CN114510964A - Bearing vibration signal fault feature extraction method and system - Google Patents

Bearing vibration signal fault feature extraction method and system Download PDF

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CN114510964A
CN114510964A CN202210026613.7A CN202210026613A CN114510964A CN 114510964 A CN114510964 A CN 114510964A CN 202210026613 A CN202210026613 A CN 202210026613A CN 114510964 A CN114510964 A CN 114510964A
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廖志强
张文化
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Guangdong Deer Smart Factory Technology Co Ltd
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Abstract

The invention relates to the technical field of vibration signal processing in bearing fault diagnosis, in particular to a bearing vibration signal fault feature extraction method and a bearing vibration signal fault feature extraction system, wherein the extraction method comprises the following steps: reconstructing a bearing vibration signal X into a d-dimensional Hankel matrix, wherein d is a positive integer greater than or equal to 2; decomposing the d-dimensional Hankel matrix by adopting a steady state subspace analysis method to obtain an n-dimensional non-stationary source signal SnN is a positive integer less than d; calculating a non-stationary source signal SnEach non-steady state component S ofiSelecting unsteady component S with the maximum kurtosis value Kmax(ii) a Calculating the unsteady state component SmaxThe kurtosis spectrum C (ω); and analyzing the kurtosis spectrum C (omega) and identifying fault characteristics in the signal. Wherein, the invention effectively eliminates the vibration signal by introducing 1.5-dimensional C0-kurtosis spectrumThe interference component inhibits background noise, improves the signal-to-noise ratio, and enhances the fault characteristics, thereby being convenient for extracting and identifying the fault characteristics.

Description

Bearing vibration signal fault feature extraction method and system
Technical Field
The invention relates to the technical field of vibration signal processing in bearing fault diagnosis, in particular to a method and a system for extracting fault characteristics of a vibration signal of a bearing.
Background
When the bearing is in fault, the vibration signal generates regular impact characteristics, which are key information for diagnosing the bearing fault. However, due to the complex working environment of the bearing, serious background noise exists in the vibration signal extracted by the acceleration sensor, so that the regular impact characteristics are submerged, and the fault characteristics are difficult to extract. Moreover, the non-stationary vibration signal with the modulation phenomenon and the heavier background noise further increase the difficulty of extracting weak fault features.
Disclosure of Invention
In view of this, the present invention provides a method and a system for extracting fault characteristics of a bearing vibration signal, and mainly solves the technical problems that: how to extract fault features in the bearing vibration signal.
In order to achieve the purpose, the invention mainly provides the following technical scheme:
on one hand, the embodiment of the invention provides a bearing vibration signal fault feature extraction method, which comprises the following steps:
reconstructing a bearing vibration signal X into a d-dimensional Hankel matrix, wherein d is a positive integer greater than or equal to 2; decomposing the d-dimensional Hankel matrix by adopting a steady state subspace analysis method to obtain an n-dimensional non-stationary source signal SnN is a positive integer less than d;
calculating a non-stationary source signal SnEach non-steady state component S ofiSelecting unsteady component S with the maximum kurtosis value Kmax；
Calculating the unsteady state component SmaxThe kurtosis spectrum C (ω);
and analyzing the kurtosis spectrum C (omega) and identifying fault characteristics in the signal.
Optionally, the non-stationary component S is calculatedmaxThe method of kurtosis spectrum C (ω) of (a) is as follows:
first, the unsteady state component S is calculatedmaxC (τ) of the third-order cumulant, wherein C (τ) is E [ S ]max(a)Smax(a+τ)Smax(a+τ)]In the formula, the unsteady component SmaxThe signal length of (a) is M, M is a positive integer greater than 1, a is a positive integer greater than or equal to 1 and less than or equal to M; tau is a time delay parameter, E is an expected operation;
then, Fourier transform is carried out on the C (tau) to obtain a 1.5-dimensional C0-kurtosis spectrum C (omega),
Figure BDA0003464962620000021
optionally, each unsteady component S is calculatediThe kurtosis value K of (1) is as follows:
Figure BDA0003464962620000022
wherein, N is a time domain signal X in the bearing vibration signal XiThe number of (2); y isiThe calculation method of (2) is as follows:
1) fourier transform is adopted to obtain a time domain signal xiOf the frequency domain signal xk：
xk＝FFT(xi)
2) For a frequency domain signal x according to the following formulakScreening is carried out:
Figure BDA0003464962620000023
wherein λ is greater than 1 and less than 10;
3) for the screened frequency domain signal
Figure BDA0003464962620000024
Performing inverse Fourier transform to obtain time domain signal yiWherein, in the step (A),
Figure BDA0003464962620000025
in another aspect, an embodiment of the present invention further provides a bearing vibration signal fault feature extraction system, which may include:
the signal decomposition module is used for reconstructing the bearing vibration signal X into a d-dimensional Hankel matrix, wherein d is a positive integer greater than or equal to 2; then, a steady state subspace analysis method is adopted to decompose the d-dimensional Hankel matrix to obtain an n-dimensional unsteady state component SnN is a positive integer less than d;
a signal processing module for calculating a stationary source signal SnEach non-steady state component S ofiSelecting kurtosis value KMaximum unsteady component Smax(ii) a And calculating the unsteady state component SmaxThe kurtosis spectrum C (ω);
and the identification module is used for analyzing the kurtosis spectrum C (omega) and identifying fault characteristics in the signal.
Optionally, the system for extracting fault characteristics of bearing vibration signals further includes: and the signal acquisition module is used for acquiring a bearing vibration signal X.
By means of the technical scheme, the bearing vibration signal fault feature extraction method and the bearing vibration signal fault feature extraction system have the following beneficial effects:
the invention provides a bearing vibration signal fault feature extraction method based on a 1.5-dimensional C0-kurtosis spectrum, which effectively eliminates interference components in a vibration signal, inhibits background noise, improves the signal-to-noise ratio and enhances the fault feature by introducing the 1.5-dimensional C0-kurtosis spectrum, thereby facilitating the extraction and identification of the fault feature.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical solutions of the present invention more clearly understood and to implement them in accordance with the contents of the description, the following detailed description is given with reference to the preferred embodiments of the present invention and the accompanying drawings.
Drawings
FIG. 1 is a vibration signal of a bearing outer race fault;
FIG. 2 is a bearing outer race fault frequency spectrum;
fig. 3 is a flow chart of a method for extracting fault characteristics of a bearing vibration signal according to an embodiment of the present invention;
FIG. 4 is a steady state subspace analysis decomposed signal of a bearing outer ring fault;
FIG. 5 is a 1.5 dimensional C0-kurtosis spectrum of the best unsteady-state component of FIG. 4.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that, if directional indications (such as up, down, left, right, front, and back … …) are involved in the embodiment of the present invention, the directional indications are only used to explain the relative positional relationship between the components, the movement situation, and the like in a specific posture (as shown in the drawing), and if the specific posture is changed, the directional indications are changed accordingly.
In addition, if there is a description of "first", "second", etc. in an embodiment of the present invention, the description of "first", "second", etc. is for descriptive purposes only and is not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In addition, technical solutions between various embodiments may be combined with each other, but must be realized by a person skilled in the art, and when the technical solutions are contradictory or cannot be realized, such a combination should not be considered to exist, and is not within the protection scope of the present invention.
As shown in fig. 1, a large amount of noise is contained in a bearing outer ring fault vibration signal, regular impact caused by a fault is submerged by the noise, and in the frequency spectrum of fig. 2, fault characteristic frequency cannot be accurately extracted.
The invention provides a bearing vibration signal fault feature extraction method, which can easily extract fault features in a vibration signal. The advantages of the present invention will be discussed below by specific laboratory data. As shown in fig. 1, a method for extracting a fault characteristic of a vibration signal of a bearing according to an embodiment of the present invention includes the following steps:
step S1: and reconstructing the bearing vibration signal X into a d-dimensional Hankel matrix, wherein d is a positive integer greater than or equal to 2. Wherein, the bearing vibration signal X is composed of N time domain signals XiN is a positive integer of 2 or more. In one example, N may be 3 or more, and thus the bearing vibration signal X may beExpressed as: x ═ X1,x2,…xN}。
Decomposing the d-dimensional Hankel matrix by adopting a steady state subspace analysis method to obtain an m-dimensional stationary source signal SsAnd n-dimensional non-stationary source signal SnM and n are positive integers less than d, and m + n is d. In one example, d is 8 and m and n are both 4. Thus in this example, the bearing vibration signal X (X ═ { X) } is given1,x2,…xN}) into an 8-dimensional Hankel matrix (X ═ X1,X2,…,X8]) Then, the steady state subspace analysis method is adopted to decompose the signal, and a 4-dimensional stationary source signal S can be obtaineds(Ss＝[S1,S2,S3,S4]) And 4-dimensional non-stationary source signal Sn(Sn＝[S5,S6,S7,S8]). Thus, the bearing vibration signal X after decomposition can be expressed as:
Figure BDA0003464962620000051
in the formula: from AsThe space formed by the column vectors is respectively called stationary (s-) space, consisting of AnThe space formed by the column vectors is referred to as the non-stationary (n-) space, respectively. As shown in FIG. 3, the left side of FIG. 3 is the decomposed 4-dimensional stationary source signal SsFrom top to bottom are respectively S1、S2、S3And S4(ii) a The right side of FIG. 3 is the decomposed 4-dimensional non-stationary source signal SnWhich from top to bottom are each S5、S6、S7And S8。
Step S2: calculating the non-stationary source signal SnEach non-steady state component S ofiSelecting unsteady component S with the maximum kurtosis value Kmax. Following the above example, Sn＝[S5,S6,S7,S8]，SiIs S5、S6、S7Or S8. Preferably, each unsteady component S is calculatediThe kurtosis value K of (1) is as follows:
K＝argmin(g(Si))；
Figure BDA0003464962620000061
wherein X is a vector matrix, and X is { X ═ X1,x2,…xNN is a time domain signal X in the bearing vibration signal XiThe σ parameter is the variance. y isiThe calculation method of (2) is as follows:
1) fourier transform is adopted to obtain a time domain signal xiOf the frequency domain signal xk：
xk＝FFT(xi)；
2) For a frequency domain signal x according to the following formulakScreening is carried out:
Figure BDA0003464962620000062
wherein λ is greater than 1 and less than 10. In one specific application example, λ is 3;
3) for the screened frequency domain signal
Figure BDA0003464962620000063
Performing inverse Fourier transform to obtain time domain signal yiWherein, in the step (A),
Figure BDA0003464962620000064
according to the method described above, each unsteady component S can be calculatediC0-kurtosis value K of (1), the results are shown in Table 1.
TABLE 1
Unsteady state component Si C0-kurtosisValue K
S5 7.79
S6 8.65
S7 11.13
S8 8.43
Comparing the unsteady state components SiC0-kurtosis value K, C0-kurtosis value K max indicates that the most fault feature information is contained in the unsteady state component, and based on the principle of C0-kurtosis value K max, the best unsteady state component S is selectedmax. In this embodiment, as can be seen from table 1, the third unsteady component S7C0-kurtosis value K is maximal, so that it contains the most fault information, and is the best unsteady component, i.e. SmaxIs S7。
Step S3: calculating the unsteady state component SmaxThe kurtosis spectrum C (ω). Here, it should be noted that: kurtosis spectra may also be referred to as spectral kurtosis.
Step S4: and analyzing the kurtosis spectrum C (omega) to identify fault characteristics in the signal.
In the above example, the non-stationary source signal in the bearing vibration signal X can be decomposed by using the steady-state subspace analysis method, and compared with the stationary source signal, because the non-stationary source signal contains more fault information, the kurtosis spectrum of the non-stationary source signal is calculated, so that the fault features in the non-stationary source signal can be extracted and identified more conveniently.
In a specific application example, in the aforementioned step S3, the calculation is performedUnsteady state component SmaxThe method of kurtosis spectrum C (ω) of (a) is as follows: 1. first, the unsteady state component S is calculatedmaxThe diagonal tangents C (τ), S of the third-order cumulant of (1)maxIs C0-the unsteady state component S with the maximum kurtosis value KiWherein C (τ) ═ E [ S ]max(a)Smax(a+τ)Smax(a+τ)]In the formula, the unsteady component SmaxThe signal length of (a) is M, M is a positive integer greater than 1, a is a positive integer greater than or equal to 1 and less than or equal to M; such as SmaxWhen the signal length of (a) is 10000, that is, M is 10000, a is a positive integer of 1 or more and 10000 or less. τ is a delay parameter and E is an expected operation. Then, Fourier transform is carried out on the C (tau) to obtain a 1.5-dimensional C0-kurtosis spectrum C (omega),
Figure BDA0003464962620000071
FIG. 4 shows the optimal unsteady state component S in this embodiment7The 1.5-dimensional C0-kurtosis spectrum C (omega), as can be seen from FIG. 4, the energy of the bearing fault characteristic frequency and its harmonic is far higher than the edge frequency, the noise is effectively suppressed, and the fault characteristic is obviously improved.
In the above example, the invention provides a bearing vibration signal fault feature extraction method based on a 1.5-dimensional C0-kurtosis spectrum, which can filter background noise of a vibration signal and enhance fault features when a bearing is in fault, so that the fault features in the bearing vibration signal can be extracted more conveniently.
The embodiment of the invention also provides a bearing vibration signal fault feature extraction system which comprises a signal decomposition module, a signal processing module and an identification module. The signal decomposition module is used for reconstructing the bearing vibration signal X into a d-dimensional Hankel matrix, wherein d is a positive integer greater than or equal to 2; then, a steady state subspace analysis method is adopted to decompose the d-dimensional Hankel matrix to obtain an n-dimensional unsteady state component SnAnd n is a positive integer less than d. The signal processing module is used for calculating a stationary source signal SnEach non-steady state component S ofiSelecting unsteady component S with the maximum kurtosis value Kmax(ii) a And calculating the unsteady state component SmaxOfDegree spectrum C (ω). And the identification module is used for analyzing the kurtosis spectrum C (omega) and identifying fault characteristics in the signal.
Here, it should be noted that: the signal processing module calculates each unsteady component SiAnd calculating the unsteady state component SmaxThe method for the kurtosis spectrum C (ω) can refer to the corresponding description above, and will not be described herein again.
The bearing vibration signal fault feature extraction system can further comprise a signal acquisition module, wherein the signal acquisition module is used for acquiring a bearing vibration signal X, and the signal acquisition module can be an acceleration sensor and the like.
The signal decomposition module, the signal processing module and the identification module may all adopt a processor.
Here, it should be noted that: in the case of no conflict, a person skilled in the art may combine the related technical features in the above examples according to actual situations to achieve corresponding technical effects, and details of various combining situations are not described herein.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the invention.

Claims (5)

1. A bearing vibration signal fault feature extraction method is characterized by comprising the following steps:
reconstructing a bearing vibration signal X into a d-dimensional Hankel matrix, wherein d is a positive integer greater than or equal to 2; decomposing the d-dimensional Hankel matrix by adopting a steady state subspace analysis method to obtain an n-dimensional non-stationary source signal SnN is a positive integer less than d;
calculating a non-stationary source signal SnEach non-steady state component S ofiSelecting the unsteady state with the maximum kurtosis value KComponent Smax；
Calculating the unsteady state component SmaxThe kurtosis spectrum C (ω);
and analyzing the kurtosis spectrum C (omega) and identifying fault characteristics in the signal.
2. The method for extracting fault features of bearing vibration signals according to claim 1, wherein the unsteady component S is calculatedmaxThe method of kurtosis spectrum C (ω) of (a) is as follows:
first, the unsteady state component S is calculatedmaxC (τ) of the third-order cumulant, wherein C (τ) is E [ S ]max(a)Smax(a+τ)Smax(a+τ)]In the formula, the unsteady component SmaxThe signal length of (a) is M, M is a positive integer greater than 1, a is a positive integer greater than or equal to 1 and less than or equal to M; tau is a time delay parameter, E is an expected operation;
then, Fourier transform is carried out on the C (tau) to obtain a 1.5-dimensional C0-kurtosis spectrum C (omega),
Figure FDA0003464962610000011
3. the bearing vibration signal fault feature extraction method according to claim 1 or 2, wherein each unsteady-state component S is calculatediThe kurtosis value K of (1) is as follows:
K＝argmin(g(Si))，
Figure FDA0003464962610000021
wherein, N is a time domain signal X in the bearing vibration signal XiThe number of (2); y isiThe calculation method of (2) is as follows:
1) fourier transform is adopted to obtain a time domain signal xiOf the frequency domain signal xk：
xk＝FFT(xi)
2) For a frequency domain signal x according to the following formulakScreening is carried out:
Figure FDA0003464962610000022
wherein λ is greater than 1 and less than 10;
3) for the screened frequency domain signal
Figure FDA0003464962610000023
Performing inverse Fourier transform to obtain time domain signal yiWherein, in the step (A),
Figure FDA0003464962610000024
4. the utility model provides a bearing vibration signal fault feature extraction system which characterized in that includes:
the signal decomposition module is used for reconstructing the bearing vibration signal X into a d-dimensional Hankel matrix, wherein d is a positive integer greater than or equal to 2; then, a steady state subspace analysis method is adopted to decompose the d-dimensional Hankel matrix to obtain an n-dimensional unsteady state component SnN is a positive integer less than d;
a signal processing module for calculating a stationary source signal SnEach non-steady state component S ofiSelecting unsteady component S with the maximum kurtosis value Kmax(ii) a And calculating the unsteady state component SmaxThe kurtosis spectrum C (ω);
and the identification module is used for analyzing the kurtosis spectrum C (omega) and identifying fault characteristics in the signals.
5. The bearing vibration signal fault signature extraction system of claim 4, further comprising:
and the signal acquisition module is used for acquiring a bearing vibration signal X.
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