# Displacement Patterns and Predictive Modeling of Slopes in the Bayan Obo Open-Pit Iron Mine
## 3 Results
### Periodic Component Displacement Prediction  
Since the data were normalized before training, the prediction results needed to be rescaled back to their original scale for comparison with the true values. Figures 15 and 16 display the predicted results, and the corresponding evaluation metrics--RMSE, R\({}^{2}\), and MAE--are presented in Table 8. For the LSTM model, the RMSE and MAE on the training set are 0.0816 and 0.0585, respectively, with an R\({}^{2}\) value of 0.9948, indicating an excellent fit to the training data and demonstrating the model's strong ability to capture temporal patterns.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Predictive Model** & **RMSE** & **R\({}^{2}\)** & **MAE** \\ \hline GRU & 0.94794 & 0.99755 & 0.46536 \\ ARIMA & 4.379 & 0.92098 & 2.9068 \\ LSTM & 4.5071 & 0.94453 & 2.1568 \\ TCN & 5.8763 & 0.90571 & 2.7592 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Evaluation metrics of four models.  
Figure 14: Comparison of multi-model displacement predictions.  
On the test set, while the RMSE and MAE increase slightly to 0.1278 and 0.0635, and R\({}^{2}\) drops to 0.9873, the performance remains at a high level, showing that the model maintains strong generalization and prediction capability when dealing with unseen data. For the entire dataset, the overall RMSE and MAE are 0.0978 and 0.0600, respectively, and R\({}^{2}\) reaches as high as 0.9925, further validating the effectiveness of the LSTM network in periodic component prediction.  
To intuitively evaluate the prediction performance of LSTM, three other models were used for comparison: RNN, GRU, and CNN. The prediction results are shown in Figure 17, and their evaluation metrics are listed in Table 9.  
Figure 16: Ratio of the predicted values to the true values. (**a**) The ratio of the predicted values to the true values in the training set; (**b**) the ratio of the predicted values to the true values in the test set.  
Figure 15: Prediction results.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data** & **RMSE** & **R\({}^{2}\)** & **MAE** \\ \hline Training Set & 0.0816 & 0.9948 & 0.0585 \\ Test Set & 0.1278 & 0.9873 & 0.0635 \\ Overall Data & 0.0978 & 0.9925 & 0.0600 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Evaluation metrics of the LSTM model.  
From both the figure and the table, it is clear that LSTM achieves the best prediction performance. Its predicted values are the closest to the actual observations, indicating that LSTM's gating mechanism (forget gate, input gate, output gate) is highly effective in capturing long-term periodic patterns and mitigating gradient vanishing problems. LSTM has the lowest RMSE and highest R\({}^{2}\), suggesting that it nearly perfectly fits the data.  
GRU, with its simplified gating structure (update and reset gates), performs well on periodic sequences but is slightly less capable than LSTM when modeling complex periodic dynamics. Compared to RNN and CNN, GRU achieves a lower RMSE and MAE, supporting the effectiveness of gating mechanisms.  
The standard RNN model struggles with long-term dependencies due to the gradient vanishing issue, leading to significantly higher errors than LSTM and GRU. Meanwhile, CNN, being more suited for spatial data, is not ideal for purely temporal periodic sequences. Its reliance on local convolution kernels limits its ability to directly capture global periodic patterns.