## 2 Methodology
### Implementation of a Data-Driven Prediction Approach Based on Machine Learning
#### 2.3.1 Dimensionality Reduction of Variable Data
(2021) [51] investigated the mechanism of the vertical progressive collapse of deep excavations retained by a multilayer strutting system and found that when the maximum bending moment exceeds the ultimate bending capacity, the diaphragm wall will rupture, resulting in the overall collapse of the excavation. Deflection of the retaining structure is positively correlated with its bending moment, reflects the exertion level of the resistance of the retaining structure, and indicates the damage degree of the foundation pit. Thus, the maximum monitored horizontal displacement in each stage is taken as the equivalent displacement of the retaining structure in this study, considering that the failure process of excavation is a progressive failure. 3. Axial force of bracing/anchor bolts  
Previous studies have shown that the failure of excavation begins with the failure of the struts or anchor bolt [51; 52]. The earth pressure on the retaining structures at different depths is different, so the importance of bracing/anchor bolts at different depths is also different; thus, it is recommended to use the design control values of bracing/anchor bolts at different depths to divide the weight of bracing or anchor bolts in the study, which is called the depth weight. After taking the average value of the axial force of bracing/anchor bolts at the same depth, the equivalent axial force of bracing/anchor bolts is obtained by weighting the average value with the depth weight. 4. Vertical/horizontal displacement at the top of the retaining structure/slope  
Similar to the treatment method for deflection of retaining structure, the maximum value of vertical/horizontal displacement at the top of retaining structure/slope of the current period is taken as the equivalent vertical/horizontal displacement at the top of retaining structure by adopting the maximum envelope principle. Figure 5: Schematic diagram of deformations of wall and soils induced by excavation. The vertical displacement of the column leads to the eccentricity of bracing, which affects the stability of bracing. In this study, the average value of the monitoring results is used as the equivalent vertical displacement of the column. 6. Hydraulic head/Groundwater table  
Hydraulic head/groundwater table is a field variable during excavation. In order to ensure safety and the anhydrous operation of excavation, dewatering and waterproof curtains are usually required to control the groundwater. The change in hydraulic head/groundwater table will inevitably change the stress field of the site. Therefore, it is necessary to monitor the change in hydraulic head during excavation to ensure that it is within a controllable range. In this study, the lowest hydraulic head, i.e., the monitoring value at the maximum drawdown depth of hydraulic head, is used as the equivalent hydraulic head. 7. Vertical displacement of surrounding buildings  
The responses of existing buildings are an issue of great concern in excavation. In this study, the settlement of existing buildings adjacent to excavation is selected as the research object, i.e., the output variable. In order to better predict this, the maximum envelope principle is used to deal with the on-site monitoring results--that is, the maximum cumulative settlement of the measuring points in the current period is taken as the equivalent settlement of the surrounding buildings.