CN108345284A - A kind of quality dependent failure detection method becoming gauge block based on two - Google Patents

A kind of quality dependent failure detection method becoming gauge block based on two Download PDF

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CN108345284A
CN108345284A CN201810233560.XA CN201810233560A CN108345284A CN 108345284 A CN108345284 A CN 108345284A CN 201810233560 A CN201810233560 A CN 201810233560A CN 108345284 A CN108345284 A CN 108345284A
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CN108345284B (en
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童楚东
朱莹
俞海珍
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Ningbo University
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    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM]
    • G05B19/41885—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM] characterised by modeling, simulation of the manufacturing system
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
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    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
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    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

The present invention discloses a kind of quality dependent failure detection method becoming gauge block based on two, and genetic algorithm is combined by the method for the present invention with neighbour's constituent analysis algorithm, and input variable is divided into and incoherent two change gauge blocks related to quality.Then offset minimum binary (PLS) the model implementation quality dependent failure established between quality correlated variables block and output detects, and quality uncorrelated variables block then merges to PLS mode input residual errors with the uncorrelated fault detect of implementation quality.Compared to the dynamic method of tradition, the differentiation mass correlation that the method for the present invention is optimized in the way of genetic algorithm combination NCA and incoherent measurand.Secondly, the PLS mode inputs residual error of quality correlated variables measurand uncorrelated to quality is combined implementation and the incoherent fault detect of quality by the method for the present invention, and all composition informations uncorrelated to quality are more comprehensively utilized.Therefore, the method for the present invention ought to provide more accurate quality dependent failure testing result.

Description

A kind of quality dependent failure detection method becoming gauge block based on two
Technical field
The present invention relates to a kind of fault detection method of data-driven more particularly to a kind of quality phases becoming gauge block based on two Close fault detection method.
Background technology
It is to ensure the important technical of firms profitability to maintain the stability of product quality, is implemented relevant with quality Fault detect has deeper meaning.In recent years, carrying forward vigorously due to industrial information construction can acquire and store The process data and quality index data of magnanimity, this has established solid data basis for the fault detect research of data-driven. In existing scientific documents and patent, most of fault detection method purpose is to detect abnormal operating status, and It is related to relatively fewer with the relevant fault detection method of product quality.It is different from simple fault detect purpose, it is related to quality Fault detect need to distinguish whether detected failure influences whether product quality.In general, the number of product quality Usually there is prodigious lag according to information collection, if directly monitoring product quality indicator, though the inspection of quality dependent failure can be reached The purpose of survey, but since the time-delay characteristics of acquisition information can lead to fault detect not in time.A kind of feasible thinking is to pass through Hold very much the data information (such as temperature, pressure, flow) of measurement in production process reflect it is related to quality with it is incoherent Failure.Offset minimum binary (Partial Least Squares, PLS) is the most common method of such issues that solve.
From modeling process, PLS algorithms are built by potential characteristic component between input data and output data Relationship, that is to say, that the potential characteristic component of PLS models cover in input data with export relevant information.Thus, The fluctuation of potential characteristic component can reflect the fluctuation of output par, c, also can be by monitoring potential characteristic component come real The now prediction to output quality index and malfunction monitoring.However, traditional PLS methods all make the variable of all easy measurements For mode input, having considered input variable concentration, there are certain and incoherent measurands of output, if these variables Follow-up differentiation quality dependent failure can be given to cause prodigious interference effect as mode input.In the base of traditional PLS models Implement to improve on plinth, can overcome the problems, such as this respect.It is existing improve PLS models method have Total PLS methods with Concurrent PLS methods, the similarity of both methods be all be on the basis of PLS models, to potential feature at Divide and carries out going deep into excavation.Another implementing though is pre-processed to input data before establishing PLS models, is rejected The composition information orthogonal with output.If but such methods implement it is improper, it may appear that while will with export relevant information to picking It removes.However, how to implement from differentiation angle related or uncorrelated variables to quality with the relevant fault detect of quality also not Obtain more attention and concern.
Invention content
Technical problem underlying to be solved by this invention is：How to be distinguished from input variable related to quality with not phase The input variable of pass, and implement and incoherent fault detect related to quality on this basis.Specifically, the method for the present invention Genetic algorithm and neighbour's constituent analysis (Neighborhood Component Analysis, NCA) algorithm are combined, it will be defeated Enter variable and is divided into and incoherent two change gauge blocks related to quality.Then it establishes between quality correlated variables block and output PLS model implementation quality dependent failures detect, and quality uncorrelated variables block then merges with PLS mode input residual errors to implement matter Measure uncorrelated fault detect.
Technical solution is used by the present invention solves above-mentioned technical problem：A kind of quality correlation event becoming gauge block based on two Hinder detection method, includes the following steps：
(1) the data composition input training data matrix X ∈ R for being easy to measure in industrial processes are collectedn×m, and to it Being standardized makes the mean value of each process variable be 0, and standard deviation 1 obtains new data matrixWherein, n is number of training, and m is process measurement variable number, and R is set of real numbers, Rn×mIndicate n × m dimensions Real number matrix, xi∈Rm×1Representing matrixIn i-th of sample data, i=1,2 ..., n.
(2) off-line analysis means is used to obtain product quality data composition output instruction corresponding with input training data X Practice data Y ∈ Rn×1, the mean μ and standard deviation ε of vector Y are calculated, and be standardized to obtain new output data vector to it
(3) utilize the NCA methods based on genetic algorithm by input dataIn each measurand be distinguished into it is related to quality Change gauge blockAnd with the incoherent change gauge block of qualityWherein m1+m2=m, specific implementation process As follows：
1. genetic algorithm parameter is arranged, including population number N=10m, binary coding length L=m, maximum iteration Imax ＞ 1000, crossover probability c=0.8, mutation probability a=0.05；
2. the binary matrix data B of arbitrary initialization one N × m dimensions, and k=1 and iter=1 are set；
3. taking row k vector b in matrix Bk∈R1×mAfterwards, according to formula dij=bk|xi-xj| calculating matrixIn arbitrary two Sample point xiWith xjThe distance between dij, wherein | xi-xj| it indicates vector xi-xjIn element all take absolute value, lower label i, j =1,2 ..., n；
4. calculating x according to formula as followsiSelect xjProbability p as its reference data pointsij：
5. according to formula fk=∑i∑jzijpijCalculate k-th of binary vector bkCorresponding object function fk, wherein zij =(yi-yj)2；
6. judging whether to meet condition k ＜ NIf so, setting after k=k+1 return to step 3.；If it is not, obtain object function to Measure F=[f1, f2..., fN] after find out the corresponding binary vector b of maximum value in Fmax, and execute next step 7.；
7. the selection operation for implementing genetic algorithm obtains updated binary matrix data B；
8. the crossover operation for implementing genetic algorithm updates binary matrix data B again；
9. the mutation operation for implementing genetic algorithm updates binary matrix data B again；
10. changing last column in binary matrix data B into binary vector bmax；
Judge whether to meet condition iter ＜ ImaxIf so, setting return to step after iter=iter+1 and k=1 ③；If it is not, then obtaining binary vector bmaxAnd execute next step
According to binary data vector bmaxPosition where middle element 1 and 0 accordingly willIn variable partitions at With the relevant measurand data matrix of qualityWithThat is bmaxMiddle element 1 indicates and b related to qualitymax0 table of middle element Show uncorrelated to quality.
(4) PLS algorithms are utilized to establishWith outputBetween regression model, specific implementation steps are as follows：
1. set g=1 withAfterwards, initialization vector；
2. according to formulaIt calculates separately to obtain coefficient vector wg, score vector sgAnd coefficient qg, wherein | | Zug| | it indicates to calculate vector Z ugLength；
3. according to formulaCalculate vector unew；
4. judging whether to meet condition | | ug-unew| | ＜ 10-6If it is not, then setting ug=unewReturn to step is 2. afterwards；If so, It then executes 5.；
5. according to formula pg=ZTsg/(sg Tsg) g-th of projection vector p is calculatedg, and retain vectorial pg, vector wgAnd Coefficient qg；
6. judgment matrix Yg=sgpg TIn greatest member whether be more than 0.01If so, according to formula Z=Z-sgpg TUpdate Step is executed after matrix Z 7.；If it is not, then obtaining projection matrix P=[p1, p2..., pg], coefficient matrix W=[w1, w2..., wg]、 With row vector Q=[q1, q2..., qg], and execute step 8.；
7. judging g ＜ m1If so, after setting g=g+1, return to step is 2.；If it is not, then obtaining final projection matrix P= [p1, p2..., pg], coefficient matrix W=[w1, w2..., wg] and vector Q=[q1, q2..., qg]；
8. calculating projection vector Θ=Wi(Pi TWi)-1, then inputtingWith outputBetween PLS models be：
In above formula, E1With F1The model residual error with output is respectively inputted,By g potential characteristic components Composition.
(5) by residual error E1With the incoherent change gauge block of qualityForm a matrixAfterwards, Φ is implemented strange Different value is decomposed, i.e.,：, specific implementation process is as follows：
1. after r=1 and F=Φ are arranged, initializing column vector trFor the first row in matrix Φ；
2. according to formula vr=FTtr/(tr Ttr) vector v is calculatedr；
3. according to formula tnew=Fvr/(vr Tvr) calculate vector tnew；
4. judging whether to meet condition | | tnew-tr| | ＜ 10-6If so, executing next step 5.；If it is not, then setting tr= tnewReturn to step is 2. afterwards；
5. according to formulaWith μr=trλr -1It calculates separately to obtain r-th of singular value λrWith vectorial μr, and according to Formula F=F-trvr TUpdate F；
6. judging whether to meet condition λr≤10-3If it is not, r=r+1 and vector t is then arrangedrFor the first row in matrix F Return to step is 2. afterwards；If so, by all obtained singular value λ1, λ2..., λrForm diagonal matrixIt is obtained all The vectorial μ arrived1, μ2..., μrForm matrix U=[μ1, μ2..., μr], then by all vector vs1, v2..., vrComposition matrix V= [v1, v2..., vr]。
(6) according to formulaWithCalculate separately the control with the relevant malfunction monitoring statistic of quality The upper limit processedAnd the upper control limit with the incoherent malfunction monitoring statistic of qualityWhereinExpression degree of freedom is r Value of the chi square distribution under confidence alpha=99%.
(7) the data x of new easy measurement is collectedi∈R1×m, and carry out standardization identical with X to it and obtainLower label t indicates the current last samples moment.
Significantly, since quality index measurement has very big delay, therefore when the online fault detect of implementation, currently most New sampling instant can not use quality achievement data, be only easy the data x measuredi∈R1×m。
(8) according to the variable piecemeal situation in step (3), accordingly willIt is divided into two change gauge blocksWithIt is right respectively Answer quality correlated variables and quality uncorrelated variables.
(9) it is calculated and the relevant malfunction monitoring statistic D of quality according to formula as follows1：
In above formula, A=TTT/(n-1)。
(10) residual error will be inputtedWithIt is merged into a vectorAfterwards, according to as follows Formula calculates and the incoherent malfunction monitoring statistic D of quality0：
(11) implement fault detect, if, then it is determined as and the relevant failure of quality；IfAndIt is then determined as and the incoherent failure of quality.
Compared with conventional method, inventive process have the advantage that：
First, the method for the present invention most optimally distinguishes mass correlation and not phase in the way of genetic algorithm combination NCA The measurand of pass not only eliminates the interference effect of quality uncorrelated variables, but also has optimally selected quality correlated variables The relevant fault detect of implementation quality.Secondly, the method for the present invention by the PLS mode inputs residual error of quality correlated variables and quality not Measurement of correlation variable combines implementation and the incoherent fault detect of quality, be more fully utilized it is all with quality not Related Component information.Therefore, the method for the present invention ought to provide more accurate quality dependent failure testing result.
Description of the drawings
Fig. 1 is the implementing procedure figure of the method for the present invention.
Fig. 2 is the differentiation result of quality correlated variables and quality uncorrelated variables
Fig. 3 is the time series chart of quality index.
Fig. 4 is the monitoring details comparison diagram of TE process reactor cooling water inlet temperature failures.
Specific implementation mode
The method of the present invention is described in detail with specific case study on implementation below in conjunction with the accompanying drawings.
As shown in Figure 1, the present invention discloses a kind of quality dependent failure detection method becoming gauge block based on two.With reference to one The example of a specific industrial process illustrates the specific implementation process of the method for the present invention, and relative to the superior of existing method Property.
Application comes from the experiment of the U.S. Tennessee-Yi Siman (TE) chemical process, and prototype is the life of Yi Siman chemical industry Produce an actual process flow in workshop.Currently, complexity of the TE processes because of its flow, has been used as a standard test platform quilt It is widely used in fault detect research.Entire TE processes include that 22 measurands, 12 performance variables and 19 composition measurements become Amount.The data acquired are divided into 22 groups, including the data set and 21 groups of fault datas under 1 group of nominal situation.And at these In fault data, 16 are known fault types, such as the changing of cooling water inlet temperature or feed constituents, valve viscous, anti- Dynamics drift etc. is answered, also 5 fault types are unknown.In order to be monitored to the process, as shown in Table 1 33 are chosen Next a process variable is explained in detail specific implementation step of the present invention in conjunction with the TE processes.
Table 1：TE process monitoring variables.
Serial number Variable description Serial number Variable description Serial number Variable description
1 Material A flow 12 Separator liquid level 23 D material inlet valves position
2 Material D flows 13 Separator pressure 24 E material inlet valves position
3 Material E flows 14 Separator bottom of tower flow 25 A material inlet valves position
4 Combined feed flow 15 Stripper grade 26 A and C material inlet valves 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
First, Fault Model is established using the sampled data under TE process nominal situations, included the following steps：
(1) to training data matrix X ∈ R960×33Being standardized makes the mean value of each process variable be 0, standard deviation It is 1, obtains new data matrix；
(2) to corresponding product quality data Y ∈ Rn×1Execution standardization, which is handled, newly to be exported；
(3) utilize neighbour's constituent analysis (NCA) method based on genetic algorithm by input dataZhong Ge measurands area It is divided into and the relevant change gauge block of qualityAnd with the incoherent change gauge block of qualityCorresponding variable Weighted value is shown in Fig. 2, and weighted value is that 1 expression quality is related, and it is that quality is uncorrelated that weighted value, which is 0,；
(4) offset minimum binary (PLS) algorithm is utilized to establishWith outputBetween regression model；
(5) by residual error E1With the incoherent change gauge block of qualityForm a matrixAfterwards, Φ is implemented strange Different value is decomposed, i.e.,：；
(6) according to formulaWithCalculate separately the control with the relevant malfunction monitoring statistic of quality The upper limit processedAnd the upper control limit with the incoherent malfunction monitoring statistic of quality
Secondly, test data set of the acquisition TE processes under reactor cooling water inlet temperature fault condition is implemented online Process monitoring.
(7)：Collect the data x of new easy measurementi∈R1×33, and carry out standardization identical with X to it and obtain
(8)：According to the variable piecemeal situation in step (3), accordingly willIt is divided into two change gauge blocksWithIt is right respectively Answer quality correlated variables and quality uncorrelated variables；
(9)：It is calculated and the relevant malfunction monitoring statistic D of quality according to formula as follows1：
(10)：Residual error will be inputtedWithIt is merged into a vectorAfterwards, according to following institute Show that formula calculates and the incoherent malfunction monitoring statistic D of quality0；
(11)：Implement fault detect, ifIt is then determined as and the relevant failure of quality；IfAndIt is then determined as and the incoherent failure of quality；
Quality index time series chart under TE process reactor cooling water inlet temperature fault conditions is shown in Fig. 3 In, as can be seen from Figure 3 (i.e. failure is introduced after failure generation after 160 sampling instants), a period of time endoplasm of beginning Figureofmerit unusual fluctuations are apparent, after unusual fluctuations after a period of time, due to the self-control of TE Process Control Systems, the event Quality index will not be played negative effect by hindering, i.e. quality index recovery normal operation, but the cooling water inlet temperature failure Still it is present in during TE, only the amount of confrontation does not have an impact.
By the malfunction monitoring details of the method for the present invention and CPLS methods in contrast in such as Fig. 4.It can be found that originally from Fig. 4 The quality dependent failure monitoring index of inventive method can embody this situation of change of mass, and with the incoherent failure of quality Monitoring figure then shows that in failure, this is consistent with actual conditions always present in TE processes.In contrast, traditional CPLS methods are with regard to nothing Method embodies this characteristic of the failure.
Above-mentioned case study on implementation only is used for illustrating the specific implementation of the present invention, rather than limits the invention. In the protection domain of spirit and claims of the present invention, to any modification that the present invention makes, the protection of the present invention is both fallen within Range.

Claims (4)

1. a kind of quality dependent failure detection method becoming gauge block based on two, which is characterized in that include the following steps：
The implementation process in off-line modeling stage is as follows：
Step (1)：Collect the data composition input training data matrix X ∈ R for being easy to measure in industrial processesn×m, and to it Being standardized makes the mean value of each process variable be 0, and standard deviation 1 obtains new data matrixWherein, n is number of training, and m is process measurement variable number, and R is set of real numbers, Rn×mIndicate n × m dimensions Real number matrix, xi∈Rm×1Representing matrixIn i-th of sample data, i=1,2 ..., n；
Step (2)：Product quality data composition output instruction corresponding with input training data X is obtained using off-line analysis means Practice data Y ∈ Rn×1, the mean μ and standard deviation ε of vector Y are calculated, and be standardized to obtain new output data vector to it
Step (3)：Using neighbour's constituent analysis (NCA) method based on genetic algorithm by input dataZhong Ge measurands area It is divided into and the relevant change gauge block of qualityAnd with the incoherent change gauge block of qualityWherein m1+m2=m；
Step (4)：It is established using offset minimum binary (PLS) algorithmWith outputBetween regression model, i.e.,：
In above formula, E1With F1The model residual error with output is respectively inputted,It is made of g potential characteristic components；
Step (5)：By residual error E1With the incoherent change gauge block of qualityForm a matrixAfterwards, Φ is implemented strange Different value is decomposed, i.e.,：Φ=UAVT；
Step (6)：According to formulaWithCalculate separately the control with the relevant malfunction monitoring statistic of quality The upper limit processedAnd the upper control limit with the incoherent malfunction monitoring statistic of qualityWhereinIndicate that degree of freedom is r's Value of the chi square distribution under confidence alpha=99%；
Step (7)：Collect the data x of new easy measurementi∈R1×m, and carry out standardization identical with X to it and obtainLower label t indicates the current last samples moment；
The implementation process in online process monitoring stage is as follows：
Step (8)：According to the variable piecemeal situation in step (3), accordingly willIt is divided into two change gauge blocksWithIt corresponds to respectively Quality correlated variables and quality uncorrelated variables；
Step (9)：It is calculated and the relevant malfunction monitoring statistic D of quality according to formula as follows1：
In above formula, A=TTT/(n-1)；
Step (10)：Residual error will be inputtedWithIt is merged into a vectorAfterwards, according to as follows Formula calculates and the incoherent malfunction monitoring statistic D of quality0：
D0=| | fVA-1||2 (3)
In above formula, | | fVA-1| | vector length is sought in expression；
Step (11)：Implement fault detect, ifIt is then determined as and the relevant failure of quality；IfAndIt is then determined as and the incoherent failure of quality.
2. a kind of quality dependent failure detection method becoming gauge block based on two according to claim 1, which is characterized in that institute The specific implementation process stated in step (3) using the NCA methods differentiation change gauge block based on genetic algorithm is as follows：
1. genetic algorithm parameter is arranged, including population number N=10m, binary coding length L=m, maximum iteration Imax ＞ 1000, crossover probability c=0.8, mutation probability a=0.05；
2. the binary matrix data B of arbitrary initialization one N × m dimensions, and k=1 and iter=1 are set；
3. taking row k vector b in matrix Bk∈R1×mAfterwards, according to formula dij=bk|xi-xj| calculating matrixIn arbitrary two sample Point xiWith xjThe distance between dij, wherein | xi-xj| it indicates vector xi-xjIn element all take absolute value, lower label i, j=1, 2 ..., n；
4. calculating x according to formula as followsiSelect xjProbability p as its reference data pointsij：
5. according to formula fk=∑i∑jzijpijCalculate k-th of binary vector bkCorresponding object function fk, wherein zij= (yi-yj)2；
6. judging whether to meet condition k ＜ NIf so, setting after k=k+1 return to step 3.；If it is not, obtaining object function vector F= [f1, f2..., fN] after find out the corresponding binary vector b of maximum value in Fmax, and execute next step 7.；
7. the selection operation for implementing genetic algorithm obtains updated binary matrix data B；
8. the crossover operation for implementing genetic algorithm updates binary matrix data B again；
9. the mutation operation for implementing genetic algorithm updates binary matrix data B again；
10. changing last column in binary matrix data B into binary vector bmax；
Judge whether to meet condition iter ＜ ImaxIf so, setting after iter=iter+1 and k=1 return to step 3.；If It is no, then obtain binary vector bmaxAnd execute next step
According to binary data vector bmaxPosition where middle element 1 and 0 accordingly willIn variable partitions Cheng Yuzhi Measure relevant measurand data matrixWithThat is bmaxMiddle element 1 indicates and b related to qualitymaxMiddle element 0 indicates and matter It measures uncorrelated.
3. a kind of dynamic process monitoring method based on distributing AR-PLS models according to claim 1, feature exist In the step (4) is middle to be established using PLS algorithmsWith outputBetween regression model the following institute of specific implementation process Show：
1. set g=1 withAfterwards, initialization vector
2. according to formula wg=Zug/||Zug||、sg=Zwg、It calculates separately to obtain coefficient vector wg, score Vectorial sgAnd coefficient qg, wherein | | Zug| | it indicates to calculate vector Z ugLength；
3. according to formulaCalculate vector unew；
4. judging whether to meet condition | | ug-unew| | ＜ 10-6If it is not, then setting ug=unewReturn to step is 2. afterwards；If so, executing ⑤；
5. according to formula pg=ZTsg/(sg Tsg) g-th of projection vector p is calculatedg, and retain vectorial pg, vector wgAnd coefficient qg；
6. judgment matrix Yg=sgpg TIn greatest member whether be more than 0.01If so, according to formula Z=Z-sgpg TUpdate matrix Z Execute step 7. afterwards；If it is not, then obtaining projection matrix P=[p1, p2..., pg], coefficient matrix W=[w1, w2..., wg] and row Vectorial Q=[q1, q2..., qg], and execute step 8.；
7. judging g ＜ m1If so, after setting g=g+1, return to step is 2.；If it is not, then obtaining final projection matrix P=[p1, p2..., pg], coefficient matrix W=[w1, w2..., wg] and vector Q=[q1, q2..., qg]；
8. calculating projection vector Θ=Wi(Pi TWi)-1, then inputtingWith outputBetween PLS models be：
In above formula, E1With F1The model residual error with output is respectively inputted,It is made of g potential characteristic components.
4. a kind of dynamic process monitoring method based on distributing AR-PLS models according to claim 1, feature exist In the specific implementation process for implementing singular value decomposition in the step (5) to Φ is as follows：
1. after r=1 and F=Φ are arranged, initializing column vector trFor the first row in matrix Φ；
2. according to formula vr=FTtr/(tr Ttr) vector v is calculatedr；
3. according to formula tnew=Fvr/(vr Tvr) calculate vector tnew；
4. judging whether to meet condition | | tnew-tr| | ＜ 10-6If so, executing next step 5.；If it is not, then setting tr=tnewAfterwards Return to step is 2.；
5. according to formulaWith μr=trλr -1It calculates separately to obtain r-th of singular value λrWith vectorial μr, and according to formula F =F-trvr TUpdate F；
6. judging whether to meet condition λr≤10-3If it is not, r=r+1 and vector t is then arrangedrTo be returned after the first row in matrix F Step is 2.；If so, by all obtained singular value λ1, λ2..., λrForm diagonal matrix A ∈ Rr×r, by all obtained vectors μ1, μ2..., μrForm matrix U=[μ1, μ2..., μr], then by vector v1, v2..., vrForm matrix V=[v1, v2..., vr]。
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CN109409425A (en) * 2018-10-09 2019-03-01 宁波大学 A kind of fault type recognition method based on neighbour's constituent analysis
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