## 4 Experimental Signal Analysis  
In actual operation, a bearing is an important part of rotating machinery, and the inner ring, outer ring and rolling elements are related to each other. Therefore, there is a strong correlation between the different vibration sources. Limited by the experimental conditions, only one channel observation signal is monitored. The proposed method in this paper is used to detect the coupling faults such as the inner ring, outer ring and rolling elements. The multiple-fault experimental data about bearing in this paper are provided by the University of Cincinnati, USA [38]. Experimental apparatus is shown as Figure 11. There are four Rexnord ZA-2115 double row tapered roller bearings with the circle diameter of 2.815 cm installed on the spindle, and each race has 16 rollers. The roller diameter is 0.331 cm, taper is 15.17\({}^{\circ}\), the spindle Speed is 2000 r/min and the data sampling frequency is 20 kHz. The data analyzed in this paper are the No. 1 dataset in the database, in which the bearing with outer ring and inner ring fault is simulated. The fault frequencies of inner ring and rolling element in the bearing are calculated as follows:  
\[f_{i}=\frac{n}{2}(1+\frac{d}{D}\cos\alpha)f_{r} \tag{17}\]  
\[f_{b}=\frac{D}{2d}[1-{(\frac{d}{D})}^{2}\cos^{2}\alpha]f_{r} \tag{18}\]  
Figure 10: The analysis result provided by the proposed method: (**a**) recovered shock signal in time-domain; and (**b**) recovered harmonic signal in time-domain. Figure 9: The result provided by canonical decomposition and parallel factors by alternating least squares method (CP-ALS): (**a**) shock signal in time-domain; and (**b**) harmonic signal in time-domain. where \(f_{i}\) is the characteristic frequency of the inner ring fault of rolling bearing, \(f_{b}\) is the characteristic frequency of the rolling element fault, \(f_{r}\) is the rotational frequency, \(n\) is the number of the rolling element, \(d\) is the diameter of the rolling element, \(D\) is the pitch circle diameter of bearing, and \(\alpha\) is the contact angle of rolling element. Finally, we calculate and determine the fault frequency of inner ring as \(f_{i}=296.8\) Hz. The rolling element faulty frequency is \(f_{b}=139.84\) Hz, and the rotational frequency is equal to \(f_{r}=33.3\) Hz. The specific parameters of bearing are shown in Table 2.  
To realize the blind source separation of single-channel composite signal in an experiment station, firstly, the EMD is used to decompose the composite signal, and the mode components IIMF1-IMF10 are obtained. Then, the original signal and the decomposed mode components are decomposed by SVD to obtain characteristic values. Finally, the number of source signals is determined as \"2\" by using the BIC, as shown in Figure 12.  
The collected composite original single-channel signals in the time-domain and the frequency-domain are shown in Figure 13a,b, respectively. According to Figure 13a, we notice that the characteristics of original signals in the time domain performance cannot be clearly identified due to the strong background noise, which makes it hard to identify whether the bearing fails and to find the location of the fault. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(d\) & \(D\) & \(n\) & \(\alpha\) & \(f_{r}\) & \(f_{i}\) & \(f_{b}\) \\ \hline
0.331 & 2.815 & 16 & 15.17\({}^{\circ}\) & 33.33 & 296.8 & 139.84 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The specific parameter of bearing. Figure 11: Bearing Fault experimental table. Figure 12: The BIC value of experimental signal. In order to accurately evaluate the effectiveness of proposed method in this paper, the EMD-ICA and the conventional TSSA based on CP-ALS are used in the comparative study. The EMD is used to decompose the composite signal, and pluralities of IMFs are obtained. Then, two IMFs are chosen according to the maximum correlation coefficient between the IMFs and the composite signal, which can be regarded as the input data of ICA.