## 5 Analysis and Result
### Machine Learning Analysis  
For developing the setting of the post-distribution region and predictive model of the data through ML, the large value in Figure 11c takes a long time, and a problem regarding overload exists, so the analysis was conducted using normalized values. The training sets for the predictive model formation were divided into (class1 and class2), (class1 and class3), (class1 and class4), (class2 and class3), (class2 and class4), and (class3 and class4). Here, class1 and class2 are the normal and the damaged cap data of alumina, and class3 and class4 are the normal and the damaged cap data of cristobalite. Finally,  
Figure 11: 2D plot according to division of frequency range using principal component: (**a**) feature set A (0–10 kHz); (**b**) feature set B (0–4 kHz); (**c**) feature set C (4–10 kHz); (**d**) feature set D (4–7 kHz); (**e**) feature set E (7–10 kHz). a classification model was merged and formed through six learning phases. The entire data as a test set was evaluated with the developed model. The ML results are shown in Figure 12 and were obtained by estimating the post-distribution area using SVM, bagging, kNN, and DA methods. In Figure 12a, the SVM performed nonlinear analysis with multi-SVMs using the radial basis function (RBF) as the nonlinear kernel, which is suitable for classification of many classes because the accuracy of the classification is reduced when commonly used linear classifications are employed. Multi-SVM performed analysis by creating a separate classification model for four classes and merging them. In Figure 12b, the bagging method is used as one of the ensemble methods. It uses several weak learners to extract bootstrap samples several times to train each model and aggregate the learning results. Three bootstraps were used in this study. The bagging method increases the accuracy of class classification by increasing the number of bootstraps, but because it randomly selects bootstrap samples, the range of one class can be separated rather than appear continuously, if data present inside are selected. Therefore, a small number of bootstraps was used. In Figure 12c, the kNN method creates a template for the search of the nearest neighbors and standardizes and analyzes the predictors. In order to consider the continuity of the class region, the nearest neighbors are designated as one of three types to classify the entire class. Figure 12: Analysis of post-distribution area using machine learning methods: (**a**) support vector machine (SVM) classification; (**b**) bagging classification; (**c**) k-nearest neighbor (kNN) classification; (**d**) discriminant analysis (DA) classification. In Figure 12d, the DA method was developed using regularized quadratic discriminant analysis to find the class with the lowest false classification cost, if different classes generate data based on different Gaussian distributions. A more accurate second-order discriminant analysis method was used for multiclass classification. Because a series of processes was carried out, including feature extraction and setting up of frequencies of FRF interest, and eliciting features with significant contributions by NCA, it was possible to clearly distinguish between the normal and damaged cap conditions. Through this, via analysis using four ML methods, a model was developed that distinguishes 100% of normal and gold tool damage data. In addition, the predicted accuracy of the four classes was analyzed using the developed model, and is shown in Figure 13 as a heatmap chart for comparison. As a result of heatmap chart analysis, the classification accuracy of the normal data was similar for the four classification methods, but the bagging method showed the highest accuracy in classification of the damaged cap data. For this reason, for the SVM, KNN, and DA methods, the boundary was separated by the correlation of the two classed for the damaged cap class, so one alumina data with cap damage was determined to be cristobalite.