Bearing weak fault feature extraction method based on parameter dictionary and omp algorithm

Abstract

The application discloses a bearing weak fault feature extraction method based on a parameter dictionary and an OMP algorithm, and establishes a sparse representation model of a rolling bearing vibration signal according to collected rolling bearing vibration data; the rolling bearing vibration data comprises rolling bearing vibration signals with useful fault information and useless background noise information; according to a Laplace wave parameter dictionary, an orthogonal matching pursuit algorithm is adopted to solve a sparse coefficient matrix of the signal sparse representation model of the rolling bearing; the sparse coefficient matrix is reconstructed with the Laplace wave parameter dictionary, envelope analysis is performed on the reconstructed signal, weak fault features are extracted, and bearing fault diagnosis is realized. The application can not only effectively reduce the algorithm complexity of the original method, but also more accurately extract bearing weak fault features under strong background noise, and can simply and effectively perform rolling bearing fault diagnosis in engineering practice.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of fault diagnosis of mechanical rotating equipment rolling bearings, and particularly relates to a bearing weak fault feature extraction method based on a parameter dictionary and an OMP algorithm. BACKGROUND

[0002] Rolling bearings are widely used in various rotating mechanical equipment and are indispensable core components in mechanical systems. However, long-term operation and complex and variable harsh working conditions often cause rolling bearings to fail. Rolling bearings do not have obvious abnormalities when they are in early failure, and the fault features are very weak, which makes them more difficult to detect under the interference of strong background noise. However, as the fault point expands and deepens, early failure will quickly evolve into a serious failure, which may cause economic losses or even safety accidents. Therefore, the study of rolling bearing fault diagnosis has a very positive significance for practical engineering. Meanwhile, the extraction of weak fault features of rolling bearings under strong background noise is a key problem that needs to be solved urgently.

[0003] In recent years, the feature extraction method based on sparse representation has been developed and widely applied in the field of signal processing. Mallet et al. first proposed the idea of adaptive decomposition of signals on an overcomplete dictionary, which sparsely represents the original signal by selecting as few atoms as possible from the overcomplete dictionary that are most similar to the signal. The sparse representation method can capture the key fault information in the signal and ignore the interference information irrelevant to the fault, and thus it is simple and efficient in expressing the original signal. Therefore, the sparse representation method itself has a certain noise filtering capability. In view of this characteristic of the sparse representation method, many scholars have carried out research on bearing fault diagnosis based on the sparse representation method, mainly focusing on the construction of the atom dictionary and the optimization algorithm for solving sparse coefficients.

[0004] The wavelet parameter dictionary is relatively flexible, and can be adjusted by changing the wavelet type and adjusting the wavelet parameters to adapt to different types of fault signals. The commonly used method for determining the wavelet parameters is the correlation filtering method. However, since the determination of wavelet parameters requires traversing all the wavelet parameter library, the correlation filtering method is very time-consuming.

[0005] In addition, when the fault impact feature is relatively weak, the correlation filtering method is easily disturbed by noise during the search for the optimal wavelet parameters, making it difficult to obtain accurate wavelet parameters. The traditional OMP algorithm stopping criterion is the sparsity stopping criterion and the energy stopping criterion. The sparsity stopping criterion needs to rely on experience or a large number of parameter tuning to find a suitable sparsity, while the energy stopping criterion is easily affected by noise, which may cause the iteration to stop too early under strong background noise, affecting the signal reconstruction accuracy and thus failing to extract effective weak fault features. SUMMARY

[0006] In view of the deficiencies of the prior art and the engineering problems faced, the purpose of the present application is to provide a bearing weak fault feature extraction method based on a parameter dictionary and an OMP algorithm, which can effectively extract bearing weak fault features in a strong background noise and is very suitable for the engineering practical background.

[0007] To achieve the above purpose, the technical scheme of the present application is:

[0008] The bearing weak fault feature extraction method based on a parameter dictionary and an OMP algorithm comprises the following steps:

[0009] 1) A sparse representation model of a rolling bearing vibration signal is established according to the collected rolling bearing vibration data; the rolling bearing vibration data are rolling bearing vibration signals including useful fault information and useless background noise information;

[0010] 2) The sparse coefficient matrix of the signal sparse representation model of the rolling bearing is solved by using an orthogonal matching pursuit algorithm according to a Laplace wavelet parameter dictionary; the rolling bearing vibration signals including useful fault information and useless background noise information are reconstructed by the sparse coefficient matrix and the Laplace wavelet parameter dictionary, envelope analysis is performed on the reconstructed signals, weak fault features are extracted, and rolling bearing fault diagnosis is realized.

[0011] Further improvement of the present application is that the rolling bearing vibration signals including useful fault information and useless background noise information are:

[0012] y=Dα+n

[0013] Wherein, D={d1,d2,...d n} is an atomic dictionary, d i (i=1,2...n) is an atom in the atomic dictionary, α={α (1) ,α (2) ,...α (m)} T is a sparse coefficient matrix, α (1) ,α (2) ...α (m) are sparse coefficients corresponding to different atoms.

[0014] Further improvement of the present application is that the sparse representation model of the rolling bearing vibration signal is:

[0015]

[0016] Wherein, ||α||1 is the minimum l1 norm of the sparse coefficient matrix, ε is the residual, y is the rolling bearing vibration signal including useful fault information and useless background noise information, D is the atomic dictionary, and α is the sparse coefficient matrix.

[0017] The further improvement of the present application is that the atomic dictionary is obtained by the following process:

[0018] The particle swarm algorithm is used to optimize the correlation filtering method to traverse the Laplace wavelet parameter library, find the optimal Laplace wavelet parameter, make the Laplace wavelet most similar to the rolling bearing vibration signal, and thus obtain the optimal Laplace wavelet; and the optimal Laplace wavelet atom is expanded into a Laplace wavelet parameter dictionary.

[0019] The further improvement of the present application is that the optimal Laplace wavelet parameter is obtained by the following process:

[0020] The Laplace wavelet most similar to the signal is searched by traversing the Laplace wavelet parameter library, the correlation coefficient of the Laplace wavelet and the signal is obtained, and when the correlation coefficient of the Laplace wavelet and the signal is the largest, the parameter corresponding to the Laplace wavelet is the optimal Laplace wavelet parameter.

[0021] The further improvement of the present application is that the correlation coefficient of the Laplace wavelet and the signal is calculated by the following formula:

[0022]

[0023] Wherein, ψ is the Laplace wavelet, y is the signal, <·> is the inner product operation, ||·||2 is the two norm, and cc is the correlation coefficient of the Laplace wavelet and the signal.

[0024] The further improvement of the present application is that the optimal Laplace wavelet atom is expanded into a Laplace wavelet parameter dictionary according to different time shift parameters τ.

[0025] The further improvement of the present application is that the optimal Laplace wavelet parameter is calculated by the following formula:

[0026]

[0027] Wherein, The optimal Laplace wavelet parameter, F is the parameter set of the natural frequency f, Z is the parameter set of the viscous damping ratio ξ, T is the parameter set of the time shift parameter τ, and cc is the correlation coefficient of the Laplace wavelet and the signal.

[0028] The further improvement of the present application is that according to the Laplace wavelet parameter dictionary, the specific process of solving the sparse coefficient matrix of the signal sparse representation model of the rolling bearing by using the orthogonal matching pursuit algorithm is as follows:

[0029] When the improved square envelope spectrum negative entropy IΔIE When the maximum is reached, the iteration of the orthogonal matching pursuit algorithm is stopped, and a sparse coefficient matrix is obtained.

[0030] The further improvement of the application is that the improved square envelope spectrum negative entropy IΔI E is calculated by the following formula:

[0031] IΔI E = SD·ΔI E

[0032] wherein IΔI E is the improved square envelope spectrum negative entropy, SD is the signal standard deviation, and ΔI E is the square envelope spectrum negative entropy of the signal.

[0033] The formula for calculating the signal standard deviation SD is:

[0034]

[0035] wherein N is the sampling point number of the signal, and μ is the mean value of the signal.

[0036] The square envelope spectrum negative entropy ΔI E of the signal is calculated by the following formula:

[0037]

[0038] wherein <·> is the mean value calculation, E x is the square envelope spectrum of the discrete signal x(n) (n=0,…,L) in the frequency range [f-Δf / 2,f+Δf / 2], and the expression is as follows:

[0039]

[0040] wherein ε x (n;f,Δf) is the square envelope of the discrete signal x(n) (n=0,…,L) in the frequency range [f-Δf / 2,f+Δf / 2], and the expression is as follows:

[0041] ε x (n;f,Δf) = |x(n;f,Δf)| 2 .

[0042] Compared with the prior art, the application has the beneficial effects that:

[0043] The application uses Laplace wavelet to construct a parameter dictionary, can accurately match fault impact in rolling bearing vibration signal, and can more accurately extract weak fault features of the rolling bearing; the application adopts an orthogonal matching pursuit algorithm (OMP algorithm) to optimize and solve a sparse coefficient matrix, the algorithm can quickly converge and accurately reconstruct the signal; the application uses an improved square envelope spectrum negative entropy criterion to replace the original stop criterion in the OMP algorithm, so that the OMP algorithm can automatically stop iteration, and the adaptability of the OMP algorithm is improved. The application can well extract bearing weak fault features under strong background noise, and is easy to realize fault diagnosis of the rolling bearing in engineering practice.

[0044] Further, the application uses a particle swarm algorithm to optimize a Laplace wavelet parameter searching process of the correlation filtering method, reduces the algorithm complexity, and improves the similarity of the optimal Laplace wavelet searched and the signal;

[0045] Further, the application expands optimal Laplace wavelet atoms into a Laplace wavelet parameter dictionary according to different time shift variables, so that each atom in the dictionary is most similar to the signal, and the signal reconstruction accuracy in subsequent sparse decomposition is improved; BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 A flowchart of the bearing weak fault feature extraction method based on the Laplace wavelet parameter dictionary and the improved OMP algorithm is provided for the application;

[0047] Figure 2 A bearing life cycle RMS curve is provided;

[0048] Figure 3 A bearing time domain waveform graph and an envelope spectrum graph are provided, wherein (a) is a time domain waveform graph, and (b) is an envelope spectrum graph;

[0049] Figure 4 A reconstructed signal waveform graph and an envelope spectrum graph after the bearing vibration signal is decomposed by a traditional CFA and OMP method are provided, wherein (a) is a signal time domain waveform graph, and (b) is a reconstructed signal envelope spectrum graph;

[0050] Figure 5 A reconstructed signal waveform graph and an envelope spectrum graph after the bearing signal is decomposed by the improved CFA and OMP method provided by the application are provided, wherein (a) is a signal time domain waveform graph, and (b) is a reconstructed signal envelope spectrum graph. DETAILED DESCRIPTION

[0051] The application will be described in detail below with reference to the drawings.

[0052] In view of the problem that bearing weak fault features are difficult to extract under strong background noise interference, the application provides a bearing weak fault feature extraction method based on a Laplace wavelet parameter dictionary and an improved OMP algorithm. First, a signal sparse representation model is established, the particle swarm algorithm is introduced to optimize the parameter searching process of the correlation filtering method in view of the problem that the optimal Laplace wavelet parameter calculation has high complexity, and the disadvantages of the correlation filtering method, such as high calculation complexity and being easily affected by interference information, are overcome; then, the optimal Laplace wavelet atom is expanded into a Laplace wavelet parameter dictionary according to different time shift variables. Then, in view of the problem that the iteration stopping criterion of the orthogonal matching pursuit algorithm lacks self-adaptation and is easily affected by noise, an iteration stopping criterion based on an improved square envelope spectrum negative entropy index is provided, the index can uniformly represent the impact characteristics and cyclostationary characteristics of the bearing vibration signal. Then, an iteration stopping criterion based on the improved square envelope spectrum negative entropy index is provided to replace the original stopping criterion of the OMP algorithm, and the index can make the OMP algorithm automatically stop iteration; finally, the reconstructed signal after sparse decomposition is subjected to envelope spectrum analysis, the weak fault features are extracted, and fault diagnosis is realized.

[0053] Through example analysis verification, the test results show that the application can not only effectively reduce the algorithm complexity of the original method, but also more accurately extract the bearing weak fault features under strong background noise, and can simply and effectively realize fault diagnosis of the rolling bearing in engineering practice.

[0054] Specifically, the application comprises the following steps:

[0055] 1) First, according to the collected rolling bearing vibration data, the data is a rolling bearing vibration signal including useful fault information and useless background noise information, a sparse representation model of the rolling bearing vibration signal is established based on the sparse representation theory, and the sparse representation model mainly includes two parts of parameter dictionary construction and sparse coefficient solving optimization algorithm; the specific process is as follows:

[0056] 1.1) The rolling bearing vibration signal including useful fault information and useless background noise information is re-expressed according to the sparse representation theory, and specifically:

[0057] y=x+n

[0058] Wherein, y is the rolling bearing vibration signal, x is the fault feature component in the vibration signal, and n is the background noise.

[0059] The sparse representation theory re-expresses the original signal by selecting as few atoms as possible from the atom dictionary, which are most similar to the signal, so the vibration signal of the rolling bearing can be further expressed by the sparse representation theory as follows:

[0060] y=Dα+n

[0061] Where D = {d1, d2, ... d} n} represents the atomic dictionary, d i (i = 1, 2, ..., n) are atoms in the atom dictionary, α = {α (1) ,α (2) ,…α (m)} T is a sparse coefficient matrix, where α represents the sparse coefficients corresponding to different atoms;

[0062] 1.2) Solving the linear combination solution based on the sparse representation model of rolling bearing vibration signals. The process of solving the sparse representation model is based on the atomic dictionary to find the minimum l0 norm of the sparse coefficient matrix. Therefore, the objective function of the sparse representation model can be expressed as:

[0063]

[0064] Where ||α||0 is the l0 norm of the sparse coefficient matrix, and ε is the residual. Since this is an NP-hard problem that cannot be solved directly, the classic OMP algorithm is chosen to approximate it, transforming the problem of finding the minimum l0 norm into the problem of finding the minimum l1 norm.

[0065]

[0066] Where ||α||1 is the l1 norm of the sparse coefficient matrix;

[0067] 2) Secondly, during the construction of the parameter dictionary, considering that the Laplace wavelet waveform is most similar to the rolling bearing fault impact waveform, a Laplace wavelet parameter dictionary is constructed based on the Laplace wavelet. The correlation filtering algorithm (CFA) is used to traverse the Laplace wavelet parameter library to find the optimal Laplace wavelet parameters that make the Laplace wavelet most similar to the rolling bearing vibration signal, thus obtaining the optimal Laplace wavelet. To address the high computational complexity of CFA, a particle swarm optimization algorithm is introduced to optimize the parameter search process of the correlation filtering algorithm, enabling it to find the optimal Laplace wavelet parameters more quickly. The obtained optimal Laplace wavelet atoms are then expanded into a Laplace wavelet parameter dictionary.

[0068] The specific process is as follows:

[0069] 2.1) The principle of using the particle swarm optimization algorithm is as follows:

[0070] The idea of particle swarm optimization comes from the study of bird foraging behavior. Each individual is abstracted as a particle, and each particle represents a candidate solution to the optimization problem. The candidate solution gets a fitness value according to the fitness function, and the final result is the global optimal fitness value among different candidate solutions. The update formula of the particle swarm optimization is:

[0071]

[0072]

[0073] where, and are the velocity and position vectors of the dth dimension of particle i in the kth iteration, w is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random numbers in the interval [0:1], is the individual optimal position of the dth dimension of particle i in the kth iteration, is the global optimal position of the dth dimension of the particle swarm in the kth iteration.

[0074] 2.2) The particle swarm optimization algorithm is used to optimize the parameter search of CFA to determine the optimal Laplace wavelet parameters. The specific process is as follows:

[0075] The correlation coefficient of CFA is selected as the fitness function of the particle swarm optimization algorithm, and the optimization goal is to solve the maximum fitness value, i.e. the maximum correlation coefficient;

[0076] The mathematical expression of the Laplace wavelet is:

[0077]

[0078] where f∈R + is the natural frequency, ξ∈[0,1) is the viscous damping ratio, and τ is the time shift parameter. These three parameters directly determine the waveform characteristics of the Laplace wavelet. CFA searches for the Laplace wavelet that is most similar to the signal by traversing the Laplace wavelet parameter library, and quantitatively represents the similarity between the Laplace wavelet and the signal through the correlation coefficient:

[0079]

[0080] where ψ is the Laplace wavelet, y is the signal, <·> is the inner product operation, ||·||2 is the two-norm, and cc is the correlation coefficient of the Laplace wavelet and the signal;

[0081] The optimal Laplace wavelet parameters are the parameters corresponding to the maximum similarity between the Laplace wavelet and the signal y, i.e.

[0082]

[0083] wherein, are the optimal Laplace wavelet parameters, F is the parameter set of the natural frequency f, Z is the parameter set of the viscous damping ratio ξ, and T is the parameter set of the time shift τ.

[0084] 2.3) After finding the optimal Laplace wavelet parameters, considering that the fault impact of the rolling bearing exhibits a periodic cycle characteristic, it is necessary to expand the optimal Laplace wavelet atom into a Laplace wavelet parameter dictionary according to different time shift parameters τ;

[0085] 3) Finally, according to the constructed Laplace wavelet parameter dictionary, an orthogonal matching pursuit (OMP) algorithm is used to solve the sparse coefficients of the signal sparse representation model of the rolling bearing; the OMP algorithm is based on the Laplace wavelet parameter dictionary to decompose and reconstruct the rolling bearing vibration signal, filter the interference information while retaining the fault impact information of the rolling bearing, and thus extract the weak fault features of the rolling bearing; in view of the problem that the iteration stopping criterion of the OMP algorithm lacks self-adaptation and is easily affected by noise, an iteration stopping criterion based on an improved negative entropy index of square envelope spectrum is proposed, and the original stopping criterion of the OMP algorithm is replaced by the criterion;

[0086] The specific process is as follows:

[0087] 3.1) The detailed algorithm steps for using OMP to solve sparse coefficients are as follows:

[0088] Input: vibration signal y, atom dictionary D, sparsity K.

[0089] Initialization: initial residual r0=y, support index set Iteration initial value k=1.

[0090] Iteration process: steps 1-4 are performed in the kth iteration.

[0091] Step 1: find the support index:

[0092]

[0093] Step 2: add the matched most relevant atom index to the index set:

[0094] Λ k =Λ k-1 ∪{λ k}

[0095] Step 3: update the residual by least squares method:

[0096]

[0097] Step 4: k = k + 1, return to step 1, stop iteration when k = K.

[0098] Output: support index set Λ k = Λ k-1 , sparse coefficient matrix

[0099] 3.2) Using the improved square envelope spectrum negative entropy index based on the iteration stopping criterion, instead of the original iteration stopping criterion of OMP, the specific process is as follows:

[0100] The objective function of OMP algorithm for solving sparse coefficient is:

[0101]

[0102] where, IΔI E (Dα) is the IΔI E value of the reconstructed signal after each iteration in the sparse decomposition process, μ is the penalty factor, is the sparse coefficient matrix obtained by solving.

[0103] The formula of the improved square envelope spectrum negative entropy index is:

[0104] IΔI E = SD·ΔI E

[0105] where, IΔI E is the improved square envelope spectrum negative entropy, SD is the signal standard deviation, ΔI E is the square envelope spectrum negative entropy of the signal;

[0106] The formula of the signal standard deviation SD is:

[0107]

[0108] where, N is the number of sampling points of the signal, μ is the mean value of the signal;

[0109] The formula of the square envelope spectrum negative entropy ΔI E of the signal is:

[0110]

[0111] where, <·> is the mean value calculation, E x (α; f, Δf) is the square envelope spectrum of the discrete signal x(n) (n = 0, …, L) in the frequency range [f-Δf / 2, f+Δf / 2], and its expression is:

[0112]

[0113] where, ε x (n; f, Δf) is the square envelope of the discrete signal x(n) (n = 0,..., L) in the frequency range [f-Δf / 2, f+Δf / 2], and its expression is:

[0114] ε x (n; f, Δf) = |x(n; f, Δf)| 2

[0115] The improved OMP iteration stopping criterion is:

[0116] The original stopping criterion is to set a certain sparsity K, and when the iteration number reaches K times, the iteration is stopped. The improved iteration stopping criterion does not need to set the sparsity K, and in each iteration process of the algorithm, the IΔI E value of the reconstructed signal is calculated, and when the IΔI E reaches the maximum, the iteration is stopped, and the sparse coefficient matrix is obtained.

[0117] The sparse coefficient matrix and the Laplace wavelet parameter dictionary are used to reconstruct the signal, the reconstructed signal filters the useless interference information and retains the fault information as much as possible, and the envelope analysis (the process of envelope analysis is a known technology in the art) is performed on the reconstructed signal to extract the weak fault feature.

[0118] The content of the application will be further described in detail below in combination with the drawings and examples.

[0119] Example 1

[0120] This example uses the IMS bearing full life test public data set to verify the effectiveness of the application.

[0121] Figure 1 is a flowchart of a bearing weak fault feature extraction method based on a Laplace wavelet parameter dictionary and an improved OMP algorithm, as shown in Figure 1 , and the following describes the bearing weak fault feature extraction according to the flowchart.

[0122] The main process of the method includes three parts: establishing a sparse representation model of the rolling bearing vibration signal, constructing a Laplace wavelet parameter dictionary, and using an OMP algorithm to solve a sparse coefficient matrix.

[0123] (1) First, the rolling bearing vibration signal is re-expressed according to the sparse representation theory, specifically:

[0124] y = x + n

[0125] where y is the rolling bearing vibration signal, x is the fault feature component in the vibration signal, and n is the background noise.

[0126] Sparse representation theory re-expresses the original signal by selecting as few atoms as possible from the atom dictionary that are most similar to the signal, so the vibration signal of the rolling bearing can be further represented by sparse representation theory as follows:

[0127] y=Dα+n

[0128] wherein D={d1,d2,…d n} is an atom dictionary, d is an atom in the atom dictionary, α={α (1) ,α (2) ,…α (m)} T is a sparse coefficient matrix, and α is a sparse coefficient corresponding to different atoms;

[0129] Secondly, the solution of the linear combination is solved based on the sparse representation model, and the process of solving the sparse representation model is a process of solving the minimum l0 norm of the sparse coefficient matrix based on the atom dictionary, so the objective function of the sparse representation model can be expressed as:

[0130]

[0131] wherein ||α||0 is the l0 norm of the sparse coefficient matrix, and ε is a residual error, since it is an NP-hard problem, it cannot be directly solved, so the classic OMP algorithm is selected to approximate it, and the problem of solving the minimum l0 norm is converted into the problem of solving the minimum l1 norm:

[0132]

[0133] wherein ||α||1 is the l1 norm of the sparse coefficient matrix;

[0134] (2) First, the specific process of determining the optimal parameters of the Laplace wavelet using the CFA method is as follows:

[0135] The mathematical expression of the Laplace wavelet is as follows:

[0136]

[0137] In the formula, f∈R + is the natural frequency, ξ∈[0,1) is the viscous damping ratio, and τ is the time shift parameter, and the three parameters directly determine the waveform characteristics of the Laplace wavelet, and the CFA searches for the Laplace wavelet most similar to the signal by traversing the Laplace wavelet parameter library, and quantitatively characterizes the similarity between the Laplace wavelet and the signal through the correlation coefficient:

[0138]

[0139] Where, ψ is Laplace wavelet, y is signal, <·> is inner product operation, ||·||2 is two norm, cc is the correlation coefficient of Laplace wavelet and signal;

[0140] The optimal wavelet parameter is the parameter corresponding to the maximum similarity between Laplace wavelet and signal y, that is,

[0141]

[0142] Where, is the optimal wavelet parameter, F, Z, T is the wavelet parameter space;

[0143] Secondly, the CFA parameter searching process is optimized by using particle swarm algorithm, which is specifically:

[0144] The idea of particle swarm algorithm comes from the study of bird foraging behavior. Each individual is abstracted as a particle, and each particle represents a candidate solution to the optimization problem. The candidate solution gets a fitness value according to the fitness function, and the final result is to get the global optimal fitness value in different candidate solutions. The update formula of particle swarm algorithm is:

[0145]

[0146]

[0147] Where, and are the velocity and position vectors of the d-th dimension of particle i in the k-th iteration, w is the inertia weight, c1 and c2 are learning factors, r1 and r2 are random numbers in the interval [0:1], is the individual optimal position of the d-th dimension of particle i in the k-th iteration, is the global optimal position of the d-th dimension of particle swarm in the k-th iteration. The parameter searching process of CFA optimized by particle swarm algorithm selects the correlation coefficient of CFA as the fitness function of particle swarm algorithm, and the optimization goal is to solve the maximum fitness value, that is, the maximum correlation coefficient;

[0148] Finally, after finding the optimal Laplace wavelet, considering that the fault impact of rolling bearing shows the characteristics of cycle period, it is necessary to expand the optimal Laplace wavelet atom into Laplace wavelet parameter dictionary according to different time shift variables;

[0149] (3) First, use OMP to solve sparse coefficients, and the detailed algorithm steps are:

[0150] Input: vibration signal y, atom dictionary D, sparsity K.

[0151] Initialization: initial residual r0=y, support index set Initialize k = 1.

[0152] Iteration process: Steps 1-4 are performed in the kth iteration.

[0153] Step 1: Find support index:

[0154]

[0155] Step 2: Add the most relevant atom index matched to the index set:

[0156] Λ k = Λ k-1 ∪ {λ k}

[0157] Step 3: Update the residual using least squares:

[0158]

[0159] Step 4: k = k + 1, return to step 1, stop iteration when k = K.

[0160] Output: Support index set Λ k = Λ k-1 , sparse coefficient matrix

[0161] Secondly, the improved square envelope spectrum negative entropy index-based iteration stopping criterion is used to replace the original iteration stopping criterion of OMP, and the specific process is as follows:

[0162] The formula of the improved square envelope spectrum negative entropy index is:

[0163] IΔI E = SD·ΔI E

[0164] Where IΔI E is the improved square envelope spectrum negative entropy, SD is the signal standard deviation, and ΔI E is the square envelope spectrum negative entropy of the signal.

[0165] The formula for calculating the signal standard deviation is:

[0166]

[0167] Where N is the number of signal sampling points, and μ is the mean of the signal.

[0168] The formula for calculating the square envelope spectrum negative entropy of the signal is:

[0169]

[0170] Where <·> is the mean calculation, and Ex (α; f, Δf) is the squared envelope spectrum of the discrete signal x(n) (n = 0, ..., L) in the frequency range [f - Δf / 2, f + Δf / 2], and its expression is:

[0171]

[0172] Where, ε x (n; f, Δf) is the square envelope of the discrete signal x(n) (n = 0, ..., L) in the frequency range [f - Δf / 2, f + Δf / 2], and its expression is:

[0173] ε x (n;f,Δf)=|x(n;f,Δf)| 2

[0174] The improved OMP iteration stopping criterion is as follows:

[0175] The original stopping criterion set a certain sparsity K, and stopped iteration when the number of iterations reached K. The improved stopping criterion does not require setting the sparsity K; instead, it calculates the IΔI of the reconstructed signal during each iteration of the algorithm. E Value, when IΔI E Stop iterating when the maximum is reached;

[0176] Finally, the OMP algorithm based on the improved stopping criterion is used to decompose and reconstruct the signal; the specific process is as follows:

[0177] The objective function for solving the sparse coefficients using the proposed method is:

[0178]

[0179] Where, IΔI E (Dα) represents the reconstructed signal IΔI after each iteration in the sparse decomposition process. E Value, μ is the penalty factor, This is the sparse coefficient matrix obtained by solving the problem.

[0180] The analysis was performed using the IMS bearing public dataset and the methods described above.

[0181] like Figure 2 As shown, when the bearing is in the early stage of failure, there will be obvious transient impact, which will quickly develop into a serious failure. In order to better verify the effectiveness of the present invention, this embodiment uses the 564th data point marked in the figure for analysis. When the bearing is in this time period, the amplitude does not fluctuate abnormally, and the bearing failure characteristics are very weak under the interference of noise background.

[0182] like Figure 3As shown in (a) and (b), the time domain waveform diagram of the bearing has no obvious periodicity, and the bearing fault characteristic frequency cannot be found in the envelope spectrum.

[0183] As Figure 4 As shown in (a) and (b), the reconstructed signal waveform is quite different from the bearing fault impact waveform, and the bearing fault characteristic frequency cannot be found in the envelope spectrum.

[0184] As Figure 5 As shown in (a) and (b), the reconstructed signal waveform is quite different from the bearing fault impact waveform, and the bearing fault characteristic frequency cannot be found in the envelope spectrum.

[0185] The results of the embodiment show that the bearing weak fault feature extraction method based on the Laplace wavelet parameter dictionary and the improved OMP algorithm can extract the bearing weak fault feature under the interference of strong background noise, can diagnose the bearing fault in the early stage, and can better warn the health state of the bearing.

[0186] The present application can better extract the weak fault feature of the rolling bearing under strong background noise based on the Laplace wavelet parameter dictionary and the improved OMP algorithm, so as to realize the fault diagnosis of the rolling bearing, can be used for early weak fault diagnosis in engineering practice, and can warn the health state of the rolling bearing.

[0187] The present application can not only effectively reduce the algorithm complexity of the original method, but also more accurately extract the weak fault feature of the bearing under strong background noise, 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

1. A bearing weak fault feature extraction method based on a parameter dictionary and an OMP algorithm, characterized in that, The method comprises the following steps: 1) according to the collected rolling bearing vibration data, a sparse representation model of rolling bearing vibration signal is established; the rolling bearing vibration data is a rolling bearing vibration signal comprising useful fault information and useless background noise information; 2) according to a Laplace wavelet parameter dictionary, an orthogonal matching pursuit algorithm is used to solve a sparse coefficient matrix of the signal sparse representation model of the rolling bearing; the rolling bearing fault diagnosis is realized by reconstructing the rolling bearing vibration signal comprising useful fault information and useless background noise information through the sparse coefficient matrix and the Laplace wavelet parameter dictionary, and then performing envelope analysis on the reconstructed signal to extract weak fault features; the specific process of solving the sparse coefficient matrix of the signal sparse representation model of the rolling bearing according to the Laplace wavelet parameter dictionary by using the orthogonal matching pursuit algorithm is as follows: When the improved square envelope spectrum negentropy The iteration of the orthogonal matching pursuit algorithm is stopped when the improved square envelope spectrum negentropy reaches the maximum, and a sparse coefficient matrix is obtained. Improved square envelope spectrum negentropy is calculated by the formula: wherein, is the improved square envelope spectrum negentropy, is the signal standard deviation, is the square envelope spectrum negentropy of the signal; the formula for calculating the signal standard deviation SD is: wherein, is the number of sampling points of the signal, is the mean value of the signal; Squared envelope spectrum negentropy of signals The calculation formula is: where is the mean value, is the discrete signal n = 0,..., L The square envelope spectrum in the frequency range is given by wherein is a discrete signal n = 0,..., L is a square envelope in the frequency range with expression 。 2. The bearing weak fault feature extraction method based on parameter dictionary and OMP algorithm according to claim 1, characterized in that, the rolling bearing vibration signal comprising useful fault information and useless background noise information is as follows: wherein, is an atom dictionary, is an atom in the atom dictionary, = 1,2... k , is a sparse coefficient matrix, is a sparse coefficient corresponding to different atoms.

3. The bearing weak fault feature extraction method based on parameter dictionary and OMP algorithm according to claim 1, characterized in that, the sparse representation model of the rolling bearing vibration signal is as follows: wherein, is a sparse coefficient matrix, norm, is a residual, y is a rolling bearing vibration signal comprising useful fault information and useless background noise information, is an atomic dictionary, is a sparse coefficient matrix.

4. The bearing weak fault feature extraction method based on parameter dictionary and OMP algorithm according to claim 3, characterized in that, the atom dictionary is obtained through the following process: the optimal Laplace wavelet parameter is searched by traversing the Laplace wavelet parameter library after the particle swarm algorithm is used to optimize the correlation filtering method, so that the Laplace wavelet is most similar to the rolling bearing vibration signal, thereby obtaining the optimal Laplace wavelet; the optimal Laplace wavelet atom is expanded into the Laplace wavelet parameter dictionary.

5. The bearing weak fault feature extraction method based on parameter dictionary and OMP algorithm according to claim 4, characterized in that, the optimal Laplace wavelet parameter is obtained through the following process: the Laplace wavelet most similar to the signal is searched by traversing the Laplace wavelet parameter library, the correlation coefficient of the Laplace wavelet and the signal is obtained, and when the correlation coefficient of the Laplace wavelet and the signal is maximum, the parameter corresponding to the Laplace wavelet is the optimal Laplace wavelet parameter.

6. The bearing weak fault feature extraction method based on parameter dictionary and OMP algorithm according to claim 4, characterized in that, the correlation coefficient of the Laplace wavelet and the signal is calculated by the following formula: where, is the Laplace wavelet, is the signal, is the inner product operation, is the two-norm, is the correlation coefficient of the Laplace wavelet and the signal.

7. The bearing weak fault feature extraction method based on parameter dictionary and OMP algorithm according to claim 1, characterized in that, The optimal Laplace wavelet atoms are expanded into a Laplace wavelet parameter dictionary according to different time shift parameters The optimal Laplace wavelet atoms are expanded into a Laplace wavelet parameter dictionary according to different time shift parameters 8. The bearing weak fault feature extraction method based on parameter dictionary and OMP algorithm according to claim 1, characterized in that, the optimal Laplace wavelet parameter is calculated by the following formula: wherein, is a parameter set for the optimal Laplace wavelet, is a parameter set for the natural frequency f, is a parameter set for the viscous damping ratio is a parameter set for the viscous damping ratio is a parameter set for the time shift parameter is a parameter set for the time shift parameter, and cc is a correlation coefficient of the Laplace wavelet with the signal.

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