## 4 Results and Discussion
### Experiment Results from UNC  
The test rig (see Figure 9) consisted of a shaft driven by a 1.5 HP DC electric motor able to reach 1720 rpm through the equipped rigid coupling. The test rig had two HTH-UC206  
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline  & [33] & [34] & [35] & **SK** & **SSK** & **SE** & **SSE** \\ \hline Without removing engine influence & - & - & - & ✓ & ✓ & ✓ & ✓ \\ \hline Visual inspection & - & - & - & ✓ & ✓ & ✓ & ✓ \\ \hline Accuracy & & **98.95** & **99.83** & 90.46 & \(87.64\pm 2.26\) & \(90.24\pm 2.31\) & \(87.27\pm 2.95\) & \(\textbf{94.53\pm 2.26}\) \\ \hline \hline \end{tabular}
\end{table}
Table 7: Training classifier accuracy of each filtering approach in Case Western Reserve University (CWRU) dataset compared with several recently reported state-of-the-art works.  
Figure 8: Confusion matrix of classification stage in CWRU dataset using SK, SSK, SE, and SSE.  
bearings with two drilling wheels to simulate bearing and unbalanced faults. The dataset held 42 vibration records lasting 4 s at a sampling rate of 25.6 kHz and variable speed (coast-down). Vibration records were collected in the horizontal plane, employing several accelerometers mounted on bearing supports. The following failures were considered (14 records per failure): inner race (IR), outer race (OR), and ball elements. Damage is was simulated on the bearing located at the shaft end, introducing a crack on the surface of interest with a motor tool. The considered bearing failures had failure frequencies of 5.4783 for BPFI, 3.5217 for BPFO, 2.1913 for BSF, and 0.3913 for the fundamental train frequency (FTF).  
Figure 9(a) displays the spectrogram of a record with IR for which the time-varying signal is presented on the top plot. Because the dataset had no tachometer record, the speed profile was computed using the approach developed in [36], resulting in confident estimates for all OR records. However, the 8 signals' speed profile (6, ball records; 2, IR) was hardly interpretable mainly because of their low signal-to-noise ratio.  
For illustration purposes, the vibration record was downsampled (by 32 times) to delineate the speed profile (see Figure 9(b)). This profile remained similar across the tested record datasets. The spectrogram in Figure 9(c) shows that IAS influence was excluded by transforming it into the angular domain.  
Figure 10: Examples of spectrograms estimated for a single IR fault record.  
Figure 9: Experimental test rig (**left**): (1) motor driven; (2) rigid coupling; (3) drilling wheels; (4) bearing housing. sensor location: (**a**) accelerometers; and (**b**) microphones. Simulated OR, IR, and ball defects (**right**).  
Figure 11 shows the resulting envelope spectrum computed for each considered filtering scenario. Although BPFI fault frequency appeared after applying each filtering approach, fault frequencies were more visible and dominant in the spectrum performed by SK and SSK (see Figure 11a,g. In BPFO, fault frequency was indistinguishable from noise applying each feature-extraction strategy, except in SSK (see Figure 11h), for which the first fault harmonic was dominant. In ball failure, fault frequency and harmonics were clear and contained the most spectral energy regardless of feature extraction. SSE (see Figure 11l) presented an improvement concerning SE (see Figure 11f).  
Figure 11: Envelope-spectrum examples of failures (IR (left column), OR (middle column), and Ball (right column)) computed by SK (top row), SE (second row), SSK (third row), and SSE (fourth row).