## 5 Prediction Performance of Tunneling Excavation Speed under Various Machine-Learning Algorithms
### Data Processing  
The shield machine's sensors gathered 36 types of data, focusing on key parameters like the slurry pressure, grouting pressure, grouting amount, unearthed amount total thrust, cutter torque, cutter speed, and excavation speed. Real-time collection of the shield tunneling parameters was prioritized. To ensure data reliability, the mean value of each tunneling parameter within the same ring, under normal tunneling conditions, was considered as the ring representative. To enhance the data quality, the box diagram method was applied to filter out abnormal data, resulting in the selection of tunneling parameters from a total of 555 rings as variable data.  
Figure 14 reveals that the linear correlation coefficient between the excavation speed and other parameters is generally small, with the maximum correlation coefficient reaching 0.46. Linear correlation analysis struggles to determine the extent of influence of the other tunneling parameters on tunneling excavation speed due to the highly nonlinear relationship within the data. Traditional linear analysis methods are inadequate in this context.  
The Maximum Information Coefficient (MIC) serves as a method for detecting nonlinear correlations between variables, addressing the limitations of linear correlation measures like the Pearson correlation coefficient in handling nonlinear relationships. Calculating the MIC relies on information theory principles, quantifying the correlation degree between two variables. A higher MIC value indicates a stronger nonlinear correlation, ranging from 0 to 1. A value close to 1 signifies a robust nonlinear correlation, while proximity to 0 implies a minimal nonlinear correlation. The MIC calculation formula is presented in Formulas (1) and (2).  
\[I[X;Y]=\sum_{X,Y}p(X,Y)\text{log}_{2}\frac{p(X,Y)}{p(X)p(Y)} \tag{1}\]  
\[\text{MIC}[X;Y]=\max_{|X|Y|<N^{0.6}}\frac{I(X;Y)}{\text{log}_{2}[\text{min}( |X|,|Y|)} \tag{2}\]  
In these formulas, \(X\) and \(Y\) are variable names, \(N\) is the number of samples, and \(p(X,\)\(Y)\) is the joint probability of variables \(X\) and \(Y\).  
After data preprocessing, Python 3.6 software is employed to compute the MIC values between the excavation speed and the seven other tunneling parameters. The calculation outcomes are presented in Table 11. Given the shield tunneling context, the slurry pressure, excavation volume, grouting pressure, and cutter head torque, exhibiting MIC values surpassing 0.4, are ultimately chosen as the reference variables.  
In machine-learning algorithms, data standardization (or normalization) is a widely employed preprocessing technique. Its primary purpose is to mitigate the impact of different scales between features, ensuring each feature holds equal importance. This facilitates a comprehensive analysis and comparison of indicators with varying units or magnitudes, enhancing the model accuracy and stability. Z-score standardization is utilized  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Tunneling Parameters** & **MIC Values** \\ \hline Slurry pressure & 0.657 \\ Unearthed amount & 0.659 \\ Grouting pressure & 0.441 \\ Cutter torque & 0.407 \\ Cutter speed & 0.344 \\ Total thrust & 0.248 \\ Grouting amount & 0.170 \\ \hline \hline \end{tabular}
\end{table}
Table 11: The MIC values between the excavation speed and other parameters.  
for a linear transformation of the original data, mapping the results to the range \([-1,1]\), as depicted in Formula (3).  
\[x^{\prime}=\frac{x-\mu}{\sigma} \tag{3}\]  
In the formula, \(x^{\prime}\) is a standardized value, \(x\) is the original data value, \(\mu\) is the mean value of the sample data, and \(\sigma\) is the standard deviation of the sample data.