CN115266094A - Rolling bearing fault diagnosis method based on TVD and MED - Google Patents

Rolling bearing fault diagnosis method based on TVD and MED Download PDF

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CN115266094A
CN115266094A CN202210775339.3A CN202210775339A CN115266094A CN 115266094 A CN115266094 A CN 115266094A CN 202210775339 A CN202210775339 A CN 202210775339A CN 115266094 A CN115266094 A CN 115266094A
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fault
rolling bearing
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王林军
邹腾枭
徐洲常
蔡康林
刘洋
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China Three Gorges University CTGU
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    • G01—MEASURING; TESTING
    • G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
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    • G01M13/04—Bearings
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Abstract

The invention relates to a fault diagnosis method for a rolling bearing based on TVD and MED, which comprises the following steps: acquiring a vibration signal of a rolling bearing; preliminarily judging whether the rolling bearing has a fault or not by adopting a peak coefficient method; performing total variation noise reduction on original rolling bearing fault signals, and determining regularization parameters by using correlation coefficients and weighted indexes of Teager energy operatorsaThe optimum value of (d); the noise reduction signals are subjected to minimum entropy deconvolution filtering, and the propagation of an impulse response function is reduced; finally, envelope demodulation is carried out on the enhanced signal, clear fault characteristic frequency and frequency multiplication thereof are extracted, and the type of the bearing fault is diagnosed. The method solves the problem that the envelope demodulation cannot rapidly identify the fault characteristic frequency in the high-frequency range, and the TVD-MED composite method has better extraction effect on the frequency doubling fault frequency in the high-frequency range; in the noise reduction process of the original bearing vibration signal, the correlation and the impact characteristic are considered at the same time, and the optimal regularization parameters are selected by using the weighting indexesAnd the noise reduction effect is better.

Description

Rolling bearing fault diagnosis method based on TVD and MED
Technical Field
The invention belongs to the field of mechanical fault diagnosis, and particularly relates to a rolling bearing fault diagnosis method based on TVD and MED.
Background
The rolling bearing is an important part of mechanical equipment, and the stability of the rolling bearing during operation cannot be ensured due to the fact that the rolling bearing is in a loaded state and a severe environment for a long time. Generally, collected rolling bearing fault signals comprise noise signals, and fault types cannot be accurately and quickly judged by adopting a single analysis method and means. Therefore, how to extract the bearing fault characteristics in the noise signals becomes a main research content.
The vibration signal generated by the fault of the rolling bearing is generally a nonlinear, non-circularly stable high-frequency signal, so that certain difficulty exists in extracting the fault frequency. Common denoising methods are wavelet threshold denoising, autocorrelation denoising, and the like. Wavelet thresholding denoising requires the determination of basis functions and thresholds, which is poorly adaptive. Autocorrelation noise reduction, while ensuring signal similarity to some extent, is only applicable to high signal-to-noise ratio signals. Total Variation Denoising (TVD) is to reduce noise by using a regularization technique, so as to effectively reduce the influence of noise. The Suitai waves and the like apply TVD to the field of bearing failure and propose the combination of kurtosis and related coefficients as indexes for parameter selection. The MM algorithm is adopted by FIGUEIREDOMAT and the like to solve the problem of TVD objective function optimization, so that a good noise reduction effect is obtained, but the parameter selection has a great influence on the noise reduction effect. However, the total variation noise reduction is used as a noise reduction method, and the fault characteristics cannot be extracted. And Endo and the like are combined with Minimum Entropy Deconvolution (MED) to amplify fault characteristics, so that the fault frequency can be extracted more easily, but the order of the filter influences the extraction of the fault frequency. The Wangyun break and the like aim at the problem and combine deep research on the bearing to design an optimal filter to extract the fault frequency. Because the bearing fault characteristics are weak, fault signals under the background of strong noise can be submerged by the noise, and the fault characteristic extraction is seriously influenced.
Disclosure of Invention
When the noise of a signal is reduced through the TVD, how to ensure the correlation and the impact characteristic of the original signal while improving the noise reduction effect of the original signal and how to select the regularization parameter a are the difficulties in mechanical fault signal analysis.
The invention aims to solve the technical problems that how to select the regularization parameter a to improve the signal noise reduction effect and a single method are difficult to effectively extract the fault characteristic frequency, thereby influencing the bearing fault diagnosis effect.
The invention aims to solve the problems, and provides a rolling bearing fault diagnosis method based on TVD and MED, which effectively eliminates the interference noise contained in the original vibration signal of the rolling bearing to obtain a signal clearly reflecting the actual fault information, and the noise reduction signal is subjected to minimum entropy deconvolution to enhance the fault impact characteristic, reduce the propagation of an impulse response function and carry out fault diagnosis on the envelope spectrum of the fault signal.
The technical scheme of the invention is a rolling bearing fault diagnosis method based on TVD and MED, which comprises the following steps:
step 1: acquiring a vibration signal of a rolling bearing through an acceleration sensor;
step 2: calculating a peak value factor of a vibration signal of the rolling bearing to preliminarily judge whether the bearing has a fault;
and step 3: calculating a first-order total variation of the original rolling bearing fault vibration signal;
and 4, step 4: selecting an optimal regularization coefficient a by using the correlation coefficient and a weighting index of a Teager energy operator, and obtaining a noise reduction signal by combining first-order total variation;
and 5: the minimum entropy deconvolution is adopted to enhance the fault signals in the noise reduction signals, and the propagation of the impulse response function is reduced;
step 6: finally, envelope demodulation is carried out on the rolling bearing fault type detection signal to obtain an envelope spectrogram, clear fault characteristic frequency and frequency doubling frequency of the fault characteristic frequency are extracted, the clear fault characteristic frequency and the frequency doubling frequency are compared with a theoretical value of the fault characteristic frequency of the rolling bearing obtained through calculation, and the fault type of the rolling bearing is obtained through diagnosis.
Further, in step 2, the calculation formula of the peak factor of the vibration signal of the rolling bearing is as follows:
Xp＝max{|xi|} (1)
Figure BDA0003727292350000021
Figure BDA0003727292350000022
in the formula XpRepresenting the peak of the signal X (t), XrmsRepresenting the root mean square value of the signal x (t), C representing the crest factor of the signal x (t), xiDenotes the ith sample point, and N denotes the number of sample points.
Step 3 comprises the following substeps:
step 3.1: defining the first order total variation of the original signal:
TV＝||Dx||1 (4)
wherein TV represents a first order total variation of the signal; x represents the original vibration signal; d represents a matrix with N-1 rows and N columns, and N represents the length of x; i | · | live through1Represents the L1 norm;
where matrix D is defined as follows:
Figure BDA0003727292350000023
step 3.2: and 3, denoising the first-order total variation obtained in the step 3.1, and obtaining a target optimization problem as follows:
Figure BDA0003727292350000024
wherein TVD (y, a) represents the total variation noise reduction function; a is a regularization parameter; y is a signal containing noise, and x is an original vibration signal; i | · | live through1Representing L1 norm, | · | non-calculation2Represents the L2 norm;
step 3.3: the MM algorithm (optimization-Minimization) is used for solving the formula (6), and the following results are obtained:
Figure BDA0003727292350000031
in the formula xi、xi+1Are respectively provided withRepresenting an original signal, a noise reduction signal; diag () represents a diagonal matrix.
Step 4 comprises the following substeps:
step 4.1: calculating the correlation coefficient of the original signal, wherein the formula is as follows:
Figure BDA0003727292350000032
wherein C represents a cross-correlation coefficient;
Figure BDA0003727292350000034
and
Figure BDA0003727292350000035
mean values of x and y, respectively; sigmaxAnd σyThe standard deviations of x and y, respectively, are indicated, and E indicates expectation.
And 4.2: calculating a Teager energy operator, wherein the formula is as follows:
T[x(n)]＝x(n)2-x(n-1)x(n+1) (9)
wherein T () represents Teager energy operator; x (n-1), x (n) and x (n + 1) respectively represent three continuous sampling points;
step 4.3: in order to make the noise reduction signal have correlation and impact characteristics at the same time, the two indexes are combined to obtain a weighting index as follows:
Tc＝T×Cr (10)
in the formula TcRepresenting a weighting indicator; t represents Teager energy operator; r is an adjusting parameter, and r is 1.2 in the invention.
In step 5, the calculation process of the minimum entropy deconvolution is as follows:
1) Suppose that the vibration signal y (n) can be expressed as follows:
y(n)＝h(n)·x(n)+e(n) (11)
wherein h (n) is a transfer function; x (n) is a fault signal; e (n) is a noise signal
2) And eliminating the convolution influence by searching an optimal inverse filter w (n) to obtain an inverse convolution signal I (n) close to the fault signal x (n), wherein the calculation formula is as follows:
Figure BDA0003727292350000033
Figure BDA0003727292350000041
wherein w (i) represents the ith inverter; y (n-i) represents a vibration signal; l represents the number of inverse wave devices;
3) The magnitude of the entropy of the deconvolution signal I (n) is measured by calculating the norm of the signal, and the magnitude is taken as an objective function to obtain the optimal output:
Figure BDA0003727292350000042
in the formula O2() Entropy values representing the deconvolution signal; i is2(i) Represents the square of the magnitude of the deconvolved signal;
4) To maximize the norm of equation (14), let it be derived:
Figure BDA0003727292350000043
5) The following results were obtained in combination with equation (12) and expressed in matrix form:
Figure BDA0003727292350000044
C＝WA (17)
W＝CA-1 (18)
wherein W is a coefficient matrix of the inverse filter; c is a cross-correlation matrix of the output signal and the input signal; and A is an input signal autocorrelation matrix.
In step 6, the calculation formula of the fault characteristic frequency of the inner ring of the rolling bearing is as follows:
Figure BDA0003727292350000045
in the formula f0Expressing the theoretical value of the characteristic frequency of the inner ring, Z representing the number of rolling elements, D representing the diameter of the rolling elements, D representing the diameter of a pitch circle, alpha representing the contact angle of the bearing, FrRepresenting a frequency conversion;
the calculation formula of the fault characteristic frequency of the outer ring of the rolling bearing is as follows:
Figure BDA0003727292350000046
in the formula f1A theoretical value representing the outer ring characteristic frequency;
the conversion frequency Fr is calculated as follows:
Figure BDA0003727292350000047
in the formula niIndicating the rotational speed.
Compared with the prior art, the invention has the beneficial effects that:
(1) According to the method, the original signal is denoised through total variation denoising, after a signal which clearly reflects actual fault information is obtained, the denoised signal is subjected to minimum entropy deconvolution, the propagation of an impulse response function is reduced, fault diagnosis is carried out by utilizing an envelope spectrum of a reconstructed signal, and the accuracy of fault diagnosis of the rolling bearing is effectively improved;
(2) According to the method, the correlation coefficient and the Teager energy operator are combined to serve as a weighting index for selecting the regularization parameter a, the correlation between the noise reduction signal and the original signal is guaranteed, meanwhile, the fault impact characteristic of the noise reduction signal can be highlighted, the Teager energy operator in the weighting index has higher operation efficiency compared with the kurtosis, and the noise reduction efficiency of the signal is improved;
(3) The method solves the optimization problem of the total variation target according to the MM algorithm, and the obtained result continuously reduces the noise influence through iterative computation, thereby improving the noise reduction effect;
(4) Compared with a TVD single method, the TVD and MED composite method can extract the fault frequency, and has a good extraction effect on the frequency doubling fault frequency in a high frequency range.
Drawings
The invention is further illustrated by the following figures and examples.
Fig. 1 is a schematic flow chart of a rolling bearing fault diagnosis method according to an embodiment of the present invention.
Fig. 2a is a time-frequency distribution diagram of a simulated original signal according to an embodiment of the present invention.
Fig. 2b is a time-frequency distribution diagram of the noise signal according to the embodiment of the present invention.
FIG. 3 shows an exemplary simulation signal parameter a versus weighting index TcThe influence of (c).
Fig. 4a is a time domain waveform diagram of a TVD signal according to an embodiment of the present invention.
FIG. 4b is a time domain waveform diagram of a TVD-MED signal according to an embodiment of the present invention.
Fig. 5a is a TVD signal envelope spectrum according to an embodiment of the present invention.
FIG. 5b is a diagram of the envelope spectrum of the TVD-MED signal according to the embodiment of the present invention.
Fig. 6a is a time domain waveform diagram of a fault vibration signal of an inner ring of a rolling bearing according to an embodiment of the invention.
Fig. 6b is a frequency domain waveform diagram of a fault vibration signal of the inner ring of the rolling bearing according to the embodiment of the invention.
Fig. 7 is a time domain waveform diagram of a wavelet threshold denoising signal of an inner ring of a rolling bearing according to an embodiment of the invention.
FIG. 8 shows a rolling bearing inner ring parameter a versus a weighting index T according to an embodiment of the present inventioncThe influence of (c).
Fig. 9a is a time domain waveform diagram of TVD signal of inner ring of rolling bearing according to the embodiment of the present invention.
FIG. 9b is a time domain waveform diagram of TVD-MED signal of the inner ring of the rolling bearing according to the embodiment of the present invention.
Fig. 10a is a TVD envelope spectrum of the inner ring of the rolling bearing according to the embodiment of the present invention.
FIG. 10b is a TVD-MED envelope spectrum of the inner ring of the rolling bearing in the embodiment of the present invention.
Fig. 11a is a time domain waveform diagram of the vibration signal of the outer ring fault of the rolling bearing according to the embodiment of the invention.
FIG. 11b is a frequency domain waveform diagram of the vibration signal of the outer ring fault of the rolling bearing according to the embodiment of the present invention.
Fig. 12 is a time domain waveform diagram of a wavelet threshold denoising signal of an outer ring of a rolling bearing according to an embodiment of the invention.
FIG. 13 shows a rolling bearing outer ring parameter a vs. a weighting index T according to an embodiment of the present inventioncThe influence of (c).
Fig. 14a is a time domain waveform diagram of a TVD signal of an outer ring of a rolling bearing according to an embodiment of the present invention.
FIG. 14b is a time domain waveform diagram of TVD-MED signal of the outer ring of the rolling bearing according to the embodiment of the present invention.
Fig. 15a is a TVD envelope spectrum of the outer ring of the rolling bearing according to the embodiment of the present invention.
FIG. 15b is the TVD-MED envelope spectrum of the outer ring of the rolling bearing according to the embodiment of the present invention.
Detailed Description
The bearing of the embodiment is a 6205-2RS JEM SKF deep groove ball bearing, and the bearing parameters are shown in Table 1.
TABLE 1 DEEP-CHANNEL BALL BEARING PARAMETERS TABLE
Figure BDA0003727292350000061
The experimental sampling frequency fs =12kHz, the motor speed is 1750r/min, and the corresponding conversion frequency fr =29.17Hz. And (4) calculating the fault frequency fi =157.76Hz of the inner ring of the bearing according to the formula (19). The filter order of the present invention is 56.
As shown in fig. 1, the rolling bearing fault diagnosis method based on TVD and MED includes the following steps:
step 1: acquiring a vibration signal of a rolling bearing through an acceleration sensor;
step 2: calculating a peak value factor of a vibration signal of the rolling bearing to preliminarily judge whether the rolling bearing has a fault;
the calculation formula of the peak value factor of the vibration signal of the rolling bearing is as follows:
Xp＝max{|xi|} (1)
Figure BDA0003727292350000062
Figure BDA0003727292350000063
in the formula XpRepresenting the peak of the signal X (t), XrmsRepresents the root mean square value of the signal x (t), and C represents the crest factor of the signal x (t).
And step 3: calculating a first-order total variation of the original rolling bearing fault vibration signal;
step 3.1: defining the first order total variation of the original signal:
TV＝||Dx||1 (4)
where matrix D is defined as follows:
Figure BDA0003727292350000071
step 3.2: and 3, denoising the first-order total variation obtained in the step 3.1, and obtaining a target optimization problem as follows:
Figure BDA0003727292350000072
where a (a > 0) is a regularization parameter, whose purpose is to control the degree of smoothing of the signal,
step 3.3: solving equation (6) by using MM (optimization-Minimization) algorithm, and obtaining the following results:
Figure BDA0003727292350000073
and 4, step 4: selecting an optimal regularization coefficient a by using the correlation coefficient and a weighting index of a Teager energy operator, and obtaining an optimal noise reduction signal;
step 4.1: calculating the correlation coefficient of the original signal, wherein the formula is as follows:
Figure BDA0003727292350000074
in the formula
Figure BDA0003727292350000075
And
Figure BDA0003727292350000076
mean values of x and y, respectively; sigmaxAnd σyThe standard deviations of x and y, respectively, are indicated, and E indicates expectation.
And 4.2: calculating a Teager energy operator, wherein the formula is as follows:
T[x(n)]＝x(n)2-x(n-1)x(n+1) (9)
step 4.3: in order to make the noise reduction signal have correlation and impact characteristics at the same time, the indexes of the two signals are combined to obtain a weighting index as follows:
Tc＝T×Cr (10)
wherein r is a regulating parameter, and r is 1.2 in the invention.
And 5: the minimum entropy deconvolution is adopted to enhance the fault signals in the noise reduction signals, and the propagation of the impulse response function is reduced;
1) Suppose that the vibration signal y (n) can be expressed as follows:
y(n)＝h(n)·x(n)+e(n) (11)
wherein h (n) is a transfer function; x (n) is a fault signal; e (n) is a noise signal
2) And eliminating the convolution influence by searching an optimal inverse filter w (n) to obtain an inverse convolution signal I (n) close to the fault signal x (n), wherein the calculation formula is as follows:
Figure BDA0003727292350000081
Figure BDA0003727292350000082
3) The magnitude of the entropy of the signal I (n) is measured by calculating the norm of the signal I (n), and the signal I (n) is taken as an objective function to obtain the optimal output:
Figure BDA0003727292350000083
4) To maximize the norm of equation (14), let it be derived:
Figure BDA0003727292350000084
5) The following results are obtained in conjunction with equation (12) and expressed in matrix form as:
Figure BDA0003727292350000085
C＝WA (17)
W＝CA-1 (18)
wherein W is a coefficient matrix of the inverse filter; c is a cross-correlation matrix of the output signal and the input signal; a is the input signal autocorrelation matrix.
And 6: finally, envelope demodulation is carried out on the rolling bearing fault type detection signal to obtain an envelope spectrogram, clear fault characteristic frequency and frequency multiplication frequency of the fault characteristic frequency are extracted, the extracted fault characteristic frequency is compared with a theoretical value of the fault characteristic frequency of the rolling bearing obtained through calculation, and the fault type of the rolling bearing is obtained through diagnosis.
The calculation formula of the fault characteristic frequency of the inner ring of the rolling bearing is as follows:
Figure BDA0003727292350000086
in the formula f0Expressing the theoretical value of the characteristic frequency of the inner ring, Z representing the number of the rolling bodies, D representing the diameter of the rolling bodies, D representing the diameter of the pitch circle, alpha representing the contact angle of the bearing, FrRepresenting a frequency conversion;
the calculation formula of the fault characteristic frequency of the outer ring of the rolling bearing is as follows:
Figure BDA0003727292350000087
in the formula f1A theoretical value representing the outer ring characteristic frequency;
the conversion frequency Fr is calculated as follows:
Figure BDA0003727292350000091
in the formula niIndicating the rotational speed.
The expression formula of the periodic impact signal and the Gaussian white noise synthesized simulation signal generated after the rolling bearing is simulated to have a fault is as follows:
x(t)＝x0exp(-2πfnξt)sin(2πfnt)+n(t) (22)
displacement constant x in formula0=5; carrier frequency fn=3000Hz; damping coefficient xi =0.1; sampling frequency fs=20kHz; the number of sampling points N =4096; impact period T =0.01s; t is sampling time; n (t) is white noise.
Time domain waveform diagrams of an original signal and a noise-added signal are shown in fig. 2a and 2b, periodic impact characteristics in the noise-added signal are not obvious, and most effective signals are covered by noise. Therefore, TVD noise reduction is carried out on the noise adding signals, and the parameter a is used for weighting index TcAs shown in fig. 3, it can be seen from fig. 3 that when a =3.1, the weighting index T is givencThe value of (c) reaches a maximum value. And selecting the optimal parameter a to perform TVD noise reduction, and enhancing the impact characteristic of the denoised signal by adopting an MED method, as shown in fig. 4a and 4 b. From fig. 4a and 4b, it can be seen that the TVD denoising eliminates the influence of a large amount of noise, and the signal has the characteristic of periodic impulse. After MED processing, the method reduces the dispersion and propagation of pulse signals, and makes the impact characteristics of the signals more obvious.
As shown in fig. 5a and 5b, although the frequency spectrogram after TVD noise reduction can clearly analyze the bearing fault frequency in the low frequency range, the fault characteristic frequency cannot be extracted in the high frequency range, and the fault frequency can be more accurately analyzed in the high frequency range after MED. Simulation results show that the method provided by the invention can be used for extracting the fault characteristics of the rolling bearing under the noise background.
Fig. 6a and 6b are time domain waveforms and frequency spectrograms of fault vibration signals of an inner ring of a rolling bearing respectively, and firstly, a wavelet threshold denoising method is adopted for comparison to obtain an envelope spectrum of a wavelet threshold denoising signal, which is shown in fig. 7. Then, TVD denoising is performed on the inner ring vibration signal, and the influence of the parameter a on the weighting index is shown in fig. 8. When a =1.2, the index T is weightedcWhen the value reaches the maximum value, the maximum value of the parameter a is selected for TVD noise reduction, and MED is adopted to enhance the impact characteristic of the noise-reduced signal, as shown in FIGS. 9a and 9 b. Finally, an envelope spectrogram is obtained through envelope demodulation, as shown in fig. 10a and 10 b. As can be seen from fig. 10a and 10b, although both of the TVD and TVD-MED methods can analyze the inner ring fault frequency, the TVD-MED method can not only extract the rotation frequency of 29.80Hz, the double rotation frequency of 58.50Hz, and the fault frequency of 158.20Hz, but also can clearly extract the multiple fault frequencies in the high frequency range, thereby determining the type of the inner ring fault of the bearing. Compared with the method provided by the invention, the envelope spectrogram obtained by the wavelet threshold denoising method cannot rapidly and accurately identify the fault characteristic frequency. Meanwhile, the wavelet threshold denoising method is not obvious in the inner ring fault characteristic frequency extracted in the high-frequency range, and the analysis effect is not good enough. Through comparison, the method can accurately diagnose the fault of the outer ring of the rolling bearing.
In another embodiment, the outer ring faults of the same type of bearing are diagnosed, and the bearing parameters are shown in the table 1. The characteristic frequency of the fault of the outer ring of the bearing calculated by the formula (20) is fo =104.44Hz, and the conversion frequency is fr =29.17Hz.
Similarly, the bearing outer ring fault signal is analyzed in the same manner as the inner ring fault feature extraction, and the time domain waveform and the frequency spectrum of the bearing outer ring fault signal are shown in fig. 11a and 11 b. The wavelet thresholding method is also used for comparison, as shown in FIG. 12. The influence of the parameter a on the weighting index is shown in fig. 13, and when a =3.1, the weighting index T iscValue arrivalA maximum value. Firstly, noise reduction is carried out on an outer ring fault signal through a TVD, and then the MED is adopted to enhance the periodic impact characteristic of the fault signal, so that the result is shown in figures 14a and 14b, and the impact characteristic of the signal processed by the MED is clearer and more obvious. Finally, an envelope spectrum is obtained through envelope demodulation, as shown in fig. 15a and 15b, it can be seen from fig. 15a and 15b that the frequency conversion of the fault signal after MED is 29.29Hz, the frequency doubling of the fault signal after MED is 59.59Hz, and the fault characteristic frequency of the fault signal after MED is 105.46Hz, which are relatively close to theoretical values, and in addition, the fault characteristic frequency is relatively obvious in a high-frequency range, which shows that the method can accurately diagnose the fault of the outer ring of the rolling bearing.

Claims (8)

1. The rolling bearing fault diagnosis method based on TVD and MED is characterized by comprising the following steps:
step 1: acquiring a vibration signal of a rolling bearing;
and 2, step: calculating a peak value factor of a vibration signal of the rolling bearing, and primarily judging whether the bearing has a fault or not;
and step 3: calculating a first-order total variation of the original rolling bearing fault vibration signal;
and 4, step 4: selecting an optimal regularization coefficient a by using the correlation coefficient and a weighting index of a Teager energy operator, and obtaining a noise reduction signal by combining first-order total variation;
and 5: the minimum entropy deconvolution is adopted to enhance fault signals in the noise reduction signals, and the propagation of impulse response functions is reduced;
and 6: finally, envelope demodulation is carried out on the rolling bearing fault type detection signal to obtain an envelope spectrogram, clear fault characteristic frequency and frequency multiplication frequency of the fault characteristic frequency are extracted, the extracted fault characteristic frequency is compared with a theoretical value of the fault characteristic frequency of the rolling bearing obtained through calculation, and the fault type of the rolling bearing is obtained through diagnosis.
2. The rolling bearing failure diagnosis method according to claim 1, wherein in step 2, the peak factor of the rolling bearing vibration signal is calculated as follows:
Xp＝max{|xi|} (1)
Figure FDA0003727292340000011
Figure FDA0003727292340000012
in the formula XpRepresenting the peak of the signal X (t), XrmsRepresenting the root mean square value of the signal x (t), C representing the crest factor of the signal x (t), xiDenotes the ith sample point and N denotes the length of x.
3. The rolling bearing failure diagnosis method according to claim 2, characterized in that step 3 comprises the sub-steps of:
step 3.1: a first order total variation of the original signal is defined,
TV＝||Dx||1 (4)
wherein TV represents the first order total variation; x represents the original vibration signal; d represents a matrix with N-1 rows and N columns, and N represents the length of x; i | · | purple wind1Represents the L1 norm;
wherein matrix D is defined as follows:
Figure FDA0003727292340000013
step 3.2: the first order total variation obtained in step 3.1 is ascribed to the objective optimization problem
Figure FDA0003727292340000014
Wherein TVD (y, a) represents the total variation noise reduction function; a is a regularization parameter; y is a signal containing noise, x is an original vibration signal, | · | | calcualting1Represents L1 norm, | ·| non-woven phosphor2Represents the L2 norm;
step 3.3: solving equation (6) by using MM algorithm (optimization-Minimization) algorithm yields the following results:
Figure FDA0003727292340000021
in the formula xi、xi+1Respectively representing an original signal and a noise reduction signal; diag () represents a diagonal matrix.
4. A rolling bearing failure diagnosis method according to claim 3, characterized in that step 4 comprises the sub-steps of:
step 4.1: calculating the correlation coefficient of the original signal, wherein the formula is as follows:
Figure FDA0003727292340000022
wherein C represents a cross-correlation coefficient;
Figure FDA0003727292340000023
respectively representing the mean values of x and y; sigmax、σyRespectively representing the standard deviation of x and y, and E represents expectation;
and 4.2: calculating a Teager energy operator, wherein the formula is as follows:
T(x(n))＝x(n)2-x(n-1)x(n+1) (9)
t () represents Teager energy operator; x (n-1), x (n) and x (n + 1) respectively represent three continuous sampling points;
step 4.3: in order to make the noise reduction signal have correlation and impact characteristics at the same time, the correlation index and the impact characteristic index are combined to obtain a weighting index, which is as follows:
Tc＝T×Cr (10)
in the formula TcRepresenting a weighting indicator; t represents Teager energy operator; r is an adjusting parameter.
5. The rolling bearing fault diagnosis method according to claim 4, wherein in step 5, the minimum entropy deconvolution is calculated as follows:
1) The vibration signal y (n) is expressed as follows:
y(n)＝h(n)·x(n)+e(n) (11)
wherein h (n) is a transfer function; x (n) is a fault signal; e (n) is a noise signal;
2) And eliminating the convolution influence by searching an optimal inverse filter w (n) to obtain an inverse convolution signal I (n) close to the fault signal x (n), wherein the calculation formula is as follows:
Figure FDA0003727292340000024
Figure FDA0003727292340000031
wherein w (i) represents the ith inverse filter; y (n-i) represents a vibration signal; l represents the number of filters;
3) The magnitude of the entropy of the deconvolution signal I (n) is measured by calculating the norm of the signal, and the magnitude is taken as an objective function to obtain the optimal output:
Figure FDA0003727292340000032
in the formula O2() Entropy values representing the deconvolution signal; i is2(i) Represents the square of the magnitude of the deconvolved signal;
4) To maximize the norm of equation (14), let its derivative be 0,
Figure FDA0003727292340000033
5) The following results were obtained in combination with equation (12) and expressed in matrix form:
Figure FDA0003727292340000034
C＝WA (17)
W＝CA-1 (18)
wherein W is a coefficient matrix of the inverse filter; c is a cross-correlation matrix of the output signal and the input signal; a is the input signal autocorrelation matrix.
6. The rolling bearing failure diagnosis method according to any one of claims 1 to 5, wherein in step 6, the rolling bearing inner ring failure characteristic frequency is calculated as follows:
Figure FDA0003727292340000035
in the formula f0Expressing the theoretical value of the characteristic frequency of the inner ring, Z representing the number of the rolling bodies, D representing the diameter of the rolling bodies, D representing the diameter of the pitch circle, alpha representing the contact angle of the bearing, FrIndicating a frequency transition.
7. The rolling bearing failure diagnosis method according to claim 6, wherein the calculation formula of the failure characteristic frequency of the outer ring of the rolling bearing is as follows:
Figure FDA0003727292340000036
in the formula f1And a theoretical value representing the outer ring characteristic frequency.
8. The rolling bearing failure diagnosis method according to claim 6, wherein the rotation frequency Fr is calculated as follows:
Figure FDA0003727292340000041
in the formula niIndicating the rotational speed.
CN202210775339.3A 2022-07-03 2022-07-03 Rolling bearing fault diagnosis method based on TVD and MED Pending CN115266094A (en)

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Publication number Priority date Publication date Assignee Title
CN116304648A (en) * 2023-05-23 2023-06-23 北京化工大学 Gear fault identification method based on optimized pulse enhancement and envelope synchronous averaging

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116304648A (en) * 2023-05-23 2023-06-23 北京化工大学 Gear fault identification method based on optimized pulse enhancement and envelope synchronous averaging
CN116304648B (en) * 2023-05-23 2023-08-29 北京化工大学 Gear fault identification method based on optimized pulse enhancement and envelope synchronous averaging

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