# Two-Channel Information Fusion Weak Signal Detection Based on Correntropy Method +
## 1 Introduction  
Singular value decomposition (SVD) is a simple and effective method for denoising [1]. A large number of scholars have studied this method in feature extraction [2]. [PERSON] et al. [3] proposed a method to quantify the complexity of the power signal with the idea of assessing the signal complexity in terms of the entropy computed from the singular value distribution. [PERSON] et al. conducted an in-depth study on the decomposition results and noise effects of SVD [4]. Additionally, this team proposed to use the difference spectrum to select the effective singular components (SCs). Inspired byprevious research on SVD, [PERSON] and [PERSON] [5] proposed a novel strategy for signal denoising using reweighted SVD. The traditional SVD denoising method based on energy is not suitable for weak faults detection [6], so it is necessary to find other methods for selecting singular value (SV), such as information-based methods [7]. Due to the urgent need for feature extraction of weak signals, many scholars have begun to shift focus from signal energy to signal information, such as introducing entropy theory into signal processing. [PERSON] and his team [8] proposed divergence entropy based on the finding that the existing entropy method lacks systematic consistency, and then applying it to fault diagnosis, the classification accuracy of which is higher than other entropy methods. Additionally, for multi-channel features extraction, they proposed the variational embedding multiscale diversity entropy [9]. The concept of correntropy (CE) was proposed by [PERSON] et al. [10] based on the information theoretic learning (ITL) and kernel method [11]. Subsequently, the team and many scholars [12] in the field of statistical signal processing systematically studied the mathematical, physical meaning, properties, and application of CE, and constructed the theoretical framework of CE signal processing [13]. A new cyclostationary analysis technology named cyclic correntropy (CCE) analysis has emerged to suppress impulsive noise. CCE is a kernel-based similarity measure of cyclostationary modeling signals [14]. [PERSON] [15] researched a large number of signal processing methods based on the second-order stationary characteristics of the signal and proposed a time delay estimation (TDE) based on CE and CCE [16] which has a good ability to suppress non-Gaussian impulse noise. [PERSON] and [PERSON] [17] applied the CE and CCE on rolling element bearing fault diagnosis under impulsive noise environment and compared the cyclic correntropy spectrum (CCES) with the spectral kurtosis (SK) -based fast kurtogram to highlight the superiority of the CCES. This is the first case where the CCES method was introduced to fault diagnosis. To make full use of the information in all channels, a feature extraction method capable of multi-source information fusion is essential. The multivariate embedding theory proposed by [PERSON] uses the same embedding dimension to construct a phase space for each channel and then splices the phase spaces of different channels to construct a multivariate phase space [18]. Additionally, PCA was first introduced by [PERSON] in 1901 and later developed by [PERSON] [19] in 1933. PCA is a multivariate statistical method that converts multiple variables into a few principal components (i.e., comprehensive variables) through dimensionality reduction techniques. These principal components can reflect most of the information of the original variables and are expressed as the linearity of the original variables. To make sure the information contained in these principal components do not overlap each other, it is required that the principal components are not related to each other. PCA has a wide range of applications in many fields. Generally, when the research question involves multiple variables and the correlation between the variables are obvious, that is, when the information contained overlaps, the method of principal component analysis can be considered.