# Deep Learning CNN-GRU Method for GNSS Deformation Monitoring Prediction
## 3 Experiment
### The Experiment for the Dividual Model  
The first experiment aimed to analyze and validate the individual cases of the CNN model and GRU model. The CNN model and GRU model are conducted separately using the aforementioned data. The loss function of the CNN modeling is shown in the following Figure 5. The loss function is typically used to measure the difference between the model's predictions and observations, serving as the objective to be minimized during optimization. To validate the performance of the neural network, 50 training epochs were used for iterative training in the experiments. The loss function is the MSE parameter in Equation (8).  
As for the CNN model, the change in the loss function graph is used to describe the variation of loss values during the model training process. During training, the change in the loss function graph reflects the trend of loss values across different epochs. In Figure 5, the loss function of the CNN sharply decreases from the 1 st to the 5 th epoch, and then gradually stabilizes from the 6 th to the 10 th iteration. Between the 10 th and 50 th epoch, the change in the loss function is extremely small, indicating that the model gradually fits the training dataset better. The CNN model typically requires approximately 10 training epochs to achieve consistency between the training dataset and the test dataset.  
Figure 4: The change in the loss function before and after data normalization.  
Figure 6 presents the variation curve of the observations and predictions in the test dataset and the extrapolated predictions over 24 h in the CNN model. Overall, there is good consistency between the observations and predictions in the test dataset, with fewer outliers and smoother curves in the predictions. In the interval around the 870 th hour, the predictions have fewer and smaller abnormal fluctuations, demonstrating the superiority of the CNN model in GNSS time series modeling and predictions. However, the predictions have a systematic upward deviation relative to the observations, approximately 0.04 mm, which has a minimal impact on GNSS positioning. Additionally, the extrapolated predictions of the CNN model have the same trend as the observation, but there is a significant discrepancy between the predictions and observations in the extrapolated predictions over 24 h.  
The above experiment shows the strengths and weaknesses of the CNN model. The change in Figure 7 is used to describe the variation in the loss values of the GRU model. The loss function of the GRU sharply decreases from the 1 st to the 4 th epoch, and then gradually stabilizes from the 5 th to the 12 th iteration. Between the 13 th and 50 th epoch, the change in the loss function is extremely small, indicating that the model gradually fits  
Figure 5: The loss function diagram of the CNN model.  
Figure 6: The time series diagram of the CNN model.  
the training dataset better. The GRU model typically requires approximately 12 training epochs to achieve consistency between the training dataset and the test dataset.  
Similar to Figure 5, Figure 8 presents the variation curve of the observations and predictions of the GRU model. The predictions have good consistency with the observations in the test dataset. However, there are still some areas of obvious inconsistency between the two, such as around the 80 th hour and the 700 th hour. In the interval around the 870 th hour, the predictions have fewer and smaller outliers of about 0.08 mm, demonstrating the superiority of the GRU model in GNSS time series modeling and predictions. However, in the extrapolated predictions over 24 h, there is a significant discrepancy between the predictions and observations, with a maximum error of approximately 0.2 mm. This suggests that while the GRU model can be applied to time series predictions in GNSS deformation monitoring, there are still some shortcomings in extrapolation predictions.