# An Optimal Resonant Frequency Band Feature Extraction Method Based on Empirical Wavelet Transform
## 5 Application to Roller Bearings Testing
### Case 2: Analysis of NASA Outer Ring Fault Vibration Signal
#### 5.2.2 Analysis of Noise-Adding Fault Vibration Signal  
To explore the robustness of the proposed algorithm under the background of strong noise, Gaussian white noise with SNR = 10 dB is added to the original signal. The proposed method is applied to the mixed signal, and the MEWT method is applied to the same vibration signal for comparative analysis. As shown in Figure 24a, the parameterless clustering scale-space segmentation is performed on the Fourier spectrum of the mixed signal, and a total of 15 empirical modes are decomposed; meanwhile, according to the suggestion in [18], the scale parameter is set to \(\sqrt{n}=3 fc\). Results of the MEWT method are shown in Figure 24b for a total of four empirical modes decomposed. As the interference component in the signal increases, the parameterless clustering method becomes too narrow for spectrum segmentation. Therefore, it is necessary to comprehensively consider the characteristic information carried on each frequency band and reconstruct the appropriate resonance demodulation bandwidth. As shown in Table 4, the highest value of the AASN is the same as the highest value of the ASN, which appears in mode 2, and the highest value of correlation coefficient appears in mode 13. Obviously, compared with the analysis results of the original signal in the previous section, there is a misjudgment in the selection of mode 13. It can also be concluded that when the background noise is enhanced, the mode with a strong correlation may not reflect the pulse characteristics of the signal to a greater degree. To further analyze the feature information of each mode, modes 1-6 near the determination condition are shown in Figure 25a, and the corresponding envelope spectra are shown in Figure 25b. As shown in the dotted circle, the fault frequency can be  
Figure 23: Results using spectral kurtosis. Figure 24: The analyzed result of the boundaries detected: (**a**) The parameterless scale-space method. (**b**) The MEWT method. found in mode 2, which indicates that the center position selected by AASN is accurate. However, due to the narrow frequency band setting, the characteristics are very weak and no more harmonic components can be found. Therefore, it is necessary to consider combining adjacent modes to set up the optimal resonant demodulation bandwidth. According to the results of Table 4, mode 1, mode 3 and mode 4 meet the merging requirements. The combined envelope spectrum is shown in Figure 26. Although there are more interference components, the reconstructed envelope spectrum can clearly identify the fault frequency and harmonic components. Meanwhile, as a comparison, Figure 27 shows the envelope spectrum of mode 1 in Figure 24b, and it can be found that the burrs in the envelope spectrum are increased and the fault characteristics and harmonic component peaks are weakened. This means that the visualization ability of the proposed method is better than that of the MEWT method under different noise intensities. To demonstrate the superiority of the proposed method, the same data are applied to the EMD and FK method. Figure 28a shows the first six IMFs of the EMD and the corresponding envelope spectra. It can be seen from Figure 28b that due to the influence of noise, only the weak fault frequency can be identified in the envelope spectrum of mode 1, as shown in the dotted line ellipse, while the fault frequencies and harmonic components cannot be identified in other envelope spectra. Similarly, as shown by the dotted circle in Figure 29a, the center of the demodulation band displayed by the kurtogram is 8125 Hz, and the bandwidth is 1250 Hz, and the selected center position is larger than that of the proposed method. Figure 29b shows the corresponding envelope spectrum. Since the resonance demodulation band is not determined, the fault frequency and harmonic components cannot be found in the envelope spectrum.