# Deep Learning CNN-GRU Method for GNSS Deformation Monitoring Prediction
## 1 Introduction  
The accelerated progress of global climate change and urbanization makes hydraulic infrastructures increasingly prominent. The hydraulic structures are of paramount importance in safeguarding the safety of people's lives and properties and promoting sustainable economic and social development [1, 2, 3]. However, there may be various challenges during their long-term operation, such as geological disasters, land subsidence, and structural deformation. Untimely monitoring and ineffective prediction may lead to serious safety accidents and economic losses. Many approaches are applied for the monitoring and prediction of hydraulic structures. The traditional approaches rely on engineering surveys [4, 5] and geological investigations [6, 7]. However, these approaches are limited by their restricted monitoring range and complex processing workflows, making them inadequate for meeting the needs of hydraulic structures [8]. As an all-weather and full-automation piece of technology, GNSS introduces an innovative approach to the deformation monitoring of hydraulic structures [9, 10]. It provides real-time and high-precision deformations, facilitating effective analysis and predictions. However, the complex environment around hydraulic structures leads to measurement errors, such as atmospheric delays [11, 12, 13] and multipath effects [14, 15, 16, 17]. These errors are difficult to process, which adds obstacles to the predictionof GNSS deformation monitoring. The prediction model necessitates the capability to handle the unmodeled factors and observation noise. A Kalman filter is a Bayesian-based minimum mean-square estimation method, which lies in adding state constraints to the observation equations, thereby constructing reliable function models and stochastic models [18; 19; 20]. However, it is difficult to handle state equations and system errors in complex environments. The grey model is suitable for analyzing and modeling short GNSS time series with limited datasets and incomplete information [21; 22; 23]. Nevertheless, it is only suitable for short-term and exponential growth predictions. The Autoregressive Integrated Moving Average (ARIMA) model extracts time series for prediction through the autocorrelation and difference of the dataset [24; 25; 26], but it requires the dataset to be stable, essentially capturing linear relationships. The Multiple regression analysis (MRA) model quantitatively describes a dependent variable's linear dependence on multiple independent variables, offering simplicity, high precision, and wide applicability [27; 28; 29]. However, it suffers from multicollinearity issues, lacks causal inference capability, and makes assumptions about error terms. The genetic algorithms are inspired by natural evolution theory, dealing with problems lacking mathematical expressions [30; 31; 32]. However, it requires special definitions and cannot guarantee the quality of solutions. Methods based on deep learning are popular for deformation prediction, which is also applied to the chaotic time series prediction [33; 34]. The deep learning methods have powerful feature extraction and recognition capabilities, enabling accurate predictions by learning representations from GNSS time series. The CNN model and Recurrent Neural Networks (RNN) have been applied in the fields of image processing and sequence modeling. Meanwhile, the GRU model represents an improved model of the RNN, adept at capturing long-term dependencies in the dataset [35]. Previous studies have applied CNN for GNSS residual processing [36] and classification [37], GRU for landslide prediction [38] and multipath modeling [39], as well as CNN-GRU for forecasting wind power [40], particulate matter concentrations [41], and the pressure of a concrete dam [42]. The CNN-GRU model integrates the characteristics of CNN and GRU, which has better a performance in predictions of GNSS deformation monitoring. This study proposes to apply the CNN-GRU model for the GNSS deformation monitoring prediction of hydraulic structures.