图 8振动系统真实相图与SINDy, ESINDy重构系统相图
Figure 8.Real phase diagram of vibration system, SINDy and ESINDy reconstruction system
表 1ESINDy算法流程
Table 1.ESINDy algorithm
Input:X, ${\lambda _1}$, ${\lambda _2}$, iter fori= 1:iter (1) Using${\lambda _1}$for curvature filtering (2) Using${\lambda _2}$for SINDy (3) Calculate sparsitySp (4) Updating regularization parameters according toSp 
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表 2x分量识别结果
Table 2.xcomponent identification result
Parameter Theoretical result SINDy ESINDy C 0 0 0 x 0 0.0605 0 y −1 −0.9868 −1.0030 z −1 −1.1658 −0.9638 x2 0 0 0 x y 0 0 0 x z 0 0.0267 0 y2 0 0 0 y z 0 0 0 z2 0 0 0 下载:
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表 3部分参数识别结果
Table 3.Partial parameter identification results
Parameter Theoretical result SINDy ESINDy α 0.2 0.2803 0.2242 β 0.2 0.2289 0.2034 γ 5.7 4.0227 4.9240 recognition accuracy 76.43% 91.93% 下载:
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表 4Ansys仿真采用的模型参数
Table 4.Model parameters used in Ansys simulation
Symbol Physical significance Parameter value Unit R outer radius 0.032 5 m r inner radius 0.005 0 m h thickness 0.000 3 m E Young's modulus $9.4 \times {10^6}$ Pa μ Poisson ratio 0.28 D membrane bending stiffness $2.3 \times {10^{ - 5}}$ ${\text{N}} \cdot {\text{m}}$ ${E_0}$ magnet stiffness $2.0 \times {10^{14}}$ Pa 下载:
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表 5理论和识别结果对比
Table 5.Comparison between theory and identification results
Parameter Theorical result SINDy ESINDy C 0.13 0.42 0.14 x $ - 1.75 \times {10^4}$ $ - 8.46 \times {10^4}$ $ - 1.98 \times {10^4}$ $\dot x$ −0.50 0 −0.31 z 1.00 1.03 1.01 ${x^2}$ $ - 3.04 \times {10^7}$ $ - 3.12 \times {10^7}$ $ - 2.53 \times {10^7}$ $ x \dot{x} $ 0 0 0 ${\dot x^2}$ 0 0 0 ${x^3}$ $ - 1.29 \times {10^{10}}$ $ - 3.14 \times {10^{10}}$ $ - 1.67 \times {10^{10}}$ ${x^2}\dot x$ 0 0 0 $ x {\dot{x}}^{2} $ 0 $ - 3.10 \times {10^6}$ 0 ${\dot x^3}$ 0 0 $ - 10.1$ 下载:
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