## 3 Results
### Prediction of VMD Components  
#### 3.2.1 Rolling Prediction of High-Frequency Components Based on DBN Model  
As described above, the DBN is used to predict high-frequency components. First, the DBN network is trained. Because the number of hidden layers of the DBN network and the number of cells in each hidden layer have a great influence on the prediction accuracy and computation time, this work focuses on the selection for these two parameters. The weight of the DBN model is initialized  
Figure 6: VMD decomposition diagram and spectrum diagram. (**a**) Modal components, (**b**) Frequency. via a normal random distribution. The threshold of the DBN model is initialized at 0, the maximum number of iterations of the RBM is 100, the learning rate is 0.1, the momentum parameter is 0.9, and the model parameters are set as in Reference [44; 45]. In the training model, the rolling prediction model with eight inputs and one output is adopted, i.e., the number of input layer nodes are the data from the first 2 h before the predicted time (eight nodes). The output layer consists of the predicted time for one node. The enumeration method is used to select the number of hidden units, layer by layer, to verify the influence of the deep network structure on the prediction effect and time consumption. First, we determine the optimal number of hidden units in the RBM1 layer and fix them; then, we add a hidden layer to determine the optimal value of the number of hidden units in the RBM2 layer. This continues until the prediction accuracy is no longer improved. The output error and time spent are obtained by changing the number of hidden layers and the number of nodes. Since the corresponding weight and threshold are automatically initialized during each training, the number of hidden cells in each layer is set to four to 32 (the interval is four), which is a total of eight levels. The number of layers of the hidden layer is sequentially set to the RBM1, RBM2, and RBM3 layers. IMF1 is taken as an illustration example, and the others will not be described again. The specific DBN parameters are shown in Table 2.  
Table 2 shows that when the number of neurons in the hidden layer RBM1 is 20, the output error reaches a minimum of 1.0242%, which takes 13.47 s; the average output error of its two neighboring neurons is 1.28281. When the number of neurons in the hidden layer RBM2 is 12, the output error reaches a minimum of 1.21242%, which takes 15.94 s; the output error is smaller than the average output errors of neurons that are adjacent to the optimal neurons in the RBM1 layer. When the number of neurons in the hidden layer RBM3 is 16, the output error reaches the minimum value of 2.81824%, which takes 33.91 s; both the output error and the training time of RBM3 are higher than the average output errors of neurons that are adjacent to the optimal neurons in the RBM2 layer. For the IMF1 component data set, the DBN prediction model has better effects when it adopts a four-layer structure of \"8-20-12-1\" (that is, the numbers of hidden units of RBM1 and RBM2 are 20 and 12, respectively, which are marked in red in the table). By using this method, the DBN model structure of the high-frequency components of IMF2 and IMF3 and the number of nodes of each hidden layer are obtained, as shown in Table 3.