## 5 Experiment Results  
In this section, the proposed method is verified by the experimental data. The fault data for the bearing roller comes from the bearing data center at the Laboratory of Case Western Reserve University. The test bed consists of two Horsepower (HP) motors, a torque transducer, and a dynamometer, as shown in Figure 12. The test bearings (SKF6205, Svenska Kullager-Fabriken group. Switzerland), including the drive end and fan end bearings, support the motor rotor shaft. Three types of Single point faults (outer race fault (ORF), inner race fault (IRF), and ball fault (BF) were introduced to the test bearings using electro-discharge machining [37]. All bearing fault data are annotated with bearing geometric, operating condition, and fault information. In the experiment, the vibration signals of the rolling bearing were collected by three accelerometers, which were mounted to the housing with magnetic bases at the three, six, and 12 o'clock positions. The fault frequency of the ball fault can be computed as follows:  
\[f_{bpfr}=\frac{D}{2d}\Bigg{(}1-(\frac{d}{D})^{2}\cos^{2}\alpha\Bigg{)}f_{r} \tag{23}\]  
where \(f_{r}\) is the rotating frequency, \(D\) is the pitch diameter, \(d\) is the balling diameter, and \(\alpha\) is the contact angle. According to the geometry size and defect frequencies multiple of running speed, the fault frequency of the ball fault is obtained, which is about \(f_{bpfr}\) = 137 Hz. In this section, the vibration signals of the drive end bearing are analyzed. To verify the effectiveness of the proposed method, ball fault 1, with fault diameters of seven miles, is analyzed. The rotation speed of ball fault 1 is 1772 r/min. The sampling frequency is set to 12 kHz in the experiment. The original signal and its envelope spectrum are plotted in Figure 13. From Figure 13, it can be found that fault frequencies are flooded by noise and irrelevant harmonic components. Therefore, the proposed ACFHNR-SVD-TEO method is employed for incipient fault feature extraction of the fault signal. Figure 11: (**a**) Optimal resonance band obtained by Kurtogram; (**b**) envelope spectrum. Figure 12: The bearing fault test bed from the bearing data center at the Laboratory of Case Western Reserve University. Firstly, the delay step is set as \(m=15\). The kurtosis value and the ACFHNR index value corresponding to these 15 singular components of SVD are calculated, as shown in Figure 14. Figure 14 exhibited that the ACFHNR value of the first singular component is larger than the ACRHNR values of the other components, which tells us that the first component is the effective signal feature. Therefore, the first singular component is processed, and its Teager energy operator spectrum is obtained, as shown in Figure 15. Fault frequencies such as the \(f_{bpfr}\), \(f_{bpfr}+f_{r}\), \(f_{bpfr}+2f_{r}\) and \(2f_{bpfr}\) can be clearly identified, demonstrating that the proposed method can successfully detect the incipient fault features of rolling element bearings. Also, it shows that the first singular component is the effective component. However, the kurtosis values corresponding to the third and fourth singular components are much larger than the other kurtosis values, as shown in Figure 14, indicating that the kurtosis values may provide the wrong information for extracting the sensitive fault information. Figure 14: The comparison of the proposed ACFHNR index and the kurtosis. Figure 13: The original signal and the envelope spectrum of ball fault 1. (**a**) The raw fault signal ; (**b**) The envelope spectrum of the raw fault signal. Figure 15: (**a**) The extracted fault feature signal and the (**b**) Teager energy operator spectrum of ball fault 1. To further evaluate the performance of the proposed method, the fault data for a bearing roller from the Intelligent Maintenance System, University of Cincinnati, are explored.