## 4 Results and Discussion
### Experiment Results from CWRU  
Figure 6 shows the test rig used for signal acquisition consisting of a 2 HP electric motor, driving a shaft on which a torque-transducer encoder was mounted. Torque was applied to the shaft via a dynamometer and an electronic control system. During testing, faults ranging in diameter from 0.18 to 0.71 mm were seeded onto the motor's drive- and fan-end bearings using electrodischarge machining (EDM). Faults were seeded on rolling elements, and inner and outer races. Each faulty bearing was separately reinstalled on the test rig, which was then run at a constant speed for motor loads of \(0-3\) horsepower (approximate motor speeds of 1797-1720 rpm). Table 4 shows the relevant bearing details and fault frequencies. During each test, acceleration was measured in the vertical direction on the drive-end bearing housing (DE). In some cases, acceleration was also acquired in the fan-end bearing housing (FE) vertical direction and the motor supporting base plate (BA). Used sample rates were 12 kHz for some tests and 48 kHz for others. Further details regarding the test setup can be found in the CWRU Bearing Data Center website at [[https://csegroups.case.edu/bearingdatacenter/pages/welcome-case-western-reserve-university-bearing-data-center-website](https://csegroups.case.edu/bearingdatacenter/pages/welcome-case-western-reserve-university-bearing-data-center-website)]([https://csegroups.case.edu/bearingdatacenter/pages/welcome-case-western-reserve-university-bearing-data-center-website](https://csegroups.case.edu/bearingdatacenter/pages/welcome-case-western-reserve-university-bearing-data-center-website)). Figure 5: Examples of envelope spectra (obtained from PSD) from aircraft-engine data (SAFRAN). Top row, SK and SE estimators; bottom row, their sliding versions (SSK; SSE).Order represents harmonics of shaft speed. The CWRU dataset holds a benchmark in bearing-failure identification comprising the following steps [32]:  
1. Discrete or random separation (DRS) to remove deterministic (discrete frequency) components. 2. Spectral kurtosis to determine the most impulsive band, followed by bandpass filtering. 3. Envelope analysis (squared envelope spectrum) of a bandpass-filtered signal. Since this benchmark contains the SK procedure within the bearing fault detection framework, it was well-suited for comparison with the proposed approach that we perform using 59 data records labeled as \"nondiagnosable\" as described in Table 5.  
In terms of interpretation, the visual inspection of estimated envelope spectra allowed for newly categorizing 7 records after SSK, 27 records after SE, and 25 records of SSE \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Rig Position** & **Model Number** & \multicolumn{3}{c}{**Fault Frequencies (IAS Multiple)**} \\ \cline{3-6}  & & **BPFI** & **BPFO** & **FTF** & **BSF** \\ \hline Drive end & SKF 6205-2 RS JEM & 5.415 & 3.585 & 0.3983 & 2.357 \\ Fan end & SKF 6203-2 RS JEM & 4.947 & 3.053 & 0.3816 & 1.994 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Bearing fault frequencies for the test rig. Figure 6: Case Western Reserve University test rig. as shown in Table 6. Thus, SE presented the best results followed by SSE. However, there was no substantial evidence of improvement after using SSK due to it being an approach designed to deal with time-varying IAS. The CWRU dataset was at constant speed. Entropy-based spectral filtering improves the SK method, meaning that entropy allows for highlighting impulsive components from complex data such as ball failure, yielding significant enhancement. Figure 7 presents the envelope spectrum estimated from the best-categorized records. Performing SSK, the inner-race (IR) fault remained N1, as shown in Figure 7d, and the ball