Penalty Parameter Selection Method for Variational Mode Decomposition and Time-Varying System Identification
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摘要: 针对变微分模态分解（variational mode decomposition，VMD）罚参量会对分解结果产生影响的问题，提出一种基于数据驱动的VMD罚参量选择方法.该方法首先通过傅里叶变换的主频峰值确定罚参量；然后调整层数参量，获得有限个固有模式分量，通过对比不同层数参量时所得固有模式分量的固有频率与阻尼比变化，剔除伪分量；最后对真实固有模式分量进行希尔伯特变换，用于识别时变系统的瞬时频率. 为证明所提方法对时变系统识别的有效性和准确性，分别对具有时变刚度的结构系统和柴油发动机的时变做功过程进行研究，将所提方法结果与经验模态分解方法结果进行比较. 比较结果表明，当罚参数取值是信号最大幅值的1.5～16.0倍时VMD分解结果最优，所提方法可以更准确地识别瞬时频率，在工程应用中的能够更有效地对系统瞬时频率进行识别.Abstract: As the penalty parameter in the variational mode decomposition (VMD) affects the decomposition performance, a penalty parameter selection method is proposed on the basis of data driven. The method firstly determines the penalty parameter at the main peak by using the Fourier transform. Then the mode parameters are adjusted to obtain the finite number of intrinsic mode function components. The pseudo component is eliminated by comparing the natural frequencies and damping ratios of the components under different mode parameters. Finally, the true intrinsic mode function components are processed with Hilbert transform to identify the instantaneous frequency of a time-varying system. In order to prove the validity and accuracy of the proposed method for time-varying system identification, the time-varying work processes of a structural system with time-varying stiffness and a diesel engine are studied respectively. The results of the proposed method are compared with those of the empirical mode decomposition method. The results show that when the penalty parameter is 1.5 to 16.0 times the maximum signal amplitude, the optimal decomposition results will be obtained. The proposed method can more accurately identify the instantaneous frequency, and be used for instantaneous frequency identification in engineering applications.
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图 1 时变系统识别方法的方法流程
Figure 1. Flowchart of identification method for time-varying systems
图 2 源信号与VMD分解后BIMF时域对比
Figure 2. Time domain comparison of BIMF after source signal decomposition and VMD decomposition
图 3 源信号与VMD分解后BIMF频率对比
Figure 3. Comparison of BIMF frequency between source signal and VMD decomposition
图 4 罚参量
$\alpha $ 对分解结果影响Figure 4. Effects of penalty parameter
$\alpha $ on decomposition results
图 5 频率误差小于1%时所需
$\alpha $ 的大小统计盒Figure 5. Box diagram of
$\alpha $ needed when the frequency error is less than 1%
图 8 非线性模型BIMF分量的固有频率与阻尼变化
Figure 8. Natural frequency and damping change of BIMF component in nonlinear model
图 9 数值模型识别时频谱与理论频率
Figure 9. Identification of time-frequency spectrum and theoretical frequency by numerical model
图 14 750 rpm柴油机振动VMD瞬时能量谱
Figure 14. Instantaneous energy spectrum of 750 rpm diesel engine vibration using VMD
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