# Chapter Detection in Robotic Milling Using Entropy Features
## 4 Results and Discussion
### Classification Models Construction  
In this paper, classification models were developed using the \"classification learner\" toolkit provided by MATLAB. Several classical classification learner models were trained, including support vector machine (SVM), k-nearest neighbor (KNN), and decision tree. A total of 540 groups of _wRCMDE_ samples for the two chatter states (chatter and chatter-free) were selected as training samples. The _wRCMDE_ samples were be normalized first, and 5-fold cross-validation was adopted to modify the classification accuracy.  
During the training of each classification model, the kernel parameters were optimized based on the training accuracy. The training accuracy of the selected models is listed in Table 2. The SVM model with the Gaussian kernel function was chosen as the final classification model.  
Furthermore, the SVM models based on ICEEMDAN and RCMDE (ICEEMDAN-RCMDE), ICEEMDAN and MDE (ICEEMDAN-MDE), EEMD and wRCMDE (EEMD-RCMDE), EEMD and RCMDE (EEMD-MDE), and EEMD and MDE (EEMD-MDE) were also constructed for comparison. It can be seen from Table 3 that the proposed model (named ICEEMDAN-wRCMDE) showed superiority over the other methods.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Classification Model** & **Parameters** & **Training Accuracy** \\ \hline SVM & Kernel function & Gaussian & 95.2\% \\  & Kernel scale & 1.45 & \\ KNN & Number of neighbors & 5 & 95.0\% \\  & Distance metric & Chebyshev & \\ Decision Tree & Max number of splits & 7 & 93.9\% \\  & Split criterion & Gini’s diversity index & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Training accuracy of classification models.  
Figure 5: _wRCMDE_ extracted from the reconstructed signals with different scale factors. Green lines indicate a chatter-free state, and blue dashed lines indicate a chatter state.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Training Accuracy** \\ \hline ICEEMDAN-wRCMDE (proposed method) & 95.2\% \\ ICEEMDAN-RCMDE & 91.9\% \\ ICEEMDAN-MDE & 90.0\% \\ EEMD-wRCMDE & 90.6\% \\ EEMD-RCMDE & 87.8\% \\ EEMD-MDE & 86.9\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Training accuracy of different methods.  
It can be seen from Figures 9 and 10 that the proposed method can realize fast and reliable chatter detection with different robot configurations and cutting parameters. Only intermittent false results can be observed, which does not affect the final decision of the chatter state and is acceptable for practice.  
Concerning the influence of the acceleration sensor position and location on the raw data acquisition, additional experiments were conducted. Configuration III denotes another  
Figure 10: Detection results for: (**a**) I\(-\)6000\(-\)6\(-\)1; (**b**) I\(-\)8000\(-\)1. 5\(-\)8; (**c**) II\(-\)6000\(-\)6\(-\)3; (**d**) II\(-\)3000\(-\)1.5\(-\)8.  
robot configuration (\(\gamma_{1}=-10^{\circ}\), \(\gamma_{2}=22^{\circ}\), \(\gamma_{3}=-164^{\circ}\), \(\gamma_{4}=-10^{\circ}\), \(\gamma_{5}=-74^{\circ}\), \(\gamma_{6}=1.5^{\circ}\)). The position of two acceleration sensors is shown in Figure 11a, where acceleration sensor 1 is mounted on the spindle and acceleration sensor 2 is mounted on the robot end. The comparison of time-domain signals obtained from the two sensors is shown in Figure 11b. As can be seen, the vibration signals obtained from acceleration sensor 1 show larger amplitudes than acceleration sensor 2, due to acceleration sensor 1 being located closer to the cutting area. Furthermore, as can be seen from Figure 12, the results of the _wRCMDE_ values are similar to those in Figure 5; this indicates that the acceleration sensor position and location have little effect on the proposed chatter detection method.