Noise reduction and rub-impact fault identification method based on information entropy and eigenvalue decomposition

Abstract

The invention discloses a noise reduction and rub-impact fault identification method based on information entropy and eigenvalue decomposition, and relates to the technical field of rotating machinery fault diagnosis, and the method comprises the following steps: obtaining an original discrete vibration signal through a sensor and a data collection card; according to the original discrete vibration signal, constructing a Hankel matrix, and through eigenvalue decomposition, obtaining an eigenvector of the Hankel matrix and an eigenvalue matrix; performing signal reconstruction according to different feature values in the feature value matrix and feature vectors corresponding to the feature values to obtain a reconstructed signal set; and selecting the reconstructed signal with the minimum information entropy in the reconstructed signal set as an optimal reconstructed signal, performing spectrum analysis on the optimal reconstructed signal, and judging the rub-impact fault according to the frequency component. Rub-impact fault recognition is realized through the optimal reconstruction signal determined by the feature value and the feature vector corresponding to the minimum information entropy, the influence of noise interference is reduced, the fault feature information is relatively prominent, and the fault recognition result is more accurate.

Description

Technical Field

[0001] This invention relates to the field of rotating machinery fault diagnosis technology, and in particular to a noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition. Background Technology

[0002] The rapid development of industry has placed higher demands on large rotating machinery, including aero engines. High thrust-to-weight ratio and high operating efficiency have become the overall goals in the design and manufacture of large rotating machinery. As a core component of large rotating machinery, the rotor system experiences a significant increase in the probability of rubbing failures during high-speed operation as the gap between the rotor and stator gradually decreases. Rubbing failures can affect the service life of the machine and even lead to major safety accidents. Therefore, accurate detection of rubbing failures is of great importance. To accurately identify rubbing failures, scholars both domestically and internationally have conducted extensive research and proposed many feasible and efficient solutions, including manual monitoring, temperature measurement, oil sample analysis, acoustic emission detection, and vibration analysis. Among these, vibration analysis, due to its rich fault information, simple testing, and visualization capabilities, has significant advantages in fault diagnosis and has become the most widely used diagnostic method.

[0003] When diagnosing collision and rubbing faults based on vibration signals, the characteristic information of collision and rubbing faults is weak and complex. In addition, the signals are easily interfered with by environmental noise, which makes it difficult to accurately extract the fault characteristic information and identify the fault accurately. Summary of the Invention

[0004] In view of this, the present invention provides a noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition, which solves the problem in the prior art that vibration signals are interfered with by environmental noise, making it difficult to accurately extract fault feature information and identify faults. The present invention provides a noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition, characterized by the following steps:

[0005] Obtain the original discrete vibration signal;

[0006] Based on the original discrete vibration signal, construct a Hankel matrix with an equal number of rows and columns using a preset delay step size;

[0007] The Hankel matrix is ​​decomposed into eigenvalues ​​to obtain the eigenvectors and eigenvalue matrix of the Hankel matrix.

[0008] The signal is reconstructed based on the different eigenvalues ​​in the eigenvalue matrix and the eigenvectors corresponding to the eigenvalues, resulting in a reconstructed signal set.

[0009] The reconstructed signal with the minimum information entropy in the reconstructed signal set is selected as the optimal reconstructed signal. Spectral analysis is performed on the optimal reconstructed signal, and the collision fault is identified based on the frequency components.

[0010] Further, the step of performing eigenvalue decomposition on the Hankel matrix to obtain the eigenvectors and eigenvalue matrix of the Hankel matrix includes:

[0011] By constructing and solving the characteristic polynomial, the eigenvalues ​​are obtained. The mathematical representation of the characteristic polynomial is as follows:

[0012] det(A N×N -γI)=0

[0013] Among them, A N×N Let I be the identity matrix, γ be the eigenvalues ​​of the Hankel matrix, det(·) represent calculating the determinant of the matrix, and N be the number of rows or columns of the Hankel matrix.

[0014] Based on the eigenvalues, the linear equation system is solved using the target formula to obtain the eigenvectors corresponding to the eigenvalues. The target formula is:

[0015] (A N×N -γ i I)*v i =0

[0016] Among them, v i Let γ represent the i-th eigenvector. i Let Γ represent the i-th eigenvalue, and I represent the identity matrix; the eigenvalues ​​are represented as Γ = [γ1, γ2, ..., γ]. i …γ N The eigenvectors corresponding to the eigenvalues ​​are represented as V = [v1, v2, ..., v]. i …v N ];

[0017] Constructing the decomposition matrix: Combining the eigenvectors as column vectors to form an eigenvector matrix: Arranging the eigenvalues ​​to construct a diagonal matrix, where the elements on the diagonal of the diagonal matrix are the eigenvalues ​​of the Hankel matrix;

[0018] Based on the eigenvector matrix and the diagonal matrix, the decomposition matrix of the Hankel matrix is ​​constructed according to a preset formula, the mathematical representation of which is:

[0019] A N×N =Q*D*Q (-1)

[0020] Among them, A N×NLet Q be the Hankel matrix, and D be a diagonal matrix. (-1) Let Q be the inverse matrix.

[0021] Further, the step of reconstructing the signal based on different eigenvalues ​​in the eigenvalue matrix and the corresponding eigenvectors to obtain the reconstructed signal set includes:

[0022] Based on the different eigenvalues ​​in the eigenvalue matrix and the corresponding eigenvectors, the signal is reconstructed according to a preset reconstruction formula to obtain a reconstructed signal set. The mathematical representation of the preset reconstruction formula is as follows:

[0023]

[0024] Where Y(j) is the reconstructed signal obtained from the 1st to the jth eigenvalues ​​and eigenvectors, j represents the jth reconstructed signal, j = 1, 2, ... N.

[0025] Further, the step of selecting the reconstructed signal with the minimum information entropy from the set of reconstructed signals as the optimal reconstructed signal includes:

[0026] Calculate the information entropy I(Y) of the reconstructed signal Y(j). j The formula used is as follows:

[0027]

[0028] M: represents Y j The number of possible states, p(Y) jm ) represents Y j The probability of the m-th state occurring.

[0029] The reconstructed signal corresponding to the minimum information entropy is selected as the optimal reconstructed signal.

[0030] Furthermore, the process of performing spectral analysis on the optimal reconstructed signal and identifying the rubbing fault based on its frequency components is as follows:

[0031] Spectral analysis is performed on the optimal reconstructed signal to obtain its frequency components;

[0032] The frequency component is matched with the characteristic frequency of the collision fault. If the frequency component matches the characteristic frequency of the collision fault, it is determined that the equipment corresponding to the original discrete vibration signal has a collision fault.

[0033] If the frequency component does not match the characteristic frequency of the rubbing fault, then it is determined that the device corresponding to the original discrete vibration signal does not have a rubbing fault.

[0034] This invention relates to a noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition. The method acquires raw discrete vibration signals using sensors and a data acquisition card. Based on the raw discrete vibration signals, a Hankel matrix with an equal number of rows and columns is constructed using a preset delay step size. Eigenvalue decomposition is performed on the Hankel matrix to obtain eigenvectors and eigenvalue matrices. The raw discrete vibration signals are reconstructed based on the different eigenvalues ​​and their corresponding eigenvectors in the eigenvalue matrix, resulting in a reconstructed signal set. The reconstructed signal with the minimum information entropy is selected as the optimal reconstructed signal from the reconstructed signal set. Spectral analysis is performed on the optimal reconstructed signal, and collision faults are determined based on its frequency components. Since using the eigenvalues ​​and eigenvectors of a signal as features is unaffected by linear or nonlinear loads and exhibits high stability, and information with obvious amplitude-frequency characteristics often corresponds to larger eigenvalues, using eigenvalues ​​and eigenvectors as signal features for fault identification reduces the impact of environmental interference and makes the identification results more accurate. Simultaneously, since information entropy can measure the overall uncertainty of information—that is, the larger the information entropy value, the more chaotic the system, the more interference information exists, and the more difficult it is to extract the fault feature information hidden within—the eigenvalues ​​of the constructed Hankel were selected based on the criterion of minimum information entropy. The signal was then reconstructed based on the selected eigenvalues ​​and their corresponding eigenvectors to obtain the optimal reconstructed signal, i.e., the reconstructed signal with the least interference information, thus reducing the impact of interference on fault identification. Attached Figure Description

[0035] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a schematic diagram summarizing the process of a noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition in an embodiment of the present invention.

[0037] Figure 2 This is a detailed flowchart illustrating another noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition in an embodiment of the present invention.

[0038] Figure 3 This is a diagram of the original vibration signal in an embodiment of the present invention;

[0039] Figure 4 This is a spectrum diagram of the original vibration signal in an embodiment of the present invention;

[0040] Figure 5 This is an information entropy map of the signal reconstructed based on different feature values ​​in an embodiment of the present invention;

[0041] Figure 6 This is a time-domain diagram of the reconstructed signal in an embodiment of the present invention;

[0042] Figure 7 This is a spectrum diagram of the reconstructed signal in an embodiment of the present invention;

[0043] Figure 8 To utilize the Singular Value Difference Spectrum (SVDS) comparison method for... Figure 3 The time-domain image obtained after denoising the original vibration signal;

[0044] Figure 9 for Figure 8 Spectrum diagram of the mid-time domain plot;

[0045] Figure 10 for Figure 7 A magnified view of the spectrum of the reconstructed signal. Detailed Implementation

[0046] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0047] Figure 1 This is a schematic diagram summarizing the process of a noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition in an embodiment of the present invention.

[0048] Figure 2 This is a detailed flowchart illustrating another noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition in an embodiment of the present invention.

[0049] An embodiment of the present invention provides a noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition, which specifically includes the following steps:

[0050] S1: Obtain the original discrete vibration signal;

[0051] S2: Based on the original discrete vibration signal, construct a Hankel matrix with an equal number of rows and columns using a preset delay step size;

[0052] S3: Perform eigenvalue decomposition on the Hankel matrix to obtain the eigenvectors and eigenvalue matrix of the Hankel matrix;

[0053] S4: Reconstruct the signal based on the different eigenvalues ​​in the eigenvalue matrix and the eigenvectors corresponding to the eigenvalues ​​to obtain a reconstructed signal set;

[0054] S5: Select the reconstructed signal with the minimum information entropy from the set of reconstructed signals as the optimal reconstructed signal, perform spectral analysis on the optimal reconstructed signal, and identify the collision fault based on the frequency components.

[0055] The steps S1 / S2 / S3 / S4 / S5 are executed sequentially;

[0056] In S1, the acquisition of the original discrete vibration signal is achieved through sensors and a data acquisition card, as detailed below:

[0057] The original discrete vibration signal U(n) = (u1, u2, u3) is obtained using an accelerometer and a data acquisition card. , …u 2N ), where 2N is the original length of the original discrete vibration signal.

[0058] In S2, based on the original discrete vibration signal and with a preset delay step size, a Hankel matrix with an equal number of rows and columns is constructed, as follows:

[0059] For a vibration signal U(n), taking a delay step of 1 as an example, constructing the Hankel matrix yields an m×n matrix A. m×n As shown in the following formula;

[0060]

[0061] Where 2N = m + n + 1, and m and n represent the number of rows (embedding dimension) and columns of the matrix, respectively. Hankel matrix A m×n The number of rows must be equal to the number of columns, i.e., m = n, denoted as a. N×N .

[0062] S3 involves eigenvalue decomposition of the Hankel matrix to obtain its eigenvectors and eigenvalue matrix. The specific process includes the following:

[0063] S31: By constructing and solving the characteristic polynomial, the eigenvalues ​​are obtained. The mathematical representation of the characteristic polynomial is as follows:

[0064] det(A N×N -γI)=0

[0065] Among them, A N×N Let I be the identity matrix, γ be the eigenvalues ​​of the Hankel matrix, det(·) represent calculating the determinant of the matrix, and N be the number of rows or columns of the Hankel matrix.

[0066] S32: Based on the eigenvalues, solve the system of linear equations using the target formula to obtain the eigenvectors corresponding to the eigenvalues. The target formula is:

[0067] (A N×N -γ i I)*v i =0

[0068] Among them, v i Let γ represent the i-th eigenvector. i Let Γ represent the i-th eigenvalue, and I represent the identity matrix; the eigenvalues ​​are represented as Γ = [γ1, γ2, ..., γ]. i …γ N The eigenvectors corresponding to the eigenvalues ​​are represented as V = [v1, v2, ..., v]. i …v N ];

[0069] S33: Construct the decomposition matrix. Combine the eigenvectors as column vectors to form an eigenvector matrix: arrange the eigenvalues ​​to construct a diagonal matrix, where the elements on the diagonal of the diagonal matrix are the eigenvalues ​​of the Hankel matrix;

[0070] Based on the eigenvector matrix and the diagonal matrix, the decomposition matrix of the Hankel matrix is ​​constructed according to a preset formula, the mathematical representation of which is:

[0071] A N×N =Q*D*Q (-1)

[0072] Among them, A N×N Let Q be the Hankel matrix, and D be a diagonal matrix. (-1) Let represent the inverse matrix Q. The process of obtaining the diagonal matrix D is as follows:

[0073] Solving for the eigenvector v i For each eigenvalue γ i Solve the system of linear equations according to the following formula to obtain the corresponding eigenvector v. i :

[0074] (A N×N -γ i I)*v i =0

[0075] Construct the eigenvector matrix: Create a matrix containing all eigenvectors v1, v2, v3, ..., v N As column vectors, they are combined to form the eigenvector matrix Q:

[0076] Q = [v1, v2, v3, ..., v N ]

[0077] Constructing a diagonal matrix: Arrange all eigenvalues ​​sequentially to form a diagonal matrix D:

[0078]

[0079] The process described in S4 for reconstructing the original discrete vibration signal based on different eigenvalues ​​in the eigenvalue matrix and the corresponding eigenvectors to obtain the reconstructed signal set is as follows:

[0080] The signal is reconstructed based on different eigenvalues ​​and their corresponding eigenvectors to obtain N reconstructed signals Y, where Y = [Y1, Y2, ..., Y]. i …Y N ];Y i This represents the reconstructed signal obtained based on the eigenvalues ​​and eigenvectors from the 1st to the 1st eigenvalue;

[0081] Based on the matrix after eigenvalue decomposition, signal reconstruction is performed, and the reconstructed vibration signal Y(i) is calculated as follows:

[0082]

[0083] Where Y(j) is the reconstructed signal obtained from the first to the ith eigenvalues ​​and eigenvectors, and j represents the j-th reconstructed signal.

[0084] In S5, the reconstructed signal with the minimum information entropy in the reconstructed signal set is selected as the optimal reconstructed signal. Spectral analysis is then performed on the optimal reconstructed signal, and the identification of the rubbing fault is achieved based on the frequency components, as follows:

[0085] S511: Calculate the probability of each reconstructed vibration signal, taking signal Y(i) as an example, Y(i) = (δ 1, δ 2, δ 3, …δ N Let the probabilities of each signal point be denoted as q(δ1), q(δ2), q(δ3), ..., q(δ...). N );

[0086] S512: The information structure S of signal Y(i) is represented as:

[0087]

[0088] S513: Calculate the information entropy I(Y) of the reconstructed signal Y(i). i ):

[0089]

[0090] S514: Calculate the information entropy I(Y) of all reconstructed signals, I(Y) = [[I(Y1),I(Y2),…I(Y3)], N )).

[0091] Choose the minimum information entropy I(Y) k The corresponding reconstructed signal Y) k This is the optimal reconstructed signal.

[0092] The process of selecting the reconstructed signal with the minimum information entropy from the reconstructed signal set as the optimal reconstructed signal, performing spectral analysis on the optimal reconstructed signal, and identifying the collision fault based on the frequency components is as follows:

[0093] S521: Perform spectral analysis on the optimal reconstructed signal to obtain the frequency components of the optimal reconstructed signal;

[0094] S522: Match the frequency component with the characteristic frequency of the collision fault. If the frequency component matches the characteristic frequency of the collision fault, then determine that the equipment corresponding to the original discrete vibration signal has a collision fault.

[0095] S523: If the frequency component does not match the characteristic frequency of the rubbing fault, then it is determined that the device corresponding to the original discrete vibration signal does not have a rubbing fault.

[0096] Since existing technologies have accurately extracted the characteristic information of rotating machinery rubbing faults under various operating conditions, the fault can be identified by matching the frequency components of the optimal reconstructed signal with the characteristic information of rotating machinery rubbing faults under various operating conditions.

[0097] In one possible implementation, the noise reduction and collision fault identification method based on information entropy and feature decomposition proposed in this embodiment is compared with the Singular Value Difference Spectrum (SVDS) method. Specifically, the method obtains, for example... Figure 3 The original vibration signal diagram shown and as follows Figure 4 The spectrum of the original vibration signal image, according to an embodiment of the present invention, is used to calculate the information entropy of the reconstructed signal based on different feature values ​​using a noise reduction and collision fault identification method based on information entropy and feature decomposition. Figure 5 As shown.

[0098] according to Figure 5 It can be seen that the information entropy reaches its minimum when the number of eigenvalues ​​is 66. Therefore, these 66 eigenvalues ​​and their corresponding eigenvectors are selected for signal reconstruction, resulting in the following: Figure 6 The time domain of the reconstructed signal shown and as Figure 7 The spectrum of the reconstructed signal, for Figure 7 By magnifying the local area, we can obtain Figure 8 ;

[0099] Using the Singular Value Difference Spectrum (SVDS) comparison method to Figure 3 The original vibration signal is denoised to obtain the following result: Figure 9 The time-domain diagram shown and as Figure 10 The spectrum diagram shown.

[0100] For the sake of brevity, the f in the tables and figures of this invention is omitted. r Both represent rotational frequency, F rf All represent the characteristic frequencies of the rubbing fault. The relationship between the typical frequency components of the optimal reconstructed signal and the rubbing fault is shown in Table 1:

[0101] Table 1 Typical frequencies and their correspondence with rubbing failures

[0102]

[0103] Combination Figure 7 , Figure 8 As shown in Table 1, the spectrum of the signal obtained by the method proposed in this invention has the following characteristics:

[0104] Noise interference was effectively suppressed; typical characteristic frequency information corresponding to collision and rubbing faults was effectively extracted (as shown in the figure). (Note), including 1073Hz (2F) rf ), 1611Hz (3F) rf ), 2145Hz (4F) rf ); At the characteristic frequency of the rubbing fault and its harmonics, there exists a frequency of f r Or its modulation sidebands spaced at multiples of its frequency (marked with "☆"), specifically including 654.3Hz (F rf +7f r ), 2162Hz (4F) rf +f r ), 2178Hz (4F) rf +2f r ), 2646Hz (5F) rf -2f r ).

[0105] right Figure 10 Analysis of Table 1 reveals that while the Singular Value Difference Spectrum (SVDS) method can resist noise interference, fault characteristic frequencies are also filtered out. Among them, 880Hz (52f)... r This frequency component has no direct correlation with the characteristic frequency of collision and friction faults, which is not conducive to the accurate identification and judgment of collision and friction faults.

[0106] In summary, the fault identification method based on the noise reduction algorithm of information entropy and eigenvalue decomposition proposed in this invention can accurately extract the features of collision and friction faults and accurately identify the faults, and has excellent engineering application value.

[0107] The above description discloses only preferred embodiments of the present invention and should not be construed as limiting the scope of the present invention. Therefore, equivalent variations made in accordance with the claims of the present invention are still within the scope of the present invention.

Claims

1. A noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition, characterized in that, Includes the following steps: Obtain the original discrete vibration signal; Based on the original discrete vibration signal, construct a Hankel matrix with an equal number of rows and columns using a preset delay step size; The Hankel matrix is ​​decomposed into eigenvalues ​​to obtain the eigenvectors and eigenvalue matrix of the Hankel matrix. The signal is reconstructed based on the different eigenvalues ​​in the eigenvalue matrix and the eigenvectors corresponding to the eigenvalues, resulting in a reconstructed signal set. The reconstructed signal with the minimum information entropy in the reconstructed signal set is selected as the optimal reconstructed signal. Spectral analysis is performed on the optimal reconstructed signal, and the collision fault is identified based on the frequency components.

2. The noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition according to claim 1, characterized in that, The process of performing eigenvalue decomposition on the Hankel matrix to obtain the eigenvectors and eigenvalue matrix of the Hankel matrix is ​​as follows: By constructing and solving the characteristic polynomial, the eigenvalues ​​are obtained. The mathematical representation of the characteristic polynomial is as follows: it(A N×N -γI)=0 Among them, A N×N Let I be the identity matrix, γ be the eigenvalues ​​of the Hankel matrix, det(·) represent calculating the determinant of the matrix, and N be the number of rows or columns of the Hankel matrix. Based on the eigenvalues, the linear equation system is solved using the target formula to obtain the eigenvectors corresponding to the eigenvalues. The target formula is: (A N×N -c i I*v i =0 Among them, v i Let γ represent the i-th eigenvector. i Let Γ represent the i-th eigenvalue, and I represent the identity matrix; the eigenvalues ​​are represented as Γ = [γ1, γ2, ..., γ]. i …γ N The eigenvectors corresponding to the eigenvalues ​​are represented as V = [v1, v2, ..., v]. i …v N ]; Construct a decomposition matrix by combining the eigenvectors as column vectors into an eigenvector matrix: arrange the eigenvalues ​​to construct a diagonal matrix, where the elements on the diagonal of the diagonal matrix are the eigenvalues ​​of the Hankel matrix; Based on the eigenvector matrix and the diagonal matrix, the decomposition matrix of the Hankel matrix is ​​constructed according to a preset formula, the mathematical representation of which is: A N×N =Q*D*Q (-1) Among them, A N×N Let Q be the Hankel matrix, and D be a diagonal matrix. (-1) Let Q be the inverse matrix.

3. The noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition according to claim 1, characterized in that, The process of reconstructing the signal based on different eigenvalues ​​in the eigenvalue matrix and the corresponding eigenvectors to obtain the reconstructed signal set includes: Based on the different eigenvalues ​​in the eigenvalue matrix and the corresponding eigenvectors, the signal is reconstructed according to a preset reconstruction formula to obtain a reconstructed signal set. The mathematical representation of the preset reconstruction formula is as follows: Where Y(j) is the reconstructed signal obtained from the 1st to the jth eigenvalues ​​and eigenvectors, j represents the jth reconstructed signal, j = 1, 2, ... N.

4. The noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition according to claim 1, characterized in that, The step of selecting the reconstructed signal with the minimum information entropy from the reconstructed signal set as the optimal reconstructed signal includes: The information entropy I(Y) of the reconstructed signal Y(i) is calculated using the following formula: M: represents Y j The number of possible states, p(Y) jm ) represents Y j The probability of the m-th state occurring; The reconstructed signal corresponding to the minimum information entropy is selected as the optimal reconstructed signal.

5. The noise reduction and collision fault identification method based on information entropy and eigenvalue decomposition according to claim 1, characterized in that, The process of performing spectral analysis on the optimal reconstructed signal and identifying the rubbing fault based on its frequency components is as follows: Spectral analysis is performed on the optimal reconstructed signal to obtain its frequency components; The frequency component is matched with the characteristic frequency of the collision fault. If the frequency component matches the characteristic frequency of the collision fault, it is determined that the equipment corresponding to the original discrete vibration signal has a collision fault. If the frequency component does not match the characteristic frequency of the rubbing fault, then it is determined that the device corresponding to the original discrete vibration signal does not have a rubbing fault.

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