The decomposition effect of variational mode decomposition (VMD) mainly depends on the choice of decomposition number $K$ and penalty factor $\alpha$. For the selection of two parameters, the empirical method and single objective optimization method are usually used, but the aforementioned methods often have limitations and cannot achieve the optimal effects. Therefore, a multi-objective multi-island genetic algorithm (MIGA) is proposed to optimize the parameters of VMD and apply it to feature extraction of bearing fault. First, the envelope entropy ($E_e$) can reflect the sparsity of the signal, and Renyi entropy ($R_e$) can reflect the energy aggregation degree of the time-frequency distribution of the signal. Therefore, $E_e$ and $R_e$ are selected as fitness functions, and the optimal solution of VMD parameters is obtained by the MIGA algorithm. Second, the improved VMD algorithm is used to decompose the bearing fault signal, and then two intrinsic mode functions (IMF) with the most fault information are selected by improved kurtosis and Holder coefficient for reconstruction. Finally, the envelope spectrum of the reconstructed signal is analyzed. The analysis of comparative experiments shows that the feature extraction method can extract bearing fault features more accurately, and the fault diagnosis model based on this method has higher accuracy.

Aiming at the problem that it is difficult to extract fault features from the nonlinear and non-stationary vibration signals of wind turbine rolling bearings, which leads to the low diagnosis and recognition rate, a feature extraction method based on multi-island genetic algorithm (MIGA) improved variational mode decomposition (VMD) and multi-features is proposed. The decomposition effect of the VMD method is limited by the number of decompositions and the selection of penalty factors. This paper uses MIGA to optimize the parameters. The improved VMD method is used to decompose the vibration signal into a number of intrinsic mode functions (IMF), and a group of components containing the most information is selected through the Holder coefficient. For these components, multi-features based on Renyi entropy feature, singular value feature, and Hjorth parameter feature are extracted as the final feature vector, which is input to the classifier to realize the fault diagnosis of rolling bearing. The experimental results prove that the proposed method can more effectively extract the fault characteristics of rolling bearings. The fault diagnosis model based on this method can accurately identify bearing signals of 16 different fault types, severity, and damage points.