CN113375940A - Fault bearing diagnosis method based on SVD and CEEMDAN - Google Patents

Fault bearing diagnosis method based on SVD and CEEMDAN Download PDF

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CN113375940A
CN113375940A CN202110594638.2A CN202110594638A CN113375940A CN 113375940 A CN113375940 A CN 113375940A CN 202110594638 A CN202110594638 A CN 202110594638A CN 113375940 A CN113375940 A CN 113375940A
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bearing
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王林军
刘洋
李立军
徐洲常
蔡康林
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China Three Gorges University CTGU
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Abstract

The invention relates to a fault bearing diagnosis method based on SVD and CEEMDAN, which comprises the following steps: collecting a bearing vibration signal; calculating time-frequency distribution, and preliminarily judging whether the bearing has a fault or not; singular value decomposition denoising reconstruction is carried out on the original fault bearing signal; carrying out self-adaptive noise complete set empirical mode decomposition on the preliminary noise reduction signal to obtain a plurality of intrinsic mode components; calculating KL divergence between each intrinsic mode component and the original signal, and eliminating invalid components; reconstructing effective eigenmode components; and performing autocorrelation denoising on the reconstructed signal, then drawing an envelope spectrum, extracting clear fault characteristic frequency, and diagnosing the type of the bearing fault. According to the method, reconstruction is carried out after singular value decomposition and denoising, modal decomposition is carried out, invalid components are removed, and fault diagnosis is carried out by utilizing the envelope spectrum of a reconstructed signal, so that the accuracy of bearing fault diagnosis is effectively improved; the invention eliminates modal aliasing, greatly reduces the consumption of computing resources and improves the signal decomposition efficiency.

Description

Fault bearing diagnosis method based on SVD and CEEMDAN
Technical Field
The invention belongs to the field of mechanical fault diagnosis, and particularly relates to a fault bearing diagnosis method based on SVD and CEEMDAN.
Background
At present, fault diagnosis technology becomes an important means for ensuring safe and reliable operation of mechanical equipment. Rolling bearings are important parts in rotary machines, and when they fail, they not only generate vibration noise but also affect the operating efficiency of the rotary machine. If bearing failure cannot be found in time, serious safety accidents and economic losses can be caused. Therefore, it is necessary to conduct a rolling bearing failure diagnosis study. When the rolling bearing has a fault, the detection signal of the rolling bearing is accompanied by noise and fault signals, and how to extract the fault signals has important significance in the actual industrial production.
In recent years, in order to improve the signal processing quality, researchers have preprocessed the original vibration signal by wavelet Decomposition, wavelet packet Decomposition, Singular Value Decomposition (SVD), and the like. The singular value decomposition can be used for processing non-stationary and non-linear signals, has the advantages of simple operation, no offset of a denoising result and the like, and is widely used for signal processing.
For the fault signal extraction, the main problem is how to adaptively extract the effective signal from the nonlinear vibration signal. Common Decomposition methods such as Empirical Mode Decomposition (EMD), Ensemble Empirical Mode Decomposition (EEMD), complete Ensemble modal Decomposition (CEEMD) have a modal aliasing problem.
After the signal is decomposed into a plurality of Intrinsic Mode components (IMFs), how to measure the degree of fault information contained in the Intrinsic Mode components is difficult to analyze for mechanical fault signals.
Disclosure of Invention
The invention aims to solve the technical problem that the existing method for extracting fault characteristic information from vibration signals, such as EMD, EEMD, CEEMD and the like, has modal aliasing and noise, and influences the bearing fault diagnosis effect.
The invention aims to solve the problems, and provides a fault bearing diagnosis method based on SVD and CEEMDAN, which effectively eliminates the interference Noise contained in the original vibration signal of the bearing, obtains a clear signal reflecting the actual fault information, performs Adaptive Noise Complete set Empirical Mode decomposition (CEEMDAN) on the Noise reduction signal to eliminate modal aliasing, eliminates the invalid modal components obtained by decomposition, reconstructs the signal, and utilizes the envelope spectrum of the reconstructed signal to diagnose the fault.
The technical scheme of the invention is a fault bearing diagnosis method based on SVD and CEEMDAN, which comprises the following steps:
step 1: collecting a bearing vibration signal;
step 2: calculating Wigner-Ville time-frequency distribution of bearing vibration signals, and primarily judging whether the bearing has faults or not;
and step 3: reconstructing the original fault bearing signal after singular value decomposition to obtain a preliminary noise reduction signal y;
and 4, step 4: carrying out self-adaptive noise complete set empirical mode decomposition on the preliminary noise reduction signal y to obtain n intrinsic mode components IMF1，IMF2，……，IMFn；
And 5: calculating Kullback-Leibler divergence between each eigenmode component and the original signal, setting a divergence threshold value, and removing the eigenmode component with the Kullback-Leibler divergence value larger than the divergence threshold value as an invalid component;
step 6: reconstructing the effective eigenmode component obtained in the step 5 to obtain a reconstructed signal;
and 7: and performing autocorrelation denoising on the reconstructed signal, then drawing an envelope spectrum, extracting clear fault characteristic frequency, comparing the fault characteristic frequency with the theoretical value of the bearing fault characteristic frequency obtained by calculation, and diagnosing to obtain the type of the bearing fault.
In step 2, the calculation formula of the Wigner-Ville time-frequency distribution of the bearing vibration signal is as follows:
Figure BDA0003090464380000021
in the formula of WVDx(t, f) representing signals x (t)The Wigner-Ville time frequency distribution result represents complex conjugate, f represents frequency, t represents time,
Figure BDA0003090464380000022
representing the instantaneous autocorrelation function of the signal x (t).
Step 3 comprises the following substeps:
step 3.1: reconstructing an original fault bearing signal to obtain a Hankel matrix:
Figure BDA0003090464380000023
wherein m is more than or equal to 2, n is more than or equal to 2, and the signal length is m + n + l;
step 3.2: and (3) carrying out singular value decomposition on the Hankel matrix obtained in the step (3.1), wherein the calculation formula is as follows:
A＝UΣVH (3)
wherein U is an m × m orthogonal matrix; v is an n × n orthogonal matrix; a diagonal matrix of singular values where Σ is mxn, and the diagonal element is λ1，λ2，……，λmin(m,n)(ii) a Wherein λiI is 1,2, …, min (m, n) is the singular value of the matrix a;
step 3.3: and reconstructing the signal by utilizing the first n effective singular values to realize signal noise reduction.
Step 4 comprises the following substeps:
step 4.1: white noise epsilon is added to the rolling bearing signal y (t)0vi(n) for the signal y (t) +. epsilon0vi(n) performing empirical mode decomposition to obtain a first modal component, wherein the formula is as follows:
Figure BDA0003090464380000031
wherein
Figure BDA0003090464380000032
Representing the first eigenmode component, IMF1 i(t)，i＝1，2…，I represents the signal y (t) +. epsilon0vi(n) each component obtained by empirical mode decomposition, wherein I represents the total collection number; epsilon0Representing the signal-to-noise ratio, v, of each stagei(n) an ith white gaussian noise expressed as an increase;
step 4.2: calculating a first stage residual component:
Figure BDA0003090464380000033
in the formula r1(t) represents a first stage margin;
step 4.3: for signal y (t) + epsilon1E1(vi(t)) performing empirical mode decomposition until the decomposition yields the position of the first modal component, and calculating the second modal component on the basis of the position:
Figure BDA0003090464380000034
in the formula E1() The 1 st IMF, denoted as Gaussian white noise processed by EMD;
step 4.4: for the remaining phases, i.e., k 2,3, … …, k, the k-th residual component is calculated:
Figure BDA0003090464380000035
step 4.5: step 4.3 is repeated and the k +1 IMF component is calculated as follows:
Figure BDA0003090464380000036
in the formula ofkRepresents the signal-to-noise ratio of the k stage;
step 4.6: repeating the steps 4.4-4.5, decomposing the residual components until the residual components can not be decomposed, and obtaining K modal components and final residual components r (t):
Figure BDA0003090464380000037
the original signal s (t) is decomposed by CEEMDAN to obtain k eigenmode components and a residual component, namely:
Figure BDA0003090464380000038
in step 5, the calculation process of the Kullback-Leibler divergence is as follows:
1) let X be ═ X1,x2,…,xn],Y＝[y1,y2,…,yn]The probability distributions of two groups of signals are p (X) and q (X), and the probability distributions of X and Y are calculated respectively:
Figure BDA0003090464380000041
where h is a constant and k is a Gaussian kernel function
Figure BDA0003090464380000042
Obtaining the probability distribution q (x) of Y in the same way;
2) calculate X, Y KL distances δ (p, q), δ (q, p):
Figure BDA0003090464380000043
obtaining delta (q, p) in the same way;
3) calculation of the KL dispersion value D (p, q) of X, Y:
D(p,q)＝δ(p,q)+δ(q,p) (13)。
in step 7, the calculation formula of the bearing inner ring fault characteristic frequency is as follows:
Figure BDA0003090464380000044
in the formula f0Indicating features of inner ringsTheoretical value of frequency, Z represents number of rolling elements, D represents diameter of rolling elements, D represents diameter of pitch circle, alpha represents contact angle of bearing, FrRepresenting a frequency conversion;
the calculation formula of the bearing outer ring fault characteristic frequency is as follows:
Figure BDA0003090464380000045
in the formula f1A theoretical value representing the outer ring characteristic frequency;
the formula for calculating the conversion frequency Fr is as follows
Figure BDA0003090464380000046
In the formula niIndicating the rotational speed.
Preferably, the divergence threshold is 0.1.
Compared with the prior art, the invention has the beneficial effects that:
(1) according to the method, the interference noise in the vibration signal of the fault detection bearing is eliminated, after the signal which clearly reflects the actual fault information is obtained, the noise reduction signal is subjected to adaptive noise complete set empirical mode decomposition, the invalid mode component obtained by decomposition is eliminated and then reconstructed, and the envelope spectrum of the reconstructed signal is used for fault diagnosis, so that the accuracy of bearing fault diagnosis is effectively improved;
(2) according to the method, the intrinsic mode component of the bearing vibration signal is obtained by adopting the self-adaptive noise complete set empirical mode decomposition, compared with the EMD), EEMD and CEEMD methods and the like, the mode aliasing is eliminated, the zero reconstruction error of the decomposed signal is realized, the consumption of computing resources is greatly reduced, and the signal decomposition efficiency is improved;
(3) the modal components are screened according to the KL divergence, and the KL divergence has the advantages of large discrimination and obvious difference effect compared with a correlation coefficient method;
(4) according to the method, the singular value decomposition method is adopted before modal decomposition to effectively eliminate the noise in the signal, so that the signal-to-noise ratio of the signal is improved, and the signal denoised and reconstructed by the singular value decomposition method has good stability without phase shift;
(5) the method and the device initially judge whether the collected bearing vibration signals are fault signals by utilizing Wigner-Ville time-frequency distribution, reserve the fault signals to carry out the next diagnosis and classification, and improve the efficiency of bearing fault diagnosis.
Drawings
The invention is further illustrated by the following figures and examples.
Fig. 1 is a schematic flow chart of a fault bearing diagnosis method according to an embodiment of the present invention.
FIG. 2 is a three-dimensional time-frequency distribution diagram of a normal bearing vibration signal according to an embodiment of the present invention.
FIG. 3 is a three-dimensional time-frequency distribution diagram of vibration signals of a bearing with an inner ring fault according to an embodiment of the invention.
FIG. 4 is a time domain diagram of the original vibration signal of the bearing with the failed inner ring according to the embodiment of the present invention.
FIG. 5 is a time domain diagram of a singular value decomposition denoising signal of an inner ring fault bearing according to an embodiment of the invention.
Fig. 6 is a time domain diagram of a modal component reconstruction signal of an inner ring faulty bearing according to an embodiment of the present invention.
Fig. 7 is a time domain diagram of a modal component reconstruction signal of a denoised inner ring fault bearing according to an embodiment of the present invention.
Fig. 8 is an envelope spectrum of a modal component reconstructed signal of an inner ring faulty bearing according to an embodiment of the present invention.
FIG. 9 is a time domain diagram of the original vibration signal of the bearing with the failed outer ring according to the embodiment of the present invention.
FIG. 10 is a time domain diagram of a singular value decomposition denoising signal of an outer ring fault bearing according to an embodiment of the invention.
Fig. 11 is a time domain diagram of a modal component reconstruction signal of an outer ring faulty bearing according to an embodiment of the present invention.
Fig. 12 is a time domain diagram of a modal component reconstruction signal of a denoised outer ring fault bearing according to an embodiment of the present invention.
Fig. 13 is an envelope spectrum of a modal component reconstruction signal of an outer ring faulty bearing according to an embodiment of the present invention.
Detailed Description
As shown in fig. 1, the method for diagnosing a faulty bearing based on SVD and CEEMDAN comprises the following steps:
step 1: and collecting a bearing vibration signal.
Step 2: calculating Wigner-Ville time-frequency distribution of bearing vibration signals, and primarily judging whether the bearing has faults or not;
the calculation formula of the Wigner-Ville time frequency distribution of the bearing vibration signal is as follows:
Figure BDA0003090464380000051
in the formula of WVDx(t, f) represents the Wigner-Ville time frequency distribution result of the signal x (t), wherein f represents the complex conjugate, f represents the frequency, t represents the time,
Figure BDA0003090464380000061
representing the instantaneous autocorrelation function of the signal x (t).
And step 3: reconstructing the original fault bearing signal after singular value decomposition to obtain a preliminary noise reduction signal y;
step 3.1: reconstructing an original fault bearing signal to obtain a Hankel matrix:
Figure BDA0003090464380000062
wherein m is more than or equal to 2, n is more than or equal to 2, and the signal length is m + n + l;
step 3.2: and (3) carrying out singular value decomposition on the Hankel matrix obtained in the step (3.1), wherein the calculation formula is as follows:
A＝UΣVH (3)
wherein U is an m × m orthogonal matrix; v is an n × n orthogonal matrix; a diagonal matrix of singular values where Σ is mxn, and the diagonal element is λ1，λ2，……，λmin(m,n)(ii) a Wherein λiI is 1,2, …, min (m, n) is the singular value of the matrix a;
step 3.3: and reconstructing the signal by utilizing the first n effective singular values to realize signal noise reduction.
And 4, step 4: carrying out self-adaptive noise complete set empirical mode decomposition on the preliminary noise reduction signal y to obtain n intrinsic mode components IMF1，IMF2，……，IMFn；
Step 4.1: white noise epsilon is added to the rolling bearing signal y (t)0vi(n) for the signal y (t) +. epsilon0vi(n) performing empirical mode decomposition to obtain a first modal component, wherein the formula is as follows:
Figure BDA0003090464380000065
wherein
Figure BDA0003090464380000066
Representing the first eigenmode component, IMF1 i(t), I ═ 1,2 …, I denotes the signal y (t) + ε0vi(n) each component obtained by empirical mode decomposition, wherein I represents the total collection number; epsilon0Representing the signal-to-noise ratio, v, of each stagei(n) an ith white gaussian noise expressed as an increase; step 4.2: calculating a first stage residual component:
Figure BDA0003090464380000063
in the formula r1(t) represents the first stage margin
Step 4.3: for signal y (t) + epsilon1E1(vi(t)) performing empirical mode decomposition until the decomposition yields the position of the first modal component, and calculating the second modal component on the basis of the position:
Figure BDA0003090464380000064
in the formula E1() The 1 st IMF, denoted as Gaussian white noise processed by EMD;
step 4.4: for the remaining phases, i.e., k 2,3, … …, k, the k-th residual component is calculated:
Figure BDA0003090464380000071
step 4.5: step 4.3 is repeated and the k +1 IMF component is calculated as follows:
Figure BDA0003090464380000072
in the formula ofkRepresenting the signal-to-noise ratio of the k-th stage
Step 4.6 repeat steps 4.4-4.5, decompose the residual component until it can not be decomposed, obtain K modal components and final residual component r (t):
Figure BDA0003090464380000073
the original signal s (t) is decomposed by CEEMDAN to obtain k eigenmode components and a residual component, namely:
Figure BDA0003090464380000074
and 5: calculating KL values between each IMF component and the original signal by using a KL divergence method, taking 0.1 as a rejection domain, taking the KL value smaller than 0.1 as an effective component, and taking the KL value smaller than 0.1 as an ineffective component otherwise;
the Kullback-Leibler divergence is calculated as follows:
1) let X be ═ X1,x2,…,xn],Y＝[y1,y2,…,yn]The probability distributions of two groups of signals are p (X) and q (X), and the probability distributions of X and Y are calculated respectively:
Figure BDA0003090464380000075
where h is a constant and k is a Gaussian kernel function
Figure BDA0003090464380000076
Obtaining the probability distribution q (x) of Y in the same way;
2) calculate X, Y KL distances δ (p, q), δ (q, p):
Figure BDA0003090464380000077
obtaining delta (q, p) in the same way;
3) calculation of the KL dispersion value D (p, q) of X, Y:
D(p,q)＝δ(p,q)+δ(q,p) (13)。
step 6: and selecting the effective IMF component for reconstruction to obtain a reconstruction signal.
And 7: and performing autocorrelation denoising on the reconstructed signal, drawing an envelope spectrum, extracting clear fault characteristic frequency, and comparing the fault characteristic frequency with the theoretical value of the bearing fault characteristic frequency obtained by calculation.
The calculation formula of the bearing inner ring fault characteristic frequency is as follows:
Figure BDA0003090464380000081
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 bearing outer ring fault characteristic frequency is as follows:
Figure BDA0003090464380000082
in the formula f1A theoretical value representing the outer ring characteristic frequency;
the formula for calculating the conversion frequency Fr is as follows
Figure BDA0003090464380000083
In the formula niIndicating the rotational speed.
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 bearing parameter table
Figure BDA0003090464380000084
The motor has a rotation speed of ni1796r/min, signal sampling frequency 12kHz, data point 4096. The characteristic frequency f of the fault of the inner ring of the bearing is calculated by the formula (14)0162.19, the bearing frequency is Fr＝29.95。
The bearing normal vibration signal time-frequency distribution three-dimensional graph and the bearing inner ring fault vibration signal time-frequency distribution three-dimensional graph are respectively shown in fig. 2 and fig. 3. Therefore, when the bearing normally vibrates, the vibration energy of the bearing is mainly concentrated in a low-frequency part and has a certain rule, and the amplitude is smaller; when its inner race fails, its high frequency portion vibration energy begins to increase and its amplitude begins to grow as well. Therefore, the bearing can be preliminarily judged to be in fault.
The time domain diagram of the original vibration signal of the inner ring is shown in fig. 4, and it can be seen that the original vibration signal contains a large amount of random noise, which affects the extraction of the fault characteristic frequency. The original vibration signals are subjected to preliminary denoising by adopting SVD to obtain a graph 5, the signal-to-noise ratio of the signals is improved, more noise is still accompanied, and clear fault signals cannot be obtained. And (3) decomposing the preliminary de-noising signal by adopting CEEMDAN to obtain each modal component, calculating KL divergence values of each modal component and the de-noising signal, selecting the modal component with the KL divergence value smaller than 0.1 to reconstruct, wherein the reconstructed signal is shown in figure 6, has a relatively obvious signal period but is still accompanied with a small amount of noise signals, and performing autocorrelation de-noising on the signal to obtain the signal shown in figure 7, and the clear fault signal characteristic can be seen from figure 7. When there is a failure in the inner race of the bearing, a value of nZf would result if there were no radial clearance between the bearings0(n-1, 2,3 …). The bearings inevitably have radial play,amplitude modulation is therefore required. The bearing of the embodiment has a frequency Fr, so that the vibration frequency of the bearing is nZf0±Fr(n-1, 2,3 …). For better highlighting of the fault signature frequency, the signal of fig. 7 is plotted as an envelope spectrum, as shown in fig. 8, from which fig. 8 a clear fault signature frequency f can be seen0And bearing frequency Fr. The characteristic frequency of the fault shown in fig. 8 is 161.1Hz and is basically the same as the calculated characteristic frequency of the fault of the inner ring, the relative error is only 0.612%, and the error is kept in a reasonable range, which shows that the method of the invention can accurately diagnose the fault of the inner ring of the bearing.
In another embodiment of the invention, the outer ring faults of the same type of bearing are diagnosed, and the bearing parameters are shown in table 1. The characteristic frequency f of the fault of the outer ring of the bearing is calculated by the formula (15)1107.36, the bearing frequency is Fr＝29.95。
The time domain diagram of the original vibration signal of the outer ring fault bearing is shown in fig. 9, and it can be seen that the original vibration signal contains a large amount of random noise, which affects the extraction of the fault characteristic frequency. The original vibration signals are subjected to preliminary denoising by adopting SVD to obtain signals shown in FIG. 10, the signal-to-noise ratio of the signals is improved, but more noise is still accompanied, and clear fault signals cannot be obtained. And decomposing the preliminary de-noising signal by adopting CEEMDAN to obtain each modal component, calculating KL divergence values of each modal component and the de-noising signal, selecting the modal component with the KL divergence value smaller than 0.1 to reconstruct to obtain a reconstructed signal as shown in figure 11, wherein the signal period is obvious but is still accompanied by a small amount of noise signals, and performing autocorrelation de-noising on the signal to obtain a signal as shown in figure 12, wherein clear fault signal characteristics can be seen in figure 12. The outer ring fault signal and the inner ring fault signal are both impact signals, the end effect of the impact signals cannot be avoided, but the outer ring fault signal presents continuity, and the interval of the impact signals is smaller than that of the inner ring fault. The envelope spectrum is drawn for the signal of fig. 12, as shown in fig. 13, the relative error between the outer ring fault characteristic frequency obtained and the calculated outer ring fault characteristic frequency is 0.43%, and the error is kept in a reasonable range, which indicates that the method of the invention can accurately diagnose the bearing outer ring fault.

Claims (7)

1. The fault bearing diagnosis method based on SVD and CEEMDAN is characterized by comprising the following steps:
step 1: collecting a bearing vibration signal;
step 2: calculating the time-frequency distribution of the bearing vibration signals, and preliminarily judging whether the bearing has a fault or not;
and step 3: reconstructing the original fault bearing vibration signal after singular value decomposition to obtain a preliminary noise reduction signal;
and 4, step 4: carrying out self-adaptive noise complete set empirical mode decomposition on the preliminary noise reduction signal to obtain a plurality of intrinsic mode components;
and 5: calculating Kullback-Leibler divergence between each eigenmode component and the original signal, setting a divergence threshold value, and removing the eigenmode component with the Kullback-Leibler divergence value larger than the divergence threshold value as an invalid component;
step 6: reconstructing the effective eigenmode component obtained in the step 5 to obtain a reconstructed signal;
and 7: and performing autocorrelation denoising on the reconstructed signal, then drawing an envelope spectrum, extracting clear fault characteristic frequency, comparing the fault characteristic frequency with the theoretical value of the bearing fault characteristic frequency obtained by calculation, and diagnosing to obtain the type of the bearing fault.
2. The method for diagnosing the faulty bearing according to claim 1, wherein in step 2, the calculation formula of the Wigner-Ville time-frequency distribution of the bearing vibration signal is as follows:
Figure FDA0003090464370000011
in the formula of WVDx(t, f) represents the Wigner-Ville time frequency distribution result of the signal x (t), wherein f represents the complex conjugate, f represents the frequency, t represents the time,
Figure FDA0003090464370000012
representing the instantaneous autocorrelation function of the signal x (t).
3. The method of diagnosing a faulty bearing according to claim 1, characterized in that step 3 comprises the sub-steps of:
step 3.1: reconstructing an original fault bearing signal to obtain a Hankel matrix H:
Figure FDA0003090464370000013
wherein m is more than or equal to 2, n is more than or equal to 2, and the signal length is m + n + l;
step 3.2: and (3) carrying out singular value decomposition on the Hankel matrix obtained in the step (3.1), wherein the calculation formula is as follows:
A＝UΣVH (3)
wherein U is an m × m orthogonal matrix; v is an n × n orthogonal matrix; a diagonal matrix of singular values where Σ is mxn, and the diagonal element is λ1,λ2,…,λmin(m,n)(ii) a Wherein λiI is 1,2, …, min (m, n) is the singular value of the matrix a;
step 3.3: and reconstructing the signal by utilizing the first n singular values to realize signal noise reduction.
4. The method of diagnosing a faulty bearing according to claim 1, characterized in that step 4 comprises the sub-steps of:
step 4.1: white noise epsilon is added to the rolling bearing signal y (t)0vi(n) for the signal y (t) +. epsilon0vi(n) performing empirical mode decomposition to obtain a first modal component, wherein the formula is as follows:
Figure FDA0003090464370000021
wherein
Figure FDA0003090464370000022
Representing the first of the eigenmode components,
Figure FDA0003090464370000023
represents the signal y (t) + ε0vi(n) each component obtained by empirical mode decomposition, wherein I represents the total collection number; epsilon0Representing the signal-to-noise ratio, v, of each stagei(n) an ith white gaussian noise expressed as an increase;
step 4.2: calculating a first stage residual component:
Figure FDA0003090464370000024
in the formula r1(t) represents a first stage margin;
step 4.3: for signal y (t) + epsilon1E1(vi(t)) performing empirical mode decomposition until the decomposition yields the position of the first modal component, and calculating the second modal component on the basis of the position:
Figure FDA0003090464370000025
in the formula
Figure FDA0003090464370000026
Representing a second eigenmode component, E1() Expressed as the 1 st component obtained by Gaussian white noise empirical mode decomposition; step 4.4: computing the k-th stage residual component rk(t)：
Figure FDA0003090464370000027
In the formula
Figure FDA0003090464370000028
Represents the kth eigenmode component, K ═ 2,3, …, K;
step 4.5: computing the k +1 modal component
Figure FDA0003090464370000029
Figure FDA00030904643700000210
In the formula ofkRepresenting the signal-to-noise ratio of the k-th stage
Step 4.6: repeating the steps 4.4-4.5, decomposing the residual components until the residual components can not be decomposed, and obtaining K modal components and final residual components r (t):
Figure FDA00030904643700000211
decomposing the original signal s (t) to obtain K eigenmode components and a residual component, namely:
Figure FDA00030904643700000212
5. the method for diagnosing a faulty bearing according to claim 1, wherein in step 5, the Kullback-Leibler divergence is calculated as follows:
1) let X be ═ X1,x2,…,xn],Y＝[y1,y2,…,yn]The probability distributions of two groups of signals are p (X) and q (X), and the probability distributions of X and Y are calculated respectively:
Figure FDA0003090464370000031
where h is a constant and k is a Gaussian kernel function
Figure FDA0003090464370000032
Obtaining the probability distribution q (x) of Y in the same way;
2) calculate X, Y KL distances δ (p, q), δ (q, p):
Figure FDA0003090464370000033
obtaining delta (q, p) in the same way;
3) calculation of the KL dispersion value D (p, q) of X, Y:
D(p,q)＝δ(p,q)+δ(q,p) (13)。
6. the faulty bearing diagnosis method according to claim 1, wherein in step 7, the characteristic frequency of the fault of the bearing inner ring is calculated as follows:
Figure FDA0003090464370000034
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 bearing outer ring fault characteristic frequency is as follows:
Figure FDA0003090464370000035
in the formula f1A theoretical value representing the outer ring characteristic frequency;
the formula for calculating the conversion frequency Fr is as follows
Figure FDA0003090464370000036
In the formula niIndicating the rotational speed.
7. The faulty bearing diagnostic method according to any one of claims 1 to 6, characterized in that the divergence threshold is 0.1.
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