CN109213120A - The method for diagnosing faults of lower multistage principal component space is indicated based on high dimensional feature - Google Patents
The method for diagnosing faults of lower multistage principal component space is indicated based on high dimensional feature Download PDFInfo
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- G—PHYSICS
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B23/00—Testing or monitoring of control systems or parts thereof
- G05B23/02—Electric testing or monitoring
- G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
- G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
- G05B23/0243—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults model based detection method, e.g. first-principles knowledge model
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- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
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Abstract
The present invention relates to the fault diagnosises of Complex Industrial Systems, more particularly to the method for diagnosing faults for indicating lower multistage principal component space based on high dimensional feature, dimensionality reduction again is first augmented on the basis of former PCA first, so that the information that cannot be expressed in luv space gives full expression to, improve the recall rate of small fault, and it is based further on feature value division principal component space, foundation projects to different subspaces step by step, by compared with different subspace control limit, it not only can detect whether the monitoring range breaks down, and out of order rank can be recognized by the space of detection failure.
Description
Technical field
The present invention relates to the fault diagnosises of Complex Industrial Systems, and in particular to indicates that lower multistage pivot is empty based on high dimensional feature
Between method for diagnosing faults.
Background technique
Fault diagnosis plays an important role the reliability for improving Complex Industrial Systems, and fault reconstruction and identification are failures
The target of diagnosis, how fast detecting failure, improve the recall rate of failure and the size of estimation failure to taking at corresponding measure
Reason failure plays important directive function.
It take pivot analysis (Principal Component Analysis, PCA) as the multi-variate statistical analysis of Typical Representative
Method is common method in fault diagnosis method, and the latent variable that sample space is decomposed into a low-dimensional using multivariate projection technology is empty
Between and a residual error space, construct statistic and diagnose fault in the two subspaces respectively, but due to by process operation number
It is analyzed again according to after measurement spatial alternation to feature space, there are serious mode complex effects, so as to system is caused
The explanation for the fault mode being abnormal becomes difficult, and dimensionality reduction is divided into principal component space and residual error space, and small information cannot get
It sufficiently indicates, the ability for distinguishing not significant mode is also affected.
In disclosed prior art, to solve the problems, such as that PCA because of mode complex effect, proposes specified meta analysis
(DCA) concept will observe on data projection to designated mode the conspicuousness size for determining each specified member by calculating, judge phase
Whether the failure answered has occurred；By gradually DCA parser, solve the problems, such as orthogonal diagnosis between the DCA group of designated mode, but
It is still non-orthogonal in group；In order to overcome traditional PCA because of the brings such as dimension difference and standardisation process deficiency, and by different changes
The relative importance of amount is introduced into system, it is established that a method of it is referred to as RPCA；It, should again from latent space projection angle
Method has extracted the subspace that can embody variable importance and sample Main change simultaneously；RPCA method is being applied to fly control system
In the fault diagnosis of system, accurately identifying and positioning for the stuck failure of actuator is realized；It is a kind of based on significant contribution by proposing
The method that rate, sensitivity coefficient and Fault-Sensitive degree seek proportion coefficients, can significantly improve the fault-detecting ability of significant variable；
By proposing a kind of method for diagnosing faults based on muti-piece Relative Transformation Independent component analysis, high dimensional data is divided into multiple sub-blocks
Unit, and carry out RTICA processing respectively in each sub-block unit, determine the position that failure occurs；And by by the variable space
It is divided into several dominant subspaces and a residual error subspace to solve the problems, such as identification failure size, improves the monitoring energy of failure
Power.
For PCA mode complex effect multistage small fault diagnosis on limitation, it is proposed that PCA project frame under
Multistage small fault diagnosis；It is smaller in view of the deviation between small fault and normal condition, it is distributed and is measured by join probability,
Using the potential score of Kullback-Leibler Quantified and referring to the residual error between score, it is proposed that be suitable for small fault
PCA algorithm control limit；Subspace partition principle is determined based on the size of characteristic value and feature vector element, it is empty to residual error
Between be finely divided, propose a kind of more space detection methods based on PCA, it is significant in residual error subspace to can be improved failure
Property；Small fault diagnostic method summary based on data-driven proposes from the new information of increase, excavates unused implicit letter
Breath and the thinking improved using new three angles of mathematical tool.
These schemes all improve the ability of the monitoring failure based on PCA method to a certain extent, though it can be used in event
Barrier detection, but due to being former space equivalent representation, the identification of fault mode caused by the mode complex effect of traditional PCA and dimensionality reduction make
Obtaining small fault cannot give full expression to, and the identification of failure size and the diagnosis of small fault encounter challenge.
Summary of the invention
The present invention discloses a kind of method for diagnosing faults that lower multistage principal component space is indicated based on high dimensional feature, can not only recognize
Out of order rank, and the information that cannot be expressed in luv space is given full expression to, improve the recall rate of small fault.
The present invention provides a kind of multistage principal component space method indicated based on high dimensional feature, comprising the following steps:
A, zero-mean and unit variance standardization are carried out by each column of the PCA algorithm to normal historical data matrix,
Covariance matrix is obtained, covariance matrix is converted to by the eigenvectors matrix with diagonal form by similarity transformation, in spy
Increase i vector on the basis of sign vector matrix, so that the i grade eigenvectors matrix of high dimensional feature representation space is formed, it is described
Normal historical data has verified that in industrial manufacturing process as data caused by normal conditions；
B, normal historical data matrix is projected to i grades of eigenvectors matrixs, obtains the feature vector under new projector space
Each column of eigenvectors matrix are carried out the standardization of zero-mean and unit variance, obtain covariance matrix by matrix, according to
The variable space is divided into k principal component subspace and a residual error subspace by the size of covariance matrix eigenvalue contribution rate, is made
For multistage pivot analysis projection model, the T of each principal component subspace and residual error subspace is calculated separately2And SPE Testing index；
C, test data set is projected to i grades of eigenvectors matrixs, obtains the coordinate under new projector space, will newly projects sky
Between under coordinate handled according to zero-mean and zero variance；
D, the test data set after calculation processing is calculated into test successively to each principal component subspace and residual error subspace projection
The T of data2And SPE index value, by judging whether to be abnormal, and pass through compared with the Testing index of normal historical data
Judgement to space is abnormal tentatively judges abnormal rank.
Further, in the step A, normal historical data matrix is by carrying out off-line training to industry spot, from offline
It is generated in training, described eigenvector matrix is identical as the dimension of the normal historical data matrix.
Further, it is connected based on the normal orthogonal sequence base head and the tail that normal historical data matrix generates, by two two-phases
I vector is inserted between adjacent base vector among linearly connected line, forms the i grade eigenvectors matrix of high dimensional feature representation space,
And then a polyhedron is formed based on adjacent multiple base vectors, by carrying out the interpolation of different densities inside polyhedron, formed
The i grade eigenvectors matrix of corresponding high dimensional feature representation space.
Further, by finding out the characteristic value and feature vector of covariance matrix, characteristic value is according to sequence from big to small
Arrangement, and feature vector corresponding with characteristic value is also arranged in sequence, to constitute normal orthogonal sequence base.
Further, i and k is natural number, and i >=1, k >=1.
The beneficial effects of the present invention are: the present invention discloses a kind of event of multistage principal component space under indicating based on high dimensional feature
Hinder diagnostic method, dimensionality reduction again is first augmented on the basis of original PCA, the primary variables space after dimensionality reduction is divided into different stage
Subspace and residual error space not only solve the problems, such as identification failure size, while improving the detectability of small fault, so that
Principal component space low level failure has the projection ability to high-level space, improves detection performance.
Detailed description of the invention
The invention will be further described with example with reference to the accompanying drawing.
Fig. 1 is a kind of flow chart for the method for diagnosing faults that lower multistage principal component space is indicated based on high dimensional feature of the present invention；
Fig. 2 be the embodiment of the present invention compared with major break down when analogous diagram；
Fig. 3 be after the embodiment of the present invention is augmented compared with major break down when；
Analogous diagram when Fig. 4 is medium outage of the embodiment of the present invention；
Fig. 5 is the analogous diagram when embodiment of the present invention is augmented rear medium outage；
Analogous diagram when Fig. 6 is small fault of the embodiment of the present invention；
Fig. 7 is the analogous diagram when embodiment of the present invention is augmented rear small fault.
Specific embodiment
Referring to Fig.1, the present invention provides a kind of method for diagnosing faults of multistage principal component space indicated based on high dimensional feature
Embodiment, comprising the following steps:
A, by carrying out off-line training to industry spot, normal historical data matrix is generated from off-line training, passes through PCA
Algorithm carries out zero-mean and unit variance standardization to each column of normal historical data matrix, obtains covariance matrix battle array S
Are as follows:
Covariance matrix is converted to tool by similarity transformation by the eigenvalue λ and feature vector U for finding out covariance matrix S
There is the eigenvectors matrix of diagonal form, characteristic value is according to λ from big to small1≥λ2≥…≥λm>=0 sequence arrangement, and will be with
The corresponding feature vector of characteristic value is also arranged in sequence, then U=(U1,U2,U3,…Un) constitute normal historical data
The normal orthogonal in equivalent projection space sorts set of bases U, as eigenvectors matrix, described eigenvector matrix and described normal
The dimension of historical data matrix is identical.
Original variable can decompose as follows:
Then t is hidden variable:
T=xU
Traditional PCA algorithm be used for fault detection when, sign it is small and be submerged in noise or larger normal processes variation
Failure can seem not applicable, and the present embodiment is first augmented on the basis of original PCA, and the information that cannot be expressed in luv space is led to
It crosses and is given full expression to when being augmented:
Increase i vector on the basis of eigenvectors matrix, thus formed the i grade feature of high dimensional feature representation space to
Moment matrix, i are natural number, and i >=1；On the basis of the characteristic value and corresponding feature vector that formula (1) obtains, adjacent two-by-two
A vector is inserted between base vector among linearly connected line, obtains level-one character representation vector matrix:
Two vectors are inserted among linearly connected between adjacent base vector two-by-two, obtaining secondary characteristics indicates vector matrix:
Similarly, according to level-one, the generation method of second level projection frame, the standard based on the generation of normal historical data matrix is just
It hands over sequence base head and the tail to be connected, is inserted into three vectors, four vectors among linearly connected line between adjacent base vector two-by-two ... i
A vector, thus formed the level-one of high dimensional feature representation space, second level ..., i grades of eigenvectors matrix Ui=(Ui1,Ui2,…
Ui[(i+1)*n-i])；It is based further on adjacent multiple base vectors and forms a polyhedron, different densities are carried out inside polyhedron
Interpolation, to form the i grade eigenvectors matrix of corresponding high dimensional feature representation space；
B, normal historical data matrix is projected to i grades of eigenvectors matrixs, obtains the feature vector under new projector space
Each column of eigenvectors matrix are carried out the standardization of zero-mean and unit variance, obtain covariance matrix by matrix, according to
The variable space is divided into k principal component subspace and a residual error subspace by the size of covariance matrix eigenvalue contribution rate, is made
For multistage pivot analysis projection model, wherein k is natural number, and k >=1；
The loading matrix U of i-th of principal component subspacei, by the sample X after higher-dimension projection frame data for projection standardizationiAssociation
The b of variance matrix Si+1+ 1 to biA feature vector is constituted, biFor the pivot number summation of preceding i principal component subspace, each son
The pivot number k in space is determined by accumulative variance contribution ratio method；
Wherein U=[u1,u2,…ur], u respectively arranges mutually orthogonal, and the length of each load vector is normalized,bi-bi-1For the pivot number and phase reserved portion square of i-th of principal component subspace
The columns of battle array, pivot score matrixEach column be it is mutually orthogonal, i.e. when i ≠ j,E is
The residual information of principal component model, the covariance matrix of pivotWherein,Table
Show the preceding b of SrA biggish characteristic value, then
Calculate separately the Hotelling T square distribution (T of each principal component subspace and residual error subspace2) and square prediction error
(SPE):
Normal historical data X is to corresponding high dimensional feature vector matrix UiAfter projection, new data X is obtainedi, it calculates as follows:
T=xiUi *
M=(I-Ui *Ui *T)xi (7)
New projection frame statistic T*2(i) it calculates as follows:
T*2(i)=tTΛ-1T=xi TUi *TΛ-1Ui *xi (8)
The statistic SPE of residual error subspace*(i) are as follows:
2 controls limit under new projected coordinate system is respectively as follows:
Control limitIt calculates as follows:
Wherein:Be freedom degree be b*,n-b*, the F distribution critical value that confidence level is α,
Control limit Qα(i), it calculates as follows:
Wherein:CαIt is standardized normal distribution at confidence level α
Threshold value；
C, test data set is projected to i grades of eigenvectors matrixs, obtains the coordinate under new projector space, will newly projects sky
Between under coordinate handled according to zero-mean and zero variance；
D, the test data set after calculation processing is calculated into test successively to each principal component subspace and residual error subspace projection
The T of data2And SPE index value, by judging whether to be abnormal, and pass through compared with the Testing index of normal historical data
Judgement to space is abnormal tentatively judges abnormal rank.
When being used for fault detection, Hotelling T square distribution (T is used2) and square prediction error (SPE) carry out detection process
In whether have occurred exception, calculate as follows:
Wherein
And T2Variable is measured in the variation of principal component space, obedience freedom degree is h, and confidence level is α'sDistribution, and by
In residual error spatial statistics:
When test data arrive after, data are projected to every sub-spaces respectively, seek statistic and with it is corresponding
Control limit is compared, and then whether deterministic process has occurred exception again.
With reference to Fig. 2-7, the present embodiment constructs following system variable:
Wherein, randn (1,1) is the random number of 1 row 1 column generated with Matlab, chooses 3000 normally for PCA
Data establish pivot pca model；It is augmented according to actual needs, establishes the principal component model after being augmented, then establish multistage pivot mould
Type, and calculate separately the control limit in each space.500 samples are chosen again as test data, to the variable x of test data1、
x3、x5201-300 moment, 301-400 moment and 501-600 moment introduce the permanent deviation fault of certain amplitude, with higher-dimension frame
Under multistage principal component space model detected respectively, and with it is no carry out the projection of higher-dimension frame model be compared.
When Fig. 2 and Fig. 3 is that failure rank is higher, it can be detected in the principal component subspace of all ranks and residual error subspace
It is abnormal；It when Fig. 4 and Fig. 5 is the failure of medium rank, is not monitored not come out in the first principal component space, although portion after being augmented in Fig. 5
Sampled point scientific research is divided to detected, but rate of failing to report is very big, but it is equal in second, third principal component subspace and residual error subspace
It can preferably detect；Fig. 6 does not carry out high dimensional feature expression when being smaller failure, empty in all principal component spaces and residual error
Between cannot detected, Fig. 7 is that initial data first carries out high dimensional feature expression, then projects and calculates corresponding control limit, imitate
Very the result shows that can preferably detect the undetectable failure of traditional PCA in residual error subspace, verification and measurement ratio is improved.
The above, only presently preferred embodiments of the present invention, the invention is not limited to above embodiment, as long as
It reaches technical effect of the invention with identical means, all should belong to protection scope of the present invention.
Claims (4)
1. indicating the method for diagnosing faults of lower multistage principal component space based on high dimensional feature, which comprises the following steps:
A, zero-mean and unit variance standardization are carried out by each column of the PCA algorithm to normal historical data matrix, obtained
Covariance matrix is converted to the eigenvectors matrix with diagonal form by similarity transformation by covariance matrix, feature to
Increase i vector on the basis of moment matrix, to form the i grade eigenvectors matrix of high dimensional feature representation space, wherein i is
Natural number, and i >=1；
B, normal historical data matrix is projected to i grades of eigenvectors matrixs, obtains the eigenvectors matrix under new projector space,
The standardization that each column of eigenvectors matrix are carried out to zero-mean and unit variance, obtains covariance matrix, according to association side
The variable space is divided into k principal component subspace and a residual error subspace by the size of poor matrix exgenvalue contribution rate, as more
Grade pivot analysis projection model, calculates separately the T of each principal component subspace and residual error subspace2And SPE Testing index, wherein k is
Natural number, and k >=1；
C, test data set is projected to i grades of eigenvectors matrixs, obtains the coordinate under new projector space, it will be under new projector space
Coordinate handled according to zero-mean and zero variance；
D, the test data set after calculation processing is calculated into test data successively to each principal component subspace and residual error subspace projection
T2And SPE index value, by judging whether to be abnormal, and by hair compared with the Testing index of normal historical data
The judgement of raw abnormal space, judges abnormal rank.
2. the method for diagnosing faults according to claim 1 for indicating lower multistage principal component space based on high dimensional feature, feature
It is, in the step A, normal historical data matrix is generated from off-line training by carrying out off-line training to industry spot.
3. the method for diagnosing faults according to claim 1 for indicating lower multistage principal component space based on high dimensional feature, feature
It is, in the step A, increases i vector on the basis of eigenvectors matrix, form corresponding high dimensional feature representation space
I grade eigenvectors matrix specifically include:
It is connected based on the normal orthogonal sequence base head and the tail that normal historical data matrix generates, by between adjacent base vector two-by-two
It is inserted into i vector among linearly connected line, forms the i grade eigenvectors matrix of high dimensional feature representation space, and then based on adjacent
Multiple base vectors form a polyhedron, by the interpolation for carrying out different densities inside polyhedron.
4. the method for diagnosing faults according to claim 3 for indicating lower multistage principal component space based on high dimensional feature, feature
It is, the obtaining step of the normal orthogonal sequence base includes: the characteristic value and feature vector for finding out covariance matrix, characteristic value
According to sequence arrangement from big to small, and feature vector corresponding with characteristic value is also arranged in sequence.
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Cited By (3)
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| CN109885022A (en) * | 2019-02-21 | 2019-06-14 | 山东科技大学 | A kind of fault detection method based on latent Fault-Sensitive subspace |
| CN112418577A (en) * | 2019-08-22 | 2021-02-26 | 北京蓝星清洗有限公司 | Visual monitoring method and system for industrial product production process |
| CN112511372A (en) * | 2020-11-06 | 2021-03-16 | 新华三技术有限公司 | Anomaly detection method, device and equipment |
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109885022A (en) * | 2019-02-21 | 2019-06-14 | 山东科技大学 | A kind of fault detection method based on latent Fault-Sensitive subspace |
| CN109885022B (en) * | 2019-02-21 | 2021-07-09 | 山东科技大学 | Fault detection method based on latent fault sensitive subspace |
| CN112418577A (en) * | 2019-08-22 | 2021-02-26 | 北京蓝星清洗有限公司 | Visual monitoring method and system for industrial product production process |
| CN112511372A (en) * | 2020-11-06 | 2021-03-16 | 新华三技术有限公司 | Anomaly detection method, device and equipment |
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