## 2 Methodology
### Implementation of a Data-Driven Prediction Approach Based on Machine Learning
#### 2.3.1 Dimensionality Reduction of Variable Data  
The monitoring points are arranged in the whole area affected by excavation, and the monitoring results of each point are controlled by its location and excavation process. In order to reduce the calculation time required for model construction and improve the operation speed, it is an effective method to weight the monitoring results according to the importance of the monitoring points and establish equivalent monitoring variables, so as to reduce the dimensions of the variable data. 1. Ground vertical displacement  
Ground vertical displacement (i.e., ground subsidence) is an important manifestation caused by excavation and a problem of great concern. Ground subsidence induced by excavation has been deeply studied by some scholars. For example, [PERSON] et al. (2007) [49] proposed a simplified semi-empirical model for predicting maximum surface settlement and the surface-settlement profile due to excavation in soft to medium clays. [PERSON] et al. (2019) [8] found that the maximum ground settlements first increase and then tend to stable with the increase in excavation width. [PERSON] and [PERSON] (2013) [50] generalized the attenuation laws of the soil movement behind the wall (as shown in Figure 5) and proposed a simplified method to calculate the soil movement induced by excavation, as shown in Equations (4)-(8). \[\mathrm{w}(x,y,z)=\left\{ \begin{array}{l}0.8u_{max}a_{z}\big{(}\frac{x}{H}+0.5\big{)}e^{-\pi(\frac{y}{R})^{2}}e^{-(\frac{\frac{x}{2}-b_{z}}{c_{z}})^{2}} (0\leq x\leq 0.5H)\\ 0.8u_{max}a_{z}\big{(}-0.6\frac{x}{H}+1.3\big{)}e^{-\pi(\frac{y}{R})^{2}}e^{ -(\frac{x}{2}-b_{z})}(0.5H\leq x\leq 2H)\\ 0.8u_{max}a_{z}\big{(}-0.05\frac{x}{H}+0.2\big{)}e^{-\pi(\frac{y}{R})^{2}}e^{ -(\frac{x}{2}-b_{z})}(2H\leq x\leq 4H)\end{array} \right. \tag{4}\]  
\[\mathrm{R}=\frac{L}{2}\bigg{(}0.069 ln\bigg{(}\frac{H}{L}\bigg{)}+1.03\bigg{)} \tag{5}\]  
\[a_{z}=1+e^{-1.56\frac{x}{H}-1.68} \tag{6}\]  
\[b_{z}=e^{-2.56\frac{x}{H}+1.02} \tag{7}\]  
\[c_{z}=e^{-2.09\frac{x}{H}+1.75} \tag{8}\]  
where \(u_{max}\) is the maximum horizontal displacement of the retaining wall. \(L\) is the excavation length of the foundation pit along the retaining wall. \(H\) is the excavation depth of the foundation pit. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Input Variables**} & \multicolumn{2}{c}{**Output Variables**} \\ \hline
**Indicators** & **Property** & **Unit** & **Indicators** & **Unit** \\ \hline Horizontal displacement at the top of & & & \\ retaining structure/slope & Response variable & mm & \\ \hline Vertical displacement at the top of & & & \\ retaining structure/slope & Response variable & mm & \\ \hline Subsurface horizontal displacement & Response variable & mm & \\ Axial force of bracing/Axial force of & & & \\ anchor bolt & Response variable & kN & \\ \hline Ground vertical displacement & Response variable & mm & \\ \hline Vertical displacement of column & Response variable & mm & \\ \hline Hydraulic head/Groundwater table & State variable & m & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The variables of the prediction model. According to engineering experience, the larger the value of the ground subsidence, the greater the security risk in excavation of a foundation pit. Therefore, it can be defined as follows: the greater the value, the greater the weight of the monitoring point. After the coordinate origin of ground settlement analysis is determined according to the position of the maximum horizontal displacement of the retaining wall, the corresponding position coordinates of monitoring points for ground settlement can be determined, their respective weights can be determined with \(\frac{w(x,y,0)}{\sum w(x,y,0)}\) according to Equation (4), and the weighted average of the monitoring values at all monitoring points is the equivalent ground settlement. 2. Subsurface horizontal displacement/Deflection of the retaining structure  
[PERSON] et al.