## 5 Results
### Ensemble Models  
Eight models were established by tuning hyperparameters and training for prediction. In this section, the whole datasets with 84 time-steps of ZK2-1 and ZK2-3 were applied to make predictions with the LSTM models and SVR models. The total prediction displacements of ZK2-1 and ZK2-3 from January 2009 to December 2015 with LSTM models and SVR models can be obtained with this process. An optimal weight can be obtained with setting the original total displacements as \(E(t)\) in Equation (12).  
The optimal weights were set as outputs, and all the inputs that show in Table 2, the obtained total prediction displacements with LSTM models, the obtained total prediction displacements with SVR models, and the difference between these two total prediction displacements were set as candidate input factors. The latter 3 new candidate factors were considered as \(f_{10}\), \(f_{11}\), \(f_{12}\).  
An SVR model using the GS method was adopted to predict the optimal weight for an ensemble model. As stated in Section 4.1, 84 measured values were adopted for finding a better model between LSTMs and SVRs. For the ensemble model runs, 72 time-steps were set as the fitting dataset, 48 time-steps were set as a training dataset to fit the models, and 24 time-steps were set as validation dataset to tune the hyperparameters of the SVR models and to determine the optimal inputs (Table 7). Twelve time-steps were set to evaluate the models. The optimal weights were set as 1 when the predicting values were more than 1, and were set as 0 when the predicting values were less than 0.  
Figure 13, Tables 8 and 9 present the comparison between measured and predicted displacement of ZK2-1 and ZK2-3 using LSTM, SVR, and ensemble models. For the total displacement term of ZK2-1, the values of RMSE and MAPE with the Ensemble model were 13.76 mm and 0.73%, while the accuracy factors of the LSTM model were 13.79 mm and 0.74%, and the accuracy factors of the SVR model were 15.12 mm and 0.74%.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**RMSE in Trend Term(mm)**} & \multicolumn{2}{c}{**RMSE in Periodic Term(mm)**} \\ \cline{2-5}  & **ZK2-1** & **ZK2-3** & **ZK2-1** & **ZK2-3** \\ \hline LSTM & 3.38 & 5.23 & 12.95 & 10.92 \\ SVR & 3.17 & 6.26 & 13.63 & 10.62 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Accuracy of the prediction in trend term and periodic term of ZK2-1 and ZK2-3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Point**} & \multirow{2}{*}{**Inputs**} & \multicolumn{2}{c}{**Hyperparameters**} \\ \cline{3-4}  & & **C** & **Gamma** \\ \hline ZK2-1 & \(f_{12}\) & 1.0 & 0.0075 \\ ZK2-3 & \(f_{1}\),\(f_{2}\),\(f_{3}\),\(f_{4}\),\(f_{5}\),\(f_{6}\),\(f_{7}\),\(f_{8}\),\(f_{9}\) & 11.0 & 0.105 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Optimal hyperparameters and inputs of SVRs used for optimal weight prediction.  
For the total displacement term of ZK2-3, the values of RMSE and MAPE with the Ensemble model were 10.70 mm and 0.40%, while the accuracy factors of the LSTM model were 12.74 mm and 0.43%, and the accuracy factors of the SVR model were 15.43 mm and 0.60%.  
The total displacements predicted by the Ensemble model were in better agreement with the measured values than those with the LSTM or SVR models. As shown in Figure 13, in point a, point b, point c, and period d, the results of the Ensemble models tend to be closer to the results of original values than at least one of the LSTM or SVR models. This suggests that when the results of the LSTM and SVR models are different, the Ensemble model gives more weight to the results of the model that are closer to the real values. As shown in Table 8, in 12 predicted points of ZK2-1, 7 of them were had lower values of absolute error than the LSTM model, 5 of them had lower values of absolute error than the SVR model. As shown in Table 9, in 12 predicted points of ZK2-3, 2 of them were had lower values of absolute error than LSTM model, 10 of them had lower values of