## 5 Results and Discussions  
### Importance of Input Variables and Model Interpretation  
For a prediction model, the choice of input variables will directly affect the accuracy of the prediction results, so it needs to be determined if the input variables can fully represent the nonlinear relationship of dam deformation and whether the input variables are redundant. To do this we adopted the RF model to conduct a deep analysis of the input variables and determine the relative importance of each. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Attribute** & **The Original Data** & **The Data Processed through DBSCAN** \\ \hline Max & 19.0791 & 13.2493 \\ Min & \(-\)6.2839 & \(-\)0.8423 \\ Mean & 5.9806 & 6.0159 \\ Median & 5.7828 & 5.7860 \\ Standard & 3.0866 & 2.8342 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary statistics of the original data and the data processed through DBSCAN. Figure 8: Dam horizontal displacement data collected from automated monitoring equipment: (**a**) the original data and (**b**) the data processed through DBSCAN. Figure 9 shows the relative importance of the nine input variables as calculated by the RF model using the GS method to optimize parameters. It can be seen that the temperature and water level factors were most relevant to dam deformation, with a relative importance of 60.97% and 21.29%, respectively. While the time component has the lowest bearing on the prediction results. From the perspective of hydraulic structural engineering, these calculated importance values demonstrated that temperature plays a central role in the deformation responses of dam structures, followed by water level, which is in line with the actual situation of the project and is reasonable. Although the time component had little influence on the model, the aging effect of the dam material and its inherent rheological characteristics may need to be analyzed as input variables to improve the nonlinear model. Using the sequential backward selection method, the input variables are sorted from top to bottom according to importance. As can be seen from Figure 9, the order of importance of the input variables was \(T_{3}\), \(T_{4}\), \(t_{2}\), \(H_{3}\), \(H_{2}\), \(T_{1}\), \(t_{1}\), \(H_{1}\), and \(T_{2}\). In this order, the number of input variables fed to the RF model for training and testing is gradually increased. In order to meet the test requirements, 70% of the original data set is used as the training set and the remaining 30% data is used as the test set. Since the input sequence of the data set will also affect the test results, a ten-fold cross-validation is used to ensure the stability and reliability of the test results. The MAE values of the test results are provided in Table 3, and shown in Figure 10 to better visualize the different combinations. There were obvious fluctuations in the MAE values of the test and training sets at the beginning, and has not yet converged. This was because the model weighs the input variables and MAE values, and the effective information provided by the few input variables may not have been enough to represent the original time series. When the process continued and more variables were input, the MAE value significantly declined and the test set and training set began to stabilize. When using four, five, and six input variables, the MAE values of the test sets were basically stable at around 0.95, while those of the training set started to stabilize around 0.35. However, as the input variables continued to increase, the MAE values of the test and training sets increased again, and the increasing trend continued with additional variables. This was because the additional input variables contained redundant data that were not conducive to the prediction results, resulting in new features being captured by the model that contradicted those of the earlier data.