CN114018581A - CEEMDAN-based rolling bearing vibration signal decomposition method - Google Patents
CEEMDAN-based rolling bearing vibration signal decomposition method Download PDFInfo
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Abstract
A CEEMDAN-based rolling bearing vibration signal decomposition method solves the problems that the existing CEEMDAN-based vibration signal decomposition can generate false mode components and residual noise, and belongs to the field of signal and information processing. According to the method, the original data of the vibration signal is firstly acquired, a series of eigenmode components with frequency ranges from high to low are acquired by adopting CEEMDAN decomposition according to the original data, then the eigenmode components are sequentially reconstructed from high to low according to the orders, Fourier transform is carried out on the reconstructed eigenmode components to acquire the frequency spectrum of the eigenmode components, then probability density function fitting is carried out on the frequency spectrum, finally, the similarity of probability density function waveforms is measured by adopting fuzzy entropy, the frequency characteristics of the eigenmode components are classified in a self-adaptive mode, and the vibration characteristics of the bearing are effectively extracted.
Description
Technical Field
The invention relates to a vibration signal decomposition method for a rolling bearing, and belongs to the field of signal and information processing.
Background
Rolling bearings are widely used in mechanical drive systems. Damage to the rolling bearing can lead to failure of the mechanical system and, in severe cases, personal injury. Therefore, an effective bearing fault analysis method is adopted, and the method has important significance for ensuring the normal operation and the personal safety of the system. In time-frequency analysis, wavelet transformation can represent the time-frequency distribution characteristics of vibration signals and can extract fault features. However, the wavelet transform has limited application in the field of bearing fault diagnosis due to the difficulty in selecting the basis functions. Later, an Empirical Mode Decomposition (EMD) method was proposed, which is an adaptive decomposition method based on data itself, can decompose signals into a series of eigenmode components (IMFs) with frequencies from high to low, and has been widely used in fault diagnosis. In order to suppress the occurrence of mode aliasing in the decomposed IMF due to EMD stopping criteria limitations, integrated empirical mode decomposition (CEEMDAN) based on adaptive noise has been proposed, which is a noise-aided analysis-based method that can suppress the mode aliasing problem to some extent. When extracting the characteristic frequency of the rolling bearing from the rolling bearing failure signal containing the complex frequency components, false frequency components occur when the vibration is decomposed due to the conventional CEEMDAN, and noise will be contained in the decomposed IMFs due to the added white noise and signal interaction. Such false IMFs and noise-containing IMFs, if directly subjected to envelope demodulation analysis, may seriously affect the extraction of fault features of the rolling bearing.
Disclosure of Invention
Aiming at the problem that the traditional CEEMDAN-based vibration signal decomposition can generate false mode components and residual noise, the invention provides a CEEMDAN-based rolling bearing vibration signal decomposition method.
The invention discloses a CEEMDAN-based rolling bearing vibration signal decomposition method, which is characterized by comprising the following steps:
s1, acquiring an original signal of vibration data of the rolling bearing, and carrying out empirical mode decomposition on the original signal by using CEEMDAN to obtain a plurality of eigenmode components IMF (intrinsic mode function) of which the frequency band is from high to lowi(t)；
S2, IMF eigenmode componenti(t) conversion to Joint mode Components CMFj(t)；
S3, pairing the joint mode component CMFj(t) Fourier transform to obtain spectral FFT (CMF)j(t)), FFT (CMF) on the spectrumj(t)) performing probability density function fitting to obtain a probability density PDF (FFT (CMF)j(t)))；
S4, obtaining each probability density PDF (FFT (CMF)j(t))) and obtaining a difference value D between two adjacent fuzzy entropy valuesq；
S5, finding DqLocal maximum value of (a) and index number k corresponding thereto1,k2,…,knN represents the number of local maxima;
s6, local poleThe large value is a boundary point, an index interval is formed by the index number corresponding to the local maximum value, and the intrinsic mode component IMF corresponding to each index number in the index interval is used as the IMFi(t) performing reconstruction to obtain a joint mode component
m＝1,2…n。
Preferably, in S6, the index section includes:
[1,k1+1],[k1+2,k2+1],......,[kn-1+2,kn+1]。
preferably, in S6, the joint mode component
Comprises the following steps:
the invention has the beneficial effects that: according to the method, the original data of the vibration signal is firstly acquired, a series of eigenmode components with frequency ranges from high to low are acquired by adopting CEEMDAN decomposition according to the original data, then the eigenmode components are sequentially reconstructed from high to low according to the orders, Fourier transform is carried out on the reconstructed eigenmode components to acquire the frequency spectrum of the eigenmode components, then probability density function fitting is carried out on the frequency spectrum, finally, the similarity of probability density function waveforms is measured by adopting fuzzy entropy, the frequency characteristics of the eigenmode components are classified in a self-adaptive mode, and the vibration characteristics of the bearing are effectively extracted. The invention improves the performance of decomposing the vibration signal by the traditional CEEMDAN, and enhances the fault diagnosis capability of the rolling bearing. The decomposition method provided by the invention can effectively avoid the occurrence of the phenomena of generating false mode components and residual noise, and can extract the fault characteristics of rolling bearings in different frequency bands.
Drawings
FIG. 1 is a flow chart of an embodiment of the present invention;
FIG. 2 is a schematic diagram of CEEMDAN decomposition;
FIG. 3 is a waveform diagram of an original signal of a fault of an inner ring of a rolling bearing provided by an embodiment of the invention;
FIG. 4 is an eigenmode component diagram of a CEEMDAN decomposition of a rolling bearing provided by an embodiment of the present invention;
FIG. 5 is a spectrum diagram of eigenmode components provided in an embodiment of the invention;
FIG. 6 is a difference graph of fuzzy entropy provided by an embodiment of the present invention;
fig. 7 shows the fault feature extraction of the original signal decomposition and the fault feature extraction of the CEEMDAN decomposition method improved by the embodiment of the invention.
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 the embodiments and features of the embodiments may be combined with each other without conflict.
The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.
As shown in fig. 1, a method for decomposing a vibration signal of a rolling bearing based on CEEMDAN according to the present embodiment includes:
step one, acquiring an original signal x (t) of vibration data of a rolling bearing, and performing empirical mode decomposition on the original signal by using CEEMDAN (center empirical mode decomposition), as shown in fig. 2, to acquire N eigenmode components IMF (intrinsic mode frequency) of which the frequency band is from high to lowi(t)：
R denotes a remainder, and N denotes the number of eigenmode components.
Step two, IMF the eigen-mode componenti(t) conversion to Joint mode Components CMFj(t)；
CMFj(t) represents the first j +1 IMFsi(t) performing a reconstruction.
Step three, pairing the joint mode component CMFj(t) Fourier transform to obtain spectral FFT (CMF)j(t)), FFT (CMF) on the spectrumj(t)) performing probability density function fitting to obtain a probability density PDF (FFT (CMF)j(t)))；
Step four, obtaining each probability density PDF (FFT (CMF)j(t))) to realize preliminary quantization and obtain the difference value D between two adjacent fuzzy entropy valuesqAnd then further quantizing;
step five, searching DqLocal maximum value of (a) and index number k corresponding thereto1,k2,…,knN represents the number of local maxima;
step six, taking the local maximum value as a demarcation point, and forming an index interval by using the index number corresponding to the local maximum value, wherein the index interval comprises: [1, k ]1+1],[k1+2,k2+1],......,[kn-1+2,kn+1]And according to the intrinsic mode component IMF corresponding to each index number in the index intervali(t) performing reconstruction to obtain a joint mode component
m＝1,2…n：
In practical application, envelope demodulation can be carried out on the reconstructed IMFs, vibration characteristics are extracted, and fault detection is carried out.
The specific embodiment is as follows:
construction rollA movable bearing fault simulation test platform is provided, wherein the sampling frequency of the platform is 12KHz, the rolling ball number n of a bearing is 9, and the pitch circle diameter Dw46.4mm, rotation frequency fr29.17Hz, a contact angle alpha of 0 DEG, and a bearing inner diameter d1Is 25mm, and the outer diameter d of the bearing2Is 52mm and the diameter d of the ballrIs 7.9 mm. The device comprises a dynamometer, a torque sensor, a driving end bearing, a driving motor, a fan end bearing and the like. Cage failure frequency f of bearingtAnd inner ring failure frequency fiAre respectively ft＝0.5(1-drcosα/Dw)fr，fi＝0.5n(1+dr/Dw)fr(frFor frequency conversion, DwBearing pitch circle diameter). Data on bearing failure, as shown in figure 3,
FIG. 4 is a decomposition of bearing fault data using CEEMDAN. It is observed from fig. 4 that CEEMDAN decomposes bearing failure data into 10 IMFs.
The joint mode scores CMF are computed and fourier transformed as shown in fig. 5. From this it can be observed that FFT (CMF)2(t)) phase comparison FFT (CMF)1(t)) has more frequency components, FFT (CMF)4(t))—FFT(CMF8(t)) are similar in spectral composition and are comparable to FFT (CMF)1(t))-FFT(CMF3(t)) also have more frequency components.
Now on FFT (CMF)2(t)) performing probability density function fitting, and calculating the fuzzy entropy value of each probability density function and the difference value of adjacent fuzzy entropies, as shown in fig. 6. As can be seen from fig. 6, the difference appears as two peaks, at 1 and 3 of its index number, respectively.
Step seven pairs of CMFs according to the present embodiment*(t) carrying out the extraction of the extract,
is made by IMF1(t) and IMF2(t) are combined,
Is made by IMF3(t) and IMF4(t) composition and the remaining composition
For comparison purposes, the first 3 IMFs of the CEEMDAN decomposition were extracted, one for each CMF*(t) and IMFs were envelope spectrum transformed, and the result of the transformation is shown in FIG. 7. As can be seen from the figure, CMF1 *(t) and IMF1(t) envelope spectra are similar, their rotation frequency f r2 times of rotation frequency 2frInner ring failure frequency fiAnd 2 times the inner ring fault frequency 2fiCan be distinguished more clearly. However, IMF2(t) inability to discriminate the rotational frequency f of the bearingr，CMF2 *(t) the rotational frequency f can likewise be identifiedrAnd 2f is absenti(ii) a In CMF3 *(t) the cage failure frequency f can be settIdentified and IMF3(t) cannot be said. From CMF1 *(t)—CMF3 *(t) it was found that the frequency decreases in order, which complies with the decomposition principle of CEEMDAN (high frequency components corresponding to small orders and low frequency components corresponding to large orders), and the bearing failure frequency is clearly visible.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that features described in different dependent claims and herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.
Claims (5)
1. A CEEMDAN-based rolling bearing vibration signal decomposition method is characterized by comprising the following steps:
s1, acquiring the original signal of the vibration data of the rolling bearing, and acquiring the original signal by using CEEMDANPerforming empirical mode decomposition to obtain multiple intrinsic mode components IMF from high to low frequency bandi(t)；
S2, IMF eigenmode componenti(t) conversion to Joint mode Components CMFj(t)；
S3, pairing the joint mode component CMFj(t) Fourier transform to obtain spectral FFT (CMF)j(t)), FFT (CMF) on the spectrumj(t)) performing probability density function fitting to obtain a probability density PDF (FFT (CMF)j(t)))；
S4, obtaining each probability density PDF (FFT (CMF)j(t))) and obtaining a difference value D between two adjacent fuzzy entropy valuesq；
S5, finding DqLocal maximum value of (a) and index number k corresponding thereto1,k2,...,knN represents the number of local maxima;
s6, using the local maximum value as a demarcation point, forming an index interval by the index number corresponding to the local maximum value, and forming an intrinsic mode component IMF corresponding to each index number in the index intervali(t) performing reconstruction to obtain a joint mode component
m＝1,2…n。
2. The CEEMDAN-based rolling bearing vibration signal decomposition method according to claim 1, wherein in S6, the index interval includes:
[1,k1+1],[k1+2,k2+1],......,[kn-1+2,kn+1]。
3. the CEEMDAN-based rolling bearing vibration signal decomposition method according to claim 2, wherein in S6, the joint mode component
Comprises the following steps:
4. the CEEMDAN-based rolling bearing vibration signal decomposition method according to claim 3, wherein in S1, the original signal x (t) is subjected to empirical mode decomposition to obtain N eigenmode components IMF with frequency bands from high to lowi(t)：
R denotes a remainder, and N denotes the number of eigenmode components.
5. The CEEMDAN-based rolling bearing vibration signal decomposition method according to claim 4, wherein in S2, j is 1,2 … N-1, and eigenmode components IMF are addedi(t) conversion to Joint mode Components CMFjThe method of (t) is:
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| CN116124456A (en) * | 2023-02-15 | 2023-05-16 | 广东海洋大学 | Self-adaptive rolling bearing fault feature extraction and diagnosis method and device |
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