CN109242008B - Compound fault identification method under incomplete sample class condition - Google Patents
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Abstract
The invention provides a composite fault identification method under the condition of incomplete sample category, which comprises the following steps: generating a fault detector; generating an evaluation function; sending the sample to be detected to a fault detector, and judging whether the output result has a fault or not; respectively sending the samples to be tested to corresponding evaluation functions to obtain corresponding index values; comprehensively evaluating the indexes; and setting a threshold value theta to diagnose whether a composite fault exists or not. The composite fault identification method respectively calculates the high-dimensional spatial positions of the samples to be detected in the fault A classifier and the fault B classifier, then estimates the possibility of AB faults occurring simultaneously, and further realizes the identification of the composite faults on the premise of not needing AB composite fault samples.
Description
Technical Field
The invention relates to a compound fault identification method, in particular to a compound fault identification method under the condition of incomplete sample categories.
Background
Under the background of artificial intelligence and big data, the diagnosis system of the current industrial system gradually changes from relying on an accurate mathematical model to relying on industrial process data and a data driving algorithm. A fault diagnosis method based on a Support Vector Machine (SVM) is a typical data-driven fault diagnosis method, which avoids the complex and even unrealizable mechanism modeling of a diagnostic object, and simultaneously avoids the requirement of an intelligent diagnosis algorithm with minimized experience risk, such as an artificial neural network, on the size of a training sample set, and can realize effective fault diagnosis on the premise of a small sample amount, thereby obtaining wide research and application in recent years.
The SVM bi-classifier is a typical bi-classifier, and given training sample sets A and B, the built SVM bi-classifier can judge whether unknown samples belong to class A or class B with higher probability. The essence of fault diagnosis based on the SVM method is that a nonlinear fault sample set is projected to a high-dimensional fault space, and a classification hyperplane is made through the SVM so that the fault space is divided into corresponding fault intervals. And the fault detection and isolation are realized by positioning the fault section of the sample to be detected in the high-dimensional space.
The performance of the traditional fault diagnosis based on SVM fundamentally depends on the quality of a data set, and accurate diagnosis can be realized by training all class samples at one time, namely the sample set is required to be complete. By taking fig. 1 as an example, if only a normal sample, a fault a sample and a fault B sample are collected, the conventional SVM diagnosis method can only diagnose three working states of normal, fault a and fault B, and cannot judge whether a composite fault occurs (fault A, B occurs simultaneously); if the diagnosis of the state needs to be realized, a fault sample under the condition of AB fault concurrence needs to be collected, and then a new classifier is constructed.
In actual engineering, the fault itself usually belongs to a small probability event, the composite fault is a small probability of a small probability, and a sample is extremely difficult to obtain, so that the sample set is usually incomplete.
Disclosure of Invention
The invention aims to: the method for identifying the compound faults under the condition of incomplete sample classes can calculate the high-dimensional spatial positions of samples to be detected in a fault A classifier and a fault B classifier respectively, then estimate the possibility of AB faults occurring simultaneously, and further realize the identification of the compound faults on the premise of not needing AB compound fault samples.
In order to achieve the above object, the present invention provides a method for identifying a compound fault under the condition of incomplete sample class, which comprises the following steps:
step 2, generating an evaluation function, which comprises the following specific steps:
step 2.1, collecting a fault sample set X of the fault AA;
Step 2.2, respectively, normal sample XNormalAnd fault sample set XASetting corresponding labels, marking the normal sample as 1 and the fault sample as-1, and further obtaining a label setN is the total number of samples;
step 2.3, solving the normal sample X by using a support vector machineNormalAnd fault sample set XAThe classification hyperplane w x + b is 0, w is a weight vector, b is a bias, and then the solution of the hyperplane is converted into the following quadratic programming problem:
min:<w·w> (3)
S.t.yi(<w·xi>+b)≥1,i=1,...,N
the support vector machine method projects the existing sample to a linearly separable high-dimensional space, if w x + b is larger than 0, the sample is considered to be a normal sample, and if w x + b is less than or equal to 0, the sample is considered to be a fault sample;
step 2.3, evaluating the sample by using the distance between the sample to be measured and the hyperplane, and giving the sample x to be measuredtThen the evaluation function for the a fault is:
in the formula, wA、bAAnd classifying the weight vector and the offset of the hyperplane by using the normal sample and the A fault sample, and generating an evaluation function of the B fault in the same way:
in the formula, wB、bBWeight vector and bias for classifying hyperplane with normal samples and B fault samples;
Step 3, sending the sample to be detected to a fault detector, if the high-dimensional projection of the sample is in the hypersphere, the sample is a normal sample, the output result is no fault, otherwise, the fault occurs, and entering step 4;
step 4, respectively sending the samples to be tested to the evaluation function f of the A faultsA(xt) And B fault evaluation function fB(xt) In the method, an index value eta is obtainedA=fA(xt) And ηB=fB(xt);
Step 5, comprehensively evaluating the indexes: giving a comprehensive evaluation function D, and calculating according to the formula:
and 6, setting a threshold value theta, wherein theta is more than or equal to 0 and less than 1, when D is less than or equal to theta, the diagnosis result is no composite fault, and if D is more than theta, the diagnosis result is composite fault.
Further, in step 1, a hyper-sphere omega is built1The method comprises the following specific steps:
is provided withFor a known set of target samples, N is the number of samples, hypersphere) Can be combined withIs completely contained, wherein a is the centre of sphere, R is the radius of the hypersphere, has:
in the formula, C is a given penalty factor, xi is misjudgment loss, the solution is realized by combining Lagrangian formula with an activity set method, and the solving formula is as follows:
in the formula, Z is a sample element in the test sample Z, and for the test sample Z, if the above formula is satisfied, the test sample Z belongs to the target class.
Further, in step 6, the value of θ is set to 0.2.
The invention has the beneficial effects that: the composite fault identification method respectively calculates the high-dimensional spatial positions of the samples to be detected in the fault A classifier and the fault B classifier, then estimates the possibility of AB faults occurring simultaneously, and further realizes the identification of the composite faults on the premise of not needing AB composite fault samples.
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FIG. 1 is the essence of SVM based fault diagnosis in the prior art;
FIG. 2 is a schematic flow diagram of the process of the present invention;
FIG. 3 is a schematic diagram of a hypersphere structure of the present invention;
FIG. 4 is a schematic diagram of a method for projecting a conventional sample into a linearly separable high-dimensional space.
Detailed Description
As shown in fig. 2, the method for identifying a compound fault under the incomplete sample category condition disclosed by the invention comprises the following steps:
step 2, generating an evaluation function, which comprises the following specific steps:
step 2.1, collecting a fault sample set X of the fault AA;
Step 2.2, respectively, normal sample XNormalAnd fault sample set XAThe corresponding label is set, the normal sample is marked 1,the fault sample is marked as-1, and a label set is further obtainedN is the total number of samples;
step 2.3, solving a normal sample X by utilizing a Support Vector Machine (SVM)NormalAnd fault sample set XAThe classification hyperplane w x + b is 0, w is a weight vector, b is a bias, and then the solution of the hyperplane is converted into the following quadratic programming problem:
min:<w·w> (3)
S.t.yi(<w·xi>+b)≥1,i=1,...,N
the support vector machine method projects the existing sample to a linearly separable high-dimensional space, as shown in fig. 4, if w x + b is greater than 0, the sample is considered as a normal sample, and if w x + b is less than or equal to 0, the sample is considered as a fault sample;
step 2.3, evaluating the sample by using the distance between the sample to be measured and the hyperplane, and giving the sample x to be measuredtThen the evaluation function for the a fault is:
in the formula, wA、bAAnd classifying the weight vector and the offset of the hyperplane by using the normal sample and the A fault sample, and generating an evaluation function of the B fault in the same way:
in the formula, wB、bBClassifying the weight vector and the offset of the hyperplane by using a normal sample and a B fault sample;
step 3, sending the sample to be detected to a fault detector, if the high-dimensional projection of the sample is in the hypersphere, the sample is a normal sample, the output result is no fault, otherwise, the fault occurs, and entering step 4;
step 4, respectively sending the samples to be detectedEvaluation function f to A faultA(xt) And B fault evaluation function fB(xt) In the method, an index value eta is obtainedA=fA(xt) And ηB=fB(xt);
Step 5, comprehensively evaluating the indexes: giving a comprehensive evaluation function D, and calculating according to the formula:
and 6, setting a threshold value theta, wherein theta is more than or equal to 0 and less than 1, when D is less than or equal to theta, the diagnosis result is no composite fault, if D is more than theta, the diagnosis result is composite fault, the value of theta is not too high, and the value of theta is preferably set to be 0.2.
Further, in step 1, the SVDD method tries to adopt a minimum hypersphere structure, and includes all training samples to establish hypersphere Ω1The method comprises the following specific steps:
is provided withFor a known set of target samples, N is the number of samples, hypersphereCan be combined withIs completely contained, wherein a is the centre of sphere, R is the radius of the hypersphere, has:
in the formula, C is a given penalty factor, xi is misjudgment loss, the solution is realized by combining Lagrangian formula with an activity set method, and the solving formula is as follows:
in the formula, Z is a sample element in the test sample Z, and for the test sample Z, if the above formula is satisfied, the test sample Z belongs to the target class, as shown in fig. 3.
The composite fault identification method under the incomplete sample class condition disclosed by the invention respectively calculates the high-dimensional spatial positions of the sample to be detected in the fault A classifier and the fault B classifier, then estimates the possibility of AB faults occurring simultaneously, and further realizes the identification of the composite fault on the premise of not needing AB composite fault samples.
Claims (3)
1. A composite fault identification method under the condition of incomplete sample category is characterized by comprising the following steps:
step 1, generating a fault detector, which comprises the following specific steps: collecting Normal sample XNormalConstructing hypersphere omega by using support vector data description method1If the sample to be measured falls into the hypersphere omega1If the range is within the range, the sample to be detected belongs to a normal sample, otherwise, the sample to be detected belongs to a fault sample;
step 2, generating an evaluation function, which comprises the following specific steps:
step 2.1, collecting a fault sample set X of the fault AA;
Step 2.2, respectively, normal sample XNormalAnd fault sample set XASetting corresponding labels, marking the normal sample as 1 and the fault sample as-1, and further obtaining a label setN is the total number of samples;
step 2.3, solving the normal sample X by using a support vector machineNormalAnd fault sample set XAThe classification hyperplane w x + b is 0, w is a weight vector, b is a bias, and then the solution of the hyperplane is converted into the following quadratic programming problem:
min:<w·w> (3)
S.t.yi(<w·xi>+b)≥1,i=1,...,N
the support vector machine method projects the existing sample to a linearly separable high-dimensional space, if w x + b is larger than 0, the sample is considered to be a normal sample, and if w x + b is less than or equal to 0, the sample is considered to be a fault sample;
step 2.4, evaluating the sample by using the distance between the sample to be measured and the hyperplane, and giving the sample x to be measuredtThen the evaluation function for the a fault is:
in the formula, wA、bAAnd classifying the weight vector and the offset of the hyperplane by using the normal sample and the A fault sample, and generating an evaluation function of the B fault in the same way:
in the formula, wB、bBClassifying the weight vector and the offset of the hyperplane by using a normal sample and a B fault sample;
step 3, sending the sample to be detected to a fault detector, if the high-dimensional projection of the sample to be detected is in the hypersphere, the sample to be detected is a normal sample, the output result is no fault, otherwise, the fault occurs, and the step 4 is entered;
step 4, respectively sending the samples to be tested to the evaluation function f of the A faultsA(xt) And B fault evaluation function fB(xt) In the method, an index value eta is obtainedA=fA(xt) And ηB=fB(xt);
Step 5, comprehensively evaluating the indexes: giving a comprehensive evaluation function D, and calculating according to the formula:
and 6, setting a threshold value theta, wherein theta is more than or equal to 0 and less than 1, when D is less than or equal to theta, the diagnosis result is no composite fault, and if D is more than theta, the diagnosis result is composite fault.
2. The method for identifying the compound fault under the incomplete sample class condition according to claim 1, wherein in the step 1, a hyper-sphere omega is built1The method comprises the following specific steps:
is provided withFor a given target sample set, N is the total number of samples, and the hyper-sphere Ω ═ a, R can be computedIs completely contained, wherein a is the centre of sphere, R is the radius of the hypersphere, has:
in the formula, C is a given penalty factor, xi is misjudgment loss, the solution is realized by combining Lagrangian formula with an activity set method, and the solving formula is as follows:
in the formula, Z is a sample element in the test sample Z, and for the test sample Z, if the above formula is satisfied, the test sample Z belongs to the target class.
3. The method for identifying the compound fault under the incomplete sample class condition according to claim 1, wherein in step 6, the value of θ is set to 0.2.
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CN103048133A (en) * | 2012-12-03 | 2013-04-17 | 陕西科技大学 | Bayesian network-based rolling bearing fault diagnosis method |
CN103136587A (en) * | 2013-03-07 | 2013-06-05 | 武汉大学 | Power distribution network operating state classification recognition method based on support vector machine |
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