## 4 Conclusions and Future Work  
In recent decades, methods that can enhance the accuracy of dam deformation prediction have been widely studied in the dam safety monitoring field. To enrich the theory of dam safety monitoring, we proposed a hybrid prediction model according to the factors influencing the deformation of arch dams. First, the original dam deformation series was decomposed into season, trend, and remainder components through the STL method. Second, an CNN-GRU model optimized using the SSA was applied to predict the three components. Finally, the outputs of all component prediction models were summed and used as the final predicted value of the dam deformation. The performance of the proposed model was tested using a parabolic variable-thickness double-curved arch dam located in China as a practical example. The results showed that the hybrid model has better forecasting effects on time series of different lengths and abnormal data compared with several existing models with statistical indicators. Therefore, the good prediction ability makes it an effective tool for dam safety monitoring tasks. The main conclusions of this work are summarized as follows:  
1. A time series decomposition method was used to divide the components of the deformation series to strengthen the data characteristics, thus eliminating the volatility of the dam deformation monitoring time series to a certain extent and reducing modeling difficulty.
2. The prediction accuracies of the GRU and LSTM models are largely identical for short-term deformation prediction and abnormal data series prediction. They were not affected by the redundant information introduced by a larger time step, and repeated simulations could yield more consistent prediction results with less uncertainty. The GRU exhibited a better prediction performance than the LSTM for long-term deformation prediction. In addition, the GRU may be the preferred method owing to its simpler structure, fewer parameters, and less training time consumption.
3. The SSA method fully explored the nonlinear mapping potential of the CNN and GRU by selecting the optimal parameter set; thus, the hybrid model exhibited better accuracy, stability, and robustness than the existing model in practical application.
4. The multi-model fusion strategy makes full use of the feature extraction potential of the CNN and the temporal feature representation of the GRU. Distributed modeling helps realize a targeted modeling of the deformation time series with different features to a certain extent and extends the scope of the model application.  
Although the feasibility of the dam deformation prediction model proposed in this study was verified using a practical case, there are still some research directions that should be carried out in the future. The first is the consideration of the impact of geospatial location factors between the monitoring points on dam deformation. The second is to solve the problem that the original dataset is not enough to build a predictive model for improving the engineering application value of the predicted model. The third is to determine early warning guidelines for dam safety to meet the requirements of life management. It is necessary to make an intensive study of dam safety monitoring to provide support for dam operation and management.  
[PERSON] and [PERSON] conceived and designed the experiments and performed the modeling. [PERSON] and [PERSON] provided relevant technical support. [PERSON] and [PERSON] analyzed the data and reviewed and edited the paper. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (Grant No. 52109118), the Young Scientist Program of Fujian Province Natural Science Foundation (Grant No. 2020J05108), and Talent Introduction Scientific Start-up Foundation of Fuzhou University (Grant No. 510890).  
The authors declare no conflict of interest.