## 2 Materials and Methods
### TBM Tunneling Big Data Preprocessing
#### 2.2.2 TBM Outlier Processing  
During TBM operation, several data indicators, e.g., cutterhead torque and a total of 186 thrusts, were generated per second. However, due to sensor failure, anomalous geological conditions, and electromagnetic interference, TBM data collected by the monitoring system may have outliers, such as the cutterhead's torque shown in Figure 4[27]. In order to ensure data quality, outliers need to be appropriately processed.  
Outlier detection methods include distance-based, density-based, and statistical analysis methods [31,32]. It should be noted that distance- and density-based identification methods are time-consuming and are not suitable for large datasets from TBM tunneling [27]. In addition, normally distributed data are required if the 3\(\sigma\)-rule of the statistical analysis method is used [33]. However, Figure 7 shows that the distribution of the four TBM tunneling parameters in the Q-Q plot differed significantly from reference function y = x, indicating that large TBM tunneling big data did not strictly obey a normal distribution. Thus, the 3\(\sigma\)-rule method can cause some errors. In summary, this study used box plots to detect outliers. The irregular relationship shown in Figure 7 is because of the following: (1) The TBM tunneling process was complex and variable, and the datasets of its tunneling parameters showed skewness. Taking the cutterhead torque dataset in Figure 7a as an example, the coefficient of skewness of the cutterhead torque dataset was calculated as \(-1.36\) (less than \(-1\)). This indicates that the cutterhead torque dataset showed a highly negative skewness phenomenon. The kurtosis value was calculated as \(1.43\), which was less than 3 (the kurtosis value of the dataset that strictly obeys normal distribution is 3, and skewness is 0). This indicates that the cutterhead torque dataset distribution was flatter than the normal distribution. This synthetically illustrated the irregular relationship in Figure 7 when using Q-Q plots for the normality test. It also proves again that the above four tunneling parameters did not strictly obey the normal distribution. (2) Due to the complexity and variability of geological conditions, abnormal sensors, and electromagnetic interference during TBM tunneling, many outliers may occur in one tunneling cycle. This was common and unavoidable. These outlier datasets also showed irregular relationships during the normality test.  
Box plots can detect outliers and graphically demonstrate the degree of dispersion and distribution of univariate data, such as the median, upper quartile, and lower quartile of datasets. An explanation of the distribution of box plots is shown in Figure 8. Figure 9 shows the data distribution of the cutterhead torque in the stable phase (Figure 4), clearly showing the median, mean, and upper and lower quartiles of the dataset; cutterhead torque outliers were accurately identified. Therefore, the box plot method is suitable for outlier detection in this paper.  
Figure 6: K-means clustering example (cutterhead torque as an example).  
Figure 8: Principle of the box plot method.  
Figure 7: Normality test of four TBM tunneling indexes: (**a**) cutterhead torque; (**b**) cutterhead rotational speed; (**c**) advance rate; (**d**) total thrust.  
Figure 9: Box plot method used to identify outliers of the cutterhead torque in Figure 4.