# Deep Learning CNN-GRU Method for GNSS Deformation Monitoring Prediction
## 3 Experiment
### The Experiment for the CNN-GRU Model  
The experiment in Section 3.1 analyzes the advantages and disadvantages of the CNN model and the GRU model separately. And this section will analyze the proposed CNN-GRU model. For comparison, the CNN-GRU model uses the same parameters as the CNN  
Figure 8: The time series diagram of the GRU model.  
Figure 7: The loss function diagram of the GRU model.  
and GRU models. The above experiment selects the adaptive moment estimation (Adam) optimizer for the CNN and GRU models. This section will analyze the performance of different optimizers of the proposed CNN-GRU model.  
The comparative evaluation of Adam, stochastic gradient descent (SGD), and Root Mean Square Propagation (RMSProp) optimizers are presented in Figure 9. The radar diagram, including the mean absolute percentage error (MAPE), root mean square error (RMSE), mean absolute error (MAE), \(R^{2}\), and validation loss, provides a comprehensive analysis of the performance of different optimizers. The average values from 10 training epochs are used as evaluation metrics. It is evident that the Adam optimizer has the best fitting with the largest \(R^{2}\) and the smallest MAE, RMSE, and Validation Loss. The SGD optimizer has a slightly inferior performance than the Adam optimizer. And the RMSProp optimizer shows the worst-fitting performance. As for the MAPE, the differences among the three optimizers are negligible. In general, the Adam optimizer has the best performance for the prediction of GNSS deformation monitoring. The subsequent sections will take the Adam optimizer as an example for the CNN-GRU model.  
The above experiment shows the strengths and weaknesses of the CNN model and the GRU model. The change in Figure 10 is used to describe the variation of loss values of the proposed CNN-GRU model. The loss function of the CNN-GRU model sharply decreases from the 1 st to the 4 th epoch, and then gradually stabilizes from the 5 th to the 21 st iteration. Between the 22 nd and 50 th epoch, the change in the loss function is extremely small, indicating that the model gradually fits the training dataset better. The GRU model typically requires approximately 22 training epochs to achieve consistency between the training dataset and the test dataset.  
Figure 11 presents the variation curve of the observations and predictions of the proposed CNN-GRU model. The predictions have good consistency with the observations in the test dataset. In contrast with Figures 6 and 8, the predictions in Figure 11 have a better performance of consistency and smoothness than the CNN model and the GRU model. However, there are still some areas of obvious inconsistency between the two, such as around the 200 th hour and around the 820 th hour. In the interval around the 870 th hour, the predictions have fewer and smaller outliers. Additionally, the extrapolated predictions of the CNN-GRU model are better than the CNN and GRU model, which is almost consistent with the observations. Figure 11 demonstrates the superiority of the proposed CNN-GRU model in GNSS time series modeling and predictions.  
Figure 9: The Radar diagram for comparing different optimizers.