An Optimal Variational Mode Decomposition Method Based On Sparse Index

Addressing the challenge of ineffective determination of the number of source signals \(K\) and the penalty factor \(\alpha \) , hindering the efficiency of Variational Mode Decomposition (VMD), a novel strategy integrating sparsity index and an enhanced Particle Swarm Optimization (PSO) algorithm is proposed for optimizing VMD. By implementing particle reset and elimination mechanisms, the algorithm can evade local optima, thereby expediting the optimization process of the PSO algorithm. Utilizing sparsity as the fitness function of the PSO algorithm, derived from the marginal spectrum that accurately captures signal energy variations with frequency, enhances the method’s accuracy. Additionally, the introduction of an energy weighting factor accounts for energy disparities among different components. This approach offers a novel solution for VMD of composite signals with unknown numbers of source signals.