Rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection

Abstract

The present invention belongs to the field of mechanical fault diagnosis and signal processing, and proposes a bearing fault diagnosis method based on RCMRDE and JMIM feature selection, and the steps are as follows: using an acceleration sensor to collect rolling bearing acceleration signals; performing VMD decomposition on the original vibration signal; calculating the RCMRDE values ​​of the original signal and each component signal after decomposition as the original fault feature set; using the JMIM feature selection algorithm to perform feature selection on the original fault feature set, selecting sensitive features that can be accurately classified, and constructing a low-dimensional fault feature set; training an RF classifier according to the selected sensitive components to obtain a trained RF model; inputting the test sample sensitive fault feature set into the trained RF classifier to diagnose the fault type. The present invention overcomes the shortcomings of multi-scale spread entropy, improves the stability, noise robustness and signal differentiation ability of fault features, and can effectively diagnose different state types of rolling bearings.

Description

Technical Field

[0001] The invention relates to the field of mechanical fault diagnosis and signal processing, and in particular to a rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection. Background Art

[0002] Condition monitoring and fault diagnosis are crucial to the safe operation of large-scale mechanical equipment. Rolling bearings are important components of rotating mechanical equipment. They have complex operating conditions and are one of the most vulnerable parts of mechanical equipment. Therefore, intelligent health status identification of rolling bearings is of great significance to improving the reliability of equipment operation.

[0003] Feature extraction is the key to rolling bearing fault diagnosis. Many nonlinear dynamic methods, such as sample entropy, permutation entropy, fuzzy entropy, and dispersion entropy, based on entropy complexity theory, can reflect the nonlinear characteristics of vibration signals and have been widely used in mechanical fault diagnosis. Dispersion entropy overcomes some of the defects of permutation entropy and sample entropy, takes into account the relationship between amplitudes, has the advantages of fast calculation speed, and is less affected by mutation signals. Inspired by dispersion entropy and multi-scale dispersion entropy, a refined composite multi-scale inverse dispersion entropy is proposed, which solves the problem of incomplete signal complexity feature extraction by single-scale dispersion entropy. Compared with the traditional coarse-grained multi-scale process, it has good stability and has certain advantages in entropy value stability, noise robustness, and signal discrimination ability.

[0004] Selecting features that accurately reflect the fault state is the key to accurate fault diagnosis. Feature selection based on information theory is a popular method because of its advantages such as high computational efficiency, good scalability of dataset dimensions, and independence from classifiers. Common disadvantages of this method are the lack of information about the interaction between features and classifiers, and the selection of redundant and irrelevant features. Therefore, choosing a reasonable feature selection method is of great significance for dimensionality reduction and improving classification accuracy. Summary of the invention

[0005] In order to solve the problems existing in the prior art, the present invention provides a rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection, which fully mines fault information on the basis of improving feature stability, noise robustness and signal differentiation ability, accurately selects features sensitive to faults, and solves the information redundancy problem existing in high-dimensional fault features.

[0006] The technical solution of the present invention is:

[0007] A rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection includes the following steps:

[0008] Step S1: using an acceleration sensor to collect the original vibration acceleration signal of the rolling bearing, including the radial vibration acceleration signal of the transmission shaft under the normal state of the bearing, the fault state of the outer ring of the bearing, the fault state of the inner ring of the bearing and the fault state of the rolling bearing;

[0009] Step S2: performing VMD decomposition on the original vibration acceleration signal of the rolling bearing;

[0010] The VMD algorithm is as follows:

[0011] f(t) is the original vibration acceleration signal of the rolling bearing, which is decomposed by VMD to obtain k IMF components, and the variational constraint problem is obtained:

[0012]

[0013] Where, f(t) is the original vibration acceleration signal of the rolling bearing; u k (t) is the kth mode; ω k is the center frequency; k is the number of modes; represents the partial derivative with respect to t; ||·|| 2 represents the norm of 2; δ(t) is the Dirac distribution; * is the convolution operator;

[0014] In order to solve the above variational constraint problem, it is necessary to transform the constraint problem into an unconstrained problem and introduce the augmented Lagrange expression:

[0015]

[0016] Among them, α is the introduced quadratic penalty factor; λ(t) is the Lagrange multiplication operator; <> represents the inner product operation;

[0017] Use the alternating direction multiplier method to solve the saddle point of the above Lagrange expression:

[0018] 2.1) Initialization n, the initial value is 0, and the preset scale k is set to a positive integer;

[0019] 2.2) Execute loop n=n+1;

[0020] 2.3) Update according to equation (3), equation (4), and equation (5), and get

[0021] 2.4) Given the judgment accuracy e>0, when When , the iteration stops and k IMF components are output and the corresponding center frequency

[0022]

[0023]

[0024]

[0025] Where n is a positive integer; ^ represents Fourier transform; τ is the noise tolerance parameter.

[0026] Step S3: Calculate the RCMRDE value of the original vibration acceleration signal of the rolling bearing and each component signal after decomposition as the original fault feature set;

[0027] The specific solution of RCMRDE value is:

[0028] (3.1) The original vibration acceleration signal of the rolling bearing and each component signal after decomposition are both time series. Take the time series X = {x(i), i = 1, 2, ..., T}, given the scale factor τ, the kth coarse-grained time series of the time series X is:

[0029]

[0030] (3.2) Calculate the probability of the scatter pattern of the coarse-grained sequence under different scale factors. For a coarse-grained time series Using the normal distribution function, we can get the normalized time series Y = {y(j), j = 1, 2, ..., N}, that is,

[0031]

[0032] (3.3) Through linear transformation, Y is mapped into C classes with integer indices from 1 to C c is a positive integer;

[0033]

[0034] (3.4) Reconstruct and calculate the embedding vector

[0035]

[0036] Among them, m is the embedding dimension, d is the delay; The corresponding scatter pattern is where v j ∈(1,2,…,c),j=1,2,…,m-1, the scatter pattern consists of m numbers, each number has C ways to be chosen, and there are a total of c m a scatter pattern;

[0037] (3.5) Calculate each scattering mode Probability:

[0038]

[0039] Among them, π i represents the i-th scattering mode;

[0040] (3.6) For each scale factor τ, the RCMRDE value of the time series X is

[0041]

[0042] For different coarse-grained sequences The average value of the scatter pattern.

[0043] Step S4: Use the JMIM feature selection algorithm to select sensitive features from the original fault feature set, and construct a low-dimensional fault training sample sensitive feature set and a low-dimensional fault test sample sensitive feature set with a ratio of 7:3;

[0044] The JMIM algorithm is as follows:

[0045] (4.1) The original vibration acceleration signal of the rolling bearing and the RCMRDE value of each component signal after decomposition constitute the original fault feature set F = {f 1 ,f 2 ,...,f N}, the data dimension is N; select K features from the original fault feature set to form a new feature subset, where k≤N; define feature f X and feature f C The mutual information I(f X ;f C ):

[0046] I(f X ;f C )=H(f C )-H(f C |f X ) (12)

[0047] Among them, H(f C ) represents f C The entropy, H(f C |f X ) represents the feature f C Under condition f X Conditional entropy under ;

[0048] (4.2) Feature f X ,f Y ,f C The calculation process of the joint mutual information between is as follows:

[0049] I(f X ;f C |f Y )=H(f X |f C )-H(f X |f C ,f Y ) (13)

[0050] I(f X ,f Y ;f C )=I(f X ;f C |f Y )+I(f Y |f C ) (14)

[0051] Where, formula (14) represents f X ,f Y Overall same f C the relationship between;

[0052] (4.3) F is the original fault feature set, S is the currently selected sensitive feature set, and the feature to be selected f i ∈FS, selected feature f s ∈S; feature f to be selected i and the selected features f in S s Highly correlated, Feature to be selected f i , selected features f s And the data label L satisfies the following two formula constraints:

[0053] I(f i ,f s ; L)=I(f s ; L)+I(f i ; L / f s ) (15)

[0054] I(f i ,f s ; L) = H(L)-H(L / f i ,f s ) (16)

[0055] H(L) represents the entropy of L; H(x,y) represents the joint entropy of x and y;

[0056] (4.4) Derivation of candidate sensitive features, currently selected feature f s And the joint mutual information formula between labels is as follows:

[0057]

[0058] Where P(x) represents the probability density function of X, P(x i ,y j ) represents the joint probability density function of variables X and Y;

[0059] (4.5) The final JMIM algorithm selects the sensitive feature formula as follows:

[0060] f JMIM = argmaxf i∈F-S (minf s ∈S(I(f i ,f s ; L))) (18).

[0061] Step S5: training the RF classifier according to the sensitive feature set of the low-dimensional fault training samples; and obtaining the RF classification model;

[0062] Step S6: Input the low-dimensional fault test sample sensitive feature set into the trained RF classification model to diagnose the fault type.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] 1. The present invention proposes a fine composite multi-scale inverse discrete entropy for rolling bearing vibration signal feature extraction. Compared with several existing entropy values, the present invention overcomes the shortcomings of multi-scale scattered entropy and has better stability, noise robustness, signal differentiation ability and feature extraction ability.

[0065] 2. The present invention fully mines fault information and selects sensitive feature components for fault classification, thereby reducing feature dimensions and improving diagnostic accuracy.

[0066] 3. The present invention can effectively diagnose different health conditions of rolling bearings. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is a flow chart of the fault diagnosis method of the present invention;

[0068] Figure 2 1 is a time domain waveform diagram of the rolling bearing in different states in the embodiment of the present invention; (a)-(i) are respectively the fault state at 0.2mm of the outer ring, the fault state at 0.4mm of the outer ring, the fault state at 0.6mm of the outer ring, the fault state at 0.2mm of the inner ring, the fault state at 0.4mm of the inner ring, the fault state at 0.6mm of the inner ring, the fault state at 0.2mm of the rolling element, the fault state at 0.4mm of the rolling element, the fault state at 0.6mm of the rolling element and the normal state;

[0069] Figure 3is the comparison result of the classification accuracy of RCMRDE, RCMDE and MDE as the sensitive features increase in the embodiment of the present invention;

[0070] Figure 4 is the comparison result of classification accuracy of JMIM, Fisher and LS feature selection methods in the embodiment of the present invention;

[0071] Figure 5 is the RF recognition result of the sensitive feature in the embodiment of the present invention;

[0072] Figure 6 It is a comparison of the classification effects of extracting feature values ​​only from the original signal and extracting feature values ​​from the original signal and the frequency band after VMD decomposition in the embodiment of the present invention, as well as a comparison of the recognition results based on different classifiers such as KNN, BPNN, SVM and RF. DETAILED DESCRIPTION

[0073] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0074] Reference Figure 1 The present invention provides a rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection, comprising the following steps:

[0075] Step S1: Collect the rolling bearing acceleration signal using an acceleration sensor:

[0076] In this implementation example, it is applied to the vibration acceleration signal analysis process under normal operation (Normal), inner ring fault (IRF), outer ring fault (ORF) and rolling element fault (BF) of rolling bearings. The NI9234 acquisition card and acceleration sensor are used to collect vibration signals with a sampling frequency of 12800HZ. The vibration acceleration signals of the N205EM / PS bearings with detachable outer rings and the NU205EM / PS bearings with detachable inner rings are collected respectively. The two different types of bearings are processed by wire cutting. The fault types are 0.2mm, 0.4mm, and 0.6mm wear of the inner ring, 0.2mm, 0.4mm, and 0.6mm cracks of the outer ring, and 0.2mm, 0.4mm, and 0.6mm wear of the rolling element. There are 50 groups of samples of each type, and each group of signal samples contains 2048 sampling points. Among them, 35 groups of samples of each type are randomly selected as training samples, and the remaining 15 groups are used as test samples. The time domain waveforms of the four states of the rolling bearing are shown in the following figure. Figure 2 As shown. Figure 2 It can be seen that it is difficult to distinguish various fault types based only on the time domain waveform of the bearing vibration signal.

[0077] Step S2: Perform VMD decomposition on the original vibration signal;

[0078] In this embodiment, the VMD algorithm is specifically:

[0079] Assume f(t) is a bearing vibration signal obtained on the test bench, which is decomposed by VMD to obtain k IMF components, and then the variational constraint problem is obtained:

[0080]

[0081] in, represents the partial derivative with respect to t; f(t) is the original signal; ||·|| 2 Represents the norm of 2.

[0082] In order to solve the above variational model, it is necessary to transform the constrained problem into an unconstrained problem and introduce the augmented Lagrange expression:

[0083]

[0084] Among them, α is the introduced quadratic penalty factor; λ(t) is the Lagrange multiplication operator; <> represents the inner product operation.

[0085] The variable expressions in the solution process are shown in equations (21)-(23):

[0086]

[0087]

[0088]

[0089] Wherein, n is a positive integer; "^" represents Fourier transform; τ is the noise tolerance parameter.

[0090] In this embodiment, step S2 is specifically as follows: decomposing the bearing vibration signal of each healthy state into 6 frequency bands, with a penalty factor of 2000 and a discrimination accuracy of 10. -7 .

[0091] Step S3: Calculate the RCMRDE value of the original signal and each component signal after decomposition as the original fault feature set;

[0092] For each scale factor τ, the RCMRDE of the time series X is:

[0093]

[0094] Among them, the RCMRDE algorithm parameters are set to N = 2048, m = 2, c = 5, d = 1, τ max =25.

[0095] Step S4: Using the JMIM feature selection algorithm to perform feature selection on the original fault feature set, select sensitive features that can be accurately classified, and construct a low-dimensional fault feature set;

[0096] In this embodiment, the JMIM algorithm is specifically:

[0097] (1) Assume that F is the original feature set, S is the currently selected feature set, and feature f i ∈FS, feature f s ∈S. If the feature f i and a feature f in S s Highly correlated, When the feature to be selected f i 、Currently selected feature f s When the data label L satisfies the following two formula constraints:

[0098] I(f,f s ; L)=I(f s ; L)+I(f i ; L / f s ) (25)

[0099] I(f,f s ; L) = H(L)-L(L / f i ,f s ) (26)

[0100] (2) Further derive the candidate features, the joint mutual information formula between the currently selected features and labels is as follows:

[0101]

[0102] (3) The characteristic formula selected by the final JMIM algorithm is:

[0103] f JMIM = argmaxf i∈F-S (minf s ∈S(I(f i ,f s ;L))) (28)

[0104] In this embodiment, according to the JMIM criterion, the top 15 RCMRDE values ​​in terms of sensitivity are selected to construct a new fault feature set.

[0105] Step S5: training the RF classifier according to the selected sensitive components to obtain a trained RF model;

[0106] Step S6: Input the sensitive fault feature set of the test sample into the trained RF classifier to diagnose the fault type.

[0107] In this embodiment, step S6 is specifically as follows:

[0108] Input into the RF model and train the RF classifier. As the number of sensitive features increases, the classification accuracy comparison results of RCMRDE, RCMDE and MDE are as follows Figure 4 As shown, according to Figure 4 It can be seen that with the increase in the number of features, the classification effect based on RCMRDE increases the fastest. This is because RCMRDE is more stable, has strong noise resistance, and can more reasonably detect the dynamic mutation of nonlinear signals.

[0109] In this embodiment, the classification accuracy comparison results of JMIM, Fisher and LS feature selection methods are shown in Figure 5. The JMIM method is superior to the Fisher and LS methods in feature selection. Secondly, combining RCMRDE with the JMIM method can improve the accuracy of diagnosis. The RF recognition results of 15 RCMRDE sensitive features in this embodiment are shown in Figure 5. Figure 6 shown.

[0110] In this embodiment, the classification effect of extracting feature values ​​only from the original signal and extracting feature values ​​from the original signal and the frequency band after VMD decomposition is compared, and the recognition results of different classifiers are compared as shown in FIG. Figure 6 shown.

[0111] The above description is only a preferred embodiment of the present invention. All equivalent changes and modifications made according to the scope of the patent application of the present invention should fall within the scope of the present invention.

Claims

1. A rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection, characterized in that: The following steps are involved: Step S1: using an acceleration sensor to collect the original vibration acceleration signal of the rolling bearing, including the radial vibration acceleration signal of the transmission shaft under the normal state of the bearing, the fault state of the outer ring of the bearing, the fault state of the inner ring of the bearing and the fault state of the rolling bearing; Step S2: performing VMD decomposition on the original vibration acceleration signal of the rolling bearing; Step S3: Calculate the RCMRDE value of the original vibration acceleration signal of the rolling bearing and each component signal after decomposition as the original fault feature set; Step S4: Use the JMIM feature selection algorithm to select sensitive features from the original fault feature set, and construct a low-dimensional fault training sample sensitive feature set and a low-dimensional fault test sample sensitive feature set with a ratio of 7:3; Step S5: training the RF classifier according to the sensitive feature set of the low-dimensional fault training samples; and obtaining the RF classification model; Step S6: input the sensitive feature set of the low-dimensional fault test sample into the trained RF classification model to diagnose the fault type; The RCMRDE value in step S3 is specifically solved as follows: (3.1) The original vibration acceleration signal of the rolling bearing and each component signal after decomposition are both time series. Take the time series X = {x(i), i = 1, 2, ..., T}, given the scale factor τ, the kth coarse-grained time series of the time series X is: (3.2) Calculate the probability of the scatter pattern of the coarse-grained sequence under different scale factors. For a coarse-grained time series Using the normal distribution function, we can get the normalized time series Y = {y(j), j = 1, 2, ..., N}, that is, (3.3) Through linear transformation, Y is mapped into C classes with integer indices from 1 to C c is a positive integer; (3.4) Reconstruct and calculate the embedding vector Among them, m is the embedding dimension, d is the delay; The corresponding scatter pattern is where v j ∈(1,2,…,c),j=1,2,…,m-1, the scatter pattern consists of m numbers, each number has C ways to be chosen, and there are a total of c m a scatter pattern; (3.5) Calculate each scattering mode Probability: Among them, π i represents the i-th scattering mode; (3.6) For each scale factor τ, the RCMRDE value of the time series X is For different coarse-grained sequences The average value of the scatter pattern.

2. The rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection according to claim 1 is characterized in that: The VMD algorithm in step S2 is specifically: f(t) is the original vibration acceleration signal of the rolling bearing, which is decomposed by VMD to obtain k IMF components, and the variational constraint problem is obtained: Where, f(t) is the original vibration acceleration signal of the rolling bearing; u k (t) is the kth mode; ω k is the center frequency; k is the number of modes; represents the partial derivative with respect to t; ||·||2 represents the norm of 2; δ(t) is the Dirac distribution; * is the convolution operator; Introduce the augmented Lagrange expression: Among them, α is the introduced quadratic penalty factor; λ(t) is the Lagrange multiplication operator; <> represents the inner product operation; Use the alternating direction multiplier method to solve the saddle point of the above Lagrange expression: 2.1) Initialization n, the initial value is 0, and the preset scale k is set to a positive integer; 2.2) Execute loop n=n+1; 2.3) Update according to equation (3), equation (4), and equation (5), and get 2.4) Given the judgment accuracy e>0, when When , the iteration stops and k IMF components are output And the corresponding center frequency Where n is a positive integer; ^ represents Fourier transform; τ is the noise tolerance parameter.

3. The rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection according to claim 1 or 2, characterized in that: The JMIM algorithm in step S4 is specifically: (4.1) The original vibration acceleration signal of the rolling bearing and the RCMRDE value of each component signal after decomposition constitute the original fault feature set F = {f1, f2, ..., f N }, the data dimension is N; select K features from the original fault feature set to form a new feature subset, where k≤N; define feature f X and feature f C The mutual information I(f X ;f C ): I(f X ;f C )=H(f C )-H(f C |f X ) (12) Among them, H(f C ) represents f C The entropy, H(f C |f X ) represents the feature f C Under condition f X Conditional entropy under ; (4.2) Feature f X ,f Y ,f C The calculation process of the joint mutual information between is as follows: I(f X ;f C |f Y )=H(f X |f C )-H(f X |f C ,f Y ) (13) I(f X ,f Y ;f C )=I(f X ;f C |f Y )+I(f Y |f C ) (14) Where, formula (14) represents f X ,f Y Overall same f C the relationship between; (4.3) F is the original fault feature set, S is the currently selected sensitive feature set, and the feature to be selected f i ∈FS, selected feature f s ∈S; feature f to be selected i and the selected features f in S s Highly correlated, Feature to be selected f i , selected features f s And the data label L satisfies the following two formula constraints: I(f i ,f s ;L)=I(f s ;L)+I(f i ;L / f s ) (15) I(f i ,f s ;L)=H(L)-H(L / f i ,f s ) (16) H(L) represents the entropy of L; H(x,y) represents the joint entropy of x and y; (4.4) Derivation of candidate sensitive features, currently selected feature f s And the joint mutual information formula between labels is as follows: Where P(x) represents the probability density function of X, P(x i ,y j ) represents the joint probability density function of variables X and Y; (4.5) The final JMIM algorithm selects the sensitive feature formula as follows: f JMIM =argmaxf i∈F-S (minf s ∈S(I(f i ,f s ;L))) (18)。

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