## 3 Case Study
### Simulation Results
#### 3.7.1 Short-Term Prediction Performance Evaluation  
A measurement index is used to evaluate the prediction abilities of the nine models, as shown in Table 4. Figure 11 shows the residual boxplots of the proposed model and other conventional models for the two monitoring points. From Table 4 and Figure 11, we find that the hyperparameters of the architecture influence the prediction accuracy of the LSTM and GRU model. For instance, the MSE value of the LSTM-SSA is reduced by approximately 30.1% for G3-HY compared with the LSTM. Compared with the GRU, the GRU-SSA prediction results show a reduction of 10.9% in terms of the MAE for G3-HY. Combined with the boxplot in Figure 11c, the median values of the outliers of the model after hyperparameter optimization are lower than those of the model without optimization, indicating that their predictive performance is better and more stable, which can improve the model prediction performance.  
The graphs on the right side of Figure 12 show a performance comparison between the models (i.e., LSTM-SSA, GRU-SSA, CNN-LSTM-SSA, CNN-GRU-SSA, and the proposed model) for short-term prediction. The models show good fitting results on the training dataset, indicating that each model can fit the dam deformation time series. It can be seen from Figure 12 that the prediction performance of the proposed model is outstanding among the nine models, and the predictive displacements are basically consistent with the observed data. Moreover, the LSTM-SSA and GRU-SSA models have prediction errors for the deformation monitoring data having crests and troughs. However, owing to the introduction of the CNN model, the prediction accuracy of the model for crests and troughs is improved. The feature extraction potentials of the CNNs are demonstrated in this case. Thus, the hybrid model reduces the computational pressure while improving the performance of extreme value prediction, so that the prediction model is more suitable for practical problems.  
Figure 11: Boxplots of residuals from the hybrid model and the benchmark models: (**a**) 60% of the data of G2-HY for training; (**b**) 30% of the data of G2-HY for training; (**c**) 60% of the data of G3-HY for training; (**d**) 30% of the data of G3-HY for training.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{_MAE_} & \multicolumn{2}{c}{_MSE_} & \multicolumn{2}{c}{_RMSE_} & \multicolumn{2}{c}{\(\mathbf{R^{2}}\)} \\ \cline{2-9}
**Models** & **G2-HY** & **G3-HY** & **G2-HY** & **G3-HY** & **G2-HY** & **G3-HY** & **G2-HY** & **G3-HY** \\ \hline Hybrid model & 0.7765 & 0.1623 & 0.9254 & 0.0382 & 0.9620 & 0.1954 & 0.9877 & 0.9327 \\ MLP & 2.0126 & 0.2791 & 6.6995 & 0.1190 & 2.588 & 0.3450 & 0.8719 & 0.7449 \\ CNN & 2.3113 & 0.2685 & 7.1580 & 0.1106 & 2.6754 & 0.3326 & 0.8686 & 0.7508 \\ LSTM & 1.8344 & 0.2961 & 6.4288 & 0.1379 & 2.5355 & 0.3713 & 0.8756 & 0.7235 \\ GRU & 1.7991 & 0.2735 & 5.1987 & 0.1146 & 2.2801 & 0.3385 & 0.8850 & 0.7420 \\ LSTM-SSA & 1.2957 & 0.2556 & 3.1196 & 0.0964 & 1.8492 & 0.3105 & 0.9302 & 0.7838 \\ GRU-SSA & 1.2801 & 0.2434 & 3.0687 & 0.0859 & 1.8079 & 0.2931 & 0.9340 & 0.7979 \\ CNN-LSTM-SSA & 1.1129 & 0.2498 & 2.1640 & 0.0906 & 1.4710 & 0.3009 & 0.9552 & 0.7981 \\ CNN-GRU-SSA & 0.9384 & 0.2429 & 1.4630 & 0.0873 & 1.2095 & 0.2955 & 0.9752 & 0.8260 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Results of different models for an arch dam with 60% of the data used for training.  
Figure 12: _Cont._