Deep learning-based methods have made remarkable achievements in rolling bearing fault diagnosis in recent years. Nevertheless, due to the diversity and complexity of rolling bearing working conditions, how to generalize deep learning models trained under limited conditions to unseen working conditions has become a popular issue in current research. The existing methods based on domain generalization usually need to train the model using a significant quantity of labeled data under multiple known working conditions to enhance its generalization capabilities under unseen working conditions. However, the acquisition of adequately labeled samples is a time-consuming and laborious task. Therefore, this paper proposes an auxiliary branch semi-supervised domain generalization network (ABSDGN). ABSDGN employs a joint learning strategy of the auxiliary and main branches. The auxiliary branch generates high-confidence pseudo-labels for the unlabeled source-domain data using the labeled source-domain data. The main branch leverages both real and pseudo labels to learn domain-invariant knowledge. Meanwhile, a quadratic neuron-based convolution (QConv) is introduced to take advantage of its powerful nonlinear and higher-order feature representation capabilities in enhancing the performance and generalization of the model in complicated situations. In addition, a weight decomposition method based on domain labels is proposed to decompose the main branch classifier into a generic feature and feature-specific classifier to better explore the universal knowledge among different domains. The experimental results show that the proposed model has better diagnostic accuracy and stability than the most advanced semi-supervised domain generalization method on two-bearing datasets.

The accurate prediction of wind power has a huge impact on the grid connection and dispatching of the power system. In order to make the prediction accuracy of wind power higher, this paper proposes a combined forecasting model based on the combination of numerical weather prediction (NWP) and wind power time series, called gray wolf algorithm-wavelet neural network-variational mode decomposition-long short-term memory-Q-learning (GWO-WNN-VMD-LSTM-Q-learning). First, the wind power prediction (WPP) is implemented based on the NWP, and prediction result 1 is obtained. In this stage, the wavelet neural network (WNN), which is optimized by the gray wolf algorithm (GWO), is used for prediction. Then, the historical time series of wind power is subjected to variational mode decomposition (VMD), and the decomposed sub-sequences are predicted by long short-term memory (LSTM) networks, respectively, and the prediction results of each sub-sequence are summed to obtain the prediction result 2. Finally, the Q-learning algorithm is used to superimpose prediction result 1 and result 2 on the basis of optimal weight and get the final WPP results. The simulation results demonstrate that this model's prediction accuracy is high and that it has a substantially greater predictive impact than other traditional models that merely take time series or numerical weather forecasts into account.