CN109459235B - Enhanced gear single fault category diagnosis method based on integrated learning - Google Patents

Enhanced gear single fault category diagnosis method based on integrated learning Download PDF

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CN109459235B
CN109459235B CN201811528966.7A CN201811528966A CN109459235B CN 109459235 B CN109459235 B CN 109459235B CN 201811528966 A CN201811528966 A CN 201811528966A CN 109459235 B CN109459235 B CN 109459235B
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gear
sphere
fault diagnosis
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曹亮
沈勇
王景霖
单添敏
林泽力
顾浩天
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AVIC Shanghai Aeronautical Measurement Controlling Research Institute
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Abstract

The invention discloses an integrated learning based enhanced gear single fault category diagnosis method. The invention trains corresponding individual fault diagnosis learners by using the diversity characteristic of ensemble learning through a data cross training mode, and integrates a certain amount of support vector data description gear fault diagnosis learners into an enhanced gear fault single classification diagnotor by using an ensemble learning method and using a voting method as an integration rule, thereby achieving the aim of enhancing the classification capability. The method is applied to the field of gear fault diagnosis, and can improve the accuracy of fault diagnosis.

Description

Enhanced gear single fault category diagnosis method based on integrated learning
Technical Field
The invention belongs to the field of fault diagnosis, and particularly relates to an enhanced gear single-fault category diagnosis method based on integrated learning.
Background
The support vector data description is a single classification method developed on the basis of a support vector machine. The two different types of samples can be distinguished by using lines or planes in a linear distinguishing mode, and if certain type of group data is inseparable in a low-latitude space, the group data can be projected into a high-dimensional space in a kernel function mode and converted into a sample group which can be linearly divided in the high-dimensional space.
The conventional gear fault diagnosis method generally comprises a hidden Markov model, a Markov distance and a neural network, and basically finishes the diagnosis of the gear fault category based on a data probability distribution model, but has larger data quantity required for a data sample and cannot ensure an accurate diagnosis result.
Disclosure of Invention
The invention discloses an integrated learning based enhanced gear single fault category diagnosis method. The invention trains corresponding individual fault diagnosis learners by using the diversity characteristic of ensemble learning through a data cross training mode, and integrates a certain amount of support vector data description gear fault diagnosis learners into an enhanced gear fault single classification diagnotor by using an ensemble learning method and using a voting method as an integration rule, thereby achieving the aim of enhancing the classification capability.
The technical scheme for realizing the purpose of the invention is as follows:
step one, a gear fault diagnosis learner based on a support vector data description model is constructed;
respectively training k gear fault diagnosis learners described by the support vector data by adopting a k-fold cross training mode;
and step three, integrating the k support vector data description gear fault diagnosis learners together through rules of a voting method, so that the aim of enhancing the fault diagnosis capability of the single-classification gear can be achieved.
Compared with the prior art, the invention has the following remarkable advantages: through the integrated learning of a plurality of single classification methods, the classification capability of the single classification method is enhanced, and the fault diagnosis accuracy is improved.
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FIG. 1 is a schematic diagram of training set construction according to the present invention.
FIG. 2 is a schematic diagram of classifier training of the present invention.
FIG. 3 is a schematic diagram of the classifier integration of the present invention.
Fig. 4 is a technical framework diagram of the enhanced gear single fault category diagnosis method based on integrated learning according to the invention.
Detailed Description
The technical scheme of the invention can be summarized as follows:
the method comprises the following steps: support vector data description gear fault diagnosis learner model construction
And constructing a support vector data classification model by introducing a kernel function.
Step two: training gear fault feature sample set construction, and support vector data description gear fault diagnosis single classification learning machine training
And cutting the original characteristic sample group by adopting a k-fold cross training method. And training a gear fault diagnosis learner described by k support vector data in a k-fold cross training mode.
Step three: integration of gear fault diagnosis learner supporting vector data description
And integrating the gear fault diagnosis learners described by the k support vector data together by using a voting method to form an enhanced gear fault diagnosis single classifier.
The invention will be further explained with reference to the drawings.
The method comprises the following steps: support vector data description gear fault diagnosis learner model construction
Assume that there are n gear fault signature data sample points xi( i 1, 2.... n), there is one hyper-sphere containing all the characteristic sample points inside the hyper-sphere centered at o radius R. The distances of all the characteristic points in the hypersphere from the sphere center o satisfy
L(xi,o)＝||xi-o||2≤R2 (1)
And R is the maximum radius which ensures that all the inner parts of the hyper-sphere are gear fault characteristic sample points. The distance constraint rule under the condition of the standard hypersphere is adopted, and in order to improve the adaptability and the feasibility of the hypersphere, a redundancy epsilon can be added to each gear fault characteristic pointiThat is, the above condition is changed to L (x)i,o)＝||xi-o||2≤R2+εi (2)
Therefore, to minimize the hypersphere, the distance from each feature point to the center of the hypersphere can satisfy the following condition:
Figure BDA0001905168850000021
for a sample group, the number n of individuals is determined to be constant, and the constraint rule may be changed to:
minL(X,o)＝R2+C∑εi (4)
c is a constant. The constraint condition is formula (2), and according to the Lagrange multiplier algorithm, the Lagrange function of the above formula problem can be obtained:
L(xi,o,εi,R,α,β)＝R2+C-∑εi-∑αi(R2+εi-||xi-o||2)-∑βiεi (5)
from its partial derivative to each variable being zero, it can be known that:
Figure BDA0001905168850000031
at the same time
Figure BDA0001905168850000032
Substituting equation (6) into equation (5) can yield:
L(xi,o,εi,R,α,β)＝∑αi||xi-o||2 (8)
namely, it is
L(xi,o,εi,R,α,β)＝∑αi(xi·xi)-∑αiαj(xi·xj) (9)
When the gear fault characteristic sample point cannot be linearly distinguished in the sample space, the characteristic sample point needs to be mapped into a high-dimensional space, namely the Lagrangian function of the characteristic sample point is changed into L (x)i,o,εi,R,α,β)＝∑αi(φ(xi)·φ(xi))-∑αiαj(φ(xi)·φ(xj)) (10)
The mapping relation only appears in the inner product operation, and the inner product operation is defined as a kernel function, namely
κ(xi,xj)＝φ(xi)·φ(xj) (11)
The lagrange function becomes L (x)i,o,εi,R,α,β)＝∑αiκ(xi,xi)-∑αiαjκ(xi,xj) (12)
To ensure that equation (4) assumes the minimum value, α in equation (5)i(R2+εi-||xi-o||2) Greater than or equal to 0 and the greater the better so there is | | | xi-o||2≥R2When there is always alphai＝0；||xi-o||2＜R2When in use, the spherical surface is positioned inside the super sphere; | xi-o||2＝R2Then, all are true and located on the surface of the hyper-sphere, this vector is called the support vector.
According to the support vector xkThe radius of the hyper-sphere can be obtained
R2＝(xk·xk)-2∑αi(xi·xk)+∑αiαj(xi·xj) (13)
Any one sample xzWhether the distance between the center o of the hyper-sphere is in the hyper-sphere can be judged by calculating the distance between the center o of the hyper-sphere and the center o of the hyper-sphere.
Figure BDA0001905168850000041
Step two: training gear fault feature sample set construction, and support vector data description gear fault diagnosis single classification learning machine training
As shown in fig. 1, a certain gear fault feature sample set contains n sample points in total, m feature value points are sampled in a back-sampling manner for k times in total, k sampled gear fault feature sample groups are used as a training set after sampling is finished, and the un-sampled features in original feature samples are used as test feature samples; repeating the above process k times to obtain k feature training sets and corresponding k feature testing sets.
As shown in fig. 2, the training process of the support vector data description gear fault diagnosis learner is performed, and each training set correspondingly trains one support vector data description gear fault diagnosis learner; after the training of the support vector data description gear fault diagnosis learner is finished, testing by using a corresponding test set, and if the result meets the requirement, finishing the training of the support vector data description gear fault diagnosis single classification learner; and if the result is not met, constructing the feature training set and training the support vector data description gear fault diagnosis learner again.
Step three: integration of gear fault diagnosis learner supporting vector data description
The support vector data describes that the gear fault diagnosis learner is a single classification method, namely, the identification of fault types cannot be realized, but fault diagnosis can be carried out; the hypersphere radius R of a training set sample can be calculated by training a gear fault diagnosis learner by using a gear characteristic sample in a normal state; when the radius R' of the hyper-sphere of the test characteristic sample is larger than R, the characteristic sample does not belong to the current category, and the gear is indicated to have a fault; otherwise, the gear belongs to the category to which the characteristic belongs, and the gear is indicated to be in a normal category. Therefore, the support vector data describes the classification of the gear failure diagnosis learner as a {0, 1} problem. When the output category belongs to the category, the output category is marked as 1; when the output category does not belong to this category, the flag is 0. Therefore, k support vector data description gear failure diagnosis learners are subjected to voting method summation, namely:
Figure BDA0001905168850000042
wherein t isiAnd T represents an output result after integration for the output mark of the ith classifier.
If T > -k/2, the sample belongs to the class of normal state samples; if T < k/2, the sample is classified as a fault state sample.
According to the invention, single classification models are integrated together in an integrated learning mode, so that the diagnosis effect of single fault categories is improved, and the accuracy of fault diagnosis can be improved by applying the method to the field of gear fault diagnosis.

Claims (3)

1. An enhanced gear single fault category diagnosis method based on integrated learning is characterized by comprising the following steps of:
the method comprises the following steps that firstly, a gear fault diagnosis learning device based on a support vector data description model is constructed;
respectively training k gear fault diagnosis learners described by the support vector data by adopting a k-fold cross training mode;
integrating k support vector data description gear fault diagnosis learners together through rules of a voting method, so that the aim of enhancing the fault diagnosis capability of the single-classification gears can be achieved;
step one, the constructed support vector data describes a kernel function introduced by a gear fault diagnosis learner;
dividing the test samples into two types through the hyper-sphere, finding out a minimum hyper-sphere which can surround the target characteristic sample point in the gear fault characteristic space, and enabling the target characteristic sample point to surround the hyper-sphere as much as possible, wherein the non-target characteristic sample point is as little as possible or is not contained in the hyper-sphere;
assume that there are n gear fault signature sample points xiN, there is a hypersphere containing all sample points inside the hypersphere with the center of o being the radius R, then all characteristic sample points inside the hypersphere are at a distance from the center o of the sphere that satisfies
L(xi，o)＝||xi-o||2≤R2 (1)
R is the maximum radius which ensures that all the interior of the hyper-sphere are target characteristic sample points;
adding a redundancy epsilon to each target point according to the distance constraint rule under the condition that the above conditions are standard hypersphereiI.e. the above-mentioned constraints are changed
L(xi，o)＝||xi-o||2≤R2+εi (2)
The distance from each point to the center of the hyper-sphere meets the following condition:
Figure FDA0002942948130000011
minimizing the hyper-sphere;
for a gear fault characteristic sample group, if the characteristic individual number n is determined to be unchanged, the constraint rule further changes to:
minL(X，o)＝R2+C∑εi (4)
c is a constant, the constraint condition is a formula (2), and a Lagrangian function of the above formula problem is obtained according to a Lagrangian multiplier algorithm:
L(xi，o，εi，R，α，β)＝R2+C∑εi-∑αi(R2+εi-||xi-o||2)-∑βiεi (5)
from its partial derivative to each variable being zero, it can be known that:
Figure FDA0002942948130000021
at the same time
Figure FDA0002942948130000022
Substituting equation (6) into equation (5) can yield:
L(xi，o，εi，R，α，β)＝∑αi||xi-o||2
i.e. L (x)i，o，εi，R，α，β)＝∑αi(xi·xi)-∑αiαj(xi·xj)
To ensure that equation (4) assumes the minimum value, α in equation (5)i(R2+εi-||xi-o||2) Greater than or equal to 0 and the larger the better;
thus having | | xi-o||2≥R2When there is always alphai＝0；||xi-o||2＜R2When in use, the spherical surface is positioned inside the super sphere; | xi-o||2＝R2When the data points are located on the surface of the hyper-sphere, the vectors designated by the data points located on the surface of the hyper-sphere are called support vectors;
according to the support vector xkObtain the radius of the hyper-sphere
R2＝(xk·xk)-2∑αi(xi·xk)+∑αiαj(xi·xj)
Any gear fault characteristic sample can be judged whether to be positioned in the super sphere or not by calculating the distance between the gear fault characteristic sample and the center o of the super sphere;
when the gear fault characteristic sample point can not be linearly distinguished in the sample space, the characteristic sample point needs to be mapped into a high-dimensional space, namely the Lagrangian function of the characteristic sample point is changed into the Lagrangian function
L(xi，o，εi，R，α，β)＝∑αi(φ(xi)·φ(xi))-∑αiαj(φ(xi)·φ(xj))
The mapping relation only appears in the inner product operation, and the inner product operation is defined as a kernel function, namely
κ(xi，xj)＝φ(xi)·φ(xj)
The lagrange function becomes
L(xi，o，εi，R，α，β)＝∑αiκ(xi，xi)-∑αiαjκ(xi，xj)
The radius of the hyper-sphere is
R2＝κ(xk·xk)-2∑αiκ(xi·xk)+∑αiαjκ(xi·xj)。
2. The method for diagnosing the single fault category of the gear based on the integrated learning enhancement mode as claimed in claim 1, wherein the method for training the gear fault diagnosis learner by adopting the k-fold cross training method in the step two comprises the following specific implementation methods:
the gear fault characteristic sample data comprises N characteristic sample points, replaced random sampling is carried out for m times, k times of sampling are repeatedly carried out, the number of each characteristic sample is the same, and k training sets comprising m samples can be obtained; taking k characteristic sample groups as training data of a support vector data gear fault diagnosis learner, and taking characteristic samples which are not sampled in an original characteristic sample group as test data of the gear fault diagnosis learner; repeating the process k times, and training k support vector data description gear fault diagnosis learners.
3. The method for diagnosing single fault category of gear based on integrated learning enhancement type of claim 1, wherein the specific method for integrating the k support vector data description gear fault diagnosis learners by adopting voting rule in step three is as follows:
the hypersphere radius R of a training set sample can be calculated by training a gear fault diagnosis learner by using a gear characteristic sample in a normal state;
when the radius R' of the hyper-sphere of the test characteristic sample is larger than R, the characteristic sample does not belong to the current category, and the gear is indicated to have a fault; otherwise, the gear belongs to the category to which the characteristic belongs, and the gear is indicated to be in a normal category;
the support vector data describes the problem that the gear fault diagnosis learner classifies the problem into {0, 1}, and when the output class belongs to the class, the output class is marked as 1; when the output category does not belong to the category, the output category is marked as 0;
and (3) carrying out voting summation on the k support vector data description gear fault diagnosis learners, namely:
Figure FDA0002942948130000031
wherein t isiMarking the output of the ith classifier, wherein T represents the output result after integration;
if T > ═ k/2, it indicates that the sample belongs to the class of normal state samples; if T < k/2, the sample is classified as a fault state sample.
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