CN111044287A - Rolling bearing fault diagnosis method based on probability output elastic convex hull - Google Patents

Rolling bearing fault diagnosis method based on probability output elastic convex hull Download PDF

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CN111044287A
CN111044287A CN201911406664.7A CN201911406664A CN111044287A CN 111044287 A CN111044287 A CN 111044287A CN 201911406664 A CN201911406664 A CN 201911406664A CN 111044287 A CN111044287 A CN 111044287A
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convex hull
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丁子杨
杨路航
程军圣
何知义
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Hunan University
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Abstract

The invention discloses a rolling bearing fault diagnosis method based on a probability output elastic convex hull, which comprises the steps of firstly extracting working signals from different sensors in each fault state of mechanical equipment; respectively extracting time domain, frequency domain and time-frequency domain characteristics to obtain characteristic vectors of each working signal, and acquiring a training sample set and a verification sample set of each fault state based on the characteristic vectors; respectively training a multi-classification model based on a probability output elastic convex hull method on a training sample set to establish an optimal diagnosis model, and classifying test samples according to the optimal diagnosis model; and identifying the working state and the fault type of the rolling bearing according to the classification result. The rolling bearing fault diagnosis method based on the probability output elastic convex hull has higher recognition degree in the mode recognition process.

Description

Rolling bearing fault diagnosis method based on probability output elastic convex hull
Technical Field
The invention belongs to the field of bearing fault diagnosis, and particularly relates to a rolling bearing fault diagnosis method based on a probability output elastic convex hull.
Background
The research on the fault diagnosis technology of the rolling bearing has important significance, and scholars at home and abroad have already made a great deal of research on the fault of the rolling bearing and have developed a plurality of intelligent fault diagnosis methods for the rolling bearing. The intelligent diagnosis method for the faults of the rolling bearing is essentially a pattern recognition problem. Among them, Back Propagation Neural Network (BPNN) and Support Vector Machine (SVM) are the most commonly used.
The SVM, as a simple and effective classification method, can be essentially regarded as a convex hull-based maximum edge distance classification algorithm, which approximates each class region by a convex hull and then constructs a classification hyperplane by using the closest points on the convex hull, except that the boundary of the convex hull tends to be infinite, and the convex hull is separated by a classification hyperplane. The learners put forward an elastic convex hull classification method for constraining the convex hull boundary, and the convex hull can be estimated compactly or loosely by changing the elastic factor, so that the classification precision of the convex hull is improved. However, when the method is used for classification hyperplane optimization, decision contributions of most sample points inside the convex hull are ignored, so that the classification accuracy of the test set is reduced, and the identification accuracy is easily influenced by outliers.
Disclosure of Invention
The invention aims to solve the problems and provides a rolling bearing fault diagnosis method based on a probability output elastic convex hull.
The invention aims to improve the output of an elastic convex hull, and discloses a probability output elastic convex hull classification method.
In order to realize the purpose, the invention adopts the technical scheme that: a rolling bearing fault diagnosis method based on a probability output elastic convex hull comprises the following steps:
step 1: acquiring a vibration acceleration signal of the rolling bearing through an acceleration sensor, and extracting time domain, frequency domain and time-frequency domain characteristics from the vibration acceleration signal to form a fault characteristic set of the rolling bearing;
step 2: dividing the fault feature set into a training set sample and a test set sample, and training the training set sample on the basis of a multi-classification model of a probability output elastic convex hull to establish an optimal diagnosis model, wherein the method specifically comprises the following steps:
1) determining a multi-classification probability output elastic convex hull model for a training sample, and training the training sample on the basis of the elastic convex hull classification model output by probability;
2) carrying out optimization probability output on two parameters of the elastic convex hull, namely a kernel parameter sigma and an elastic factor lambda by a grid search algorithm;
3) selecting an optimal parameter from the grid so as to determine a probability output elastic convex hull classification model under the optimal parameter;
and step 3: and outputting an elastic convex hull classification model according to the optimal probability to classify the test set samples, and identifying the working state and the fault type of the rolling bearing according to the classification result.
Further, the training of the elastic convex hull classification model based on probability output on the training samples in the step 2 specifically includes the following steps:
a 1: constructing an elastic convex hull, and introducing an elastic factor into the convex hull model to obtain an elastic convex hull model;
a 2: classifying the elastic convex hulls, and searching an optimal hyperplane in the sample set, wherein the optimal hyperplane is set as a connecting line segment which vertically bisects the closest point of the two elastic convex hulls, and the two elastic convex hulls are divided into a positive sample set and a negative sample set;
a 3: determining the optimal hyperplane position according to a solving method of the nearest points of the two elastic convex hulls, and solving by combining a kernel function to obtain the distance relation between the points on the convex hulls and the hyperplane as follows:
f(x)＝<w*,x>+b*
wherein, w*Classifying hyperplane normal vectors for optimal solution, b*A bias of the classification hyperplane for the optimal solution; x is a sample point;
a 4: and determining a multi-classification decision function, and mapping the output of the elastic convex hull to the position between (0,1) by adopting the following relation:
Figure BDA0002348822780000021
where f is the thresholdless output of the sample x in the third step<w*,x>+b*Y is the belonged category of the sample, and takes the value { +1, -1 };
a 5: by optimizing the solution parameters A, B by minimizing the cross entropy likelihood function on the training set, the decision function is obtained as defined by the following relation:
Figure BDA0002348822780000022
where the probability estimate that sample x belongs to the positive and negative classes is set to P+-And P-+And P is+-+P-+＝1；
a 6: adopting a one-to-one strategy, carrying out convex hull estimation on each type of sample, carrying out pairwise optimization training, constructing n (n-1)/2 classifiers, and outputting the output probability r of each classifier on the basis of two classification probability outputsij(i, j ≠ 1,2 … n, and i ≠ j) is coupled into a multi-class probability output, and the probability that x belongs to the ith class can be expressed as PiP (y ═ i | x), i ═ 1,2,3
Figure BDA0002348822780000031
The decision function to obtain the multi-class is defined as the following relation:
y＝argmax{Pi,i＝1,2,3…n}；
wherein n is the number of classifiers; piProbability of class i;
further, the step of constructing the elastic convex hull in the step a1 is as follows:
some kind of fault feature sample set extracted from training sample
Figure BDA0002348822780000032
The convex hull is represented as:
Figure BDA0002348822780000033
wherein x1,x2,x3......xiIn convex combination, α1,α2,α3......αiIs a convex combination coefficient; n is the number of sampling points;
introducing an elasticity factor λ ∈ (1, + ∞) into the convex hull, and obtaining an elastic convex hull model expressed as:
Figure BDA0002348822780000034
then the sample set is collected
Figure BDA0002348822780000035
Can be equivalently represented as a new sample set, represented as:
Figure BDA0002348822780000036
further, the positive type sample set and the negative type sample set in the step a2 satisfy the following condition:
all points of the positive type sample set satisfy:<w*,x>+b*>0；
the points of the negative class sample set satisfy:<w*,x>+b*<0；
further, the determination of the optimal hyperplane position in step a3 comprises the following steps:
according to the solution of the closest point of the two convex hulls, the relation is as follows:
Figure BDA0002348822780000037
Figure BDA0002348822780000038
Figure BDA0002348822780000039
this formula expands as follows:
Figure BDA0002348822780000041
Figure BDA0002348822780000042
Figure BDA0002348822780000043
wherein, αi+Convex combination coefficient representing the ith positive type sample set, αj-The convex combination coefficient of the jth negative class sample set; n is-Number of sampling points, n, for a negative type sample set+The number of sampling points for the positive type sample set; lambda [ alpha ]+An elasticity factor of the positive type sample set; lambda [ alpha ]-The elasticity factor is the negative class sample set; x is the number ofi+I-th sample point, x, representing a positive classj-The jth sample point representing a negative class;
solving by taking a Gaussian kernel function as a kernel function, wherein the Gaussian kernel function has the following relation:
Figure BDA0002348822780000044
Figure BDA0002348822780000045
wherein σ is a nuclear parameter;
solving convex combining coefficient α*Then the normal vector w of the optimal classification hyperplane can be determined*And bias b*The following are:
Figure BDA0002348822780000046
Figure BDA0002348822780000047
α*is the corresponding sample convex combination coefficient when the objective function value is minimum,
Figure BDA0002348822780000048
the coefficients representing the ith sample of the positive class,
Figure BDA0002348822780000049
coefficient, w, representing the jth sample of the negative class*Is a normal vector of the classification hyperplane, b*The bias for the hyperplane for optimal classification is a constant, xi+Denotes the ith sample point, x, of the positive classj-Represents the jth sample point of the negative class;
the distance between the point on the convex hull and the hyperplane is obtained by the following expression:
f(x)＝<w*,x>+b*。
can also be written as
Figure BDA0002348822780000051
Further, the solving step of the parameter A, B in the step a5 is as follows:
the cross entropy likelihood function optimization solution parameters A, B on the minimization training set are given by the following relation:
Figure BDA0002348822780000052
Figure BDA0002348822780000053
tirepresenting the corresponding weight of the probability of the ith sample in the minimized cross entropy likelihood function, where n+，n-Respectively representing the number of positive and negative samples;
and (3) acquiring an optimal solution by adopting a Newton iteration method, wherein the formula is as follows:
Figure BDA0002348822780000054
wherein n is+，n-Respectively representing the number of positive and negative samples.
Further, the step a6 couples the output probabilities of the classifiers in pairs, and the relationship is as follows:
Figure BDA0002348822780000055
transform and sum it to
Figure BDA0002348822780000056
The optimization problem can be transformed into the following model to solve
Figure BDA0002348822780000061
Spread and written in matrix form
Figure BDA0002348822780000062
Where Qij is the value in row i and column j in matrix Q;
solving by adopting a standard algorithm to obtain the probability P of each class to which the sample belongsiThe decision function to obtain multiple classifications is thus defined as:
y＝argmax{Pi,i＝1,2,3…n}。
the invention has the beneficial effects that: the core of the method is to estimate a certain class of samples through the elastic convex hull, construct a convex hull for each class of samples respectively, then construct n (n-1) classifiers according to a one-to-one strategy, and perform probability output improvement on the output of the original elastic convex hull, and perform pairwise coupling by using the output probabilities of a plurality of classifiers instead of multi-classification decision, thereby realizing the optimal decision. The original elastic convex hull directly adopts distance output decision, only considers decision contribution of convex hull fixed points, and is easily influenced by outliers, so that the classification precision of a verification set is reduced. In addition, when the multi-classification problem is processed, the invention adopts a one-to-one principle and couples the output probabilities of a plurality of classifiers in pairs, thereby further improving the multi-classification precision and robustness.
Drawings
Fig. 1 is a flow chart of the probability output elastic convex hull used for fault diagnosis of a rolling bearing.
FIG. 2 is a schematic diagram of the probabilistic output elastic convex hull classification of the present invention.
FIG. 3 is a result diagram of the search for optimal parameters based on the probability output elastic convex hull fault diagnosis grid in the present invention.
FIG. 4 is a graph of the fault identification accuracy of the present invention and comparative method for the Kaiser university of California data as a function of training set samples.
FIG. 5 is a graph of the failure recognition accuracy of the autonomous experimental platform data of the present invention and the comparison method as a function of the training set samples.
Detailed Description
As shown in fig. 1, a rolling bearing fault diagnosis method based on a probability output elastic convex hull includes the following steps: step 1: acquiring a vibration acceleration signal of the rolling bearing through an acceleration sensor, and extracting time domain, frequency domain and time-frequency domain characteristics from the vibration acceleration signal to form a fault characteristic set of the rolling bearing; the method for extracting the statistical characteristics of the time domain, the frequency domain and the time-frequency domain comprises the following steps of:
solving time domain statistical characteristics of the obtained vibration signal x (t), wherein the time domain statistical characteristics comprise a root mean square value, a square root amplitude, an absolute mean square amplitude, a kurtosis factor, a wave form factor, a kurtosis, a skewness, a pulse factor, a peak value and a margin coefficient, and the total number of the characteristic parameters is 11;
fourier transform and envelope spectrum analysis are carried out on the signal x (t), and frequency domain statistical characteristics, amplitude spectrum entropy and envelope spectrum entropy are obtained, so that two characteristic parameters are obtained in total;
carrying out 3-layer wavelet packet decomposition on the signal x (t), and solving corresponding 8 wavelet packet energies and 8 wavelet packet energy entropies, wherein 16 characteristic parameters are obtained in total;
splicing the characteristics of the time domain, the frequency domain and the time-frequency domain counted in the steps 11 to 13 into 29-dimensional characteristic vectors serving as the fault characteristic set of the rolling bearing;
step 2: dividing a fault feature set into a training set sample and a test set sample, training the training set sample on a multi-classification model based on a probability output elastic convex hull to establish an optimal diagnosis model, and constructing the multi-classification model based on the probability output elastic convex hull, wherein the input of the multi-classification model is a fault feature vector, and the output of the multi-classification model is a fault category label, and the method specifically comprises the following steps:
1) determining a multi-classification probability output elastic convex hull model for a training sample, and training the training sample on the basis of the elastic convex hull classification model with probability output, wherein the method specifically comprises the following steps:
a 1: constructing an elastic convex hull, and introducing an elastic factor into a convex hull model to obtain the elastic convex hull model, wherein the steps are as follows: firstly, a certain type of fault feature sample set extracted from training samples
Figure BDA0002348822780000071
The convex hull is represented as:
Figure BDA0002348822780000072
wherein x1,x2,x3......xiIn convex combination, α1,α2,α3......αiIs a convex combination coefficient; n is the number of sampling points;
introducing an elasticity factor lambda epsilon (1, + ∞) into the convex hull, setting upper and lower limits on lambda and the sample number n for the combined coefficients of the convex hull, no longer being non-negative, and similarly constraining the sum of the coefficients to 1 to form a new model elastic convex hull model represented as:
Figure BDA0002348822780000073
wherein λ is an elastic factor;
then obtaining a sample set through simple derivation
Figure BDA0002348822780000074
Can be equivalently represented as a new sample set, as follows:
Figure BDA0002348822780000081
in the formula (I), the compound is shown in the specification,
Figure BDA0002348822780000082
representing the center point of the sample
Figure BDA0002348822780000083
I.e. the new samples are equivalent to being along the vector
Figure BDA0002348822780000084
The direction is stretched; the elastic factor lambda has the geometrical meaning of a vector space and represents a new sample point x'iTo the collection center
Figure BDA0002348822780000088
From the original point xiTo the collection center
Figure BDA0002348822780000089
The distance ratio of (a) can be used for carrying out compact or loose estimation on the convex hull of the sample set by adjusting the size of lambda, so that the original convex hull is endowed with elasticity;
a 2: classifying the elastic convex hulls, and searching an optimal hyperplane in the sample set, wherein the optimal hyperplane is set as a connecting line segment which vertically bisects the closest point of the two elastic convex hulls, so that the plane generates the maximum interval between the positive and negative sample convex hulls, as shown in fig. 2; at the same time, the user can select the desired position,
all points of the positive sample set satisfy<w*,x〉+b*>0；
Point satisfaction of negative sample set<w*,x>+b*<0；
Wherein the content of the first and second substances,w*to classify the normal vector of the hyperplane for solving the objective optimization function as the optimal solution, b*Classifying the bias of the hyperplane when the objective optimization function is solved to be an optimal solution; x is a sample point;
a 3: determining the optimal hyperplane position according to a solving method of the nearest points of the two elastic convex hulls, and solving by combining a kernel function to obtain a distance relation between a point on the convex hull and the hyperplane, wherein the method comprises the following specific steps:
firstly, according to the solution of the closest point of the two convex hulls, the relation is as follows:
Figure BDA0002348822780000085
Figure BDA0002348822780000086
Figure BDA0002348822780000087
this formula expands as follows:
Figure BDA0002348822780000091
Figure BDA0002348822780000092
Figure BDA0002348822780000093
wherein, αi+Convex combination coefficient representing the ith positive type sample set, αj-The convex-convex combination coefficient of the jth negative sample set; n is-Number of sampling points, n, for a negative type sample set+The number of sampling points for the positive type sample set; lambda [ alpha ]+An elasticity factor of the positive type sample set; lambda [ alpha ]-The elasticity factor is the negative class sample set; x is the number ofi+Represents the ith positive type sample set point, xj-Represents the jth minusClass sample collection points;
then, the solution is a convex quadratic programming problem, and both the optimization objective function and the decision function can be written into an inner product form between samples, so that a kernel skill can be used as a support vector machine, a standard optimization algorithm is used for solving, and the kernel skill can be used for converting a linear inseparable problem of an input space into a linear separable problem of a feature space, a gaussian kernel function (RBF) is used as the kernel function for solving, and the RBF kernel function relation is as follows:
Figure BDA0002348822780000094
Figure BDA0002348822780000095
wherein σ is a nuclear parameter; x is the number ofiThe ith point in the sample set, x represents the point on the classification hyperplane;
then solving the convex combination coefficient α*Then the normal vector and the bias of the classification hyperplane can be determined
Figure BDA0002348822780000096
Figure BDA0002348822780000097
Wherein, α*Is the corresponding sample convex combination coefficient (or weight vector) when the objective function value is minimum,
Figure BDA0002348822780000098
the coefficients representing the ith sample of the positive class,
Figure BDA0002348822780000101
coefficient, w, representing the jth sample of the negative class*Is a normal vector of the classification hyperplane (i.e. a one-dimensional vector with the same sample dimension, as can be seen from the calculation), b*Is the most importantThe bias of the optimal classification hyperplane is a constant (as can be seen from the calculation formula), xi+Denotes the ith sample point, x, of the positive classj-Represents the jth sample point of the negative class;
according to the classification hyperplane normal vector and the bias, obtaining a distance expression of a point on the convex hull from the hyperplane as follows:
f(x)＝<w*,x>+b*
can also be written as
Figure BDA0002348822780000102
Gaussian kernel functions can be used) technique, mapping to kernel space as with support vector machines;
the raw decision function may be defined as the following expression:
y＝sign(<w*,x〉+b*)；
and adopting a fourth step of solving the problem that the convex hull vertex is an outlier to cause classification errors on the test set.
a 4: and determining a multi-classification decision function, and mapping the output of the elastic convex hull to the position between (0,1) by adopting the following relation:
Figure BDA0002348822780000103
where f is the thresholdless output of the sample x in the third step<w*,x〉+b*Y is the belonged category of the sample, and takes the value { +1, -1 }; the method has the advantages that the posterior probability can be well estimated while the output sparsity of the elastic convex hull is kept;
a 5: the steps for obtaining the decision function defined as the following relation by minimizing the cross entropy likelihood function optimization solution parameter A, B on the training set are as follows:
the cross entropy likelihood function optimization solution parameters A, B on the minimization training set are given by the following relation:
Figure BDA0002348822780000104
Figure BDA0002348822780000105
wherein n is+，n-Respectively representing the number of positive and negative samples; by means of the idea of probability fitting of the support vector machine, tiRepresenting the corresponding weight value of the probability of the ith sample in the minimized cross entropy likelihood function;
and (3) acquiring an optimal solution by adopting a Newton iteration method, namely, the solution with the gradient matrix of F being zero is the optimal solution, wherein the formula is as follows:
Figure BDA0002348822780000111
wherein, the optimization solving process of the parameters A and B can be actually regarded as the translation process of the classification hyperplane, and for the two classification problems, the probability estimation P that x belongs to the positive class and the negative class can be obtained+-And P-+And P is+-+P-+The improved decision function is defined as 1:
Figure BDA0002348822780000112
a 6: for the n classification problem, a one-to-one strategy is adopted, namely a classification hyperplane is constructed for any two classes during classification, and n (n-1)/2 classifiers are constructed in total; the method of the invention outputs the output probability r of each classifier on the basis of the two classification probabilitiesiji, j ≠ 1,2 … n, and i ≠ j, coupled as a multi-class probability output, and the probability that x belongs to the ith class can be represented as PiP (y ═ i | x), i ═ 1,2,3
Figure BDA0002348822780000113
The output probabilities of all classifiers are coupled in pairs, and the following relation exists:
summing the above transformations
Figure BDA0002348822780000115
To establish the above equation, the optimization problem can be transformed into the following model to solve
Figure BDA0002348822780000116
Expanding and writing the above formula into a matrix form
Figure BDA0002348822780000121
Wherein the content of the first and second substances,
Figure BDA0002348822780000122
this formula is squared to expand Pi,PjWhen i, j is 1,2,3.. n (n is the total number of classes) is written in the form of a vector P, it can be equivalently
Figure BDA0002348822780000123
In the target function, Q is a matrix of n-by-n dimensions, wherein Qij is the value of the ith row and the jth column in the matrix Q, the value can be solved through the formula description, and is a regular expression after square expansion, so that the problem of convex quadratic programming is changed into a problem which is convenient to solve, and the probability P of each class to which the sample belongs can be obtained by adopting a standard algorithm to solveiFinally, the decision function for obtaining multiple classifications of the present application is defined as:
y＝argmax{Pi,i＝1,2,3…n}
2) inputting and outputting the elastic convex hull as a fault category label; constructing a multi-classification model, and optimizing two parameters of a probability output elastic convex hull, namely a kernel parameter sigma and an elastic factor lambda by a grid search algorithm;
3) selecting an optimal parameter from the grid so as to determine a probability output elastic convex hull classification model under the optimal parameter;
and step 3: and outputting an elastic convex hull classification model according to the optimal probability to classify the test set samples, and identifying the working state and the fault type of the rolling bearing according to the classification result.
This example was verified by two experiments.
Experiment 1:
experiment 1 data was from the bearing data center of the university of kaiser west storage, usa. A deep groove ball bearing with a bearing model of 6205-2RS SKF is adopted, the sampling frequency is 48kHZ, each 12000 sampling points are divided into one sample, and the total number is 1400 samples. The fault status types are shown in table 1.
TABLE 1 bearing sample data
Figure BDA0002348822780000124
Figure BDA0002348822780000131
According to the method, the time domain, the frequency domain and the time-frequency domain statistical characteristics are extracted to be used as the fault characteristics of the rolling bearing. Data set a is used to identify the type and extent of the fault, and data set B is used only to identify the type of fault. The parameters to be optimized for the present invention are the gaussian kernel parameter σ and the elastic factor λ. 5-fold cross validation is adopted to search for optimal parameters in a grid mode, and the search range of the kernel parameter sigma is 2{-8,-7.8,…,7.8,8}Elastic factor lambda search range of 2{0,0.2,…,3.8,4}. Fig. 3 shows the grid search accuracy distribution of the probability-based output elastic convex hull method on the data set B, and the optimal parameters σ ═ 1.516 and λ ═ 2 are obtained. The 5-fold cross-validation was performed 20 times under the optimized parameters, and the recognition accuracy is shown in table 2.
TABLE 2 identification accuracy (%)
Figure BDA0002348822780000132
The original multi-classification elastic Convex hull adopts a one-to-one strategy to construct n (n-1)/2 classifiers, decision is made based on a voting principle, the method is marked as FCH (Flexible Convex Hull), the method is marked as POFCH (Flexible output Flexible Convex Hull), and the comparison method also adopts a support vector machine as a comparison test and is marked as SVM.
The experimental results show that the fault identification method can identify the faults of the rolling bearing with higher accuracy, the classification precision of the probability output elastic convex hull is higher than that of other classifiers, the superior performance of the probability output elastic convex hull can be better reflected on the data set A, and the faults of different degrees can be accurately identified.
In order to show the superiority of the method, samples with different quantities are adopted as training sets for the data set B, and the other samples are used as test sets, so that the accuracy rate of the test sets is observed. The random independent repetition is carried out 20 times under the condition that different numbers of samples are randomly drawn each time, and the average classification result is shown in figure 4.
From fig. 4, the method of the present invention can ensure that the accuracy of the test set reaches more than 94% even under the condition that the training set samples are only 10%, and the probability output elastic convex hull of the present invention is higher than the classification accuracy of the original elastic convex hull and is better than the SVM.
Experiment 2
Experiment 2 data the bearing data from the university laboratory, on the test bench, the rolling bearing model was 6205-2RSSKF, and the inner ring failure, outer ring failure and rolling element failure were simulated by the laser cutting technique. The fault sizes were all 0.2mm, and the rotational speed was 986.1r/min, the sampling frequency was 10 kHz. The samples obtained are described in table 3 below.
TABLE 3 bearing data samples
Figure BDA0002348822780000141
Similarly, the experiment was performed by the method of experiment 1, and 5-fold cross validation was performed 20 times under the optimized parameters, where the optimal parameters of the model method for outputting the elastic convex hull with probability are 2.297 and λ 1.741, and the experimental results are shown in table 4.
TABLE 4 identification accuracy (%)
Figure BDA0002348822780000142
It can be seen from the table that the classification method based on the probability output elastic convex hull still shows the highest accuracy and improves the classification precision of the original elastic convex hull. And (3) carrying out 20 random independent repeated tests, and observing a curve that the accuracy of the test set changes along with the sample amount of the training set, wherein the result is shown in figure 5, and the probability output elastic convex packet still has the best classification effect.
In order to verify the robustness of the invention, the data sets B and C are firstly split into a training set and a test set according to the ratio of 8:2, 2 samples are selected from other 3 training sets for each class of training set and added into the training set of the class, the samples are taken as outliers of the samples, then training is carried out, the accuracy of the test set is verified, the samples are randomly and independently repeated for 20 times, and the experimental result is shown in Table 5.
Table 5 robustness testing accuracy (%)
Figure BDA0002348822780000143
The parenthesis in the table represents the accuracy without outliers added, i.e., the accuracy of the 20 five-fold cross-validation runs in tables 3 and 4 (i.e., training set and test set divided by 8: 2), and the third row represents the decrease in accuracy by the percentage points relative to the absence of outliers added. It can be seen that on different data sets, the accuracy rate is still the best based on the method of the invention, and the outlier enables the percentage point of the accuracy rate reduction of the verification set to be the lowest, and the noise immunity and robustness of the original elastic convex hull are improved.
The two experiments are combined to show that the method has higher accuracy and certain stability in multiple experiments. The invention adopts the multi-classification model based on the probability output elastic convex hull, has more accurate fault identification performance and certain robustness, and thus, the rolling bearing fault diagnosis method based on the probability output elastic convex hull is practical and effective in the field of rolling bearing fault identification.

Claims (7)

1. A rolling bearing fault diagnosis method based on a probability output elastic convex hull is characterized by comprising the following steps:
step 1: acquiring a vibration acceleration signal of the rolling bearing through an acceleration sensor, and extracting time domain, frequency domain and time-frequency domain characteristics from the vibration acceleration signal to form a fault characteristic set of the rolling bearing;
step 2: dividing the fault feature set into a training set sample and a test set sample, and training the training set sample on the basis of a multi-classification model of a probability output elastic convex hull to establish an optimal diagnosis model, wherein the method specifically comprises the following steps:
1) determining a multi-classification probability output elastic convex hull model for a training sample, and training the training sample on the basis of the elastic convex hull classification model output by probability;
2) carrying out optimization probability output on two parameters of the elastic convex hull, namely a kernel parameter sigma and an elastic factor lambda by a grid search algorithm;
3) selecting an optimal parameter from the grid so as to determine a probability output elastic convex hull classification model under the optimal parameter;
and step 3: and outputting an elastic convex hull classification model according to the optimal probability to classify the test set samples, and identifying the working state and the fault type of the rolling bearing according to the classification result.
2. The rolling bearing fault diagnosis method based on the probability output elastic convex hull as claimed in claim 1, wherein the training of the elastic convex hull classification model based on the probability output on the training sample in the step 2 specifically comprises the following steps:
a 1: constructing an elastic convex hull, and introducing an elastic factor into the convex hull model to obtain an elastic convex hull model;
a 2: classifying the elastic convex hulls, and searching an optimal hyperplane in the sample set, wherein the optimal hyperplane is set as a connecting line segment which vertically bisects the closest point of the two elastic convex hulls, and the two elastic convex hulls are divided into a positive sample set and a negative sample set;
a 3: determining the optimal hyperplane position according to a solving method of the nearest points of the two elastic convex hulls, and solving by combining a kernel function to obtain the distance relation between the points on the convex hulls and the hyperplane as follows:
f(x)＝<w*,x>+b*
wherein, w*Classifying hyperplane normal vectors for optimal solution, b*A bias of the classification hyperplane for the optimal solution; x is a sample point;
a 4: and determining a multi-classification decision function, and mapping the output of the elastic convex hull to the position between (0,1) by adopting the following relation:
Figure FDA0002348822770000011
where f is the thresholdless output of the sample x in the third step<w*,x>+b*Y is the belonged category of the sample, and takes the value { +1, -1 };
a 5: by optimizing the solution parameters A, B by minimizing the cross entropy likelihood function on the training set, the decision function is obtained as defined by the following relation:
Figure FDA0002348822770000021
where the probability estimate that sample x belongs to the positive and negative classes is set to P+-And P-+And P is+-+P-+＝1；
a 6: adopting a one-to-one strategy, carrying out convex hull estimation on each type of sample, carrying out pairwise optimization training, constructing n (n-1)/2 classifiers, and outputting the output probability r of each classifier on the basis of two classification probability outputsij(i, j ≠ 1,2 … n, and i ≠ j) is coupled into a multi-class probability output, and the probability that x belongs to the ith class can be expressed as PiP (y ═ i | x), i ═ 1,2,3
Figure FDA0002348822770000022
The decision function to obtain the multi-class is defined as the following relation:
y＝arg max{Pi,i＝1,2,3…n}；
wherein n is the number of classifiers; piProbability of class i.
3. The rolling bearing fault diagnosis method based on the probability output elastic convex hull as claimed in claim 2, wherein the step of constructing the elastic convex hull in the step a1 is as follows:
some kind of fault feature sample set extracted from training sample
Figure FDA0002348822770000023
The convex hull is represented as:
Figure FDA0002348822770000024
wherein x1,x2,x3......xiIn convex combination, α1,α2,α3......αiIs a convex combination coefficient; n is the number of sampling points;
introducing an elasticity factor λ ∈ (1, + ∞) into the convex hull, and obtaining an elastic convex hull model expressed as:
Figure FDA0002348822770000025
then the sample set is collected
Figure FDA0002348822770000026
Can be equivalently represented as a new sample set, represented as:
Figure FDA0002348822770000027
4. the rolling bearing fault diagnosis method based on the probability output elastic convex hull as claimed in claim 2, wherein the positive type sample set and the negative type sample set in the step a2 satisfy the following conditions:
all points of the positive type sample set satisfy:<w*,x>+b*>0；
the points of the negative class sample set satisfy:<w*,x>+b*<0。
5. the rolling bearing fault diagnosis method based on the probability output elastic convex hull as claimed in claim 2, wherein the determination of the optimal hyperplane position in the step a3 is as follows:
according to the solution of the closest point of the two convex hulls, the relation is as follows:
Figure FDA0002348822770000031
Figure FDA0002348822770000032
Figure FDA0002348822770000033
this formula expands as follows:
Figure FDA0002348822770000034
Figure FDA0002348822770000035
Figure FDA0002348822770000036
wherein, αi+Convex combination coefficient representing the ith positive type sample set, αj-The convex combination coefficient of the jth negative class sample set; n is-Number of sampling points, n, for a negative type sample set+The number of sampling points for the positive type sample set; lambda [ alpha ]+An elasticity factor of the positive type sample set; lambda [ alpha ]-The elasticity factor is the negative class sample set; x is the number ofi+I-th sample point, x, representing a positive classj-The jth sample point representing a negative class;
solving by taking a Gaussian kernel function as a kernel function, wherein the Gaussian kernel function has the following relation:
Figure FDA0002348822770000037
Figure FDA0002348822770000038
wherein σ is a nuclear parameter;
solving convex combining coefficient α*Then the normal vector w of the optimal classification hyperplane can be determined*And bias b*The following are:
Figure FDA0002348822770000041
Figure FDA0002348822770000042
α*is the corresponding sample convex combination coefficient when the objective function value is minimum,
Figure FDA0002348822770000043
the coefficients representing the ith sample of the positive class,
Figure FDA0002348822770000044
coefficient, w, representing the jth sample of the negative class*Is a normal vector of the classification hyperplane, b*The bias for the hyperplane for optimal classification is a constant, xi+Denotes the ith sample point, x, of the positive classj-Represents the jth sample point of the negative class;
the distance between the point on the convex hull and the hyperplane is obtained by the following expression:
f(x)＝<w*,x>+b*。
can also be written as
Figure FDA0002348822770000045
6. The rolling bearing fault diagnosis method based on the probability output elastic convex hull as claimed in claim 2, wherein the solving step of the parameter A, B in the step a5 is as follows:
the cross entropy likelihood function optimization solution parameters A, B on the minimization training set are given by the following relation:
Figure FDA0002348822770000046
Figure FDA0002348822770000047
tirepresenting the corresponding weight of the probability of the ith sample in the minimized cross entropy likelihood function, where n+，n-Respectively representing the number of positive and negative samples;
and (3) acquiring an optimal solution by adopting a Newton iteration method, wherein the formula is as follows:
Figure FDA0002348822770000048
wherein n is+，n-Respectively representing the number of positive and negative samples.
7. The rolling bearing fault diagnosis method based on the probability output elastic convex hull as claimed in claim 1, wherein the step a6 couples the output probabilities of the classifier in pairs, and the relation is as follows:
Figure FDA0002348822770000051
transform and sum it to
Figure FDA0002348822770000052
The optimization problem can be transformed into the following model to solve
Figure FDA0002348822770000053
Spread and written in matrix form
Figure FDA0002348822770000054
Where Qij is the value in row i and column j in matrix Q;
solving by adopting a standard algorithm to obtain the probability P of each class to which the sample belongsiThe decision function to obtain multiple classifications is thus defined as:
y＝arg max{Pi,i＝1,2,3…n}。
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