CN114743039A - Fuzzy clustering bearing fault detection method based on feature reduction - Google Patents

Fuzzy clustering bearing fault detection method based on feature reduction Download PDF

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CN114743039A
CN114743039A CN202210540020.2A CN202210540020A CN114743039A CN 114743039 A CN114743039 A CN 114743039A CN 202210540020 A CN202210540020 A CN 202210540020A CN 114743039 A CN114743039 A CN 114743039A
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CN114743039B (en
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唐益明
张李
潘志富
李书杰
陈锐
吴玺
韩将辉
任福继
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Hefei University of Technology
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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 a 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 feature vector set to judge whether the bearing in the state has a fault. The method can effectively extract key characteristics in the bearing data and improve the accuracy of bearing fault detection.

Description

Fuzzy clustering bearing fault detection method based on feature reduction
Technical Field
The invention belongs to the field of mechanical engineering, and particularly relates to a bearing fault detection method based on fuzzy clustering of feature reduction.
Background
In conventional industrial applications, the bearing aging or damage generally has a failure mode which is not obvious in early operation and the data signal quantity does not change greatly, but the bearing may have a sudden change along with long-term operation and become an unpredictable disaster. Therefore, it is important to perform early failure diagnosis. And the bearing operation information is subjected to data analysis, so that the bearing with the fault can be diagnosed. The fault diagnosis can be regarded as a classification problem in pattern recognition in data analysis, and measured and collected data are separated and are in corresponding relation with fault categories. The related methods for fault detection mainly include a Support Vector Machine (SVM), a genetic algorithm, a neural network, and the like, but these methods need to train marked data, which has certain limitations in practical applications. In addition, a clustering method can be adopted to solve the bearing fault detection problem. Clustering analysis, as an unsupervised learning method, can mine the intrinsic structure of a data set through unmarked data. The method has the advantages of simple algorithm and good convergence, and has a great amount of applications in the field of bearing fault detection. Fuzzy clustering has been used in bearing fault detection applications as a fuzzy mathematical derivation based clustering method. Ruspine originally proposed that fuzzy set concepts were utilized for cluster partitioning, and the most classical and most used method was FCM-based bearing fault detection, which can well satisfy the compactness in the coaxial bearing features and the separability between different bearing features, but which is affected by the sensitivity of the initialization center and noise points. In addition to this, there are some fuzzy clustering based bearing fault detection methods, but they all have some problems.
The existing bearing fault detection method based on fuzzy clustering mainly has the following problems:
1) the problem of adaptability to non-linear bearing characteristic dimensions. Some bearing feature data are not fully applicable to linear feature spaces and may be better represented in non-linear feature spaces.
2) The problem of the selection and tuning of the kernel function for the bearing characteristics. The problem of non-linear bearing characteristics can be solved by mapping the bearing characteristics using a bearing characteristic kernel function, but certain experience is required to select a suitable bearing characteristic kernel function and set suitable parameters.
3) Too many bearing characteristic values lead to complex operation. Only a part of effective bearing characteristics in the bearing characteristics can be used for accurately judging whether the bearing has a fault, and the problem of complex operation is caused by not effectively reducing the bearing characteristics.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a fuzzy clustering bearing fault detection method based on feature reduction so as to effectively extract key features in bearing data and improve the accuracy of bearing fault detection.
In order to achieve the purpose, the 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 of:
step 1: extracting bearing characteristic vector set of data under bearing running state to be processed
Figure BDA0003647882850000021
XiRepresents the ith bearing feature vector, an
Figure BDA0003647882850000022
xilRepresenting the ith bearing feature vector XiL represents the shaftThe number of bearing characteristic values, N represents the number of all bearing characteristic vectors in the bearing characteristic vector set X;
and 2, step: clustering the bearing feature vector set by adopting a fuzzy clustering method based on feature reduction, and dividing the processed data of the bearing feature vector set to obtain a labeled bearing feature vector set:
step 2.1: calculating the l-th bearing characteristic value in the bearing characteristic vector set X by using the formula (1)
Figure BDA0003647882850000023
Degree of dispersion δlThereby obtaining the discrete distribution degree of all bearing characteristic values
Figure BDA0003647882850000024
Figure BDA0003647882850000025
In formula (1), var (-) represents the calculated mean value, mean (-) represents the calculated variance;
step 2.2: dividing a bearing feature vector set X into C bearing feature vector subsets;
step 2.3: defining and initializing the current iteration number iter to be 0, and initializing the bearing characteristic membership degree matrix of the iter-th iteration to be U(iter)And the weight matrix of the bearing eigenvalue is W(iter)(ii) a Defining an iteration stop threshold as epsilon, and defining the maximum iteration number as iterMax;
step 2.4: calculating the ith bearing feature vector X in the kth bearing feature vector quantum set by using the formula (2)kiThe first bearing characteristic value xkilT-th bearing characteristic value kernel function Kkt(xkil,xkil)：
Kkt(xkil,xkil)＝φ(xkil)·φ(xkil) (2)
In equation (4), φ (-) is a mapping function, φ (-) is an inner product between two mapping functions φ (-) and φ (-) is a mapping function;
step 2.5: calculating the ith bearing feature vector X in the kth bearing feature vector quantum set in the iter iteration by using the formula (3)kiThe first bearing characteristic value xkilBearing characteristic value kernel function sentinel
Figure BDA0003647882850000026
Figure BDA0003647882850000027
In the formula (3), Kkt(xki′l,xkil) Representing the ith' bearing feature vector X in the kth bearing feature vectorki′The first bearing characteristic value xki′lAnd ith bearing feature vector XkiThe first bearing characteristic value xkilT-th bearing characteristic value kernel function, K, betweenkt(xki′l,xki″l) Representing the ith' bearing feature vector X in the kth bearing feature vectorki′The first bearing characteristic value xki′lAnd the ith' bearing feature vector Xki″The first bearing characteristic value xki″lThe tth bearing characteristic value kernel function in between; m represents a blurring coefficient;
Figure BDA0003647882850000031
represents the ith bearing feature vector X in the kth bearing feature vector quantum set at the iter iterationkiThe degree of membership of the bearing characteristics of (1),
Figure BDA0003647882850000032
represents the ith bearing feature vector X of the kth bearing feature vector in the quantum set at the iter iterationki′The degree of membership of the bearing characteristics of (1),
Figure BDA0003647882850000033
represents the ith bearing feature vector X of the kth bearing feature vector in the quantum set during the iter iterationki″The degree of membership of the bearing characteristics;
of the utilization type(4) To obtain
Figure BDA0003647882850000034
The constraint of (2): 1, C:
Figure BDA0003647882850000035
step 2.6: calculating the weight of the t bearing characteristic value kernel function of the k bearing characteristic vector subset at the iter iteration by using the formula (5)
Figure BDA0003647882850000036
Figure BDA0003647882850000037
In the formula (5), the reaction mixture is,
Figure BDA0003647882850000038
representing the kth bearing characteristic value in the quantum set of the kth bearing characteristic in the iter iteration
Figure BDA0003647882850000039
The weight of (a), gamma is a regularization parameter, P represents the number of bearing characteristic value kernel functions in the kth bearing characteristic vector subset, exp (-) is an exponential function with a natural constant e as the base; 1, C, L, N, and having:
Figure BDA00036478828500000310
Figure BDA00036478828500000311
step 2.7: calculating the clustering center of the kth bearing feature vector subset and the ith bearing feature vector X in the iter iteration by using the formula (8)kiThe ith characteristic value x ofkilIs a distance ofValue of
Figure BDA00036478828500000312
Figure BDA00036478828500000313
Step 2.8: calculating the z-th bearing characteristic value of all bearing characteristic vector in the quantum set during the iter iteration
Figure BDA00036478828500000314
Sum of weights of
Figure BDA0003647882850000041
And judge
Figure BDA0003647882850000042
If yes, sequentially executing from step 2.9; otherwise, the sequence is executed from step 2.10;
step 2.9: deleting the z-th bearing characteristic value of all bearing characteristic vector subsets in the iter iteration to complete characteristic reduction, and obtaining the weight of the reduced bearing characteristic value in all bearing characteristic vector subsets through an equation (9):
Figure BDA0003647882850000043
in the formula (9), the reaction mixture is,
Figure BDA0003647882850000044
represents the first' bearing characteristic value of the reduced k-th bearing characteristic in the quantum set in the iter iteration
Figure BDA0003647882850000045
Weight of (1), xkil′Representing the ith bearing feature vector X of the kth bearing feature vector subsetiThe ith' bearing characteristic value;
Figure BDA0003647882850000046
represents the value of the kth bearing characteristic in the quantum set of the kth bearing characteristic in the iter iteration
Figure BDA0003647882850000047
The weight of (c); l ' represents the number of reduced bearing characteristic values, L ' ═ 1., L ';
assigning L 'to L, L', assigning L,
Figure BDA0003647882850000048
Assignment of value
Figure BDA0003647882850000049
Step 2.10: calculating the weight of the kth bearing characteristic to the l bearing characteristic value in the quantum set in the iter +1 iteration by using the formula (10)
Figure BDA00036478828500000410
Thereby obtaining a weight matrix of the bearing characteristic value of the bearing characteristic vector concentration
Figure BDA00036478828500000411
Figure BDA00036478828500000412
In the formula (10), η is a regularization parameter;
step 2.11: calculating the bearing feature membership of the kth bearing feature vector to the ith bearing feature vector in the quantum set in iter +1 iteration by using the formula (11)
Figure BDA00036478828500000413
Thereby obtaining a bearing feature vector centralized bearing feature membership matrix
Figure BDA00036478828500000414
Figure BDA00036478828500000415
Step 2.12: assigning iter +1 to iter, if | | | W(iter)-W(iter-1)If | | < epsilon or iter > iterMax, the membership degree matrix U of the bearing characteristic of iter-th iteration is obtained(iter)(ii) a Otherwise, re-executing step 2.5;
step 2.11: bearing characteristic membership degree matrix U of iter iteration(iter)Each row in (a) represents a bearing feature vector, such that the bearing feature membership matrix U according to the iter iteration(iter)Labeling the bearing feature vector set, and taking the column number corresponding to the maximum value of each row as the label category of the corresponding bearing feature vector, thereby obtaining the bearing feature vector set with the label category;
and step 3: and 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 less than a threshold value, indicating that the bearing of the corresponding label type is not in fault, otherwise, indicating that the bearing of the corresponding label type is in fault.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention solves the problem of high-dimensional bearing feature vector set data clustering by using the bearing feature vector subset, and divides each bearing feature value into the corresponding bearing feature vector quantum set, thereby refining the control of the clustering process and improving the utilization of the bearing data information.
2. The invention solves the problem of information loss caused by nonlinear bearing characteristic data by using the bearing characteristic value kernel function, and maps certain nonlinear bearing characteristic data to a high-dimensional linear space, thereby better displaying the information of the bearing characteristic data.
3. The invention uses the bearing characteristic reduction method to reduce the bearing characteristic data, solves the problem of high complexity, reduces the operation complexity, and effectively extracts the key characteristics in the bearing data, thereby improving the accuracy of bearing fault detection.
Drawings
FIG. 1 is a flow chart of a bearing fault detection method based on fuzzy clustering of feature reduction according to the present invention;
FIG. 2 is a normal diagram of the bearing signal of the present invention;
FIG. 3 is a diagram of a bearing signal inner race fault of the present invention.
Detailed Description
In this embodiment, as shown in fig. 1, a method for detecting a bearing fault based on fuzzy clustering of feature reduction is performed according to the following steps:
step 1: extracting bearing characteristic vector set of data under bearing running state to be processed
Figure BDA0003647882850000051
XiRepresents the ith bearing feature vector, an
Figure BDA0003647882850000052
xilRepresenting the ith bearing feature vector XiL represents the number of bearing feature values, and N represents the number of all bearing feature vectors in the bearing feature vector set X; in this embodiment, L is thirteen feature values of the mean value, the mean square value, the effective value, the variance, the standard deviation, the peak value, the peak-to-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 data of the bearing feature vector set to obtain a labeled bearing feature vector set:
step 2.1: calculating the l-th bearing characteristic value in the bearing characteristic vector set X by using the formula (1)
Figure BDA0003647882850000061
Degree of dispersion δlThereby obtaining the discrete distribution degree of all bearing characteristic values
Figure BDA0003647882850000062
Figure BDA0003647882850000063
In formula (1), var (-) represents the calculated mean value, mean (-) represents the calculated variance;
step 2.2: dividing a bearing feature vector set X into C bearing feature vector subsets;
step 2.3: defining and initializing the current iteration number iter to be 0, and initializing a bearing characteristic membership matrix of iter iteration to be U(iter)And the weight matrix of the bearing eigenvalue is W(iter)(ii) a Defining an iteration stop threshold as epsilon, and defining the maximum iteration number as iterMax;
step 2.4: calculating the ith bearing feature vector X in the kth bearing feature vector quantum set by using the formula (2)kiThe first bearing characteristic value xkilT-th bearing characteristic value kernel function Kkt(xkil,xkil)：
Kkt(xkil,xkil)＝φ(xkil)·φ(xkil) (2)
In equation (4), φ (-) is a mapping function, φ (-) is an inner product between two mapping functions φ (-) and φ (-) is a mapping function;
step 2.5: calculating the ith bearing feature vector X in the kth bearing feature vector quantum set in the iter iteration by using the formula (3)kiThe first bearing characteristic value xkilBearing characteristic value kernel function sentinel
Figure BDA0003647882850000064
Figure BDA0003647882850000065
In the formula (3), Kkt(xki′l,xkil) Expressing the kth bearing feature into a quantum concentrationIth' bearing feature vector Xki′The first bearing characteristic value x ofki′lAnd the ith bearing feature vector XkiThe first bearing characteristic value xkilT-th bearing characteristic value kernel function, Kkt(xki′l,xki″l) Representing the ith' bearing feature vector X in the kth bearing feature vectorki′The first bearing characteristic value x ofki′lAnd the ith' bearing feature vector Xki″The first bearing characteristic value xki″lThe tth bearing characteristic value kernel function in between; m represents a blurring coefficient;
Figure BDA0003647882850000066
represents the ith bearing feature vector X in the kth bearing feature vector quantum set at the iter iterationkiThe degree of membership of the bearing characteristics of (1),
Figure BDA0003647882850000071
represents the ith bearing feature vector X of the kth bearing feature vector in the quantum set at the iter iterationki′The degree of membership of the bearing characteristics of (1),
Figure BDA0003647882850000072
represents the ith bearing feature vector X of the kth bearing feature vector in the quantum set at the iter iteration timeki″The degree of membership of the bearing characteristics;
obtained by the formula (4)
Figure BDA0003647882850000073
The constraint of (2): 1, C:
Figure BDA0003647882850000074
step 2.6: calculating the weight of the t bearing characteristic value kernel function of the k bearing characteristic vector subset at the iter iteration by using the formula (5)
Figure BDA0003647882850000075
Figure BDA0003647882850000076
In the formula (5), the reaction mixture is,
Figure BDA0003647882850000077
representing the kth bearing characteristic value in the quantum set of the kth bearing characteristic in the iter iteration
Figure BDA0003647882850000078
The weight of (a), gamma is a regularization parameter, P represents the number of bearing characteristic value kernel functions in the kth bearing characteristic vector subset, exp (-) is an exponential function with a natural constant e as the base; 1, C, L, N, and having:
Figure BDA0003647882850000079
Figure BDA00036478828500000710
step 2.7: calculating the clustering center of the kth bearing feature vector subset and the ith bearing feature vector X in the iter iteration by using the formula (8)kiThe ith characteristic value x of (2)kilDistance value of
Figure BDA00036478828500000711
Figure BDA00036478828500000712
Step 2.8: calculating the z-th bearing characteristic value of all bearing characteristic vector in the quantum set during the iter iteration
Figure BDA00036478828500000713
Sum of weights of
Figure BDA00036478828500000714
And judge
Figure BDA00036478828500000715
If yes, sequentially executing from step 2.9; otherwise, the sequence is executed from step 2.10;
step 2.9: deleting the z-th bearing characteristic value in the bearing characteristic vector subset in the iter iteration to complete characteristic reduction, and obtaining the weight of the reduced bearing characteristic value in all bearing characteristic vector subsets by the formula (9):
Figure BDA0003647882850000081
in the formula (9), the reaction mixture is,
Figure BDA0003647882850000082
representing the value of the kth bearing feature after reduction in the iter iteration to the l' th bearing feature in the quantum set
Figure BDA0003647882850000083
Weight of (1), xkil′Representing the ith bearing feature vector X of the kth bearing feature vector subsetiThe ith' bearing characteristic value;
Figure BDA0003647882850000084
represents the value of the kth bearing characteristic in the quantum set of the kth bearing characteristic in the iter iteration
Figure BDA0003647882850000085
The weight of (c); l ' represents the number of reduced bearing characteristic values, L ' is 1., L ';
assigning L 'to L, L', assigning L,
Figure BDA0003647882850000086
Assignment of value
Figure BDA0003647882850000087
Step 2.10: calculating the weight of the kth bearing characteristic to the ith bearing characteristic value in the quantum set in the iter +1 iteration by using the formula (10)
Figure BDA0003647882850000088
Thereby obtaining a weight matrix of the bearing characteristic value of the bearing characteristic vector concentration
Figure BDA0003647882850000089
Figure BDA00036478828500000810
In the formula (10), η is a regularization parameter;
step 2.11: calculating bearing feature membership of kth bearing feature vector to ith bearing feature vector in quantum set in iter +1 iteration by using formula (11)
Figure BDA00036478828500000811
Thereby obtaining a bearing feature vector centralized bearing feature membership matrix
Figure BDA00036478828500000812
Figure BDA00036478828500000813
Step 2.12: assigning iter +1 to iter, if | | | W(iter)-W(iter-1)If | | < epsilon or iter > iterMax, the membership matrix U of the bearing characteristic of the iter iteration is obtained(iter)(ii) a Otherwise, re-executing step 2.5;
step 2.11: bearing characteristic membership degree matrix U of iter iteration(iter)Each row in (a) represents a bearing feature vector, such that the bearing feature membership matrix U according to the iter iteration(iter)Labeling the bearing feature vector set, and taking the maximum value of each row of the bearing feature vector setThe corresponding column number is the label category of the corresponding bearing feature vector, so that a bearing feature vector set with the label category is obtained;
and step 3: and 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 less than a threshold value, indicating that the bearing of the corresponding label type does not have a fault, otherwise, indicating that the bearing of the corresponding label type has a fault.
In order to verify the effectiveness of the proposed fuzzy clustering based feature reduction bearing fault detection method, some experiments were performed. The platform used in the experiment was the Window 11 system, and the programming languages were Matlab2013b and Python 3.5.
In this example, the method used bearing data from the electrical engineering laboratory at the university of Keiss West reservoir (CWRU) of America for comparative analysis. The data set is selected from signals of normal condition (shown in figure 2) and inner ring fault (shown in figure 3) of a bearing with the platform rotating speed of 1730r/min and the diameter of 0.1778mm, 5000 data signals are selected, and 150 data sets with 13 dimensions are extracted. The data set characteristics of the bearing rotation signal mainly include: mean, mean square, effective value, variance, standard deviation, peak-to-peak, skewness, kurtosis, waveform index, pulse index, peak index, margin index.
Analyzing an experimental result, reducing bearing characteristic value data by the fuzzy clustering bearing fault detection method based on characteristic reduction, and finding that important bearing characteristics in 13 bearing characteristics are four of effective value, mean value, peak value and peak-peak value; in addition, the accuracy of the mixed data set under one fault type and normal condition is 0.92, the accuracy of the mixed data under the two fault types and normal conditions is 0.91, and compared with a bearing fault detection method based on fuzzy clustering of FCM, the accuracy of the method is only 0.830 and 0.687, so that the method can be used for effectively extracting key features in bearing data and improving the accuracy of bearing fault detection.

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 feature vector set of data to be processed under bearing running state
Figure FDA0003647882840000011
XiRepresents the ith bearing feature vector, an
Figure FDA0003647882840000012
xilRepresenting the ith bearing feature vector XiL represents the number of bearing feature values, and N represents the number of all bearing feature vectors in the bearing feature 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 data of the bearing feature vector set to obtain a labeled bearing feature vector set:
step 2.1: calculating the ith bearing characteristic value in a bearing characteristic vector set X by using the formula (1)
Figure FDA0003647882840000013
Degree of dispersion δlThereby obtaining the discrete distribution degree of all bearing characteristic values
Figure FDA0003647882840000014
Figure FDA0003647882840000015
In formula (1), var (-) represents the calculated mean value, mean (-) represents the calculated variance;
step 2.2: dividing a bearing feature vector set X into C bearing feature vector subsets;
step 2.3: defining and initializing the current iteration number iter as 0Initializing bearing characteristic membership matrix of iter iteration to be U(iter)And the weight matrix of the bearing eigenvalue is W(iter)(ii) a Defining an iteration stop threshold as epsilon, and defining the maximum iteration number as iterMax;
step 2.4: calculating the ith bearing feature vector X in the kth bearing feature vector quantum set by using the formula (2)kiThe first bearing characteristic value xkilT-th bearing characteristic value kernel function Kkt(xkil,xkil)：
Kkt(xkil,xkil)＝φ(xkil)·φ(xkil) (2)
In equation (4), φ (-) is a mapping function, φ (-) is an inner product between two mapping functions φ (-) and φ (-) is a mapping function;
step 2.5: calculating the ith bearing feature vector X in the kth bearing feature vector quantum set in the iter iteration by using the formula (3)kiThe first bearing characteristic value xkilBearing characteristic value kernel function sentinel
Figure FDA0003647882840000016
Figure FDA0003647882840000017
In the formula (3), Kkt(xki′l,xkil) Representing the ith' bearing feature vector X in the kth bearing feature vectorki′The first bearing characteristic value xki′lAnd ith bearing feature vector XkiThe first bearing characteristic value xkilT-th bearing characteristic value kernel function, Kkt(xki′l,xki″l) Represents the ith' bearing feature vector X in the kth bearing feature vector quantum setki′The first bearing characteristic value xki′lAnd the ith' bearing feature vector Xki″The first bearing characteristic value xki″lThe tth bearing characteristic value kernel function in between; m represents a blurring coefficient;
Figure FDA0003647882840000021
represents the ith bearing feature vector X in the kth bearing feature vector quantum set at the iter iterationkiThe degree of membership of the bearing characteristics of (1),
Figure FDA0003647882840000022
represents the ith bearing feature vector X of the kth bearing feature vector in the quantum set at the iter iterationki′The degree of membership of the bearing characteristics of (1),
Figure FDA0003647882840000023
represents the ith bearing feature vector X of the kth bearing feature vector in the quantum set at the iter iteration timeki″The degree of membership of the bearing characteristics;
obtained by the formula (4)
Figure FDA0003647882840000024
The constraint of (2): 1, C:
Figure FDA0003647882840000025
step 2.6: calculating the weight of the t bearing characteristic value kernel function of the k bearing characteristic vector subset at the iter iteration by using the formula (5)
Figure FDA0003647882840000026
Figure FDA0003647882840000027
In the formula (5), the reaction mixture is,
Figure FDA0003647882840000028
representing the kth bearing characteristic value in the quantum set of the kth bearing characteristic in the iter iteration
Figure FDA0003647882840000029
The weight of (a), gamma is a regularization parameter, P represents the number of bearing characteristic value kernel functions in the kth bearing characteristic vector subset, exp (-) is an exponential function with a natural constant e as the base; 1, C, L, 1, L, i 1, N, and having:
Figure FDA00036478828400000210
Figure FDA00036478828400000211
step 2.7: calculating the clustering center of the kth bearing feature vector subset and the ith bearing feature vector X in the iter iteration by using the formula (8)kiThe ith characteristic value x ofkilDistance value of
Figure FDA00036478828400000212
Figure FDA00036478828400000213
Step 2.8: calculating the z-th bearing characteristic value of all bearing characteristic vector in the quantum set during the iter iteration
Figure FDA00036478828400000214
Sum of weights of
Figure FDA00036478828400000215
And judge
Figure FDA00036478828400000216
If yes, sequentially executing from step 2.9; otherwise, the sequence is executed from step 2.10;
step 2.9: deleting the z-th bearing characteristic value of all bearing characteristic vector subsets in the iter iteration to complete characteristic reduction, and obtaining the weight of the reduced bearing characteristic value in all bearing characteristic vector subsets through an equation (9):
Figure FDA0003647882840000031
in the formula (9), the reaction mixture is,
Figure FDA0003647882840000032
representing the value of the kth bearing feature after reduction in the iter iteration to the l' th bearing feature in the quantum set
Figure FDA0003647882840000033
Weight of (a), xkil′Representing the ith bearing feature vector X of the kth bearing feature vector subsetiThe ith' bearing characteristic value;
Figure FDA0003647882840000034
represents the value of the kth bearing characteristic in the quantum set of the kth bearing characteristic in the iter iteration
Figure FDA0003647882840000035
The weight of (c); l ' represents the number of reduced bearing characteristic values, L ' ═ 1., L ';
assigning L 'to L, L', assigning L,
Figure FDA0003647882840000036
Assignment of value
Figure FDA0003647882840000037
Step 2.10: calculating the weight of the kth bearing characteristic to the ith bearing characteristic value in the quantum set in the iter +1 iteration by using the formula (10)
Figure FDA0003647882840000038
Thereby obtaining a weight matrix of the bearing characteristic value of the bearing characteristic vector concentration
Figure FDA0003647882840000039
Figure FDA00036478828400000310
In the formula (10), η is a regularization parameter;
step 2.11: calculating the bearing feature membership of the kth bearing feature vector to the ith bearing feature vector in the quantum set in iter +1 iteration by using the formula (11)
Figure FDA00036478828400000311
Thereby obtaining a bearing feature vector centralized bearing feature membership matrix
Figure FDA00036478828400000312
Figure FDA00036478828400000313
Step 2.12: assigning iter +1 to iter, if | | | W(iter)-W(iter-1)If | | < epsilon or iter > iterMax, the membership matrix U of the bearing characteristic of the iter iteration is obtained(iter)(ii) a Otherwise, re-executing step 2.5;
step 2.11: bearing characteristic membership degree matrix U of iter iteration(iter)Each row in (a) represents a bearing feature vector, such that the bearing feature membership matrix U according to the iter iteration(iter)Labeling the bearing feature vector set, and taking the column number corresponding to the maximum value of each row as the label category of the corresponding bearing feature vector, thereby obtaining the bearing feature vector set with the label category;
and step 3: and 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 less than a threshold value, indicating that the bearing of the corresponding label type is not in fault, otherwise, indicating that the bearing of the corresponding label type is in fault.
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