## 4 Analysis and Discussions
### Mode Decomposition Algorithm-Recurrent Neural Network Combined Prediction Model
The calculations are shown in Table 5 and Figure 11.  
The results in Table 5 and Figure 11 clearly show that after combining the modal decomposition algorithm, the prediction errors of all types of neural networks are significantly reduced, indicating that the modal decomposition technique plays an important role in extracting the potential features of the time series, which effectively improves the prediction ability of the model. Specifically, in the original neural network model, the MSEs of the RNN, LSTM, and GRU are 2.0443, 1.4017, and 0.9042, the RMSEs are 1.4644, 1.0522,  
Figure 11: Radar plot of the model prediction error. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Groups**} & **RNN** & **LSTM** & **GRU** & **RNN** & **LSTM** & **GRU** & **RNN** & **LSTM** & **GRU** \\ \cline{2-10}  & & **MSE** & & & **RMSE** & & & **MAE** & \\ \hline Original & 2.0443 & 1.4017 & 0.9042 & 1.4644 & 1.0522 & 0.8974 & 1.2892 & 0.7373 & 0.8934 \\ EMD & 0.9892 & 1.0383 & 0.6453 & 0.9947 & 0.9897 & 0.6764 & 0.8595 & 0.9316 & 0.6833 \\ CEEMDAN & 0.8736 & 0.7372 & 0.5282 & 0.8632 & 0.7433 & 0.5654 & 0.8423 & 0.7354 & 0.5512 \\ WPT & 1.2237 & 0.8643 & 0.7423 & 0.9362 & 08125 & 0.7462 & 0.9823 & 0.8012 & 0.7413 \\ VMD & 0.8844 & 0.7075 & 0.4984 & 0.9974 & 0.8985 & 0.6766 & 0.7264 & 0.6993 & 0.6132 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of prediction model errors. and 0.8974, and the MAEs are 1.2892, 0.7373, and 0.8934, respectively. By introducing the modal decomposition algorithm, the MSEs, RMSEs, and MAEs of all the combined models are significantly reduced. For example, the average MSE, RMSE, and MAE of the combined model of the RNN combined with the decomposition algorithm is reduced to 1.00304, 1.05198, and 0.94094, respectively, which is a reduction of approximately 50.94% in the MSE compared with those of the single RNN model, highlighting the significant role of the decomposition algorithm in enhancing prediction performance. Further analysis reveals that there are differences in the performance of different modal decomposition algorithms. Among them, the VMD algorithm performs most prominently, and its combined model with the GRU outperforms all other combined models in terms of prediction performance. For the VMD-GRU combination, the MSE, RMSE, and MAE reach 0.4984, 0.6766, and 0.6132, respectively, which are significantly better than those of the other combination approaches. This suggests that VMD has a unique advantage in capturing the intrinsic properties of signals and handling nonstationary data. In addition, CEEMDAN has the next best performance, and its combination with LSTM also shows high prediction accuracy, while WPT and EMD are relatively weak. Combining the above results, we ranked the effectiveness of the decomposition algorithms in improving the prediction accuracy according to the decomposition algorithms as VMD > CEEMDAN > WPT > EMD. Notably, the combined VMD model performs particularly well in the prediction of abrupt short-term data changes, which is valuable for engineering applications in highly dynamic changing environments. Overall, the SSA-VMD-GRU model performs the best in terms of a number of error metrics, further verifying its excellent performance in complex data prediction. The results of this study provide theoretical support and technical guidance for practical applications in areas such as tunnel engineering. Figure 12 shows that the prediction accuracy of the EMD-combined prediction model is improved to a certain extent for short-term data changes, but the data fitting effect is poor for the fluctuation period and cannot characterize the trend in the corresponding data. The trend in the change cannot be corrected in the neural network prediction stage, eventually leading to a larger prediction error in the smooth settling period.