## 3 Case Study
### Performance Comparison between Models with Different Time Steps  
Since the MLP architecture accepts 2D tensors and does not require time series reconstruction, while the CNN, LSTM, and GRU architectures accept 3D tensors, the time step needs to be optimized. Figure 9 shows the average MAE variation in the simulation results of the CNN, LSTM, GRU, CNN-LSTM, and CNN-GRU models with different time steps. Considering the influence of the sequence of data input on the simulation results, a five-fold cross-validation is used for the model. Therefore, the training and test sets are divided differently each time, which leads to differences in the results of the five iterations for a given time-step combination. In Figure 10, the maximum and minimum values of MAE are, respectively, used as the upper and lower boundaries of the band.  
The results show that if under a fixed prediction time, the MAE of the CNN models initially decreases with the increasing time step and then increases. To accurately predict the future dam deformation, the model should be inputted with time series data containing sufficient, complete information pertaining to dam deformation events. The length of the input time series is essentially the value of the time step. For CNN models with a prediction time of one day, when the time step is from one to six days, the accuracy of the dam deformation prediction increases with the increasing time step. However, when the time step exceeds six days, the input time series has redundant information, which will become a negative factor for dam deformation prediction. Therefore, when using the CNN model to predict dam deformation, the optimal time step required by the model should  
Figure 10: Maximum and minimum MAE values for **(a)** G2-HY and **(b)** G3-HY from CNN, LSTM, GRU, CNN–LSTM, and CNN–GRU models in five repeated simulations with different time steps.  
Figure 9: Average MAE values for **(a)** G2-HY and **(b)** G3-HY from CNN, LSTM, GRU, CNN–LSTM, and CNN–GRU models in five repeated simulations with different time steps.  
be determined first, and the optimal value may change because data are collected from different dams.  
On the other hand, the results show that it is not necessary to choose the optimal time step for the LSTM, GRU, CNN-LSTM, and CNN-GRU models. As shown in Figure 9, although the CNN-LSTM and CNN-GRU models are less accurate when the time step is small and when the MAE fluctuates, the overall MAE value decreases with the increasing time step for these four models and remains nearly stable when the time steps are large. This indicates that the need to eliminate redundant information in the LSTM, GRU, CNN-LSTM, and CNN-GRU models is not as important as in the CNN model. For these models, a relatively large time step can be selected in practical applications to allow the training dataset to introduce a sufficient time series, while the introduction of unnecessary information will not negatively affect the prediction accuracy.  
Another phenomenon can be observed in Figure 10: When the time step is optimal, the MAE value band of the CNN is wider than those of the other models, indicating that the uncertainty in the prediction results of the CNN model is greater than those of the LSTM, GRU, CNN-LSTM, and CNN-GRU models, whereas the LSTM, GRU, CNN-LSTM, and CNN-GRU models have less uncertainty in practical dam deformation prediction, and repeated simulations may yield more consistent predictions.  
The experimental results show that six days is the optimal time step for the five models. We use it to discuss the short-term, long-term, and abnormal deformation events in the case study dataset.