# Long-Distance Shield Tunnelling Performance Prediction Based on Informer
## 4 Results and Analysis
### Comparative Analysis of Model Prediction Performance  
#### 4.3.1 Comparison of Different Prediction Sequence Lengths  
Table 6 shows the prediction results for the experimental group in Table 4, and we can find that the prediction performance of LSPP is better than that of LSTM and GRUs, which is more obvious in the long-distance prediction experiments. The performance of LSPP degrades more slowly. Comparing LSTM and GRUs, when the prediction sequence length is 48 mm, under this shorter prediction sequence length, the MAE of the LSPP model is only 0.59, the RMSE is 0.76, the MAPE is 0.03, and the R\({}^{2}\) is as high as 0.98, while the LSTM and GRU models do not perform as well as the LSPP in these four metrics, especially in the value of R\({}^{2}\), which is much higher than that of LSTM's 0.85 and GRU's 0.86. This indicates that the LSPP model is able to capture the trend of the data more accurately in the short-term prediction with higher prediction accuracy. When the prediction sequence length increases to 1200 mm, the LSPP still maintains good prediction performance, its error is still low, and the R\({}^{2}\) remains at a high level (0.91). However, the R\({}^{2}\) of GRUs and LSTM drop significantly to only 0.78 and 0.76. This result shows that as the prediction sequence length increases, LSPP has the advantage of stable performance. When the prediction sequence length is 6000 mm, although the prediction errors of all models have increased, the MAE, RMSE, and MAPE of LSPP are still lower than those of LSTM and GRUs, and the R\({}^{2}\) value reaches 0.87, which is significantly better than 0.73 for LSTM and 0.49 for GRUs, and the prediction advantage is more significant. This shows that in long-distance prediction, the LSPP model can maintain a relatively low error and show stronger stability. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
\begin{tabular}{c} **pred\_len** \\ **(mm)** \\ \end{tabular} & **Model** & **MAE** & **RMSE** & **MAPE** & **R\({}^{2}\)** \\ \hline \multirow{3}{*}{48} & LSPP & 0.59 & 0.76 & 0.03 & 0.98 \\  & LSTM & 1.48 & 2.2 & 0.07 & 0.85 \\  & GRU & 1.86 & 2.71 & 0.12 & 0.86 \\ \hline \multirow{3}{*}{1200} & LSPP & 1.05 & 1.51 & 0.05 & 0.91 \\  & LSTM & 1.82 & 2.72 & 0.09 & 0.78 \\  & GRU & 2.6 & 3.49 & 0.17 & 0.76 \\ \hline \multirow{3}{*}{6000} & LSPP & 1.49 & 1.8 & 0.07 & 0.87 \\  & LSTM & 2.04 & 2.98 & 0.11 & 0.73 \\ \cline{1-1}  & GRU & 2.89 & 4.09 & 0.15 & 0.49 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance comparison of different models. Figure 12: LSPP prediction results for the next 6 rings. Observe the performance degradation of the three models from Table 6. It can be found that when the predicted length increases from 1200 mm to 6000 mm, the corresponding R\({}^{2}\) of the GRU model decreases from 0.76 to 0.49, there is a large prediction bias, and the model performance degradation is serious, while at this time, the LSPP only decreases from 0.91 to 0.87 and still has excellent performance. The prediction performance of LSPP for the future 6000 mm even exceeds that of LSTM and GRUs for 1200 mm. The predicted sequences of the three models for the next 6000 mm are shown separately in Figure 13. Although there is considerable variation in penetration at 899 rings of the project, the LSPP model predicts closest to the true value and continues to reduce the error after continuous learning. While LSTM and GRUs perform similarly, the overall fluctuation is around the mean without being able to agree with the real value. After 900 rings, the actual penetration is more stable and the prediction results of all three models are close to the real situation. However, in terms of the overall prediction characteristics, LSPP has superior trend catching ability and accuracy, and it can use historical knowledge to infer future trends more effectively. The prediction accuracies of LSTM and GRUs are slightly inferior to LSPP and do not fully reflect the subtle changes in actual penetration.