# Long-Distance Shield Tunnelling Performance Prediction Based on Informer
## 4 Results and Analysis
### LSPP Prediction Performance Analysis  
In further exploring the characteristics of the proposed LSPP model, based on the results of the correlation analysis in Section 4.1, the sample data with an interval length of 48 mm (i.e., a unit distance of 48 mm) was selected for this experiment, and different prediction sequence lengths were set to analyze the characteristics of the model as the prediction sequence length increases. This study optimizes the LSPP model through the grid search method. The historical sequence time length, label sequence length, and prediction performance obtained for different prediction requirements are shown in Table 5. The results show that the overall coefficient of determination (R\({}^{2}\)) of the model tends to decrease with the increase in the prediction sequence length. The closer the R\({}^{2}\) is to 1, the more capable the model is of explaining the variability of the data. For example, at a predicted length of 48 mm, the R\({}^{2}\) reaches 0.98, indicating that the model can almost completely explain the observed variability. Meanwhile, a higher R\({}^{2}\) is often accompanied by a lower MAE, RMSE, and MAPE, which reflect a smaller gap between the LSPP predicted and actual observed values. In Table 5, when the predicted length reaches 6000 mm, R\({}^{2}\) = 0.87, which can fit the performance variation in the shield during construction well. In addition, the increase in the length of predicted sequences also leads to a corresponding increase in the length of historical sequences and the length of label sequences required by the model. Figure 10: Effect of different label sequence lengths on LSPP prediction. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**pred\_len** & **seq\_len** & **label\_len** & & & & \\
**(mm)** & **(mm)** & **(mm)** & & & & \\ \hline
48 & 1200 & 192 & 0.59 & 0.76 & 0.03 & 0.98 \\
1200 & 1200 & 192 & 1.05 & 1.51 & 0.05 & 0.91 \\
2400 & 2400 & 240 & 1.13 & 1.45 & 0.05 & 0.92 \\
3600 & 2400 & 240 & 1.74 & 2.05 & 0.08 & 0.84 \\
4800 & 3600 & 240 & 1.64 & 1.9 & 0.08 & 0.86 \\
6000 & 3600 & 576 & 1.49 & 1.8 & 0.07 & 0.87 \\
7200 & 4800 & 1200 & 1.82 & 2.13 & 0.09 & 0.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance of LSPP with different prediction sequence lengths. Figure 11 shows the model prediction effect when the length of the predicted sequence is 48 mm, 1200 mm, and 6000 mm, in which, when the length of the predicted sequence is 48 mm, the predicted value of the model keeps the trend of synchronization with the real value, and the RMSE between the predicted value and the real value is only 0.76 mm/rev. With the increase in the length of the predicted sequence, the error tends to be larger, but it is still within the acceptable range, and when the length of the predicted sequence reaches 6000 mm, the model prediction trend still remains the same with the real value. The model performance remains well stabilized in the presence of an increase in the length of the predicted sequence. To assess whether there is a significant difference between the predicted and actual values of the shielding performance of LSPP for long distances, the \(t\)-test was conducted for the predicted and actual values at the predicted length of 6000 mm. The results showed that t = 1.647, while \(p\_\)value = 0.1003, and when the significance level (\(\alpha\)) is 0.05, the \(p\_\)value > 0.05, so the original hypothesis is accepted. No significant difference was obtained between the predicted and actual values, verifying the reliability of the model performance. The prediction results of LSPP for the following six rings are shown in Figure 12. Although the actual value of the penetration has changed abruptly many times and the penetration decreased by 9.9 mm/rev from ring 821 to ring 822, a relatively large change, the model can still predict accurately.