## 3 Case Study
### Discussion of Results  
The simulation results showed that there are differences between the MLP, CNN, LSTM, and GRU models, which indicates the importance of method selection when constructing prediction models. For the dam deformation problem, the prediction accuracies of the GRU and LSTM are similar and remain stable when the time step is large, which avoids the trouble of optimizing the time step. However, the GRU model may be preferred because of its simple structure, fewer parameters, and less time consumption in model training. When using gradient descent for deep learning model optimization, there are shortcomings such as overfitting and the choice of calculation parameters [38]. In this study, the SSA method uses the adaptive scores in previous iterations to learn and select the best set of hyperparameters. To avoid overfitting, the use of recurrent dropout techniques can limit the participation of hidden units in the training process of the deep learning model. To a certain extent, it not only overcomes the existing shortcomings of the deep learning models, but also provides relatively well-predicted results. However, the deformation is affected by many external factors and the dam materials used, resulting in complexity, uncertainty, diversity, and time variation in the deformation series [5]. The noise, nonstationarity, and heteroscedastic structure of the dam deformation time series often affect the ability of models to accurately and comprehensively reflect the formation factors and changing laws of dam deformation when a single-prediction model is used, indicating that the predicted results are affected by the high volatility of the data [19]. To avoid this problem, a decomposition method is used to identify sequence features and accurately separate the sequences into multiple components for prediction, thereby significantly reducing modeling difficulty. In addition, the CNN can capture sequence characteristics through a convolution kernel. The GRU can learn these characteristics through forward and backward dependencies. Although the hybrid model has poor prediction accuracy stability when the time step is small, the prediction accuracy tends to stabilize as the time  
Figure 13: Long-term and short-term predictions for G2-HY through the different models: (**a**) LSTM-SSA with 30% data for training; (**b**) LSTM-SSA with 60% data for training; (**c**) GRU-SSA with 30% data for training; (**d**) GRU-SSA with 60% data for training; (**e**) CNN-LSTM-SSA with 30% data for training; (**f**) CNN-LSTM-SSA with 60% data for train-ing; (**g**) CNN-GRU-SSA with 30% data for training; (**h**) CNN-GRU-SSA with 60% data for training; (**i**) The hybrid model with 30% data for training; (**j**) The hybrid model with 60% data for training. step increases. Therefore, the STL-CNN-GRU hybrid model outperforms the standard deep learning methods. In the following, we analyze the possible reasons why the proposed model is better than the other models. First, the STL decomposes the observed deformation time series into three components, which is convenient for effectively identifying the influence of various factors. Second, the CNN-GRU model is used to establish a complex mapping weight matrix of the input variables and output targets of each component. The CNN is used for convolution operation of the input data to extract the characteristics of the time series data. To learn the peak characteristics, the GRU is used to store the delay information in these time series. To effectively improve the generalization ability of CNN-GRUs, the SSA method is used to specify the optimal hyperparameters of the model. Finally, the simulation output results of all the CNN-GRU models are summed to obtain a time-sensitive final prediction result, which makes the model have the generalization ability for time series with different lengths and abnormal data to a certain extent.