## 2 Methods
### Proposed Method for Dam Deformation Time Series Prediction  
To improve the predicted accuracy of dam deformation prediction, we propose the hybrid model as shown in Figure 5. This model first uses STL to decompose observed dam deformation data into different representative subcomponents. Second, the SSA method optimizes the hyperparameters in the architecture of CNN and GRU. Finally, the output results of all subcomponents predicted by CNN-GRU are added, and the final prediction result of the dam deformation at the future time is obtained. The proposed method is mainly divided into two stages: decomposition and ensemble. In the decomposition stage, the model uses STL to decompose observed dam deformation data into multiple simple subcomponents, thereby reducing the difficulty of subsequent modeling. In the ensemble stage, the feature information of the subseries is extracted and merged to obtain the final results. This hybrid method can not only reduce the volatility of the original time series but also improve the generalization ability of the forecasting model. The proposed model runs according to the following steps. Step 1: **Data acquisition. ** The corresponding dam monitoring data are acquired through the sensors installed in the dam. The HST model focuses on the correlation between water depth, temperature, and dam deformation for calculation reduction to determine the key factors that affect the performance of dams. The key factor datasets are normalized to range of [\(0\), \(1\)] and divided into training set and testing set as:  
\[x_{i}^{\prime}=\frac{x_{i}-\mu}{\sigma} \tag{16}\]  
where \(x_{i}^{\prime}\) and \(x_{i}\) are the normalized and original value of the \(i\)-th data sample, respectively. \(\mu\) is the mean value of training data and \(\sigma\) is the standard deviation of training data. Step 2: **Data decomposition. ** Using STL to extract representative sequences of original dam deformation time series, including seasonal \(S_{t}\), trend \(T_{t}\), and remainder \(R_{t}\). The seasonal component is the periodic characteristic response of the water level and seasonal temperature received during the operating period of the dam. The trend component and the remainder component comprehensively reflect the degradation process of concrete material properties and the compression deformation law of geological structures. The dataset is divided with the corresponding influencing factors. Step 3: **Model training. ** The outliers removed and normalized sequence are used as input samples for model training. In training process, the gradient descent algorithm is used to back propagation error to optimize state of each hidden layer. Using the dropout  
Figure 5: Sketch map of the proposed model for dam deformation prediction. algorithm to overcome the potential overfitting problem during training. For the model optimization, primarily, it needs to declare the search space. Second, the fitness function is determined for \(RMSE\). When its value is small, it means that it has higher fitness, and is the better prediction performance of model. Third, the optimization classifier is built. The SSA method searches the optimal parameters for all CNN-GRUs, such as the kernel size of each CNN, the number of neurons in convolution layer, the parameter of each GRU layer, the dropout rate, and the recurrent dropout rate. Finally, the prediction model, of which structure and hyperparameters are both in the optimal state, is obtained. Step 4: **Model prediction. ** The impact factors in the previously divided testing datasets are input into the trained model to predict the corresponding dam deformation. Step 5: **Model evaluation. ** Appropriate model evaluation indicators are selected and used to compare the accuracy, stability, and robustness of dam deformation prediction models based on MLP, CNN, LSTM, GRU, CNN-LSTM, and CNN-GRU. Step 6: **Engineering application. ** At this moment, each subcomponent trains its own optimal prediction model.