CN110297475A - A kind of batch process fault monitoring method based on Fourth-order moment singular value decomposition - Google Patents

A kind of batch process fault monitoring method based on Fourth-order moment singular value decomposition Download PDF

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CN110297475A
CN110297475A CN201910664867.XA CN201910664867A CN110297475A CN 110297475 A CN110297475 A CN 110297475A CN 201910664867 A CN201910664867 A CN 201910664867A CN 110297475 A CN110297475 A CN 110297475A
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CN110297475B (en
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常鹏
卢瑞炜
张祥宇
王普
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Beijing University of Technology
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • 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]
    • G05B19/41875—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 quality surveillance of production
    • 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
    • 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
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    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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Abstract

The invention discloses a kind of batch process fault monitoring methods based on Fourth-order moment singular value decomposition, for solving the non-linear and non-linear brought non-Gaussian system of data in batch process.The present invention includes " off-line modeling stage " and " on-line monitoring stage " two stages." off-line modeling stage " includes: to carry out Fourth-order moment processing to data normalization first, combine Fourth-order moment matrix；Singular value decomposition is carried out later, simplifies obtained matrix, is prepared for monitoring." on-line monitoring stage " includes: to be standardized to online data, carries out Fourth-order moment processing, combines Fourth-order moment matrix；Counting statistics amount and residual error and corresponding control line later；Finally generating process is monitored using statistic, generates alarm when a fault is found.The present invention has fully considered the non-linear and non-Gaussian system of batch process data, reduces the rate of false alarm of normal phase, reduces the rate of failing to report of failure phase and accelerates response speed, there is higher practical value.

Description

A kind of batch process fault monitoring method based on Fourth-order moment singular value decomposition
Technical field
The present invention is in industrial process malfunction monitoring field, more particularly to a kind of Fourth-order moment singularity value decomposition.This The method based on Fourth-order moment singular value decomposition malfunction monitoring of invention is specifically answering in TE (Tenessee Eastman) process With.
Background technique
Have a large amount of batch process in modern industrial process, common batch process have microbiological pharmacy, sewage treatment, Beer preparation, Yoghourt preparation etc..Batch process production lot-size is more flexible, and process reform is easier to, simultaneously for product Switching has certain compatibility, can carry out the production of a small amount of different cultivars, can adapt to raw material or service condition quickly Variation.
Industrial process data has strong non-linear non-linear due to system mostly, and collected data usually have There is non-gaussian distribution, and non-Gauss information is extremely important for the monitoring of system.In general, non-Gauss information needs High Order Analysis (data order is greater than 2).
Currently, High Order Analysis method mainly has: core principle component analysis (KPCA), multivariate core independent component analysis (MKICA), Polynary nuclear entropy constituent analysis (MKECA).The High Order Analysis method that above-mentioned algorithm uses is geo-nuclear tracin4.Nuclear energy enough maps the data into Higher-dimension, but the structural information between data can be destroyed simultaneously, can have a certain impact to fault diagnosis.
Summary of the invention
In order to overcome the above-mentioned deficiencies of the prior art, the present invention provides a kind of intervals based on Fourth-order moment singular value decomposition Procedure fault monitoring method.Itself of every kind of variable and preceding moment generate Fourth-order moment, rather than are carried out by core and total data Operation.To save the structure of lower data itself.Include significant non-Gauss information in Fourth-order moment, monitoring accuracy rate is mentioned It rises and has very great help.Mentioned method has just carried out Fourth-order moment processing to data before carrying out based on the monitoring of statistics herein.Right Data construct the stage of statistic, since inherently there is data high-order statistics of features amount just to have had high-order characteristic naturally, and It does not need additionally to create new statistical.
Present invention employs the following technical solution and realize step:
A. off-line modeling stage:
1) normal data is read in, the mean value mean of every kind of (total D kind) variable is calculateddWith standard deviation stdd, to normal data mark Standardization, formula are as follows:
Wherein, XdIndicate the data at d-th of variable whole moment, meandIndicate XdAverage value, stddIndicate XdStandard Difference；
2) to the X of total D kinddThe data at each moment carry out Fourth-order moment processing, formula is as follows；
cd(k)=xd(k)xd(k-τ1)xd(k-τ2)xd(k-τ3)
cd(k) Fourth-order moment at d-th of variable kth moment is indicated, k indicates sampling instant.xd(k) indicate d-th of variable the The value at k moment.τ1、τ2、τ3It indicates step-length, selects 1,2,3 herein, need k >=4 with this condition.
3) by cd(k) group is combined into Fourth-order moment Matrix C, and formula is as follows:
Wherein, N indicates finish time；
4) singular value decomposition (SVD) is carried out to C, svd (C)=USVT, two steps are carried out to U and are simplified.
The first step of i.U simplifies, and steps are as follows:
Calculate the minimum M value that lower section formula can be enabled to meet.
Wherein, SI, iIt is the element on S diagonal line, I is the minimum value in S row, column number,.δ is threshold value, adjustable, this Selected works select 90.
Retain the preceding M column of U, remaining deletion obtains the simplified U of the first step.
The second step of ii.U simplifies, and steps are as follows:
Judge that each element numerical values recited, formula are as follows in simplified U:
Wherein,Indicate square of the i-th row m column element in U,Indicate the i-th row whole element square Sum.M ' is the columns of U before deleting.
Work as uI, mMeet top formula Rule of judgment, is set 0, obtain the simplified U of second step.
5) s-matrix is cut, its M row M is arranged.Seek the inverse matrix S of S after cuttinginv.Will hereinbefore the simplified U of two steps and SinvIt saves, for monitoring on-line hereinafter
B. the stage is monitored on-line:
6) online data is read in, online data is standardized, formula is as follows:
Wherein, xd.onFor d-th of variate-value of online data, meand, stddFor the mean value and standard deviation of normal data；
7) to xD, onFourth-order moment processing is carried out, formula is as follows:
cD, on(k)=xD, on(k)xD, on(k-τ1)xD, on(k-τ2)xD, on(k-τ3)
And group is combined into Con
8) Counting statistics amount F2And its residual error FS:
F2=(ConU)Sinv(ConU)T
FS=(Con-ConU)(Con-ConU)T
U, S thereininvFor the matrix saved in off-line phase step 5.
9) F is calculated2, FS control line, formula is as follows:
Wherein, F (0.95, M, N '-M) indicates confidence level 95%, molecular freedom M (for the value in step 4), denominator freedom The F for spending N '-M is examined.N '=N- τ3。
L=diag (Son)
Wherein, SonThe s-matrix obtained after singular value decomposition for online data.L is the element value on its diagonal line.li For i-th of element in L.C is to be desired for 0,95% quantile that standard deviation is 1.
10) by the F at each moment2, FS and corresponding control pair ratio.Be less than it is then normal,
Return step 6；It then breaks down, alarms more than control line.
Beneficial effect
Compared with prior art, the method that the present invention constructs high-order statistic remains the information of data prototype structure, and The information of high level data has sufficiently been excavated during monitoring.The non-linear of data is fully considered, and by non-linear institute Bring non-Gaussian system.Data are analyzed by way of being Fourth-order moment by data configuration, with the data Counting statistics amount after analysis And its residual error, it completes monitoring and obtains satisfactory monitoring effect.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention；
Fig. 2 (a) is 1 F of TE procedure fault2Monitoring figure；
Fig. 2 (b) is 1 FS of TE procedure fault monitoring figure；
Fig. 3 (a) is 2 F of TE procedure fault2Monitoring figure；
Fig. 3 (b) is 2 FS of TE procedure fault monitoring figure；
Fig. 4 (a) is 5 F of TE procedure fault2Monitoring figure；
Fig. 4 (b) is 5 FS of TE procedure fault monitoring figure；
Fig. 5 (a) is 1 MKICAI of TE procedure fault2Statistic monitoring figure；
Fig. 5 (b) is 1 MKICA residual error of TE procedure fault monitoring figure；
Specific embodiment
Proposed algorithm can monitor the failure occurred in the production of industrial batch process.By to variable Fourth-order moment Processing carries out singular value decomposition, constructs statistic and corresponding control line completes monitoring.Finally can satisfactorily it be supervised Control is as a result, guarantee that the safety of production carries out.
For the accuracy for verifying the algorithm mentioned herein, it is tested using TE process data.TE(Tenessee Eastman) emulation platform be according to practical chemical reaction process establish emulation platform, generate data have time-varying, by force Coupling and nonlinear characteristic are widely used in control and the fault diagnosis model of test complex industrial process.
TE process has 21 kinds of failures, and specific descriptions are shown in Table 1
1 TE procedure fault list of table
The specific implementation step of mentioned method is as follows herein:
A. off-line modeling stage:
Step 1: reading in normal data, calculate the mean value mean of every kind of (total D kind) variabledWith standard deviation stdd, to normal number According to standardization, formula is as follows:
D terminates since 1 to D (variable total number).Xd=[xd(1), xd(2) ..., xd(n)].N is total sampling instant
Step 2: using formula cd(k)=xd(k)xd(k-τ1)xd(k-τ2)xd(k-τ3) to XdEvery time data carry out quadravalence Square processing.K is moment, initial value τ3+1；
Step 3: by cd(k) group is combined into Fourth-order moment Matrix C, and spelling is as follows:
Wherein, N is that total sampling instant n subtracts τ3Value afterwards.
Step 4: svd decomposition being carried out to C, obtains U matrix, s-matrix, two steps is carried out and simplifies.
Step 1: formula can be enabled by looking forThe minimum M value of satisfaction.Retain the preceding M column of U, remaining deletion.
Step 2: according to formulaJudge each element u in UI, m.The value of i is maximum since 1 For the line number of U.The value of m is up to M since 1.By the u for the condition that meetsI, mSet 0.
Step 5: s-matrix is cut, its M row M is arranged, remaining deletion.Seek the inverse matrix S of S after cuttinginv；
B. the stage is monitored online:
Step 6: according to formulaResistance to online data is standardized, meand、stddIt is positive The mean value and standard deviation of regular data.The value range of d is 1 to D.；
Step 7: according to formula cD, on(k)=xD, on(k)xD, on(k-τ1)xD, on(k-τ2)xD, on(k-τ3) to online data into The processing of row Fourth-order moment.And group is combined into
K is current time, initial value τ3+ 1, it is therefore desirable to proceed to τ in industrial process3Start to monitor after a moment；
Step 8: Counting statistics amount F2And its residual error FS:
The normalized set formula at whole moment are as follows:
F2=(ConU)Sinv(ConU)T
FS=(Con-ConU)(Con-ConU)T
The normalized set formula at independent kth moment is as follows:
F2(k)=(Con(k)U)Sinv(Con(k)U)T
FS (k)=(Con(k)-Con(k)U)(Con(k)-Con(k)U)T
Wherein, ConIt (k) is ConKth column.F2(k), the statistic and residual error at the k moment that FS (k) is respectively.
Step 9: the control line of Counting statistics amount and residual error, formula are as follows:
Step 10: by the F at each moment2, FS and corresponding control pair ratio.It is less than then normal, time step 6；It is more than Control line then breaks down, alarm.
Above-mentioned steps are concrete application step of the method for the present invention in TE process.
The validity of this method can be verified by Fig. 2, Fig. 3, Fig. 4.
Before 200 moment, production is in normal phase.As can be seen that method is mentioned herein statistic and residual values Entirely below control line, the case where not generating wrong report.And as seen in Figure 5, due to the wave of industrial process initial phase It moves larger, MKICA is caused to have more wrong report in early period.
The data of TE process introduce failure in 200 moment.It can be seen that the system due to constructing herein from Fig. 2,3,4 Metering has quadravalence characteristic, therefore very sensitive to the response of failure, just crosses control line by the short period, produces report It is alert.Production safety is successfully ensured.And the High Order Analysis mode that MKICA is used is geo-nuclear tracin4, the digging to the order of information of data It is effective to dig no quadravalence Moment Methods.Therefore, it can be found that the raising of MKICA statistic is more slow, without Fourth-order moment from figure The high-speed response ability of statistic.In actual industrial process, timely respond to be very important a Xiang Nengli.
By the analysis to lab diagram it can be concluded that, the proposed batch process based on Fourth-order moment singular value decomposition Method for diagnosing faults has lower rate of false alarm in normal phase, has lower rate of failing to report in failure phase and responds energy faster Power.Demonstrate the validity of proposed method.

Claims (1)

1. a kind of batch process fault monitoring method based on Fourth-order moment singular value decomposition, feature includes " off-line modeling stage " " on-line monitoring stage " two stages, the specific steps are as follows:
A. off-line modeling stage:
1) normal data is read in, the mean value mean of every kind of variable is calculateddWith standard deviation stdd, normal data is standardized, formula is such as Under:
Wherein, XdIndicate the data at d-th of variable whole moment, meandIndicate XdAverage value, stddIndicate XdStandard deviation, Shared D kind variable；
2) X to total D kind and after standardizingdThe data at each moment carry out Fourth-order moment processing, formula is as follows；
cd(k)=xd(k)xd(k-τ1)xd(k-τ2)xd(k-τ3)
cd(k) Fourth-order moment at d-th of variable kth moment is indicated, k indicates sampling instant, xd(k) indicate d-th of variable in kth The value at quarter, τ1、τ2、τ3Indicate step-length；
3) by cd(k) group is combined into Fourth-order moment Matrix C, and formula is as follows:
Wherein, N indicates finish time；
4) singular value decomposition SVD, svd (C)=USV are carried out to CT, two steps are carried out to U and are simplified.
The first step of i.U simplifies, and steps are as follows:
Calculate the minimum M value that lower section formula can be enabled to meet.
Wherein, SI, iIt is the element on S diagonal line, I is the minimum value in S row, column number,.δ is threshold value, adjustable；
Retain the preceding M column of U, remaining deletion obtains the simplified U of the first step；
The second step of ii.U simplifies, and steps are as follows:
Judge that each element numerical values recited, formula are as follows in simplified U:
Wherein,Indicate square of the i-th row m column element in simplified U,It indicates i-th in simplified U The sum of row whole element square, M ' are the columns of U before deleting；
Work as uI, mMeet top formula Rule of judgment, is set 0, obtain the simplified U of second step；
5) s-matrix is cut, its M row M is arranged, seeks the inverse matrix S of S after cuttinginv, will hereinbefore two steps simplified U and Sinv It saves, for monitoring on-line hereinafter；
B. the stage is monitored on-line:
6) online data is read in, online data is standardized, formula is as follows:
Wherein, xd.onFor d-th of variate-value of online data, meand, stddFor the mean value and standard deviation of normal data；
7) to the x after standardizationD, onFourth-order moment processing is carried out, formula is as follows:
cD, on(k)=xD, on(k)xD, on(k-τ1)xD, on(k-τ2)xD, on(k-τ3)
And group is combined into Con
8) Counting statistics amount F2And its residual error FS:
F2=(ConU)Sinv(ConU)T
FS=(Con-ConU)(Con-ConU)T
U, S thereininvFor the matrix saved in off-line phase step 5,
9) F is calculated2, FS control lineAnd FSlimit, formula is as follows:
Wherein, F (0.95, M, N '-M) indicates confidence level 95%, and molecular freedom M is the value in step 4, denominator freedom degree N '- The F of M is examined, N '=N- τ3,
Wherein,
L=diag (Son)
Wherein, SonFor the s-matrix that online data obtains after singular value decomposition, L is the element value on its diagonal line.liFor L In i-th of element, c is to be desired for 0,95% quantile that standard deviation is 1；
10) by the F at each moment2, FS and corresponding control pair ratio, be less than then normal, return step 6；It is then sent out more than control line Raw failure, alarm.
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CN111079857A (en) * 2019-12-30 2020-04-28 北京工业大学 Sewage treatment process fault monitoring method based on over-complete width learning model
CN114496209A (en) * 2022-02-18 2022-05-13 青岛市中心血站 Blood donation intelligent decision method and system
CN115372294A (en) * 2022-09-15 2022-11-22 中国市政工程东北设计研究总院有限公司 Graphite tube stability discrimination method

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