CN109143995A - A kind of fine method for monitoring operation states of closed-loop system sufficiently decomposed based on the related slow feature of quality - Google Patents
A kind of fine method for monitoring operation states of closed-loop system sufficiently decomposed based on the related slow feature of quality Download PDFInfo
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Abstract
The invention discloses a kind of fine method for monitoring operation states of closed-loop system sufficiently decomposed based on the related slow feature of quality.This method passes through the static coherence of extraction process variable and quality variable, closed loop large scale process variable is resolved into two spaces related to quality and unrelated with quality, and the static state of extraction process and multidate information model it in each space, Static State Index and dynamic indicator are established in two spaces respectively, the fault detection cooperateed with for two spaces.The monitoring changed to closed-loop system dynamic abnormal situation and operating condition not only may be implemented in this method, the really generation of failure effectively in identification closed loop failure system, and by carrying out quality correlation down to the variable space, the correlation monitoring to closed-loop system product quality can be further realized, judgement is out of order and abnormal specific generation is in which space, if influences product quality.
Description
Technical field
The invention belongs to industrial system process monitoring fields, especially for the relevant fine fortune of closed-loop system product quality
Row state monitoring method.
Background technique
With the development of science and technology, the scale of modern industry system and complexity are all increasingly improving.Complicated big system
There is exception in unified denier, may all bring great property loss and casualties.Pass through the operation shape daily to system equipment
State monitoring, detects unit exception in advance, repairs equipment timely, not only extended the time between overhauls(TBO), maintenance cost
It substantially reduces, and maintenance is more targeted, service life of equipment is extended, and the generation of serious safety accident is avoided.Cause
This, in order to guarantee system in the safety and reliability of operation, the running abnormal conditions of timely discovery system are simultaneously handled,
The security risk in production is reduced, improves life of equipment, it is quite necessary to be supervised in real time to system using effective means
Survey and fault detection.Simultaneously with the development of sensing technology, data are obtained in industry spot and are become increasingly easy, process data
In contained a large amount of procedural information, status monitoring and malfunction monitoring based on data are increasingly becoming the hot spot of research.
In the past few decades in the time, process monitoring and fault detection technique have obtained extensive research and development, largely
Research achievement is delivered, and forefathers have made corresponding research to the fault detection and diagnosis based on data.Principal component point
It analyses (PCA), the Multielement statistical analysis methods such as offset minimum binary (PLS) and Fei Sheer discriminant analysis (FDA) have been widely used
In the process monitoring field based on data.However existing most process monitoring and fault detection method are both for open loop
System design, do not account for the influence of closed loop control laws.But in real industrial system, to meet stability, fast
Speed, accuracy requirement reach actual production target and guarantee that product quality maintains reasonable level, need to apply system and close
Ring feedback control, a large amount of closed-loop control rules, such as PID control, optimum control have a large amount of application in actual production system.
The introducing of closed-loop control rule, so that relationship changes between input/output relation, system variable, and closed loop control laws make
The system of obtaining has more robustness for external disturbance, brought to influence to exist when so that failure being in early stage or smaller amplitude
It is submerged in system, can not be diagnosed in time by residual signals, cause to report by mistake and fail to report.These diagnosis studied before limiting
Method must be applied in practice, it is therefore necessary to study system state monitoring and fault detection method, under the premise of closed loop with solution
Certainly actual production security problem.It is extremely limited with fault detection research achievement currently based on the closed-loop system monitoring of data,
Also in the preliminary exploratory stage, need further to be furtherd investigate.
The present invention is directed to the process monitoring and fault detection of closed-loop system, and goes out from the angle of industrial system product quality
Hair proposes a kind of slow signature analysis of combination fine monitoring running state related to the closed-loop system quality of canonical correlation analysis
Algorithm.This method passes through the correlation of extraction process data and product quality variable, and process data space is filled in realization
Point decompose, be divided into the two spaces closely related and unrelated with quality with quality, and establish model to the dynamics of two spaces and
Static information is monitored, and this method may be implemented to become closed-loop system operating condition by the monitoring respectively to dynamic and static information
Change the differentiation occurred with real failure, and abnormal specific generation can be identified at which by the relevant spatial decomposition of quality
Whether a space influences product quality, improves to the accurate of system state monitoring, up to the present, there is not yet with the present invention
Relevant research report.
Summary of the invention
It is an object of the invention to detect for industrial closed-loop system procedure fault, and process product quality is paid close attention to, mentioned
A kind of fine method for monitoring operation states of closed-loop system sufficiently decomposed based on the related slow feature of quality is supplied.
The purpose of the present invention is what is be achieved through the following technical solutions: a kind of sufficiently to be decomposed based on the related slow feature of quality
The fine method for monitoring operation states of closed-loop system comprising the steps of:
(1) selection system normal processes measurement data and product quality data of interest: for an industrial closed-loop system
System, if its operational process includes m measurable process variable, the available 1 × m of t moment sampling vector x (t)=
(x1(t),x2(t),…,xm(t)) the data matrix X of process measurement variable under normal processes, is obtained after n times sampleM=(x
(t),x(t+1),…,x(t+N))T, select k product quality variables of interest to obtain after n times sample according to industrial process
To the data matrix Y of quality variablek(∈N*k)。
(2) data normalization: respectively to process data matrix XMWith quality variable data matrix YkThe equal of the column is subtracted by column
Value, and be standardized divided by the column standard deviation.
(3) slow signature analysis modeling is carried out to the process data matrix X after (2) Plays, obtains initial slow feature.
Here consider linear slow signature analysis, each slow feature can be regarded as the linear combination of process variable, institute
From process data matrix X to slow feature S (t)=[s1(t),s2(t),…,sm(t)] mapping is expressed as:
S (t)=W × X (1)
Wherein W=[w1,w2,…,wm]TIt is that SFA needs the coefficient matrix that optimizes, m is the number of slow feature, and can be surveyed
Cheng Bianliang is identical.The problem of solving slow feature is so that obtaining slow changing features rate Δ (si) minimum, it solves slow feature and asks
Topic, which is converted to, solves following generalized eigenvalue problem:
AW=BW Ω (2)
Wherein A indicates the first-order difference matrix of the process data matrix X of inputCovariance matrix, be expressed asCovariance matrix < XX of B expression X matrixT>t, corresponding, W=[w1,w2,…,wm]TIt is constituted for feature vector
Eigenmatrix, the variable number of m process input data；Ω is the diagonal matrix that corresponding generalized eigenvalue is constituted.Utilize two steps surprise
Different value decomposes (SVD) to solve slow feature, and detailed process is as follows:
(3.1) albefaction is carried out to matrix X first, i.e., to B matrix singular value decomposition.The covariance matrix of matrix X can table
It is shown as < XXT>t, singular value decomposition (SVD) is carried out to it to be obtained:
<XXT>t=U Λ UT (3)
Wherein U is covariance matrix < XXT>tFeature vector composition matrix, Λ is a diagonal matrix, each
Element on a diagonal line is exactly a characteristic value, then data matrix being obtained after albefaction can be expressed as:
Z=Λ-1/2UTX=QX (4)
Data matrix Z obtains covariance satisfaction < ZZ after albefactionT>t=Q < XXT>tQT。
(3.2) target for solving linear SFA problem, which is equal to, finds a matrix P=WQ-1So that S=P*Z, and make
S satisfaction < SST>t=P < ZZT>tPT=I.
Matrix P can pass through the difference matrix to ZCovariance matrixSingular value decomposition is carried out to acquire:
It is possible thereby to which initial slow feature coefficient matrix is calculated are as follows:
W=P Λ-1/2UT (6)
Initial slow feature are as follows:
S=WX=P Λ-1/2UTX (7)
(4) the initial slow feature S and quality variable Y obtained in (7) is utilizedkCanonical correlation analysis (CCA) is carried out to obtain
Canonical variable, detailed process is as follows:
For initial slow feature S and quality variable Yk, u is defined, two variables of v, wherein u, v are begin slow feature S and quality
Variable YkLinear combination it is as follows:
Wherein Ψ1=[a1,a2,…,am]T, Ψ2=[b1,b2,…,bk]T.Canonical variable u is solved, v is just to solve for coefficient
Matrix Ψ1, Ψ2So that the Pearson coefficient between u, v is maximum.It is converted to following optimization problem solving:
Wherein corr (u, v) indicates u, the Pearson coefficient between v, and cov (u, v) is u, the covariance of v, Var (u) and
Var (v) is respectively u, the variance of v.This problem is solved by construction Lagrangian equation, solves corresponding maximum Pearson
Two canonical variables u, v of coefficient.
Similarly, continue to solve the canonical variable u for finding the corresponding second largest Pearson coefficient on this basis2And v2:
N can be sought altogether to canonical variable pair, and n=min (m, k), corresponding Pearson coefficient is sequentially reduced, i.e. table
Show that the correlation between canonical variable is smaller and smaller.P corresponding Pearson coefficient before being chosen according to obtained Pearson coefficient
Biggish canonical correlation variable pair casts out remaining corresponding Pearson coefficient lesser (n-p) a canonical correlation variable pair.It utilizes
Preceding p canonical correlation variable pair utilizes the canonical variable u for acquiring the linear combination about slow feature Si(i=1,2 ..., p),
It is combined into new matrix Uy=[u1,u2,…,up], wherein ui(i=1,2 ..., p) corresponding Pearson coefficient is sequentially reduced,
And uiBetween it is mutually orthogonal.
(5) by matrix U obtained in (4)yUtilize the space offset minimum binary expression re-formation process data X, reconstruction formula
It is as follows:
EoFor reconstructed residual, i.e., and UyUnrelated part.Thus the space X can be divided into and YkRelevant part UyWith with Yk
Unrelated part XoThe quality in the space X is sufficiently decomposed in two parts, realization.
X=Uy+Xo (12)
(6) again to XoSlow signature analysis is carried out, slow feature, and the sequence arrangement by pace of change from small to large are obtained:
So=WoXo=[So1,So2,…,Som] (13)
XoIt is that raw process data subtracts quality variable YkRelevant portion data are obtained, so the slow feature obtained is not
It is all significant, selection satisfactionG slow features, E { } is that expectation computing is asked to accord with, and I is unit matrix；
According to the variation speed degree of obtained slow feature, the slower feature of q pace of change forms matrix Sod=[so1,
so2,…,soq], it is left the faster feature of (g-q) a pace of change and forms another matrix: Soe=[so(q+1),so(q+2),…,
sog]。
(7) static and dynamic indicator system is established.
In view of for actual industrial system, product quality variable of interest may be right for more than one or two
In two kinds of situations, establishes different index systems and is monitored to system
(7.1) for single quality variable the case where
Due to quality variable only one, so the canonical variable extracted also only one, so for quality
Relevant space directly utilizes canonical variable UyIt is monitored.Wherein Static State Index are as follows:
Dynamic indicator are as follows:
It is monitored for moving the method that Static State Index is all made of shewhart control figure, for Static State Index:
Wherein UTH1ForUpper control limit, LTH1ForLower control limit, μ1ForMean value,For its standard
Difference, b1For control figure thresholding width.For dynamic indicator:
Wherein UTH2ForUpper control limit, LTH2ForLower control limit, μ2ForMean value,For its standard
Difference, b2For control figure thresholding width.
For the space unrelated with quality variable, Static State Index are as follows:
Dynamic indicator are as follows:
Indicate SodThe diagonal matrix that is constituted of covariance matrix characteristic value it is inverse,Indicate SoeCovariance matrix
The diagonal matrix that characteristic value is constituted it is inverse, the control of index limit is obtained under 0.95 confidence level by kernel density function,
Respectively RespectivelyThe diagonal matrix that the characteristic value of covariance matrix is constituted it is inverse,
Control limit corresponding to two dynamic indicators is calculated under 0.95 confidence level by kernel density function, respectively
(7.2) for the case where there are two the above quality variables
Canonical variable obtained is not unique, so needing Counting statistics amount come to dividing UyIt is monitored, Static State Index
It calculates as follows:
WhereinIndicate UyThe diagonal matrix that constitutes of the corresponding characteristic value of covariance matrix it is inverse, the control limit of index is logical
Cross kernel density function is respectively under 0.95 confidence levelTo UyFirst difference is carried out to obtainDynamically refer to
It is designated as:
ForThe diagonal matrix that the characteristic value of covariance matrix is constituted it is inverse,It is right for three of them dynamic indicator
The control limit answered, is calculated under 0.95 confidence level by kernel density function.The finger in the space unrelated with quality variable
Mark calculation in step 7.1 the case where single quality variable it is identical.
(8) process dynamics of closed-loop system and steady-state operating conditions can be supervised respectively using dynamic Static State Index
It surveys.
For space relevant to quality variable:
1) Static State IndexIt transfinites, dynamic indicatorIt is following that control limit is restored to after transfiniting again, is shown and quality variable phase
The space of pass is adjusted by control action reaches a new operating condition, and quality variable is restored to setting water after there are brief fluctuations again
It is flat；
2) Static State IndexIt transfinites, dynamic indicatorAlso it transfinites always, shows that event occurs in space relevant to quality variable
Barrier, controller adjust failure, and product quality is destroyed；
3) Static State IndexDynamic indicatorIt does not transfinite, then shows that space relevant to quality variable is in good
Operating status, product quality maintain near setting value.
For the space unrelated with quality variable:
1) the unrelated Static State Index of qualityWith dynamic indicatorIt is of short duration transfinite after return to control limit with
Under, show of short duration exception occur in the space unrelated with quality variable, after the adjusting that is acted on by closed-loop control, the space is again extensive
It is multiple to occur to run under preceding identical steady state condition to abnormal；
2) with the Static State Index of the quality independent spaceIt transfinites always, dynamic indicatorIt is of short duration transfinite after
It is following to return to control limit, shows that of short duration exception occurs in the space unrelated with quality variable, but passes through the tune of closed-loop control effect
The space is saved to be restored to before an abnormal generation and run under different steady state condition, static properties has occurred and that change, but
It is that dynamic property still remains normal；
3) the unrelated Static State Index of qualityWith dynamic indicatorIt transfinites, shows that event occurs in the space
Barrier, and the space correlation controller adjusts failure, static and dynamic performance is all destroyed；
4) the unrelated Static State Index of qualityWith dynamic indicatorIt remains normal, shows that the space is protected
Hold a good operating status.
The invention has the benefit that the present invention industrial closed-loop system can be divided into it is related to product quality and with production
The unrelated two spaces of quality not only can effectively distinguish failure and specifically occur in which space, and then judge that failure is
No influence product quality, and the monitoring by moving static information to system, can efficiently identify operating condition variation and really
The fine monitoring running state of closed-loop system is realized in the differentiation of failure.
Detailed description of the invention
Fig. 1 is flow chart of the invention；
Fig. 2 is the closed loop TE process flow chart of this method concrete application；
Fig. 3 is the failure classes display diagram that TE process provides；
Fig. 4 is that this method applies Static State Index monitoring result in TE procedure fault 1；
Fig. 5 is that this method applies dynamic indicator monitoring result in TE procedure fault 1；
Fig. 6 is corresponding product quality A and product quality A comparison diagram under normal circumstances in the case of TE procedure fault 1；
Fig. 7 is corresponding product quality B and product quality B comparison diagram under normal circumstances in the case of TE procedure fault 1；
Fig. 8 is corresponding product quality C and product quality C comparison diagram under normal circumstances in the case of TE procedure fault 1；
Fig. 9 is that this method applies Static State Index monitoring result in TE procedure fault 4；
Figure 10 is that this method applies dynamic indicator monitoring result in TE procedure fault 4；
Figure 11 is corresponding product quality A and product quality A comparison diagram under normal circumstances in the case of TE procedure fault 4；
Figure 12 is corresponding product quality A and product quality A comparison diagram under normal circumstances in the case of TE procedure fault 4；
Figure 13 is corresponding product quality A and product quality A comparison diagram under normal circumstances in the case of TE procedure fault 4.
Specific embodiment
With reference to the accompanying drawing and specific example, invention is further described in detail.
Tenessee Eastman (TE) process is to be based on Tenessee Eastman chemical company reality by Downs et al.
The analogue system that border chemical production process proposes, in the research in process system engineering field, TE process is one common
Typical problem (Benchmark problem), preferably simulate many typical special of actual complex industrial process systems
Sign, therefore be widely used in the research of control, optimization, process monitoring and fault diagnosis as examples of simulation.In this research,
Using the closed loop TE process of the Lyman and Georgakis full factory's control strategy proposed.TE process includes four kinds of gas raw materials
A, C, D and E, two kinds of liquid products G and H also include by-product F and inert gas B.
TE process includes five formants: reactor, condenser, compressor, separator and stripper, as shown in Fig. 2,
It altogether include 41 measurands and 12 control variables.Such as Fig. 3, TE process provides 21 failure classes, available.
As shown in Figure 1, the present invention the following steps are included:
(1) data select: process measurement data XMEAS (1-22) and XMV (1-11) when selection TE process operates normally
Totally 33 variables product volume variable Y of interest as three variables of process input variable X, XMEAS (29-31) samples every time
Available vector x (t)=(x1(t),x2(t),…,xm(t)) dimension is 1 × m, it is obtained after n times sample
Journey measurand X=(x (t), x (t+1) ..., x (t+N))T, product quality variable obtains quality variable after n times sample
Data matrix Yk(∈N*k)。
(2) data normalization: respectively to process data matrix X and quality variable data matrix YkBy column go mean value and divided by
Standard deviation is standardized.
(3) slow signature analysis modeling is carried out to the process data matrix X after (2) Plays, obtains initial slow feature.
Here consider linear slow signature analysis, each slow feature can be regarded as the linear combination of process variable, institute
From process data matrix to slow feature S (t)=[s1(t),s2(t),…,sm(t)] mapping can be expressed as:
S (t)=W × X
Wherein W=[w1,w2,…,wm]TIt is the coefficient matrix that SFA needs to optimize, m is the number of slow feature, is become with process
It is identical to measure number.The problem of solving slow feature is so that obtaining slow changing features rate Δ (si) minimum, solve slow Characteristic Problem
It can be converted to and solve following generalized eigenvalue problem:
AW=BW Ω
Wherein A indicates the first-order difference matrix of input data XCovariance matrix, can be expressed asB table
Show covariance matrix < XX of X matrixT>t, W=[w1,w2,…,wm]TFor the eigenmatrix that feature vector is constituted, m is process input
The variable number of data, Ω are the diagonal matrix that corresponding generalized eigenvalue is constituted, also.It is unusual equally to can use two steps
Value decomposes (SVD) to solve slow feature, and detailed process is as follows:
(3.1) albefaction is carried out to matrix X first, i.e., to B matrix singular value decomposition.The covariance matrix of matrix X can table
It is shown as < XXT>t, singular value decomposition (SVD) is carried out to it to be obtained:
<XXT>t=U Λ UT
Wherein U is covariance matrix < XXT>tFeature vector composition matrix, Λ is a diagonal matrix, each
Element on a diagonal line is exactly a characteristic value, then data matrix being obtained after albefaction can be expressed as:
Z=Λ-1/2UTX=QX
Data matrix Z obtains covariance satisfaction < ZZ after albefactionT>t=Q < XXT>tQT。
(4.2) target for solving linear SFA problem, which is equal to, finds a matrix P=WQ-1So that S=P*Z, and make
S satisfaction < SST>t=P < ZZT>tPT=I.
Matrix P can pass through the difference matrix to ZCovariance matrixSingular value decomposition is carried out to acquire:
It is possible thereby to which initial slow feature coefficient matrix is calculated are as follows:
W=P Λ-1/2UT
Initial slow feature are as follows:
S=WX=P Λ-1/2UTX
(5) the initial slow feature S and quality variable Y obtained in step (4) is utilizedkIt carries out canonical correlation analysis (CCA)
Canonical variable is obtained, detailed process is as follows:
(5.1) for initial slow feature S and quality variable Yk, u is defined, two variables of v, wherein u, v are the slow feature S that begins
With quality variable YkLinear combination it is as follows:
Canonical variable u is solved, v is just to solve for coefficient matrices A, and B makes u, and the Pearson coefficient between v is maximum.It can be converted to
Following optimization problem solving:
Maximizeu2
Wherein corr (u, v) indicates that Pearson coefficient, cov (u, v) are u, and the covariance of v, Var (u) and Var (v) are respectively
The variance of u, v.This problem can be solved by construction Lagrangian equation, solve two of corresponding maximum Pearson coefficient
Canonical variable u, v.
(5.1) similarly, can continue to solve the canonical variable u for finding the corresponding second largest Pearson coefficient on this basis2
And v2:
N can be sought altogether to canonical variable pair, and n=min (m, k), corresponding Pearson coefficient is sequentially reduced, i.e. allusion quotation
Correlation between type variable is smaller and smaller.Preceding p correspondence is generally chosen most according to obtained Pearson coefficient as needed
The canonical correlation variable pair of big related coefficient casts out (n-p) a canonical correlation variable of remaining corresponding Pearson coefficient very little
It is right.Using preceding p canonical correlation variable pair, new matrix is combined into using the canonical variable of the linear combination of the slow feature S of correspondence
Uy=[u1,u2,…,up], ui(i=1,2 ..., p) is the canonical variable acquired, and corresponding Pearson coefficient is sequentially reduced, and
And uiBetween it is irrelevant.
(6) by canonical variable U obtained in (5)yX is returned using offset minimum binary expression re-formationdSpace, reconstruction formula is such as
Under:
X=UyPT+E
PT=(Uy TUy)-1Uy TXd
And the space X is divided into and YkRelevant part UyWith with YkUnrelated part XoTwo parts are realized to the space X
Quality is sufficiently decomposed.
X=Uy+Xo
(7) again to XoSlow signature analysis is carried out, slow feature, and the sequence arrangement by pace of change from small to large are obtained:
So=WoXo=[So1,So2,…,Som]
XoIt is that raw process data subtracts quality variable YkRelevant portion data are obtained, so the slow feature obtained is not
It is all significant, selection satisfactionG slow features.And according to the variation speed journey of obtained slow feature
Degree chooses the slower feature of q pace of change and forms Sod=[so1,so2,…,soq], it is special faster to be left (g-q) a pace of change
Levy Soe=[so(q+1),so(q+2),…,sog]。
(8) static and dynamic indicator system is established.
In view of for actual industrial system, product quality variable of interest may be one or more, for two
Kind situation, establishes different index systems and is monitored to system
(8.1) for single quality variable the case where
Due to quality variable only one, so the canonical variable extracted also only one, so for quality
Relevant space directly utilizes canonical variable UyIt is monitored.Wherein Static State Index are as follows:
Dynamic indicator are as follows:
It is monitored for moving the method that Static State Index is all made of shewhart control figure, by taking Static State Index as an example:
Wherein UTH isUpper control limit, LTH is lower control limit, and μ isMean value,For its standard deviation, b is
Control figure thresholding width.
For the space unrelated with quality variable, Static State Index are as follows:
Dynamic indicator are as follows:
Indicate SodThe diagonal matrix that is constituted of covariance matrix characteristic value it is inverse,Indicate SoeCovariance matrix
The diagonal matrix that characteristic value is constituted it is inverse, the control of index limit is divided under 0.95 confidence level by kernel density function
It is not RespectivelyThe diagonal matrix that the characteristic value of covariance matrix is constituted it is inverse,The limit of control corresponding to respectively two dynamic indicators, through kernel density function under 0.95 confidence level
It is calculated.
(8.2) for there is the case where multiple quality variables
Canonical variable obtained is not unique, so needing Counting statistics amount come to dividing UyIt is monitored, Static State Index
It calculates as follows:
WhereinIndicate UyThe diagonal matrix that constitutes of the corresponding characteristic value of covariance matrix it is inverse, the control limit of index is equal
It is respectively under 0.95 confidence level by kernel density functionTo UyFirst difference is carried out to obtainDynamically
Index are as follows:
ForThe diagonal matrix that the characteristic value of covariance matrix is constituted it is inverse,It is right for three of them dynamic indicator
The control limit answered, is calculated under 0.95 confidence level by kernel density function,
The index calculation in the space unrelated with quality variable is same as above.
The process dynamics of closed-loop system and steady-state operating conditions can be monitored respectively using dynamic Static State Index.It is right
In space relevant to quality variable:
1) Static State IndexIt transfinites, dynamic indicatorIt is following that control limit is restored to after transfiniting again, is shown and quality variable phase
The space of pass is adjusted by control action reaches a new operating condition, and quality variable is restored to setting water after there are brief fluctuations again
It is flat；
2) Static State IndexIt transfinites, dynamic indicatorAlso it transfinites always, shows that event occurs in space relevant to quality variable
Barrier, controller adjust failure, and product quality is destroyed；
3) Static State IndexDynamic indicatorIt does not transfinite, then shows that space relevant to quality variable is in good
Operating status, product quality maintenance are reset near value.
For the space unrelated with quality variable:
1) the unrelated Static State Index of qualityWith dynamic indicatorIt is of short duration transfinite after return to control limit with
Under, show of short duration exception occur in the space unrelated with quality variable, after the adjusting that is acted on by closed-loop control, the space is again extensive
It is multiple to occur to run under preceding identical steady state condition to abnormal；
2) with the Static State Index of the quality independent spaceIt transfinites always, dynamic indicatorIt is of short duration transfinite after
It is following to return to control limit, shows that of short duration exception occurs in the space unrelated with quality variable, but passes through the tune of closed-loop control effect
The space is saved to be restored to before an abnormal generation and run under different steady state condition, static properties has occurred and that change, but
It is that dynamic property still remains normal；
3) the unrelated Static State Index of qualityWith dynamic indicatorIt transfinites, shows that event occurs in the space
Barrier, and the space correlation controller adjusts failure, static and dynamic performance is all destroyed；
4) the unrelated Static State Index of qualityWith dynamic indicatorIt remains normal, shows that the space is protected
Hold a good operating status.
Two spaces are mutually indepedent, and corresponding dynamic Static State Index indicates respectively the variation of the dynamic static information in respective space,
It whether can help us judge failure and abnormal specific generation in which space, will affect product quality.
Fig. 4,5 this method are used for the monitoring result of 1 data of TE procedure fault, and Fig. 6,7,8 are selected three product matter
Quantitative change amount changes under normal circumstances and the variation comparison at failure 1.According to figure as can be seen that related to product quality y
Space, Static State Index and dynamic indicator, which transfinite, is restored to control limit hereinafter, illustrating the space by failure after a period of time
Of short duration interference, by controller adjust a period of time after Static and dynamic performance be restored to initial level, product quality is also restored
To initial set value；The space unrelated with product quality, Static State Index transfinite always, but tend to be steady, and dynamic indicator transfinites one
Control limit is restored to after the section time hereinafter, illustrating to be restored to a new steady state condition by adjusting after the space is interfered
Under.Fig. 9,10 are monitoring result of this method for 4 data of TE procedure fault, as can be seen from the figure related to product quality y
The quiet dynamic indicator in space do not transfinite, illustrate that the space motion is normal, product quality does not generate variation, from Figure 11,12,13
Each product quality is compared with the variation in the case of failure four it is also seen that the judgement of monitoring result is correct under normal circumstances
's；In the space unrelated with product quality, Static State Index transfinites always, dynamic indicator is of short duration transfinite after be restored to control limit with
Under, illustrate that failure occurs in the closed loop unrelated with product quality, a new stable state work is reached by the adjusting of controller again
Condition.Traditional slow signature analysis can only distinguish work condition abnormality and failure occurs, and can further discriminate between failure by this method
The space that is occurred and whether influence product quality.
Claims (1)
1. a kind of fine method for monitoring operation states of closed-loop system sufficiently decomposed based on the related slow feature of quality, feature are existed
In comprising the steps of:
(1) selection system normal processes measurement data and product quality data of interest: for an industrial closed-loop system, if
Its operational process includes m measurable process variable, samples vector x (t)=(x of an available 1 × m in t moment1(t),x2
(t),…,xm(t)) the data matrix X of process measurement variable under normal processes, is obtained after n times sampleM=(x (t), x (t+
1),…,x(t+N))T, k product quality variables of interest are selected according to industrial process, after n times sample, obtain quality change
The data matrix Y of amountk(∈N*k)。
(2) data normalization: respectively to process data matrix XMWith quality variable data matrix YkThe mean value of the column is subtracted by column,
And it is standardized divided by the column standard deviation.
(3) slow signature analysis modeling is carried out to the process data matrix X after (2) Plays, obtains initial slow feature.
Here considering linear slow signature analysis, each slow feature can be regarded as the linear combination of process variable, so from
Process data matrix X to slow feature S (t)=[s1(t),s2(t),…,sm(t)] mapping is expressed as:
S (t)=W × X (1)
Wherein W=[w1,w2,…,wm]TIt is the coefficient matrix that SFA needs to optimize, m is the number of slow feature, with measurable process variable
It is identical.The problem of solving slow feature is so that obtaining slow changing features rate Δ (si) minimum, solve slow Characteristic Problem conversion
At the following generalized eigenvalue problem of solution:
AW=BW Ω (2)
Wherein A indicates the first-order difference matrix of the process data matrix X of inputCovariance matrix, be expressed asB
Indicate covariance matrix < XX of X matrixT>t, corresponding, W=[w1,w2,…,wm]TFor the eigenmatrix that feature vector is constituted, m
The variable number of process input data；Ω is the diagonal matrix that corresponding generalized eigenvalue is constituted.Utilize two step singular value decompositions
(SVD) slow feature is solved, detailed process is as follows:
(3.1) albefaction is carried out to matrix X first, i.e., to B matrix singular value decomposition.The covariance matrix of matrix X can be expressed as <
XXT>t, singular value decomposition (SVD) is carried out to it to be obtained:
<XXT>t=U Λ UT (3)
Wherein U is covariance matrix < XXT>tFeature vector composition matrix, Λ is a diagonal matrix, each of which diagonal line
On element be exactly a characteristic value, then after albefaction data matrix can be expressed as:
Z=Λ-1/2UTX=QX (4)
Data matrix Z obtains covariance satisfaction < ZZ after albefactionT>t=Q < XXT>tQT。
(3.2) target for solving linear SFA problem, which is equal to, finds a matrix P=WQ-1So that S=P*Z, and make S full
Foot < SST>t=P < ZZT>tPT=I.
Matrix P can pass through the difference matrix to ZCovariance matrixSingular value decomposition is carried out to acquire:
It is possible thereby to which initial slow feature coefficient matrix is calculated are as follows:
W=P Λ-1/2UT (6)
Initial slow feature are as follows:
S=WX=P Λ-1/2UTX (7)
(4) the initial slow feature S and quality variable Y obtained in (7) is utilizedkIt carries out canonical correlation analysis (CCA) and obtains typical become
Amount, detailed process is as follows:
For initial slow feature S and quality variable Yk, u is defined, two variables of v, wherein u, v are the slow feature S and quality variable Y that beginsk
Linear combination it is as follows:
Wherein Ψ1=[a1,a2,…,am]T, Ψ2=[b1,b2,…,bk]T.Canonical variable u is solved, v is just to solve for coefficient matrix
Ψ1, Ψ2So that the Pearson coefficient between u, v is maximum.It is converted to following optimization problem solving:
Subjectto:
Wherein corr (u, v) indicates that u, the Pearson coefficient between v, cov (u, v) are u, the covariance of v, Var (u) and Var
It (v) is respectively u, the variance of v.This problem is solved by construction Lagrangian equation, solves corresponding maximum Pearson coefficient
Two canonical variables u, v.
Similarly, continue to solve the canonical variable u for finding the corresponding second largest Pearson coefficient on this basis2And v2:
N can be sought altogether to canonical variable pair, and n=min (m, k), corresponding Pearson coefficient is sequentially reduced, i.e. expression allusion quotation
Correlation between type variable is smaller and smaller.P corresponding Pearson coefficient is larger before being chosen according to obtained Pearson coefficient
Canonical correlation variable pair, cast out remaining corresponding Pearson coefficient lesser (n-p) a canonical correlation variable pair.Utilize preceding p
Canonical correlation variable pair utilizes the canonical variable u for acquiring the linear combination about slow feature Si(i=1,2 ..., p), combination
The matrix U of Cheng Xiny=[u1,u2,…,up], wherein ui(i=1,2 ..., p) corresponding Pearson coefficient is sequentially reduced, and ui
Between it is mutually orthogonal.
(5) by matrix U obtained in (4)yUsing the space offset minimum binary expression re-formation process data X, reconstruction formula is as follows:
EoFor reconstructed residual, i.e., and UyUnrelated part.Thus the space X can be divided into and YkRelevant part UyWith with YkUnrelated
Part XoThe quality in the space X is sufficiently decomposed in two parts, realization.
X=Uy+Xo (12)
(6) again to XoSlow signature analysis is carried out, slow feature, and the sequence arrangement by pace of change from small to large are obtained:
So=WoXo=[So1,So2,…,Som] (13)
XoIt is that raw process data subtracts quality variable YkRelevant portion data are obtained, so the slow feature obtained is not complete
Portion is all significant, chooses and meetsG slow features, E { } is that expectation computing is asked to accord with, and I is unit matrix；
According to the variation speed degree of obtained slow feature, the slower feature of q pace of change forms matrix Sod=[so1,so2,…,
soq], it is left the faster feature of (g-q) a pace of change and forms another matrix: Soe=[so(q+1),so(q+2),…,sog]。
(7) static and dynamic indicator system is established.
In view of for actual industrial system, product quality variable of interest may be more than one or two, for two
Kind situation, establishes different index systems and is monitored to system
(7.1) for single quality variable the case where
Due to quality variable only one, so the canonical variable extracted also only one, so for related to quality
Space directly utilize canonical variable UyIt is monitored.Wherein Static State Index are as follows:
Dynamic indicator are as follows:
It is monitored for moving the method that Static State Index is all made of shewhart control figure, for Static State Index:
Wherein UTH1ForUpper control limit, LTH1ForLower control limit, μ1ForMean value,For its standard deviation, b1
For control figure thresholding width.For dynamic indicator:
Wherein UTH2ForUpper control limit, LTH2ForLower control limit, μ2ForMean value,For its standard deviation, b2
For control figure thresholding width.
For the space unrelated with quality variable, Static State Index are as follows:
Dynamic indicator are as follows:
Indicate SodThe diagonal matrix that is constituted of covariance matrix characteristic value it is inverse,Indicate SoeCovariance matrix feature
The diagonal matrix that value is constituted it is inverse, the control of index limit is obtained under 0.95 confidence level by kernel density function, respectively
For RespectivelyThe diagonal matrix that the characteristic value of covariance matrix is constituted it is inverse, two
Control limit corresponding to dynamic indicator is calculated under 0.95 confidence level by kernel density function, respectively
(7.2) for the case where there are two the above quality variables
Canonical variable obtained is not unique, so needing Counting statistics amount come to dividing UyIt is monitored, Static State Index calculates such as
Under:
WhereinIndicate UyThe diagonal matrix that constitutes of the corresponding characteristic value of covariance matrix it is inverse, the control limit of index passes through core
Density function is respectively under 0.95 confidence levelTo UyFirst difference is carried out to obtainDynamic indicator are as follows:
ForThe diagonal matrix that the characteristic value of covariance matrix is constituted it is inverse,For corresponding to three of them dynamic indicator
Control limit, is calculated under 0.95 confidence level by kernel density function.The index meter in the space unrelated with quality variable
Calculation mode in step 7.1 the case where single quality variable it is identical.
(8) process dynamics of closed-loop system and steady-state operating conditions can be monitored respectively using dynamic Static State Index.
For space relevant to quality variable:
1) Static State IndexIt transfinites, dynamic indicatorIt is following that control limit is restored to after transfiniting again, is shown relevant to quality variable
Space is adjusted by control action reaches a new operating condition, and quality variable is restored to setting level after there are brief fluctuations again；
2) Static State IndexIt transfinites, dynamic indicatorAlso it transfinites always, shows that space relevant to quality variable is broken down,
Controller adjusts failure, and product quality is destroyed；
3) Static State IndexDynamic indicatorIt does not transfinite, then shows that space relevant to quality variable is in good operation
State, product quality maintain near setting value.
For the space unrelated with quality variable:
1) the unrelated Static State Index of qualityWith dynamic indicatorIt is of short duration transfinite after to return to control limit following,
Show of short duration exception occur in the space unrelated with quality variable, after the adjusting that is acted on by closed-loop control, which restores again
Occur to run under preceding identical steady state condition to abnormal；
2) with the Static State Index of the quality independent spaceIt transfinites always, dynamic indicatorIt is of short duration transfinite after return to
Control limit is following, shows that of short duration exception occurs in the space unrelated with quality variable, but should by the adjusting that closed-loop control acts on
Space is restored to before an abnormal generation and runs under different steady state condition, and static properties has occurred and that change, but dynamic
State property can still remain normal；
3) the unrelated Static State Index of qualityWith dynamic indicatorIt transfinites, shows that the space is broken down, and
The space correlation controller adjusts failure, and static and dynamic performance is all destroyed；
4) the unrelated Static State Index of qualityWith dynamic indicatorIt remains normal, shows that the space keeps one
A good operating status.
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