Empirical Variational Mode Decomposition Based on Binary Tree Algorithm

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(n²), good decomposition effect and strong robustness.