CN109839271A - A kind of bearing fault characteristics extracting method based on match tracing Corresponding Sparse Algorithm - Google Patents
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Abstract
The present invention relates to rotating machineries and field of signal processing, it is related to a kind of bearing fault characteristics extracting method based on match tracing Corresponding Sparse Algorithm, the vibration signal of rolling bearing is acquired first, and determine attenuation range, damping ratio range and the time delay of the vibration signal, and according to the attenuation range, damping ratio range and time delay wavelet structure basic function to construct the excessively complete dictionary in rarefaction representation；Later, match tracing is carried out to the vibration signal using the excessively complete dictionary to reconstruct the sparse coefficient of the vibration signal, until meeting iteration stopping condition；Finally, it can be seen that at the rolling bearing fault shock response moment, impact moment and inaction interval to identify from the sparse coefficient.This method replaces the inner product operation of matching pursuit algorithm, and in the case where performance is constant, computational complexity is effectively reduced, improves arithmetic speed.
Description
Technical Field
The invention relates to the field of rotating machinery and signal processing, in particular to a bearing fault feature extraction method based on a matching pursuit sparse algorithm.
Background
As a key part of mechanical equipment, a rolling bearing is often easy to break down when operating under high temperature, high pressure and complex mechanical environment for a long time. Therefore, monitoring and diagnosing the operating state of the rolling bearing are important. Once the rolling bearing in operation breaks down, periodic impact components appear in the vibration signal of the rolling bearing, so that the vibration signal of the rolling bearing is modulated. However, in the initial stage of a fault, the impact component is often weak, and is interfered by surrounding noise, so that weak fault features are difficult to extract. Therefore, how to effectively extract the weak fault characteristics of the rolling bearing is the key of fault diagnosis of the rolling bearing, and the method has important significance for guaranteeing safe and reliable operation of the rolling bearing.
In order to realize more flexible, more concise and adaptive representation of signals, on the basis of wavelet analysis, Mallat and Zhang summarize the research results of predecessors, and in 1993, a matching pursuit algorithm (MP) based on a time-frequency atomic library is proposed, which is a strategy for solving sparse representation of signals by gradual approximation. When the matching tracking algorithm is used for each iteration, the atom which is most matched with the input signal result in the over-complete atom library is selected, so that the purpose of approaching the signal is achieved. However, the traditional matching tracking algorithm often has a large calculation amount in the application of signal processing, and for a bearing vibration signal with a composite fault, due to the fact that the existing background noise components are more, the data volume is large, and the fault characteristic signal is complex, the analysis and calculation are complex, the analysis and transportation speed is slow, and the analysis effect has a further improved space.
Disclosure of Invention
In order to solve the problems, the invention provides a bearing fault feature extraction method based on a matching pursuit sparse algorithm, which replaces the inner product operation of the matching pursuit algorithm, effectively reduces the operation complexity and improves the operation speed under the condition of unchanged performance.
The invention adopts the following technical scheme to achieve the aim of the invention.
Firstly, acquiring a vibration signal of a rolling bearing, determining an attenuation range, a damping ratio range and time delay of the vibration signal, and constructing a wavelet basis function according to the attenuation range, the damping ratio range and the time delay so as to construct an over-complete dictionary in sparse representation; then, matching and tracking the vibration signal by using the over-complete dictionary to reconstruct a sparse coefficient of the vibration signal until an iteration stop condition is met; finally, the impact response time of the rolling bearing fault can be seen from the sparse coefficient, so that the impact time and the fault period can be identified.
Further, the method comprises the steps of: the method comprises the following steps: collecting a vibration signal y of a rolling bearing as a signal to be analyzed; step two: determining the attenuation range of the vibration signal y according to the frequency spectrum analysis of the acquired vibration signal y; step three: determining the damping ratio range of the vibration signal y according to a Laplace wavelet correlation filtering method; step four: determining the time delay of the acquired vibration signal y according to the acquired vibration signal y; step five: constructing a wavelet basis function to construct an overcomplete dictionary in the sparse representation; step six: matching and tracking the vibration signal y by adopting the over-complete dictionary in the step 5 to obtain a sparse coefficient, and reconstructing a vibration signal sparse coefficient according to the sparse coefficient until an iteration stop condition is met; step seven: and step six, obtaining the fault impact response time of the rolling bearing according to the vibration signal sparse coefficient, so as to identify the impact time and the fault period and output a fault result.
Further, by setting a threshold value CoDetermining the iteration number, namely the iteration stop condition, wherein the threshold value CoComprises the following steps:
in the formula: r isforRepresenting the previous signal residual, rafRepresenting the signal residual of the latter time, and stopping iteration when the iteration number is equal to the threshold value.
Further, the overcomplete dictionary in the fifth step is composed of Laplace wavelets with different parameters (τ, f, ζ).
Further, the Laplace wavelet adopts a real Laplace wavelet form:
in the formula: f is attenuation frequency, zeta is viscous damping ratio, tau is time delay, WsFor the support interval, A is used to normalize the wavelet function.
Further, in the sixth step, the vibration signal y is subjected to matching pursuit based on fast fourier transform cross-correlation to obtain sparse coefficients, and at each matching time, a time interval between each sparse coefficient is a fault period.
According to the method, the overcomplete dictionary is constructed by directly selecting the Laplace wavelet basis which is similar to the fault vibration signal, the effect of sparse representation of the fault vibration signal of the rolling bearing is improved, the problems of large calculation amount and low algorithm efficiency of a sparse representation algorithm of matching pursuit are solved, the fast cross-correlation operation is realized by using the fast calculation characteristic of fast Fourier transform, the inner product operation in the original algorithm is replaced, and the algorithm operation speed is improved.
When the matching tracking algorithm is used for each iteration, the atom which is most matched with the input signal result in the over-complete atom library is selected, so that the purpose of approaching the signal is achieved. The method has the advantages that Laplace wavelet bases which are similar to fault vibration signals are directly selected as overcomplete dictionaries, inner product operation speed of matching pursuit is low, cross-correlation operation is achieved through fast Fourier transform instead of inner product operation, better sparse representation of impact components in the fault signals of the rolling bearing can be achieved, calculation efficiency can be remarkably improved, and weak impact components in the rolling bearing signals can be extracted quickly and effectively.
Drawings
FIG. 1 is a flow chart of a bearing fault feature extraction method based on a matching pursuit sparse algorithm.
Fig. 2 is a diagram showing the analysis result of a bearing failure simulation signal in embodiment 2.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
Example 1
As shown in fig. 1, assuming that a vibration signal y of the rolling bearing is collected, the damping range, the damping ratio range, and the time delay are determined based on the vibration signal y.
Wherein, the damping ratio range of the vibration signal y is determined according to a Laplace wavelet correlation filtering method.
The Laplace wavelet is a complex exponential wavelet with unilateral attenuation, and the actually acquired vibration signals are mostly real signals, so that a Laplace wavelet real number form is adopted:
in the formula: f is attenuation frequency, zeta is viscous damping ratio, tau is time delay, WsFor the support interval, A is used to normalize the wavelet function. The Laplace wavelet is similar to the rolling bearing fault vibration signal in characteristics, so the Laplace wavelet is selected as an atom in a sparse representation overcomplete dictionary.
The overcomplete atom library D is composed of Laplace wavelets with different parameters (tau, f, zeta), a value range of zeta is determined by utilizing a correlation filtering method, and a wavelet atom most similar to a bearing state component is preferred. f is determined by a fault signal frequency spectrum peak value, tau is in the same change range with time t, the matching degree of each atom in the formed overcomplete atom library and a transient impact response component in the bearing fault signal is high, sparse representation is carried out by using the overcomplete atom library D, the overcomplete atom library is called a dictionary for short, the matching degree of atoms in the dictionary and noise is low, and noise interference can be effectively eliminated by using the method.
Let the different parameters (tau, f, zeta) be gamma (tau, f, zeta), psiγIs an atom of the atom library. Wherein,
laplace correlation filtering uses the inner product of each wavelet atom in the wavelet atom library and the vibration signal y to estimate the similarity between them. First, the wavelet function is discretized in the time domain into vectors of the same length and time resolution as the vibration signal y, and the correlation can be expressed as an inner product or dot product:
<ψγ(t),y>＝||ψγ(t)||2||y||2cosθ。
the angle θ is a metric parameter indicating correlation, and is 0 when both vectors are completely linearly correlated. By correlation coefficient k in generalγTo quantify the size of the angle:
then k isγ∈[0,1]。
When t is set, different f and zeta are selected, the correlation coefficient k is obtainedγMaximum value of kγmCorresponding frequency and damping parameters are respectivelyThen, the relevant filtering is to find the wavelet atom ψ corresponding to the maximum value on the k (τ) set corresponding to each time shift parameter τγIn the correlation filtering result, the peak time of the correlation coefficient, namely the position of the pulse response in the original signal, can obtain the corresponding Laplace wavelet damping ratio, thereby determining the range of the damping ratio.
The method is used for generating an over-complete atom library, namely a dictionary D, matching tracking based on fast Fourier transform cross-correlation is carried out on the bearing fault vibration signal to obtain each matching moment, the time interval between each sparse coefficient is a fault period, and meanwhile envelope analysis is carried out on the reconstructed signal to obtain the fault period.
And matching and tracking the vibration signal y by adopting the over-complete dictionary to obtain a sparse coefficient.
Suppose an atom in the atom library consists of a parameter (u)i,vi,wi,si) It is determined that, in the course of sparse decomposition, if a certain atomic parameter (u) in the atom library is matchedi,vi,wi,si) The selection method of (a) is kept unchanged, u can be taken as N/2, and the parameter (u) can be obtained by translationi,vi,wi,si) Atom (u) ofiNot equal to N/2), u takes all possible values [0: N-1 ] in order not to affect the sparse decomposition result]. For having a parameter (u)i,vi,wi,si) One atom g ofγThis atom is inner-product-computed N times with the residual signal. Due to uiTaking values from 0 to N-1 continuously, and performing inner product operation for all N times<Rkf,gγk>Can be converted into two vectors Rkf and gγk is cross-correlated. The process of finding the maximum value of the inner product is actually the process of finding the maximum value of the cross-correlation, and the calculation amount of atom translation is negligible, so that the atom generation time can be shortened, the storage space can be reduced, and better compromise is achieved.
In addition, the cross-correlation operation can be realized by utilizing the fast Fourier transform, the algorithm is further improved, the improvement does not influence the effect of sparse decomposition, and the speed of sparse decomposition can be greatly improved. For signals g and S, the cross-correlation function is defined as R ═ g × S, and the cross-correlation function R is subjected to fast fourier transform, that is:
fft(R)＝fft(g*S)＝fft(g)×fft(S)，
then R is ifft (g) xfft (S), where g is an atom in the overcomplete atom library, S is the inverse of the signal or signal residual, and R is the cross-correlation of g, S.
And reconstructing a vibration signal sparse coefficient according to the sparse coefficient until an iteration stop condition is met. The iteration stop judgment condition comprises the following specific analysis process: when the similarity between atoms in the dictionary D and signal impact components is high, the main impact components of the original signals can be obtained through several iterations, noise components can be introduced through excessive iterations, and in order to avoid the situation, a threshold value C is setoDetermining the number of iterations as an iteration stop condition, wherein the threshold value C isoComprises the following steps:
in the formula: r isforRepresenting the previous signal residual, rafRepresenting the last signal residual. And stopping iteration when the iteration times are equal to the threshold, and iterating all the time to obtain the main impact component of the original signal when the iteration times are smaller than the threshold, wherein the threshold is set to avoid the situation of introducing a noise component.
Example 2
As shown in FIG. 2, a bearing simulation signal is constructed, where t ∈ [0,1 ]]，f0＝300Hz，ζ0＝0.05，τ0＝0.05s，T00.1s, n (t) is white noise, AnFor the noise amplitude, take An＝0.5m/s2The sampling frequency was 2000 Hz.
From fig. 2(c), the average period T of the periodic impulse signal is 0.1s, and the set value T is obtained0Similarly, it can be seen that the proposed method can achieve good analysis effect under the condition of low signal-to-noise ratio.
Under the same conditions, the difference of the tracking algorithm of the method of the invention and the traditional basic matching tracking algorithm in the operation time is shown in table 1:
wherein MP is an english abbreviation of the matching pursuit algorithm.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions.
Claims (6)
1. A bearing fault feature extraction method based on a matching pursuit sparse algorithm is characterized by comprising the steps of firstly collecting vibration signals of a rolling bearing, determining an attenuation range, a damping ratio range and time delay of the vibration signals, and constructing a wavelet basis function according to the attenuation range, the damping ratio range and the time delay so as to construct an over-complete dictionary in sparse representation; then, matching and tracking the vibration signal by using the over-complete dictionary to reconstruct a sparse coefficient of the vibration signal until an iteration stop condition is met; finally, the impact response time of the rolling bearing fault can be seen from the sparse coefficient, so that the impact time and the fault period can be identified.
2. The bearing fault feature extraction method based on the matching pursuit sparse algorithm as claimed in claim 1, wherein the method comprises the following steps:
the method comprises the following steps: collecting a vibration signal y of a rolling bearing as a signal to be analyzed;
step two: determining the attenuation range of the vibration signal y according to the frequency spectrum analysis of the acquired vibration signal y;
step three: determining the damping ratio range of the vibration signal y according to a Laplace wavelet correlation filtering method;
step four: determining the time delay of the acquired vibration signal y according to the acquired vibration signal y;
step five: constructing a wavelet basis function to construct an overcomplete dictionary in the sparse representation;
step six: matching and tracking the vibration signal y by adopting the over-complete dictionary in the step 5 to obtain a sparse coefficient, and reconstructing a vibration signal sparse coefficient according to the sparse coefficient until an iteration stop condition is met;
step seven: and step six, obtaining the fault impact response time of the rolling bearing according to the vibration signal sparse coefficient, so as to identify the impact time and the fault period and output a fault result.
3. The bearing fault feature extraction method based on the matching pursuit sparse algorithm as claimed in claim 1 or 2, wherein a threshold value C is setoDetermining the iteration number, namely the iteration stop condition, wherein the threshold value CoComprises the following steps:
in the formula: r isforRepresenting the previous signal residual, rafRepresenting the next signal residual;
the iteration is stopped when the number of iterations equals a threshold.
4. The method for extracting bearing fault features based on the matching pursuit sparse algorithm as claimed in claim 2, wherein the overcomplete dictionary in the step five is composed of Laplace wavelets with different parameters (τ, f, ζ).
5. The method for extracting bearing fault features based on the matching pursuit sparse algorithm as claimed in claim 2 or 4, wherein the Laplace wavelet adopts a Laplace wavelet real number form:
in the formula: f is attenuation frequency, zeta is viscous damping ratio, tau is time delay, WsFor the support interval, A is used to normalize the wavelet function.
6. The method for extracting bearing fault features based on the matching pursuit sparse algorithm as claimed in claim 2, wherein in the sixth step, the vibration signal y is subjected to matching pursuit based on fast fourier transform cross-correlation to obtain sparse coefficients, and the time interval between the sparse coefficients is the fault period at each matching time.
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| CN113836732A (en) * | 2021-09-29 | 2021-12-24 | 华东理工大学 | Vibration signal sparse reconstruction method guided by impact characteristic index and application |
| CN114778113A (en) * | 2022-03-29 | 2022-07-22 | 北京化工大学 | Bearing fault feature extraction method based on unilateral attenuation wavelet convolution sparsity |
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| CN110940524A (en) * | 2019-12-06 | 2020-03-31 | 西安交通大学 | Bearing fault diagnosis method based on sparse theory |
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| CN111007281A (en) * | 2019-12-27 | 2020-04-14 | 华中科技大学 | Method and system for diagnosing faults of rotating speed sensor based on wavelet function correlation |
| CN111678691A (en) * | 2020-07-27 | 2020-09-18 | 江南大学 | Gear fault detection method based on improved sparse decomposition algorithm |
| CN113836732A (en) * | 2021-09-29 | 2021-12-24 | 华东理工大学 | Vibration signal sparse reconstruction method guided by impact characteristic index and application |
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| CN114778113B (en) * | 2022-03-29 | 2024-05-28 | 北京化工大学 | Bearing fault feature extraction method based on unilateral attenuation wave convolution sparseness |
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