# Spatiotemporal Prediction and Proactive Control Method for Excavation-Induced Wall Deflection
## 6 Conclusions  
This study proposes an ST-GAT-based PID controller method, which proactively controls wall deflection by adjusting servo axial forces. The ST-GAT model accurately predicts wall deflection by extracting spatial relationships between monitoring points and assigning weights to their importance. By visualizing the weight distribution between nodes in the GAT network and the feature attribution map across different features, the interpretability of the model is enhanced. The predicted values from the ST-GAT model replace the current monitoring values in the PID control system, enabling the proactive control of wall deflection. By adjusting multiple servo axial forces, the deflections at four monitoring points are simultaneously adjusted to target deflections. The main conclusions are as follows:  
1. The proposed ST-GAT model outperforms other alternative models in terms of MSE and MAE, achieving the lowest error values. Specifically, it outperforms CNN, which has a significantly higher MSE, which is likely due to its difficulty in handling sequential data. Furthermore, it performs better than GCN-GRU and GCN-LSTM, demonstrating that the attention mechanisms in GAT, which assign varying importance to nodes, are more effective for predicting wall deflections.
2. The interpretability of the model is improved by visualizing attention weights between nodes and the feature attribution map across input features. In both layers, node 2 has strong connections to node 3, while node 6 shows weaker links to other nodes. These weights reflect how GAT assigns importance to different monitoring points based on spatial relationships. The feature attribution map reveals that wall deflections are significantly influenced by adjacent points.
3. The proposed ST-GAT-based PID controller can adjust wall deflection to a target value. Specifically, a larger \(\mathrm{kp}\) value results in a faster response, meaning the deflection approaches the target more rapidly as \(\mathrm{kp}\) increases. When adjusting \(\mathrm{kp}\) alone cannot bring the deflection to the desired target, the integral component is added. With appropriate \(\mathrm{kp}\) and \(\mathrm{ki}\) settings, the proposed control model can achieve the proactive control of wall deflection.  
Conceptualization, W.L. and S.Z.; methodology, W.L. and K.C.; software, S.Z. and K.C.; writing--original draft preparation, W.L., K.C. and S.Z.; writing--review and editing, W.L. and X.P.; supervision, X.P.; project administration, X.P.; funding acquisition, X.P. All authors have read and agreed to the published version of the manuscript.  
This study is supported by the National Natural Science Foundation of China (Grant No. 52378377) and the Natural Science Foundation of Zhejiang Province (Grant No. LTZ21E080001).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
Author [PERSON] was employed by the company China Construction First Group Construction & Development Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.