## 4 Validation and Analysis
### Study Results and Discussion  
To evaluate the performance of a classifier, the confusion matrix for binary classification problems is showed in Table 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**True Class** & **Predicted Class** & **Positive** & **Negative** \\ \hline Positive & TP (true positive) & FN (false negative) \\ Negative & FP (false positive) & TN (true negative) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Confusion matrix for binary classification problems. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Features Value** \\ \hline Rock type & Type index \\ UCS & Average value \\ Advance rate & Average value, Peak value, Variance \\ Trust & Average value, Peak value, Variance \\ RSP & Average value, Peak value, Variance \\ Advance mileage & Interval value from the last disc cutter replacement \\ Advance displacement & Sample range \\ Drive motor current & Maximum, Minimum, Average value, Peak of 10 motor \\ current variance, Peak of 5 min motor current kurtosis index \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Selected parameters and their augmented features. Precision rate of a binary classifier is given by:  
\[\text{Precision}=\frac{N_{TP}}{N_{TP}+N_{FP}} \tag{28}\]  
Recall rate of a binary classifier is:  
\[\text{Recall}=\frac{N_{TP}}{N_{TP}+N_{FN}} \tag{29}\]  
The classification model for classifier evaluation is based on precision rate and recall rate. As shown in Equations (28) and (29), when \(N_{FP}\) and \(N_{FN}\) change, precision rate and recall rate change inversely, hence the optimization goal for most models is to improve one of the rates while guaranteeing the other. \(F_{\beta}\) score is used when these two targets come into conflict. \(F_{\beta}\) combines the precision and recall rates into a single score, where the weight of recall rate is \(\beta\) times that of precision rate. The most common \(F_{1}\) score takes recall rate to be as important as accuracy rate:  
\[F_{1}=2.\frac{\text{precision}\cdot\text{recall}}{\text{precision}+\text{ recall}} \tag{30}\]  
The 46,629 instances were divided into training set and testing set according to a 4:1 ratio. The five most commonly used classification algorithms were compared with KSVM, namely decision tree (DT), k-nearest neighbors (KNN), naive Bayesian (NB), convolutional neural network (CNN), and stacked autoencoder (SAE). The Bayesian optimization was used to find the best hyper-parameters of the former four machine learning models. For KSVM, optimized hyper-parameters are kernel function, kernel scale, box constraint level, and penalty factor; For DT, optimized hyper-parameters are maximum number of splits and split criteria; For k-NN, optimized hyper-parameters are the number of neighbors, distance metric, and distance weight; For NB, optimized hyper-parameters are distribution and kernel type. For deep learning algorithms, several layers are used in CNN and SAE to extract deep features from input parameters. The specific hyper-parameters and their corresponding performance results are shown in Table 5. Because KSVM showed a good prediction performance among six models and can acquire this accuracy with a short training time, it was thus selected as a tool to predict disc cutter replacements. In some publications [12; 45], it is believed that TBM operational data is enough to reflect accurate information of the tunnel geological conditions, thus geological data are not considered as an input. In Table 6, a model with only operational data as inputs is compared with the proposed KSVM model, which uses both operational and geological data. More specifically, the former uses 16 features as inputs, ignoring two geological features. As Table 6 shows, although geological survey information can not accurately reflect the geological conditions of every moment, it can reveal the approximate range of geological conditions, thus significantly improving the prediction performance.