Rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model
Through a method based on cyclic correlation entropy and low-rank sparse model, the fault diagnosis problem of cyclostationary signal processing under non-Gaussian noise is solved, and effective fault feature extraction is achieved in the case of a mixture of impulse noise and strong Gaussian noise, achieving the accuracy of fault features and diagnostic precision.
Patent Information
- Application Number
- CN202510750644.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-06
- Publication Date
- 2025-09-12
AI Technical Summary
Traditional cyclostationary signal processing technology is not effective when processing non-Gaussian noise, especially when the fault diagnosis method fails under impulse noise interference, and the cyclic correlation entropy spectrum is submerged in the presence of strong Gaussian noise and impulse mixed noise.
A sparse model based on cyclic correlation entropy and low-rank sparsity is adopted. The Gaussian kernel length is determined by the Silverman criterion, the time-varying correlation entropy is calculated and Fourier series transform is performed, and the truncated nuclear norm is used for low-rank sparse decomposition to extract the fault characteristic frequency and identify the fault type.
In the case of impulse noise and strong Gaussian mixed noise, the accuracy of fault feature extraction is improved, high diagnostic accuracy is maintained, and the fault feature frequency can be effectively extracted.
Smart Images
Figure CN120628609A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of bearing fault diagnosis, and in particular relates to a rolling bearing weak fault diagnosis method based on cyclic correlation entropy and a low-rank sparse model. Background Art
[0002] Rolling bearings are mechanical components that support rotating shafts and reduce friction using rolling elements (such as steel balls or rollers). They are widely used in various industrial and mechanical equipment, including aerospace and wind power generation. However, they are prone to various types of failures during long-term operation and under high loads. Bearing failure is a common failure mode in mechanical systems, potentially leading to equipment downtime, reduced efficiency, and even major accidents. Consequently, research related to bearing degradation prediction and fault diagnosis has recently attracted widespread attention. Over the past few decades, various signal processing methods have been proposed for rotating machinery fault detection, such as spectral kurtosis (SK), wavelet transform (WT), minimum entropy decomposition (MED), variational mode decomposition (VMD), and sparse representation. In addition to these methods, cyclic spectrum analysis has received increasing attention due to its effectiveness in rotating machinery fault diagnosis. The random cyclostationarity of rolling bearing vibration has been demonstrated, and this property can be exploited for diagnosis. Cyclostationary signal processing, which uses a dual-frequency plane consisting of the cyclic frequency ε and the frequency f to characterize the spectral structure of the signal, has become an important signal processing method, widely used in technical fields such as radar and communication signal detection and rotating machinery gear and bearing fault diagnosis.
[0003] Traditional cyclostationary signal processing technology is based on the second-order statistical moments of the signal. When the noise component in the signal is Gaussian noise, a clearer cyclic frequency ε-frequency f dual-frequency plane is generally obtained. However, when processing non-Gaussian noise (such as impulse noise), it often fails to achieve satisfactory results or even fails. Therefore, the present invention proposes a rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model. This solves the problem that general fault diagnosis methods fail under impulse noise interference, and also solves the problem that fault information extracted by a simple cyclic correlation entropy spectrum will be submerged in the presence of strong Gaussian noise and impulse mixed noise. Summary of the Invention
[0004] In order to solve the above technical problems, the present invention proposes a rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model to solve the problems existing in the above-mentioned prior art.
[0005] To achieve the above objectives, the present invention provides a rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model, comprising:
[0006] collecting a vibration signal of the rolling bearing, and determining a Gaussian kernel length based on the vibration signal using a Silverman criterion;
[0007] Based on the Gaussian kernel length, calculating the time-varying correlation entropy of the vibration signal using a Gaussian kernel function;
[0008] Performing Fourier series transformation on the time-varying correlation entropy to obtain cyclic correlation entropy;
[0009] Performing Fourier transform on the cyclic correlation entropy to obtain a cyclic correlation entropy spectrum;
[0010] Performing a low-rank sparse decomposition on the cyclic correlation entropy spectrum using a truncated nuclear norm to obtain a sparse matrix;
[0011] An enhanced envelope spectrum is obtained for the sparse matrix, a fault characteristic frequency is extracted based on the enhanced envelope spectrum, and a fault type is determined based on the fault characteristic frequency.
[0012] Alternatively, the calculation expression for determining the Gaussian kernel length using the Silverman criterion is:
[0013] σ=0.9AN -1 / 5
[0014] Where N is the data length, A is the minimum value of the empirical standard deviation of the data, and σ is the Gaussian kernel length.
[0015] Optionally, based on the Gaussian kernel length, a calculation expression for calculating the time-varying correlation entropy of the vibration signal using a Gaussian kernel function is:
[0016]
[0017] Where V σ (t, τ) represents the time-varying autocorrelation entropy of the bearing fault signals X and X(t-τ), σ represents the Gaussian kernel length, t is the time variable, and τ represents the time delay.
[0018] Optionally, the calculation expression for the cyclic correlation entropy obtained by performing Fourier series transform on the time-varying correlation entropy is:
[0019]
[0020] Where, represents the cycle correlation entropy, ε represents the cycle frequency, τ represents the time delay, V (t,τ) represents the time-varying autocorrelation entropy, T0 represents the period of the time-varying autocorrelation entropy, and j represents the Fourier transform variable.
[0021] Optionally, the expression for calculating the cyclic correlation entropy spectrum is:
[0022]
[0023] Where f is the spectrum frequency, represents the distribution of the cyclostationary signal with respect to the spectral frequency f and the cyclic frequency ε, and X represents the bearing fault signal used.
[0024] Optionally, the expression for performing low-rank sparse decomposition of the cyclic correlation entropy spectrum using the truncated nuclear norm is:
[0025] Minimize‖L‖ r +γ‖S‖ l1
[0026] Subject.to L+S=M
[0027] Where, ||L|| r represents the truncated nuclear norm of L, ||S|| l1 represents the l1 norm of the S matrix, γ is the balance parameter for weighing the low-rank matrix and sparse matrix, M is the cyclic correlation entropy spectrum matrix, L is the low-rank matrix, which is the noise part, and S is the sparse matrix, which is the fault component.
[0028] Optionally, the process of obtaining an enhanced envelope spectrum for the sparse matrix includes:
[0029] A filtering operation is performed to optimize the sparse matrix to obtain a sparser matrix, which is recorded as a two-dimensional sparse matrix E;
[0030] Based on the two-dimensional sparse matrix E, for each cyclic frequency ε, an enhanced envelope spectrum is obtained by integrating with respect to the frequency f.
[0031] Compared with the prior art, the present invention has the following advantages and technical effects:
[0032] The present invention applies cyclic correlation entropy spectrum to mixed noise containing impulse noise and strong Gaussian noise, and uses the decomposed CCES sparse components to extract fault features, thereby improving the accuracy of fault feature extraction in mixed noise containing impulse noise.
[0033] To further filter strong Gaussian noise components in sparse matrices, this paper proposes a CCES-based TNN model for the first time, using the truncated nuclear norm to replace RPCA for bearing fault diagnosis. By leveraging CCES's ability to handle impulse noise and its highly sparse nature, combined with the denoising capabilities of TNN, this method maintains high diagnostic accuracy even when strong impulse interference and strong Gaussian noise coexist in the fault signal. BRIEF DESCRIPTION OF THE DRAWINGS
[0034] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:
[0035] Figure 1 is a flow chart of an embodiment of the present invention;
[0036] Figure 2 This is a time domain waveform diagram of a rolling bearing outer ring fault signal according to an embodiment of the present invention;
[0037] Figure 3 This is a spectrum diagram of a rolling bearing outer ring fault signal according to an embodiment of the present invention;
[0038] Figure 4 This is an envelope spectrum of a rolling bearing outer ring fault signal according to an embodiment of the present invention;
[0039] Figure 5 This is a cyclic correlation entropy projection diagram of an embodiment of the present invention, that is, the obtained cyclic correlation entropy matrix is projected in the direction of the cyclic frequency α;
[0040] Figure 6 It is the feature matrix after the envelope spectrum is enhanced on the sparse matrix after TNN decomposition in the embodiment of the present invention. DETAILED DESCRIPTION
[0041] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.
[0042] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.
[0043] Example 1
[0044] like Figure 1 As shown, this embodiment provides a rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model, including the following steps:
[0045] S1. Use sensors to collect bearing fault signals x(t).
[0046] Specifically, the bearing outer ring fault signal collected by the bearing fault signal acquisition experimental platform is used as the test basis for analysis. The vibration signal of the test bearing is collected using an acceleration sensor. The motor speed is set to 3000rpm and the sampling frequency is 20kHz. Strong random pulse interference is introduced by knocking on the bearing base. The specific time domain waveform signal is as follows: Figure 2 The bearing model used in this embodiment is SKF-6205, and its related parameter information is shown in Table 1. The theoretical failure frequency of the bearing outer ring is calculated to be 179.25 Hz.
[0047] Perform Fourier transform on the bearing vibration signal x(t) to obtain the spectrum X(f) of the bearing vibration signal, as shown in Figure 3 As shown, from Figure 3 It can be seen that it is seriously affected by noise interference, and only relatively obvious shaft frequency components can be observed, making it difficult to identify the fault frequency and determine the type of fault in the bearing. Similarly, no obvious fault frequency can be observed from the spectrum diagram of the time domain envelope signal, such as Figure 4 Therefore, the original signal needs to be further analyzed and processed.
[0048] Table 1
[0049]
[0050] S2. Use the Silverman criterion to find the optimal Gaussian kernel length to minimize the impact of noise.
[0051] Specifically, the Silverman Criteria are as follows:
[0052] σ=0.9AN -1 / 5
[0053] Where N is the data length. A represents the minimum empirical standard deviation of the data. N is determined by the length of the selected fault data segment. The Silverman criterion is a classic method due to its low computational cost and robust performance. Here, the data length is selected as 8092, so N is 8092.
[0054] S3. Due to the good suppression effect of Gaussian function on impulse noise, Gaussian function is selected as the kernel function of correlation entropy, and the time-varying correlation entropy is calculated using the calculated kernel length.
[0055] Specifically, the time-varying correlation entropy using the Gaussian kernel function is calculated as follows:
[0056]
[0057] Among them, V σ (t, τ) represents the time-varying autocorrelation entropy of the bearing fault signals X and X(t-τ), where t is the time variable, τ represents the time delay, and σ represents the Gaussian kernel length, which is determined by the Silverman criterion and calculated in S2. When calculating the time-varying autocorrelation entropy of the bearing fault signal x(t), the autocorrelation entropy is calculated using x(t) and x(t-τ). Therefore, the time-varying autocorrelation entropy is a two-dimensional matrix with respect to the random variables t and τ.
[0058] S4. The obtained time-varying correlation entropy is a function of time t and time delay τ. The cyclic correlation entropy (CCE) is obtained by calculating the Fourier series with respect to the time variable t.
[0059] Specifically, the specific formula for calculating the cycle correlation entropy (CCE) is:
[0060]
[0061] in Represents the cyclic frequency, m is a positive integer (m = 1, 2, 3...), and T0 represents the period of the time-varying autocorrelation entropy. From the meaning of the Fourier series, we can know that the cyclic autocorrelation entropy reflects the size of the frequency component contained in the time-varying autocorrelation entropy. σ (x,y) is calculated by S3.
[0062] S5. Calculate the Fourier transform of the cyclic correlation entropy (CCE) with respect to the time delay variable τ to obtain the cyclic correlation entropy spectrum (CCES), which is a two-dimensional matrix of frequency (f)-cyclic frequency (ε).
[0063] Specifically, the specific formula for calculating the cyclic correlation entropy spectrum (CCES) is as follows:
[0064]
[0065] Where f is called the spectrum frequency and X represents the bearing fault signal used. represents the distribution of a cyclostationary signal with respect to the spectral frequency f and the cyclic frequency ε. The spectral frequency f is related to the system's resonant frequency, and the cyclic frequency ε is also called the fault frequency. The cyclic correlation entropy spectrum is continuous at the frequency f and discrete at the cyclic frequency ε. In other words, the CSD has nonzero values at the discrete cyclic frequency ε. The rest of the value is zero, i.e.:
[0066]
[0067] Since the bearing fault signal x(t) has the characteristics of second-order cyclostationarity, its CCES only has values at the cyclic frequency, and the rest is 0, so its cyclic correlation entropy spectrum can be regarded as a two-dimensional sparse matrix. Impulse noise is effectively suppressed by the cyclic correlation entropy spectrum, and Gaussian noise has the characteristics of low rank, so the noise can be approximately regarded as a low rank matrix. Its projection diagram with respect to the cyclic frequency ε is as follows Figure 5 As shown in the figure, the fault frequency 179.25Hz and the double frequency 358.5Hz are submerged in the strong background noise, making it difficult to extract accurate fault information from them. Therefore, further decomposition is required.
[0068] S6. Since the matrix nuclear norm is not the optimal convex approximation of the rank function, the truncated nuclear norm (TNN) is used instead of the matrix nuclear norm to perform low-rank sparse decomposition, and the obtained sparse matrix is the fault feature.
[0069] Specifically, the formula for low-rank sparse decomposition using the truncated nuclear norm (TNN) instead of the matrix nuclear norm is as follows:
[0070] Minimize‖L‖ r +γ‖S‖ l1
[0071] Subject.to L+S=M
[0072] ||L|| r represents the truncated nuclear norm of L, which is defined as the sum of the minimum min(M,N)-r singular values of L, that is, ||S|| l1 represents the l1 norm of the S matrix, that is, the maximum sum of the absolute values of each column. γ is a trade-off parameter for low-rank and sparse matrices, and in this example, its value is set to 5. M is the cyclic correlation entropy spectrum matrix. After decomposition, L is the low-rank matrix representing the noise component, and S is the sparse matrix representing the fault component. A filtering operation is then performed to optimize the resulting sparse matrix. This operator can be expressed as follows:
[0073]
[0074] Then, the sparse matrix is filtered as follows:
[0075] E=S⊙G
[0076] Where ⊙ is called the Hadamard product. By choosing different values for k, we can filter out some of the unfiltered noise in the sparse matrix S, resulting in a sparser matrix. In this example, k is set to 1.5.
[0077] S7. Calculate the enhanced envelope spectrum of the obtained sparse matrix, extract the fault characteristic frequency from the envelope spectrum and identify the fault type.
[0078] Specifically, the enhanced envelope spectrum formula is as follows:
[0079]
[0080] For the two-dimensional sparse matrix E, for each cyclic frequency ε, perform integration with respect to the frequency f. In this example, the integration interval is selected as the full frequency band. The processed matrix is as follows Figure 6 As shown in the figure, we can observe the bearing outer ring fault frequency of 179.25Hz and the double frequency of the fault frequency of 358.5Hz. Therefore, we can judge that there is a fault in the bearing outer ring.
[0081] This invention utilizes the aforementioned rolling bearing weak fault diagnosis method based on cyclic correlation entropy and a low-rank sparse model to address the difficulty in extracting fault features in environments containing both impulse noise and strong Gaussian noise. Furthermore, to further filter out the strong Gaussian noise component in the sparse matrix, this invention proposes a CCES TNN model, using the truncated nuclear norm to replace RPCA for bearing fault diagnosis. This method maintains high diagnostic accuracy even when both strong impulse interference and strong Gaussian noise are present in the fault signal.
[0082] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.
Claims
1. A rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model, characterized in that: The following steps are involved: collecting a vibration signal of the rolling bearing, and determining a Gaussian kernel length based on the vibration signal using a Silverman criterion; Based on the Gaussian kernel length, calculating the time-varying correlation entropy of the vibration signal using a Gaussian kernel function; Performing Fourier series transformation on the time-varying correlation entropy to obtain cyclic correlation entropy; Performing Fourier transform on the cyclic correlation entropy to obtain a cyclic correlation entropy spectrum; Performing a low-rank sparse decomposition on the cyclic correlation entropy spectrum using a truncated nuclear norm to obtain a sparse matrix; An enhanced envelope spectrum is obtained for the sparse matrix, a fault characteristic frequency is extracted based on the enhanced envelope spectrum, and a fault type is determined based on the fault characteristic frequency.
2. The rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model according to claim 1 is characterized in that: The calculation expression for determining the Gaussian kernel length using the Silverman criterion is: σ=0.9AN -1 / 5 Where N is the data length, A is the minimum value of the empirical standard deviation of the data, and σ is the Gaussian kernel length.
3. The rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model according to claim 2 is characterized in that: Based on the Gaussian kernel length, the calculation expression for calculating the time-varying correlation entropy of the vibration signal using the Gaussian kernel function is: Where V σ (t, τ) represents the time-varying autocorrelation entropy of the bearing fault signals X and X(t-τ), σ represents the Gaussian kernel length, t is the time variable, and τ represents the time delay.
4. The rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model according to claim 3 is characterized in that: The calculation expression of the cyclic correlation entropy obtained by performing Fourier series transform on the time-varying correlation entropy is: Where, represents the cycle correlation entropy, ε represents the cycle frequency, τ represents the time delay, V (t,τ) represents the time-varying autocorrelation entropy, T0 represents the period of the time-varying autocorrelation entropy, and j represents the Fourier transform variable.
5. The rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model according to claim 4 is characterized in that: The expression for calculating the cyclic correlation entropy spectrum is: Where f is the spectrum frequency, represents the distribution of the cyclostationary signal with respect to the spectral frequency f and the cyclic frequency ε, and X represents the bearing fault signal used.
6. The rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model according to claim 5, characterized in that: The expression for performing low-rank sparse decomposition of the cyclic correlation entropy spectrum using the truncated nuclear norm is: Minimize‖L‖ r +γ‖S‖ l1 Subject.to L+S=M Where, ||L|| r represents the truncated nuclear norm of L, ||S|| l1 represents the l1 norm of the S matrix, γ is the balance parameter for weighing the low-rank matrix and sparse matrix, M is the cyclic correlation entropy spectrum matrix, L is the low-rank matrix, which is the noise part, and S is the sparse matrix, which is the fault component.
7. The rolling bearing weak fault diagnosis method based on cyclic correlation entropy and low-rank sparse model according to claim 6, characterized in that: The process of obtaining the enhanced envelope spectrum of the sparse matrix includes: A filtering operation is performed to optimize the sparse matrix to obtain a sparser matrix, which is recorded as a two-dimensional sparse matrix E; Based on the two-dimensional sparse matrix E, for each cyclic frequency ε, an enhanced envelope spectrum is obtained by integrating with respect to the frequency f.