# 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
Near the third harmonics of the fault frequency, the interference of the red line is much less than that of the blue line. Additionally, it is difficult to distinguish the third harmonics of the fault frequency in the blue line. This shows that the method of using CIM to select SCs performs better than the method of selecting SCs based on the differential spectrum. The method of using CCES can show the fault characteristics more directly than the frequency spectrum obtained by the Fourier transform. Figure 16: CCES of reconstructed signals at drive end with two method. Figure 15: Difference spectrum and CIM. (**a**) Difference spectrum of the SVD. (**b**) CIM between the SCs and original signal. The fan-end signal is processed with the proposed method, and the CCES is shown in Figure 17, from which the characteristic frequency and the second harmonic frequency of the fault can be found clearly. However, since the fan end is far away from the faulty component, its peak frequency is not at the fundamental frequency of the signal. Then analyze the signals of the two channels:  
1. Construct each signal column into a 3073-by-1024 matrix, and then splice the two matrices into a 3073-by-2048 matrix. 2. Perform PCA on the newly constructed matrix with each column as one-dimensional, and obtain a new 3073-by-2048 matrix. 3. To maintain the consistency of the signal length, the first 1024 dimensions are preferred as the principal components. 4. However, to prove that the selected principal components can represent the main information of the original matrix, the cumulative contribution of the selected matrix should be calculated. The cumulative contribution of the first 352-dimensional vector reaches 95%, and the cumulative contribution of the first 1024-dimensional vector reaches 99.66%. Therefore, it can be considered that the first 1024 dimensional vectors can express most of the information of the original matrix. After the two-channel signal is reduced in dimensionality, SVD is performed on the signal, then the CIM between the SCs and the reduced-dimensional signal is calculated. Next, select the SCs that can be reconstructed according to the aforementioned method. Finally, estimate the CCES of the reconstructed signal. Figure 18 is the CCES of the dimensionality reduction signal (blue line) and the signal processed by the proposed method (red line). Only the characteristic frequency of the fault is obvious in the blue line in Figure 18, which means that after two-channel information fusion, the fundamental frequency of the fault characteristic is enhanced, but the harmonic frequency that can indicate the fault characteristic is not displayed. After the SVD-CIM method is adopted for denoising the signal, its odd multiple of harmonic frequency is reflected in CCES. From Figure 18, we can find that the two-channel information can enhance the amplitude of the characteristic frequency at 155.3 Hz compared to Figures 16 and 17. The amplitude of the red line is above 0.003, the amplitude of the blue line is above 0.005 in Figure 18. The red line of the single-channel in Figure 16 is below 0.002, and the amplitude of the blue line is below 0.004. The amplitude of the characteristic frequency in Figure 17 is close to 0.003. Additionally, combined with the SVD-CIM, there is obvious characteristics frequency of third harmonics and fifth harmonics. This shows that compared to single-channel information, two-channel information can enhance the signal's fault characteristics, and through the processing of the SVD-CIM method, its CCES can make the characteristics more obvious. Usually, for the fault signal generated by the rotating component,  
Figure 17: CCES of the signal at the fan end. the proposed method is added to the envelope spectrum analysis to demodulate the signal. However, the estimated CCES in this work does not need to perform the envelope demodulation analysis, which replaces the role of envelope spectrum. See Section 4.2 for specific analysis.