# Deep Learning CNN-GRU Method for GNSS Deformation Monitoring Prediction
## 3 Experiment
### The Experiment for Comparison  
The above experiments provide a visual comparison of the CNN model, the GRU model, and the proposed CNN-GRU model. More details will be provided in the following experiment. Figures 6, 8 and 11 indicate that these three models have good consistency with the actual observations. Figure 12 has a similar conclusion, with the CNN-GRU model performing the best, followed by the GRU model, and the CNN model performing the worst. In terms of the \(R^{2}\) comparison, the CNN-GRU model has the best performance, with little difference from the other two models. NSE (Nash-Sutcliffe Efficiency) is a metric used to evaluate the matching degree between predictions and observations in hydrological models, which is used to assess the consistency between predictions and observations in GNSS deformation monitoring for hydraulic structures. The CNN-GRU model has the best performance, while the CNN model has the worst performance. Similar to NSE, the CNN-GRU model significantly outperforms the CNN and GRU models in terms of the RMSE. In addition, the proposed method has an improvement of about 45% compared with the CNN model. In summary, the proposed CNN-GRU model combines the advantages of CNN and GRU, resulting in a better predictive performance. Figure 11: The time series diagram of the CNN-GRU model. Figure 10: The loss function diagram of the CNN-GRU model. Figure 13 shows the comparison of the residual between the three models. The CNN model has the worst performance, with a maximum residual of about 1.2 mm. The GRU model has a better performance, with a maximum residual of about 1.2 mm. And it has fewer outliers. Furthermore, the proposed CNN-GRU model has the best performance, with a maximum residual of about 1.19 mm. And it has smaller median residuals. This proves that the proposed CNN-GRU model has a better applicability in GNSS deformation monitoring for hydraulic structures. For further comparison, Figure 14 compares the error statistics of the CNN model, the GRU model, and the proposed CNN-GRU model. The left panel displays the error distribution and curve fitting of the CNN model, with errors mainly concentrated in the \((-0.4,\,1.4)\) range and a central value of approximately 0.7 mm for the fitted curve. The middle is for the GRU model, with errors mainly concentrated in the \((-0.3,\,1.4)\) range and a central value of approximately 0.7 mm for the fitted curve. The right is for the CNN-GRU model, with errors primarily distributed in the \((-0.2,\,1.2)\) range and a central value of about 0.7 mm for the fitted curve. In general, the proposed method, by combining the CNN model and the GRU model, achieves a better prediction performance. The above experiment demonstrates the feasibility of the proposed CNN-GRU method. This section presents a comparison between the proposed method and the Extended Kalman Filter (EKF). The experiment was also conducted at Sanhe Sluice, with another monitoring point illustrated in Figure 15. The experimental period was from 10 September 2023 to 24 April 2024 and other configure parameters are the same as the above experiment. Figure 12: The comparison of the heatmap (the left is the CNN model, the middle is the GRU model, and the right is the CNN-GRU model). Figure 13: Box diagram of the residuals. Table 2 illustrates the performance metrics for both the EKF and the proposed CNN-GRU method. A comprehensive evaluation indicates significant improvements across all metrics with the CNN-GRU method compared to the EKF, showcasing its superior accuracy and reliability in GNSS deformation monitoring for hydraulic structures. Specifically, in comparison to the EKF, the adoption of the CNN-GRU method results in a remarkable 92.41% reduction in the MSE, a notable 72.44% decrease in the RMSE, a substantial 76.29% decrease in the MAE, and a noteworthy 8.02% increase in the coefficient of the determination of R\({}^{2}\).