Bearing fault identification method based on SVD and variance

Abstract

The invention provides a bearing fault identification method based on SVD and variance, and the method comprises the following steps: S1, carrying out the decomposition of a collected vibration signal through a signal decomposition algorithm, and obtaining a plurality of component signals; s2, constructing a Hankel matrix of each component signal; s3, performing singular value decomposition on the constructed Hankel matrix; s4, determining the effective length / optimal scale of the variance sequence by calculating the signal evaluation index of the new signal; s5, according to the effective length / optimal scale of the obtained variance sequence, constructing an optimal Hankel matrix for each component signal in sequence by taking variance as a criterion; and S6, reconstructing each component signal based on the constructed optimal Hankel matrix, and carrying out spectrum analysis on each noise reduction signal obtained after reconstruction to carry out fault identification on the bearing. Noise in the vibration signals can be reduced, fault information is highlighted, effective detection of the bearing state and accurate judgment of the composite fault type can be achieved, and the method has excellent engineering application value.

Description

Technical Field

[0001] The present invention relates to the technical field of rolling bearing fault diagnosis, and in particular to a bearing fault identification method based on SVD and variance. Background Art

[0002] Rotating machinery is widely used in the industrial field. The health of its key component, rolling bearing, will directly affect the operating status of the equipment. Since the working environment of the equipment is usually very harsh, and the key components of the rolling bearing are in high temperature and high speed operation for a long time, it is very easy to fail. At the same time, the working performance of the rolling bearing will gradually deteriorate with the increase of service life, which will have a significant impact on the safety of the entire system and the stability of the equipment operation. Therefore, accurate identification and diagnosis of rolling bearing faults are of great significance to the reliable operation of the equipment.

[0003] When a rolling bearing fails, it is easily disturbed by the surrounding equipment and environmental noise, which greatly increases the difficulty of extracting fault feature information. When the equipment fails, the vibration signal has strong nonlinear and non-stationary characteristics. Singular value decomposition (SVD), as a simple nonlinear signal processing method, has unique advantages in denoising and feature extraction and is widely used in signal fault diagnosis. When using SVD to reduce the noise of the signal, the key is how to use the signal to construct a suitable matrix and determine the effective singular value.

[0004] At present, the most widely used matrix form in SVD denoising is the Hankel matrix. The conventional way to select singular values ​​is to divide the boundaries of singular values ​​by a certain standard, and then select all singular values ​​before the boundaries for signal reconstruction. Among them, the most common is the singular value difference spectrum, which determines the boundary between useful signals and noise signals by finding mutation points. However, this method also has certain limitations. Generally, information with obvious signal amplitude-frequency characteristics often corresponds to larger singular values. When the collected signal contains interference information with obvious amplitude-frequency characteristics, the selected larger singular values ​​are often mixed with a large amount of interference information. At this time, this method will not be able to extract the required feature information. At the same time, it was found in the application process that if the noise is large or the effective order of the determined singular value is inaccurate, the SVD noise reduction effect is usually not ideal, and the extraction of signal fault feature information will also be more difficult. Summary of the invention

[0005] In view of this, the purpose of the present invention is to propose a bearing fault identification method based on SVD and variance to solve the technical problem that the existing SVD denoising method has poor denoising effect when the collected signal contains interference information with obvious amplitude-frequency characteristics.

[0006] The technical means adopted by the present invention are as follows:

[0007] A bearing fault identification method based on SVD and variance includes the following steps:

[0008] S1. Decompose the collected vibration signal using the signal decomposition algorithm to obtain several component signals, which are denoted as a1(n), a2(n), ..., a k (n), n = 1, 2, ... Nm, Nm is the signal length;

[0009] S2, calculate each component signal a1(n)-a k (n) The signal evaluation index of the signal after denoising the singular value sequence of different scales is used to construct the optimal scale d corresponding to the multi-scale singular value sequence. optimal ;

[0010] S3, based on the optimal scale d of each component signal obtained optimal , construct the multi-scale singular value sequence of each component signal in turn based on the variance as the criterion;

[0011] S4. Reconstruct the signal based on the constructed new multi-scale singular value sequence, perform spectral analysis on the reconstructed denoised signal, and identify bearing faults.

[0012] Furthermore, in S1, the original discrete signal x(t) is decomposed into k component signals a1(n), a2(n), ..., a k (n), where: a k (n) represents the kth component, n=1, 2, ... Nm, Nm is the signal length.

[0013] Further, S2 includes the following steps:

[0014] S21, input a certain component signal;

[0015] S22, for a discrete one-dimensional component signal, a(n) = (x 1, x 2, x3,…x N ) indicates that the Hankel matrix is ​​constructed, with 1 as the delay step, and the corresponding m×n matrix is ​​obtained:

[0016]

[0017] Where: n = N-m + 1;

[0018] S23. Since there is an orthogonal matrix U∈R m×m and V∈R n×n So that:

[0019] A=USV T (2)

[0020] Formula (1) is the singular value decomposition of the matrix, where U is the left singular value matrix, V is the right singular value matrix, and S is the singular value matrix, where:

[0021] S1=diag(σ1,σ2,σ3,…σ r ) (3)

[0022] And σ1≥σ2≥σ3≥…≥σ r ≥0, r is the rank of matrix A;

[0023] S24, construct a multi-scale singular value sequence for the component signal with scale d, d = 1, 2, ... D, D is the set upper limit of the scale, the singular value sequence S1 = [σ1, σ2, σ3, ... σ r ], q j is the average value of the singular values ​​within the jth segment, j is the number of segments, j = 1, 2, ... r + 1-d, d is the scale of the selected singular value, d = 1, 2, ... D, D is the upper limit of the set scale, then:

[0024]

[0025] Sequence c j is the variance of the singular value sequence within the jth segment, then the variance of all singular value sequences C = {c1, c2, c3, ... c r+1-d}, C is the newly constructed multi-scale singular value sequence;

[0026] S25. From equation 1 and equation 2, we can know that A can be expressed as:

[0027]

[0028] Where: u i and v i Represent the column vectors of the i-th column of U and V respectively;

[0029] S26, from formula 4, we can know that each singular value σ i Corresponding to a matrix component A i

[0030]

[0031] The original signal is denoised, and the denoised signal X(t) is converted into a series of component superpositions, namely:

[0032]

[0033] Signal sequence component P i Ai Transformation results;

[0034] S27, repeat S24 to S26, and calculate the signal evaluation index of the noise reduction signal X(t) obtained at different scales;

[0035] S28, storing different scales d and corresponding signal evaluation indicators into matrix B;

[0036] S29. Select the scale corresponding to the minimum or maximum signal evaluation index in matrix B, which is the optimal scale corresponding to the component signal.

[0037] Furthermore, in S3, a multi-scale singular value sequence is constructed for each component signal in turn using the variance as a criterion.

[0038] Further, in S4, the signal is reconstructed according to the constructed new multi-scale singular value sequence, and the rolling bearing fault is identified according to the spectrum analysis of the noise reduction signal obtained after the reconstruction; specifically:

[0039] For the component signals a1(n), a2(n), ..., a k (n) performing spectrum analysis on the signal after noise reduction; extracting prominent characteristic frequencies based on the spectrum analysis, and performing feature extraction and fault identification on the rolling bearing fault by calculating whether the prominent frequencies contain characteristic frequencies that can reflect the bearing fault obtained by theoretical calculation of the group of data.

[0040] The present invention also provides a storage medium, which includes a stored program, wherein when the program is run, any one of the above-mentioned methods for bearing fault identification based on SVD and variance is executed.

[0041] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes any one of the above-mentioned methods for bearing fault identification based on SVD and variance through the computer program.

[0042] Compared with the prior art, the present invention has the following advantages:

[0043] The method of the present invention utilizes a signal decomposition algorithm to decompose the vibration signal when a rolling bearing fails.

[0044] Considering the characteristic that the greater the difference between the singular values ​​of the signal, the more obvious the characteristic information is, the present invention utilizes the sensitivity of variance to the change of signal strength, proposes a method for constructing a Hankel matrix based on the variance characteristics of the signal by replacing the singular value itself with the variance of the signal singular value. In the process of constructing the Hankel matrix, the signal evaluation index can be used to effectively measure the regularity of the signal and detect the characteristics of the weak change of the signal, and a method for determining the effective length (optimal scale) of the variance sequence by the signal evaluation index is proposed.

[0045] The present invention reconstructs each component signal according to the reconstructed Hankel matrix to achieve signal noise reduction, and describes the fault characteristic information of the rolling bearing and identifies the fault type according to the spectrum analysis of the noise-reduced signal. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0047] Figure 1 Flowchart of the optimal scale determination method for multi-scale singular value sequences.

[0048] Figure 2 This is a block diagram of the bearing fault identification method of the present invention.

[0049] Figure 3 a is a time domain diagram of the original signal in an embodiment of the present invention; Figure 3 b is Figure 3 The spectrum of a; Figure 3 c is Figure 3 a Each component after VMD; Figure 3 d is Figure 3 The spectrum of c; Figure 3 e is the sample entropy value of each component at different scales; Figure 3 f is Figure 3 e is a partial enlarged view; Figure 3 g is the time domain image after denoising based on the proposed method; Figure 3 h is Figure 3 The spectrum of g. DETAILED DESCRIPTION

[0050] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0051] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0052] like Figure 1 As shown, the present invention provides a bearing fault identification method based on SVD and variance, and the specific implementation steps are as follows:

[0053] S1. Decompose the collected vibration signal using the signal decomposition algorithm to obtain several component signals, which are denoted as a1(n), a2(n), ..., a k (n), n = 1, 2, ... Nm, Nm is the signal length;

[0054] S2, calculate each component signal a1(n)-a k (n) The signal evaluation index of the signal after denoising the singular value sequence of different scales is used to construct the optimal scale d corresponding to the multi-scale singular value sequence. optimal ;

[0055] S3, based on the optimal scale d of each component signal obtained optimal , construct the multi-scale singular value sequence of each component signal in turn based on the variance as the criterion;

[0056] S4. Reconstruct the signal based on the constructed new multi-scale singular value sequence, perform spectral analysis on the reconstructed denoised signal, and identify bearing faults.

[0057] S2 is specifically:

[0058] S21, input a certain component signal;

[0059] S22, for a discrete one-dimensional component signal, a(n) = (x1, x2, x 3, …x N ) indicates that the Hankel matrix is ​​constructed, with 1 as the delay step, and the corresponding m×n matrix is ​​obtained:

[0060]

[0061] Where: n = N-m + 1;

[0062] S23. Since there is an orthogonal matrix U∈R m×m and V∈R n×n So that:

[0063] A=USV T (2)

[0064] Formula (1) is the singular value decomposition of the matrix, where U is the left singular value matrix, V is the right singular value matrix, and S is the singular value matrix, where:

[0065] S1=diag(σ1,σ2,σ3,…σ r ) (3)

[0066] And σ1≥σ2≥σ3≥…≥σ r ≥0, r is the rank of matrix A;

[0067] S24, construct a multi-scale singular value sequence for the component signal with scale d, d = 1, 2, ... D, D is the set upper limit of the scale, the singular value sequence S1 = [σ1, σ2, σ3, ... σ r ], q j is the average value of the singular values ​​within the jth segment, j is the number of segments, j = 1, 2, ... r + 1-d, d is the scale of the selected singular value, d = 1, 2, ... D, D is the upper limit of the set scale, then:

[0068]

[0069] Sequence c j is the variance of the singular value sequence within the jth segment, then the variance of all singular value sequences C = {c1, c2, c 3, ……c r+1-d}, C is the newly constructed multi-scale singular value sequence;

[0070] S25. From equation 1 and equation 2, we can know that A can be expressed as:

[0071]

[0072] Where: ui and v i Represent the column vectors of the i-th column of U and V respectively;

[0073] S26, from formula 4, we can know that each singular value σ i Corresponding to a matrix component A i

[0074]

[0075] The original signal is denoised, and the denoised signal X(t) is converted into a series of component superpositions, namely:

[0076]

[0077] Signal sequence component P i A i Transformation results;

[0078] S27, repeat S24 to S26, and calculate the signal evaluation index of the noise reduction signal X(t) obtained at different scales;

[0079] S28, storing different scales d and corresponding signal evaluation indicators into matrix B;

[0080] S29. Select the scale corresponding to the minimum (or maximum) signal evaluation index in matrix B as the optimal scale corresponding to the component signal (different signal evaluation indexes have different ways of selecting the minimum and maximum).

[0081] The specific idea of ​​the proposed method is shown in the attached figure. Figure 2 According to the calculation formula of bearing fault characteristic frequency in Table 1, the rolling bearing fault characteristic information is extracted and its fault type is identified.

[0082] Table 1 Parameters represented by each symbol and calculation formula of each characteristic frequency of rolling bearing

[0083]

[0084] Example

[0085] The signal decomposition algorithm of the embodiment of the present invention takes variational mode decomposition (VMD) as an example, and takes the decomposition level as 4 and the penalty factor as 2000 as an example; the signal evaluation index takes sample entropy as an example; the spectral analysis takes frequency spectrum analysis as an example; but it is not limited to the decomposition algorithm and the spectral analysis method.

[0086] Take the case of a rolling bearing with a composite fault of the inner ring and rolling element as an example. The rotation speed corresponding to this composite fault is 1526r / min (rotation frequency f r=25.45Hz). According to the calculation formula of bearing fault characteristic frequency in Table 1 and the bearing geometric dimensions, the characteristic frequencies of the bearing faults at this time are calculated as follows: f b =44.32Hz, f i =112.81Hz, f o =65.31Hz, f c =9.33Hz.

[0087] Figure 3 (a) is the time domain diagram of the original signal; Figure 3 (b) Figure 3 (a) Spectrum diagram of the experiment. Figure 3 (c) Figure 3 (a) Intrinsic mode components (IMFs) obtained after VMD. Figure 3 (d) Figure 3 (c) Spectrum diagram. Figure 3 (e) is the sample entropy value of the corresponding IMF1-IMF4 signal after singular value denoising at different scales. Figure 3 (f) Figure 3 (e) is a partial enlarged view of Figure 3 (f) It can be found that the optimal scales corresponding to IMF1-IMF4 are: IMF1→2, IMF2→2, IMF3→5, IMF4→2. Figure 3 (g) is the time domain of the signal obtained by IMF1→IMF4 according to the proposed method. Figure 3 (h) Figure 3 (g) Normalized spectrum diagram.

[0088] analyze Figure 3 (h) It can be found that when the fault types are different, the proposed method has the following characteristics:

[0089] The noise component in the spectrum is greatly reduced and the characteristic frequency is further highlighted.

[0090] The frequency components corresponding to the bearing fault type can be obtained. Specifically, Figure 3 In (h), the typical rolling element fault characteristic frequency (f b ) and its multiples; it can be found that the inner race fault characteristic frequency (f i ) and its multiples. Figure 3 The corresponding relationship between each typical frequency component in (h) and the characteristic frequency and fault type of the bearing fault is shown in Table 2.

[0091] Table 2 Figure 3 (h) Relationship between bearing characteristic frequency and fault type (combined fault of inner ring and rolling element)

[0092]

[0093] Analysis Table 2 Figure 3 (a)~ Figure 3 (g) It can be found that the proposed method can effectively reduce the noise while accurately extracting the prominent characteristic frequencies corresponding to the inner ring fault and rolling element fault of the bearing, which is completely consistent with the composite fault type of the bearing.

[0094] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein by equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A bearing fault identification method based on SVD and variance, characterized in that: The steps include: S1. Decompose the collected vibration signal using the signal decomposition algorithm to obtain several component signals, which are denoted as a1(n), a2(n), ..., a k (n), n = 1, 2, ... Nm, Nm is the signal length; S2, calculate each component signal a1(n)-a k (n) The signal evaluation index of the signal after denoising the singular value sequence of different scales is used to construct the optimal scale d corresponding to the multi-scale singular value sequence. optimal ; S3, based on the optimal scale d of each component signal obtained optimal , construct the multi-scale singular value sequence of each component signal in turn based on the variance as the criterion; S4. Reconstruct the signal based on the constructed new multi-scale singular value sequence, perform spectral analysis on the reconstructed denoised signal, and identify bearing faults.

2. The bearing fault identification method based on SVD and variance according to claim 1 is characterized in that: In S1, the original discrete signal x(t) is decomposed into k component signals a1(n), a2(n), ..., a k (n), where: a k (n) represents the kth component, n=1, 2, ... Nm, Nm is the signal length.

3. The bearing fault identification method based on SVD and variance according to claim 1 is characterized in that: S2 includes the following steps: S21, input a certain component signal; S22, for a discrete one-dimensional component signal, a(n) = (x1, x2, x3, ... x N ) indicates that the Hankel matrix is ​​constructed, with 1 as the delay step, and the corresponding m×n matrix is ​​obtained: Where: n = N-m + 1; S23. Since there is an orthogonal matrix U∈R m×m and V∈R n×n So that: A=USV T (2) Formula (1) is the singular value decomposition of the matrix, where U is the left singular value matrix, V is the right singular value matrix, and S is the singular value matrix, where: And σ1≥σ2≥σ3≥…≥σ r ≥0, r is the rank of matrix A; S24, construct a multi-scale singular value sequence for the component signal with scale d, d = 1, 2, ... D, D is the set upper limit of the scale, the singular value sequence S1 = [σ1, σ2, σ3, ...σ r ], q j is the average value of the singular values ​​within the jth segment, j is the number of segments, j = 1, 2, ... r + 1-d, d is the scale of the selected singular value, d = 1, 2, ... D, D is the upper limit of the set scale, then: Sequence c j is the variance of the singular value sequence within the jth segment, then the variance of all singular value sequences C = {c1, c2, c3, ... c r+1-d }, C is the newly constructed multi-scale singular value sequence; S25. From equation 1 and equation 2, we can know that A can be expressed as: Where: u i and v i Represent the column vectors of the i-th column of U and V respectively; S26, from formula 4, we can know that each singular value σ i Corresponding to a matrix component A i The original signal is denoised, and the denoised signal X(t) is converted into a series of component superpositions, namely: Signal sequence component P i A i Transformation results; S27, repeat S24 to S26, and calculate the signal evaluation index of the noise reduction signal X(t) obtained at different scales; S28, storing different scales d and corresponding signal evaluation indicators into matrix B; S29. Select the scale corresponding to the minimum or maximum signal evaluation index in matrix B, which is the optimal scale corresponding to the component signal.

4. The bearing fault identification method based on SVD and variance according to claim 1 is characterized in that: In S3, a multi-scale singular value sequence is constructed for each component signal in turn using the variance as a criterion.

5. The bearing fault identification method based on SVD and variance according to claim 1 is characterized in that: In S4, the signal is reconstructed according to the constructed new multi-scale singular value sequence, and the rolling bearing fault is identified according to the spectrum analysis of the noise reduction signal obtained after the reconstruction; specifically: For the component signals a1(n), a2(n), ..., a k (n) performing spectrum analysis on the signal after noise reduction; The prominent characteristic frequencies are extracted based on spectrum analysis. By calculating whether the prominent frequencies contain the characteristic frequencies that can reflect the bearing faults obtained by theoretical calculation of the group of data, the characteristics of the rolling bearing faults are extracted and the faults are identified.

6. A storage medium, characterized in that: The storage medium includes a stored program, wherein when the program is run, the bearing fault identification method based on SVD and variance described in any one of claims 1 to 5 is executed.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: The processor executes the bearing fault identification method based on SVD and variance as described in any one of claims 1 to 5 by running the computer program.

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