## 3 Case Study
### Model Development  
To illustrate the superiority of the hybrid model we proposed, it is compared with a total of nine models including multivariable linear regression (MLR), multilayer perceptron (MLP), 1D-CNN, LSTM, GRU, LSTM-SSA, GRU-SSA, CNN-LSTM-SSA, and CNN-GRU-SSA. This section provides detailed information about these models. The experimental configuration for this study was CPU Intel(r) Core i7-9750H and NVIDIA 1660 Ti GPU. All algorithmic models in the framework were conducted in the python 3.6 environment, and the CNN, LSTM, and  
Figure 8: Decomposition results obtained using STL (**a**) G2-HY; (**b**) G3-HY. GRU networks were implemented in the TensorFlow framework developed by the artificial intelligence team of Google. The final experimental results are listed in Tables 2 and 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multirow{2}{*}{**Hyperparameters**} & \multirow{2}{*}{**Search Range**} & \multicolumn{2}{c}{**Optimal Value**} \\ \cline{3-5}  & & & **G2-HY** & **G3-HY** \\ \hline MLP & the number of neurons & (32, 128) & 60 & 64 \\ dropout rate & [0.1, 0.2, 0.3, 0.4, 0.5] & 0.2 & 0.2 \\ \hline CNN & the number of neurons & (64, 256) & 128, 70 & 62, 55 \\ the size of kernel & [3, 5, 7] & 7 & 7 \\ recurrent dropout rate & [0.3, 0.4, 0.5, 0.6, 0.7] & 0.4, 0.5 & 0.5, 0.5 \\ \hline LSTM & the number of neurons & (64, 128) & 120, 70, 76 & 110, 56 \\ recurrent dropout rate & [0.4, 0.5, 0.6, 0.7, 0.8] & 0.5, 0.5, 0.5 & 0.6, 0.6, 0.6 \\ \hline GRU & the number of neurons & [64, 128] & 80, 64, 60 & 100, 78 \\ recurrent dropout rate & [0.4, 0.5, 0.6, 0.7, 0.8] & 0.4, 0.5, 0.5 & 0.5, 0.5 \\ \hline CNN–LSTM & the number of neurons for CNN & (128, 256) & 160 & 122 \\ the size of kernel & [3, 5, 7] & 5 & 5 \\ recurrent dropout rate for CNN & [0.2, 0.3, 0.4, 0.5, 0.6] & 0.5 & 0.5 \\ the number of neurons for LSTM & (64, 128) & 117, 89 & 109, 88 \\ recurrent dropout rate for LSTM & [0.2, 0.3, 0.4, 0.5, 0.6] & 0.4, 0.4 & 0.4, 0.5 \\ \hline CNN–GRU & the number of neurons for CNN & (128, 256) & 146 & 115 \\ the size of kernel & [3, 5, 7] & 7 & 7 \\ recurrent dropout rate for CNN & [0.3, 0.4, 0.5, 0.6, 0.7] & 0.5 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Basic information of model parameter tuning. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Hyperparameters**} & \multicolumn{4}{c}{**G2-HY**} & \multicolumn{4}{c}{**G3-HY**} \\ \cline{2-7}  & **Seasonality** & **Trend** & **Residual** & **Seasonality** & **Trend** & **Residual** \\ \hline the number of neurons for CNN & 128 & 156 & 222 & 68 & 108 & 188 \\ the size of kernel & 7 & 7 & 7 & 7 & 5 & 5 \\ recurrent dropout rate for CNN & 0.4 & 0.5 & 0.4 & 0.6 & 0.3 & 0.4 \\ the number of neurons for GRU & 146 & 133 & 196 & 128 & 88 & 214 \\ recurrent dropout rate for GRU & 0.5 & 0.5 & 0.3 & 0.5 & 0.4 & 0.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The determined parameters of the proposed model. The deep LSTM and GRU models were used in this study, and the original radial dam displacement was selected as the target object. This stacked-layers mechanism made the output of the previous hidden layer from the model be the input of the next hidden layer. Moreover, adding a recurrent dropout layer limits the hyperparameters of the model from being too large, which would cause overfitting. The number of stacker-layers were set to two. The number of neurons and recurrent dropout rate were determined by the empirical method. The output layer is a fully connected layer. The purpose of establishing the LSTM-SSA model and the GRU-SSA model is to verify the importance of the optimal parameters. Then the SSA method found the appropriate value for the number of hidden neurons and the recurrent dropout rate. The model frameworks were the same as those discussed above. CNN-LSTM-SSA and CNN-GRU-SSA models  
The CNN layer was used for the convolution operation of input data to extract local features of the original time series.