## 5 Results and Discussions
### Performance of Prediction Accuracy and Interpretation in Time Dimension  
The LSTM model coupled with the attention mechanism was compared to a variety of advanced algorithms. As was done for the proposed model, all models were trained with 70% of the original data set and tested with the remaining 30%. The evaluation index value of each model is listed in Table 4, where the best performing model is marked in bold. The evaluation indexes showed that, except for SVM-poly model which had too low a fitting accuracy for the high-dimensional data of the training set, all of the models fit the observation data well. The LSTM models exhibited the best fitting performances, and the model in which the LSTM layer was preceded by an attention mechanism performed better than all other models. The RMSE, MAE, and AEmax values of this model were all significantly lower than the other models, indicating its prediction results were the best. Figure 10: The MAE values of each group under ten-fold cross-validation. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Serial**} & \multicolumn{8}{c}{**Search Range**} & \multicolumn{8}{c}{**MAE**} \\ \cline{2-13} \multicolumn{1}{c}{**Number**} & \(\mathbf{T_{3}}\) & \(\mathbf{T_{4}}\) & \(\mathbf{t_{2}}\) & \(\mathbf{H_{3}}\) & \(\mathbf{H_{2}}\) & \(\mathbf{T_{1}}\) & \(\mathbf{t_{1}}\) & \(\mathbf{H_{1}}\) & \(\mathbf{T_{2}}\) & **Training** & **Test** \\ \hline
1 & \(\surd\) & & & & & & & & & & 1.2022 & 1.0520 \\
2 & \(\surd\) & \(\surd\) & & & & & & & & & 1.1023 & 1.1563 \\
3 & \(\surd\) & \(\surd\) & \(\surd\) & & & & & & & & 0.8505 & 1.0482 \\
4 & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & & & & & & & 0.3405 & 0.9541 \\
5 & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & & & & & 0.3802 & 0.9581 \\
6 & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & & & & 0.3453 & 0.9550 \\
7 & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & & & 0.3990 & 1.0633 \\
8 & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & & 0.4280 & 1.0584 \\
9 & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & 0.4392 & 1.0821 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation of simulation results for different input factors. To further compare the stabilities of the prediction results, the prediction residuals of all models were plotted, shown in Figure 11. The plot showed that the residual distribution of the HST model was right-skewed, and the prediction result gradually tended towards the average level of the training model over time. This was because linear fitting is more inclined towards the training data and does not consider non-linear effects of influencing factors, making linear fitting unable to accurately predict displacement caused by extreme weather. Although the distribution of the SVM-poly model was not skewed, its accuracy was not sufficient to meet the needs of dam deformation prediction through the median and quartiles. The SVR-rbf and MLP models showed improved prediction accuracy, but there were still problems with overfitting. The RF model did not exhibit overfitting, due to its own architecture, but it did exhibit generalization errors [32]. Therefore, the RF model had obvious right skewness, and would eventually tend to predict the average level like the HST model. Due to the introduction of time-dependent storage, the resulting LSTM has greatly improved the prediction accuracy and has a strong ability to represent nonlinear features, but it is still unable to predict peaks, as shown in Figure 12.