CN109669415A - A kind of dynamic process monitoring method based on the analysis of structuring canonical variable - Google Patents
A kind of dynamic process monitoring method based on the analysis of structuring canonical variable Download PDFInfo
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Abstract
The present invention discloses a kind of dynamic process monitoring method based on the analysis of structuring canonical variable, it is intended to infer structuring canonical variable parser, and implement dynamic process monitoring based on this algorithm.Specifically, the present invention implements to improve by the optimization aim to canonical variable parser, and the thinking of structuring is taken into account, to infer the new algorithm of one kind to excavate autocorrelation characteristic.The method of the present invention is during extracting potential feature, while the correlation between data and passing data that looks to the future, that is, considers the autocorrelation feature in time series.In addition, realizing the monitoring to autocorrelation characteristic by constructing passing score vector and the following score vector respectively in monitoring.It can be said that the method for the present invention has inferred a kind of completely new dynamic modeling algorithm: structuring canonical variable parser, dynamic process monitoring is implemented on basis herein ought to have more superior malfunction monitoring performance.
Description
Technical field
The present invention relates to a kind of process monitoring methods of data-driven, more particularly to a kind of structuring canonical variable that is based on to divide
The dynamic process monitoring method of analysis.
Background technique
Under the promotion of industrial " big data " upsurge, modern industry process gradually moves towards digital management, industrial process pair
The producing level of data embodies the management level of modernization.This mainly has benefited from the at full speed of advanced instrumental technique and computing technique
Development and extensive use, production process object can be with the data of offline storage and on-line measurement magnanimity.These data contain energy
The useful information for embodying production process operating status as a result obtains the monitoring of process operation state using sampled data realization
The favor of more scholars.In academic research field and industrial practice field, researcher and enterprise technology personnel are put into
How a large amount of manpower and material resources research pass through the method for data reflection process operation state.In the process monitoring of data-driven
In field, multivariate statistical process monitoring is to be studied most methods, wherein when with pivot analysis (Principal
Component Analysis, PCA) algorithm be most commonly seen implementation technological means.The core of multivariate statistical process monitoring
Essence is: by implementing feature mining to the sampled data under nominal situation, and the model singly classified is established using this feature
To implement monitoring.
When establishing statistical process monitoring model, need sufficiently to excavate the feature of nominal situation down-sampled data.Due to the modern times
Industrial process sampling time interval shortens dramatically, and sampled data inevitably has the autocorrelation in time series.Therefore,
This behavioral characteristics of the autocorrelation of data are the problems that must be taken into consideration.For the research of dynamic process monitoring problem, most
Common thinking is exactly to use augmented matrix, after the autocorrelation of data and crossing dependency are obscured together, is calculated using PCA
Method implements feature extraction, and here it is dynamic PCA methods most classic in scientific documents.In addition, there are also scholars to propose using typical
Variable analysis (Canonical Variate Analysis, CVA) algorithm estimates the state variable of dynamical system, which becomes
Amount has embodied the dynamic relationship feature between passing data and Future Data.However, these two types of algorithms be all by auto-correlation with
Crosscorrelation obscures processing strategie together, is unfavorable for the behavioral characteristics hidden in independent analysis nominal situation data.
In recent years, there is researcher to propose a kind of novel dynamic process monitoring method, i.e., by optimization feature extraction to
Amount, making the potential feature extracted, there are significant autocorrelation performances.Such methods are distinguished by the way that the thinking of structuring is external
Autocorrelation characteristic opens the new way of dynamic process monitoring.Fail to consider as CVA algorithm however, this carrys out method
Toward the dynamic relationship feature between data and Future Data, correlation cannot be reflected from time series.Therefore, structuring
Further expansion of the modeling approach on CVA algorithm, need to be goed deep into expansion.
Summary of the invention
Technical problem underlying to be solved by this invention is: how to infer structuring canonical variable parser, and with
Implement dynamic process monitoring based on this algorithm.For this purpose, the present invention is implemented by the optimization aim to canonical variable parser
It improves, the thinking of structuring is taken into account, to infer a kind of new algorithm: the analysis of structuring canonical variable.
The technical scheme of the invention to solve the technical problem is: it is a kind of based on structuring canonical variable analysis
Dynamic process monitoring method, including step as shown below:
(1) sample under production process accidental conditions is acquired, training data matrix X ∈ R is formedn×m, and calculating matrix
The mean μ of each column vector in X1, μ2..., μmAnd standard deviation δ1, δ2..., δm, corresponding composition mean vector μ=[μ1, μ2...,
μm]TWith standard difference vector δ=[δ1, δ2..., δm], wherein n is number of training, and m is process measurement variable number, and R is real number
Collection, Rn×mIndicate the real number matrix of n × m dimension, the transposition of upper label T representing matrix or vector.
(2) according to formulaMatrix X execution standardization is handled to obtain matrixWherein, U ∈ Rn×mThe matrix being made of n identical mean vector μ, i.e. U=[μ, μ ..., μ
]T, the element in diagonal matrix Φ=diag (δ) on diagonal line is made of standard difference vector δ, and diag () expression changes vector
The diagonally operation of matrix, xi∈Rm×1For i-th of data vector after standardization, i=1,2 ..., n.
(3) after passing data dependence order A and Future Data correlation order F being arranged, according to formula structure as follows
Build matrix X1, X2..., XA+F:
Xj=[xj, xj+1..., xn-A-F+j]T ①
Above formula 1. in, j=1,2 ..., A+F.
(4) number of setting structure canonical variable is D, and feature is calculated using structuring canonical variable parser
Extract matrix B ∈ Rm×D, matrix W ∈ Rm×D, passing data weighting Matrix C ∈ RA×D, Future Data weight matrix H ∈ RF×D。
Before the specific implementation step for providing structuring canonical variable parser, the substantially former of the algorithm is first introduced
Reason.Objective function shown in being defined as follows:
Wherein, passing data matrix Zp=[X1, X2..., XA], Future Data matrix Zf=[XA+1, XA+2..., XA+F], under
Label p and f respectively represent past and future, vector w ∈ Rm×1For projective transformation vector, c ∈ RA×1With β ∈ RF×1Respectively cross
Toward the weight vectors of data and Future Data, symbolIndicate Kronecker product,The specific following institute of calculated result
Show:
In above formula, vector c=[c1, c2..., cA].Formula 2. defined in objective function and classics CVA algorithm target
Function is intended to the correlation maximized between passing data and Future Data, the difference is that the shape of projective transformation vector
Formula is different.Solution formula 2. in optimization problem method of Lagrange multipliers can be used, i.e., introducing multiplier λ, γcAnd γβConstruction
LagrangianL as follows:
Then, partial derivative of the function L relative to w, c and β is calculated separately:
In above formula, Im、IAAnd IFRespectively indicate the unit matrix of dimension of m m, A × A dimension and F × F dimension.It will be inclined in above formula
Derivative is all arranged to after being equal to zero, and following equilibrium relationships can be obtained:
(Gw+Gw T) w=2 λ w
Above formula 8. in, matrixMatrix
It can be seen that under the premise of known to vector c and the β projective transformation vector w can be obtained by solving feature vector problem, to
Under the premise of measuring known to w, weight vectors c can be obtained by solving feature vector problem, and then vector β is calculated.
The solution procedure of above-mentioned vector w, c and β intercouple, can be by reciprocal iteration until convergent implementation process meter
Calculation obtains w, c and β, and corresponding structuring canonical variable isDue to needing to solve multiple structuring canonical variables,
It, need to be according to formula before solving next structuring canonical variableFromIt is middle to reject the s extracted, wherein
In conclusion the specific implementation step of structuring canonical variable parser as follows can be obtained:
(4.1) initialization d=1 and initialization vector wd=[1,0 ..., 0]T。
(4.2) GG is solvedTcd=4 γ cdFeature vector c corresponding to maximum eigenvalue γd, and according to formula cd=cd/||
cd| | unitization processing vector cd, whereinWithCalculating knot
Fruit is as follows:
(4.3) according to formula βd=GTcdCalculate vector βdAfterwards, then to βdExploiting entityization handles βd=βd/||βd||。
(4.4) (G is solvedw+Gw T)wd=2 λ wdFeature vector w corresponding to maximum eigenvalued, and to wdExploiting entity
Handle wd=wd/||wd| |, whereinWithCalculated result such as
Shown in lower:
(4.5) judge wdRestrain? if it is not, then return step (4.2)；Become if so, obtaining d-th of structuring typical case
AmountExecute step (4.6) afterwards.
(4.6) successively according to formulaWithUpdated matrix is calculated
(4.7) and judge whether to meet condition: d < D? if so, setting d=d+1 and wd=[1,0 ..., 0]TAfter return
Step (4.2)；If it is not, then output matrix W=[w1, w2..., wD], passing data weighting Matrix C=[c1, c2..., cD], future
Data weighting matrix H=[β1, β2..., βD] and feature extraction matrix B=W (PW)-1, wherein matrix P=[p1, p2...,
PD]。
(5) remember row vectorFor each row vector in Matrix C, row vector h is remembered1, h2..., hFFor in matrix H
Each row vector, and according to formula construction matrix as followsWith
In above formula, diag () indicates the operation that vector is become to diagonal matrix.
(6) according to formulaAfter calculating score matrix S, further according to formula Sj=S (j:n-A-F+j) structural matrix
S1, S2..., SA+F, wherein S (j:n-A-F+j) is indicated the row vector composition matrix of jth row in matrix S to the n-th-A-F+j row
Operation, j=1,2 ..., A+F.
(7) according to formula Sp=YpΘpWith Sf=YfΘfCalculate separately passing score matrix SpWith the following score matrix Sf,
Middle matrix Yp=[S1, S2..., SA], matrix Yf=[SA+1, SA+2..., SA+F]。
(8) according to formula Λp=Sp TSp/ (n-A-F) and Λf=Sf TSf/ (n-A-F) calculates covariance matrix ΛpWith Λf。
(9) upper limit of monitoring and statistics amount is determined according to formula as follows:
In upper two formula, FD, n-D, αThe F distribution that expression confidence level is α (generally taking α=99%), freedom degree is respectively D and n-D
Corresponding value,Indicate that freedom degree is h, confidence level is that α is value corresponding to chi square distribution, a and τ are respectively Q statistical magnitude
Estimate mean value and estimate variance.
Above-mentioned steps (1) to step (9) are the off-line modeling stage of the method for the present invention, wherein step (4.1) to step
It (4.7) is the implementation process of structuring canonical variable parser in the method for the present invention.After the completion of the off-line modeling stage, need to protect
Model parameter is stayed in case the on-line monitoring invocation of procedure as follows.
(10) the data sample x at last samples moment is collectedt∈Rm×1, and according to formulaTo xtIt is real
It applies standardization and obtains vectorAfter finding out t-1 to the normalized processing of data of t-q sampling instant simultaneously
Obtain vectorWherein lower label t indicates the last samples moment, and lower label q=max { A, F } is both A and F
Between maximum value.
(11) according to formulaCalculate score vectorWherein k=0,1 ..., q, and construct to
AmountWith vector
(12) according to formulaWith formulaCalculate passing score vectorWith the following score vectorFurther according to formulaCalculate residual vector et。
(13) according to formula Counting statistics amount ψ as followsp、ψfAnd the specific value of Q:
(14) judge whether to meet condition: ψp≤ψlimAnd ψf≤ψlimAnd Q≤QlimIf so, current sample collection is from just
Normal operating condition, return step (10) continue to monitor the sample data of subsequent time；If it is not, then the currently monitored sample collection is from failure work
Condition.
It is compared with the traditional method, inventive process have the advantage that:
The method of the present invention is during extracting potential feature, while it is related between data and passing data to look to the future
Property, that is, consider the autocorrelation feature in time series.In addition, in monitoring by respectively construct passing score vector with not
Carry out score vector, realizes the monitoring to autocorrelation characteristic.It is built it can be said that the method for the present invention has inferred a kind of completely new dynamic
Modulo n arithmetic: structuring canonical variable parser, dynamic process monitoring is implemented on basis herein ought to have more superior failure prison
Survey performance.
Detailed description of the invention
Fig. 1 is the implementation flow chart of the method for the present invention.
Fig. 2 is the implementation flow chart of structuring canonical variable parser in the method for the present invention.
Fig. 3 is the monitoring detail drawing of TE process materials C inlet temperature failure
Specific embodiment
The method of the present invention is described in detail with specific case study on implementation with reference to the accompanying drawing.
As shown in Figure 1, the present invention discloses a kind of dynamic process monitoring method based on the analysis of structuring canonical variable.Below
Illustrate the specific implementation process of the method for the present invention in conjunction with the example of a specific industrial process, and relative to existing method
Superiority.
Application comes from the experiment of U.S.'s Tennessee-Yi Siman (TE) chemical process, and prototype is that Yi Siman chemical industry is raw
Produce an actual process process in workshop.Currently, complexity of the TE process because of its process, has been used as a standard test platform quilt
It is widely used in fault detection research.Entire TE process includes that 22 measurands, 12 performance variables and 19 composition measurements become
Amount.The TE process object can be with a variety of different fault types of analog simulation, such as the variation of material inlet temperature jump, cooling water event
Barrier variation etc..In order to be monitored to the process, 33 process variables as shown in Table 1 are chosen.Due to sampling interval duration
Shorter, inevitably there is sequence self correlation in TE process sampling data, next combine the TE process specific to the present invention
Implementation steps are explained in detail.
Table 1:TE process monitoring variable.
| Serial number | Variable description | Serial number | Variable description | Serial number | Variable description |
| 1 | Material A flow | 12 | Separator liquid level | 23 | D material inlet valve position |
| 2 | Material D flow | 13 | Separator pressure | 24 | E material inlet valve position |
| 3 | Material E flow | 14 | Separator tower bottom flow | 25 | A material inlet valve position |
| 4 | Combined feed flow | 15 | Stripper grade | 26 | A and C material inlet valve position |
| 5 | Circular flow | 16 | Pressure of stripping tower | 27 | Compressor cycle valve location |
| 6 | Reactor feed | 17 | Stripper bottom rate | 28 | Empty valve location |
| 7 | Reactor pressure | 18 | Stripper temperature | 29 | Separator liquid phase valve location |
| 8 | Reactor grade | 19 | Stripper upper steam | 30 | Stripper liquid phase valve location |
| 9 | Temperature of reactor | 20 | Compressor horsepower | 31 | Stripper steam valve position |
| 10 | Rate of evacuation | 21 | Reactor cooling water outlet temperature | 32 | Reactor condensate flow |
| 11 | Separator temperature | 22 | Separator cooling water outlet temperature | 33 | Condenser cooling water flow |
Firstly, establishing dynamic process monitoring model using 960 sampled datas under TE process nominal situation, including following
Step:
Step (1): the sample under acquisition production process accidental conditions forms training data matrix X ∈ R960×33, and
The mean μ of each column vector in calculating matrix X1, μ2..., μ33And standard deviation δ1, δ2..., δ33, corresponding composition mean vector μ=
[μ1, μ2..., μ33]TWith standard difference vector δ=[δ1, δ2..., δ33]。
Step (2): according to formulaMatrix X execution standardization is handled to obtain matrixWherein, U ∈ R960×33The matrix being made of 960 identical mean vector μ, i.e. U=[μ,
μ ..., μ]T, the element in diagonal matrix Φ=diag (δ) on diagonal line is made of standard difference vector δ.
Step (3): after passing data dependence order A=3 and Future Data correlation order F=4 is arranged, according to formula
1. constructing matrix X1, X2..., XA+F。
Step (4): the number of setting structure canonical variable is D=12, utilizes structuring canonical variable parser meter
Calculation obtains feature extraction matrix B ∈ Rm×D, matrix W ∈ Rm×D, passing data weighting Matrix C ∈ RA×D, Future Data weight matrix H
∈RF×D.The implementation flow chart of structuring canonical variable parser involved in the method for the present invention is illustrated in Fig. 2, specifically
Implementation process following steps (4.1) are to shown in step (4.8).
Step (4.1): initialization d=1 and initialization vector wd=[1,0 ..., 0]T；
Step (4.2): according to formula Zp=[X1, X2..., XA] and formula Zf=[XA+1, XA+2..., XA+F] the passing number of construction
According to matrix ZpWith Future Data matrix Zf；
Step (4.3): GG is solvedTcd=4 γ cdFeature vector c corresponding to maximum eigenvalue γd, and according to formula cd=
cd/||cd| | unitization processing vector cd, wherein
Step (4.4): according to formula βd=GTcdCalculate vector βdAfterwards, then to βdExploiting entityization handles βd=βd/||βd|
|；
Step (4.5): (G is solvedw+Gw T)wd=2 λ wdFeature vector w corresponding to maximum eigenvalued, and to wdImplement single
Positionization handles wd=wd/||wd| |, wherein
Step (4.6): judge wdRestrain? if it is not, then return step (4.3)；If so, obtaining d-th of structuring
Canonical variableExecute step (4.7) afterwards；
Step (4.7): successively according to formulaWithUpdated square is calculated
Battle array
Step (4.8): and judge whether to meet condition: d < D? if so, setting d=d+1 and wd=[1,0 ..., 0]TAfterwards
Return step (4.2)；If it is not, then output matrix W=[w1, w2..., wD], passing data weighting Matrix C=[c1, c2..., cD],
Future Data weight matrix H=[β1, β2..., βD] and feature extraction matrix B=W (PW)-1, wherein matrix P=[p1,
p2..., pD]。
Step (5): note row vectorFor each row vector in Matrix C, row vector h is remembered1, h2..., hFFor matrix H
In each row vector, and according to formula 9. structural matrix ΘpWith Θf。
Step (6): according to formulaAfter calculating score matrix S, further according to formula Sj=S (j:n-A-F+j) construction
Matrix S1, S2..., SA+F。
Step (7): according to formula Sp=YpΘpWith Sf=YfΘfCalculate separately passing score matrix SpWith the following score square
Battle array Sf, wherein matrix Yp=[S1, S2..., SA], matrix Yf=[SA+1, SA+2..., SA+F]。
Step (8): according to formula Λp=Sp TSp/ (n-A-F) and Λf=Sf TSf/ (n-A-F) calculates covariance matrix Λp
With Λf。
Step (9): according to formula 10. withDetermine the upper limit ψ of monitoring and statistics amountlimWith Qlim。
Data 960 are acquired under condenser cooling water inlet temperature Spline smoothing fault condition in TE process, wherein before
160 data are positive normal operating condition, and fault condition is introduced from the 161st sampling instant.Implemented such as using this 960 sample datas
Online process monitoring shown in lower step.
Step (10): the data sample x at last samples moment is collectedt∈Rm×1, and according to formulaIt is right
xtExecution standardization handles to obtain vectorT-1 are found out simultaneously to the normalized place of data of t-q sampling instant
Reason obtains vector
Step (11): according to formulaCalculate score vectorWherein k=0,1 ..., q, and
Construct vectorWith vector
Step (12): according to formulaWith formulaCalculate passing score vectorWith the following score
VectorFurther according to formulaCalculate residual vector et。
Step (14): judge whether to meet condition: ψp≤ψlimAnd ψf≤ψlimAnd Q≤QlimIf so, current sample collection
From nominal situation, return step (10) continues to monitor the sample data of subsequent time；If it is not, then the currently monitored sample collection event certainly
Hinder operating condition.
The details of malfunction monitoring are shown in Fig. 3, it can be found that the method for the present invention from preceding two subgraphs in Fig. 3
It can be in triggering fault warning in time after the failure occurred.
Above-mentioned case study on implementation is only used to illustrate specific implementation of the invention, rather than limits the invention.?
In the protection scope of spirit and claims of the present invention, to any modification that the present invention makes, protection of the invention is both fallen within
Range.
Claims (2)
1. a kind of dynamic process monitoring method based on the analysis of structuring canonical variable, which comprises the following steps:
The implementation process in off-line modeling stage is as follows:
Step (1): the sample under acquisition production process accidental conditions forms training data matrix X ∈ Rn×m, and calculate square
The mean μ of each column vector in battle array X1, μ2..., μmAnd standard deviation δ1, δ2..., δm, corresponding composition mean vector μ=[μ1,
μ2..., μm]TWith standard difference vector δ=[δ1, δ2..., δm], wherein n is number of training, and m is process measurement variable number, and R is
Set of real numbers, Rn×mIndicate the real number matrix of n × m dimension, the transposition of upper label T representing matrix or vector；
Step (2): according to formulaMatrix X execution standardization is handled to obtain matrix
Wherein, U ∈ Rn×mThe matrix being made of n identical mean vector μ, i.e. U=[μ, μ ..., μ]T, diagonal matrix Φ=diag
Element in (δ) on diagonal line is made of standard difference vector δ, and diag () indicates the operation that vector is transformed into diagonal matrix, xi
∈Rm×1For i-th of data vector after standardization, i=1,2 ..., n；
Step (3): after passing data dependence order A and Future Data correlation order F is arranged, according to formula structure as follows
Build matrix X1, X2..., XA+F:
Xj=[xj, xj+1..., xn-A-F+j]T ①
Above formula 1. in, j=1,2 ..., A+F；
Step (4): the number of setting structure canonical variable is D, and spy is calculated using structuring canonical variable parser
Sign extracts matrix B ∈ Rm×D, matrix W ∈ Rm×D, passing data weighting Matrix C ∈ RA×D, Future Data weight matrix H ∈ RF×D；
Step (5): note row vectorFor each row vector in Matrix C, row vector h is remembered1, h2..., hFFor in matrix H
Each row vector, and according to formula construction matrix Θ as followspWith Θf:
In above formula, diag () indicates the operation that vector is become to diagonal matrix；
Step (6): according to formulaAfter calculating score matrix S, further according to formula Sj=S (j:n-A-F+j) structural matrix
S1, S2..., SA+F, wherein S (j:n-A-F+j) is indicated the row vector composition matrix of jth row in matrix S to the n-th-A-F+j row
Operation, j=1,2 ..., A+F；
Step (7): according to formula Sp=YpΘpWith Sf=YfΘfCalculate separately passing score matrix SpWith the following score matrix Sf,
Wherein matrix Yp=[S1, S2..., SA], matrix Yf=[SA+1, SA+2..., SA+F]；
Step (8): according to formula Λp=Sp TSp/ (n-A-F) and Λf=Sf TSf/ (n-A-F) calculates covariance matrix ΛpWith Λf；
Step (9): the upper limit ψ of monitoring and statistics amount is determined according to formula as followslimWith Qlim:
In upper two formula, FD, n-D, αExpression confidence level is α, freedom degree is respectively value corresponding to the F distribution of D and n-D,It indicates
Freedom degree is h, confidence level is that α is value corresponding to chi square distribution, and a and τ are respectively estimation mean value and the estimation side of Q statistical magnitude
Difference；
The implementation steps of on-line fault monitoring are as follows:
Step (10): the data sample x at last samples moment is collectedt∈Rm×1, and according to formulaTo xtIt is real
It applies standardization and obtains vectorAfter finding out t-1 to the normalized processing of data of t-q sampling instant simultaneously
Obtain vectorWherein lower label t indicates the last samples moment, and lower label q=max { A, F } is both A and F
Between maximum value；
Step (11): according to formulaCalculate score vectorWherein k=0,1 ..., q, and construct
VectorWith vector
Step (12): according to formulaWith formulaCalculate passing score vectorWith the following score vectorFurther according to formulaCalculate residual vector et；
Step (13): according to formula Counting statistics amount ψ as followsp、ψfAnd the specific value of Q:
Step (14): judge whether to meet condition: ψp≤ψlimAnd ψf≤ψlimAnd Q≤QlimIf so, current sample collection is from just
Normal operating condition, return step (10) continue to monitor the sample data of subsequent time；If it is not, then the currently monitored sample collection is from failure work
Condition.
2. a kind of dynamic process monitoring method based on the analysis of structuring canonical variable according to claim 1, feature
It is, the specific implementation process of the step (4) is as follows:
Step (4.1): initialization d=1 and initialization vector wd=[1,0 ..., 0]T；
Step (4.2): according to formula Zp=[X1, X2..., XA] and formula Zf=[XA+1, XA+2..., XA+F] the passing data square of construction
Battle array ZpWith Future Data matrix Zf；
Step (4.3): GG is solvedTcd=4 γ cdFeature vector c corresponding to maximum eigenvalue γd, and according to formula cd=cd/|
|cd| | unitization processing vector cd, whereinIAWith IFRespectively indicate A × A dimension with F ×
The unit matrix of F dimension, symbolIndicate Kronecker product,WithCalculated result it is as follows:
Step (4.4): according to formula βd=GTcdCalculate vector βdAfterwards, then to βdExploiting entityization handles βd=βd/||βd||；
Step (4.5): (G is solvedw+Gw T)wd=2 λ wdFeature vector w corresponding to maximum eigenvalued, and to wdExploiting entity
Handle wd=wd/||wd| |, wherein matrixImIndicate the unit matrix of dimension of m m,WithCalculated result it is as follows:
Step (4.6): judge wdRestrain? judgment criteria are as follows: vector wdElement be no longer changed until, if it is not, then returning
It returns step (4.3)；If so, obtaining d-th of structuring canonical variableExecute step (4.7) afterwards；
Step (4.7): successively according to formulaWithUpdated matrix is calculated
Step (4.8): and judge whether to meet condition: d < D? if so, setting d=d+1 and wd=[1,0 ..., 0]TAfter return
Step (4.2)；If it is not, then output matrix W=[w1, w2..., wD], passing data weighting Matrix C=[c1, c2..., cD], future
Data weighting matrix H=[β1, β2..., βD] and feature extraction matrix B=W (PW)-1, wherein matrix P=[p1, p2...,
pD]。
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