CN114018581B - Rolling bearing vibration signal decomposition method based on CEEMDAN - Google Patents
Rolling bearing vibration signal decomposition method based on CEEMDAN Download PDFInfo
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- G01M13/00—Testing of machine parts
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Abstract
A rolling bearing vibration signal decomposition method based on CEEMDAN solves the problem that false mode components and residual noise can be generated in the existing CEEMDAN-based vibration signal decomposition, and belongs to the field of signal and information processing. According to the invention, firstly, original data of a vibration signal are obtained, CEEMDAN decomposition is adopted according to the original data, a series of eigenvalue components with frequency ranges from high to low are obtained, then, the eigenvalue components are sequentially reconstructed according to the order, fourier transformation is carried out on the reconstructed eigenvalue components to obtain a frequency spectrum of the eigenvalue components, probability density function fitting is carried out on the frequency spectrum, finally, similarity of probability density function waveforms is measured by adopting fuzzy entropy, frequency characteristics of the eigenvalue components are classified in a self-adaptive mode, and vibration characteristics of a bearing are effectively extracted.
Description
Technical Field
The invention relates to a rolling bearing vibration signal decomposition method, and belongs to the field of signal and information processing.
Background
Rolling bearings are widely used in mechanical drive systems. Damage to the rolling bearings can lead to failure of the mechanical system and in severe cases can cause personal injury. Therefore, an effective bearing fault analysis method is adopted, and the method has important significance for ensuring the normal operation of the system and personal safety. In the time-frequency analysis, the wavelet transform may represent the time-frequency distribution characteristic of the vibration signal and may extract the fault characteristics. However, the application of the wavelet transformation in the field of bearing fault diagnosis is limited because the basis function of the wavelet transformation is difficult to select. Later, an Empirical Mode Decomposition (EMD) method, which is an adaptive decomposition method based on data itself, is proposed, which can decompose a signal into a series of eigenmode components (IMFs) with frequencies ranging from high to low, and is widely used in fault diagnosis. In order to suppress the occurrence of pattern aliasing in decomposed IMFs due to EMD stop criteria limitations, integrated empirical mode decomposition (CEEMDAN) based on adaptive noise, which is a method based on noise-aided analysis, has been proposed, which can suppress the pattern aliasing problem to some extent. When extracting the characteristic frequency of the rolling bearing from the rolling bearing failure signal containing complex frequency components, false frequency components occur when decomposing vibrations due to the conventional CEEMDAN, and noise will be contained in the decomposed IMFs due to the added white noise and signal interactions. Such false IMFs and noise-containing IMFs, as directly subjected to envelope demodulation analysis, can seriously affect the fault feature extraction of rolling bearings.
Disclosure of Invention
Aiming at the problem that false mode components and residual noise can be generated in the existing CEEMDAN-based vibration signal decomposition, the invention provides a CEEMDAN-based rolling bearing vibration signal decomposition method.
The invention discloses a rolling bearing vibration signal decomposition method based on CEEMDAN, which is characterized by comprising the following steps of:
s1, acquiring an original signal of vibration data of a rolling bearing, and performing empirical mode decomposition on the original signal by using CEEMDAN to obtain a plurality of eigenmode components IMF with frequency bands from high to low i (t)；
S2, IMF of the eigen mode component i (t) conversion to Joint mode component CMF j (t)；
S3, matching die type component CMF j (t) performing Fourier transform to obtain a spectrum FFT (CMF) j (t)) for spectral FFT (CMF) j (t)) to obtain probability density PDF (FFT (CMF) j (t)))；
S4, acquiring each probability density PDF (FFT (CMF) j (t)) and obtaining the difference value D of two adjacent fuzzy entropy values q ；
S5, searching for D q Local maxima of (a) and corresponding index number k 1 ,k 2 ,…,k n N represents the number of local maxima;
s6, taking the local maximum value as a demarcation point, forming an index interval by the index number corresponding to the local maximum value, and according to the intrinsic mode component IMF corresponding to each index number in the index interval i (t) reconstructing to obtain joint pattern componentsm＝1,2…n。
Preferably, in the step S6, the index section includes:
[1,k 1 +1],[k 1 +2,k 2 +1],......,[k n-1 +2,k n +1]。
preferably, in the step S6, the joint pattern componentThe method comprises the following steps:
the invention has the beneficial effects that: according to the invention, firstly, original data of a vibration signal are obtained, CEEMDAN decomposition is adopted according to the original data, a series of eigenvalue components with frequency ranges from high to low are obtained, then, the eigenvalue components are sequentially reconstructed according to the order, fourier transformation is carried out on the reconstructed eigenvalue components to obtain a frequency spectrum of the eigenvalue components, probability density function fitting is carried out on the frequency spectrum, finally, similarity of probability density function waveforms is measured by adopting fuzzy entropy, frequency characteristics of the eigenvalue components are classified in a self-adaptive mode, and vibration characteristics of a bearing are effectively extracted. The invention improves the performance of decomposing vibration signals by aiming at 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 false mode components and residual noise, and can extract the fault characteristics of the 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 illustration of CEEMDAN decomposition;
FIG. 3 is a waveform chart of original signals of faults of an inner ring of a rolling bearing according to the embodiment of the invention;
FIG. 4 is a diagram of eigen-mode components of a CEEMDAN decomposition for a rolling bearing according to an embodiment of the present invention;
FIG. 5 is a spectrum diagram of eigenmode components provided by an embodiment of the present invention;
FIG. 6 is a difference plot of fuzzy entropy provided by an embodiment of the present invention;
fig. 7 is a diagram illustrating the extraction of fault features from the original signal decomposition and the extraction of fault features from the CEEMDAN decomposition method modified according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
The invention is further described below with reference to the drawings and specific examples, which are not intended to be limiting.
As shown in fig. 1, a rolling bearing vibration signal decomposition method based on CEEMDAN of the present embodiment includes:
step one, obtaining an original signal x (t) of vibration data of the rolling bearing, performing empirical mode decomposition on the original signal by using CEEMDAN, and obtaining N eigenmode components IMF with frequency bands from high to low as shown in figure 2 i (t)：
R represents the remainder and N represents the number of eigen-mode components.
Step two, intrinsic mode component IMF i (t) conversion to Joint mode component CMF j (t)；
CMF j (t) represents the number of IMFs for the first j+1 i (t) performing reconstruction.
Step three, coupled mode type component CMF j (t) performing Fourier transform to obtain a spectrum FFT (CMF) j (t)) for spectral FFT (CMF) j (t)) to obtain probability density PDF (FFT (CMF) j (t)))；
Step four, obtaining each probabilityDensity PDF (FFT (CMF) j (t)) to realize preliminary quantization and obtain the difference value D of two adjacent fuzzy entropy values q Further quantifying;
step five, searching D q Local maxima of (a) and corresponding index number k 1 ,k 2 ,…,k n N 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],[k 1 +2,k 2 +1],......,[k n-1 +2,k n +1]And according to the intrinsic mode component IMF corresponding to each index number in the index interval i (t) reconstructing to obtain joint pattern componentsm＝1,2…n：
In practical application, the reconstructed IMFs can be subjected to envelope demodulation, vibration characteristics are extracted, and fault detection is performed.
Specific examples:
constructing a rolling bearing fault simulation test platform, wherein the sampling frequency of the platform is 12KHz, the number n of rolling balls of the bearing is 9, and the pitch diameter D w 46.4mm, rotation frequency f r 29.17Hz, contact angle alpha of 0 DEG, bearing inner diameter d 1 25mm, bearing outer diameter d 2 Is 52mm and the diameter d of the ball r 7.9mm. The device consists of a dynamometer, a torque sensor, a driving end bearing, a driving motor, a fan end bearing and the like. Cage failure frequency f of bearing t Frequency f of inner ring failure i Respectively f t ＝0.5(1-d r cosα/D w )f r ，f i ＝0.5n(1+d r /D w )f r (f r For frequency conversion, D w Is the bearing pitch diameter). Data on bearing failure, as shown in figure 3,
FIG. 4 is a decomposition of bearing failure data using CEEMDAN. From fig. 4, it is observed that CEEMDAN breaks down bearing failure data into 10 IMFs.
The joint mode division CMF is calculated and fourier transformed as shown in fig. 5. From this, it can be seen that FFT (CMF 2 (t)) compared to FFT (CMF) 1 (t)) is added with frequency components, FFT (CMF) 4 (t))—FFT(CMF 8 (t)) is similar in spectral content and compared to FFT (CMF) 1 (t))-FFT(CMF 3 (t)) also has more frequency components.
Pair FFT (CMF) 2 (t)) performs probability density function fitting and calculates the fuzzy entropy value of each probability density function and the difference between adjacent fuzzy entropies, as shown in fig. 6. As can be seen from fig. 6, the difference value thereof exhibits two peaks at 1 and 3 of the index numbers thereof, respectively.
Step seven of the present embodiment * (t) carrying out the extraction,is made of IMF 1 (t) and IMF 2 (t) combination of->Is made of IMF 3 (t) and IMF 4 (t) composition and the remaining composition->
For comparison purposes, the first 3 IMFs of CEEMDAN decomposition were extracted, for CMFs respectively * And (t) and IMFs perform envelope spectrum transformation, and the transformation result is shown in FIG. 7. From the figure, it can be seen that the CMF 1 * (t) and IMF 1 Envelope spectrum of (t) is similar, its rotation frequency f r 2 times rotation frequency 2f r Frequency f of inner ring failure i Frequency of failure 2f of 2 times inner ring i The distinction can be made more clearly. However, IMF 2 The rotational frequency f of the bearing cannot be discriminated in (t) r ，CMF 2 * The rotation frequency f can be identified in (t) as well r And there is no 2f i The method comprises the steps of carrying out a first treatment on the surface of the At the position ofCMF 3 * The failure frequency f of the retainer can be set in (t) t Identification of IMF 3 (t) cannot be performed. From CMF 1 * (t)—CMF 3 * (t) it was found that the frequencies were successively lower, which met the resolution objectives of CEEMDAN (corresponding high frequency components with small orders and corresponding low frequency components with large orders), and the frequency of bearing failure was 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 the different dependent claims and the features described herein may be combined in ways other than as described in the original claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.
Claims (4)
1. A method for vibration signal decomposition of a rolling bearing based on CEEMDAN, the method comprising:
s1, acquiring an original signal of vibration data of a rolling bearing, and performing empirical mode decomposition on the original signal by using CEEMDAN to obtain a plurality of eigenmode components IMF with frequency bands from high to low i (t), i=1, 2 … N, N representing the number of eigen-mode components;
s2, IMF of the eigen mode component i (t) conversion to Joint mode component CMF j (t)，j＝1,2…N-1；
S3, matching die type component CMF j (t) performing Fourier transform to obtain a spectrum FFT (CMF) j (t)) for spectral FFT (CMF) j (t)) to obtain probability density PDF (FFT (CMF) j (t)))；
S4, acquiring each probability density PDF (FFT (CMF) j (t)) and obtaining the difference value D of two adjacent fuzzy entropy values q ；
S5, searching for D q Local maxima of (a) and corresponding index number k 1 ,k 2 ,...,k n N represents the number of local maxima;
s6, taking the local maximum value as a demarcation point, forming an index interval by the index number corresponding to the local maximum value, and according to the intrinsic mode component IMF corresponding to each index number in the index interval i (t) reconstructing to obtain joint pattern components
Joint pattern componentThe method comprises the following steps:
2. the method for decomposing a vibration signal of a rolling bearing based on CEEMDAN according to claim 1, wherein in S6, the index section includes:
[1,k 1 +1],[k 1 +2,k 2 +1],......,[k n-1 +2,k n +1]。
3. the method for decomposing vibration signals of a rolling bearing based on CEEMDAN according to claim 1, wherein in S1, an empirical mode decomposition is performed on an original signal x (t) to obtain N eigenmode components IMF with frequency bands from high to low i (t)：
R represents the remainder.
4. A method of vibration signal decomposition for a rolling bearing according to claim 3, wherein in said S2, an eigenmode component IMF is obtained i (t) conversion to Joint mode component CMF j The method of (t) is as follows:
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