## 2 Experiment and Measurements
### Signal Processing
The reconstructed signals and their envelopes were then analyzed to extract the interior features. The FFT spectrum analysis was employed to extract the frequency-domain features of the reconstructed signals as well as their corresponding envelope signals. As indicated [18; 19], the frequency-domain features include the spindle rotating speed-related ones and the spindle rotating speed-unrelated ones. The spindle rotating speed-unrelated features can be attributed to the machine structural vibrations as well as the external noises. As illustrated in Figure 3, the spectra of the vibration signals reveal that the vibration energy is concentrated at the same certain frequencies even though the spindle rotating frequencies are different. Therefore, the vibration energy levels at specific frequencies (such as 469-470 Hz) can be classified to the spindle rotating speed-unrelated features in frequency-domain. On the other hand, the frequencies at which the signal energy is concentrated vary along with the spindle rotating speed, as shown in Figure 4a that illustrates the spectrum of a vibration signal set under different spindle rotating speed. The frequencies were then normalized by the spindle rotating frequency to obtain the order spectra as shown in Figure 4b. It is apparently observed that the spectral peak can be found at order-2 since there are two blades in one cutter, and thus the vibration energy concentration is noted at the frequency of two times the spindle rotating frequency, which is the tool passing frequency. Therefore, the vibration amplitude levels at the indicated orders represent the spindle rotating speed-related features in frequency-domain. Figure 3: Illustration of spindle rotating speed-unrelated frequency-domain features: Spectrum of vibration signal under different spindle rotating speeds. Besides the features in frequency-domain, the statistical quantities of the measured time series were computed to extract the features in time-domain. In this study, the time-domain features that were extracted from the measurements include the following quantities. 1. Multiscale entropy (MSE): the MSE was extensively applied to quantify the complexity or disorderliness of a time series [20]. Therefore, the sample entropy [21] was calculated to estimate the complexity of the measurement in different scales, which represent the dynamic features of the system [22]. 2. Root-mean-square value (RMS): the RMS value is broadly employed to indicate the statistical mean amplitude of a time series. Figure 4: Illustration of spindle rotating speed-related frequency-domain features: (**a**) Spectrum of vibration signal under different spindle rotating speeds; (**b**) Order spectrum of vibration signal under different spindle rotating speeds. 3. Standard deviation (STD): the STD is generally to measure the amount of variation or dispersion of a time series. 4. Skewness: the skewness value is the measure of the extent to which a probability distribution of the time series leans to one side of mean. 5. Kurtosis: the kurtosis value describes the measure of tailedness of the distribution relative to the normal distribution (kurtosis value is 3). 6. Peak-to-peak value: the peak-to-peak value of a time series describes the change between the peak and valley in the data set, which indicates the range of oscillating data. 7. Crest factor (CF): the CF value is a parameter of waveform indicating the peak measurement that is normalized by the mean amplitude of the data set. 8. Coefficient of variation (CV): the CV value is a measure of the extent variability relative to the mean of the data set.