Engineering Research Center for Metallurgical Automation and Measurement Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China.
School of Physics and Electronic Information, Huanggang Normal University, Huanggang 438000, China.
Sensors (Basel). 2022 Jun 30;22(13):4961. doi: 10.3390/s22134961.
Aiming at non-stationary signals with complex components, the performance of a variational mode decomposition (VMD) algorithm is seriously affected by the key parameters such as the number of modes K, the quadratic penalty parameter α and the update step τ. In order to solve this problem, an adaptive empirical variational mode decomposition (EVMD) method based on a binary tree model is proposed in this paper, which can not only effectively solve the problem of VMD parameter selection, but also effectively reduce the computational complexity of searching the optimal VMD parameters using intelligent optimization algorithm. Firstly, the signal noise ratio (SNR) and refined composite multi-scale dispersion entropy (RCMDE) of the decomposed signal are calculated. The RCMDE is used as the setting basis of the α, and the SNR is used as the parameter value of the τ. Then, the signal is decomposed into two components based on the binary tree mode. Before decomposing, the α and τ need to be reset according to the SNR and MDE of the new signal. Finally, the cycle iteration termination condition composed of the least squares mutual information and reconstruction error of the components determines whether to continue the decomposition. The components with large least squares mutual information (LSMI) are combined, and the LSMI threshold is set as 0.8. The simulation and experimental results indicate that the proposed empirical VMD algorithm can decompose the non-stationary signals adaptively, with lower complexity, which is O(), good decomposition effect and strong robustness.
针对具有复杂分量的非平稳信号，变分模态分解（VMD）算法的性能受到模式数 K、二次惩罚参数α和更新步长τ等关键参数的严重影响。为了解决这个问题，本文提出了一种基于二叉树模型的自适应经验变分模态分解（EVMD）方法，该方法不仅可以有效地解决 VMD 参数选择问题，还可以有效地降低使用智能优化算法搜索最优 VMD 参数的计算复杂度。首先，计算分解信号的信噪比（SNR）和细化复合多尺度弥散熵（RCMDE）。RCMDE 用作α的设置依据，SNR 用作τ的参数值。然后，根据二叉树模式对信号进行分解。在分解之前，需要根据新信号的 SNR 和 MDE 重新设置α和τ。最后，由分量的最小二乘互信息和重构误差组成的循环迭代终止条件来确定是否继续分解。将具有较大最小二乘互信息（LSMI）的分量进行组合，并将 LSMI 阈值设置为 0.8。仿真和实验结果表明，所提出的经验 VMD 算法能够自适应地分解非平稳信号，具有较低的复杂度 O()，良好的分解效果和较强的鲁棒性。
