## 4 Results and Discussion
### Clustering and Tool Condition Identification  
The dataset obtained from Test I is inputted into CAGS, where the noise coefficient is set to 0.2, the resolution coefficient is set to 0.5, the halo coefficient is set to 2, and the merge coefficient is set to 0.1. The clustering results are shown in Figure 16. The samples of 35 cuttings are finally partitioned into six clusters, that is, the samples of NO. 1 to NO. 7 are recognized as cluster I, the samples of NO. 8 to NO. 14 are recognized as cluster II, the samples of NO. 15 to NO. 16 are recognized as cluster III, the samples of NO. 17 to NO. 20 are recognized as cluster V, the samples of NO. 21 to NO. 27 are recognized as cluster IV, and the samples of NO. 28 to NO. 35 are recognized as cluster VI. In addition, some samples that deviate from the core samples are detected as noise points. For a clustering method, clustering labels are randomly generated and have no specific meaning. That is, tool wear  
Figure 14: Raw cutting force signals in Test III: (**a**) force in feed direction under initial wear, (**b**) force in vertical radial direction under initial wear, (**c**) force in feed direction under middle wear, (**d**) force in vertical radial direction under middle wear, (**e**) force in feed direction under severe wear, (**f**) force in vertical radial direction under severe wear. conditions could not be obtained from clustering labels. Thus, most of the unsupervised methods are difficult to use for online monitoring. To address the above problem, Formulas (15) and (16) are used to reveal the robust information of tool wear conditions from cluster densities. The results are listed in Table 2, which shows the corresponding relationship between the actual tool wear conditions and the predicted wear conditions. It can be found that the density factor \(War\) effectively matches VB. Therefore, almost all of the predicted wear conditions obtained by using \(War\) successfully match the actual tool wear conditions obtained by VB. Figure 16: Clustering results of Test I.  
Figure 15: Sample distribution diagram in Test III. In Test II, all samples with different cutting parameters of this test are fed into CAGS, where the noise coefficient is set to 0.2, the resolution coefficient is set to 1, the halo coefficient is set to 1, and the merge coefficient is set to 0.1. The clustering results are shown in Figure 17, where six clusters are discovered by CAGS. The samples of NO. 1, NO. 2, NO. 3, NO. 5, NO. 9, NO. 10 and NO. 11 are recognized as cluster I, the samples of NO. 6 and NO. 7 are recognized as cluster II, the samples of NO. 12 are recognized as cluster III, the samples of NO. 8 are recognized as cluster IV, the samples of NO. 4 are recognized as cluster V and VI classes. In this stage, less tool wear information than seen in Test I can be directly seen in the distribution of cutting force features, because of the influence of the change cutting parameters. Specifically, samples with the same tool wear condition (NO. 1 and NO. 6) may be distributed in different regions, and vice versa (NO. 7 and NO. 12). Thus, tool wear information is difficult to be separated from cutting parameters. However, as shown in Table 3, the cluster density can be used to indicate tool wear conditions as its insensitivity to cutting parameters. In addition, the cluster density factor \(War\) is used to predict tool wear states under three different cutting parameters. It can be found that \(War\) provides fault tolerance to the whole TCM system, although an incorrect partition is obtained by CAGS. For example, the samples of NO. 4 are partitioned into cluster V and VI, which should be recognized as a  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cutting** & **VB (mm)** & **The Actual Tool** & **Clustering** & **Cluster** & **War** & **The Predicted Tool** \\
**Number** & **(mm)** & **(Wear Condition)** & **(Label)** & **(Density)** & **(Wear Condition)** \\ \hline NO. 1 & 0.05 & Initial wear & I & 7.01 & 0 & Initial wear \\ NO.