# Prediction Model for Shield Tunneling Roll Angle and Pitch Angle: A PCA-PSO-LGBM Approach
## 3 Case Study
### Data Analysis and Processing
#### 3.2.2 Analysis and Processing of Geological Parameters  
The collection of geological parameters was also carried out on a ring basis, mainly including the burial depth of each ring's face and the strata information it passes through. Compared to the easily obtainable burial depth, the stratigraphic information at the face requires more complex operations. This is because the thickness of each stratum encountered during the shield excavation process varies continuously, and different strata correspond to different physical and mechanical indices. Here, six main physical and mechanical indices were selected: natural density, deformation modulus, internal friction angle, cohesion, lat  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Abbreviation** & **Min.** & **Max.** & **Mean.** \\ \hline Roll angle (\({}^{\circ}\)) & / & 0.304 & 2.402 & 1.692 \\ Pitch angle (\({}^{\circ}\)) & / & \(-\)0.743 & 1.588 & 0.511 \\ Cutterhead speed (rpm) & CS & 1.842 & 4.215 & 3.518 \\ Advancing pressure of group A (bar) & PA & 14.2 & 95.3 & 37.6 \\ Advancing pressure of group B (bar) & PB & 25.6 & 136.5 & 81.8 \\ Advancing pressure of group C (bar) & PC & 116.3 & 241.6 & 197.1 \\ Advancing pressure of group D (bar) & PD & 24.9 & 119.4 & 72.3 \\ Advancing pressure of group E (bar) & PE & 14.3 & 98.2 & 32.8 \\ Advancing pressure of group F (bar) & PF & 14.0 & 118.5 & 35.5 \\ Hinged thrust (kN) & HT & 530.4 & 216.4 & 973.2 \\ Hinged pull (kN) & HP & 1754.1 & 849.5 & 520.1 \\ Belt conveyor speed (rpm) & BCS & 0 & 2.937 & 2.560 \\ Screw conveyor speed (rpm) & SCS & 0.0004 & 0.0186 & 0.0016 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Statistical table of shield tunnelling parameters.  
Figure 9: T box plot of roll angle and pitch angle for Ring 636: (**a**) roll angle; (**b**) pitch angle.  
eral pressure coefficient, and Poisson's ratio. The values of these physical and mechanical indices for different strata that the shield machine passes through are shown in Table 2.  
Since the shield's face mostly traverses through a combination of two or three types of strata, this paper calculated the physical and mechanical indices for each ring's strata based on the area proportion of each stratum within the face. As shown in Figure 10, assuming the thickness of the topmost soil layer in a shield ring is \(h\) and the radius of the face is \(r\), then the area of the topmost soil layer \(S_{u}\) can be calculated using the following equation:  
\[S_{u}=\arccos\frac{r-h}{r}\cdot r^{2}-(r-h)\cdot\sqrt{r^{2}-(r-h)^{2}}, \tag{15}\]  
Then, the weighted value \(PI^{\prime}_{i}\) of the \(i\)-th physical and mechanical index for this ring is as follows:  
\[PI^{\prime}_{i}=\sum_{j=1}^{n}\frac{S_{j}}{S}\cdot PI^{j}_{i}, \tag{16}\]  
\[S=\sum_{j=1}^{n}S_{j}, \tag{17}\]  
where \(n\) is the number of types of strata in the ring, \(S_{j}\) is the area of the \(j\)-th strata in the ring, \(S\) is the total area of all strata in the ring, and \(PI^{j}_{i}\) is the \(i\)-th physical and mechanical index value for the \(j\)-th strata in the ring.  
After obtaining the dataset of shield tunnelling parameters and geological parameters on a ring basis, it is necessary to normalize each parameter in the dataset according to the following formula to convert data with different characteristics onto a common scale, thereby improving the efficiency and accuracy of model training:  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  
Figure 10: Schematic diagram of geological distribution on the shield tunnel face.  
\[y^{\prime}_{t}=\frac{y_{t}-y_{\min}}{y_{\max}-y_{\min}}, \tag{18}\]  
where \(y_{t}\) represents the original data at time \(t\), \(y_{\min}\) is the minimum value of this set of data, \(y_{\max}\) is the maximum value of this set of data, and \(y^{\prime}_{t}\) is the normalized data at time \(t\).