CN110297475B - Intermittent process fault monitoring method based on fourth-order moment singular value decomposition - Google Patents

Intermittent process fault monitoring method based on fourth-order moment singular value decomposition Download PDF

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CN110297475B
CN110297475B CN201910664867.XA CN201910664867A CN110297475B CN 110297475 B CN110297475 B CN 110297475B CN 201910664867 A CN201910664867 A CN 201910664867A CN 110297475 B CN110297475 B CN 110297475B
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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
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    • 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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Abstract

The invention discloses an intermittent process fault monitoring method based on fourth-order moment singular value decomposition, which is used for solving the problem of data nonlinearity in an intermittent process and non-Gaussian property caused by nonlinearity. The invention comprises two stages of an off-line modeling stage and an on-line monitoring stage. The "offline modeling phase" includes: firstly, standardizing data, performing fourth-order moment processing, and combining a fourth-order moment matrix; and then singular value decomposition is carried out, and the obtained matrix is simplified to prepare for monitoring. The "on-line monitoring phase" includes: standardizing the online data, performing fourth-order moment processing, and combining a fourth-order moment matrix; then calculating the statistic and the residual error and the corresponding control line; and finally, monitoring the generation process by using the statistic, and generating an alarm when a fault is found. The invention fully considers the nonlinearity and non-Gaussian property of the intermittent process data, reduces the false alarm rate in the normal stage, reduces the false alarm rate in the fault stage, accelerates the response speed and has higher practical value.

Description

Intermittent process fault monitoring method based on fourth-order moment singular value decomposition
Technical Field
The invention belongs to the field of industrial process fault monitoring, and particularly relates to a four-order moment singular value decomposition technology. The method for monitoring the fault based on the fourth-order moment singular value decomposition is specifically applied to the TE (Tennessee Eastman) process.
Background
Modern industrial processes have a large number of intermittent processes, and common intermittent processes include microbial pharmacy, sewage treatment, beer preparation, yoghourt preparation and the like. Batch production in the intermittent process is flexible in scale, the process is easy to change, meanwhile, the product switching has certain compatibility, a small amount of production of different varieties can be carried out, and the method can adapt to the change of raw materials or operation conditions quickly.
Due to the nonlinearity of the system, the collected data generally has a non-Gaussian distribution, and non-Gaussian information is very important for monitoring the system. Typically, non-gaussian information requires high order analysis (data order greater than 2).
Currently, the high-order analysis methods mainly include: kernel Principal Component Analysis (KPCA), Multivariate Kernel Independent Component Analysis (MKICA), Multivariate Kernel Entropy Component Analysis (MKECA). The high-order analysis method used by the above algorithm is a kernel technique. The kernel can map data to high dimension, but structural information among the data is damaged at the same time, and fault diagnosis is influenced to a certain extent.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an intermittent process fault monitoring method based on fourth-order moment singular value decomposition. Each variable generates a fourth moment with itself at the previous time, rather than operating with the entire data through a kernel. Thereby preserving the structure of the underlying data itself. The fourth-order moment contains remarkable non-Gaussian information, and the monitoring accuracy is greatly improved. The method presented herein performs fourth-order moment processing on the data prior to performing the statistics-based monitoring. In the stage of constructing the statistic on the data, the statistic naturally has high-order characteristics due to the fact that the data have high-order characteristics, and a new statistic mode does not need to be additionally created.
The invention adopts the following technical scheme and implementation steps:
A. an off-line modeling stage:
1) reading in normal data, calculating mean value mean of each (total D) variabledAnd standard deviation stddNormalized to normal data, the formula is as follows:
Figure DEST_PATH_IMAGE001
wherein the content of the first and second substances,
Figure 900097DEST_PATH_IMAGE002
data representing all the time instants of the d-th variable,
Figure 551658DEST_PATH_IMAGE003
to represent
Figure 65816DEST_PATH_IMAGE002
Is determined by the average value of (a) of (b),
Figure 320080DEST_PATH_IMAGE004
to represent
Figure 868873DEST_PATH_IMAGE002
Standard deviation of (d);
2) for a total of D species
Figure 425756DEST_PATH_IMAGE002
The data of each moment is processed by fourth moment, and the formula is as follows;
Figure 427210DEST_PATH_IMAGE005
Figure 485165DEST_PATH_IMAGE006
representing the fourth moment at the kth instant of the d-th variable, k representing the sampling instant.
Figure 888465DEST_PATH_IMAGE007
Indicating the value of the d-th variable at the k-th time.
Figure 616249DEST_PATH_IMAGE008
Denotes the step size, 1, 2, 3 are selected in this text, under which conditions
Figure 104999DEST_PATH_IMAGE009
。
3) Will be provided with
Figure 205460DEST_PATH_IMAGE006
The combination is a fourth moment matrix C, and the formula is as follows:
Figure 463266DEST_PATH_IMAGE010
wherein N represents an end time;
4) singular Value Decomposition (SVD) of C, SVD (C) = USVTA two-step simplification of U is performed.
i.U, the first step is simplified as follows:
the minimum value of M that the following formula can satisfy is calculated.
Figure 627531DEST_PATH_IMAGE011
Wherein the content of the first and second substances,
Figure 603578DEST_PATH_IMAGE012
is the element on the diagonal of S, and I is the minimum in the number of S rows and columns.
Figure 878701DEST_PATH_IMAGE013
Is a threshold value, which can be adjusted, here 90.
And (5) reserving the first M columns of the U, and deleting the rest to obtain the U after the first step of simplification.
A second step simplification of u, steps as follows:
judging the numerical value of each element in the simplified U, wherein the formula is as follows:
Figure 381227DEST_PATH_IMAGE014
wherein the content of the first and second substances,
Figure 450814DEST_PATH_IMAGE015
representing the square of the ith row and mth column element in U,
Figure 914156DEST_PATH_IMAGE016
representing the sum of the squares of all elements in row i.
Figure 727391DEST_PATH_IMAGE017
The number of columns of U before deletion.
When in use
Figure 84423DEST_PATH_IMAGE018
And (4) satisfying the judgment condition of the formula above, and setting the judgment condition to be 0 to obtain the simplified U in the second step.
5) And cutting the S matrix into M rows and M columns. Inverse matrix S of the clipped S is solvedinv. U and after two steps in the foregoing are simplifiedSinvPreservation for later on-line monitoring
B. And (3) an online monitoring stage:
6) reading in on-line data and standardizing the on-line data, wherein the formula is as follows:
Figure 590491DEST_PATH_IMAGE019
wherein the content of the first and second substances,
Figure 275550DEST_PATH_IMAGE020
for the value of the d-th variable of the online data,
Figure 892477DEST_PATH_IMAGE021
mean and standard deviation of normal data;
7) to pair
Figure 104015DEST_PATH_IMAGE022
Fourth moment processing is carried out, and the formula is as follows:
Figure 780984DEST_PATH_IMAGE023
and combined into Con
Figure 953339DEST_PATH_IMAGE024
8) Computing statistics
Figure 373956DEST_PATH_IMAGE025
And residual error FS:
Figure 580947DEST_PATH_IMAGE026
Figure 54916DEST_PATH_IMAGE027
wherein U is,
Figure 714567DEST_PATH_IMAGE028
The matrix saved in step 5 of the off-line phase.
9) Computing
Figure DEST_PATH_IMAGE029
The control line of (2) is as follows:
Figure 407717DEST_PATH_IMAGE030
wherein the content of the first and second substances,
Figure DEST_PATH_IMAGE031
the confidence coefficient is 95%, the numerator degree of freedom M (the value in step 4), and the denominator degree of freedom
Figure 62689DEST_PATH_IMAGE032
-F-test of M.
Figure 81461DEST_PATH_IMAGE033
。
Figure 228408DEST_PATH_IMAGE034
Figure DEST_PATH_IMAGE035
Figure 115462DEST_PATH_IMAGE036
Wherein the content of the first and second substances,
Figure 31465DEST_PATH_IMAGE037
the matrix is an S matrix obtained after the on-line data is subjected to singular value decomposition. L is the value of the element on its diagonal.
Figure 955559DEST_PATH_IMAGE038
Is in LThe ith element. c is the 95% quantile expected to be 0 with a standard deviation of 1.
Figure DEST_PATH_IMAGE039
10) At each moment
Figure 448857DEST_PATH_IMAGE029
In contrast to the corresponding control line. If not, returning to the step 6; if the control line is exceeded, a fault occurs, and an alarm is given.
Advantageous effects
Compared with the prior art, the method for constructing the high-order statistics keeps the information of the original structure of the data, and fully excavates the information of the high-order data in the monitoring process. The nonlinearity of the data and the non-Gaussian property caused by the nonlinearity are fully considered. Data are analyzed in a mode of constructing the data into fourth moment, and statistics and residual errors of the statistics are calculated by the analyzed data, so that a satisfactory monitoring effect is achieved.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2(a) shows TE process fault 1F2Monitoring a graph;
FIG. 2(b) is a TE process fault 1 FS monitoring diagram;
FIG. 3(a) is a TE process fault 2F2Monitoring a graph;
FIG. 3(b) is a TE process fault 2 FS monitoring diagram;
FIG. 4(a) shows TE process fault 5F2Monitoring a graph;
FIG. 4(b) is a TE process fault 5 FS monitor diagram;
FIG. 5(a) is TE process failure 1 MKICA I2A statistic monitoring graph;
FIG. 5(b) is a TE process fault 1 MKICA residual monitoring diagram;
Detailed Description
The algorithm presented herein can monitor faults that occur in industrial batch process production. And performing singular value decomposition by processing the variable fourth moment, and constructing statistics and corresponding control lines to complete monitoring. And finally, a satisfactory monitoring result can be obtained, and the safe production is ensured.
To verify the accuracy of the algorithms presented herein, tests were performed using TE process data. The TE (Tennessee Eastman) simulation platform is a simulation platform established according to the actual chemical reaction process, the generated data has time-varying, strong coupling and nonlinear characteristics, and the TE (Tennessee Eastman) simulation platform is widely used for testing control and fault diagnosis models of complex industrial processes.
There are 21 kinds of failures in TE process, and the detailed description is shown in Table 1
TABLE 1 TE Process Fault List
Fault numbering Cause of failure
1 A, C feed rate, B composition constant (stream 4)
2 Composition B, constant feed ratio of A, C (stream 4)
3 D feed temperature (stream 2)
4 Reactor cooling water entry temperature
5 Condenser cooling water entry temperature
6 A feed reduction (stream 1)
7 C head pressure reduction (stream 4)
8 A, B, C feed combination (stream 4)
9 D feed temperature (stream 2)
10 C feed temperature (stream 4)
11 Reactor cooling water entry temperature
12 Condenser cooling water entry temperature
13 Kinetics of the reaction
14 Cooling water valve of reactor
15 Cooling water valve of condenser
16 Is unknown
17 Is unknown
18 Is unknown
19 Is unknown
20 Is unknown
21 The valve of flow 4 is fixed
The method comprises the following specific implementation steps:
A. an off-line modeling stage:
step 1: reading in normal data, calculating mean value mean of each (total D) variabledAnd standard deviation stddNormalized to normal data, the formula is as follows:
Figure 749388DEST_PATH_IMAGE040
Figure 785477DEST_PATH_IMAGE041
Figure 146052DEST_PATH_IMAGE042
d starts at 1 and ends at D (total number of variables).
Figure 267591DEST_PATH_IMAGE043
. n is the total sampling time
Step 2: by the formula
Figure 994982DEST_PATH_IMAGE044
To XdThe data at each moment in time of (2) is subjected to fourth moment processing. k is time, startHas a value of
Figure 619999DEST_PATH_IMAGE045
；
And step 3: will be provided with
Figure 151474DEST_PATH_IMAGE006
The combination is a fourth moment matrix C, and the spelling method is as follows:
Figure 494731DEST_PATH_IMAGE010
where N is the total sampling time N minus
Figure 527278DEST_PATH_IMAGE046
The latter value.
And 4, step 4: and svd decomposition is carried out on the C to obtain a U matrix and an S matrix, and two-step simplification is carried out.
The first step is as follows: find the equation of the command
Figure 272380DEST_PATH_IMAGE047
Minimum M value satisfied. The first M columns of U are retained, and the remainder are deleted.
The second step is that: according to the formula
Figure 974757DEST_PATH_IMAGE048
Judging each element in U
Figure 805310DEST_PATH_IMAGE018
. The value of i starts from 1 and is the maximum number of rows of U. The value of M is from 1 and is at most M. Will satisfy the conditions
Figure 375968DEST_PATH_IMAGE018
And setting 0.
And 5: and cutting the S matrix into M rows and M columns, and deleting the rest. Inverse matrix S of the clipped S is solvedinv；
B. And (3) an online monitoring stage:
step 6: according to the formula
Figure 975577DEST_PATH_IMAGE049
The on-line data is standardized and,
Figure 114434DEST_PATH_IMAGE050
mean and standard deviation of normal data. D ranges from 1 to D. (ii) a
And 7: according to the formula
Figure 432283DEST_PATH_IMAGE051
And performing fourth-order moment processing on the online data. And are combined into
Figure 275474DEST_PATH_IMAGE052
。
k is the current time and the initial value is
Figure 260748DEST_PATH_IMAGE045
Therefore, it is necessary to go to the second step in the industrial process
Figure 304927DEST_PATH_IMAGE046
Starting monitoring after each moment;
and 8: computing statistics
Figure 110072DEST_PATH_IMAGE025
And residual error FS:
the statistic calculation formula at all the moments is as follows:
Figure 897899DEST_PATH_IMAGE053
Figure 567040DEST_PATH_IMAGE054
the statistic calculation formula for the k-th time alone is as follows:
Figure 782121DEST_PATH_IMAGE055
Figure 933617DEST_PATH_IMAGE056
wherein the content of the first and second substances,
Figure 525135DEST_PATH_IMAGE057
is composed of
Figure 953842DEST_PATH_IMAGE058
The k-th column of (1).
Figure 339824DEST_PATH_IMAGE059
The statistic and residual error at time k are shown.
And step 9: the control line for calculating the statistic and the residual error is as follows:
Figure 244195DEST_PATH_IMAGE060
Figure 373825DEST_PATH_IMAGE039
step 10: at each moment
Figure 922618DEST_PATH_IMAGE029
In contrast to the corresponding control line. If not, returning to the step 6; if the control line is exceeded, a fault occurs, and an alarm is given.
The steps are the specific application steps of the method in the TE process.
The validity of the method can be verified by means of fig. 2, 3 and 4.
Before time 200, production was in the normal phase. It can be seen that the statistics and residual values proposed by the method herein are all lower than the control line, and no false positives are generated. As can be seen from fig. 5, MKICAs have more false alarms in the early stage due to the large fluctuation in the initial stage of the industrial process.
The data of the TE process introduced a fault at time 200. As can be seen from fig. 2, 3 and 4, since the statistics constructed herein are of fourth order nature, and therefore very sensitive to fault response, the control line is crossed over a short period of time, generating an alarm. The production safety is successfully ensured. The high-order analysis mode used by MKICA is a nuclear technique, and no four-order moment method is effective for mining high-order information of data. Therefore, it can be seen from the graph that the MKICA statistic rises more slowly, without the high-speed response capability of the fourth-order moment statistic. In an actual industrial process, timely response is a very important capability.
The analysis of the experimental graph can be used for obtaining that the intermittent process fault diagnosis method based on the fourth-order moment singular value decomposition has a lower false alarm rate in a normal stage and a lower false negative rate and a faster response capability in a fault stage. The effectiveness of the proposed method is demonstrated.

Claims (1)

1. A method for monitoring intermittent process faults based on fourth-order moment singular value decomposition is characterized by comprising an off-line modeling stage and an on-line monitoring stage, and comprises the following specific steps:
A. an off-line modeling stage:
1) reading in normal data, calculating mean value mean of each variabledAnd standard deviation stddNormalized to normal data, the formula is as follows:
Figure FDA0003062089200000011
wherein, XdData representing all the times of the d-th variable, meandRepresents XdAverage value of (std)dRepresents XdThe standard deviation of (a), there are D variables;
2) for X which is totally D and standardizeddThe data of each moment is processed by fourth moment, and the formula is as follows;
cd(k)＝xd(k)xd(k-τ1)xd(k-τ2)xd(k-τ3)
cd(k) representing the fourth moment of the kth moment of the d-th variable, k representing the sampling moment, xd(k) Denotes the value of the d-th variable at the k-th instant, τ1、τ2、τ3Represents a step size;
3) c is tod(k) The combination is a fourth moment matrix C, and the formula is as follows:
Figure FDA0003062089200000012
wherein N represents an end time;
4) singular Value Decomposition (SVD), SVD (C) USV for CTThe U is simplified in two steps,
i.U, the first step is simplified as follows:
the minimum value of M that can be satisfied by the following formula is calculated,
Figure FDA0003062089200000021
wherein S isi，iIs the element on the diagonal of S, I is the minimum value in the S row and column number, and delta is the threshold value which can be adjusted;
reserving the first M columns of the U, and deleting the rest to obtain the U after the first step of simplification;
a second step simplification of u, steps as follows:
judging the numerical value of each element in the simplified U, wherein the formula is as follows:
Figure FDA0003062089200000022
wherein the content of the first and second substances,
Figure FDA0003062089200000023
representing the square of the element in row i and column m in the simplified U,
Figure FDA0003062089200000024
representing the sum of squares of all elements in the ith row in the simplified U, wherein M' is the number of columns of the U before deletion;
when u isi，mThe judgment condition of the formula above is met, and the judgment condition is set to 0 to obtain the simplified U in the second step;
5) cutting the S matrix into M rows and M columns, and obtaining the inverse matrix S of the S after cuttinginvU and S simplified by the two steps in the foregoinginvStoring for later on-line monitoring;
B. and (3) an online monitoring stage:
6) reading in on-line data and standardizing the on-line data, wherein the formula is as follows:
Figure FDA0003062089200000025
wherein x isd.onFor the value of the d-th variable of the online data, meand，stddMean and standard deviation of normal data;
7) for normalized xd，onFourth moment processing is carried out, and the formula is as follows:
cd，on(k)＝xd，on(k)xd，on(k-τ1)xd，on(k-τ2)xd，on(k-τ3)
and combined into Con
Figure FDA0003062089200000031
8) Computing statistic F2And residual error FS:
F2＝(ConU)Sinv(ConU)T
FS＝(Con-ConU)(Con-ConU)T
u, S thereininvFor the matrix saved in step 5 of the off-line phase,
9) computingF2Control line of FS
Figure FDA0003062089200000032
And FSlimitThe formula is as follows:
Figure FDA0003062089200000033
where F (0.95, M, N ' -M) represents a confidence of 95%, and the numerator degree of freedom M, which is the value in step 4, is the F test of the denominator degree of freedom N ' -M, N ' ═ N- τ3，
Figure FDA0003062089200000034
Wherein the content of the first and second substances,
L＝diag(Son)
Figure FDA0003062089200000035
Figure FDA0003062089200000036
wherein S isonIs an S matrix obtained by performing singular value decomposition on the online data, L is an element value on a diagonal line thereof, LiIs the ith element in L, c is the desired 95% quantile with a standard deviation of 1, 0;
10) f at each moment2FS is compared with the corresponding control line, if not, the control line is normal, and the step 6 is returned; if the control line is exceeded, a fault occurs, and an alarm is given.
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