## 3 Case Study
### Data Standardization and Preprocessing
#### 3.3.2 Data Preprocessing  
Effective data preprocessing is important to ensure data quality and model performance [52]. The data preprocessing in this study includes box plot analysis and data denoising. The outliers in shield attitude and total thrust obtained using the box analysis method are shown in Figure 7. The solid line in the center of the box plot represents the median of the measurements. The bottom and top of the box correspond to the lower quartile (one-fourth of the measurements are smaller than these) and upper quartile (one-fourth of the measurements are larger than these), respectively. The upper and lower bounds indicate the maximum and minimal values. The box plot analysis results for shield attitudes in HDSH, HDST, VDSH, and VDST are displayed in Figure 7a. The result for total thrust is presented in Figure 7b. Specifically, the data for HDSH and HDST are mostly concentrated around 0 mm, and the majority of VDSH data is located around -50 mm, which is the warning value for shield attitude deviation. The outliers for HDSH and HDST are significantly more than for VDSH and VDST, and most of these outliers far exceed the warning range of \(\pm\)50. Therefore, some corrective measures should be employed to adjust these attitudes to bring them within a reasonable range.  
Since the data recorded by the shield machine is affected by interference from surrounding construction activities and noise due to mechanical vibrations, the Daubechies wavelet [53] is used for denoising the raw data [17]. The main parameters that influence the effect of wavelet denoising include the wavelet basis function and the number of decomposition layers. Specifically, the number of decomposition layers is generally set to 5-8 because too few layers may not effectively eliminate the noise, while too many layers may lose information. In this study, the number of wavelet layers is set to 6. The Daubechies wavelet family consists of 10 wavelet basis functions, i.e., from Daubechies 1 (db1) to Daubechies 10 (db10). As shown in Figure 8a, this study uses the mean square error (MSE) to evaluate the denoising effect of each wavelet basis function and selects the optimal wavelet basis function (taking advance rate as an example). The MSE equation is defined as:  
\[\text{MSE}=\frac{1}{n}\sum_{i=1}^{n}(y_{i}-g_{i})^{2} \tag{8}\]  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Maximum** & **Minimum** & **Average** & **Unit** \\ \hline Wet density (\(\rho\)) & 2.55 & 2.43 & 2.51 & g/cm\({}^{3}\) \\ Cohesion (\(c\)) & 1.85 & 1.21 & 1.42 & MPa \\ Compression modulus (\(E_{s}\)) & 56.85 & 46.71 & 51.24 & MPa \\ Internal friction angle (\(\varphi\)) & 46 & 45 & 45.9 & \(\circ\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Standardized stratum parameters.  
Figure 7: Output parameter processing based on the box analysis method: (**a**) shield attitude; (**b**) total thrust.  
where \(y_{i}\) is the value of raw data, \(\hat{y}_{i}\) is the value of denoised data, and \(n\) is the number of data points. The MSE indicator represents the error between the raw data and the denoised data. When the db7 wavelet basis function is used, the denoised data exhibits the smallest discrepancy with the raw data [Figure 8a]. The denoised data is smoother than the raw data [Figure 8b]. These results show that the db7 wavelet-based function can remove the noise, while maximizing the retention of the raw data information. Finally, to accelerate model convergence and to constrain the range of each feature value within [\(-\)1, 1], the min-max normalization method is used.