## 4 Experiment and Analysis
### Compare Experiments  
Our experimental platform is shown below: our model is based on python 3.6, pytorch 1.9.0, and the experiments are done on a computer with an Intel i7-7700 CPU and 32 GB of RAM.  
Our experiments were conducted with L2 loss function, Adam optimizer, initial learning rate set to 0.0001, batch size set to 32, learning rate changed to 1/2 of the original rate after each run of training data, encoder input length set to 96, decoder input length set to 48+O (96, 192, 336, 720), encoder layer set to 4, and decoder layer set to 2. The number of heads h for multi-head auto-correlation is set to 8. The auto-correlation hyperparameter c is set to 0.3, the training number 20, the number of early stops 3. Each experiment is repeated three times, and the model performance is measured according to the average metrics of the three experiments. The detailed training procedure is shown in Algorithm 1.  
We compare autoformer, informer, lstm, and vmd-lstm as baseline comparison models with our model to further demonstrate the superiority of our model. The dimension of the hidden layer of the LSTM is set to 256 and the number of network layers is set to 3. The parameter settings in the VMD-LSTM remain the same as those of the LSTM. The parameters of autoformer and informer are set according to the default configuration of the author.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**K** & **IMF1** & **IMF2** & **IMF3** & **IMF4** & **IMF5** & **IMF6** & **IMF7** & **IMF8** \\ \hline
2 & 0.02011 & 0.25129 & & & & & & \\
3 & 0.01700 & 0.04149 & 0.33699 & & & & & \\
4 & 0.01844 & 0.04184 & 0.25042 & 0.33892 & & & & \\
5 & 0.01845 & 0.10044 & 0.17884 & 0.26595 & 0.41738 & & & \\
6 & 0.01788 & 0.04046 & 0.10638 & 0.25459 & 0.33735 & 0.42155 & & \\
7 & 0.02001 & 0.03570 & 0.06523 & 0.18236 & 0.25355 & 0.33450 & 0.42184 & \\
8 & 0.01869 & 0.03885 & 0.10596 & 0.18952 & 0.27130 & 0.32840 & 0.37020 & 0.43156 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The center frequency of IMF at different K.  
Figure 6: Data plot (original data, normalized data, and decomposed imf components).  
Figure 8: Partial prediction results for a prediction length of 96.  
Figure 7: Comparison of prediction results of different models.  
Figure 9: Partial prediction results for a prediction length of 192.  
Figure 11: Partial prediction results for a prediction length of 720.  
Figure 12: Comparison of the results of ablation experiments.  
Figure 10: Partial prediction results for a prediction length of 336.  
The model with the correction module removed is compared with the model with the VMD and correction module removed to verify the key role played by VMD in the prediction. In experiments with prediction lengths of 96, 192, 336, and 720, MSE decreases by 4.5% (0.314 \(\rightarrow\) 0.300), 2.2% (0.363 \(\rightarrow\) 0.355), 9.8% (0.396 \(\rightarrow\) 0.357), and 28.5% (0.515 \(\rightarrow\) 0.368), respectively. The role played by VMD in longer predictions is more obvious; the model with VMD removed is compared with the model with VMD and correction module removed to verify the usefulness of the correction module. In the experiments with prediction lengths of 96, 192, 336, and 720, the MSE decreased by 1.3% (0.314 \(\rightarrow\) 0.310), 1.1% (0.363 \(\rightarrow\) 0.359), 2.8% (0.396 \(\rightarrow\) 0.385), and 7.3% (0.515 \(\rightarrow\) 0.477), respectively. The application of the correction module has resulted in a slight improvement in the performance of the model. From the Figure 12, it can be seen that the longer the prediction length, the more obvious the effect of VMD and correction module on the prediction accuracy, especially the VMD is very effective for long-term prediction.