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The selection of variational mode decomposition (VMD) parameters usually adopts the empirical method, trial-and-error method, or single-objective optimization method. The above-mentioned method cannot achieve the global optimal effect. Therefore, a multi-objective particle swarm optimization (MOPSO) algorithm is proposed to optimize the parameters of VMD, and it is applied to the composite fault diagnosis of the gearbox. The specific steps are: first, symbol dynamic entropy (SDE) can effectively remove background noise, and use state mode probability and state transition to preserve fault information. Power spectral entropy (PSE) reflects the complexity of signal frequency composition. Therefore, the SDE and PSE are selected as fitness functions and then the Pareto frontier optimal solution set is obtained by the MOPSO algorithm. Finally, the optimal combination of VMD parameters (<inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\alpha$ </tex-math></inline-formula>) is obtained by normalization. The improved VMD is used to analyze the simulation signal and gearbox fault signal. The effectiveness of the proposed method is verified by comparing with the ensemble empirical mode decomposition (EEMD).

Application of Parameter Optimized Variational Mode Decomposition Method in Fault Diagnosis of Gearbox