CN114743039B - Fuzzy clustering bearing fault detection method based on feature reduction - Google Patents
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Abstract
The invention discloses a bearing fault detection method based on fuzzy clustering of feature reduction, which comprises the following steps: 1. extracting a bearing characteristic vector set to be processed from the bearing characteristic value data; 2, clustering the bearing feature vector set to be processed by adopting a fuzzy clustering bearing fault detection method based on feature reduction; and 3, detecting the processed bearing characteristic vector set to judge whether the bearing in the state has faults or not. The invention can effectively extract key characteristics in bearing data and improve the accuracy of bearing fault detection.
Description
Technical Field
The invention belongs to the field of mechanical engineering, and particularly relates to a fuzzy clustering bearing fault detection method based on feature reduction.
Background
In conventional industrial applications, the failure mode of a typical bearing aging or damage in early operation is not obvious, the data signal quantity is not changed greatly, but the bearing can be suddenly changed and becomes an unpredictable disaster along with long-term operation. Therefore, it is particularly important to perform early failure diagnosis. By analyzing the data of the bearing operation information, the method can help us diagnose the bearing with faults. Fault diagnosis can be regarded as a classification problem in pattern recognition in data analysis, and the measured and collected data are separated and are correspondingly related to fault categories. The fault detection related methods mainly include Support Vector Machines (SVMs), genetic algorithms, neural networks and the like, but these methods require training of marked data, which has a certain limitation in practical application. In addition, the bearing fault detection problem can be solved by adopting a clustering method. Cluster analysis, as an unsupervised learning method, can mine the internal structure of the dataset through unmarked data. The method has the advantages of simple algorithm and good convergence, and has a great deal of application in the field of bearing fault detection. Wherein fuzzy clustering has been applied to bearing fault detection applications as a clustering method based on fuzzy mathematical derivation. Ruspini has first proposed using fuzzy set concepts to perform cluster division, wherein the most classical and most used is the FCM-based bearing fault detection method, which can well meet the compactness in the coaxial bearing features and the separability between different bearing features, but has the problems of being sensitive to an initialization center and influenced by noise points. In addition to this, there are some bearing failure detection methods based on fuzzy clustering, but they all have some problems.
The problems of the existing bearing fault detection method based on fuzzy clustering mainly include the following 3:
1) Adaptability to nonlinear bearing feature dimensions. Some bearing feature data is not fully applicable to linear feature space and may be more effective in non-linear feature space.
2) And the problem of the type selection and tuning of the bearing characteristic kernel function is solved. Mapping bearing features using bearing feature kernel functions can solve the problem of non-linear bearing features, but selecting appropriate bearing feature kernel functions and setting appropriate parameters requires some experience.
3) Too many characteristic values of the bearing cause the problem of complex operation. Only a part of effective bearing characteristics in the bearing characteristics can be used for accurately judging whether the bearing has faults or not, and the problem of complex operation is not caused by effective reduction of the bearing characteristics.
Disclosure of Invention
The invention aims to solve the defects in the prior art, and provides a fuzzy clustering bearing fault detection method based on feature reduction, so that key features in bearing data can be effectively extracted, and the accuracy of bearing fault detection is improved.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the invention relates to a bearing fault detection method based on fuzzy clustering of feature reduction, which is characterized by comprising the following steps:
step 1: extracting bearing characteristic vector set of data under running state of bearing to be processedX i Represents the ith bearing feature vector, and +.>x il Representing the ith bearing feature vector X i L represents the number of the bearing characteristic values, and N represents the number of all the bearing characteristic vectors in the bearing characteristic vector set X;
step 2: clustering the bearing feature vector set by adopting a fuzzy clustering method based on feature reduction, and dividing the processed bearing feature vector set data to obtain a bearing feature vector set with labels:
step 2.1: calculating the first bearing characteristic value in the bearing characteristic vector set X by using the method (1)Degree of discrete distribution delta of (2) l Thereby obtaining the discrete distribution degree of all the bearing characteristic values +.>
In the formula (1), var (·) represents a calculated average value, mean (·) represents a calculated variance;
step 2.2: dividing the bearing feature vector set X into C bearing feature vector subsets;
step 2.3: defining and initializing the current iteration number iter=0, and initializing a bearing characteristic membership matrix of the ith iteration to U (iter) And the weight matrix of the characteristic values of the bearing is W (iter) The method comprises the steps of carrying out a first treatment on the surface of the Defining an iteration stop threshold as epsilon and the maximum iteration times as iterMax;
step 2.4: calculating an ith bearing feature vector X in the kth bearing feature vector subset using (2) ki Is the first bearing characteristic value x kil Is the t-th bearing characteristic value kernel function K kt (x kil ,x kil )：
K kt (x kil ,x kil )＝φ(x kil )·φ(x kil ) (2)
In the formula (4), phi (·) is a mapping function, and phi (·) is an inner product between two mapping functions phi (·);
step 2.5: calculating an ith bearing feature vector X in the kth bearing feature vector subset at the ith iteration by using (3) ki Is the first bearing characteristic value x kil Bearing characteristic value kernel function sentinel
In the formula (3), K kt (x ki′l ,x kil ) Representing the ith' bearing feature vector X in the kth bearing feature vector subset ki′ Is the first bearing characteristic value x ki′l And ith bearing feature vector X ki Is the first bearing characteristic value x kil The t bearing characteristic value kernel function between K kt (x ki′l ,x ki″l ) Representing the kth bearing featureVector subset ith' bearing feature vector X ki′ Is the first bearing characteristic value x ki′l And the i' th bearing feature vector X ki″ Is the first bearing characteristic value x ki″l A t-th bearing characteristic value kernel function between the two; m represents a blur coefficient;represents the ith bearing feature vector X in the kth bearing feature vector subset at the ith iteration ki Bearing characteristic membership of>Represents the ith' bearing feature vector X in the kth bearing feature vector subset at the ith iteration ki′ Bearing characteristic membership of>Represents the ith' bearing feature vector X in the kth bearing feature vector subset at the ith iteration ki″ Bearing feature membership of (2);
obtained by using (4)Is a constraint on (c): k=1.., C:
step 2.6: calculating the weight of the t bearing feature value kernel function of the k bearing feature vector subset at the ith iteration by using the method (5)
In the formula (5), the amino acid sequence of the compound,representing the first bearing feature value in the kth bearing feature vector subset at the ith iterationGamma is a regularization parameter, P represents the number of bearing eigenvalue kernel functions in the kth bearing eigenvector subset, exp (·) is an exponential function with the base of the natural constant e; k=1, a., C, l=1.. L, i=1,.. N, and has:
step 2.7: calculating the clustering center of the kth bearing feature vector subset and the ith bearing feature vector X in the ith iteration by using the method (8) ki Is the first eigenvalue x of (2) kil Distance value of (2)
Step 2.8: calculating the z-th bearing characteristic value in all bearing characteristic vector subsets in the ith iterationSum of weights->And judge->Whether or not it is true, if so, sequentially executing from step 2.9The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, sequentially executing from the step 2.10;
step 2.9: deleting the z-th bearing characteristic value in all bearing characteristic vector subsets during the ith iteration to complete characteristic reduction, and obtaining the weight of the bearing characteristic value after the reduction in all bearing characteristic vector subsets through the formula (9):
in the formula (9), the amino acid sequence of the compound,represents the first bearing characteristic value in the kth bearing characteristic vector subset after the reduction in the ith iteration +.>Weights, x kil′ Represents the kth bearing feature vector subset, the ith bearing feature vector X i A first bearing characteristic value; />Representing the first bearing feature value in the kth bearing feature vector subset at the ith iterationWeights of (2); l 'represents the number of bearing feature values after reduction, L' =1,..;
assigning L 'L, L' L,Assignment->
Step 2.10: calculating the weight of the first bearing characteristic value in the kth bearing characteristic vector subset in the ith (item+1) iteration by using the method (10)Thereby obtaining a weight matrix of bearing feature values in the bearing feature vector set>
In the formula (10), η is a regularization parameter;
step 2.11: calculating the bearing characteristic membership degree of the kth bearing characteristic vector in the kth bearing characteristic vector subset in the ith iteration by using the (11)Thereby obtaining the bearing feature membership matrix in the bearing feature vector set
Step 2.12: assigning iter+1 to iter, if W (iter) -W (iter-1) If I < epsilon or iter > iterMax, the bearing characteristic membership matrix U for obtaining the ith iteration is represented (iter) The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, re-executing the step 2.5;
step 2.11: bearing characteristic membership matrix U of the ith iteration (iter) Each row of (a) represents a bearing feature vector, whereby a bearing feature membership matrix U according to the ith iteration (iter) Carrying out labeling treatment on the bearing feature vector set, and taking the column number corresponding to the maximum value of each row as the label type of the corresponding bearing feature vector, thereby obtaining the bearing feature vector set with the label type;
step 3: calculating the average value of the bearing characteristic values of each label class in the bearing characteristic vector set with the label class, taking the average value as the representative value of the corresponding label class, comparing the representative value with the clustering center value of normal bearing data, if the difference value between the representative value and the clustering center value is smaller than a threshold value, indicating that the bearing of the corresponding label class does not fail, otherwise, indicating that the bearing of the corresponding label class fails.
Compared with the prior art, the invention has the beneficial effects that:
1. according to the invention, the bearing feature vector subset is used for solving the problem of data clustering of the high-dimensional bearing feature vector set, and each bearing feature value is divided into the bearing feature vector subsets corresponding to each bearing feature value, so that the control of the clustering process is refined, and the utilization of bearing data information is improved.
2. According to the invention, the problem of information loss caused by nonlinear bearing characteristic data is solved by using a bearing characteristic value kernel function, and certain nonlinear bearing characteristic data are mapped to a high-dimensional linear space, so that the information of the bearing characteristic data is better displayed.
3. According to the invention, the bearing characteristic data is reduced by using the bearing characteristic reduction method, so that the problem of high complexity is solved, the operation complexity is reduced, and meanwhile, key characteristics in the bearing data are effectively extracted, thereby improving the accuracy of bearing fault detection.
Drawings
FIG. 1 is a flow chart of a method for detecting bearing faults based on fuzzy clustering with feature reduction;
FIG. 2 is a normal view of the bearing signals of the present invention;
FIG. 3 is a fault chart of the inner ring of the bearing signal according to the invention.
Detailed Description
In this embodiment, as shown in fig. 1, a method for detecting bearing faults based on fuzzy clustering with feature reduction is performed according to the following steps:
step 1: extracting bearing characteristic vector set of data under running state of bearing to be processedX i Representing the i-th bearing feature vector,and->x il Representing the ith bearing feature vector X i L represents the number of the bearing characteristic values, and N represents the number of all the bearing characteristic vectors in the bearing characteristic vector set X; in this embodiment, l=13, i is the mean value, the mean square value, the effective value, the variance, the standard deviation, the peak value, the peak-peak value, the skewness, the kurtosis, the waveform index, the pulse index, the peak index, and the margin index of the bearing signal in sequence.
Step 2: clustering the bearing feature vector set by adopting a fuzzy clustering method based on feature reduction, and dividing the processed bearing feature vector set data to obtain a bearing feature vector set with labels:
step 2.1: calculating the first bearing characteristic value in the bearing characteristic vector set X by using the method (1)Degree of discrete distribution delta of (2) l Thereby obtaining the discrete distribution degree of all the bearing characteristic values +.>
In the formula (1), var (·) represents a calculated average value, mean (·) represents a calculated variance;
step 2.2: dividing the bearing feature vector set X into C bearing feature vector subsets;
step 2.3: defining and initializing the current iteration number iter=0, and initializing a bearing characteristic membership matrix of the ith iteration to U (iter) And the weight matrix of the characteristic values of the bearing is W (iter) The method comprises the steps of carrying out a first treatment on the surface of the Defining an iteration stop threshold as epsilon and the maximum iteration times as iterMax;
step 2.4: calculating a kth bearing feature using (2)Ith bearing feature vector X in feature vector subset ki Is the first bearing characteristic value x kil Is the t-th bearing characteristic value kernel function K kt (x kil ,x kil )：
K kt (x kil ,x kil )＝φ(x kil )·φ(x kil ) (2)
In the formula (4), phi (·) is a mapping function, and phi (·) is an inner product between two mapping functions phi (·);
step 2.5: calculating an ith bearing feature vector X in the kth bearing feature vector subset at the ith iteration by using (3) ki Is the first bearing characteristic value x kil Bearing characteristic value kernel function sentinel
In the formula (3), K kt (x ki′l ,x kil ) Representing the ith' bearing feature vector X in the kth bearing feature vector subset ki′ Is the first bearing characteristic value x ki′l And ith bearing feature vector X ki Is the first bearing characteristic value x kil The t bearing characteristic value kernel function between K kt (x ki′l ,x ki″l ) Representing the ith' bearing feature vector X in the kth bearing feature vector subset ki′ Is the first bearing characteristic value x ki′l And the i' th bearing feature vector X ki″ Is the first bearing characteristic value x ki″l A t-th bearing characteristic value kernel function between the two; m represents a blur coefficient;represents the ith bearing feature vector X in the kth bearing feature vector subset at the ith iteration ki Bearing characteristic membership of>Represents the ith' bearing feature vector X in the kth bearing feature vector subset at the ith iteration ki′ Bearing characteristic membership of>Represents the ith' bearing feature vector X in the kth bearing feature vector subset at the ith iteration ki″ Bearing feature membership of (2);
obtained by using (4)Is a constraint on (c): k=1.., C:
step 2.6: calculating the weight of the t bearing feature value kernel function of the k bearing feature vector subset at the ith iteration by using the method (5)
In the formula (5), the amino acid sequence of the compound,representing the first bearing feature value in the kth bearing feature vector subset at the ith iterationGamma is a regularization parameter, P represents the number of bearing eigenvalue kernel functions in the kth bearing eigenvector subset, exp (·) is an exponential function with the base of the natural constant e; k=1, a., C, l=1.. L, i=1,.. N, and has:
step 2.7: calculating the clustering center of the kth bearing feature vector subset and the ith bearing feature vector X in the ith iteration by using the method (8) ki Is the first eigenvalue x of (2) kil Distance value of (2)
Step 2.8: calculating the z-th bearing characteristic value in all bearing characteristic vector subsets in the ith iterationSum of weights->And judge->If so, sequentially executing from the step 2.9; otherwise, sequentially executing from the step 2.10;
step 2.9: deleting the z-th bearing characteristic value in all bearing characteristic vector subsets during the ith iteration to complete characteristic reduction, and obtaining the weight of the bearing characteristic value after the reduction in all bearing characteristic vector subsets through the formula (9):
in the formula (9), the amino acid sequence of the compound,represents the first bearing characteristic value in the kth bearing characteristic vector subset after the reduction in the ith iteration +.>Weights, x kil′ Represents the kth bearing feature vector subset, the ith bearing feature vector X i A first bearing characteristic value; />Representing the first bearing feature value in the kth bearing feature vector subset at the ith iterationWeights of (2); l 'represents the number of bearing feature values after reduction, L' =1,..;
assigning L 'L, L' L,Assignment->
Step 2.10: calculating the weight of the first bearing characteristic value in the kth bearing characteristic vector subset in the ith (item+1) iteration by using the method (10)Thereby obtaining a weight matrix of bearing feature values in the bearing feature vector set>
In the formula (10), η is a regularization parameter;
step 2.11: calculation of kth at the ith+1th iteration using equation (11)Bearing feature membership of the ith bearing feature vector in the bearing feature vector subsetThereby obtaining the bearing feature membership matrix in the bearing feature vector set
Step 2.12: assigning iter+1 to iter, if W (iter) -W (iter-1) If I < epsilon or iter > iterMax, the bearing characteristic membership matrix U for obtaining the ith iteration is represented (iter) The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, re-executing the step 2.5;
step 2.11: bearing characteristic membership matrix U of item iteration (iter) Each row of (a) represents a bearing feature vector, whereby a bearing feature membership matrix U according to the ith iteration (iter) Carrying out labeling treatment on the bearing feature vector set, and taking the column number corresponding to the maximum value of each row as the label type of the corresponding bearing feature vector, thereby obtaining the bearing feature vector set with the label type;
step 3: calculating the average value of the bearing characteristic values of each label type in the bearing characteristic vector set with the label type, taking the average value as the representative value of the corresponding label type, comparing the representative value with the clustering center value of the normal bearing data, if the difference value between the representative value and the clustering center value is smaller than the threshold value, indicating that the bearing of the corresponding label type does not have faults, otherwise, indicating that the bearing of the corresponding label type has faults.
In order to verify the effectiveness of the proposed bearing fault detection method based on fuzzy clustering of feature reduction, some experiments were performed. The platforms used in the experiments are Window 11 systems, and the programming languages are Matlab2013b and Python3.5.
In this example, the present method uses the electrical engineering laboratory bearing data of kesixi Chu Da, U.S. (CWRU) for comparative analysis. The data set is selected from a signal (shown in figure 2) of normal condition of a bearing with the rotating speed of 1730r/min and the diameter of 0.1778mm and a signal (shown in figure 3) of inner ring fault, 5000 data signals are selected, and 150 data sets with 13 dimensions are extracted. The data set features of the bearing rotation signal are mainly: mean, mean square, effective, variance, standard deviation, peak-to-peak, skewness, kurtosis, waveform index, pulse index, peak index, margin index.
Analyzing the experimental result, the bearing characteristic value data is reduced by the fuzzy clustering bearing fault detection method based on characteristic reduction, and the important bearing characteristics of the 13 bearing characteristics are found to be four of an effective value, an average value, a peak value and a peak-peak value; in addition, the accuracy of the mixed data set of the fault type and the normal condition is 0.92, and the accuracy of the mixed data of the fault type and the normal condition is 0.91, compared with the accuracy of the bearing fault detection method based on fuzzy clustering of FCM, which is only 0.830 and 0.687, the method can obtain that the key characteristics in the bearing data can be effectively extracted, and the accuracy of bearing fault detection is improved.
Claims (1)
1. A bearing fault detection method based on fuzzy clustering of feature reduction is characterized by comprising the following steps:
step 1: extracting bearing characteristic vector set of data under running state of bearing to be processedX i Represents the ith bearing feature vector, and +.>x il Representing the ith bearing feature vector X i L represents the number of the bearing characteristic values, and N represents the number of all the bearing characteristic vectors in the bearing characteristic vector set X;
step 2: clustering the bearing feature vector set by adopting a fuzzy clustering method based on feature reduction, and dividing the processed bearing feature vector set data to obtain a bearing feature vector set with labels:
step 2.1: calculating the first bearing characteristic value in the bearing characteristic vector set X by using the method (1)Degree of discrete distribution delta of (2) l Thereby obtaining the discrete distribution degree of all the bearing characteristic values +.>
In the formula (1), var (·) represents a calculated average value, mean (·) represents a calculated variance;
step 2.2: dividing the bearing feature vector set X into C bearing feature vector subsets;
step 2.3: defining and initializing the current iteration number iter=0, and initializing a bearing characteristic membership matrix of the ith iteration to U (iter) And the weight matrix of the characteristic values of the bearing is W (iter) The method comprises the steps of carrying out a first treatment on the surface of the Defining an iteration stop threshold as epsilon and the maximum iteration times as iterMax;
step 2.4: calculating an ith bearing feature vector X in the kth bearing feature vector subset using (2) ki Is the first bearing characteristic value x kil Is the t-th bearing characteristic value kernel function K kt (x kil ,x kil )：
K kt (x kil ,x kil )＝φ(x kil )·φ(x kil ) (2)
In the formula (4), phi (·) is a mapping function, and phi (·) is an inner product between two mapping functions phi (·);
step 2.5: calculating an ith bearing feature vector X in the kth bearing feature vector subset at the ith iteration by using (3) ki Is the first bearing characteristic value x kil Bearing characteristic value kernel function sentinel
In the formula (3), K kt (x ki′l ,x kil ) Representing the ith' bearing feature vector X in the kth bearing feature vector subset ki′ Is the first bearing characteristic value x ki′l And ith bearing feature vector X ki Is the first bearing characteristic value x kil The t bearing characteristic value kernel function between K kt (x ki′l ,x ki ″ l ) Representing the ith' bearing feature vector X in the kth bearing feature vector subset ki′ Is the first bearing characteristic value x ki′l And the i' th bearing feature vector X ki″ Is the first bearing characteristic value x ki″l A t-th bearing characteristic value kernel function between the two; m represents a blur coefficient;represents the ith bearing feature vector X in the kth bearing feature vector subset at the ith iteration ki Bearing characteristic membership of>Represents the ith' bearing feature vector X in the kth bearing feature vector subset at the ith iteration ki′ Bearing characteristic membership of>Represents the ith' bearing feature vector X in the kth bearing feature vector subset at the ith iteration ki″ Bearing feature membership of (2);
obtained by using (4)Is a constraint on (c): k=1.., C:
step 2.6: calculating the weight of the t bearing feature value kernel function of the k bearing feature vector subset at the ith iteration by using the method (5)
In the formula (5), the amino acid sequence of the compound,represents the first bearing feature value in the kth bearing feature vector subset at the ith iteration +.>Gamma is a regularization parameter, P represents the number of bearing eigenvalue kernel functions in the kth bearing eigenvector subset, exp (·) is an exponential function with the base of the natural constant e; k=1, a., C, l=1.. L, i=1,.. N, and has:
step 2.7: calculating the clustering center and the clustering center of the kth bearing feature vector subset in the ith iteration by using the method (8)Ith bearing feature vector X ki Is the first eigenvalue x of (2) kil Distance value of (2)
Step 2.8: calculating the z-th bearing characteristic value in all bearing characteristic vector subsets in the ith iterationSum of weights->And judge->If so, sequentially executing from the step 2.9; otherwise, sequentially executing from the step 2.10;
step 2.9: deleting the z-th bearing characteristic value in all bearing characteristic vector subsets during the ith iteration to complete characteristic reduction, and obtaining the weight of the bearing characteristic value after the reduction in all bearing characteristic vector subsets through the formula (9):
in the formula (9), the amino acid sequence of the compound,represents the first bearing characteristic value in the kth bearing characteristic vector subset after the reduction in the ith iteration +.>Weights, x kil′ Represents the kth bearing feature vector subset, the ith bearing feature vector X i A first bearing characteristic value; />Represents the first bearing feature value in the kth bearing feature vector subset at the ith iteration +.>Weights of (2); l 'represents the number of bearing feature values after reduction, L' =1,..;
assigning L 'L, L' L,Assignment->
Step 2.10: calculating the weight of the first bearing characteristic value in the kth bearing characteristic vector subset in the ith (item+1) iteration by using the method (10)Thereby obtaining a weight matrix of bearing feature values in the bearing feature vector set>
In the formula (10), η is a regularization parameter;
step 2.11: calculating the bearing characteristic membership degree of the kth bearing characteristic vector in the kth bearing characteristic vector subset in the ith iteration by using the (11)Thereby obtaining the bearing feature membership matrix in the bearing feature vector set>
Step 2.12: assigning iter+1 to iter, if W (iter) -W (iter-1) If I < epsilon or iter > iterMax, the bearing characteristic membership matrix U for obtaining the ith iteration is represented (iter) The method comprises the steps of carrying out a first treatment on the surface of the Otherwise, re-executing the step 2.5;
step 2.11: bearing characteristic membership matrix U of the ith iteration (iter) Each row of (a) represents a bearing feature vector, whereby a bearing feature membership matrix U according to the ith iteration (iter) Carrying out labeling treatment on the bearing feature vector set, and taking the column number corresponding to the maximum value of each row as the label type of the corresponding bearing feature vector, thereby obtaining the bearing feature vector set with the label type;
step 3: calculating the average value of the bearing characteristic values of each label class in the bearing characteristic vector set with the label class, taking the average value as the representative value of the corresponding label class, comparing the representative value with the clustering center value of normal bearing data, if the difference value between the representative value and the clustering center value is smaller than a threshold value, indicating that the bearing of the corresponding label class does not fail, otherwise, indicating that the bearing of the corresponding label class fails.
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