## 4 Results and Discussion
### ANFIS-GA Model  
To predict the advance rate of shield machine with high accuracy, a hybrid ANFIS-GA was applied in this study. The ANFIS provided the search space and utilized GA for finding the best solution by tuning the membership functions required to reach the lower error. The idea of hybrid technique was proposed to predict the EPB shield performance that creates a non-linear relationship between the input variables and targets to estimate the outputs. As a result, machine performance parameters, such as cutter head torque (CT), rotational speed of screw rate (SC), and cutter head rotation speed (CR), were set as input parameters, and advance rate (AR) was set as the output parameter. The hybrid model was programmed in MATLAB software. ANFIS-GA model was applied in the form of Takaji Sugeno model to integrate the best features of fuzzy inference systems and neural networks. The MFs were considered by Gaussian shapes and the GA parameters were adjusted by the trial and error method. In the study, several attempts were performed to select the various parameter values that are required for GA. As a result of these attempts, population size was selected as 50, crossover rate was chosen as 0.8 and mutation rate was chosen as 0.02. More discussions regarding the hybrid model were presented in Table 3. To evaluate the hybrid model for predicting the advance rate, the multi-objective fitness function is minimized with the following statistical parameters:  
\[RMSE=\sqrt{\frac{\sum\left(x_{maa}-x_{pre}\right)^{2}}{n}} \tag{14}\]  
\[R^{2}=1-\frac{\sum\limits_{i=1}^{n}\left(x_{maa}-x_{pre}\right)^{2}}{\sum \limits_{i=1}^{n}\left(x_{maa}-x_{m}\right)^{2}} \tag{15}\]  
\[VA=\left[1-\frac{\text{var}(x_{\text{mea}}-x_{\text{pre}})}{\text{var}(x_{ \text{mea}})}\right] \tag{16}\]  
where \(x_{\text{mea}}\), \(x_{\text{pre}}\), \(x_{\text{m}}\), and \(n\) were the measured, predicted, mean of the \(x\) values, and the total number of datasets, respectively. Theoretically, a predictive model with high accuracy is desired when route mean square error (\(RMSE\)) is equal to 0 and correlation coefficient (\(R^{2}\)) and variance account (\(VA\)) are equal to 1. Figure 8: Comparison between measured and predicted AR from ANFIS model: (**a**) training set and (**b**) testing set. In the proposed model, the goal of the optimization process was to find the best design variables to maximize correlation coefficient (\(R^{2}\)), variance account (\(VA\)), and decrease route mean square error (\(RMSE\)) at the same time, as displayed in the following Equation:  
\[Minimize\;Fit(RMSE,R^{2},VA)=(-w_{1}\times RMSE+w_{2}\times R^{2}+w_{3}\times VA) \tag{17}\]  
where \(w_{1}\), \(w_{2}\), \(w_{3}\) \(\in\) (0, 1), satisfying \(w_{1}+w_{2}+w_{3}\) = 1. In this model, the values of \(w_{1}\), \(w_{2}\), and \(w_{3}\) were determined as 0.8, 0.1, and 0.1, respectively. Figure 9 shows the relationship between the measured and predicted values acquired from ANFIS-GA predictive model for the training and testing dataset. It can be deduced that the predicted values of AR are less scattered and close to the measured values signified by its closeness to the line of equality (dashed line). To further clarify, the error deviations of outputs of ANFIS-GA model are depicted in Table 4. The relative deviations of the hybrid model were mostly in the range of \(\pm\)15%, demonstrating the more reliability of the proposed model. To illustrate the performance of the EPB shield machine during the tunneling process, the values of measured advance rate from field and the predicted values through ANFIS-GA model were plotted for all datasets, as shown in Figure 10. It can be concluded that the measured and predicted data agreed well with each other. Figure 11 shows the assessment results of the hybrid ANFIS-GA compared with ANFIS model.