CN111122155B - Gear fault diagnosis method based on telescopic shifting super-disc - Google Patents

Gear fault diagnosis method based on telescopic shifting super-disc Download PDF

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CN111122155B
CN111122155B CN201911406600.7A CN201911406600A CN111122155B CN 111122155 B CN111122155 B CN 111122155B CN 201911406600 A CN201911406600 A CN 201911406600A CN 111122155 B CN111122155 B CN 111122155B
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丁子杨
胡天桢
程军圣
何知义
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Hunan University
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Abstract

The invention discloses a gear fault diagnosis method based on a telescopic shifting super-disc, which comprises the following specific steps of: measuring vibration signals of an object under different working states or fault types; extracting features commonly used for gear fault diagnosis from the vibration signals; dividing the characteristic values of different working states into a training sample and a testing sample; training the telescopic shifting super-disc classifier by using the training samples to establish an optimal diagnosis model; classifying the test sample by using the optimal diagnosis model; and identifying the working state or fault type of the object according to the classification result. The gear fault diagnosis method based on the telescopic shifting super-circular disc has high recognition degree in the mode recognition process.

Description

Gear fault diagnosis method based on telescopic shifting super-disc
Technical Field
The invention belongs to the field of gear fault diagnosis, and particularly relates to a gear fault diagnosis method based on a telescopic shifting super-disc.
Background
The reasonable and effective fault diagnosis of the rotary machine is the key for guaranteeing the working reliability of the rotary machine, and the gear serving as a key component is widely applied to the rotary machine equipment, so that the research on the gear fault diagnosis method has important practical significance. Among them, the intelligent diagnosis method has been receiving wide attention from researchers as an important research content in the field of fault diagnosis.
Intelligent fault diagnosis is essentially a pattern recognition problem. Common pattern recognition methods include methods based on probability statistics, neural networks, Support Vector Machines (SVMs), and the like. When applied to gear failure diagnostics, probabilistic-based methods require enough failure training samples to make the estimated probability statistically significant, however it is generally difficult in engineering practice to obtain a large number of failure samples. Likewise, the neural network approach also requires a large number of samples for training. Meanwhile, the neural network also has the problems of lack of a theoretical framework, easy occurrence of a local optimal solution, overfitting, long training time and the like. Compared with the first two methods, the SVM has the advantages of no need of a large number of training samples, convenience and quickness in solving, capability of obtaining a global optimal solution and the like. However, SVMs also have problems of poor generalization ability and robustness. This is because from a geometric point of view, the essence of SVM classification is to treat the individual class distributions as a cloud of convex hulls in the feature space, i.e., equivalently to use the convex hulls to estimate each class distribution, and then find a classification hyperplane separating the convex hulls. Since the convex hull is the minimum convex set containing limited samples, the way of estimating the class distribution using the convex hull may be too compact, underestimating the true range of the class distribution, and further, underestimation problems occur.
For this purpose, a more relaxed geometric model can be used for the estimation of the class distribution. The scholars propose class distribution estimation using the disk (HD) model. HD is a simple geometric model that can be viewed as the intersection of a hypersphere and an affine bag, and estimates the class using a hypersphere centered at some point with the smallest radius. For the category to be estimated, no matter how distributed the samples are, a super-disk with the smallest radius can be found to estimate the samples. Compared with the convex hull, the method has the advantages that the category distribution can be estimated loosely, more reasonable category and boundary estimation is realized, a more real classifier is provided, and the underestimation problem of the convex hull is avoided. However, since the super-disk employs a simpler geometric model, the presence of outliers can affect the classification accuracy. And the irregulability of compactness or looseness affects a more reasonable estimation of the class distribution. Therefore, for the super-disk, its reasonable estimation capability, generalization capability, and robustness to the class distribution need to be further improved.
Disclosure of Invention
The invention aims to solve the problems and provides a gear fault diagnosis method based on a telescopic shifting super-disc.
In order to realize the purpose, the invention adopts the technical scheme that:
a gear fault diagnosis method based on a telescopic shifting super-disc comprises the steps of measuring vibration signals of a fault object by using an acceleration sensor; extracting features commonly used for gear fault diagnosis from the vibration signals; dividing the characteristic values of different working states into training samples and testing samples; also comprises the following steps:
a. training a telescopic shifting super-disc classifier by using the training samples to establish an optimal diagnosis model, and specifically comprising the following steps of:
constructing a telescopic shifting super-disc classifier model aiming at a specific fault diagnosis problem;
optimizing the kernel parameters, the expansion coefficients and the shift coefficients of the telescopic shift super-disc model by using a grid search algorithm;
performing model training by using a training sample to obtain an optimal diagnosis model;
b. classifying the test samples by using a scalable shifting super-disc model;
c. and identifying the working state or fault type of the object according to the classification result.
Further, the building of the scalable shifting hyper-discal classifier model in the step a includes the following steps:
1) constructing a super-disk model, and for a certain type of sample set X ═ XiI ═ 1., l }, where l is the number of samples in the class, the supercompax model can be expressed as:
Figure BDA0002348803600000021
wherein alpha is1,α2,α3......αiIs a convex combination coefficient, s is the center of the telescopic shifting super-disc, and r is the radius;
converting into the following relation to solve:
Figure BDA0002348803600000022
2) constructing a model of the telescopic shifting super-disc, introducing a telescopic factor lambda epsilon [1, infinity ] and a shifting factor mu epsilon (0, 1) to form the model of the telescopic shifting super-disc, wherein the expression is as follows:
Figure BDA0002348803600000023
3) determining an optimal hyperplane, wherein the optimal hyperplane is a connecting line segment which vertically bisects the closest point of the two super-disc models, and a positive sample set and a negative sample set are arranged on the optimal hyperplane, and the optimal hyperplane satisfies the following relational expression:
all points of the positive type sample set: < w, x > + b >0,
points of the negative class sample set: < w, x > + b <0,
wherein w is a normal vector of the classification hyperplane, and b is the bias of the classification hyperplane; x is a sample point;
4) applying a kernel function to obtain decision functions of positive and negative samples;
further, the determination of the optimal hyperplane in step 3) includes the following steps:
let X+And X-Matrices respectively representing positive and negative type samples, nearest point pairs being denoted x+＝X+α+，x-＝X-α-(ii) a Coefficient vector alpha+And alpha-This can be obtained by solving the quadratic constraint quadratic programming problem as follows:
Figure BDA0002348803600000031
Figure BDA0002348803600000032
Figure BDA0002348803600000033
wherein alpha isi+The combination coefficient, alpha, representing the ith sample of the positive classj-A combination coefficient representing a negative class jth sample; alpha is alpha+For vectors of coefficients of positive type samples, alpha-Is a negative class sample coefficient vector; s+Scalable shifted superplate center, S, for class-one sample set-A scalable shifting super-disk center for the negative type sample set; lambda [ alpha ]+Scaling factor, λ, for a positive type sample set-Scaling factors of the negative sample set; l+Number of samples of positive type sample set, l-The number of samples in the negative sample set;
let alpha be [ alpha ]+,α-]T，X＝[X+,X-]The expression is:
Figure BDA0002348803600000034
Figure BDA0002348803600000035
Figure BDA0002348803600000036
wherein Q is XTX，
Figure BDA0002348803600000037
Q-＝X-X-；r+Scalable shift supercompus radius, r, for a positive type sample set-A scalable shift super-disk radius for negative class sample sets;
determining a classification hyperplane parameter, the classification hyperplane parameter being solved by:
Figure BDA0002348803600000038
Figure BDA0002348803600000039
further, step 4) determining a decision function, which includes the following steps:
adopting a kernel technique to solve, taking a Gaussian kernel function as a kernel function, and obtaining the following expression:
Figure BDA0002348803600000041
converting quadratic constraint quadratic programming problem expression into
Figure BDA0002348803600000042
Figure BDA0002348803600000043
Figure BDA0002348803600000044
In the formula K, K+，K-For corresponding kernel matrices, β+And beta-Respectively obtaining coefficient vectors when solving the two super disc models;
a decision function for obtaining positive and negative samples is defined as:
Figure BDA0002348803600000045
the invention has the beneficial effects that:
the scalable shifting super-disc model provided by the invention is a new mode identification method, and the method inherits the advantage that the super-disc model can loosely estimate the category distribution, meanwhile, the compactness or the looseness of the model can be reasonably adjusted due to the introduction of the scaling factors, and the outlier problem is more effectively solved due to the introduction of the shifting factors, so that more reasonable category estimation can be obtained, and the generalization capability and the robustness can be improved. Experiments prove that the method can effectively improve the accuracy of gear fault diagnosis.
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FIG. 1 is a schematic diagram of the scalable shifting superplate classification of the present invention.
FIG. 2 is a diagram comparing the scalable shifted supercomputer model of the present invention with a convex hull model.
Fig. 3 is a flow chart of the implementation steps of the present invention.
FIG. 4 is a flow chart of the steps of the present invention for implementing the training of the scalable shifted super-discal classifier using training samples to build an optimal diagnostic model.
Fig. 5 is a classification accuracy distribution diagram under an optimal kernel parameter (σ) of 11.314, which is obtained by searching an optimal parameter based on a scalable shifted super-disk classifier grid according to the present invention.
Fig. 6 is a classification accuracy distribution diagram obtained by optimizing a shift factor by using a grid search algorithm while keeping a kernel parameter and a scaling coefficient unchanged in a robustness experiment based on the scalable shift super-disk classifier in the present embodiment.
Detailed Description
The fault object of the embodiment of the present invention may be a gear, but is not limited to a gear, and after reading the present invention, the gear fault diagnosis method based on the telescopic shifting super-disc adopted by the method of the present invention by those skilled in the art is within the protection scope of the present invention. The method of the present invention is explained in the detailed description with reference to gears as the preferred embodiment, and not as a limitation of the invention. In addition, the present invention does not require strict execution in the order of steps in the following drawings, and all methods that can achieve the purpose of fault diagnosis according to the above method belong to the scope of protection of the present invention.
Referring to fig. 3, the invention provides a gear fault diagnosis method based on a telescopic shifting super-disc, which comprises the following steps:
1) measuring a vibration signal of a fault object by using an acceleration sensor;
2) extracting features commonly used for gear fault diagnosis from the vibration signals;
3) dividing the characteristic values of different working states into a training sample and a testing sample;
4) training the telescopic shifting super-disc classifier by using the training samples to establish an optimal diagnosis model;
5) classifying the test samples by using a scalable shifting super-disc model;
6) and identifying the working state or fault type of the object according to the classification result.
Extracting features commonly used for gear fault diagnosis in the step 2), and the method comprises the following steps:
A. extracting time domain characteristics of the vibration signal, and extracting 5 dimensional characteristics including a peak value, a peak-peak value, an absolute average value, a square root amplitude value and a root mean square value, and 6 dimensionless characteristics including a waveform index, a peak value index, a pulse index, a margin index, a skewness index and a kurtosis index from the vibration signal;
B. extracting amplitude spectral entropy and envelope spectral entropy of the vibration signal, respectively performing FFT (fast Fourier transform) and Hilbert transform on the vibration signal, and then solving an entropy value;
C. extracting wavelet packet energy and wavelet packet energy entropy from the vibration signal, firstly carrying out 3-layer wavelet packet decomposition on the vibration signal to obtain 8 groups of sub-signals, and then respectively calculating normalized wavelet packet energy of each sub-signal and a corresponding wavelet packet energy spectrum.
Referring to fig. 4, in step 4, training the scalable shift super-discal classifier by using the training samples to establish an optimal diagnostic model specifically includes the following steps:
a. constructing a telescopic shifting super-disc classifier model aiming at a specific fault diagnosis problem;
b. optimizing the kernel parameters, the expansion coefficients and the shift coefficients of the telescopic shift super-disc model by using a grid search algorithm;
c. and carrying out model training by using the training sample to obtain an optimal diagnosis model.
The method comprises the following steps of constructing a telescopic shifting super-disc classifier model aiming at specific fault diagnosis problems, and specifically comprises the following steps:
for a class of sample sets X ═ XiI ═ 1., l }, where l is the number of samples in the class, the supercompax model can be expressed as:
Figure BDA0002348803600000061
wherein alpha is1,α2,α3......αiIs a convex combination coefficient, s is the center of the telescopic shifting super-disc, and r is the radius;
both can be solved by the following quadratic programming problem:
minr2
s.t.||x-s||2≤r2
introducing a scaling factor λ ∈ [1, + ∞ ]) and a shifting factor μ ∈ (0,1], setting upper and lower bounds on λ, μ and the number of samples n for the combined coefficients of the convex hull, and likewise constraining the sum of the coefficients to 1, forms a new model, called a scalable shifted supercomputer, which can be expressed as:
Figure BDA0002348803600000062
by adjusting the size of lambda, the degree of tightness estimated for the sample set super-disc can be adjusted, so that the original super-disc is endowed with elasticity. By adjusting the size of μ, adjustment of the position of the sample set superplate can be achieved and the superplate can be contracted to get rid of the effects of outliers.
The principle of scalable shift superparallel classification is to find an optimal hyperplane, which, as shown in fig. 1, bisects the two superparallel closest point connecting line segments perpendicularly, so that the plane produces the largest separation between the positive and negative sample superparallels. Wherein the content of the first and second substances,
all points of the positive type sample set: < w, x > + b >0,
points of the negative class sample set: < w, x > + b <0,
wherein w is a normal vector of the classification hyperplane, and b is the bias of the classification hyperplane; x is a sample point;
the determination of the classification hyperplane is the solving problem of the closest point of the two telescopic shifting hyperplanes; let X+And X-Matrices respectively representing positive and negative type samples, nearest point pairs being denoted x+＝X+α+，x-＝X-α-(ii) a Coefficient vector alpha+And alpha-This can be obtained by solving the quadratic constraint quadratic programming problem as follows:
Figure BDA0002348803600000071
Figure BDA0002348803600000072
Figure BDA0002348803600000073
let alpha be [ alpha ]+,α-]T，X＝[X+,X-]Then, the above formula can be:
Figure BDA0002348803600000074
Figure BDA0002348803600000075
Figure BDA0002348803600000076
wherein Q is XTX，
Figure BDA0002348803600000077
Q-＝X-X-，αi+The combination coefficient, alpha, representing the ith sample of the positive classj-A combination coefficient representing a negative class jth sample; alpha is alpha+For vectors of coefficients of positive type samples, alpha-Is a negative class sample coefficient vector; s+Scalable shifted superplate center, S, for class-one sample set-A scalable shifting super-disk center for the negative type sample set; lambda [ alpha ]+Scaling factor, λ, for a positive type sample set-Scaling factors of the negative sample set; l+Number of samples of positive type sample set, l-The number of samples in the negative sample set; r is+Scalable shift supercompus radius, r, for a positive type sample set-A scalable shift supercompar radius for negative class sample sets.
After solving for the nearest point pair, the classification hyperplane parameter can be solved by the following formula:
Figure BDA0002348803600000078
Figure BDA0002348803600000079
the linear indivisible problem of the input space can be converted into the linear separable problem of the feature space using a kernel technique. The method adopts a Gaussian kernel function (RBF) as a kernel function, and the form of the RBF is as follows
Figure BDA00023488036000000710
Quadratic constraint quadratic programming problem expression conversion
Figure BDA0002348803600000081
Figure BDA0002348803600000082
Figure BDA0002348803600000083
The decision function of the positive and negative samples is defined as
Figure BDA0002348803600000084
For the n-class problem, a one-to-one strategy is adopted, a class hyperplane is constructed for any two classes, and n (n-1)/2 classifiers are constructed in total. And (3) for a certain sample, performing n (n-1)/2 times of classification during classification, recording the decision result of each time, and finally classifying the sample into the class which wins the most pairwise decisions.
The scalable shifting hyper-disc model and the convex hull model are paired, as shown in fig. 2, wherein the real range of the distribution of the samples in the feature space is represented by a dotted line; approximating the distribution area of the training sample by using a convex hull generally underestimates the true range of the class, which leads the corresponding SVM classifier to overestimate the class area interval to obtain an inappropriate classification hyperplane; the super-disc classifier adopts a loose model to estimate the class region, and compared with a convex hull, the super-disc model can estimate the interval of the class region more truly, so that a more reasonable classification hyperplane is provided.
Here, the input variables of the model are all the feature values extracted according to the steps of fig. 4, and the output is the operating state type number of the gear.
In particular use of the present embodiment, the effectiveness of the present invention was verified using the southeast university gear data set as an example of a malfunctioning object. Data processing is first performed, dividing each 8192 sampling points into one sample, for a total of 500 samples. The data sample descriptions used are shown in table 1.
TABLE 1 Gear sample data
Figure BDA0002348803600000091
Feature extraction is performed according to the method proposed by the present invention. The parameters to be optimized for the present invention are the gaussian kernel parameter σ, the scaling factor λ and the shifting factor μ. The grid search algorithm is adopted to search for the optimal parameters, and the evaluation method of the classification precision in the search process comprises the following steps: at each search, 50 samples are randomly drawn from each state for training, the remaining 50 samples are used for testing, the process is independently repeated for 20 times, and the classification precision is the average value of 20 recognition accuracy results. Search range of σ is {2-5,2-4.5,...,24.5,25Is in the search range of {2 }0,20.05,…,22.45,22.5The search range of μ is {1/49, 1/48.., 1/2,1 }. This yields the optimum parameter σ 23.5≈11.314，λ＝21.75And 3.364, and 1/18, and the classification precision of the proposed method is obtained under the optimal parameters by using the classification precision evaluation method again. Then, for the SVM and HD methods, parameter tuning is performed by using a similar method to obtain the corresponding classification accuracy, and the final result is shown in table 2.
TABLE 2 Classification accuracy comparison table
Figure BDA0002348803600000092
The experimental result is shown in fig. 5, and it can be seen from the experimental result that the invention can perform fault identification with higher accuracy on the gear, and the classification precision of the telescopic shifting super-disc is higher than that of other classifiers.
To further demonstrate the advantages of the methods presented herein, the following robustness experiments were performed.
In a robustness experiment, the kernel parameters and the scaling factors are kept unchanged, and only the scaling factors are optimized. The experimental method was essentially the same as the previous experiment, only the way the data set was processed was changed. First, 50 samples were randomly drawn from each state for training, and the remaining 50 were used for testing. Then for each state, 1 sample is randomly selected from the other 4 states to add to the training set for that state. The newly added samples are outliers. The optimal contraction factor is obtained by optimizing, namely mu is 1/31 and 0.032. The classification accuracy obtained by each classifier is shown in table 3.
TABLE 3 Classification precision comparison table
Figure BDA0002348803600000101
The experimental result is shown in fig. 6, and it can be seen from the experimental result that the classification accuracy of each classifier is significantly reduced when the training set has outliers. The classification precision of the EDHD method is obviously higher than that of other classifiers, and the effect of the shifting factor and the robustness of the method are proved to be better.

Claims (3)

1. A gear fault diagnosis method based on a telescopic shifting super-disc comprises the steps of measuring vibration signals of a fault object by using an acceleration sensor; extracting the characteristics for gear fault diagnosis from the vibration signals; dividing the characteristic values of different working states into training samples and testing samples; it is characterized by also comprising the following steps:
a. training a telescopic shifting super-disc classifier by using the training samples to establish an optimal diagnosis model, and specifically comprising the following steps of:
a scalable shifting super-disc classifier model is constructed aiming at specific fault diagnosis problems, and the method specifically comprises the following steps:
1) constructing a super-disk model, and for a certain type of sample set X ═ XiI ═ 1., l }, where l is the number of samples in the class, the supercompax model can be expressed as:
Figure FDA0003170071380000011
wherein alpha is1,α2,α3......αiIs a convex combination coefficient, s is the center of the telescopic shifting super-disc, and r is the radius;
converting into the following relation to solve:
min r2
s.t.||x-s||2≤r2；
2) constructing a model of the telescopic shifting super-disc, introducing a telescopic factor lambda epsilon [1, infinity ] and a shifting factor mu epsilon (0, 1) to form the model of the telescopic shifting super-disc, wherein the expression is as follows:
Figure FDA0003170071380000012
3) determining an optimal hyperplane, wherein the optimal hyperplane is a connecting line segment which vertically bisects the closest point of the two super-disc models, and a positive sample set and a negative sample set are arranged on the optimal hyperplane, and the optimal hyperplane satisfies the following relational expression:
all points of the positive type sample set: < w, x > + b >0,
points of the negative class sample set: < w, x > + b <0,
wherein w is a normal vector of the classification hyperplane, and b is the bias of the classification hyperplane; x is a sample point;
4) applying a kernel function to obtain decision functions of positive and negative samples;
optimizing the kernel parameters, the expansion coefficients and the shift coefficients of the telescopic shift super-disc model by using a grid search algorithm;
performing model training by using a training sample to obtain an optimal diagnosis model;
b. classifying the test samples by using a scalable shifting super-disc model;
c. and identifying the working state or fault type of the object according to the classification result.
2. The gear fault diagnosis method based on the telescopic shifting super-disc as claimed in claim 1, wherein the optimal super-plane is determined in step 3) by the following steps:
let X+And X_Matrices respectively representing positive and negative type samples, nearest point pairs being denoted x+＝X+α+，x-＝X-α_(ii) a Coefficient vector alpha+And alpha-This can be obtained by solving the quadratic constraint quadratic programming problem as follows:
Figure FDA0003170071380000021
Figure FDA0003170071380000022
Figure FDA0003170071380000023
wherein alpha isi+The combination coefficient, alpha, representing the ith sample of the positive classj-A combination coefficient representing a negative class jth sample; alpha is alpha+For vectors of coefficients of positive type samples, alpha-Is a negative class sample coefficient vector; s+Scalable shifted supercomputer center, s, for positive type sample set_A scalable shifting super-disk center for the negative type sample set; lambda [ alpha ]+Scaling factor, λ, for a positive type sample set_Scaling factors of the negative sample set; l+Number of samples of positive type sample set, l-The number of samples in the negative sample set;
let alpha be [ alpha ]+,α-]T，X＝[X+,X-]The expression is:
Figure FDA0003170071380000024
Figure FDA0003170071380000025
Figure FDA0003170071380000026
wherein Q is XTX，
Figure FDA0003170071380000027
Q-＝X-X-，r+Scalable shift supercompus radius, r, for a positive type sample set-A scalable shift super-disk radius for negative class sample sets;
determining a classification hyperplane parameter, the classification hyperplane parameter being solved by:
Figure FDA0003170071380000028
Figure FDA0003170071380000029
3. the gear fault diagnosis method based on the telescopic shifting super-disc as claimed in claim 2, wherein the decision function is determined in step 4) by the following steps:
adopting a kernel technique to solve, taking a Gaussian kernel function as a kernel function, and obtaining the following expression:
Figure FDA0003170071380000031
converting quadratic constraint quadratic programming problem expression into
Figure FDA0003170071380000032
Figure FDA0003170071380000033
Figure FDA0003170071380000034
In the formula, K+，K_For corresponding kernel matrices, β+And beta_Respectively obtaining coefficient vectors when solving the two super disc models;
a decision function for obtaining positive and negative samples is defined as:
Figure FDA0003170071380000035
in the formula (I), the compound is shown in the specification,
Figure FDA0003170071380000036
K(X+x) is the kernel vector of the positive training sample and the test sample, K (X)_And x) is the kernel vector of the negative training sample and the test sample.
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