# Spatiotemporal Prediction and Proactive Control Method for Excavation-Induced Wall Deflection
## 1 Introduction  
With the development of urbanization, more buildings are constructed near subway lines. Excavation projects adjacent to existing subway lines must not only meet the requirements of excavation construction but also ensure the normal operation and structural safety of subway tunnels [1, 2]. Traditional steel supports only passively control soil deformation and are prone to axial force loss and temperature sensitivity, making them inadequate for strict control requirements [3, 4, 5]. The development of the servo system makes proactive deformation control possible by adjusting axial force in steel supports [6, 7, 8, 9, 10, 11]. For example, [PERSON] et al. [12] proposed the implementation of an axial force compensation system to address the issue of real-time adjustment in support axial forces. [PERSON] et al. [13] validated that using a steel servo to enhance axial loading capacity can effectively reduce wall deflection and bending moments in excavations. These methods have demonstrated the potential for excavation-induced deformation control, but their control capabilities are insufficient. An effective framework for deformation control is the proportional-integral-differentiation (PID) control method, which is widely used in engineering fields such as industrial automation,robotics, and aerospace due to its simplicity and robustness [14; 15; 16; 17; 18; 19; 20; 21; 22; 23]. This method adjusts system outputs by calculating the error between a desired setpoint and a measured process variable, then applying corrective actions based on proportional, integral, and differentiation terms. Existing studies mostly focused on optimizing the hyperparameters of the PID controller to improve its control performance [24; 25; 26; 27; 28]. However, the current system relies on monitored data for adjustments, which introduces a certain lag in deformation control. In braced excavation deformation control, this lag may lead to excavation risks because the excessive deformations cannot be adjusted in time. To overcome this lag, a possible solution is to use predictions from predictive methods to replace current monitoring data. Predictive methods, such as analytical solutions, numerical models, and data-driven models, are widely applied. In geotechnical engineering, data-driven models have proven more accurate than other methods due to their ability to utilize real data [29; 30; 31; 32; 33; 34]. For soil deformation, [PERSON] et al. [35] developed a maximum deformation prediction model for braced excavations based on gated recurrent unit (GRU) algorithms and field observation data. The reliability of the model is verified through two engineering cases. [PERSON] et al. [36] employed seven intelligent methods, including long short-term memory (LSTM) networks and deep neural networks (DNNs), to predict the maximum surface settlement in urban tunneling. The results showed that the DNN method performed the best. Recently, several studies have considered the spatiotemporal relationships in braced excavation deformations [37; 38; 39; 40; 41; 42; 43]. [PERSON] et al. [44] developed a deep learning model based on convolutional neural networks (CNNs) to consider spatial relationships between multiple monitoring points, improving the prediction of braced excavation deformations. Furthermore, [PERSON] et al. [45] proposed a deep transfer learning method to achieve early-stage deformation predictions during excavations. However, these studies mainly rely on CNNs to extract spatial features, assigning equal weight to each node. Consequently, these approaches cannot differentiate the importance of monitoring points. This study proposes a spatiotemporal graph attention network (ST-GAT)-based proportional-integral-differentiation (PID) controller method, which aims to actively control excavation-induced wall deflections. The contributions of this study are twofold.