# Two-Channel Information Fusion Weak Signal Detection Based on Correntropy Method +
## 5 Validation of the Proposed Method on Weak Signal Detection
### Features Extraction of Two-Channel Information Fusion  
Rolling bearing fault signals are typically non-stationary, always modulated by the rotate frequency of the shaft, and too weak to be extracted from the heavy noise by the traditional method. The public dataset Case Western Reserve University (CWRU) bearing data are used to verify the method [24]. The data of the inner race faults numbered 108 are chosen for analysis, which is obtained through the test bench in Figure 13. Its fault is 0.007-inch diameter and 0.011-inch depth. The sampling frequency is 12 kHz, the rotate speed is 1721 rpm (28.68 Hz), and the fault frequency of the bearing is 155.33 Hz (which can be calculated by the formula with the parameters given by the dataset introduction). Take 4096 points from the data of the two channels on the fan end and the drive end, respectively. Figure 14 shows the time-domain waveform and frequency spectrum of the original signal in the drive end (Figure 14a,b) and fan end (Figure 14c,d). It is obvious that the frequency of the spectrum is mainly concentrated in the high-frequency range. To avoid redundant description of the method, the following takes the signal of the driver end as an example for detailed description, and the processing method of the fan end is the same. Figure 12: CCES of two methods. (**a**) CCES of signals. (**b**) Partially enlarged view of the CCES. SVD is applied to the original signal, and the difference spectrum is shown in Figure 15a. It can be seen from the difference spectrum that the difference values corresponding to 20, 26, and 70 are relatively large. Starting from 70, the difference becomes very small, indicating that the SV changes slowly after 70. Therefore, reconstruct the first 70 SCs to obtain the denoised signal. Next, refer to CIM to select the SCs involved in reconstruction. The function of CIM points out that the farther the two variables are, the greater the CIM value. Figure 15b gives the CIM between every SV and the original signal. As the sequence of SV increases, the change trend of CIM is first to increase and then to stabilize. In Figure 15b, the CIM value of sequence number 232 is 2.107, the CIM value of sequence number 121 is 2.105, and the CIM value of sequence numbers 81 and 93 is 2.104. Therefore, 2.104 is an ideal threshold choice, but consider that a small CIM value is what we want, so we believe that the valley  
Figure 14: The 108 th data of the database. (**a**) Time-domain waveform of the original signal at the drive end. (**b**) Frequency spectrum of the original signal at the drive end. (**c**) Time-domain waveform of the original signal at the fan end. (**d**) Frequency spectrum of the original signal at the fan end. Figure 13: Balling bearing fault experiment bench. can better reflect the change of CIM, and the value of the serial number 81 is not at a valley, then a value of 2.103 was found. This value is not far from the fluctuation range when the trend is stable, and will not cause all singular components to be filtered out. Based on the above considerations, 2.103 is selected as the threshold (shown as the black dotted line in Figure 15b). Then select the SV lower than this value, and the corresponding SCs are selected to reconstruct the signal. Then estimate CCES of SVD with difference spectrum method and SVD with CIM method. To compare the methods of using differential spectrum and CIM selection more intuitively, the estimated CCES of the two methods are displayed in Figure 16 where the red line represents the CCES of the reconstructed signal based on the CIM-selection of SCs, and the blue line represents that based on the first 70 SCs selected from the difference spectrum. For convenience, the method of difference spectrum selection is called SVD-70, because it used the first 70 SCs for reconstruction, and the method of CIM selection is called SVD-CIM in this case. The fault characteristic frequency and its second harmonics can be seen from the blue and red lines.