A correlation entropy efficient algorithm based on sparse reconstruction

Abstract

The application discloses a related entropy efficient algorithm based on sparse reconstruction, and relates to reducing the calculation complexity and space storage complexity of kernel learning. The method comprises the following steps: given a signal x(i) and a kernel function κ(·); calculating an incomplete Cholesky decomposition low rank approximation matrix Z of a kernel matrix K of the signal x(i) so that K≈ZZ T ; calculating sparse coefficients L 21 (j) of each column vector of the lower triangular matrix Z; calculating a sparse reconstruction matrix of the lower triangular matrix Z; calculating a sparse reconstruction matrix of the kernel matrix K; and calculating a related entropy of the signal x(i). The application can significantly reduce the calculation complexity and space storage complexity of kernel learning, improve the sparsity of the related entropy, highlight the characteristic information of the signal, and is beneficial to extracting the signal features.

Description

Technical Field

[0001] This invention relates to the field of modern signal processing technology, and in particular to an efficient correlation entropy algorithm based on sparse reconstruction. Background Technology

[0002] Correlation entropy reflects both the temporal structure and statistical characteristics of a signal, including higher-order statistics. Therefore, correlation entropy can effectively suppress Gaussian and non-Gaussian noise in a signal and has been widely used in radar and communication signal detection, direction of arrival estimation, and other fields.

[0003] Traditional correlation entropy estimation requires the use of double loop statements to calculate the kernel matrix, which has high computational and spatial storage complexity. This makes it difficult to meet the fast and real-time requirements of signal detection in radar and other applications, thus limiting the application of correlation entropy. Summary of the Invention

[0004] To address the above technical issues, this invention provides a high-efficiency algorithm based on sparse reconstruction correlation entropy, which can be applied to engineering fields such as bearing fault diagnosis, radar signal detection, and direction of arrival estimation.

[0005] This invention provides an efficient algorithm for correlation entropy based on sparse reconstruction, the specific steps of which are as follows: Step 1, given signal and kernel function Let the signal be... This is a vibration signal indicating a fault in the bearing's inner ring. column vectors, ,use Kernel function ,Right now: , in: These are the parameters of the kernel function. It is an absolute value operator. It is a natural exponential function. It is a delayed variable. ; Step 2, Calculate the signal kernel matrix incomplete Decomposition of low-rank approximation matrices , making Among them, the kernel matrix yes The square formation, yes The lower triangular matrix, It is the matrix transpose operator; Step 3, calculate the lower triangular matrix. sparsity coefficients of each column vector , , , Representation matrix The line, number Column elements; will Sort in descending order, and simultaneously arrange the matrices The column vectors are also arranged according to Arranged in descending order; Step 4, calculate the lower triangular matrix. sparse reconstruction matrix Set threshold ,calculate , When The smallest integer at time, It is a matrix The former A matrix consisting of column vectors, for Matrix; Step 5, calculate the kernel matrix sparse reconstruction matrix ,in, , yes Array; Step 6, Calculate the signal Relevant entropy , ,in, It is the expected mean operator. , , yes Column vectors.

[0006] The beneficial effects of this invention are as follows: This invention provides a kernel matrix calculation method based on sparse reconstruction, which can be implemented without calculating the kernel matrix. In the case of a given signal and kernel function , due to incomplete Decomposition and sparse reconstruction methods for calculating kernel matrix Low-rank approximation matrix The space storage complexity of the kernel matrix is ​​reduced from Reduced to The computational complexity is reduced from Reduced to ,when This will significantly reduce the computational and spatial storage complexity of kernel learning; and make the kernel matrix... It is more sparse, which increases the sparsity of the correlation entropy, not only highlighting the characteristic information of the signal, but also making the physical meaning of the signal clear, which is more conducive to extracting signal features. Attached Figure Description

[0007] Figure 1 This is a flowchart of the method of the present invention; Figure 2 Signal for Example 2 The time-domain waveform; Figure 3 Signal for Example 2 The Fast Fourier Transform (FFT) diagram; Figure 4 The lower triangular matrix in Example 2 sparsity coefficients of each column vector picture; Figure 5 Signal for Example 2 ,when Time-related entropy picture; Figure 6 Signal for Example 2 ,when Time-related entropy Fast Fourier Transform (FFT) graph; Figure 7 For the comparative example 1 signal ,when Traditional correlation entropy graph of time; Figure 8 For the comparative example 1 signal ,when The traditional correlation entropy fast Fourier transform diagram. Detailed Implementation

[0008] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings.

[0009] Example 1

[0010] like Figure 1 As shown, this invention discloses an efficient algorithm for correlation entropy based on sparse reconstruction, comprising the following steps: Step S1, given signal and kernel function Let the signal This is a vibration signal indicating a fault in the bearing's inner ring. column vectors, ,use Kernel function ,Right now: , in: These are the parameters of the kernel function. It is an absolute value operator. It is a natural exponential function. It is a delayed variable. ; Step S2, calculate the signal kernel matrix incomplete Decomposition of low-rank approximation matrices , making Among them, the kernel matrix yes The square formation, yes The lower triangular matrix, It is the matrix transpose operator; Step S3, calculate the lower triangular matrix. sparsity coefficients of each column vector , , , Representation matrix The line, number Column elements; Sort in descending order, and simultaneously arrange the matrices The column vectors are also arranged according to Arranged in descending order; Step S4, calculate the lower triangular matrix. sparse reconstruction matrix Set a threshold. ,calculate , Is when The smallest integer at time, It is a matrix The former A matrix consisting of column vectors, for Matrix; Step S5, calculate the kernel matrix sparse reconstruction matrix ,in, , yes Array; Step S6, calculate the signal Relevant entropy , ,in, It is the expected mean operator. , , yes Column vectors; Example

[0011] This embodiment verifies the method of Embodiment 1, specifically using a bearing inner ring fault vibration signal. The bearing model is a deep groove ball bearing 6205; the shaft speed... r (frequency conversion) Sampling frequency Number of sampling points The bearing's geometric dimensions are: major diameter =52.0mm; Ball diameter = 7.94mm; Number of balls =9; Pressure angle The characteristic frequency of bearing inner ring failure was obtained through calculation. characteristic cycle of bearing inner ring failure .

[0012] Vibration signal of bearing inner ring fault in Example 2 Time-domain graphs, such as Figure 2 As shown; vibration signal Fast Fourier Transform, such as Figure 3 As shown, according to step S2 of Embodiment 1, the signal is calculated. kernel matrix incomplete Decomposition of low-rank approximation matrices ,use Kernel function, kernel parameters According to step S3 of Example 1, calculate the lower triangular matrix. sparsity coefficients of each column vector ,like Figure 4 As shown, the lower triangular matrix for The matrix with maximum sparsity coefficients According to step S4 of Example 1, the triangular matrix is ​​removed. The first two columns of the reconstruction matrix , yes The matrix; according to step S5 of Example 1, calculate the kernel matrix. sparse reconstruction matrix Finally, according to step S6 of Example 1, the signal is calculated. Relevant entropy ,like Figure 5 As shown, from Figure 5 The data shows periodic transient impacts, with an interval of 0.0064 s between adjacent transient impacts, corresponding to the characteristic period of the bearing inner ring failure, and the relevant entropy. Fast Fourier Transform, such as Figure 6 As shown, from Figure 6As can be seen from the data, the characteristic frequency of the bearing inner ring fault and its higher harmonics have a high signal-to-noise ratio.

[0013] The algorithm in Example 2 is mounted on a signal processing hardware platform. After the physical signal is acquired by the signal acquisition module, it is input into the algorithm. Features are extracted by sparse reconstruction correlation entropy calculation, and then passed to the feature recognition module to match fault features. Finally, the fault diagnosis module outputs the diagnosis result.

[0014] Comparative Example 1

[0015] To illustrate the sparsity of the correlation entropy calculation method of the present invention, the present invention is compared with a correlation entropy algorithm without sparse reconstruction. According to step S2 of Example 1, the signal is calculated... kernel matrix incomplete Decomposition of low-rank approximation matrices Then, calculate the kernel matrix. The signal is calculated according to step S6 of Example 1. Relevant entropy ,like Figure 7 As shown, although in Figure 7 The system also exhibits periodic transient shocks, but the correlation entropy is not sparsity and the signal-to-noise ratio is low. Figure 7 The related entropy shown Fast Fourier Transform, such as Figure 8 As shown, although obvious spectral peaks appear at the fault characteristic frequency of the bearing inner ring and its higher harmonics, the signal-to-noise ratio is low.

[0016] Comparative Example 2

[0017] To illustrate the high efficiency of the method of this invention, it is compared with the traditional correlation entropy algorithm. When calculating the traditional correlation entropy, please refer to: Fontes AIR, et al, Cyclostationary correntropy: definition and application, Expert Systems With Application. 2017, 69(1):110-117. The signal used is the same as in Example 2, when the nuclear length... ,Signal Number of sampling points Table 1 shows the computation time of the two algorithms for different values. The hardware and software parameters used were: Intel i7-2600, dual-core CPU 3.4GHz, 3GB memory, Windows XP operating system, and Matlab Release 12.1 software.

[0018] Table 1 Comparison of Calculation Time (Unit: seconds) This invention calculates time 0.015 0.094 0.234 0.422 Traditional methods for calculating time 3.467 21.485 62.681 243.368

[0019] As can be seen from Table 1 of Comparative Example 2 above, the present invention significantly improves the computational efficiency of correlation entropy by employing an efficient correlation entropy algorithm based on sparse reconstruction.

Claims

1. An efficient algorithm based on sparse reconstruction and correlation entropy, characterized in that... Includes the following steps: Step 1, given signal and kernel function Let the signal This is a vibration signal indicating a fault in the bearing's inner ring. column vectors, ,use Kernel function ,Right now: , in: These are the parameters of the kernel function. It is an absolute value operator. It is a natural exponential function. It is a delayed variable. ; Step 2, Calculate the signal kernel matrix incomplete Decomposition of low-rank approximation matrices , making Among them, the kernel matrix yes The square formation, yes The lower triangular matrix, It is the matrix transpose operator; Step 3, calculate the lower triangular matrix. sparsity coefficients of each column vector , , , Representation matrix The line, number Column elements; Sort in descending order, and simultaneously arrange the matrix The column vectors are also arranged according to Arranged in descending order; Step 4, calculate the lower triangular matrix. sparse reconstruction matrix Set threshold ,calculate , When The smallest integer at time, It is a matrix The former A matrix consisting of column vectors, for Matrix; Step 5, calculate the kernel matrix sparse reconstruction matrix ,in, , yes Array; Step 6, Calculate the signal Relevant entropy , ,in, It is the expected mean operator. , , yes Column vectors.

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