A Time-Domain Feature Extraction Method Based on Shift-Invariant Sparse Feature Wavelet Basis

Abstract

A time-domain feature extraction method based on feature wavelet basis shift-invariant sparsity belongs to the field of condition monitoring and fault diagnosis. According to the one-dimensional periodic vibration signal generated during bearing faults, this invention conducts matrix transformation on it to obtain a square matrix for singular value decomposition, and acquires the eigenvector corresponding to the largest eigenvalue. This eigenvector is used as the feature wavelet basis, and based on the shift-invariant sparse algorithm, the time-domain impact components of the signal that are relatively similar to the eigenvector are matched and extracted. Then, time-domain pulse interval analysis is performed on the extracted time-domain results, as well as envelope spectrum analysis and comparison before and after signal analysis to determine the characteristic components in the signal. Finally, by comparing with the theoretical data of bearing faults, the condition monitoring and fault diagnosis of the bearing are realized.

Description

Technical Field

[0001] The present invention belongs to a data-driven signal feature sparse representation diagnosis method, and relates to shift-invariant sparse representation based on bearing monitoring data of key mechanical components, extracting the main feature components in the signal for bearing fault diagnosis. This invention obtains the eigenvector corresponding to the maximum eigenvalue as the feature wavelet basis through singular value decomposition after matrixing the monitoring data, and particularly relates to a shift-invariant sparse coding algorithm based on the feature wavelet basis to extract the time-domain periodic vibration components in the signal for monitoring and diagnosing the operating state of the bearing. Background Art

[0002] The safe operation of equipment is the premise for the stable system function of mechanical equipment and the creation of production value. The condition monitoring and fault diagnosis of mechanical equipment are important strategies to ensure the long-term stable production of equipment. With the development of mechanical equipment towards large-scale, specialized, integrated, and intelligent directions, establishing a perfect fault diagnosis scheme or operation and maintenance platform is a key measure to promote the rapid diagnosis and operation and maintenance of equipment.

[0003] As one of the key mechanical components of major mechanical equipment, the bearing mainly bears mechanical rotation and reduces the friction coefficient. The operating conditions of the bearing are complex. When faults such as spalling and wear occur, the generated periodic impact characteristics are interfered by noise components, posing a severe challenge to equipment condition monitoring and diagnosis.

[0004] Therefore, based on the periodic pulse signal generated during bearing faults, the present invention obtains a square matrix through matrix transformation for singular value decomposition (SVD, Singular Value Decomposition) to obtain the eigenvector corresponding to the maximum eigenvalue. Using this eigenvector as the feature wavelet basis dictionary, based on the shift-invariant sparse algorithm, the signal time-domain impact components that are relatively similar to the eigenvector are matched and extracted. Through the analysis of the signal time-domain pulse interval and the comparison of the envelope spectrum analysis before and after signal analysis, the characteristic components in the signal are determined, and through comparison with the theoretical data of bearing faults, the condition monitoring and fault diagnosis of the bearing are realized. Summary of the Invention

[0005] For the condition monitoring and fault diagnosis of bearings, it is mainly to reflect their operating state by analyzing the periodic feature components contained in the time-domain signal. When damage faults such as cracks and spalling occur during the operation of the bearing, periodic vibration impact characteristics are accompanied. However, these time-domain periodic vibration characteristics are easily interfered by noise components, resulting in the characteristics being obscured.

[0006] Parsing the time-domain sparse solution of the signal from the monitoring data is a key step in judging the underlying characteristics of the signal. The time-series source data collected by each sensor are independent. Mining the main features of the signal from the unknown source data and identifying the main component types in the unlabeled data through the analysis of the main features are the keys to realizing tasks such as condition monitoring, fault identification, and anomaly detection. Therefore, to solve the problem of bearing time-domain fault feature extraction, the present invention proposes a time-domain feature extraction method based on feature wavelet basis shift-invariant sparsity. By analyzing the feature components of the time-domain signal, the operating state of the bearing is determined to judge whether the bearing has a fault. The main steps of this method include: S1 Monitoring the signal y of the bearing operating state; S2 Reshaping the dimension of the monitoring signal y and performing matrix SVD operation to obtain the feature wavelet basis; S3 Using the feature wavelet basis, based on the shift-invariant sparse coding algorithm, sparsely matching the components of the time-domain signal; S4 Performing time-domain analysis and envelope spectrum analysis and comparison on the time-domain sparse result to determine the main components in the signal.

[0007] The steps of this method are as follows:

[0008] S1 Signal acquisition; An acceleration sensor is used to monitor the operating state of the bearing. For the vibration signal y collected by the acceleration sensor, it is mostly a one-dimensional time series with a dimension of N×1, where N is a positive integer;

[0009] S2 Feature wavelet basis extraction; Without changing the elements in the vibration signal y, reshape the dimension of y into a square matrix I with a dimension of n×n, where n is a positive integer satisfying n≥100 and n×n = N; Perform matrix analysis method based on eigenvalue decomposition on this matrix I to obtain the eigenvector corresponding to the maximum eigenvalue of the signal, and use it as the feature wavelet basis denoted as w to match and detect the main features in the signal;

[0010] S3 Shift-invariant sparse time-domain feature extraction; Through the shift-invariant sparse coding algorithm, using the shift invariance of the vibration signal y, based on the basis function with the maximum correlation between the feature wavelet basis and the residual r of each sparse operation, through k iterations, the time-domain sparse representation of the signal y is realized:

[0011] r k+1 = r k - τ max = r k - argmax(r k * w) τ k∈[0,1,2,....k] (Formula 1)

[0012] Where r is the residual of each shift-invariant sparse operation, initialized as r = y, τ maxRepresents the maximum offset value, where * represents the convolution operation. Through k - iteration sparse operations, the final offset is obtained, denoted as: r k+1 ;

[0013] Therefore, the final time - domain signal can be reconstructed and is denoted as:

[0014]

[0015] S4 Sparse result Analysis; Through time - domain feature analysis and envelope spectrum feature analysis, determine the periodic components in the signal; Based on the analysis of the time - domain pulse interval (C) of the signal and the comparison of the envelope spectrum analysis before and after signal analysis, determine the characteristic frequency components in the signal; And through the comparison with the theoretical time - domain pulse interval and theoretical fault frequency data of bearing faults, realize the state monitoring and fault diagnosis of bearings; Theoretical fault calculation methods for inner - ring and outer - ring faults of rolling bearings: The theoretical fault frequency of the outer ring is The theoretical fault frequency of the inner ring is where f0 is the rotational speed of the rotating shaft, m is the number of rolling elements of the rolling bearing, D is the outer diameter of the bearing, d is the inner diameter of the bearing, and θ is the contact angle of the rolling elements; Fault signal time - domain pulse interval calculation method, the outer - ring fault time - domain interval C out = 1 / f out ; The inner - ring fault time - domain interval C in = 1 / f in ; After the signal is processed, confirm whether C is equal to the theoretically calculated C. If they are equal, it indicates a fault. Brief Description of the Drawings

[0016] Figure 1 is a schematic diagram of the analysis process of the invention;

[0017] Figure 2 is the time - domain diagram of the original signal of the outer ring of the faulty bearing;

[0018] Figure 3 is the result of the envelope spectrum analysis of the original signal of the outer ring of the faulty bearing;

[0019] Figure 4 Characteristic wavelet basis waveform diagram;

[0020] Figure 5 is the time - domain sparse result obtained by the present invention;

[0021] Figure 6 is the result of the envelope spectrum analysis of the time - domain sparse result obtained by the present invention. Detailed Embodiments

[0022] The time - domain feature extraction method based on shift - invariant sparsity of characteristic wavelet basis proposed by the present invention, the schematic diagram of its analysis process is asFigure 1 as shown

[0023] S1 signal acquisition: An acceleration sensor is used to monitor the operating state of the bearing outer ring fault. For the vibration signal y collected by the acceleration sensor, it is mostly a one-dimensional time series with a dimension of N×1, where N = 40,000, and the sampling frequency of this signal is 100 kHz. The time-domain diagram of this signal is as Figure 2 shown. The analysis result of the envelope spectrum characteristics of this original signal is as Figure 3 shown

[0024] S2 characteristic wavelet basis extraction. Without changing the elements in the vector y, y is reshaped in matrix dimension and transformed into a square matrix I, a square matrix with a dimension of n×n, and n×n = N is satisfied. A matrix analysis method based on eigenvalue decomposition is performed on this matrix I to obtain the eigenvector corresponding to the maximum eigenvalue of the signal, and it is used as the characteristic wavelet basis w for matching and detecting the main features in the signal

[0025] The singular matrix decomposition operation obtains eigenvalues and eigenvectors, and the definitions of eigenvalues and eigenvectors are as follows

[0026] Ie = μe (Formula 3)

[0027] Among them, I is a square matrix, e is an n-dimensional vector, μ is an eigenvalue of matrix I, and then e is the eigenvector corresponding to the eigenvalue μ of matrix I. The one-dimensional vibration signal data obtained can be folded into a matrix, and the matrix is subjected to eigenvalue decomposition to obtain the eigenvector in the signal, as shown in Formula 4

[0028] I = W∑W -1 (Formula 4)

[0029] Among them: W is an n×n-dimensional matrix spanned by these n eigenvectors, and Σ is an n×n-dimensional matrix with these n eigenvalues as the main diagonal, that is, the n eigenvalues μ1 ≤ μ2 ≤... ≤ μ n of matrix I are obtained, and then the eigenvectors corresponding to these n eigenvalues are expressed as w1, w2... w n , so as to realize the eigenvalue decomposition of the matrix

[0030] Usually, the n eigenvectors are normalized, that is, W satisfies the unitary matrix, that is, the eigenvector satisfies Formula 5

[0031] ||w i ||2 = 1 (Formula 5)

[0032] Among them, ||·||2 represents the Euclidean norm, which refers to the square root of the sum of the squares of all elements in the vector, and matrix W satisfies Formula 6

[0033] WT = W -1 (Equation 6)

[0034] where W T represents the transpose of matrix W, and W -1 represents the inverse of matrix W. Therefore, the signal eigenvalue decomposition can be expressed as:

[0035] I = WΣW T (Equation 7)

[0036] The condition for its equation decomposition is that the matrix is a square matrix with matrix dimension n×n, W is the left singular vector of I, and W T is the right singular vector of I, and Σ is the singular value matrix of I. Therefore, the signal y is folded and arranged to form a square matrix I, and the signal eigenvalue decomposition is performed to obtain the maximum eigenvector as the eigenwavelet basis, denoted as w, as Figure 4 shown;

[0037] S3 Shift-invariant sparse time-domain feature extraction. For bearing fault signals, it has shift invariance, as shown in Equation 8:

[0038] y = x(t - t0) (Equation 8)

[0039] where: y represents the monitored signal, t represents the time shift parameter, t0 represents the initial time node, and x represents the pulse component of the fault. For the periodic fault characteristic impact component of the bearing, it can be approximately expressed as Equation 9:

[0040]

[0041] where: C is the time interval between two adjacent impacts of a fault type; k represents the number of iterations to obtain the vibration impact component.

[0042] The structure of different fault signals is fixed on the time scale, and it is easier to construct a matching sparse dictionary in the time domain; using the eigenwavelet basis of matrix decomposition, the time-domain sparse representation is extracted based on shift-invariant sparse coding;

[0043] For a set of time signals y, which is a finite sequence set with m real-valued variables:

[0044] y = [y1,..., y m T (Equation 10)

[0045] The convolution of the signal y and the eigenwavelet basis w can be expressed as:

[0046]

[0047] where: τ represents the offset in the positive direction. Therefore, for the optimal offset τ​max The maximum value that satisfies its convolution operation, denoted as:

[0048] τ max = argmax(y * w) τ (Equation 12)

[0049] According to the effective convolution result, then τ max can be calculated and updated within time;

[0050] Through the shift-invariant sparse coding algorithm, using the shift invariance of the vibration signal y, based on the basis function with the maximum correlation between the characteristic wavelet basis and the residual r of each sparse operation, through k iterations, the time-domain sparse representation of the signal y is realized;

[0051] r k+1 = r k - τ max = r k - argmax(r k * w) τ k ∈ [0, 1, 2,....k] (Equation 13)

[0052] where r is the residual of each shift-invariant sparse operation, initialized as r = y, and τ max represents the maximum offset value, where * represents the convolution operation. Through k iterations of sparse operations, the final offset is obtained, denoted as: r k+1 ;

[0053] For the given signal y, its time-domain shift-invariant sparse coding minimization model can be expressed as:

[0054]

[0055] According to the iterative process, the finally obtained time-domain signal can be reconstructed, denoted as:

[0056]

[0057] S4 Sparse result Analysis. Through time-domain feature analysis and envelope spectrum feature analysis of, determine the periodic components in the signal. Based on the analysis of the time-domain pulse interval (C) of the signal and the envelope spectrum analysis results before and after signal analysis, as shown in Figure 5 , Figure 6 respectively, thus determining the characteristic frequency components in the signal. And by comparing with the theoretical fault frequency data of bearing faults, the condition monitoring and fault diagnosis of the bearing are realized. The theoretical fault calculation methods for the inner ring fault and outer ring fault of the rolling bearing: The theoretical fault frequency of the outer ring is The theoretical fault frequency of the inner ring is Among them, f0 is the rotational speed of the rotating shaft, m is the number of rolling elements of the rolling bearing, D is the outer diameter of the bearing, d is the inner diameter of the bearing, and θ is the contact angle of the rolling element; the calculation method of the time-domain pulse interval of the fault signal, the time-domain interval C of the outer-ring fault out = 1 / fout; the time-domain interval C of the inner-ring fault in = 1 / f in ; after the signal is processed, confirm whether C is equal to the theoretically calculated C. If they are equal, it means a fault has occurred.

Claims

1. A time-domain feature extraction method based on feature wavelet basis shift-invariant sparsity, characterized in that The steps are as follows: S1 Signal acquisition: An acceleration sensor is used to monitor the operating state of the bearing. For the vibration signal y collected by the acceleration sensor, where it is a one-dimensional time series with a dimension of N×1; S2 Feature wavelet basis extraction: Without changing the elements in y, the dimension of y is reshaped into a matrix, transformed into a square matrix I with a dimension of n×n, where n is a positive integer satisfying n≥100 and n×n = N; A matrix analysis method based on eigenvalue decomposition is performed on this matrix I to obtain the eigenvector corresponding to the maximum eigenvalue of the signal, and it is used as the feature wavelet basis w for matching and detecting features in the signal; Singular matrix decomposition operation to obtain eigenvalues and eigenvectors, where the definitions of eigenvalues and eigenvectors are as follows: Ie = μe (Formula 1) Where, I is a square matrix, e is an n-dimensional vector, μ is an eigenvalue of matrix I, and then e is the eigenvector corresponding to the eigenvalue μ of matrix I; The one-dimensional vibration signal data is obtained, folded into a matrix, and the matrix is eigen-decomposed to obtain the eigenvector in the signal, as shown in Equation (2): I = W∑W -1 (Formula 2) Where: W is an n×n matrix spanned by these n eigenvectors, and Σ is an n×n matrix with these n eigenvalues on the main diagonal, that is, obtaining the n eigenvalues μ1 ≤ μ2 ≤... ≤ μ of matrix I n , then the eigenvectors corresponding to these n eigenvalues are denoted as w1, w2... w n , thereby realizing the eigenvalue decomposition of the matrix; Normalize the n eigenvectors, that is, W satisfies the unitary matrix, that is, the eigenvectors satisfy the following formula: ||w i ||2 = 1 (Equation 3) Where, ||·||2 represents the Euclidean norm, which refers to the square root of the sum of the squares of all elements in the vector, and matrix W satisfies Equation (4): W T = W -1 (Equation 4) Among them, W T represents the transpose of matrix W, and W -1 represents the inverse of matrix W; therefore, the signal eigenvalue decomposition is expressed as: I = W∑W T (Equation 5) The condition for its equation decomposition is that the matrix is a square matrix with matrix dimension n×n. W is the left singular vector of I, and W T is the right singular vector of I, and Σ is the singular value matrix of I. Therefore, the signal y is arranged in a folded manner to form a square matrix I, and the eigenvalue decomposition of the signal is performed to obtain the maximum eigenvector as the eigenwavelet basis, denoted as w; S3 Shift-invariant sparse time-domain feature extraction: The bearing fault signal has shift invariance, as shown in Equation (6): y = x(t - t0) (Formula 6) Where: y represents the monitored signal, t represents the time shift parameter, t0 represents the initial time node, and x represents the pulse component of the fault; For the periodic fault feature impact component of the bearing, it can be approximately expressed as Equation (7): Where: C is the time interval between two adjacent impacts of a fault type; k represents the number of iterations to obtain the vibration impact component; The structure of different fault signals is fixed on the time scale, and it is easier to construct a matching sparse dictionary in the time domain; Using the feature wavelet basis obtained by matrix decomposition, the time-domain sparse representation is extracted based on shift-invariant sparse coding; For a set of time signals y, it is a finite sequence set with m real-valued variables: y = [y1,...,y m T (Formula 8)​ The convolution of signal y and feature wavelet basis w is expressed as: where: τ represents the offset in the positive direction; thus, for the optimal offset τ max satisfies the maximum value of its convolution operation, expressed as: τ max = argmax(y * w) τ (Formula 10) Based on the valid convolution result, τ max is calculated and updated within the time. Through the shift-invariant sparse coding algorithm, using the shift invariance of the vibration signal y, based on the basis function with the maximum correlation between the feature wavelet basis and the residual r of each sparse operation, through k iterations, the time-domain sparse representation of signal y is realized; r k+1 = r k - τ max = r k - argmax(r k * w) τ k ∈ [0, 1, 2,....k] (Formula 11) where r is the residual of each shift-invariant sparse operation, initialized as r = y, and τ max represents the maximum offset value, where * represents the convolution operation; through k iterations of sparse operations, the final offset is obtained, denoted as: r k+1 ; For a given signal y, its time-domain shift-invariant sparse coding minimization model is expressed as: According to the iterative process, the finally obtained time-domain signal can be reconstructed, expressed as: S4 Sparse Result Analysis; By Time-domain feature analysis and envelope spectrum feature analysis, determine the periodic components in the signal; Based on the analysis of the time-domain pulse interval C of the signal and the comparison of the envelope spectrum analysis before and after signal analysis, determine the characteristic frequency components in the signal; And through the comparison with the theoretical time-domain pulse interval and theoretical fault frequency data of bearing faults, realize the condition monitoring and fault diagnosis of bearings; Theoretical fault calculation methods for inner race faults and outer race faults of rolling bearings: The theoretical fault frequency of the outer race is The theoretical fault frequency of the inner race is where f0 is the rotational speed of the rotating shaft, m is the number of rolling elements of the rolling bearing, D is the outer diameter of the bearing, d is the inner diameter of the bearing, and θ is the contact angle of the rolling elements; Fault signal time-domain pulse interval calculation method, outer race fault time-domain interval C out = 1 / f out ; Inner race fault time-domain interval C in = 1 / f in ; After the signal is processed, confirm whether C is equal to the theoretically calculated C. If they are equal, it indicates that a fault has occurred.

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