# TBM Enclosure Rock Grade Prediction Method Based on Multi-Source Feature Fusion
## 3 Case Study
### Data Analysis  
In order to further understand the multi-source data characteristics of the input models, the following data analyses were conducted: (1) basic statistical analysis and data distribution visualisation for each TBM data input variable; (2) correlation analysis for each multi-source data input variable; and (3) causal analysis for each multi-source data input variable. As illustrated in Figure 10, the violin plots for each TBM parameter input variable were used to demonstrate the shape of the data distribution and concentration trends. Table 5 provides basic statistical information for each TBM parameter input variable. Figure 10: Violin diagram of TBM parameter input variables. Figure 9: Comparison of the distribution of reflection intensity classes after the introduction of random noise. (**a**) Original data; (**b**) noisy data. We assess the correlation between paired variables using the Pearson linear correlation coefficient (PLCC) [39] and the maximum information coefficient (MIC) [40] in order to further examine the association between various tunnelling characteristics. While the second approach can capture nonlinear correlations, the first method determines the degree of linear connection. The following is how PLCC and MIC are calculated:  
\[PLCC=\frac{cov(X,Y)}{\sigma_{X}\sigma_{Y}} \tag{31}\]  
\[MIC(X,Y)=max\bigg{\{}\frac{I(X,Y)}{log_{2}min\{n_{X},n_{Y}\}}\bigg{\}} \tag{32}\]  
where the term \(cov(X,Y)\) denotes the covariance between the paired variables \(X\) and \(Y\), while \(\sigma_{X}\) and \(\sigma_{Y}\) represent their respective standard deviations. For the MIC calculation (see Equation (32)), \(I(X,Y)\) denotes the mutual information between \(X\) and \(Y\), calculated based on the partitioning of the variables into \(n_{X}\) and \(n_{Y}\) bins, respectively. PLCC and MIC heat map matrices were plotted for each of the multi-source data input variables (see Figure 11). For the raw TBM data, the linear correlation between \(T\), \(RPM\), and \(F\) is higher than their nonlinear correlation, while V is not highly correlated with all three of them. This phenomenon can be attributed to the fact that V, in its capacity as an active driving parameter, is significantly influenced by human factors. In the context of the rock fragmentation index, the linear and nonlinear correlations between FPI, TPI, and WR are notably higher, attributable to the theoretically derived relationship between the calculation formulas of the three. In the context of 3D spatial data, the correlation patterns are further complex, exhibiting significant linear and nonlinear dependencies not only among the three variables but also with the TBM data, the rock fragmentation index, and the HSP data. This observation signifies that the spatial distribution exerts a notable influence on the TBM data. This phenomenon can be attributed to the existence of specific spatial distribution patterns within diverse rock masses, which are influenced by geological factors such as rock lithology and the presence of fissures. These spatial patterns, in turn, affect the alterations in boring parameters and acoustic wave reflections. The correlation between the HSP data and various TBM data, as well as the rock fragmentation index, is not significant. This may be attributed to the distinct modes of the two data sources, resulting in a low degree of correlation between them. However, this does not diminish the significance of their role in the prediction process.