## 5 Experimental Analysis
### Comparative Analysis  
In order to verify the advantages of this method, the blind source separation method of independent component analysis (BSS-ICA) [25] and ensemble empirical mode decomposition (EEMD) [26] were used for comparison experiments. The separation effect was compared by considering four aspects: time-domain waveforms, envelope spectrum, signal-to-signal ratio (SSR), and fault classification.  
(1) The time-domain waveforms  
The experimental results of the BBS-ICA and the EEMD are shown in Figure 10. From Figure 10, the waveform of the signal corresponding to the outer ring fault is a series of impact-waveforms, but the waveform of the eccentric fault signal is a consecutive sine-waveform according to the EEMD. The waveform of the signal corresponding to the outer ring fault is a series of impact-waveforms, but the waveform of the eccentric fault signal is not a continuous sine-waveform according to the BSS-ICA. However, this assumption is not consistent with reality.  
The amplitude of the separated signal is 400 mV, which is much larger than the original signal. From Figure 10, the amplitude of the separated signal according to the BSS-ICA is 5 mV, which is much smaller than the original signal. The separated time-domain waveform has distortion problems by the EEMD and BSS-ICA.  
Figure 8: The separation results.  
Figure 9: The envelope spectrum of the outer ring fault and eccentric fault.  
2. Envelope spectrum The corresponding envelope spectrums are shown in Figure 11.\(f_{o}\) can be obtained in the envelope spectrum of the outer ring fault, and \(f_{e}\) can be obtained in the envelope spectrum of the eccentric fault by EEMD. This shows that EEMD can separate the two vibration source signals corresponding to two faults. At the same time, \(f_{o}\) and \(f_{e}\) can be obtained in the envelope spectrum of the outer ring fault and the eccentric fault by BSS-ICA. This shows that BSS-ICA cannot separate the two vibration source signals corresponding to two faults. (3) The signal-to-signal ratio (SSR) In order to quantitatively describe the separation results, the signal-to-signal ratio (SSR) method [27] was used to evaluate the quality of the separated signal. The mathematical expression of the SSR is as follows: \[\text{SSR}_{i}=\underset{1\leq j\leq q,j\
eq n:i}{min}\Bigg{(}10 log\frac{\text {PSD}_{i}}{\text{PSD}_{j}}\Bigg{)}\] (20)  
Figure 11: The envelope spectrums by EEMD and BBS-ICA.  
Figure 10: The separated time domain waveforms by the EEMD and BBS-ICA.  
where PSD\({}_{i}\) and PSD\({}_{j}\) are the power spectral densities of signals \(i\) and \(j\) in the \"home\" spectrum of signal \(i\), respectively [27].  
The SSR values of the two separated vibration source signals obtained by the method of this paper were 5.6 and 3.2. The SSR values by EEMD were 3.2 and 2.2. The SSR values by BBS-ICA were 1.1 and 0.1. Therefore, the SSR value obtained by the separation method in this study is higher than that obtained by the EEMD method. The SSR value obtained by the EEMD was higher than that obtained by the BSS-ICA method.  
The fault classification  
In order to compare the effects of the two methods on the fault diagnosis results, a self-organizing map (SOM) was used to cluster the separated vibration source signals. The clustering results are shown in Figure 12. Type 1 represents the vibration source signal of the outer ring fault, and type 2 represents the vibration source signal of the eccentric fault. From Figure 12, the two types of fault vibration source signals could be grouped into two types by the method in this paper. There is a certain amount of aliasing between the two types of faults by EEMD, which has a negative effect on fault diagnosis. However, the two types of faults could not be distinguished by BBS-ICA. Therefore, the method in this paper achieved a better clustering result, and is more advantageous than EEMD and BSS-ICA for fault diagnosis.