# Modeling of Tunneling Total Loads Based on Symbolic Regression Algorithm
## 4 Case Study
### Preprocessing of In Situ Tunneling Data  
There are some outliers in the original tunneling data files of the Yin-Song Project, as shown in Figure 5a,b. These outliers mainly include null push data and abnormal data. When any of the operating parameters, such as the tunneling speed, cutter head speed, total thrust, and total torque, is 0 or close to 0, they are assumed to be \"null push\" data [28; 39]. Such data are eliminated directly through numerical screening. Outliers usually exhibit the characteristics of mutation relative to their surrounding data points. However, although some of these abrupt data are outliers, others may be caused by geological changes. Therefore, it is necessary to combine professional knowledge with statistical methods to eliminate abnormal data effectively and maximize the retention of the regular characteristics of data. Load mutations caused by geological changes often affect more than one data point, so the difference method combined with box diagrams is proposed to distinguish the abnormal data. First, the forward and backward differences of all total thrust and torque data are calculated, and then the outliers in the difference results are identified by the box diagram method. Finally, the intersection of the forward and backward difference outliers is noted, and the corresponding load data points are identified as abnormal values. The union of the total thrust and torque abnormal values constitutes the abnormal data of the project. Compared with a direct statistical method for identifying the outliers of the tunneling load, this approach has the advantage that it, not only deals with anomalies effectively, but also avoids the mistake of deleting maximum or minimum values that deviate from the overall data mean, but exhibit regular changes. The box diagram method is a statistical technique for outlier detection when processing data. Unlike the 3\(\sigma\) rule, Z-score method, and so on, it does not presuppose the data distribution and follows the original characteristics of the data [40]. Its structure and outlier identification method are shown in Figure 6. A total of five statistics are calculated based on the data to be identified: median, lower quartile (Q1), upper quartile (Q3), lower limit (Q1 \(-\) 1.5 IQR), and upper limit (Q3 \(+\) 1.5 IQR), where IQR is the difference between the upper quartile and the lower quartile. Data sample points with values less than the lower limit or greater than the upper limit are considered to be outliers. The load data from the Yin-Song Project after outlier processing are shown in Figure 5c,d. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Physical Parameters** & **Maximum** & **Minimum** & **Average** \\ \hline \multirow{2}{*}{Operating Parameters} & Driving speed \(v\) (mm/min) & 81.00 & 1.00 & 18.04 \\  & Cutterhead rotation speed \(\omega\) (r/min) & 7.00 & 0.24 & 5.75 \\ \hline \multirow{6}{*}{Geologic Parameters} & Rock density \(\rho\) (g/cm\({}^{3}\)) & 2.70 & 2.64 & 2.65 \\  & Shear modulus \(G\) (MPa) & 7.15 & 3.75 & 4.04 \\ \cline{1-1}  & Poisson’s ratio \(\mu\) & 0.27 & 0.23 & 0.26 \\ \cline{1-1}  & Cohesive force \(c\) (kPa) & 1.91 & 1.45 & 1.50 \\ \cline{1-1}  & Compressive strength \(c_{\mathrm{c}}\) (MPa) & 106.57 & 74.99 & 78.82 \\ \cline{1-1}  & Tensile strength \(c_{\mathrm{t}}\) (MPa) & 6.59 & 4.75 & 4.96 \\ \hline \multirow{2}{*}{Target Parameters} & Total thrust \(F\) (kN) & 18,458.00 & 151.00 & 16,843.48 \\ \cline{1-1}  & Total torque \(T\) (kN \(\cdot\) m) & 2712.00 & 12.00 & 1408.90 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The statistical characteristics of the parameters. Considering the large differences in the magnitude of each \(\pi\) quantity, the dataset should be normalized before the machine learning algorithm is used to train the model. This prevents the magnitude from affecting the weight of different features. In this paper, decimal scaling normalization is used to restrict the data to the range 0-10.