## 5 Experiment Validation
### Case 1: Bearing Outer Race Fault  
The time-domain waveform and its envelope spectrum of the outer raceway faulty signal with the bearing type of 30,304 are illustrated in Figure 12. As seen in the time-domain waveform, the heavy background noise makes it difficult to identify the fault-related periodic impulses. The envelope spectrum in Figure 12b is unable to extract the defect-related characteristic frequency from the vibration signal under the interference of strong noise. We cannot accurately identify the fault frequency component which is covered with other interference frequency parts including the rotating frequency \(fr\) and low-frequency heavy noise etc. The rotating speed of shaft is 900 Hz and corresponds to a rotating frequency 15 Hz. Then the fault characteristic frequency of outer raceway flaw is calculated to 75.8 Hz. To improve the accuracy of defect identification and fault diagnosis, the proposed method is applied to the analyzed signal. Table 2 displays the parameters in the method. Firstly, the corresponding entropy value sequences in different scales of the _MEVM_ are illustrated in Figure 13 and all the waveforms show quite similar periodic impulses with time. However, it is still difficult to recognize the fault signature from heavy noise. The waveform of the traditional vector entropy sequence is presented in Figure 14a. As a comparison, the waveform of the proposed MEVS of 1-scale and the final _MFEVS_ are displayed in Figure 14b,c and both have a better remarkable stability than Figure 14a. Moreover, it can be seen that the final _MFEVS_ in Figure 14c presents relatively obvious periodic impulses. Secondly, the waveform of the optimal short sliding segment with minimum MDE_rms_ is illustrated in Figure 15. According to its envelope spectrum in Figure 15b, the resonance frequency 7000 Hz can \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **o** & \(m\) & \(c\) & \(d\) & _Nw_ \\ \hline value & 6 & 2 & 6 & 1 & 128 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The parameter in the proposed method. Figure 12: The signal with outer-race defect: (**a**) the waveform in time domain; (**b**) the envelope spectrum. be identified and then applied to the designed FIR filter. As a result, the time-domain waveform of the filtered signal is plotted in Figure 16a, where the defect-induced impacts appear periodically. From the envelope spectrum of that in Figure 16b, the fault characteristic frequency and its harmonics can be clearly recognized, which is near to the theoretical calculation \(f_{op}\). Besides, the corresponding envelope waveform of the filtered signal is shown in Figure 17, where \(T_{r}\) and \(T_{op}\) are the rotating period of shaft and the interval period of the outer race fault. Thus, it can be confirmed that the defect should locate in the outer-race of the 30,304 bearing by the proposed method. Figure 14: Comparison results of the outer-race fault signal by different methods: (**a**) the traditional vector entropy value sequence; (**b**) the proposed MEVS of 1-scale; (**c**) The proposed Multiscale Fusion Entropy Value Sequence (_MFEVS_). Figure 13: Plot of the Multiscale Entropy Value Sequences (MEVS) for the bearing signal with outer race fault. Figure 16: The comparison results of the outer-race fault signal by different methods: (**a**,**b**) the proposed method; (**c**,**d**) the Essential Empirical Mode Decomposition (EEMD) method; (**e**,**f**) the Wavelength Packet (WP) method; (**g**,**h**) the filter method by fast kurtogram. Figure 15: (**a**) The waveform of the reconstructed optimal short time sliding signal, (**b**) the corresponding frequency spectrum. To further verify the advantage and superiority of the proposed method in terms of removing irrelevant noise and enhancing fault diagnosis, three traditional feature extraction methods are introduced to make a comparison. The four methods are separately employed to get rid of the heavy noise and extract the defective impulses.