An optimal variational mode decomposition method based on sparse index

A sparse index-based variational mode decomposition ( VMD) method was presented in this work to deal with the challenge of determining the decomposition mode number K when the number of composite signal sources is unknown. Based on the sparse prior theory of each component in the VMD decomposition, the adaptive optimal K value of VMD was discovered as the turning point of the sparse index from rising to falling. Considering the energy difference between different components, the energy weight factor was added in the computation of sparsity index. Finally, the sparsity index was determined as the average value of the marginal spectral sparsity of each component after decomposition. The results of simulations and real-world signal decomposition experiments prove the superiority of the method. Compared with another two modified VMD methods, the proposed method determines a more accurate K value and is more adaptive. Moreover, the results of experiment show that the method has a better decomposition effect than other signal decomposition methods like empirical mode decomposition ( EMD). The proposed method introduces a novel concept for adaptive and efficient VMD decomposition of composite signals with unknown source numbers. To the next level，the robust noise experiment demonstrates that the suggested sparse index approach has a certain anti-noise ability. It shows that the method is relatively robust and can be developed and applied to practical engineering. © 2023 Chinese Vibration Engineering Society. All rights reserved.