## 5 Verification
### Engineering Verification  
The engineering test object is a water pump unit of a paper mill, whose structure diagram is shown in Figure 8: the centrifugal water pump is driven directly by motor. The rotating speed and rated power of the driving motor are 1480 RPM and 250 kW, respectively. The unit is tested by the off-line signal collection and analysis equipment produced by Zhengzhou Expert Technology Co., Ltd. An acceleration sensor is used and its model and sensitivity are EAG01-100 and 100 mv/g, respectively. The measuring points of the unit and the amplitudes of each measured points are displayed in Table 3. The sampling frequency is set as \(f_{s}\) = 6400 Hz. Based on Table 3, the vibration amplitude corresponding to the driving end of the pump is the largest. The bearing locating on the driving end of the pump is disassembled after shutting off the unit and it is found that the fault arises on the inner ring. The disassembled bearing and its fault location are shown in Figure 9 The type of the bearing and its FCFs are detailed in Table 4. The channel with the largest vibration value at the driving end of the pump in Table 3, that is, the horizontal direction channel is chosen for analyzing.  
The time domain analysis result of the selected original signal is as shown in Figure 10a based on which the transient features of the faulty bearing could be identified roughly. Apply ES analysis on the original engineering vibration signal over the full frequency band and the corresponding result is shown in Figure 10b. Unfortunately, the inner race FCF could not be extracted due to the influence of the other interferences. Apply AMF on the original signal and the de-noised signal is provided in Figure 10c, whose transient features are enhanced evidently compared with the original engineering vibration signal and the de-noising ability of AMF is proven again. Apply full frequency band ES analysis on the de-noised signal and the corresponding result is shown in Figure 10d and the enhancement effect of AMF on the impulse signal is further demonstrated because the FCF of the inner race is extracted evidently on Figure 10d. Although an inner race fault diagnosis conclusion could be obtained preliminarily based on Figure 10d, the spectral line energy components corresponding to other components are also stronger, which affects the sufficiency of the diagnosis conclusion. Section 5.1 is the same as the experimental signal; FBS analysis is required for de-noising signal using AMF to obtain better effect. The FBS analysis result of the signal shown in Figure 10c is presented in Figure 10e, based on which the key parameters (center frequency \(f_{c}\) and bandwidth \(B_{w}\)) of the selected optimal frequency band with the biggest SI (SI = 4.2) for envelope spectral analysis are as follows: \(f_{c}\) = 400 Hz and \(B_{w}\) = 800 Hz. Construct an optimal band-pass filter using the obtained key parameters to further filter the de-noised signal shown in Figure 10c and the envelope of the further de-noised signal is provided in Figure 10f. At last, apply FFT on the envelope signal shown in Figure 10f and the final envelope spectral extraction result is displayed in Figure 10g, based on which the perfect effect is achieved.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Type** & **Inner Race** & **Outer Race** & **Cage** & **Rolling Element** \\ \hline
7320 & 175.38 & 120.62 & 10.11 & 98.91 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Fault characteristic frequencies.  
Figure 10: _Cont._