## 4 Analysis of Attitude-Prediction Results
### Prediction Model Validation
The correlation degree of vectors is typically determined by the following value ranges: \(P\) = 0.8-1.0 highly correlated, \(P\) = 0.6-0.8 strongly correlated, \(P\) = 0.4-0.6 moderately correlated, \(P\) = 0.2-0.4 weakly correlated, and \(P\) = 0.0-0.2 weakly correlated or not correlated. The \(P\) value was defined as shown in (13). \[P=\frac{\sum_{i=1}^{n}\left(x_{i}y_{i}\right)-\frac{\sum_{i=1}^{n}x_{i}\sum_{i= 1}^{n}y_{i}}{n}}{\sqrt{\left(\sum_{i=1}^{n}x_{i}^{2}-\frac{\left(\sum_{i=1}^{ n}x_{i}\right)^{2}}{n}\right)\left(\sum_{i=1}^{n}y_{i}^{2}-\frac{\left(\sum_{i=1}^{ n}y_{i}\right)^{2}}{n}\right)}}, \tag{15}\]  
where \(x_{i}\) denotes the \(i\)-th input variable, \(y_{i}\) denotes the \(i\)-th output variable, and \(n\) denotes the total number of samples. Figure 10 shows the Pearson correlation analysis results of the input parameters listed in Table 4, including the tunneling, geometric, and geological parameters. The correlation between the geometric and geological parameters of the shield was generally strong (\(P\) = 0.2-0.8). RA and C were positively correlated with the attitude parameters, whereas SW, IFA, and CM were negatively correlated with the attitude parameters. Figure 10a shows that the HHD and HVD were strongly correlated with the horizontal and vertical deviation, respectively (\(P\) = 0.6-0.8). Figure 10: _Cont._  
In addition, Figure 10a shows that the propulsion system pressure in area 1 (UP) was weakly correlated with the FHD and FVD (\(P\) = 0.2-0.4), whereas the propulsion system pressure in area 6 (LUP) was negatively correlated with the FHD and BHD (\(P\) = 0.4-0.8). The propulsion system in area 5 (LLP) was negatively correlated with the FHD (\(P\) = 0.4-0.6), whereas the propulsion system in area 2 (RLP) was positively correlated with the FHD (\(P\) = 0.4-0.6). CT was weakly correlated with the FHD and BHD; TH was weakly correlated with the FVD and FVD; the upper and lower SD was weakly correlated with the FHD, FVD, and BVD; and the cut water pressure was weakly correlated with the BVD (\(P\) = 0.2-0.4). MY was negatively and positively correlated with the FVD and BVD, respectively. A poor linear relationship existed between the other driving parameters and the output parameters (most \(p\) values \(<\) 0.2). Figure 10: Pearson correlation coefficient for input parameters. (**a**) Table 4 input parameters except SP; (**b**) SP05–SP33 in Table 4; (**c**) SP34–SP56 and SP01–SP04 in Table 4.  
The trajectory deviation of shield attitude motion was continuously monitored to avoid exceeding the warning deviation. The shield operator generally controlled the attitude of the shield by adjusting the angle between the shield head and tail (Figure 4). This was achieved by adjusting the pressure of the propulsion cylinder in different areas, which frequently had SDs. Figure 4 shows the layout of jack cylinders in the propulsion system of the shield machine. Thrust cylinders S01-S56 were divided into six areas and distributed clockwise. Figure 10b,c show that the pressure of the propulsion cylinder in different regions had different correlations with the attitude deviation parameters. The correlation between the pressure of the propulsion cylinder and the attitude deviation parameters in each area was more consistent. The pressure of each thrust cylinder was generally more correlated with the attitude deviation of the shield head than the attitude deviation of the shield tail. The pressure of propulsion cylinders SP05-SP13 (area 2) and SP14-SP22 (area 3) was positively correlated with the FHD. The pressure of propulsion cylinders SP34-SP42 (area 5) and SP43-SP51 (area 6) was negatively correlated with the FHD and BHD. SP14-SP22 was weakly correlated with the FHD (\(P\) = 0.2-0.4), and SP43-SP51 was moderately correlated with the FHD and BHD (\(P\) = 0.4-0.6). The pressure of propulsion cylinders SP52-SP56 and SP01-SP04 (area 1) was positively correlated with the FVD, whereas the pressure of propulsion cylinder SP23-SP33 (area 4) was negatively correlated with the FVD and BVD.