CN115169396A - Bearing weak fault feature extraction method based on parameter dictionary and OMP algorithm - Google Patents
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Abstract
The invention discloses a bearing weak fault feature extraction method based on a parameter dictionary and an OMP algorithm, wherein a sparse representation model of a rolling bearing vibration signal is established according to collected rolling bearing vibration data; the vibration data of the rolling bearing comprise rolling bearing vibration signals with useful fault information and useless background noise information, and the sparse coefficient matrix of the signal sparse representation model of the rolling bearing is solved by adopting an orthogonal matching pursuit algorithm according to a Laplace wavelet parameter dictionary; and reconstructing the signal by using the sparse coefficient matrix and the Laplace wavelet parameter dictionary, carrying out envelope analysis on the reconstructed signal, and extracting weak fault characteristics to realize bearing fault diagnosis. The method can effectively reduce the algorithm complexity of the original method, can more accurately extract the weak fault characteristics of the bearing under the noise under the strong background, and can simply and effectively diagnose the fault of the rolling bearing in engineering practice.
Description
Technical Field
The invention belongs to the field of fault diagnosis of rolling bearings of mechanical rotating equipment, and particularly relates to a method for extracting weak fault characteristics of a bearing based on a parameter dictionary and an OMP algorithm.
Background
Rolling bearings are widely used in various types of rotating machinery and are indispensable core components in mechanical systems. However, long-time operation and complicated and variable severe working conditions often cause the rolling bearing to be in failure. When the rolling bearing is in early failure, no obvious abnormality exists, the failure characteristics are very weak, and the rolling bearing is more difficult to perceive under the interference of strong background noise. However, as the fault point is enlarged and deepened, the early fault can rapidly become a serious fault, which may result in the damage of mechanical equipment to cause economic loss, and may result in safety accidents to cause casualties. Therefore, developing fault diagnosis research of the rolling bearing has a very positive significance for practical engineering. Meanwhile, the extraction of weak fault characteristics of the rolling bearing under strong background noise is a key difficult problem to be solved urgently.
In recent years, feature extraction methods based on sparse representation have been developed and widely applied in the field of signal processing. Mallet et al first proposed the idea of adaptive decomposition of a signal on an overcomplete dictionary, sparsely representing the original signal by selecting as few atoms from the overcomplete dictionary as possible that are most similar to the signal. The sparse representation method can capture key fault information in the signals, neglect interference information irrelevant to the fault, and express the original signals simply and efficiently, so that the sparse representation method has certain noise filtering capability. In view of the characteristics of the sparse representation method, a plurality of scholars develop bearing fault diagnosis research based on the sparse representation method, and the main research direction is the construction of an atomic dictionary and a sparse coefficient solution optimization algorithm.
The wavelet parameter dictionary is flexible, and can adapt to different types of fault signals by changing wavelet types and adjusting wavelet parameters. A common method for determining wavelet parameters is correlation filtering. However, the correlation filtering method is very time consuming because all wavelet parameter libraries need to be traversed to determine the wavelet parameters.
In addition, when the fault impact characteristics are weak, the related filtering method is easily interfered by noise in the process of searching the optimal wavelet parameters, and the accurate wavelet parameters are difficult to obtain. The traditional OMP algorithm stopping criterion is a sparsity stopping criterion and an energy stopping criterion, the sparsity stopping criterion needs to be used for finding out proper sparsity by depending on experience or a large number of parameters, the energy stopping criterion is easily influenced by noise, iteration can be stopped too early under strong background noise, the signal reconstruction precision is influenced, and therefore effective weak fault features cannot be extracted.
Disclosure of Invention
Aiming at the defects and the engineering problems in the prior art, the invention aims to provide a bearing weak fault feature extraction method based on a parameter dictionary and an OMP algorithm, which can effectively extract the bearing weak fault features under strong background noise and is very fit with the actual engineering background.
In order to achieve the above purpose, the technical scheme of the invention is as follows:
the method for extracting the weak fault characteristics of the bearing based on the parameter dictionary and the OMP algorithm comprises the following steps:
1) Establishing a sparse representation model of a rolling bearing vibration signal according to the collected rolling bearing vibration data; the rolling bearing vibration data are rolling bearing vibration signals comprising useful fault information and useless background noise information;
2) Solving a sparse coefficient matrix of a signal sparse representation model of the rolling bearing by adopting an orthogonal matching tracking algorithm according to the Laplace wavelet parameter dictionary; and reconstructing the vibration signal of the rolling bearing comprising useful fault information and useless background noise information through a sparse coefficient matrix and a Laplace wavelet parameter dictionary, carrying out envelope analysis on the reconstructed signal, extracting weak fault characteristics and realizing fault diagnosis of the rolling bearing.
The invention is further improved in that the vibration signal of the rolling bearing including useful fault information and useless background noise information is:
y＝Dα+n
wherein D = { D 1 ,d 2 ,…d n Is an atom dictionary, d i (i =1,2.. N) is an atom in the atom dictionary, α = { α } (1) ,α (2) ,…α (m) } T Being a sparse coefficient matrix, alpha (1) 、α (2) ...α (m) Sparse coefficients corresponding to different atoms.
The invention is further improved in that the sparse representation model of the vibration signal of the rolling bearing is as follows:
wherein | a | | calucity 1 Is the minimum l of the sparse coefficient matrix 1 And the norm, wherein epsilon is a residual error, y is a rolling bearing vibration signal comprising useful fault information and useless background noise information, D is an atomic dictionary, and alpha is a sparse coefficient matrix.
The invention is further improved in that the atom dictionary is obtained by the following process:
traversing a Laplace wavelet parameter library after optimizing a related filtering method by adopting a particle swarm algorithm, and searching an optimal Laplace wavelet parameter to enable the Laplace wavelet to be most similar to a vibration signal of a rolling bearing, so as to obtain an optimal Laplace wavelet; and expanding the optimal Laplace wavelet atoms into a Laplace wavelet parameter dictionary.
The further improvement of the invention is that the optimal Laplace wavelet parameter is obtained by the following processes:
and searching a Laplace wavelet most similar to the signal by traversing the Laplace wavelet parameter library to obtain a correlation coefficient of the Laplace wavelet and the signal, wherein when the correlation coefficient of the Laplace wavelet and the signal is maximum, the parameter corresponding to the Laplace wavelet is an optimal Laplace wavelet parameter.
The invention is further improved in that the correlation coefficient of the Laplace wavelet and the signal is calculated by the following formula:
where ψ is a Laplace wavelet, y is a signal,<·>for inner product operation, | · (| non-conducting phosphor) 2 Is a two-norm, cc is the correlation coefficient of the Laplace wavelet and the signal.
The invention has the further improvement that the optimal Laplace wavelet atom is expanded into a Laplace wavelet parameter dictionary according to different time-shifting parameters tau.
The further improvement of the invention is that the optimal Laplace wavelet parameter is calculated by the following formula:
wherein, the first and the second end of the pipe are connected with each other,
for an optimal Laplace wavelet parameter, F is a parameter set of natural frequency F, Z is a parameter set of viscous damping ratio xi, T is a parameter set of time shifting parameter tau, and cc is a correlation coefficient of the Laplace wavelet and a signal.
The invention has the further improvement that the specific process of solving the sparse coefficient matrix of the signal sparse representation model of the rolling bearing by adopting the orthogonal matching pursuit algorithm according to the Laplace wavelet parameter dictionary is as follows:
when improved square envelope spectrum negative entropy I delta I E And when the maximum value is reached, stopping the iteration of the orthogonal matching tracking algorithm to obtain a sparse coefficient matrix.
The invention is further improved in that the improved square envelope spectrum negative entropy I delta I E Calculated by the following formula:
IΔI E ＝SD·ΔI E
wherein, I Delta I E For improved negative entropy of the square envelope spectrum, SD is the signal standard deviation, delta I E Is the square envelope spectrum negative entropy of the signal;
the calculation formula SD of the signal standard deviation is as follows:
wherein, N is the number of sampling points of the signal, and mu is the mean value of the signal;
negative entropy Δ I of squared envelope spectrum of signal E ComputingThe formula is as follows:
wherein the content of the first and second substances,<·>for mean calculation, E x (α; f, Δ f) is a discrete signal x (n) (n =0, \8230;, L) at a frequency [ f- Δ f/2, f + Δ f/2]The squared envelope spectrum in the range, expressed as:
wherein epsilon x (n; f, Δ f) is a discrete signal x (n) (n =0, \8230;, L) at a frequency [ f- Δ f/2, f + Δ f/2]The squared envelope within the range, expressed as:
ε x (n；f,Δf)＝|x(n；f,Δf)| 2 。
compared with the prior art, the invention has the beneficial effects that:
according to the method, the Laplace wavelet is used for constructing the parameter dictionary, so that the fault impact in the vibration signal of the rolling bearing can be accurately matched, and the weak fault characteristics of the rolling bearing can be more accurately extracted; the sparse coefficient matrix is optimized and solved by adopting an orthogonal matching pursuit algorithm (OMP algorithm), and the algorithm not only can be rapidly converged, but also can be used for accurately reconstructing signals; the invention adopts the improved square envelope spectrum negative entropy criterion to replace the original stopping criterion in the OMP algorithm, so that the OMP algorithm can automatically stop iteration, and the adaptability of the OMP algorithm is improved. The method can well extract the weak fault characteristics of the bearing under strong background noise, and is easy to realize fault diagnosis of the rolling bearing in engineering practice.
Furthermore, the Laplace wavelet parameter searching process of the related filtering method is optimized by using a particle swarm algorithm, so that the complexity of the algorithm is reduced, and the similarity between the searched optimal Laplace wavelet and a signal is improved;
furthermore, the optimal Laplace wavelet atom is expanded into a Laplace wavelet parameter dictionary according to different time-shifting variables, so that each atom in the dictionary has the most similar signal, and the signal reconstruction precision in subsequent sparse decomposition is improved;
drawings
FIG. 1 is a flow chart of a bearing weak fault feature extraction method based on a Laplace wavelet parameter dictionary and an improved OMP algorithm, which is provided by the invention;
FIG. 2 is a life cycle RMS curve for a bearing;
FIG. 3 is a time domain waveform diagram and an envelope spectrogram of a bearing, wherein (a) is the time domain waveform diagram, and (b) is the envelope spectrogram;
fig. 4 is a waveform diagram and an envelope spectrogram of a reconstructed signal obtained by decomposing a bearing vibration signal by a conventional CFA and OMP method, where (a) is a signal time domain waveform diagram and (b) is a reconstructed signal envelope spectrogram;
fig. 5 is a waveform diagram and an envelope spectrum of a reconstructed signal obtained by decomposing a bearing signal by the improved CFA and OMP methods, where (a) is a signal time domain waveform diagram and (b) is a reconstructed signal envelope spectrum.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
The invention provides a bearing weak fault feature extraction method based on a Laplace wavelet parameter dictionary and an improved OMP algorithm, aiming at the problem that the bearing weak fault features are difficult to extract under the interference of strong background noise. Firstly, establishing a signal sparse representation model, aiming at the problem of high calculation complexity of determining optimal Laplace wavelet parameters, introducing a particle swarm optimization to optimize a parameter searching process of a related filtering method, and overcoming the defects of high calculation complexity and susceptibility to interference information of the related filtering method; and expanding the optimal Laplace wavelet atoms into a Laplace wavelet parameter dictionary according to different time shifting variables. Then, aiming at the problems that the iteration stopping criterion of the orthogonal matching pursuit algorithm is lack of self-adaption and is easily influenced by noise, the iteration stopping criterion based on the improved square envelope spectrum negative entropy index is provided, and the index can uniformly represent the impact characteristic and the cyclostationarity characteristic of the bearing vibration signal. Then, an iteration stopping criterion based on an improved square envelope spectrum negative entropy index is provided to replace the original stopping criterion of the OMP algorithm, and the index can enable the OMP algorithm to automatically stop iteration; finally, envelope spectrum analysis is carried out on the reconstructed signal after sparse decomposition, weak fault features are extracted, and fault diagnosis is achieved.
The embodiment analysis verifies that the test result shows that the method not only can effectively reduce the algorithm complexity of the original method, but also can more accurately extract the weak fault characteristics of the bearing under the noise under the strong background, and can simply and effectively diagnose the fault of the rolling bearing in the engineering practice.
Specifically, the method comprises the following steps:
1) Firstly, according to collected rolling bearing vibration data which are rolling bearing vibration signals including useful fault information and useless background noise information, establishing a sparse representation model of the rolling bearing vibration signals based on a sparse representation theory, wherein the sparse representation model mainly comprises a parameter dictionary construction part and a sparse coefficient solving optimization algorithm part; the specific process is as follows:
1.1 According to the sparse representation theory, the rolling bearing vibration signal of useful fault information and useless background noise information is re-expressed, specifically:
y＝x+n
wherein y is a vibration signal of the rolling bearing, x is a fault characteristic component in the vibration signal, and n is background noise.
The sparse representation theory reforms the original signal by selecting as few as possible linear combinations of atoms most similar to the signal from the atom dictionary, and thus, the vibration signal of the rolling bearing can be further represented by the sparse representation theory as:
y＝Dα+n
wherein D = { D = 1 ,d 2 ,…d n Is an atom dictionary, d i (i =1,2.. N) is an atom in the atom dictionary, α = { α = (1) ,α (2) ,…α (m) } T A sparse coefficient matrix is adopted, and alpha is a sparse coefficient corresponding to different atoms;
1.2 Solving a solution of the linear combination based on a sparse representation model of the vibration signal of the rolling bearing, the process of solving the sparse representation model being as followsBased on atom dictionary, solving minimum l of sparse coefficient matrix 0 Norm procedure, therefore, the objective function of the sparse representation model can be expressed as:
wherein | a | | calucity 0 Is a sparse coefficient matrix 0 Norm and epsilon are residual errors, and because the problem is an NP-hard problem and cannot be directly solved, a classical OMP algorithm is selected to carry out approximate approximation on the residual errors, and the minimum l is solved 0 The norm problem is converted into the solution of the minimum l 1 Norm problem:
wherein | α | Y phosphor 1 Is a sparse coefficient matrix 1 A norm;
2) Secondly, in the construction process of the parameter dictionary, considering that the Laplace wavelet waveform is most similar to the fault impact waveform of the rolling bearing, constructing the Laplace wavelet parameter dictionary based on the Laplace wavelet; traversing a Laplace wavelet parameter base by adopting a Correlation Filtering Algorithm (CFA) to find an optimal Laplace wavelet parameter so that the Laplace wavelet is most similar to a rolling bearing vibration signal, and obtaining an optimal Laplace wavelet; aiming at the problem of high computational complexity of CFA (computational fluid dynamics), a parameter searching process of a particle swarm optimization related filtering method is introduced, so that the optimal Laplace wavelet parameters are searched more quickly, and the obtained optimal Laplace wavelet atoms are expanded into a Laplace wavelet parameter dictionary;
the specific process is as follows:
2.1 Using a particle swarm algorithm) is:
the idea of the particle swarm optimization is derived from research on foraging behavior of a bird swarm, each individual is abstracted into a particle, each particle represents a candidate solution of an optimization problem, the candidate solutions obtain fitness values according to fitness functions, and the final result is that the globally optimal fitness values are obtained in different candidate solutions. The updating formula of the particle swarm algorithm is as follows:
wherein the content of the first and second substances,
and
respectively, the d-dimension velocity and position vector of the particle i in the k-th iteration, w is the inertia weight, c 1 And c 2 Is a learning factor, r 1 And r 2 Is the interval [0]The random number of the inner part of the random number,
for the individual optimal position of the particle i in the d-th dimension in the k-th iteration,
and the global optimal position of the d-dimension of the particle swarm in the k-th iteration is defined.
2.2 Adopting a particle swarm algorithm to optimize the reference of CFA and determine the optimal Laplace wavelet parameter, the specific process is as follows:
selecting a correlation coefficient of the CFA as a fitness function of the particle swarm algorithm, and solving a maximum fitness value, namely a maximum correlation coefficient, as an optimization target;
the Laplace wavelet has the mathematical expression as follows:
wherein f ∈ R + Is the natural frequency, xi is the viscous damping ratio in 0, 1), tau is the time shift parameter,the three parameters directly determine the waveform characteristics of the Laplace wavelet, the CFA searches for the Laplace wavelet most similar to the signal by traversing a Laplace wavelet parameter library, and quantitatively represents the similarity of the Laplace wavelet and the signal by a correlation coefficient:
where ψ is a Laplace wavelet, y is a signal,<·>for inner product operation, | · (| non-conducting phosphor) 2 Is a two-norm, cc is a correlation coefficient of the Laplace wavelet and the signal;
the optimal Laplace wavelet parameter is the parameter corresponding to the Laplace wavelet with the maximum similarity to the signal y, namely:
wherein, the first and the second end of the pipe are connected with each other,
for the optimal Laplace wavelet parameter, F is a parameter set of the inherent frequency F, Z is a parameter set of the viscous damping ratio xi, and T is a parameter set of the time shifting parameter tau.
2.3 After finding the optimal Laplace wavelet parameter, considering that the fault impact of the rolling bearing shows a cyclic periodic characteristic, expanding the optimal Laplace wavelet atom into a Laplace wavelet parameter dictionary according to different time-shifting parameters tau;
3) Finally, according to the constructed Laplace wavelet parameter dictionary, solving the sparse coefficient of the signal sparse representation model of the rolling bearing by adopting an orthogonal matching pursuit algorithm (OMP); the OMP algorithm decomposes and reconstructs the rolling bearing vibration signal based on a Laplace wavelet parameter dictionary, and filters interference information while keeping the rolling bearing fault impact information, thereby extracting the weak fault characteristics of the rolling bearing; aiming at the problems that an OMP algorithm iteration stopping criterion is lack of self-adaption and is easily influenced by noise, the method provides an iteration stopping criterion based on an improved square envelope spectrum negative entropy index, and the criterion is used for replacing the original stopping criterion of the OMP algorithm;
the specific process is as follows:
3.1 Using OMP to solve for sparse coefficients, the detailed algorithm steps are:
inputting: vibration signal y, atom dictionary D, sparsity K.
Initialization: initial residual r 0 = y, support index set
The iteration initial value k =1.
And (3) an iterative process: step 1-step 4 are performed in the kth iteration.
Step 1: finding a support index:
step 2: adding the matched most relevant atom indexes into an index set:
Λ k ＝Λ k-1 ∪{λ k }
and 3, step 3: and (3) updating residual errors by using a least square method:
and 4, step 4: k = K +1, return to step 1, when K = K, stop iteration.
And (3) outputting: support index set Λ k ＝Λ k-1 Sparse coefficient matrix
3.2 The iteration stop criterion based on the improved square envelope spectrum negative entropy index is used for replacing the original iteration stop criterion of the OMP, and the specific process is as follows:
the objective function for solving the sparse coefficient by the OMP algorithm is as follows:
wherein, I Delta I E (D α) is the I Δ I of the reconstructed signal after each iteration in the sparse decomposition process E The value, mu, is a penalty factor,
the resulting sparse coefficient matrix is solved.
The improved square envelope spectrum negative entropy index formula is as follows:
IΔI E ＝SD·ΔI E
wherein, I.DELTA.I E For improved negative entropy of the square envelope spectrum, SD is the signal standard deviation, delta I E Is the square envelope spectrum negative entropy of the signal;
the calculation formula SD of the signal standard deviation is:
wherein, N is the number of sampling points of the signal, and mu is the mean value of the signal;
negative entropy Δ I of squared envelope spectrum of signal E The calculation formula is as follows:
wherein, the first and the second end of the pipe are connected with each other,<·>for mean calculation, E x (α; f, Δ f) is a discrete signal x (n) (n =0, \8230;, L) at a frequency [ f- Δ f/2, f + Δ f/2]The squared envelope spectrum in the range, expressed as:
wherein epsilon x (n; f, Δ f) is a discrete signal x (n) (n =0, \8230;, L) at a frequency [ f- Δ f/2, f + Δ f/2]Squared envelope within a range, expression thereofThe formula is as follows:
ε x (n；f,Δf)＝|x(n；f,Δf)| 2
the improved OMP iteration stop criteria are:
the original stopping criterion is to set a certain sparsity K, the iteration is stopped when the iteration times reach K times, the improved iteration stopping criterion does not need to set the sparsity K, and the I delta I of the reconstructed signal is calculated in each iteration process of the algorithm E Value when I.DELTA.I E And stopping iteration when the maximum value is reached, and obtaining a sparse coefficient matrix at the moment.
And reconstructing the signal by using the sparse coefficient matrix and the Laplace wavelet parameter dictionary, filtering useless interference information by using the reconstructed signal, reserving fault information as much as possible, carrying out envelope analysis on the reconstructed signal (the process of the envelope analysis is a known technology in the field), and extracting weak fault characteristics.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Example 1
The embodiment uses an IMS bearing life test to disclose a data set, and verifies the effectiveness of the invention.
Fig. 1 is a flow chart of a bearing weak fault feature extraction method based on a Laplace wavelet parameter dictionary and an improved OMP algorithm, and referring to fig. 1, the bearing weak fault feature extraction is performed according to the flow chart.
The method mainly comprises the following steps: establishing a sparse representation model of the vibration signal of the rolling bearing, constructing a Laplace wavelet parameter dictionary, and solving a sparse coefficient matrix by using an OMP algorithm.
(1) Firstly, according to the sparse representation theory, the rolling bearing vibration signal is re-expressed as follows:
y＝x+n
wherein y is a vibration signal of the rolling bearing, x is a fault characteristic component in the vibration signal, and n is background noise.
The sparse representation theory reforms the original signal by selecting as few as possible linear combinations of atoms most similar to the signal from the atom dictionary, and thus, the vibration signal of the rolling bearing can be further represented by the sparse representation theory as:
y＝Dα+n
wherein D = { D = 1 ,d 2 ,…d n Is an atom dictionary, d is an atom in the atom dictionary, α = { α = { α } (1) ,α (2) ,…α (m) } T A sparse coefficient matrix is adopted, and alpha is a sparse coefficient corresponding to different atoms;
secondly, solving the solution of the linear combination based on the sparse representation model, wherein the process of solving the sparse representation model is based on an atomic dictionary and the minimum l of a sparse coefficient matrix is solved 0 Norm procedure, therefore, the objective function of the sparse representation model can be expressed as:
wherein | a | | calucity 0 Is a sparse coefficient matrix 0 Norm and epsilon are residual errors, and because the problem is an NP-hard problem and cannot be directly solved, a classical OMP algorithm is selected to carry out approximate approximation on the residual errors, and the minimum l is solved 0 The norm problem is converted into the solution of the minimum l 1 Norm problem:
wherein | a | | calucity 1 Is a sparse coefficient matrix 1 A norm;
(2) Firstly, the specific process of determining the Laplace wavelet optimal parameters by using the CFA method comprises the following steps:
the Laplace wavelet has the mathematical expression as follows:
wherein f ∈ R + For the natural frequency, xi is epsilon [0, 1) as the viscous damping ratio, tau is the time shift parameter, and the three parameters directly determineThe CFA searches for the Laplace wavelet most similar to the signal by traversing a Laplace wavelet parameter library, and quantitatively represents the similarity of the Laplace wavelet and the signal through a correlation coefficient:
wherein psi is Laplace wavelet, y is signal,<·>for inner product operation, | · (| non-conducting phosphor) 2 Is a two-norm, cc is a correlation coefficient of the Laplace wavelet and the signal;
the optimal wavelet parameters are the parameters corresponding to the maximum similarity between the Laplace wavelet and the signal y, namely:
wherein the content of the first and second substances,
f, Z and T are wavelet parameter spaces for the optimal wavelet parameters;
secondly, optimizing the CFA parameter searching process by using a particle swarm optimization algorithm specifically comprises the following steps:
the idea of the particle swarm optimization is derived from research on foraging behaviors of bird swarms, each individual is abstracted into a particle, each particle represents a candidate solution of an optimization problem, the candidate solutions obtain fitness values according to fitness functions, and the final result is that globally optimal fitness values are obtained in different candidate solutions. The updating formula of the particle swarm algorithm is as follows:
wherein the content of the first and second substances,
and
respectively, the d-dimension velocity and position vector of the particle i in the k-th iteration, w is the inertia weight, c 1 And c 2 Is a learning factor, r 1 And r 2 Is the interval [0]The random number of the inner part of the random number,
for the individual optimal position of particle i in the d-th dimension in the k-th iteration,
and the global optimal position of the d-dimension of the particle swarm in the k-th iteration is defined. Optimizing a parameter searching process of the CFA by the particle swarm optimization, selecting a correlation coefficient of the CFA as a fitness function of the particle swarm optimization, and solving a maximum fitness value, namely a maximum correlation coefficient, as an optimization target;
finally, after the optimal Laplace wavelet is found, considering that the fault impact of the rolling bearing shows a cycle characteristic, expanding the optimal Laplace wavelet atom into a Laplace wavelet parameter dictionary according to different time shift variables;
(3) Firstly, OMP is used for solving sparse coefficients, and the detailed algorithm steps are as follows:
inputting: vibration signal y, atom dictionary D, sparsity K.
Initialization: initial residual r 0 = y, supporting index set
The iteration initial value k =1.
And (3) an iterative process: step 1-step 4 are performed in the kth iteration.
Step 1: finding a support index:
step 2: adding the matched most relevant atom indexes into an index set:
Λ k ＝Λ k-1 ∪{λ k }
and step 3: and (3) updating residual errors by using a least square method:
and 4, step 4: k = K +1, return to step 1, and stop iteration when K = K.
And (3) outputting: support index set Λ k ＝Λ k-1 Sparse coefficient matrix
Secondly, an improved square envelope spectrum negative entropy index-based iteration stop criterion is used for replacing the original iteration stop criterion of the OMP, and the specific process is as follows:
the improved square envelope spectrum negative entropy index formula is as follows:
IΔI E ＝SD·ΔI E
wherein, I Delta I E For improved negative entropy of the square envelope spectrum, SD is the signal standard deviation, Δ I E Is the square envelope spectrum negative entropy of the signal;
the calculation formula of the standard deviation of the signals is as follows:
wherein, N is the number of sampling points of the signal, and mu is the mean value of the signal;
the square envelope spectrum negative entropy calculation formula of the signal is as follows:
wherein the content of the first and second substances,<·>for mean calculation, E x (α; f, Δ f) is a dispersionThe signal x (n) (n =0, \8230;, L) is at frequency [ f- Δ f/2, f + Δ f/2]The squared envelope spectrum in the range, expressed as:
wherein epsilon x (n; f, Δ f) is a discrete signal x (n) (n =0, \8230;, L) at a frequency [ f- Δ f/2, f + Δ f/2]The squared envelope within the range, expressed as:
ε x (n；f,Δf)＝|x(n；f,Δf)| 2
the improved OMP iteration stop criterion is:
the original stopping criterion is to set a certain sparsity K, the iteration is stopped when the iteration times reach K times, the improved iteration stopping criterion does not need to set the sparsity K, and the I delta I of the reconstructed signal is calculated in each iteration process of the algorithm E Value when I.DELTA.I E Stopping iteration when the maximum value is reached;
finally, decomposing and reconstructing the signal based on an OMP algorithm of an improved stopping criterion; the specific process is as follows:
the objective function for solving sparse coefficients using the proposed method is:
wherein, I.DELTA.I E (D α) is the I Δ I of the reconstructed signal after each iteration in the sparse decomposition process E The value, μ, is a penalty factor,
to solve the resulting sparse coefficient matrix.
The analysis was performed using the IMS bearing public data set, using the method described above.
As shown in fig. 2, when the bearing is in early failure, there is a significant transient impact and it soon develops into a severe failure, and to better verify the effectiveness of the invention, this embodiment uses the 564 th data point marked in the figure for analysis, the amplitude of the bearing is not abnormally fluctuating during this time period, and the bearing failure characteristics are very weak under the influence of the noise background.
As shown in fig. 3 (a) and (b), the time domain waveform of the bearing has no obvious periodicity, and the characteristic frequency of the bearing fault is not found in the envelope spectrum.
As shown in fig. 4 (a) and (b), the original CFA and OMP methods are used to analyze the fault signal, and the difference between the waveform of the reconstructed signal and the fault impact waveform of the bearing is large, which indicates that the reconstruction effect is not good, and the characteristic frequency of the bearing fault cannot be found in the envelope spectrum.
As shown in (a) and (b) of fig. 5, by using the method of the present invention, the waveform of the reconstructed signal is very similar to the fault impact waveform of the bearing, and the fault frequency of the outer ring of the bearing and the frequency doubling and frequency tripling thereof can also be found in the envelope spectrum of the reconstructed signal.
The embodiment result shows that the method for extracting the weak fault characteristics of the bearing based on the Laplace wavelet parameter dictionary and the improved OMP algorithm can extract the weak fault characteristics of the bearing under the interference of strong background noise, can diagnose the fault of the bearing at the initial stage of the fault, and can better perform early warning on the health state of the bearing.
The method is based on the Laplace wavelet parameter dictionary and the improved OMP algorithm, can better extract the weak fault characteristics of the rolling bearing under strong background noise, thereby realizing the fault diagnosis of the rolling bearing, can be used for early weak fault diagnosis in engineering practice, and can early warn the health state of the rolling bearing.
The method can effectively reduce the algorithm complexity of the original method, can more accurately extract the weak fault characteristics of the bearing under the noise under the strong background, can simply and effectively diagnose the fault of the rolling bearing in engineering practice, and provides a new idea for the fault diagnosis of the rolling bearing.
Claims (10)
1. The method for extracting the weak fault characteristics of the bearing based on the parameter dictionary and the OMP algorithm is characterized by comprising the following steps of:
1) Establishing a sparse representation model of a rolling bearing vibration signal according to the collected rolling bearing vibration data; the rolling bearing vibration data are rolling bearing vibration signals comprising useful fault information and useless background noise information;
2) Solving a sparse coefficient matrix of a signal sparse representation model of the rolling bearing by adopting an orthogonal matching tracking algorithm according to the Laplace wavelet parameter dictionary; reconstructing the vibration signals of the rolling bearing comprising useful fault information and useless background noise information through a sparse coefficient matrix and a Laplace wavelet parameter dictionary, carrying out envelope analysis on the reconstructed signals, extracting weak fault characteristics, and realizing fault diagnosis of the rolling bearing.
2. The method for extracting weak fault features of a bearing based on a parameter dictionary and an OMP algorithm according to claim 1, wherein the vibration signals of the rolling bearing comprising useful fault information and useless background noise information are as follows:
y＝Dα+n
wherein D = { D = 1 ,d 2 ,…d n Is an atom dictionary, d i (i =1,2.. N) is an atom in the atom dictionary, α = { α = (1) ,α (2) ,…α (m) } T Being a sparse coefficient matrix, alpha (1) 、α (2) ...α (m) The sparse coefficients correspond to different atoms.
3. The method for extracting weak fault features of a bearing based on a parameter dictionary and an OMP algorithm according to claim 1, wherein the sparse representation model of the vibration signals of the rolling bearing is as follows:
wherein | α | Y phosphor 1 Is a sparse coefficient matrix 1 Norm, epsilon is residual error, y is rolling bearing vibration signal including useful fault information and useless background noise information, D is an atom dictionary, and alpha is a sparse coefficient matrix.
4. The method for extracting the weak fault features of the bearing based on the parameter dictionary and the OMP algorithm according to claim 3, wherein the atom dictionary is obtained by the following process:
traversing a Laplace wavelet parameter library after optimizing a related filtering method by adopting a particle swarm algorithm, and searching an optimal Laplace wavelet parameter to enable the Laplace wavelet to be most similar to a rolling bearing vibration signal, so as to obtain an optimal Laplace wavelet; and expanding the optimal Laplace wavelet atoms into a Laplace wavelet parameter dictionary.
5. The method for extracting the weak fault characteristics of the bearing based on the parameter dictionary and the OMP algorithm according to claim 4, wherein the optimal Laplace wavelet parameters are obtained through the following processes:
and searching a Laplace wavelet most similar to the signal by traversing the Laplace wavelet parameter library to obtain a correlation coefficient of the Laplace wavelet and the signal, wherein when the correlation coefficient of the Laplace wavelet and the signal is maximum, the parameter corresponding to the Laplace wavelet is an optimal Laplace wavelet parameter.
6. The method for extracting weak fault characteristics of a bearing based on a parameter dictionary and an OMP algorithm as claimed in claim 4, wherein the correlation coefficient between a Laplace wavelet and a signal is calculated by the following formula:
where ψ is a Laplace wavelet, y is a signal,<·>for inner product operation, | · (| non-conducting phosphor) 2 Is a two-norm, cc is the correlation coefficient of the Laplace wavelet and the signal.
7. The method for extracting the weak fault characteristics of the bearing based on the parameter dictionary and the OMP algorithm as claimed in claim 1, wherein the optimal Laplace wavelet atoms are expanded into the Laplace wavelet parameter dictionary according to different time-shifting parameters τ.
8. The method for extracting the weak fault characteristics of the bearing based on the parameter dictionary and the OMP algorithm according to claim 1, wherein the optimal Laplace wavelet parameter is calculated by the following formula:
wherein the content of the first and second substances,
for the optimal Laplace wavelet parameter, F is a parameter set of the natural frequency F, Z is a parameter set of the viscous damping ratio xi, T is a parameter set of the time shifting parameter tau, and cc is a correlation coefficient of the Laplace wavelet and the signal.
9. The method for extracting the weak fault characteristics of the bearing based on the parameter dictionary and the OMP algorithm according to claim 1, wherein the specific process of solving the sparse coefficient matrix of the signal sparse representation model of the rolling bearing by adopting the orthogonal matching pursuit algorithm according to the Laplace wavelet parameter dictionary is as follows:
when improved square envelope spectrum negative entropy I delta I E And when the maximum value is reached, stopping the iteration of the orthogonal matching tracking algorithm to obtain a sparse coefficient matrix.
10. The method for extracting weak fault characteristics of bearing based on parameter dictionary and OMP algorithm as claimed in claim 9, wherein improved negative entropy of square envelope spectrum I Δ I E Calculated by the following formula:
IΔI E ＝SD·ΔI E
wherein, I Delta I E For improved negative entropy of the square envelope spectrum, SD is the signal standard deviation, delta I E Is the square envelope spectrum negative entropy of the signal;
the calculation formula SD of the signal standard deviation is as follows:
wherein, N is the number of sampling points of the signal, and mu is the mean value of the signal;
negative entropy Δ I of squared envelope spectrum of signal E The calculation formula is as follows:
wherein the content of the first and second substances,<·>for mean calculation, E x (α; f, Δ f) is a discrete signal x (n) (n =0, \8230;, L) at a frequency [ f- Δ f/2, f + Δ f/2]The squared envelope spectrum in the range, expressed as:
wherein epsilon x (n; f, Δ f) is a discrete signal x (n) (n =0, \8230;, L) at a frequency [ f- Δ f/2, f + Δ f/2]The squared envelope within the range, expressed as:
ε x (n；f,Δf)＝|x(n；f,Δf)| 2 。
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| CN115982625A (en) * | 2023-01-06 | 2023-04-18 | 哈尔滨工业大学（深圳） | Long-term working mode analysis method and detection method based on prior information |
| CN116202771A (en) * | 2023-05-05 | 2023-06-02 | 中国铁路南昌局集团有限公司南昌车辆段 | Bearing fault diagnosis method driven by self-adaptive cascade dictionary |
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| CN115982625A (en) * | 2023-01-06 | 2023-04-18 | 哈尔滨工业大学（深圳） | Long-term working mode analysis method and detection method based on prior information |
| CN115982625B (en) * | 2023-01-06 | 2023-10-03 | 哈尔滨工业大学（深圳） | Priori information-based long-term working mode analysis method and detection method |
| CN116202771A (en) * | 2023-05-05 | 2023-06-02 | 中国铁路南昌局集团有限公司南昌车辆段 | Bearing fault diagnosis method driven by self-adaptive cascade dictionary |
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