## 2 Experiment and Measurements
### Correlation Analysis  
The Ra values of all cutting routes on the work-piece were measured after the slot milling process was finished for each block of Inconel 718. The correlation analysis between the Ra values and extracted features were then applied for feature selection. Tables 3-5 show the Pearson correlation coefficients between the statistical features and the Ra values. It is noted from Table 3 that the entropy of wise vibration in X-direction has relatively high correlation (absolute value of correlation coefficient \(\geq\) 0.4) with the Ra values within more scales than the other measurement points and directions. Additionally, Table 4 shows the observation that the statistical features of vibration signals have more correlation with respect to the Ra values in X-direction. It can be inferred that the cutting process of Inconel 718 consists of more essential vibration characteristics in X-direction due to reasons of the cutting resistance of Inconel 718 (material property) as well as the feeding direction. The result of correlation analysis for the spindle current (Table 5) depicts that the RMS, STD, peak-to-peak and CV values have more correlation coefficients with respect to the Ra values. The correlation analysis in frequency-domain was also employed to the vibration signals and their corresponding envelope signals in three directions. As the aforementioned, the frequency-domain features include the rotation speed-related and unrelated features. In order to extract the rotation speed-unrelated features, the correlation coefficients were calculated to quantify the correlation between the power spectrum densities of vibration signals and the Ra values within 8 kHz. The correlation coefficients were also computed to assess the correlation between the corresponding envelope of vibration signals and the Ra values. To obtain the rotation speed-related features of vibration signals and their corresponding envelope signals, on the other hand, the correlation coefficients of their order spectra (normalized frequency by rotation speed) with respect to the Ra values were also computed from 0 to 100\(\times\) orders. Additionally, the correlation coefficients among the Ra values and the power spectrum densities of spindle currents were calculated within the frequency range of 1 kHz as well. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c} \hline \hline Spindle vibration & Scale & 6 & 7 & 11 & 12 & 13 & & & & & & & & \\ \(X\)-axis & Correlation coefficient & 0.42 & 0.41 & 0.44 & 0.44 & 0.42 & & & & & & & \\ \hline \multirow{2}{*}{Vise vibration \(X\)-axis} & Scale & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 \\  & Correlation coefficient & 0.44 & 0.46 & 0.51 & 0.52 & 0.53 & 0.55 & 0.54 & 0.53 & 0.48 & 0.46 & 0.45 & 0.42 & 0.42 \\ \hline \multirow{2}{*}{Relative vibration \(X\)-axis} & Scale & 6 & 7 & & & & & & & & & & & \\  & Correlation coefficient & 0.40 & 0.41 & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Pearson correlation coefficients (absolute value \(\geq\) 0.4) between multiscale entropy and the Ra values. The correlation analysis results in frequency-domain are illustrated in Figures 5 and 6. Figure 5 shows the correlation coefficients among the Ra values and the power spectrum densities of the spindle vibration signals as well as their corresponding envelopes in three directions. The correlation coefficients of the order spectra of spindle vibration signals and their corresponding envelopes with respect to the Ra values are shown in Figure 6. It can be noted that the correlation coefficients of high value (absolute value \(\geq\) 0.4) were computed at more frequencies/orders in vibration signals than in their corresponding envelopes. The results are reasonable since the frequency-domain characteristics reveal the information inside the vibration signal while the envelope signal represents the amplitude modulation behavior in time-domain.