## 4 Results and Discussion
### Clustering Results and Tool Wear Status Identification  
In order to realize the continuous monitoring of tool wear on the whole path in corner milling, the optimal feature set of acoustic emission obtained in this paper must be used. Below, the clustering sample set is constructed using the first two features in Table 9 to illustrate the clustering process. The sample distribution is shown in Figure 13.  
Figure 12: The variations in the time-domain characteristics of acoustic emission with cutting. (**a**) Variation law of effective value; (**b**) Variation law of peak value; (**c**) Variation law of variance; (**d**) Variation law of crest factor.  
Figure 13: Distribution of samples in the 1 st and 2 nd dimensions of the optimal feature set.  
There are 1201 samples in the sample set, including 301 samples of class 1 (VB = 0.025 mm), 302 samples of class 2 (VB = 0.053 mm), 299 samples of class 3 (VB = 0.078 mm) and 299 samples of class 4 (VB = 0.09 mm). The sample set was input into CAGS, and the clustering result was obtained as shown in Figure 14.  
As can be seen from Figures 13 and 14, the algorithm basically identifies the first and second types of samples, but for the third and fourth types of samples, because the sample points are highly mixed, the algorithm can only identify the two classes as one class. In addition, in the initial clustering results, the algorithm marked the first class in the real label as class II, the second class in the real label as class III, and the first class in the real label as class III. Classes III and IV are marked as Class I. However, this problem can be successfully solved by the density factor \(War\) proposed in Section 2.5.  
As shown in Table 10, although the cluster tag and the real tag cannot be matched, the density factor \(War\) corresponding to the cluster tag can effectively match the tool wear value corresponding to the real tag, and the density factor gradually increases as the wear value increases. In order to more intuitively represent the effectiveness of \(War\) for estimating wear value, (a) and (b) in Figure 15 give the double-coordinate curves of \(VB\) to \(War\) and \(VB_{max}\) to War, respectively. From the figure, it can be seen that the density factor can effectively estimate the changing trend of tool wear.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Real Label** & \(VB\) (mm) & \(VB_{max}\) (mm) & **Label Clustering** & \(War\) \\ \hline
1 & 0.025 & 0.18 & II & 0 \\
2 & 0.053 & 0.24 & III & 0.59 \\
3 & 0.078 & 0.26 & I & 0.80 \\
4 & 0.09 & 0.27 & I & 0.80 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Tool wear state assessment results based on \(War\).  
Figure 14: Cluster monitoring results of tool wear during peripheral corner milling.  
Finally, this paper verifies the effectiveness of the CAGS clustering results by comparing the identification accuracy with the currently popular classification algorithms, including the BP neural network, Bayesian network and SVM. BP neural network uses feedforward network, randomly selecting 150 samples of 4 different wear state samples as training data and setting 2 hidden layers and 10 neurons in each layer. The Bayesian network chose a minimum error rate-based method and evenly divided all samples corresponding to each wear state into four samples, forming four training datasets for cross-training. The SVM uses the radial basis kernel function, and the training data are the same as in the Bayesian network. The proposed recognition accuracy evaluation indexes are calculated respectively, and the comparison results are shown in Table 11.  
We can see that the BP neural network outperforms other methods in _PUR_, _CSM_, _NMI_, and _CluCE_, while the Bayesian network provides the best results considering _CluCE_. However, the CAGS performs better than others on all the indexes, and compared with those supervised methods, the CAGS does not rely on extensive experiments to obtain the training data.