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.

Accurate and reliable wind speed forecasting is crucial for wind farm planning and grid operation security. To improve the accuracy of wind speed forecasting, a novel combined model is proposed for wind speed forecasting in this paper. First, the complete ensemble empirical mode decomposition adaptive noise (CEEMDAN) and permutation entropy (PE) are employed to decompose the original wind speed time series into the sub-series with obvious complexity different; To overcome the disadvantage of weak generalization ability of single deep learning method when facing diversiform data, a cluster of gated recurrent unit networks (GRUs) with different hidden layers and neurons are applied to capturing the unsteady characteristics and implicit information of each sub-series; The predictions of the GRUs of each sub-series are aggregated into a nonlinear-learning regression top-layer which is consisted of radial basis function neural network (RBFNN), and improved bat algorithm (IBA) is introduced to optimize the parameters of RBFNN; Lastly, the prediction values of each nonlinear-learning top-layer are superimposed to obtain the final prediction values. To validate the effectiveness of the model, 15-min and 1-h wind speed data from the wind farm in Zhangjiakou, China, are used as test cases. The experimental results demonstrate that the proposed combined model can achieve the best performance and stability compared to other models. Such as the performance evaluation indexes (RMSE=0.3294, MAPE=2.6169%) are smallest obtained from case study 1, and (RMSE=0.5876, MAPE=4.7875%) are smallest obtained from case study 2.