CN114638251A - Rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection - Google Patents

Abstract

The invention belongs to the field of mechanical fault diagnosis and signal processing, and provides a bearing fault diagnosis method based on RCMRDE and JMIM characteristic selection, which comprises the following steps: acquiring an acceleration signal of the rolling bearing by using an acceleration sensor; performing VMD decomposition on the original vibration signal; calculating the RCMRDE value of the original signal and each decomposed component signal as an original fault feature set; performing feature selection on the original fault feature set by adopting a JMIM feature selection algorithm, selecting sensitive features capable of being accurately classified, and constructing a low-dimensional fault feature set; training an RF classifier according to the selected sensitive component to obtain a trained RF model; and inputting the sensitive fault feature set of the test sample into the trained RF classifier, and diagnosing to obtain the fault type. The method overcomes the defects of the multi-scale dispersion entropy, improves the stability of fault characteristics, the noise robustness and the signal distinguishing capability, and can effectively diagnose different state types of the rolling bearing.

Description

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

Technical Field

The invention relates to the field of mechanical fault diagnosis and signal processing, in particular to a rolling bearing fault diagnosis method based on RCMRDE and JMIM characteristic selection.

Background

Condition monitoring and fault diagnosis are critical to the safe operation of large mechanical equipment. The rolling bearing is an important part of rotary mechanical equipment, has complex operation conditions and is one of the most easily damaged parts of the mechanical equipment. Therefore, the intelligent health state identification on the rolling bearing has great significance for improving the operation reliability of the equipment.

The feature extraction is the key of fault diagnosis of the rolling bearing, and a plurality of nonlinear dynamics methods such as sample entropy, permutation entropy, fuzzy entropy, dispersion entropy and the like based on entropy complexity theory can reflect the nonlinear features of vibration signals and are widely applied to mechanical fault diagnosis. The distributed entropy overcomes partial defects of the permutation entropy and the sample entropy, considers the relation between the amplitudes, and has the advantages of high calculation speed, small influence of a mutation signal and the like. The method is inspired by the dispersion entropy and the multi-scale dispersion entropy, provides the fine composite multi-scale reverse dispersion entropy, solves the problem that the signal complexity characteristic is not complete when the single-scale dispersion entropy is extracted, has good stability compared with the traditional coarse graining multi-scale process, and has certain advantages in the aspects of entropy stability, noise robustness, signal distinguishing capability and the like.

Selecting features that accurately reflect the fault condition is critical to accurate fault diagnosis. Feature selection based on information theory is a popular method because it has the advantages of high computational efficiency, good extensibility of dataset dimension, and independence from classifier. Common drawbacks of this approach are the lack of information about the interaction between features and classifiers, and the selection of redundant and irrelevant features. Therefore, the reasonable feature selection method is of great significance to dimensionality reduction and improvement of classification accuracy.

Disclosure of Invention

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

The technical scheme of the invention is as follows:

a rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection comprises the following steps:

step S1, acquiring original vibration acceleration signals of the rolling bearing by using an acceleration sensor, wherein the original vibration acceleration signals comprise radial vibration acceleration signals 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, VMD decomposition is carried out on the original vibration acceleration signal of the rolling bearing;

the VMD algorithm is specifically as follows:

f (t) is an original vibration acceleration signal of the rolling bearing, k IMF components are obtained through VMD decomposition, and the variation constraint problem is obtained:

wherein, f (t) is the original vibration acceleration signal of the rolling bearing; u. u_k(t) is the kth mode; omega_kIs the center frequency; k is the number of modes;

representing partial derivative of t; i | · | purple wind₂A norm representing 2; δ (t) is the dirac distribution; is the convolution operator;

in order to solve the variation constraint problem, the constraint problem needs to be converted into an unconstrained problem, and an augmented Lagrange expression is introduced:

wherein, alpha is an introduced secondary penalty factor; λ (t) is Lagrange multiplier; < > represents inner product operation;

solving the saddle point of the Lagrange expression number by using an alternative direction multiplier method:

2.1) initialization

n, setting the initial values to be 0, and setting the preset scale k as a positive integer;

2.2) executing a loop n ═ n + 1;

2.3) according to the formula (3), the formula (4) and the formula (5) to obtain

2.4) given decision accuracy e>0, when

Stopping iteration and outputting k IMF components

And corresponding center frequency

Wherein n is a positive integer; the power factor represents Fourier transform; τ is a noise margin parameter.

Step S3, calculating the RCMRDE value of the original vibration acceleration signal of the rolling bearing and each decomposed component signal as an original fault feature set;

the RCMRDE value is specifically solved as:

(3.1) the original vibration acceleration signal of the rolling bearing and each decomposed component signal are time series, and taking the time series X { X (i) }, i ═ 1, 2.. multidot.T }, and giving a scale factor tau, wherein the k-th coarse-grained time series of the time series X is as follows:

(3.2) calculating the probability of the spreading pattern of the coarse grained sequences under different scale factors, and aiming at a certain coarse grained time sequence

Using a normal distribution function, a normalized time sequence Y ═ { Y (j) }, j ═ 1,2

(3.3) mapping Y into class C with integer index from 1 to C by linear transformation

c is a positive integer;

(3.4) mixing

Reconstructing, and calculating the embedded vector

Wherein m is the embedding dimension and d is the time delay;

corresponding to a scatter pattern of

Wherein v is_jE (1,2, …, C), j is 1,2, …, m-1, the scattering pattern is composed of m numbers, each number has C kinds of access, and C is total^mA spreading pattern;

(3.5) calculating each of the scatter patterns

Probability of (c):

wherein, pi_iRepresents the ith scattering mode;

(3.6) the RCMRDE value of the time series X is, for each scale factor τ

For different coarse-grained sequences

Average value of the scattering pattern of (a).

Step S4, adopting a JMIM feature selection algorithm to perform sensitive feature selection on an original fault feature set, and constructing a low-dimensional fault training sample sensitive feature set and a low-dimensional fault testing sample sensitive feature set with a ratio of 7: 3;

the JMIM algorithm is specifically as follows:

(4.1) the original vibration acceleration signal of the rolling bearing and the RCMRDE value of each component signal after decomposition form an original fault characteristic set F ═ F₁,f₂,...,f_N}, the data dimension is N; selecting K characteristics from original fault characteristic set to form new characteristic subsetWherein k is less than or equal to N; defining a feature f_XAnd feature f_CMutual information I (f) between_X；f_C)：

I(f_X；f_C)＝H(f_C)-H(f_C|f_X) (12)

Wherein, H (f)_C) Represents f_CEntropy of H (f)_C|f_X) Representative feature f_CUnder condition f_XConditional entropy under conditions;

(4.2) feature f_X,f_Y,f_CThe calculation process of the joint mutual information 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)

wherein formula (14) represents f_X,f_YThe whole is as same as f_CThe relationship between;

(4.3) F is the original failure feature set, S is the sensitive feature set which has been selected currently, and the feature F to be selected_iE.g. F-S, selected characteristic F_sBelongs to S; feature to be selected f_iAnd selected features f in S_sIs highly correlated to obtain

Feature to be selected f_iSelected characteristic f_sAnd 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) deriving candidate sensitive features, the currently selected feature f_sAnd the joint mutual information formula between the labels is as follows:

wherein P (X) represents the probability density function of X, P (X)_i,y_j) A joint probability density function representing 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)。

step S5, training an RF classifier according to the low-dimensional fault training sample sensitive feature set; the obtained RF classification model;

and step S6, inputting the low-dimensional fault test sample sensitivity characteristic set into a trained RF classification model, and diagnosing the fault type.

Compared with the prior art, the invention has the following beneficial effects:

1. compared with the existing several entropy values, the invention overcomes the defects of the multi-scale diffusion entropy and has better stability, noise robustness, signal distinguishing capability and feature extraction capability.

2. The invention fully excavates fault information, and simultaneously selects sensitive characteristic components for fault classification, thereby reducing characteristic dimension and improving diagnosis precision.

3. The invention can effectively diagnose different health states of the rolling bearing.

Drawings

FIG. 1 is a flow chart of a fault diagnosis method of the present invention;

FIG. 2 is a time domain waveform diagram of a rolling bearing in different states according to an embodiment of the present invention; (a) - (i) a fault state at 0.2mm of the outer ring, a fault state at 0.4mm of the outer ring, a fault state at 0.6mm of the outer ring, a fault state at 0.2mm of the inner ring, a fault state at 0.4mm of the inner ring, a fault state at 0.6mm of the inner ring, a fault state at 0.2mm of the rolling element, a fault state at 0.4mm of the rolling element, a fault state at 0.6mm of the rolling element and a normal state are sequentially arranged;

FIG. 3 is a comparison result of classification accuracy of RCMRDE, RCMDE and MDE with the increase of sensitive features in the embodiment of the present invention;

FIG. 4 is a comparison result of classification accuracy of JMIM, Fisher and LS feature selection methods in the embodiment of the present invention;

FIG. 5 is a result of RF identification of a sensitive feature in an embodiment of the present invention;

fig. 6 is a comparison of classification effects of extracting feature values from only the original signal and extracting feature values from the original signal and the frequency band after the VMD decomposition, and a comparison of recognition results of different classifiers based on KNN, BPNN, SVM, and RF in the embodiment of the present invention.

Detailed Description

The invention is further explained with reference to the drawings and the embodiments.

Referring to fig. 1, the present invention provides a rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection, comprising the steps of:

step S1: acquiring an acceleration signal of the rolling bearing by using an acceleration sensor:

in the present embodiment, it is applied to a vibration acceleration signal analysis process in a Normal operation (Normal) of a rolling bearing, with an Inner Ring Failure (IRF), an Outer Ring Failure (ORF), and a rolling element failure (BF). An NI9234 acquisition card and an acceleration sensor are used for acquiring vibration signals, the sampling frequency is 12800HZ, and the vibration acceleration signals of the N205EM/PS bearing with a detachable outer ring and the NU205EM/PS bearing with a detachable inner ring are respectively acquired under four states. The processing mode of the bearings with two different models is linear cutting, the fault types are 0.2mm, 0.4mm and 0.6mm abrasion of an inner ring, 0.2mm, 0.4mm and 0.6mm cracks of an outer ring, and 0.2mm, 0.4mm and 0.6mm abrasion of a rolling body. Each sample type comprises 50 groups, and each group of signal samples comprises 2048 sampling points. Wherein 35 groups of samples of each type are randomly selected as training samples, the remaining 15 groups are used as testing samples, and time domain oscillograms of the rolling bearing in four states are shown in fig. 2. As can be seen from fig. 2, it is difficult to distinguish the types of faults from the time-domain waveform of the bearing vibration signal alone.

Step S2, VMD decomposition is carried out on the original vibration signal;

in this embodiment, the VMD algorithm specifically includes:

and f (t) is a section of bearing vibration signal acquired on the test bed, k IMF components are obtained through VMD decomposition, and then the variation constraint problem is obtained:

wherein,

representing partial derivative of t; f (t) is the original signal; i | · | purple wind₂Representing a norm of 2.

In order to solve the variation model, a constraint problem needs to be converted into an unconstrained problem, and an augmented Lagrange expression is introduced:

wherein, alpha is an introduced secondary penalty factor; λ (t) is Lagrange multiplier; and < > represents inner product operation.

The variable expression in the solving process is shown in formulas (21) to (23)

Wherein n is a positive integer; "^" means Fourier transform; τ is a noise margin parameter.

In this embodiment, the step S2 specifically includes: each health stateBearing vibration signals of states are decomposed into 6 frequency bands, penalty factor is 2000, and discrimination precision is 10^-7。

Step S3, calculating the RCMRDE value of the original signal and each decomposed component signal as an original fault feature set;

for each scale factor τ, the RCMRDE of the time series X is:

wherein, the RCMRDE algorithm parameters are set as N2048, m 2, c 5, d 1, tau_max＝25。

Step S4, a JMIM feature selection algorithm is adopted to perform feature selection on the original fault feature set, sensitive features capable of being accurately classified are selected, and a low-dimensional fault feature set is constructed;

in this embodiment, the JMIM algorithm specifically includes:

(1) let F be the set of raw features, S be the set of features that have been currently selected, feature F_iE.g. F-S, characteristic F_sE.g. S. If the feature f_iAnd a feature f in S_sHighly correlated, then

When feature f is to be selected_iCurrent selected characteristic f_sWhen the data label L satisfies the following two formula constraints:

I(f,f_s；L)＝I(f_s；L)+I(f_i；L/f_s) (25)

I(f,f_s；L)＝H(L)-L(L/f_i,f_s) (26)

(2) and further deducing candidate characteristics, wherein a joint mutual information formula between the currently selected characteristics and the labels is as follows:

(3) and (3) selecting a characteristic formula by the final JMIM algorithm:

f_JMIM＝argmaxf_i∈F-S(minf_s∈S(I(f_i,f_s；L))) (28)

the embodiment selects the RCMRDE value of the sensitivity ranking 15 to construct a new failure feature set according to the JMIM criterion.

Step S5, training an RF classifier according to the selected sensitive component to obtain a trained RF model;

and step S6, inputting the sensitive fault feature set of the test sample into the trained RF classifier, and diagnosing to obtain the fault type.

In this embodiment, the step S6 specifically includes:

and inputting the data into an RF model, and training an RF classifier. The comparison result of the classification accuracy of the RCMRDE, the RCMDE and the MDE is shown in fig. 4 as the number of the sensitive features increases, and it can be seen from fig. 4 that the classification effect based on the RCMRDE increases fastest as the number of the features increases, because the RCMRDE is more stable and has strong anti-noise capability, and the dynamic mutation of the nonlinear signal is more reasonably detected.

In this example, the classification accuracy comparison results of the JMIM, Fisher, and LS feature selection methods are shown in fig. 5, and the JMIM method is superior to the Fisher and LS methods in feature selection. Secondly, the RCMRDE is combined with the JMIM method, so that the diagnosis accuracy can be improved. The results of RF identification of 15 RCMRDE sensitive features in this example are shown in fig. 6.

In the present embodiment, the comparison of the classification effect of extracting feature values from only the original signal and extracting feature values from the original signal and the frequency band after the VMD decomposition, and the comparison of the recognition results of different classifiers are shown in fig. 6.

The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.

Claims (4)

1. A rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection is characterized by comprising the following steps:

step S1, acquiring original vibration acceleration signals of the rolling bearing by using an acceleration sensor, wherein the original vibration acceleration signals comprise radial vibration acceleration signals 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, VMD decomposition is carried out on the original vibration acceleration signal of the rolling bearing;

step S3, calculating the RCMRDE value of the original vibration acceleration signal of the rolling bearing and each decomposed component signal as an original fault feature set;

step S4, adopting a JMIM feature selection algorithm to perform sensitive feature selection on an original fault feature set, and constructing a low-dimensional fault training sample sensitive feature set and a low-dimensional fault testing sample sensitive feature set with a ratio of 7: 3;

step S5, training an RF classifier according to the low-dimensional fault training sample sensitive feature set; the obtained RF classification model;

and step S6, inputting the low-dimensional fault test sample sensitivity feature set into the trained RF classification model, and diagnosing the fault type.

2. The rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection according to claim 1, wherein the VMD algorithm in step S2 is specifically:

(t) is the original vibration acceleration signal of the rolling bearing, k IMF components are obtained through VMD decomposition, and the variation constraint problem is obtained:

wherein, f (t) is the original vibration acceleration signal of the rolling bearing; u. u_k(t) is the kth mode; omega_kIs the center frequency; k is the number of modes;

representing partial derivative of t; i | · | purple wind₂A norm representing 2; δ (t) is the dirac distribution; is the convolution operator;

introducing an augmented Lagrange expression:

wherein, alpha is an introduced secondary penalty factor; λ (t) is Lagrange multiplier; < > represents inner product operation;

solving the saddle point of the Lagrange expression number by using an alternative direction multiplier method:

2.1) initialization

n, setting the initial values to be 0, and setting the preset scale k as a positive integer;

2.2) executing a loop n ═ n + 1;

2.3) according to the formula (3), the formula (4) and the formula (5) to obtain

2.4) given decision accuracy e>0, when

Stopping iteration and outputting k IMF components

And corresponding center frequency

Wherein n is a positive integer; the power factor represents Fourier transform; τ is a noise margin parameter.

3. The rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection according to claim 1 or 2, wherein the RCMRDE value in step S3 is specifically solved as:

(3.1) the original vibration acceleration signal of the rolling bearing and each decomposed component signal are time series, and taking the time series X { X (i) }, i ═ 1, 2.. multidot.T }, and giving a scale factor tau, wherein the k-th coarse-grained time series of the time series X is as follows:

(3.2) calculating the probability of the spreading pattern of the coarse grained sequences under different scale factors, and aiming at a certain coarse grained time sequence

Using a normal distribution function, a normalized time sequence Y ═ { Y (j) }, j ═ 1,2

(3.3) mapping Y into class C with integer index from 1 to C by linear transformation

c is a positive integer;

(3.4) mixing

Performing reconstruction and calculating embedded vector

Wherein m is the embedding dimension and d is the time delay;

the corresponding scattering pattern is

Wherein v is_jE (1,2, …, C), j is 1,2, …, m-1, the scattering pattern is composed of m numbers, each number has C kinds of access, and C is total^mA scatter pattern;

(3.5) calculating each of the scatter patterns

Probability of (c):

wherein, pi_iRepresents the ith scattering mode;

(3.6) the RCMRDE value of the time series X is, for each scale factor τ

For different coarse grain sequences

Average value of the scattering pattern of (a).

4. The rolling bearing fault diagnosis method based on RCMRDE and JMIM feature selection according to claim 1 or 2, wherein 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 form an original fault characteristic set F ═ F₁,f₂,...,f_N}, the data dimension is N; selecting K features from the original fault feature set to form a new feature subset, wherein K is less than or equal to N; defining a feature f_XAnd feature f_CMutual information I (f) between_X；f_C)：

I(f_X；f_C)＝H(f_C)-H(f_C|f_X) (12)

Wherein, H (f)_C) Represents f_CEntropy of H (f)_C|f_X) Representative feature f_CUnder condition f_XConditional entropy under conditions;

(4.2) feature f_X,f_Y,f_CThe calculation process of the joint mutual information 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)

wherein formula (14) represents f_X,f_YThe whole is as same as f_CThe relationship between;

(4.3) F is the set of raw failure features, S is the set of sensitivity features that have been currently selected,feature to be selected f_iE.g. F-S, selected characteristic F_sBelongs to S; feature to be selected f_iAnd selected features f in S_sIs highly correlated to obtain

Feature to be selected f_iSelected characteristic f_sAnd 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) deriving candidate sensitive features, the currently selected feature f_sAnd the joint mutual information formula among the labels is as follows:

wherein P (X) represents the probability density function of X, P (X)_i,y_j) A joint probability density function representing 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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