CN108490908B - A kind of dynamic distributed monitoring method towards gigawatt extra-supercritical unit variable parameter operation - Google Patents

A kind of dynamic distributed monitoring method towards gigawatt extra-supercritical unit variable parameter operation Download PDF

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CN108490908B
CN108490908B CN201810141761.7A CN201810141761A CN108490908B CN 108490908 B CN108490908 B CN 108490908B CN 201810141761 A CN201810141761 A CN 201810141761A CN 108490908 B CN108490908 B CN 108490908B
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CN108490908A (en
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赵春晖
孙鹤
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Zhejiang University ZJU
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    • 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
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Abstract

The invention discloses a kind of dynamic distributed monitoring methods towards gigawatt extra-supercritical unit variable parameter operation.The identification that the present invention this typical extensive non-stationary process for gigawatt extra-supercritical unit, the sparse cointegrating analysis of R. concomitans and dynamic feature extraction method change for fault detection and operating condition.Large scale process variable automatically can be divided into different set of variables by this method, while extraction process static state and multidate information be distinguished in each set of variables, and the two is modeled and monitored respectively.It realizes depth mining process information, and effectively realizes the transformation and actual process failure of differentiation process nominal situation.This method effective solution process monitoring difficulty problem of this extensive non-stationary dynamical system of gigawatt extra-supercritical unit, substantially increase the performance of process monitoring, facilitate field engineer and accurately grasp operating states of the units, to guarantee the safety of gigawatt extra-supercritical unit and improve productivity effect.

Description

A kind of dynamic distributed prison towards gigawatt extra-supercritical unit variable parameter operation Survey method
Technical field
The invention belongs to extensive non-stationary process statistical monitoring fields, super towards gigawatt especially for one kind The dynamic distributed monitoring method of criticality benchmark variable parameter operation.
Background technique
Power industry is the emphasis of Chinese national economy most important basic energy resource industry and Strategy for economic development.China lacks The few gas of oil, rich coal resources, coal electricity is always China's main power source for a long time.Coal fired generation process is increasingly sophisticated Change, enlargement development.Large-scale coal fired generation process environment is complicated, and scene has the features such as high temperature, high pressure, strong noise.1001000 Watt extra-supercritical unit be in the world it is state-of-the-art efficiently, large capacity coal powerplant, there is apparent efficiency advantage, be me The representative unit and main flow direction of state's electric power industry development.China's gigawatt extra-supercritical unit ownership the first in the world, And development space is huge.
Gigawatt extra-supercritical unit has apparent extensive, non-stationary and dynamic characteristic.In order to guarantee million The safety of kilowatt extra-supercritical unit simultaneously improves productivity effect, it is necessary to use effective process monitoring method.Process monitoring is just It is monitoring process operation state, is sounded an alarm in time when occurring extremely.With the development of technology, data are obtained in industry spot It becomes increasingly easy, a large amount of procedural information has been contained in process data, then, the process monitoring method based on data has become For the hot spot of research.
Forefathers have done corresponding research to the process monitoring based on data.Principal component analysis (PCA), offset minimum binary (PLS) etc. Multielement statistical analysis methods have been widely used in data procedures monitoring field.However, these methods assumed that Journey is that smoothly, there is no the dynamic characteristics for considering process.Actually since process is disturbed in gigawatt extra-supercritical unit Dynamic, the reasons such as ageing equipment process can have apparent non-stationary property.Simultaneously because frequently peak regulation process is in dynamic change Among.Therefore, gigawatt extra-supercritical unit has apparent extensive, non-stationary and dynamic characteristic, this is supervised to process Survey brings very big challenge.
For gigawatt extra-supercritical unit, this typical extensive, dynamic non-stationary process proposes a kind of knot to the present invention Close the process monitoring method that sparse cointegrating analysis and behavioral characteristics extract.This method goes out non-stationary identification variables in the process Come, establishes sparse co-integration model using these non-stationary variables and variable is divided into different set of variables using alternative manner.It mentions The method of dynamic feature extraction is for multidate information and static information to be distinguished from out, and the two is modeled and monitored respectively. Variable can be automatically divided into different set of variables by this method, while can effectively extract process dynamics and static letter Breath, the effective change and actual process failure for distinguishing normal operating conditions, substantially increases the performance of process monitoring.To current Until, there is not yet research related to the present invention is reported.
Summary of the invention
It is an object of the invention to this typical extensive, dynamic non-stationary mistakes for gigawatt extra-supercritical unit Journey provides a kind of fault detection method and diagnostic method towards large-scale Thermal generation unit non-stationary process.
The purpose of the present invention is what is be achieved through the following technical solutions: one kind is towards large-scale Thermal generation unit non-stationary mistake The fault detection method of journey, comprising the following steps:
(1) normal processes data are obtained: being set comprising J process variable in a gigawatt extra-supercritical unit, every time The vector of an available 1 × J is sampled, obtains the two-dimensional matrix X under a normal processes after sampling M timesn(M×J)；
(2) it identifies non-stationary variable: identifying Two-Dimensional Moment using Augmented Dickey-Fuller (ADF) method of inspection Battle array XnNon-stationary variable in (M × J) obtains non-stationary variable data matrix Xns(M × N), N indicate non-stationary variable number；
(3) non-stationary variable data matrix X obtained in (2) is utilizedns(M × N)=[x1,x2,…,xN], xt=(x1, x2,…,xN)TSparse co-integration model is established, wherein xtFor data matrix XnsThe transposition of a row vector in (M × N) indicates The sampled value of t moment, t=1,2 ..., M.It establishes sparse co-integration model and specifically includes following sub-step:
(3.1) to xtEstablish Vector Autoression Models
xt=Π1xt-1+…+Πpxt-p+c+μt (1)
Wherein, Π1~ΠpIt is the coefficient matrix of (N × N), μtFor (N × 1) matrix, white Gaussian noise, μ are indicatedt~N (0, Ξ), c are (N × 1) matrix, indicate constant, p is model order；
(3.2) x is subtracted at formula (1) both endst-1Obtain error correction model
Figure BDA0001577779790000031
Wherein,
Figure BDA0001577779790000032
INFor the unit square of (N × N) Battle array；
(3.3) Γ in step (3.2) is decomposed into matrix Γ=Α Β of two sequency spectrumsT, formula (2) becomes
Wherein, Α (N × R), Β (N × R)；
(3.4) the whole vector matrix Β of association in formula (3) is estimated by Maximum Likelihood Estimation
Figure BDA0001577779790000034
Wherein, L (*) indicates maximum likelihood function, the mark of tr (*) representing matrix.X=(Δ xp+1,...,ΔxM)T, Y= (ΔYp+1,...,ΔYM)T,
Figure BDA0001577779790000036
L=p+1 ..., M, Ω=(Ω1,...,Ωp-1)T, Z= (xt-1,...,xM-1)T, Θ=Ξ-1；
(3.5) characteristic equation solution procedure can be converted into the Maximum-likelihood estimation of formula (4)
Figure BDA0001577779790000035
Wherein,
Figure BDA0001577779790000041
Wherein parameter matrix ΘiAnd Φi, i=1,2 ..., p-1 can be acquired by least-squares algorithm；
(3.6) penalty is added to the objective function of formula (4) and obtains the sparse whole vector of association
Figure BDA0001577779790000042
Wherein, P1, P2, P3For parameter Β, the penalty of Ω, Θ, using a normal form；Wherein Β is to assist whole vector Matrix, Ω, Θ are parameters to be estimated；Adjusting parameter λ1And λ2It is determined using crosscheck, adjusting parameter λ3Using Bayes Information criterion determines.Pass through the available whole vector of sparse association of solution to formula (6).
(4) variable can be divided using the whole vector of sparse association obtained in formula (6), specifically includes following sub-step It is rapid:
(4.1) the sparse whole vector matrix Β of association is obtained according to formula (6)s(N × K)=[βs,1,βs,2,...,βs,K], wherein K indicates the number of the sparse whole vector of association；
(4.2) steady residual sequence is obtained according to the sparse whole vector of association
Figure BDA0001577779790000043
Wherein k=1,2 ..., K, t=1, 2 ..., M.The consistent level for measuring residual sequence, and record residual difference sequence γ are examined using ADFk,tADF test statistics tk
(4.3) to obtained test statistics tkCarry out ascending sort, the corresponding sparse association of the smallest inspection statistics magnitude Whole vector is retained.The corresponding variable of nonzero element in the sparse whole vector of association is assigned in subgroup, and is denoted as Xb。
(4.4) by XbIn variable from initial data concentrate remove, raw data set is denoted as X at this timeL。
(4.5) iteration step (4.1)-(4.4) are all assigned in different subgroups until all variables, original at this time Variable is divided into Z different set of variables.
(5) local static, dynamic monitoring statistic are established in each set of variables:
(5.1) local static monitoring and statistics amount is established
Figure BDA0001577779790000051
Wherein,
Figure BDA0001577779790000052
γs,b,tFor the steady residual sequence in each set of variables, Bf,bFor the whole moment of a vector of association calculated in each set of variables Battle array, Λs,b=(XbBf,b)T(XbBf,b)/(M-1) (b=1 ..., Z) be covariance matrix, M be sampled point number.Z is variable point The number of group indicates that original variable is divided into Z set of variables, xb,tFor XbThe transposition of middle row vector indicates the sampling in t moment Point.
(5.2) local dynamic station monitoring and statistics amount is established
Figure BDA0001577779790000053
Wherein,
Figure BDA0001577779790000054
B indicates b-th of set of variables, and p indicates time lag, Δ xp+1,bIndicate the Difference Terms, that is, Δ x at p+1 momentp+1,b= xp+1,b-xp,b, xp,bFor XbThe transposition of middle row vector indicates the sampled point at the p moment, ΘbAnd Φb(b=1 ..., Z) it is wait estimate Parameter is counted, can be acquired by least square.Be,bAnd Bf,bFor EbAnd FbCalculate the weight matrix obtained after canonical correlation analysis.It is dynamic State monitoring and statistics amount is
Figure BDA0001577779790000055
Wherein, te,bFrom matrix Te,b, it is Te,bMiddle column vector.
(6) global monitoring and statistics amount is established
(6.1) global static monitoring techniques statistic is established:
Figure BDA0001577779790000061
Wherein, Z indicates the number of set of variables；
Figure BDA0001577779790000062
PS(xb)=P (xb|Ns)P(Ns)+P(xb|Fs)P(Fs)；P(Ns) it is confidence interval, i.e. P (Ns)=α, P (Fs)=1- α；
Figure BDA0001577779790000063
Figure BDA0001577779790000064
For sample xb'sMonitoring and statistics Amount,
Figure BDA0001577779790000066
For monitoring and statistics amount
Figure BDA0001577779790000067
Control limit；
(6.2) global dynamic monitoring statistic is established:
Figure BDA0001577779790000068
Wherein, Z indicates the number of set of variables；
Figure BDA0001577779790000069
Pe(xb)=P (xb |Ne)P(Ne)+P(xb|Fe)P(Fe)；P(Ne) it is confidence interval, i.e. P (Ne)=α, P (Fe)=1- α；
Figure BDA00015777797900000610
Figure BDA00015777797900000611
For sample xb's
Figure BDA00015777797900000612
Monitoring and statistics Amount,
Figure BDA00015777797900000613
For monitoring and statistics amount
Figure BDA00015777797900000614
Control limit；
(7) online process monitoring
(7.1) to new collected non-stationary variable sample xnew,t(N × 1) carries out variable grouping, which is divided into Z Set of variables, that is, xnew,b,t, b=1,2 ..., Z.
(7.2) method recorded according to step 5 calculates local static monitoring and statistics amount
Figure BDA00015777797900000615
xnewi,tWith xnew,t(N × 1) what relationship, xnewi,tWhat is indicated
(7.3) local dynamic station monitoring and statistics amount is calculated
Figure BDA0001577779790000071
(7.4) global static, dynamic monitoring statistic is calculated
If
Figure BDA0001577779790000073
WithIt is limited beyond control, it is meant that static, dynamic long-run equilibrium relationship is broken, process hair Raw failure；IfWhile alarm,
Figure BDA0001577779790000076
Beyond normal range (NR) is returned to after control limit, meaned at this time The operating point of journey changes；If
Figure BDA0001577779790000077
With
Figure BDA0001577779790000078
It is all limited without departing from control, means process work in new work at this time Static state, dynamic long-run equilibrium relationship under condition, but between variable are not broken or the operating condition is included in modeling data.
If local static, dynamic monitoring statistic are influenced by failure, BICsOr BICeAlso it beyond control limit, anticipates at this time Taste the failure not only influence the local state of process, while global state is also affected, if BICsOr BICeDo not exceed Control limit, indicates the local state of the failure influence process.
The invention has the benefit that extensive non-stationary process can be divided into different set of variables by the present invention to be reduced The complexity of process, while by monitoring static and dynamic change in different set of variables, the identification of operating condition variation may be implemented With the detection to failure, provides local monitoring information while providing global monitoring information.
Detailed description of the invention
Fig. 1 is the flow chart of the dynamic distributed monitoring the present invention is based on sparse cointegrating analysis；
Fig. 2 is area monitoring's result of this method；
Fig. 3 is the global monitoring result of this method；
Fig. 4 is the monitoring result of traditional cointegrating analysis.
Fig. 5 is the monitoring result of traditional cointegrating analysis.
Specific embodiment
With reference to the accompanying drawing and specific example, invention is further described in detail.
Gigawatt extra-supercritical unit is typical non-stationary process, and a portion variable has apparent non-stationary special Property, such as condenser circulating water pressure, high-pressure heater initial steam pressure, oxygen-eliminating device incoming condensing water amount.The present invention is to praise Hua Ran For the unit of power plant 8, it is gigawatt extra-supercritical unit, including 159 that the power of the unit, which is 10000MW, Process variable, these variables are related to pressure, temperature, water level, flow velocity etc..
As shown in Figure 1, the present invention is a kind of towards the dynamic distributed of gigawatt extra-supercritical unit variable parameter operation Monitoring method, comprising the following steps:
Step 1: acquisition process data: setting in a gigawatt extra-supercritical unit comprising J process variable, adopt every time The vector of the available 1 × J of sample, the data obtained after sampling K times can be described as a two-dimensional matrix X (K × J).It obtains Take normal data Xn(M × J), wherein subscript n indicates normal data.In this example, the sampling period is 1 minute, for normal number According to 740 samples of acquisition, 159 process variables.So normal data sample is Xn(740×159)。
Step 2: identification non-stationary variable: normal using the identification of Augmented Dickey-Fuller (ADF) method of inspection Data XnNon-stationary variable in (740 × 159), is examined by ADF, wherein 51 variables are non-stationary variable, is obtained non-flat Steady variable data Xns(740 × 51), wherein subscript n s indicates Non-stationary Data.Below for convenience of expression, by sampled point number 740 It is indicated with M, non-stationary variables number 51 is indicated with N.
Step 3: utilizing non-stationary variable data matrix X obtained in (2)ns(M × N)=[x1,x2,…,xN], xt= (x1,x2,…,xN)TSparse co-integration model is established, wherein xtFor data matrix XnsThe transposition of a row vector in (M × N), table Show the sampled value in t moment, t=1,2 ..., M.It establishes sparse co-integration model and specifically includes following sub-step:
(3.1) to xtEstablish Vector Autoression Models
xt=Π1xt-1+…+Πpxt-p+c+μt (1)
Wherein, Π1~ΠpIt is the coefficient matrix of (N × N), μtFor (N × 1) matrix, white Gaussian noise, μ are indicatedt~N (0, Ξ), c are (N × 1) matrix, indicate constant, p is model order；
(3.2) x is subtracted at formula (1) both endst-1Obtain error correction model
Figure BDA0001577779790000091
Wherein,
Figure BDA0001577779790000092
INFor the unit square of (N × N) Battle array；
(3.3) Γ in step (3.2) is decomposed into matrix Γ=Α Β of two sequency spectrumsT, formula (2) becomes
Figure BDA0001577779790000093
Wherein, Α (N × R), Β (N × R)；
(3.4) the whole vector matrix Β of association in formula (3) is estimated by Maximum Likelihood Estimation
Figure BDA0001577779790000094
Wherein, L (*) indicates maximum likelihood function, the mark of tr (*) representing matrix.X=(Δ xp+1,...,ΔxM)T, Y= (ΔYp+1,...,ΔYM)T,L=p+1 ..., M, Ω=(Ω1,...,Ωp-1)T, Z= (xt-1,...,xM-1)T, Θ=Ξ-1；
(3.5) characteristic equation solution procedure can be converted into the Maximum-likelihood estimation of formula (4)
Figure BDA0001577779790000095
Wherein, Wherein parameter matrix ΘiAnd Φi, i=1,2 ..., p-1 can be acquired by least-squares algorithm；
(3.6) penalty is added to the objective function of formula (4) and obtains the sparse whole vector of association
Figure BDA0001577779790000102
Wherein, P1, P2, P3For parameter Β, the penalty of Ω, Θ, using a normal form；Wherein Β is to assist whole vector Matrix, Ω, Θ are parameters to be estimated；Adjusting parameter λ1And λ2It is determined using crosscheck, adjusting parameter λ3Using Bayes Information criterion determines.Pass through the available whole vector of sparse association of solution to formula (6).
(4) variable can be divided using the whole vector of sparse association obtained in formula (6), specifically includes following sub-step It is rapid:
(4.1) the sparse whole vector matrix Β of association is obtained according to formula (6)s(N × K)=[βs,1,βs,2,...,βs,K], wherein K indicates the number of the sparse whole vector of association；
(4.2) steady residual sequence is obtained according to the sparse whole vector of association
Figure BDA0001577779790000103
Wherein k=1,2 ..., K, t= 1,2 ..., M.The consistent level for measuring residual sequence, and record residual difference sequence γ are examined using ADFk,tADF test statistics tk
(4.3) to obtained test statistics tkCarry out ascending sort, the corresponding sparse association of the smallest inspection statistics magnitude Whole vector is retained.The corresponding variable of nonzero element in the sparse whole vector of association is assigned in subgroup, and is denoted as Xb。
(4.4) by XbIn variable from initial data concentrate remove, raw data set is denoted as X at this timeL。
(4.5) iteration step (4.1)-(4.4), all variables are all assigned in 5 different subgroups.
(5) local static, dynamic monitoring statistic are established in each set of variables:
(5.1) local static monitoring and statistics amount is established
Figure BDA0001577779790000111
Wherein,
γs,b,tFor the steady residual sequence in each set of variables, Bf,bFor the whole moment of a vector of association calculated in each set of variables Battle array, Λs,b=(XbBf,b)T(XbBf,b)/(M-1) (b=1 ..., 5) be covariance matrix, M be sampled point number. xb,tFor Xb The transposition of middle row vector indicates the sampled point in t moment.
(5.2) local dynamic station monitoring and statistics amount is established
Figure BDA0001577779790000113
Wherein,
Figure BDA0001577779790000114
Indicate b-th of set of variables, p indicates time lag, Δ xp+1,bIndicate the Difference Terms, that is, Δ x at p+1 momentp+1,b=xp+1,b-xp,b, xp,bFor XbThe transposition of middle row vector indicates the sampled point at the p moment, ΘbAnd Φb(b=1 ..., Z) is parameter to be estimated, can It is acquired by least square.Be,bAnd Bf,bFor EbAnd FbCalculate the weight matrix obtained after canonical correlation analysis.Dynamic monitoring statistics Amount is
Figure BDA0001577779790000115
Wherein, te,bFrom matrix Te,b, it is Te,bMiddle column vector.
(6) global monitoring and statistics amount is established
(6.1) global static monitoring techniques statistic is established:
Figure BDA0001577779790000116
Wherein,
Figure BDA0001577779790000117
PS(xb)=P (xb|Ns)P(Ns)+P(xb|Fs)P(Fs)；P(Ns) be Confidence interval, i.e. P (Ns)=α, P (Fs)=1- α；
Figure BDA0001577779790000122
For sample xb's
Figure BDA0001577779790000123
Monitoring and statistics amount,
Figure BDA0001577779790000124
For monitoring and statistics amount
Figure BDA0001577779790000125
Control limit；
(6.2) global dynamic monitoring statistic is established:
Wherein,Pe(xb)=P (xb|Ne)P(Ne)+P(xb|Fe)P(Fe)；P(Ne) be Confidence interval, i.e. P (Ne)=α, P (Fe)=1- α；
Figure BDA0001577779790000128
Figure BDA0001577779790000129
For sample xb's
Figure BDA00015777797900001210
Monitoring and statistics amount,For monitoring and statistics amount
Figure BDA00015777797900001212
Control limit；
Step 7: online process monitoring
(7.1) to new collected non-stationary variable sample xnew,t(N × 1) carries out variable grouping, which is divided into Z Set of variables, that is, xnew,b,t, b=1,2 ..., 5.
(7.2) method recorded according to step 5 calculates local static monitoring and statistics amount
(7.3) local dynamic station monitoring and statistics amount is calculated
(7.4) global static, dynamic monitoring statistic is calculated
Figure BDA0001577779790000131
If
Figure BDA0001577779790000132
With
Figure BDA0001577779790000133
Mean that static, dynamic long-run equilibrium relationship is broken beyond control limit, at this time process It breaks down；If
Figure BDA0001577779790000134
While alarm,Beyond normal range (NR) is returned to after control limit, mean at this time The operating point of process changes；If
Figure BDA0001577779790000136
With
Figure BDA0001577779790000137
It is all limited without departing from control, means that process may work at this time Static state, dynamic long-run equilibrium relationship under new operating condition, but between variable are not broken or the operating condition is included in modeling data In.
If local static, dynamic monitoring statistic are influenced by failure, BICsOr BICeAlso it beyond control limit, anticipates at this time Taste the failure not only influence the local state of process, while global state is also affected, if BICsOr BICeDo not exceed Control limit indicates the local state of the failure influence process.
Table 1 is set of variables dividing condition, and non-stationary variable is divided into 5 different set of variables.It can be seen from Fig. 2 The load of gigawatt extra-supercritical unit often changes, it means that the operating condition of unit does not stop to change.Fig. 3 is the prison of this method Survey result, it can be seen that the static monitoring techniques statistic of set of variables 1-4 is beyond control limit after operating point changes, it means that Static long-run equilibrium relationship is broken.However dynamic monitoring statistic connects only after operating point changes beyond control limit Get off to return to normal range (NR).The static state and dynamic monitoring statistic of set of variables 5 are all limited without departing from control, this indicates the change of work Change does not influence the variable in set of variables 5.Fig. 4 is global monitoring result, it can be seen that global monitoring result and area monitoring As a result consistent.Fig. 5 illustrates the monitoring result of traditional cointegrating analysis, it can be seen that monitoring and statistics amount after operating point changes It is constantly in alarm condition, this can impact field engineer, so that engineer is mistakenly considered process and be in abnormality.Pass through This method can help field engineer effectively to distinguish the influence of the change and failure of process operating point to process, ensure that hundred The efficient operation of ten thousand kilowatts of extra-supercritical units.
1. set of variables division result of table
Set of variables Variable
1 4,7,15,16,20,22,26,27,29,30,33,34,37,39,43,47,49
2 5,6,13,18,24,31,35,40,41,42,45,50,51
3 28,44,46,48
4 8,9,11,12,17,19,21,23,25,36,38,
5 1,2,3,10,14,32,

Claims (1)

1. a kind of dynamic distributed monitoring method towards gigawatt extra-supercritical unit variable parameter operation, which is characterized in that The following steps are included:
(1) normal processes data are obtained: setting in a gigawatt extra-supercritical unit comprising J process variable, samples every time The vector of an available 1 × J obtains the two-dimensional matrix X under a normal processes after sampling M timesn(M×J)；
(2) it identifies non-stationary variable: identifying two-dimensional matrix X using Augmented Dickey-Fuller (ADF) method of inspectionn(M × J) in non-stationary variable, obtain non-stationary variable data matrix Xns(M × N), wherein N is the number of non-stationary variable；
(3) non-stationary variable data matrix X obtained in (2) is utilizedns(M × N)=[x1,x2,…,xN], xt=(x1,x2,…, xN)TEstablish sparse co-integration model；It establishes sparse co-integration model and specifically includes following sub-step:
(3.1) to xtEstablish Vector Autoression Models:
xt=Π1xt-1+…+Πpxt-p+c+μt (1)
Wherein, Π1~ΠpIt is the coefficient matrix of (N × N), μtFor (N × 1) matrix, white Gaussian noise, μ are indicatedt~N (0, Ξ), C is (N × 1) matrix, indicates constant, xtIndicate data matrix XnsThe transposition of a row vector in (M × N) is indicated in t moment Sampled value, t=1,2 ..., M, p is model order；
(3.2) x is subtracted at formula (1) both endst-1Obtain error correction model:
Figure FDA0002151845070000011
Wherein,
Figure FDA0002151845070000012
INFor the unit matrix of (N × N)；
(3.3) Γ in step (3.2) is decomposed into matrix Γ=Α Β of two sequency spectrumsT, formula (2) becomes:
Figure FDA0002151845070000021
Wherein, Α (N × R), Β (N × R)；
(3.4) the whole vector matrix Β of association in formula (3) is estimated by Maximum Likelihood Estimation:
Figure FDA0002151845070000022
Wherein, L (*) indicates maximum likelihood function, the mark of tr (*) representing matrix；X=(Δ xp+1,...,ΔxM)T, Y=(Δ Yp+1,...,ΔYM)T,
Figure FDA0002151845070000023
Ω=(Ω1,...,Ωp-1)T, Z= (xt-1,...,xM-1)T, Θ=Ξ-1；
(3.5) characteristic equation solution procedure can be converted into the Maximum-likelihood estimation of formula (4):
Figure FDA0002151845070000024
Wherein, Wherein parameter matrix ΘiAnd Φi, i=1,2 ..., p-1 can be acquired by least-squares algorithm；
(3.6) penalty is added to the objective function of formula (4) and obtains the sparse whole vector of association:
Figure FDA0002151845070000026
Wherein, P1, P2, P3For parameter Β, the penalty of Ω, Θ, using a normal form；Wherein Β is to assist whole vector matrix, Ω, Θ are parameters to be estimated；Adjusting parameter λ1And λ2It is determined using crosscheck, adjusting parameter λ3Using Bayesian Information Criterion determines；Pass through the available whole vector of sparse association of solution to formula (6)；
(4) variable can be divided using the whole vector of sparse association obtained in formula (6), specifically includes following sub-step:
(4.1) the sparse whole vector matrix Β of association is obtained according to formula (6)s(N × K)=[βs,1,βs,2,...,βs,K], wherein K is indicated The number of the sparse whole vector of association；
(4.2) steady residual sequence is obtained according to the sparse whole vector of associationWherein k=1,2 ..., K, t=1,2 ..., M；The consistent level for measuring residual sequence, and record residual difference sequence γ are examined using ADFk,tADF test statistics tk；
(4.3) to obtained test statistics tkCarry out ascending sort, the corresponding sparse whole vector of association of the smallest inspection statistics magnitude It is retained；The corresponding variable of nonzero element in the sparse whole vector of association is assigned in subgroup, and is denoted as Xb；
(4.4) by XbIn variable from initial data concentrate remove, raw data set is denoted as X at this timeL；
(4.5) iteration step (4.1)-(4.4) are all assigned in different subgroups until all variables, at this time original variable It is divided into Z different set of variables；
(5) local static, dynamic monitoring statistic are established in each set of variables:
(5.1) local static monitoring and statistics amount is established
Figure FDA0002151845070000032
Wherein,
Figure FDA0002151845070000033
γs,b,tFor the steady residual sequence in each set of variables, Bf,bFor the whole vector matrix of association calculated in each set of variables, Λs,b=(XbBf,b)T(XbBf,b)/(M-1) (b=1 ..., Z) it is covariance matrix；Z is the number of variable grouping, is indicated original Variable is divided into Z set of variables, xb,tFor XbThe transposition of middle row vector indicates the sampled point in t moment；
(5.2) local dynamic station monitoring and statistics amount is established:
Figure FDA0002151845070000034
Wherein,
B indicates b-th of set of variables, and p indicates time lag, Δ xp+1,bIndicate the Difference Terms, that is, Δ x at p+1 momentp+1,b= xp+1,b-xp,b, xp,bFor XbThe transposition of middle row vector indicates the sampled point at the p moment, ΘbAnd Φb(b=1 ..., Z) it is wait estimate Parameter is counted, can be acquired by least square；Be,bAnd Bf,bFor EbAnd FbCalculate the whole moment of a vector of association obtained after canonical correlation analysis Battle array；Dynamic monitoring statistic is
Wherein, te,bFrom matrix Te,b, it is Te,bMiddle column vector；
(6) global monitoring and statistics amount is established:
(6.1) global static monitoring techniques statistic is established:
Figure FDA0002151845070000043
Wherein, Z indicates the number of set of variables；
Figure FDA0002151845070000044
PS(xb)=P (xb| Ns)P(Ns)+P(xb|Fs)P(Fs)；P(Ns) it is confidence interval, i.e. P (Ns)=α, P (Fs)=1- α；
Figure FDA0002151845070000045
Figure FDA0002151845070000046
For sample xb'sMonitoring and statistics Amount,
Figure FDA0002151845070000048
For monitoring and statistics amount
Figure FDA0002151845070000049
Control limit；
(6.2) global dynamic monitoring statistic is established:
Figure FDA00021518450700000410
Wherein, Z indicates the number of set of variables；
Figure FDA00021518450700000411
Pe(xb)=P (xb|Ne)P (Ne)+P(xb|Fe)P(Fe)；P(Ne) it is confidence interval, i.e. P (Ne)=α, P (Fe)=1- α； For sample xb's
Figure FDA0002151845070000053
Monitoring and statistics Amount,
Figure FDA0002151845070000054
For monitoring and statistics amount
Figure FDA0002151845070000055
Control limit；
(7) online process monitoring:
(7.1) to new collected non-stationary variable sample xnew,t(N × 1) carries out variable grouping, which is divided into Z variable Group is xnew,b,t, b=1,2 ..., Z；
(7.2) method recorded according to step 5 calculates local static monitoring and statistics amount
Figure FDA0002151845070000056
(7.3) local dynamic station monitoring and statistics amount is calculated:
Figure FDA0002151845070000057
(7.4) global static, dynamic monitoring statistic is calculated:
Figure FDA0002151845070000058
If
Figure FDA0002151845070000059
With
Figure FDA00021518450700000510
It is limited beyond control, it is meant that static, dynamic long-run equilibrium relationship is broken, and event occurs for process Barrier；IfWhile alarm,
Figure FDA00021518450700000512
Beyond normal range (NR) is returned to after control limit, mean process at this time Operating point changes；If
Figure FDA00021518450700000513
With
Figure FDA00021518450700000514
It is all limited without departing from control, means process work in new operating condition at this time Under, but the static state, dynamic long-run equilibrium relationship between variable are not broken or the operating condition is included in modeling data；
If local static, dynamic monitoring statistic are influenced by failure, BICsOr BICeAlso beyond control limit, mean at this time The failure not only influences the local state of process, while also affecting global state, if BICsOr BICeNot beyond control Limit, indicates the local state of the failure influence process.
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