## 2 Statistical Analysis for the Determination of Operating Parameter Requirements
### Estimation of Requirements for Operating Parameters  
Multiple regression analysis used IBM SPSS Statistics, a widely known program for statistical analysis and data mining. The analysis was conducted according to the procedures suggested by [PERSON] [16] and [PERSON] [17]. To derive the most reliable regression equations, regression analysis was conducted repeatably using diverse combinations and forms of independent variables. Table 1 summarizes the resulting variables determined for use in multiple regression analysis. The dependent variables were the four operating parameters that needed to be estimated (thrust requirement, cutterhead torque requirement, cutterhead rotation speed requirement, and advance rate); they were each applied as quantitative variables. The independent variables comprised the ground conditions and TBM specifications. The specifications are represented by four variables: TBM type; diameter; the ratio of the maximum capacities of thrust and torque; and the maximum capacity of the rotation speed. Figure 1: Scatter matrix for correlations of operating parameters’ requirements with TBM specifications. The TBM type was a qualitative variable with two classes: EPB and slurry. The different classes had different weights: an EPB type has a weight value of one, and three is used if slurry is applied. The machine's diameter and maximum rotation speed were applied as quantitative variables, as was the ratio of the maximum capacities of thrust and cutterhead torque (i.e., the maximum thrust divided by maximum torque). This ratio was chosen considering multicollinearity. Multicollinearity or variance inflation factor (VIF) refers to a phenomenon caused by a strong linear relationship between independent variables found in multi regression analysis. This phenomenon affects calculations concerning independent and dependent variables. [PERSON] (2016) stated that an estimated VIF of more than 10 indicates multicollinearity. Multicollinearity emerged using maximum thrust and cutterhead torque variables together during multi regression analysis and could be managed by using one combined variable (i.e., their ratio). The other independent variables were related to the ground conditions. All were qualitative variables, as insufficient quantitative information was available. Three factors were considered: boulder and cobble; gravel, sand, and silt; and clay. Each was given a weight of one if present or zero if absent. Figure 2 shows the results of multiple regression analysis to estimate the required TBM operating parameters for excavating soil. The analysis used data from seven projects. Figure 2a compares actual thrust values with estimations represented by a regression line (R\({}^{2}\) = 0.68). Figure 2b similarly compares the results for cutterhead torque; the regression line has (R\({}^{2}\) = 0.81). The regression line for the rotation speed data has R\({}^{2}\) = 0.90 (Figure 2c), and that for advance rate has R\({}^{2}\) = 0.90 (Figure 2d). Although the four regression equations have relatively high R\({}^{2}\), more data are required for regression analysis. Figure 3 presents verification results for the estimated regression equations using four datasets that were not used in the multiple regression analysis. The verification datasets are extracted from three different projects. Comparison of the actual results with the estimations shows that the equations for cutterhead torque (Figure 3b) and rotation speed (Figure 3c) are quite reliable, whereas those for thrust (Figure 3a) and advance rate (Figure 3d) have low reliability.