CN105911977B - The method for diagnosing faults that nested iterations Fei Sheer discriminant analyses are combined with opposite variation - Google Patents
The method for diagnosing faults that nested iterations Fei Sheer discriminant analyses are combined with opposite variation Download PDFInfo
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- 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
Abstract
The invention discloses the method for diagnosing faults that a kind of nested iterations Fei Sheer discriminant analyses are combined with opposite variation.In a kind of fault data, often existing simultaneously two kinds of fault types --- biasing and data fluctuations increase, fault message is extracted in both fault type R. concomitans nested iterations Fei Sheer discriminant analyses and opposite mutation analysis that this method is directed in same fault data, then its reconstruction model is determined according to the fault message per a kind of fault data, is used for on-line fault diagnosis.The shortcomings that being unable to fully extraction fault characteristic the method overcome single method, substantially increases the performance of on-line fault diagnosis, and helps quickly and accurately to repair failure, to ensure that process safety and improve productivity effect.
Description
Technical field
The invention belongs to chemical process statistical monitoring field, more particularly to a kind of nested iterations Fei Sheer discriminant analyses with
The method for diagnosing faults that opposite mutation analysis is combined.
Background technology
With the development of science and technology chemical process production system increasingly complex.In order to ensure process safety and improve life
Produce benefit, it is necessary to use effective fault detection and fault diagnosis method.Fault detect is exactly to monitor process operation, in abnormal work
Alarm is sent out when condition occurs in time；Fault diagnosis acts on after alarm signal, for determining fault type and handling abnormal letter
Number.With the development of technology, obtaining data in industry spot becomes increasingly easier, then, the fault diagnosis side based on data
Method has become the hot spot of research.
Forefathers have made corresponding research to fault diagnosis, propose corresponding diagnostic method from different aspect, have as follows
It is several：The side of method based on analytic modell analytical model, the method based on signal processing, Knowledge based engineering method and multi-variate statistical analysis
Method.Principal component analysis (PCA), the Multielement statistical analysis methods such as offset minimum binary (PLS) and Fei Sheer discriminant analyses (FDA) are
It is widely used in data procedures monitoring field, the characteristics of Data Dimensionality Reduction helps to handle high-dimensional, high correlation data.
Original higher-dimension measurement data is projected to the monitoring space of low-dimensional, fault diagnosis essence is improved with this by they by constructing latent variable
Degree.The each have their own feature of above-mentioned several multivariate statistical methods and applicable situation.In fault diagnosis, a kind of fault data with
When normal data, often there is biasing and increase two kinds of fault conditions with data fluctuations.The direction of FDA methods extraction is to make two classes
Between class distance is as big as possible and tightens as far as possible in class, and then it can extract and bias relevant fault direction；And relatively event
The opposite variation of barrier data and normal data can then be extracted increases relevant fault direction with data fluctuations.
Invention content
In view of the above-mentioned deficiencies in the prior art, it is an object of the present invention to provide a kind of nested iterations Fei Sheer discriminant analyses with
The method for diagnosing faults that opposite mutation analysis is combined.The present invention is directed to simultaneous two kinds of fault types in fault data,
Different method extraction fault messages is respectively adopted, the reconstruct of the fault type on-line fault diagnosis is determined according to the fault message
Model.This method targetedly extracts fault message, fully excavates fault characteristic, substantially increases the property of on-line fault diagnosis
Energy.
The purpose of the present invention is achieved through the following technical solutions：A kind of nested iterations Fei Sheer discriminant analyses and opposite variation
In conjunction with method for diagnosing faults, this approach includes the following steps：
(1) data are obtained：For a chemical process with J variable, sampling can obtain 1 × J's every time
Vector, the data obtained after sampling K times can be described as a two-dimensional matrix X (K × J).Normal data X is obtained respectivelyn(Nn×
) and fault data X Jf,m(Nf,m× J), wherein subscript n indicates that normal data, subscript f indicate that fault data, m indicate failure
Classification；
(2) PCA analyses are carried out to normal data, obtains the pivot load P (J × R) and residual error space RS of principal component space PCS
Residual error load Pe(J×(J-R))；
Wherein, R is the principal component number of pivot load；
To score matrix TnWith residual error EnCalculate T2Statistic and SPE statistics；
Wherein,Indicate the mean value of normal data score matrix；S indicates pair that the variance of normal data score matrix is constituted
Angular moment battle array；
Due to T2Index obeys F distributions, and SPE indexs obey chi square distribution, establishes control limit respectively according to the distribution
And CtrSPE；
(3) normal data sample X is chosenn(Nn× J) and a kind of fault data sample Xf(Nf×J)；
(4) it uses nested iterations Fei Sheer Discrimination Analysis Algorithms to analyze and biases relevant fault message：
(4.1) to XnAnd XfWith nested iterations Fei Sheer Discrimination Analysis Algorithms, the final coefficient matrix of fault data is obtainedAnd load matrixWherein, N is the discriminatory element number chosen；
(4.2) fault message is reconstructed
Wherein,It is the final discriminatory element matrix of fault data；It indicates to bias relevant failure variation；
(5) the removal biasing failure from primary fault data, obtains new fault data for opposite mutation analysis；
Wherein, EfIt is the correction data corrected after biasing relevant failure variation, using the feature of normal data to school
Correction data is standardized, and the correction data after standardization is denoted as XRC,f；
(6) relevant fault direction is increased with data fluctuations using opposite mutation analysis Algorithm Analysis：
(6.1) data preparation：With X in step (5)RC,fThe primary data as fault data in opposite mutation analysis,
And normal data still uses initial normal data Xn；
(6.2) there is the direction of opposite variation in extraction：
The space PCSt and load P in the presence of opposite variation are found out in the spaces PCS that step (2) obtainst,r(J×Rt,r)；
RS finds out in space the space RSt and load P in the presence of opposite variatione,r((J-R)×Re,r).Wherein, Rt,rAnd Re,rIt indicates respectively
The number in the spaces PCSt and RSt spatial PCAs；
(6.3) PCA analyses are carried out respectively to the spaces PCSt and RSt again, compresses fault direction, obtains the spaces PCSt and RSt
The main fault direction in spaceWith
(7) normal data and another kind of fault data are chosen as total sample, repeats step (4)-(6), obtains such event
Hinder each coefficient matrix and load matrix of sample；
(8) step (7) is repeated until all coefficient matrixes of M class failures, load matrix are all found out；
(9) on-line fault monitoring：
New samples xnew(J × 1) is to P and PeDirection projection calculates T2StatisticWith SPE statistics SPEnew,
Itself and the control limit in step (2) are compared, if transfinited, illustrate to break down, conversely, not sending out then
Raw failure；
(10) on-line fault diagnosis：
(10.1) in the relevant fault message of new samples lieutenant colonel's positive bias.
Wherein,Indicate reconstruct according to m class fault models with the relevant fault message of biasing,Table
Show the data for correcting and biasing relevant fault message；
(10.2) existMiddle correction increases relevant fault message with data fluctuations；
Wherein,WithIndicate that increasing relevant failure with data fluctuations in the spaces PCS and RS believes respectively
Breath；WithData after the correction of a final proof in the spaces expression PCS and RS respectively；
(10.3) data after correction are projected into the spaces PCS and RS again, and calculates the T of corrected data2StatisticWith SPE statistics SPErec；
Wherein,Indicate the mean value of normal data score matrix；S indicates pair that the variance of normal data score matrix is constituted
Angular moment battle array；
(10.4) compareWithSPErecWith CtrSPEIf statistic all within control limits, illustrates this event
Barrier data belong to m classes, otherwise, choose another kind of fault type, step (10.1)-(10.3) are repeated, until finding number of faults
Until affiliated fault type；If the statistic of all classes is not controlling within limit entirely, illustrate the fault type for having new
It generates.
The beneficial effects of the invention are as follows：This method is directed to simultaneous two kinds of fault types in fault data --- biasing
Increase with data fluctuations, different method extraction fault messages is respectively adopted, the weight of the fault type is determined according to fault message
Structure model.This method targetedly extracts fault message, overcomes the shortcomings that single method is unable to fully excavate fault characteristic,
Out of order classification can be effectively diagnosed, the performance of on-line fault diagnosis is substantially increased, contributes to engineer quickly and accurately
Failure is repaired, to ensure that process safety and improve productivity effect.
Description of the drawings
Fig. 1 is the flow chart of the method for the present invention；
Fig. 2 is the monitoring result of failure #2 and the on-line fault diagnosis result figure of the method for the present invention；(a) it is failure #2
Monitoring result；(b) it is diagnostic results of the model #2 for failure #2；(c) it is diagnostic results of the model #5 for failure #2；(d)
It is diagnostic results of the model #8 for failure #2；(e) it is diagnostic results of the model #10 for failure #2；
Fig. 3 is the comparing result figure of single nested iterations Fei Sheer discriminant analysis methods and the method for the present invention；(a) it is embedding
Cover diagnostic result of the iteration Fei Sheer discriminant analysis methods for failure #2；(b) it is diagnosis of the method for the present invention for failure #2
As a result.
Specific implementation mode
Below in conjunction with the accompanying drawings and specific example, invention is further described in detail.
By taking Tennessee-Yi Siman processes as an example, Tennessee-Yi Siman processes are typical chemical process, the change of the process
Amount includes：41 measurands and 11 performance variables.Variable is shown in Table 1.
1 Tennessee-Yi Siman process variable tables of table
As shown in Figure 1, a kind of nested iterations Fei Sheer discriminant analyses proposed by the invention are mutually tied with opposite mutation analysis
The method for diagnosing faults of conjunction, includes the following steps：
Step 1：Obtain data：For a chemical process with J variable, sampling every time can obtain a 1 × J
Vector, obtained data can be described as a two-dimensional matrix X (K × J) after sampling K times.Normal data X is obtained respectivelyn(Nn
× J) and fault data Xf,m(Nf,m× J), wherein subscript n indicates that normal data, subscript f indicate that fault data, m indicate failure
Classification.In this example, the sampling period is three minutes, and 480 samples, mistake are all acquired for normal data and per class fault data
Cheng Bianliang 52.So the normal data sample chosen is Xn(480 × 52), a kind of fault data sample are Xf,m(480×
52).Tetra- kinds of failures of failure #2, #5, #8, #10 are acquired altogether, and failure-description is as shown in table 2.
2 Tennessee-Yi Siman procedure fault tables of table
| Serial number | Failure variable | Occurrence type |
| 2 | Ingredient B variations | Transition |
| 5 | Cooler cooling water velocity variations | Transition |
| 8 | ABC change of component in charging 4 | At random |
| 10 | Feed 4 temperature changes | At random |
Step 2：PCA analyses are carried out to normal data, pivot load P (J × R) and the residual error for obtaining principal component space PCS are empty
Between RS residual error load Pe(J×(J-R))。
Wherein, R is the principal component number of pivot load.It is more than 90% according to contribution rate of accumulative total, principal component space can be obtained
Principal component number R=31, residual error spatial PCA number are (J-R)=21.
To score matrix TnWith residual error EnCalculate T2With SPE statistics
Wherein,Indicate the mean value of normal data score matrix；S indicates pair that the variance of normal data score matrix is constituted
Angular moment battle array.
Due to T2Index obeys F distributions, and SPE indexs obey chi square distribution, establishes control limit respectively according to the distributionCtrSPE=8.99.
Step 3：Choose normal data sample Xn(480 × 52) and a kind of fault data sample Xf(480×52)。
Step 4：Using NeLFDA Algorithm Analysis and the relevant fault message of biasing：
(4.1) to XnAnd XfWith NeLFDA algorithms, the final coefficient matrix of fault data is obtainedWith it is negative
Carry matrixWherein, N is the discriminatory element number chosen.N can be by the partial information pair in the method for the present invention
The interpretability for biasing failure determines, here N=2.
Final coefficient matrixAnd load matrixIt can be obtained by following steps：
(4.1.1)XnAnd XfIt is referred to as Xi(480 × 52), subscript i indicate the classification of data.Total sampleBy Xi(i=1,2) it is arranged above and below.
(4.1.2) seeks making the maximum weight vectors of inter _ class relationship, that is, asks the maximum eigenvalue institute of scatter matrix between class
Corresponding feature vector w, and compress the information per class sample
T=Xw
pr T=(tTt)-1tTX (3)
Ei=Xi-Xiwpr T
Wherein, t indicates initial discriminatory element, prIndicate load vector, EiIt indicates per the class sample residual error unrelated with t.
(4.1.3) uses EiInstead of the X in (4.1.1)i, it is scattered between its number is equal to class that initial discriminatory element is extracted in repetition
Cloth order of matrix number r.The weight matrix W (J × r) that can obtain w compositions, by prThe load matrix P of compositionr(J×r).Initially sentence
Coefficient matrix R=W (the P of other ingredientr TW)-1, initial discriminatory element can find out by matrix coefficient
(4.1.4) is with TiInstead of XiRecalculate in class scatter matrix between scatter matrix and class, ask between making class scatter matrix and
Feature vector w in class corresponding to the ratio maximum of scatter matrix*：
WhereinWithIndicate that scatter matrix, λ indicate the spy more corresponding than value matrix between scatter matrix and class in class respectively
Value indicative.
(4.1.5) compression is per class sample information
Wherein, θ is weight vectors, pi *It is the load vector of every class, Ei *It is and ti *Unrelated residual error.
(4.1.6) uses Ei *Instead of the X in step (4.1.1)i, extract by step (4.1.2)-(4.1.5) and finally sentence again
Other ingredient ti *, until obtaining N=2 final discriminatory elements；Correspondingly, weight matrix Θ (J × N) and load matrix can be obtained
(4.1.7) seeks final coefficient matrix
So far, the final coefficient matrix of such failureAnd load matrixAll sought out
Come.
(4.2) fault message is reconstructed
Wherein,It is the final discriminatory element matrix of fault data；It indicates to bias relevant failure variation.
Step 5：The removal biasing failure from primary fault data, obtains new fault data for opposite mutation analysis.
Wherein, EfIt is the correction data corrected after biasing relevant failure variation, using the feature of normal data to school
Correction data is standardized, and the correction data after standardization is denoted as XRC,f。
Step 6：Relevant fault direction is increased using opposite mutation analysis Algorithm Analysis and data fluctuations：
(6.1) data preparation：With the X in step (5)RC,fAs the primary data of fault data in opposite mutation analysis,
And normal data still uses initial normal data Xn。
(6.2) there is the direction of opposite variation in extraction：
The space spaces PCSt and load P in the presence of opposite variation are found out in the PCS that step (2) obtainst,r(J×Rt,r)；
The space RSt and load P in the presence of opposite variation are found out in the spaces RSe,r(J×Re,r).Wherein, Rt,rAnd Re,rPCSt is indicated respectively
The number in space and RSt spatial PCAs.
(6.3) PCA analyses are carried out respectively to the spaces PCSt and RSt again, compresses fault direction, obtains the spaces PCSt and RSt
The main fault direction in spaceWith
Step 7：Normal data and another kind of fault data are chosen as total sample, step (4)-(6) is repeated, obtains such
Therefore each coefficient matrix and load matrix of sample.
Step 8：Step (7) is repeated until all coefficient matrixes of M class failures, load matrix are all found out.
Step 9：On-line fault monitoring：
New samples xnew(J × 1) is to P and PeDirection projection calculates T2StatisticWith SPE statistics SPEnew
Itself and the control limit in step (2) are compared, if transfinited, illustrate to break down, conversely, not sending out then
Raw failure.
Step 10：On-line fault diagnosis：
(10.1) in the relevant fault message of new samples lieutenant colonel's positive bias.
Wherein,Indicate reconstruct according to m class fault models with the relevant fault message of biasing,It indicates
Correct the data for biasing relevant fault message.
(10.2) existMiddle correction increases relevant fault message with data fluctuations.
Wherein,WithIndicate that increasing relevant failure with data fluctuations in the spaces PCS and RS believes respectively
Breath；WithData after the correction of a final proof in the spaces expression PCS and RS respectively.
(10.3) data after correction are projected into the spaces PCS and RS again, and calculates the T of corrected data2StatisticWith SPE statistics SPErec。
Wherein,Indicate the mean value of normal data score matrix；S indicates pair that the variance of normal data score matrix is constituted
Angular moment battle array.
(10.4) compareWithSPErecWith CtrSPEIf statistic all within control limits, illustrates this event
Barrier data belong to m classes, otherwise, choose another kind of fault type, step (10.1)-(10.3) are repeated, until finding number of faults
Until affiliated fault type；If the statistic of all classes is not controlling within limit entirely, illustrate the fault type for having new
It generates.
According to the reconstruction model that normal data and fault data are established, engineer new sampled data can be monitored with
Diagnosis, and take corresponding reclamation activities.When the reconstruction model established based on historical data can explain letter failure sample well
This fault message, i.e., the data after being corrected with the reconstruction model of such failure do not transfinite in principal component space and residual error space,
Then illustrate that new samples belong to such failure, then current failure is come out by Accurate Diagnosis.As seen from Figure 2, for failure #2,
Fault data could be only corrected in normal range (NR) with the model of failure #2, institute can just truly have with the inventive method
The troubleshooting of effect ground.In order to show the performance of fault diagnosis, we are respectively compared the method for the present invention and single nested iterations
Fei Sheer discriminant analyses and single opposite mutation analysis method.
First, for method more of the invention and single opposite mutation analysis method, we define two fingers
Mark --- leakage structure rate (MRR%) and paramnesia rate (FRR%).Leakage structure rate expression belongs to such failure but is not corrected to normal monitoring
Sample number in range accounts for the percentage of total number of samples；The expression of paramnesia rate is not belonging to such failure but by error correction to normal prison
Sample number in control range accounts for the percentage of total number of samples.
Comparison of 3 single-phase of table to mutation analysis method and the method paramnesia rate of the present invention
4 single-phase of table leaks mutation analysis method with the method for the present invention comparison of structure rate
As can be seen from the table, method of the invention leakage structure rate and paramnesia rate all decrease, and improve online failure and examine
Disconnected reliability, the method that performance is better than single opposite mutation analysis.
Over time, fault characteristic can drift about.In figure 3, the case where drifting about for fault characteristic, it is single
Nested iterations Fei Sheer discriminant analysis methods can occur mistake in troubleshooting, and the method for the present invention still can be correct
Effectively it is diagnosed to be fault type.On the whole, its on-line fault diagnosis performance of method of the invention has superiority, Ke Yibang
It helps engineer accurately and effectively to diagnose and repairs failure, ensure that the safety and reliability of production process.
It is every to be familiar with this field it should be understood that the present invention is not limited to the Tennessee-Yi Siman processes of examples detailed above
Technical staff can also make equivalent modifications or replacement under the premise of without prejudice to contest of the present invention, these equivalent modifications or replace
It changes and is all contained in the application claim limited range.
Claims (1)
1. the method for diagnosing faults that a kind of nested iterations Fei Sheer discriminant analyses are combined with opposite variation, which is characterized in that the party
Method includes the following steps：
(1) data are obtained：For a chemical process with J variable, sampling every time can obtain the vector of a 1 × J,
The data obtained after sampling K times can be described as a two-dimensional matrix X (K × J)；Normal data X is obtained respectivelyn(Nn× J) and therefore
Hinder data Xf,m(Nf,m× J), wherein subscript n indicates that normal data, subscript f indicate that fault data, m indicate fault category；
(2) PCA analyses are carried out to normal data, obtains the residual of the pivot load P (J × R) and residual error space RS of principal component space PCS
Difference load Pe(J × (J-R)), wherein R is the principal component number of pivot load；
To score matrix TnWith residual error EnCalculate T2Statistic and SPE statistics；
Wherein,Indicate the mean value of normal data score matrix；S indicate normal data score matrix variance constitute to angular moment
Battle array；
Due to T2Index obeys F distributions, and SPE indexs obey chi square distribution, establishes control limit respectively according to the distributionWith
CtrSPE；
(3) normal data sample X is chosenn(Nn× J) and a kind of fault data sample Xf(Nf×J)；
(4) it uses nested iterations Fei Sheer Discrimination Analysis Algorithms to analyze and biases relevant fault message：
(4.1) to XnAnd XfWith nested iterations Fei Sheer Discrimination Analysis Algorithms, the final coefficient matrix of fault data is obtainedAnd load matrixWherein, N is the discriminatory element number chosen；
(4.2) fault message is reconstructed
Wherein,It is the final discriminatory element matrix of fault data；It indicates to bias relevant failure variation；
(5) the removal biasing failure from primary fault data, obtains new fault data for opposite mutation analysis；
Wherein, EfIt is the correction data corrected after biasing relevant failure variation, using the feature of normal data to correction data
It is standardized, the correction data after standardization is denoted as XRC,f；
(6) relevant fault direction is increased with data fluctuations using opposite mutation analysis Algorithm Analysis：
(6.1) data preparation：With X in step (5)RC,fThe primary data as fault data in opposite mutation analysis, and it is normal
Data still use initial normal data Xn；
(6.2) there is the direction of opposite variation in extraction：
The space PCSt and load P in the presence of opposite variation are found out in the spaces PCS that step (2) obtainst,r(J×Rt,r)；In RS skies
Between find out space RSt and load P in the presence of opposite variatione,r((J-R)×Re,r)；Wherein, Rt,rAnd Re,rIndicate that PCSt is empty respectively
Between and RSt spatial PCAs number；
(6.3) PCA analyses are carried out respectively to the spaces PCSt and RSt again, compresses fault direction, obtains the spaces PCSt and the spaces RSt
Main fault directionWith
(7) normal data and another kind of fault data are chosen as total sample, step (4)-(6) is repeated, obtains such failure sample
This each coefficient matrix and load matrix；
(8) step (7) is repeated until all coefficient matrixes of M class failures, load matrix are all found out；
(9) on-line fault monitoring：
New samples xnew(J × 1) is to P and PeDirection projection calculates T2StatisticWith SPE statistics SPEnew,
Itself and the control limit in step (2) are compared, if transfinited, illustrate to break down, conversely, then that event does not occur
Barrier；
(10) on-line fault diagnosis：
(10.1) in the relevant fault message of new samples lieutenant colonel's positive bias；
Wherein,Indicate reconstruct according to m class fault models with the relevant fault message of biasing,Indicate correction
The data of the relevant fault message of biasing；
(10.2) existMiddle correction increases relevant fault message with data fluctuations；
Wherein,WithIt indicates to increase relevant fault message with data fluctuations in the spaces PCS and RS respectively；WithData after the correction of a final proof in the spaces expression PCS and RS respectively；
(10.3) data after correction are projected into the spaces PCS and RS again, and calculates the T of corrected data2StatisticWith
SPE statistics SPErec；
Wherein,Indicate the mean value of normal data score matrix；S indicate normal data score matrix variance constitute to angular moment
Battle array；
(10.4) compareWithSPErecWith CtrSPEIf statistic all within control limits, illustrates this number of faults
According to m classes are belonged to, otherwise, another kind of fault type is chosen, step (10.1)-(10.3) are repeated, until finding fault data institute
Until the fault type of category；If the statistic of all classes is not controlling within limit entirely, illustrate there is new fault type to generate.
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| US5544077A (en) * | 1994-01-19 | 1996-08-06 | International Business Machines Corporation | High availability data processing system and method using finite state machines |
| CN101169623A (en) * | 2007-11-22 | 2008-04-30 | 东北大学 | Non-linear procedure fault identification method based on kernel principal component analysis contribution plot |
| CN104536439A (en) * | 2015-01-20 | 2015-04-22 | 浙江大学 | Fault diagnosis method based on nested iterative Fisher discriminant analysis |
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| US5544077A (en) * | 1994-01-19 | 1996-08-06 | International Business Machines Corporation | High availability data processing system and method using finite state machines |
| CN101169623A (en) * | 2007-11-22 | 2008-04-30 | 东北大学 | Non-linear procedure fault identification method based on kernel principal component analysis contribution plot |
| CN104536439A (en) * | 2015-01-20 | 2015-04-22 | 浙江大学 | Fault diagnosis method based on nested iterative Fisher discriminant analysis |
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