## 2 Statistical Analysis for the Determination of Operating Parameter Requirements
### Correlation of Operational Actions and Mechanical Responses
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable Type** & **Variable Name** & **Symbol** & **Maximum Capacity** \\ \hline \multirow{6}{*}{Independent variable (=operational action)} & Cutterhead rotation speed & \(A_{1}\) & 1.0 rev/min \\  & Shield jack speed & \(A_{2}\) & 60 mm/min \\  & Screw conveyor rotation speed & \(A_{3}\) & 14.2 rev/min \\ \cline{1-1}  & Opening ratio of screw gate & \(A_{4}\) & 100\% \\ \cline{1-1}  & Number of shield jacks used & \(A_{5}\) & 25 ea \\ \cline{1-1}  & Number of cutterhead motors used & \(A_{6}\) & 7 ea \\ \hline \multirow{6}{*}{Dependent variable (=mechanical response)} & Shield jack pressure & \(Y_{1}\) & 35.0 MPa \\  & Thrust & \(Y_{2}\) & 50,000 kN \\ \cline{1-1}  & Cutterhead torque & \(Y_{3}\) & 9637 kN-m \\ \cline{1-1}  & Screw conveyor jack pressure & \(Y_{4}\) & 27.2 MPa \\ \cline{1-1}  & Left earth pressure & \(Y_{5}\) & 0.5 MPa \\ \cline{1-1}  & Right earth pressure & \(Y_{6}\) & 0.5 MPa \\ \cline{1-1}  & Inner cutter seal temperature & \(Y_{7}\) & 65\({}^{\circ}\)C \\ \cline{1-1}  & Outer cutter seal temperature & \(Y_{8}\) & 65\({}^{\circ}\)C \\ \cline{1-1}  & Oil tank temperature & \(Y_{9}\) & 60\({}^{\circ}\)C \\ \cline{1-1}  & Cooling water temperature & \(Y_{10}\) & 60\({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Descriptions of operational actions and mechanical responses used for multiple regression analysis. The estimates of both shield jack pressure (\(Y_{1}\)) and thrust (\(Y_{2}\)) are related to the propulsion force of the TBM. They are positively correlated with the cutterhead rotation (\(A_{1}\)) and shield jack (\(A_{2}\)) speeds. These output variables represent the propulsion force driving the TBM's advance. As the TBM operator can control the propulsion via its driving speed, regression equations for the estimations of \(Y_{1}\) and \(Y_{2}\) seem to be reasonable. The cutterhead torque represents the rotational force required to rotate the cutterhead. Generally, the TBM operator decreases the shield jack speed and increases the number of additives being injected if the cutterhead torque increases during excavation. However, the obtained equation has a negative coefficient (\(-0.02\)) for shield jack speed (\(A_{2}\)). The cutterhead torque is one of the essential operating parameters monitored during excavation, the regression equation for its estimation is revised to be the same as that for estimating the thrust, as these parameters generally show a proportional relationship. A hydraulic motor drives the screw conveyor. Therefore, the operating pressure of the screw conveyor jack (\(Y_{4}\)) can be raised by increasing the screw conveyor rotation speed (\(A_{3}\)). The left (\(Y_{5}\)) and right (\(Y_{6}\)) earth pressures are measured for the soil pressure at the respective sides of the chamber. They are the most important indicators informing excavation management. They are usually regulated by adjusting the shield jack speed (\(A_{2}\)) and the screw conveyor rotation speed (\(A_{3}\)). As the earth pressure gradually increases during excavation, the TBM operator attempts to decrease the shield jack speed and increase the screw conveyor rotation speed to balance pressure conditions at the tunnel face. Therefore, the regression analysis considered only these two actions (\(A_{2}\) and \(A_{3}\)). As there is very little difference between the left and right earth pressures, the equation was estimated by the regression analysis using both earth pressure datasets together. The other output variables associated with temperature (\(Y_{7}\), \(Y_{8}\), \(Y_{9}\), and \(Y_{10}\)) were clearly positively correlated with the cutterhead rotation speed (\(A_{1}\)). This follows intuitively from accelerated cutterhead rotation generating more heat, and thus increasing the measured temperature.