Two-Channel Information Fusion Weak Signal Detection Based on Correntropy Method †
2. Fundamental Theory
2.1. Principal Components Analysis for Multi-Channel Information Fusion
- Form the original data into an n-by-m data Hankel matrix X;
- Each row of matrix X is subtracted from its corresponding mean value, that is, zero mean value;
- Calculate the covariance matrix ;
- Calculate the eigenvalues and corresponding eigenvectors of the covariance matrix;
- Arrange the eigenvectors into a matrix according to the size of the corresponding eigenvalues from large to small, and take the first k (determined by the cumulative contribution rate of the principal components) columns to form a matrix P;
- is the principal component matrix of the original data X after dimensionality reduction.
2.2. Theory of Singular Value Decomposition
2.3. Definition of Correntropy
3. Presentation of the Proposed Method
4. Simulation for Correntropy Induced Metrics and Cyclic Correntropy Spectrum
4.1. The Effect of Correntropy Induced Metrics
4.2. The Role of Cyclic Correntropy Spectrum
5. Validation of the Proposed Method on Weak Signal Detection
5.1. Weak Electrical Signal Detection
5.2. Features Extraction of Two-Channel Information Fusion
- Construct each signal column into a 3073-by-1024 matrix, and then splice the two matrices into a 3073-by-2048 matrix.
- Perform PCA on the newly constructed matrix with each column as one-dimensional, and obtain a new 3073-by-2048 matrix.
- To maintain the consistency of the signal length, the first 1024 dimensions are preferred as the principal components.
- 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.
- A method called SVD-CIM is proposed to extract the weak signal features, which includes using CIM to select the SCs from the SVD and estimating CCES for the reconstructed signal.
- CIM is a similarity measure based on frequency components.
- Compared with the frequency spectrum of the reconstructed signals, CCES can express more useful information for the cyclostationary signals.
- Compare with the method of difference spectrum selection, the CIM selection has a better performance on weak signal features.
- For two-channel information, two-SVD-CIM is proposed, and the two-channel information fusion can enhance the fault characteristics.
Data Availability Statement
Conflicts of Interest
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Gong, S.; Lu, J.; Li, S.; Ma, H.; Wang, Y.; Teng, G. Two-Channel Information Fusion Weak Signal Detection Based on Correntropy Method. Appl. Sci. 2022, 12, 1414. https://doi.org/10.3390/app12031414
Gong S, Lu J, Li S, Ma H, Wang Y, Teng G. Two-Channel Information Fusion Weak Signal Detection Based on Correntropy Method. Applied Sciences. 2022; 12(3):1414. https://doi.org/10.3390/app12031414Chicago/Turabian Style
Gong, Siqi, Jiantao Lu, Shunming Li, Huijie Ma, Yanfeng Wang, and Guangrong Teng. 2022. "Two-Channel Information Fusion Weak Signal Detection Based on Correntropy Method" Applied Sciences 12, no. 3: 1414. https://doi.org/10.3390/app12031414