CN108664002B - Quality-oriented nonlinear dynamic process monitoring method - Google Patents

Quality-oriented nonlinear dynamic process monitoring method Download PDF

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CN108664002B
CN108664002B CN201810394768.XA CN201810394768A CN108664002B CN 108664002 B CN108664002 B CN 108664002B CN 201810394768 A CN201810394768 A CN 201810394768A CN 108664002 B CN108664002 B CN 108664002B
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曹玉苹
邓晓刚
黄琳哲
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China University of Petroleum East China
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    • 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] or computer integrated manufacturing [CIM] characterised by quality surveillance of production
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Abstract

The invention relates to a quality-oriented nonlinear dynamic process monitoring method, which comprises the following steps: (1) acquiring process data and quality data of a nonlinear process under a normal working condition, constructing modeling data and standardizing; (2) calculating a quality-related scoreStandard sum of squares of type vectors
Figure DDA0001644322790000011
And its control limit; (3) calculating the standard sum of squares of principal component vectors that are not related to quality
Figure DDA0001644322790000012
Sum squared prediction error SPEexAnd its control limit; (4) real-time monitoring data of process variable and quality variable in nonlinear dynamic process, calculating
Figure DDA0001644322790000013
And SPEexAnd (5) statistics, namely judging whether a fault occurs or not and whether the process fault affects the product quality or not. The invention can effectively filter out process fault alarms which do not affect the product quality, improve the reliability of process monitoring, enhance the logic integrity and the practicability of a real-time process monitoring system, and adapt to the requirements of the real-time process monitoring of the nonlinear dynamic chemical process; the process fault judgment is accurate, the real-time process monitoring efficiency is high, and the application range is wide.

Description

Quality-oriented nonlinear dynamic process monitoring method
Technical Field
The invention relates to the technical field of chemical production process monitoring, in particular to a quality-oriented nonlinear dynamic process monitoring method.
Background
The production process of the modern chemical industry is increasingly complex, and the safety and the reliability of the process are very important. The process monitoring technology is to utilize the measured data to monitor the running state of the process and to alarm the abnormal condition. Therefore, the process monitoring technology is the key to ensure the safety, stability and long-term operation of the process. Process variables are often collected online, quality variables are often assayed offline, the sampling frequency is low, and there is a time lag. In consideration of real-time performance of process monitoring, the conventional data-driven process monitoring method monitors the operating state of the process only by using process data, such as principal component analysis, independent component analysis, typical variable analysis, and the like. Therefore, the process monitoring method can only indicate whether the process variable is abnormal, and cannot judge whether the product quality is abnormal. According to the influence of process faults on product quality, the process faults can be classified into 2 types: 1. process variables are abnormal and further result in product quality anomalies; 2. the process variable is abnormal, but the product quality is not affected by the adjustment of the controller. Operators in the chemical production process often care whether the product quality is normal, and the type 2 fault is often regarded as false alarm, so that the reliability of the process monitoring system is greatly reduced. Therefore, how to distinguish the fault affecting the product quality from the fault not affecting the product quality becomes an urgent problem to be solved in process monitoring. In recent years, a projection method of a latent structure, a dynamic CPLS method, a CPLS method, an improved CPLS method, and a dynamic input-output typical variable analysis method have been proposed in succession in some research results, which assume that a process is linear, whereas an actual chemical industrial process often has strong nonlinear dynamic characteristics. For the nonlinear dynamic process, a quality-oriented real-time process monitoring technology with complete logic and strong practicability is not available.
Disclosure of Invention
The technical problem to be solved by the invention is to provide a quality-oriented nonlinear dynamic process monitoring method, which can distinguish faults affecting product quality from faults not affecting product quality in process monitoring.
In order to solve the technical problems, the technical scheme of the invention is as follows: a quality-oriented nonlinear dynamic process monitoring method comprises the following steps: (1) setting a process variable and a quality variable in a nonlinear dynamic process, collecting process data and quality data of the nonlinear process under a normal working condition, constructing modeling data and carrying out standardized processing;
(2) performing subspace decomposition by utilizing nonlinear typical variable analysis, extracting process characteristics related to quality, and calculating standard square sum T of typical vectors related to qualitys 2And its control limit;
(3) performing subspace decomposition by utilizing nonlinear principal component analysis, extracting process features irrelevant to quality, and calculating standard square sum of principal component vectors irrelevant to quality
Figure BDA0001644322770000022
Sum squared prediction error SPEexAnd its control limit;
(4) and monitoring the process: real-time monitoring of non-linear motionData of process variables and quality variables in the state process, calculating T using the process datas 2、
Figure BDA0001644322770000023
And SPEexAnd (5) statistics, namely judging whether the nonlinear dynamic process fails or not and whether the process failure affects the product quality or not.
As a preferred technical solution, the step (1) specifically comprises: collecting process data and quality data of nonlinear continuous process under normal working condition, respectively mapping phi with unknown nonlinearity according to nonlinearity characteristic of processx(x) And phiy(y) projecting the process augmentation vector x and the mass vector y into a high-dimensional linear feature space, where u is an m-dimensional process vector and y is an n-dimensional mass vector, and then phix(x) Is a m-dimensional vector, phiy(y) is an n-dimensional vector; sampling time i, i ═ h +1, h + 2.., h + N, constructing a process augmentation vector according to the dynamic characteristics of the nonlinear dynamic process
Figure BDA0001644322770000024
Wherein h represents the hysteresis order; acquiring process data and quality data at h + N sampling moments under normal working conditions, and if the sampling rate of the quality data is low, filling up missing quality data; constructing process augmentation data matrix X belongs to RN×(h+1)mAnd the quality data matrix Y is belonged to RN×n(ii) a Calculating the standard deviation sigma corresponding to n quality variablesrR 1, 2.., n; the matrices X and Y are normalized so that the mean value of each column of data is 0 and the variance is 1.
As a preferred technical solution, the step (2) specifically comprises: extracting the maximum phi in a high-dimensional linear characteristic space by utilizing linear typical variable analysisx(x) And phiy(y) typical variables of relevance; finding projection vectors
Figure BDA0001644322770000025
And
Figure BDA0001644322770000026
maximizing the following correlation coefficient
Figure BDA0001644322770000027
Wherein, the matrix
Figure BDA0001644322770000028
Is indicative of phix(x) And phiy(y) a cross-covariance matrix of (y),
Figure BDA0001644322770000029
is indicative of phix(x) The covariance matrix of (a) is determined,
Figure BDA00016443227700000210
is indicative of phiy(y) a covariance matrix; due to the non-linear mapping phix(x) And phiy(y) difficult to determine, unable to directly perform linear typical variable analysis in a high-dimensional linear feature space, and extract process features related to quality;
projection vectors alpha and beta are present such that
Figure BDA0001644322770000031
Conversion of formula (1) to
Figure BDA0001644322770000032
Wherein, the kernel matrix [ Kx]i,j＝kx(xi,xj)＝<φx(xi)·φx(xj)>Kernel matrix [ K ]y]i,j＝ky(yi,yj)＝<φy(yi)·φy(yj)>，kx(xi,xj) And ky(yi,yj) Is a kernel function, i 1., N, j 1., N; typically using a Gaussian kernel function k (x)1,x2)＝exp(-||x1-x2||2C); the optimization problem of equation (2) can be transformed into a generalized eigenvalue solution problem:
Figure BDA0001644322770000033
wherein λ is a characteristic value, [ α ]T βT]TIs a feature vector corresponding to lambda; to avoid the ill-conditioned matrix solving problem, K is used separatelyxKx+ η I and KyKy+ η I instead of KxKxAnd KyKyIs obtained by
Figure BDA0001644322770000034
Wherein η represents a regularization constant, and I represents an identity matrix having dimensions N × N; obtaining k maximum eigenvalues λ from equation (4)1≥λ2≥…≥λkCorresponding projection vector alpha1,α2,…,αkAnd beta1,β2,…,βk；
The eigenvalue lambda represents a correlation coefficient of the process augmentation vector and the quality vector, and the larger the eigenvalue lambda is, the stronger the correlation is;
determining a parameter k according to the magnitude of the correlation coefficient;
constructing a projection matrix Ak＝[α1,α2,…,αk]For process-augmented vector sample x, the corresponding low-dimensional process-representative vector is
c＝Ak TKx(X,x) (5)；
Wherein the kernel vector Kx(X,x)＝[kx(x1,x),kx(x2,x),…,kx(xN,x)]T；
The correlation between the process typical vector c and the quality vector is strongest, and the process typical vector is used as the characteristic of a process subspace related to the quality; under the condition of quality data missing, if the process typical vector c is abnormal, the quality vector can be deduced to be abnormal; construct statistics
Ts 2＝cTc (6)；
Calculating T using data of normal operating conditionss 2Statistic, calculating T by a kernel density estimation methods 2A control limit for the statistic.
As a preferred technical solution, the step (3) specifically comprises:
projecting the process subspace characteristic c which is calculated by the formula (5) and is related to the quality back to a high-dimensional linear characteristic space to obtain phix(x) Is estimated value of
Figure BDA0001644322770000041
Estimating residual error
Figure BDA0001644322770000042
Information is described that is not related to the quality vector due to the non-linear mapping phix(x) Difficult to determine, unable to calculate the estimated residual
Figure BDA0001644322770000043
Linear principal component analysis and extraction of process features irrelevant to quality cannot be directly carried out in a residual error space, namely a process subspace irrelevant to quality;
estimated value
Figure BDA0001644322770000044
Is a function of a process representative vector c, which is a function of a process augmentation vector x; thus, the estimated value
Figure BDA0001644322770000045
Is a non-linear function of the process-augmented vector x, estimates the residual error
Figure BDA0001644322770000046
Is also a non-linear function of the process spread vector x
Figure BDA0001644322770000047
In the process subspace where there is no correlation with quality,converting the principal component feature extraction problem into a feature value solving problem:
λexvex＝CFvex (8)；
wherein, the matrix CFIs indicative of phiex(x) Of the covariance matrix, λexRepresenting a characteristic value, vexDenotes λexA corresponding feature vector; presence of projection vector alphaexSo that v isex＝φex(X)TαexConversion of equation (8) to
Figure BDA0001644322770000048
Wherein, the matrix
Figure BDA0001644322770000049
Core matrix
Figure BDA00016443227700000410
j ═ 1.., N; the kernel function can be derived from equation (7)
Figure BDA00016443227700000411
Expression (c):
Figure BDA0001644322770000051
according to the formula (10),
Figure BDA0001644322770000052
is a kernel function kx(xi,xj) In a high-dimensional linear and mass-dependent process subspace, selecting a kernel function kx(xi,xj) Then, no kernel function needs to be selected
Figure BDA0001644322770000053
But a kernel function is calculated using equation (10)
Figure BDA0001644322770000054
Obtaining k from formula (9)exA maximum eigenvalue
Figure BDA0001644322770000055
Corresponding projection vector
Figure BDA0001644322770000056
In order to ensure that the feature vector satisfies | | | vex||2For projection vector α of 1exThe following normalization was performed:
Figure BDA0001644322770000057
characteristic value lambdaexInformation representing the variance of a subspace not related to the quality, the eigenvalues lambdaexThe larger the process change corresponding to the pivot feature description is, the stronger the parameter k is determined according to the accumulated sum of the variancesex；
Constructing a projection matrix
Figure BDA0001644322770000058
For the process-augmented vector sample x, the corresponding quality-independent principal element feature is
Figure BDA0001644322770000059
Wherein the kernel vector
Figure BDA00016443227700000510
Principal component texReflecting the main change of the process subspace irrelevant to the quality, taking the principal element as the characteristic of the subspace, and constructing
Figure BDA00016443227700000511
Statistics and SPEexStatistics
Figure BDA00016443227700000512
Figure BDA00016443227700000513
Wherein, the diagonal matrix
Figure BDA00016443227700000514
Respectively calculating by using data of normal working conditions
Figure BDA00016443227700000515
Statistics and SPEexStatistics calculated by the kernel density estimation method respectively
Figure BDA00016443227700000516
Statistics and SPEexA control limit for the statistic.
As a preferred technical solution, the step (4) specifically comprises:
(4.1) acquiring data of a process variable and a quality variable at the current moment, constructing a process augmentation vector x and carrying out standardization processing on the process augmentation vector x;
(4.2), calculating the feature c of the process subspace related to the quality using equation (5), and then calculating T according to equation (6)s 2Statistics; judgment of Ts 2Whether the statistic exceeds the control limit; if the process exceeds the control limit, the process is abnormal, the product quality is abnormal, and the step (4.1) is returned to after the alarm is given; otherwise, performing the step (4.3);
(4.3) calculating the feature t of the quality-independent process subspace by using the formula (12)exThen, it is calculated from the equations (13) and (14)
Figure BDA0001644322770000061
Statistics and SPEexStatistics; judgment of
Figure BDA0001644322770000062
Statistics and SPEexWhether or not to countExceeding the control limit; if it is
Figure BDA0001644322770000063
Statistics or SPEexIf the statistic exceeds the control limit, the process is abnormal but the product quality is not influenced or the influence is small, and the step (4.1) is returned to be executed after prompting; otherwise, performing the step (4.4);
(4.4) judging whether the quality data y is collected at the current moment; if the quality data are collected, standardizing the quality data, and performing the step (4.5); otherwise, returning to execute the step (4.1);
(4.5) judging whether the quality data exceeds the control limit, and if the quality data exceeds the control limit, judging whether the quality data exceeds the control limit or not, and if the quality data exceeds the control limit, judging whether the quality data exceeds the control limit, and if the quality data exceeds the control limit, judging the quality data tor|＞3σrIf r is 1,2, and n, the r-th quality variable is abnormal, and the step (4.1) is returned to after the alarm is given; otherwise, directly returning to the step (4.1).
Due to the adoption of the technical scheme, the invention has the beneficial effects that:
compared with the prior art, the invention has the following advantages: firstly, through analyzing the nonlinear correlation between process data and quality data, extracting process characteristics related to quality and process characteristics unrelated to quality, judging whether the process is abnormal or not and whether the process is abnormal or not to influence the product quality or not by utilizing the characteristics, wherein the logical judgment link can effectively filter out process fault alarms which do not influence the product quality, thereby improving the reliability of process monitoring, enhancing the logical integrity and the practicability of a real-time process monitoring system, realizing the quality-oriented real-time process monitoring and adapting to the requirement of the nonlinear dynamic chemical process real-time process monitoring; secondly, combining kernel function technology and typical variable analysis, analyzing the nonlinear correlation between the process data and the quality data by using a kernel typical variable analysis method, extracting process characteristics related to the quality, and solving the problems that nonlinear mapping is difficult to determine and correlation analysis cannot be directly carried out in a high-dimensional linear characteristic space; thirdly, combining a kernel function technology and principal component analysis, analyzing the non-linear correlation between the process data irrelevant to the quality by using a kernel principal component analysis method, extracting the process characteristics irrelevant to the quality, and solving the problems that the non-linear mapping is difficult to determine and the characteristics can not be directly extracted in a high-dimensional linear residual error space; the whole process is simple, the principle is reliable, the process fault judgment is accurate, the real-time process monitoring efficiency is high, the application range is wide, the logic is strong, and the environment is friendly.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the principle of operation of an embodiment of the present invention;
FIG. 2 is a block diagram of a nonlinear chemical model Tennessee-Ishmann process;
FIG. 3 shows a nonlinear dynamic pivot analysis method T when a fault 1 occurs according to an embodiment of the present invention2A plot of the statistics;
FIG. 4 is a graph of the SPE statistics of the nonlinear dynamic principal component analysis method in case of a fault 1 according to the embodiment of the present invention;
FIG. 5 shows a quality-oriented nonlinear dynamic process monitoring method T when a fault 1 occurs in an embodiment of the present inventions 2A plot of the statistics;
FIG. 6 is a quality-oriented nonlinear dynamic process monitoring method when a fault 1 occurs in an embodiment of the present invention
Figure BDA0001644322770000071
A plot of the statistics;
FIG. 7 is a diagram illustrating a quality-oriented method for monitoring a nonlinear dynamic process SPE when a fault 1 occurs according to an embodiment of the present inventionexA plot of the statistics;
FIG. 8 shows a nonlinear dynamic pivot analysis method T when a fault 2 occurs in an embodiment of the present invention2A plot of the statistics;
FIG. 9 is a graph of the SPE statistics of the nonlinear dynamic principal component analysis method in the case of a fault 2 according to the embodiment of the present invention;
FIG. 10 is a quality-oriented nonlinear dynamic process monitoring method T when a failure 2 occurs according to an embodiment of the present inventions 2A plot of the statistics;
FIG. 11 is a quality-oriented nonlinear dynamic process monitoring method when a failure 2 occurs in an embodiment of the present invention
Figure BDA0001644322770000084
A plot of the statistics;
FIG. 12 is a diagram illustrating a quality-oriented method for monitoring a nonlinear dynamic process SPE when a failure 2 occurs according to an embodiment of the present inventionexA plot of the statistics;
FIG. 13 shows a nonlinear dynamic pivot analysis method T when a fault 3 occurs in the embodiment of the present invention2A plot of the statistics;
FIG. 14 is a graph of the SPE statistics of the nonlinear dynamic principal component analysis method in the case of a failure 3 according to an embodiment of the present invention;
FIG. 15 is a quality-oriented nonlinear dynamic process monitoring method T when a failure 3 occurs in an embodiment of the present inventions 2A plot of the statistics;
FIG. 16 is a quality-oriented nonlinear dynamic process monitoring method when a failure 3 occurs according to an embodiment of the present invention
Figure BDA0001644322770000082
A plot of the statistics;
FIG. 17 is a block diagram of a quality-oriented method for monitoring a nonlinear dynamic process SPE when a failure 3 occurs according to an embodiment of the present inventionexA graph of the statistics.
Detailed Description
A quality-oriented nonlinear dynamic process monitoring method comprises the following steps:
(1) the method comprises the following steps of setting a process variable and a quality variable in a nonlinear dynamic process, collecting process data and quality data of the nonlinear process under a normal working condition, constructing modeling data and carrying out standardized processing, wherein the process variable and the quality variable are specifically as follows:
collecting process data of a non-linear continuous process under normal operating conditionsAnd quality data, respectively using the unknown non-linear mapping phi according to the non-linear characteristics of the processx(x) And phiy(y) projecting the process augmentation vector x and the mass vector y into a high-dimensional linear feature space, where u is an m-dimensional process vector and y is an n-dimensional mass vector, and then phix(x) Is a m-dimensional vector, phiy(y) is an n-dimensional vector; sampling time i, i ═ h +1, h + 2.., h + N, constructing a process augmentation vector according to the dynamic characteristics of the nonlinear dynamic process
Figure BDA0001644322770000083
Wherein h represents the hysteresis order; acquiring process data and quality data at h + N sampling moments under normal working conditions, and if the sampling rate of the quality data is low, filling up missing quality data; constructing process augmentation data matrix X belongs to RN ×(h+1)mAnd the quality data matrix Y is belonged to RN×n(ii) a Calculating the standard deviation sigma corresponding to n quality variablesrR 1, 2.., n; the matrices X and Y are normalized so that the mean value of each column of data is 0 and the variance is 1.
(2) Performing subspace decomposition by utilizing nonlinear typical variable analysis, extracting process characteristics related to quality, and calculating standard square sum T of typical vectors related to qualitys 2And control limits thereof, specifically as follows:
extracting the maximum phi in a high-dimensional linear characteristic space by utilizing linear typical variable analysisx(x) And phiy(y) typical variables of relevance; finding projection vectors
Figure BDA0001644322770000091
And
Figure BDA0001644322770000092
maximizing the following correlation coefficient
Figure BDA0001644322770000093
Wherein, the matrix
Figure BDA0001644322770000094
Is indicative of phix(x) And phiy(y) a cross-covariance matrix of (y),
Figure BDA0001644322770000095
is indicative of phix(x) The covariance matrix of (a) is determined,
Figure BDA0001644322770000096
is indicative of phiy(y) a covariance matrix; due to the non-linear mapping phix(x) And phiy(y) difficult to determine, unable to directly perform linear typical variable analysis in a high-dimensional linear feature space, and extract process features related to quality;
projection vectors alpha and beta are present such that
Figure BDA0001644322770000097
Conversion of formula (1) to
Figure BDA0001644322770000098
Wherein, the kernel matrix [ Kx]i,j＝kx(xi,xj)＝<φx(xi)·φx(xj)>Kernel matrix [ K ]y]i,j＝ky(yi,yj)＝<φy(yi)·φy(yj)>，kx(xi,xj) And ky(yi,yj) Is a kernel function, i 1., N, j 1., N; typically using a Gaussian kernel function k (x)1,x2)＝exp(-||x1-x2||2C); the optimization problem of equation (2) can be transformed into a generalized eigenvalue solution problem:
Figure BDA0001644322770000099
wherein λ is a characteristic value, [ α ]T βT]TIs λ corresponding toThe feature vector of (2); to avoid the ill-conditioned matrix solving problem, K is used separatelyxKx+ η I and KyKy+ η I instead of KxKxAnd KyKyIs obtained by
Figure BDA00016443227700000910
Wherein η represents a regularization constant, and I represents an identity matrix having dimensions N × N; obtaining k maximum eigenvalues λ from equation (4)1≥λ2≥…≥λkCorresponding projection vector alpha1,α2,…,αkAnd beta1,β2,…,βk；
The eigenvalue lambda represents a correlation coefficient of the process augmentation vector and the quality vector, and the larger the eigenvalue lambda is, the stronger the correlation is;
determining a parameter k according to the magnitude of the correlation coefficient;
constructing a projection matrix Ak＝[α1,α2,…,αk]For process-augmented vector sample x, the corresponding low-dimensional process-representative vector is
c＝Ak TKx(X,x) (5)；
Wherein the kernel vector Kx(X,x)＝[kx(x1,x),kx(x2,x),…,kx(xN,x)]T；
The correlation between the process typical vector c and the quality vector is strongest, and the process typical vector is used as the characteristic of a process subspace related to the quality; under the condition of quality data missing, if the process typical vector c is abnormal, the quality vector can be deduced to be abnormal; construct statistics
Ts 2＝cTc (6)；
Monitoring a quality-related process subspace variation;
calculating T using data of normal operating conditionss 2Statistic, calculating T by a kernel density estimation methods 2Control of statisticsAnd (4) limiting.
(3) Performing subspace decomposition by utilizing nonlinear principal component analysis, extracting process features irrelevant to quality, and calculating standard square sum of principal component vectors irrelevant to quality
Figure BDA0001644322770000104
Sum squared prediction error SPEexAnd control limits thereof, specifically as follows:
projecting the process subspace characteristic c which is calculated by the formula (5) and is related to the quality back to a high-dimensional linear characteristic space to obtain phix(x) Is estimated value of
Figure BDA0001644322770000101
Estimating residual error
Figure BDA0001644322770000102
Information is described that is not related to the quality vector due to the non-linear mapping phix(x) Difficult to determine, unable to calculate the estimated residual
Figure BDA0001644322770000103
Linear principal component analysis and extraction of process features irrelevant to quality cannot be directly carried out in a residual error space, namely a process subspace irrelevant to quality;
estimated value
Figure BDA0001644322770000111
Is a function of a process representative vector c, which is a function of a process augmentation vector x; thus, the estimated value
Figure BDA0001644322770000112
Is a non-linear function of the process-augmented vector x, estimates the residual error
Figure BDA0001644322770000113
Is also a non-linear function of the process spread vector x
Figure BDA0001644322770000114
In the process subspace irrelevant to the quality, converting the principal component feature extraction problem into a feature value solving problem:
λexvex＝CFvex (8)；
wherein, the matrix CFIs indicative of phiex(x) Of the covariance matrix, λexRepresenting a characteristic value, vexDenotes λexA corresponding feature vector; presence of projection vector alphaexSo that v isex＝φex(X)TαexConversion of equation (8) to
Figure BDA0001644322770000115
Wherein, the matrix
Figure BDA0001644322770000116
Core matrix
Figure BDA0001644322770000117
j ═ 1.., N; the kernel function can be derived from equation (7)
Figure BDA0001644322770000118
Expression (c):
Figure BDA0001644322770000119
according to the formula (10),
Figure BDA00016443227700001110
is a kernel function kx(xi,xj) In a high-dimensional linear and mass-dependent process subspace, selecting a kernel function kx(xi,xj) Then, no kernel function needs to be selected
Figure BDA00016443227700001111
But a kernel function is calculated using equation (10)
Figure BDA00016443227700001112
Obtaining k from formula (9)exA maximum eigenvalue
Figure BDA00016443227700001113
Corresponding projection vector
Figure BDA00016443227700001114
In order to ensure that the feature vector satisfies | | | vex||2For projection vector α of 1exThe following normalization was performed:
Figure BDA00016443227700001115
characteristic value lambdaexInformation representing the variance of a subspace not related to the quality, the eigenvalues lambdaexThe larger the process change corresponding to the pivot feature description is, the stronger the parameter k is determined according to the accumulated sum of the variancesex；
Constructing a projection matrix
Figure BDA00016443227700001116
For the process-augmented vector sample x, the corresponding quality-independent principal element feature is
Figure BDA0001644322770000121
Wherein the kernel vector
Figure BDA0001644322770000122
Principal component texReflecting the main change of the process subspace irrelevant to the quality, taking the principal element as the characteristic of the subspace, and constructing
Figure BDA0001644322770000123
Statistics and SPEexStatistics
Figure BDA0001644322770000124
Figure BDA0001644322770000125
Wherein, the diagonal matrix
Figure BDA0001644322770000126
Respectively calculating by using data of normal working conditions
Figure BDA0001644322770000127
Statistics and SPEexStatistics calculated by the kernel density estimation method respectively
Figure BDA0001644322770000128
Statistics and SPEexA control limit for the statistic.
(4) And monitoring the process: monitoring data of process variable and quality variable in nonlinear dynamic process in real time, and calculating T by using process datas 2、
Figure BDA0001644322770000129
And SPEexAnd statistics is carried out to judge whether the nonlinear dynamic process fails or not and whether the process failure affects the product quality, and the method specifically comprises the following steps:
(4.1) acquiring data of a process variable and a quality variable at the current moment, constructing a process augmentation vector x and carrying out standardization processing on the process augmentation vector x;
(4.2), calculating the feature c of the process subspace related to the quality using equation (5), and then calculating T according to equation (6)s 2Statistics; judgment of Ts 2Whether the statistic exceeds the control limit; if the process exceeds the control limit, the process is abnormal, the product quality is abnormal, and the step (4.1) is returned to after the alarm is given; otherwise, performing the step (4.3);
(4.3) calculation of Mass-independent excess using equation (12)Characteristic t of the program subspaceexThen, it is calculated from the equations (13) and (14)
Figure BDA00016443227700001210
Statistics and SPEexStatistics; judgment of
Figure BDA00016443227700001211
Statistics and SPEexWhether the statistic exceeds the control limit; if it is
Figure BDA00016443227700001212
Statistics or SPEexIf the statistic exceeds the control limit, the process is abnormal but the product quality is not influenced or the influence is small, and the step (4.1) is returned to be executed after prompting; otherwise, performing the step (4.4);
(4.4) judging whether the quality data y is collected at the current moment; if the quality data are collected, standardizing the quality data, and performing the step (4.5); otherwise, returning to execute the step (4.1);
(4.5) judging whether the quality data exceeds the control limit, if the r-th quality variable yr＞3σrIf r is 1,2, and n, the r-th quality variable is abnormal, and the step (4.1) is returned to after the alarm is given; otherwise, directly returning to the step (4.1).
The principle of judging whether the quality of the nonlinear dynamic process is abnormal or not by using real-time process data is as follows: the quality variable is often obtained by off-line assay, the sampling rate is low, and time lag exists; if the quality is judged to be abnormal only by using the quality data, the monitoring instantaneity is poor; the traditional data-driven process monitoring method only utilizes process data to carry out modeling, although the real-time performance is strong, whether the quality is abnormal or not cannot be judged; the method decomposes the process data space by analyzing the nonlinear correlation between the process data and the quality data, and extracts the process characteristics related to the quality and the process characteristics unrelated to the quality; during real-time monitoring, if the process characteristics related to the quality are abnormal, the process is indicated to be abnormal, and the product quality is abnormal; if the process characteristics related to the quality are normal and the process characteristics unrelated to the quality are abnormal, the process is abnormal, but the product quality is not influenced or the influence is small; by the judgment, quality-oriented nonlinear dynamic process monitoring can be realized, process fault alarm which does not affect product quality is filtered, and the reliability of process monitoring is effectively improved.
The principle of extracting the process characteristics related to the quality by utilizing the nonlinear typical variable analysis is as follows: the actual chemical industrial process often has strong nonlinear dynamic characteristics, and nonlinear correlations exist among process variables, among quality variables and between the process variables and the quality variables; the linear statistical analysis method does not consider the nonlinear characteristics of the process, can not accurately divide the process subspace relevant to the quality and the process subspace irrelevant to the quality, and can cause wrong alarm when the real-time process monitoring is carried out; if the original data are projected to a high-dimensional linear feature space, linear statistical analysis cannot be directly performed on the high-dimensional linear feature space due to the fact that nonlinear mapping is difficult to determine; the method comprises the steps of combining a kernel function technology and typical variable analysis, converting a correlation analysis problem of a high-dimensional linear space into a generalized eigenvalue solving problem of a kernel matrix, analyzing nonlinear correlation between process data and quality data by using a kernel typical variable analysis method, extracting process features related to quality, and dividing the process high-dimensional linear feature space into a subspace related to the quality and a subspace unrelated to the quality.
The principle of extracting the process characteristics irrelevant to the quality by utilizing the nonlinear principal component analysis is as follows: in a diameter ofx(x) In the high-dimensional linear feature space of the formed process, though phi can be obtained by nonlinear typical variable analysisx(x) Is estimated value of
Figure BDA0001644322770000131
But due to the non-linear mapping phix(x) Difficult to determine, unable to calculate the estimated residual
Figure BDA0001644322770000132
The linear principal component cannot be performed directly in the residual space, i.e. the quality-independent process subspaceSeparating out; combining a kernel function technology and principal component analysis, converting the feature extraction problem of a high-dimensional linear residual error space into a feature value solving problem of a kernel matrix, analyzing the non-linear correlation between process data irrelevant to quality by using a kernel principal component analysis method, and extracting process features irrelevant to quality.
As shown in fig. 1 to 17, in the present embodiment, a quality-oriented nonlinear dynamic process monitoring method is applied to a Tennessee-Eastman (TE) process, which is a complex nonlinear chemical model based on a real chemical process proposed by Downs and Vogel of Eastman chemicals, and is regarded as a reference process of a process monitoring simulation study, as shown in fig. 2; the Tennessee-Iseman process includes five main units including reactor, condenser, compressor, separator and stripping tower, and components A-H8; the reference numerals 1,2,3,4,5,6,7,8,9,10,11,12,13 in fig. 2 denote a fluid, hereinafter simply referred to as: stream 1, stream 2, stream 3, stream 4, stream 5, stream 6, stream 7, stream 8, stream 9, stream 10, stream 11, stream 12, stream 13. The tennessee-issman process of this example included 12 control variables (as shown in table 1) and 41 measurement variables (as shown in table 2), with the control and measurement variables XMEAS (1) -XMEAS (22) sampled every 3 minutes; measurement variables XMEAS (23) -XMEAS (36) are constituent measurements, sampled every 6 minutes; measurement variables XMEAS (37) -XMEAS (41) are ingredient measurements of the final product, sampled every 15 minutes.
The following description will take 3 process faults as an example, and the fault descriptions are shown in table 3, where fault 1 and fault 2 are quality-independent faults, and fault 3 is quality-dependent fault.
TABLE 1 control variables of the Tennessee-Ishmann Process
Variables of Description of the invention Variables of Description of the invention
XMV(1) D feed rate (stream 2) XMV(7) Separator tank flow (stream 10)
XMV(2) E feed rate (stream 3) XMV(8) Stripper liquid product flow (stream 11)
XMV(3) A feed rate (stream 1) XMV(9) Stripper water flow valve
XMV(4) Total feed (stream 4) XMV(10) Reactor cooling water flow
XMV(5) Compressor recirculation valve XMV(11) Flow rate of cooling water of condenser
XMV(6) Draw off valve (stream 9) XMV(12) Stirring speed
TABLE 2 Tennessee-Ishmann Process measurement variables
Figure BDA0001644322770000151
TABLE 3 Fault description of the Tennessee-Ishmann Process
Fault of Description of the invention Type (B)
1 Reactor cooling water inlet temperature Step change
2 Stream 4C with pressure loss-reduced availability Step change
3 Dynamic of reaction Slow offset
The specific implementation steps of adopting the quality-oriented nonlinear dynamic process monitoring method to carry out real-time process monitoring on the Tennessee-Ishmann process are as follows:
(1) collecting the measured data of the Tennessee-Ishmann process under normal operating conditions, wherein the control variable XMV (12) is kept unchanged without using the changeCarrying out process monitoring; taking component measurement variables XMEAS (37) -XMEAS (41) of the final product as quality variables, and taking measurement variables XMEAS (1-36) and control variables XMV (1-11) as process variables; unifying the sampling intervals of all process variables and quality variables into 3 minutes, and supplementing missing data by using a sampling and holding method; the lag order h is 2, and a process augmentation data matrix X and a quality data matrix Y are constructed by using process data and quality data of 960 sampling moments; calculating the standard deviation sigma corresponding to 5 quality variablesrR 1, 2.., 5; respectively carrying out standardization processing on the matrixes X and Y to enable the mean value of each line of data to be 0 and the variance to be 1;
(2) performing subspace decomposition by utilizing nonlinear typical variable analysis, extracting process characteristics related to quality, and calculating Ts 2Statistics and their control limits; computing kernel matrix KxAnd Ky，kx(xi,xj) And ky(yi,yj) All adopt a Gaussian kernel function k (x)1,x2)＝exp(-||x1-x2||2C); calculating an eigenvalue lambda and an eigenvector alpha from lambda using equation (4)>0.5, determining the number k of the characteristic values to be 4; substituting each process augmentation vector sample x into equation (5) to calculate a quality-related process feature c, and calculating T according to equation (6)s 2Statistics; calculating T by a kernel density estimation methods 2A control limit corresponding to a confidence interval of 99.73% of the statistic;
(3) performing subspace decomposition by utilizing nonlinear principal component analysis, extracting process features irrelevant to quality, and calculating
Figure BDA0001644322770000161
And SPEexStatistics and their control limits; utilizing the kernel function k in step (2)x(xi,xj) And equation (10) compute kernel matrix
Figure BDA0001644322770000162
Calculation of the eigenvalue λ using equation (9)exAnd the projection vector alphaexAnd normalizing the projection vector according to equation (11)Determining the number k of characteristic values according to the sum of variance and the sum of variance greater than 0.99ex94; substituting each process augmented vector sample x into equation (12) to compute quality-independent process feature texCalculated according to equations (13) and (14)
Figure BDA0001644322770000163
Statistics and SPEexStatistics; calculated by a kernel density estimation method
Figure BDA0001644322770000164
Statistics and SPEexA control limit corresponding to a confidence interval of 99.73% of the statistic;
(4) and during real-time monitoring, calculating T by using process datas 2、
Figure BDA0001644322770000165
And SPEexAnd (3) statistics, namely judging whether the process fails or not and whether the process failure affects the product quality, wherein the specific flow is as follows:
4.1) acquiring process measurement data at the current moment, constructing a process augmentation vector x and standardizing the process augmentation vector x;
4.2), calculating the feature c of the process subspace related to the quality using equation (5), and then calculating T according to equation (6)s 2Statistics; judgment of Ts 2Whether the statistic exceeds the control limit; if the control limit is exceeded, the process is abnormal, the product quality is abnormal, and the step 4.1 is returned to be executed after the alarm is given out; otherwise, performing step 4.3);
4.3), calculating the feature t of the quality-independent process subspace by using the formula (12)exThen, it is calculated from the equations (13) and (14)
Figure BDA0001644322770000171
Statistics and SPEexStatistics; judgment of
Figure BDA0001644322770000172
Statistics and SPEexWhether the statistic exceeds the control limit; if it is
Figure BDA0001644322770000173
Statistics or SPEexThe statistic exceeds the control limit, which indicates that the process is abnormal but does not affect the product quality or has small influence, and the step 4.1 is returned to be executed after prompting; otherwise, performing step 4.4);
4.4) judging whether the quality analysis data y is collected at the current moment; if the quality data are collected, standardizing the quality data, and performing the step 4.5); otherwise, returning to execute the step 4.1);
4.5), judging whether the quality data y exceeds the control limit, and if the r-th quality variable | yr|＞3σrIf r is 1,2, 5, it indicates that the r-th quality variable is abnormal, and the step 4.1 is returned to after alarming; otherwise, directly returning to execute the step 4.1).
The failure 1 related to the embodiment is that the temperature of the cooling water inlet of the reactor changes in a step mode at the 160 th sampling moment, when the failure occurs, the temperature of the reactor increases suddenly, the product quality is not affected due to the adjusting function of the controller, and the process monitoring result is shown in fig. 3-7; FIGS. 3 and 4 are process monitoring curves, T in FIG. 3, obtained using a nonlinear dynamic pivot analysis method2The statistic and the SPE statistic in FIG. 4 both exceed the control limit, and the process monitoring system gives out a fault alarm; because the actual product quality is not affected, the operator deems it a false positive, and the reliability of the process monitoring system is reduced.
FIGS. 5-7 are mass-oriented non-linear dynamic process monitoring curves, T in FIG. 5 being mass-dependents 2The statistic does not exceed the control limit, the quality obtained by inference is not abnormal, and the process monitoring system does not give an alarm; in FIG. 6
Figure BDA0001644322770000174
Statistics and SPE in FIG. 7exThe statistics exceed the control limit, which indicates that the process irrelevant to the quality has a fault and the product quality is not influenced.
For the fault 1, the quality-oriented nonlinear dynamic process monitoring is adopted in the embodiment, and compared with a nonlinear dynamic principal component analysis method, the process fault alarm which does not affect the product quality is filtered, and the reliability of the process monitoring is effectively improved.
Fault 2 is a step pressure loss at flow 4C at the 160 th sampling instant, and the process monitoring results are shown in fig. 8-12; FIGS. 8 and 9 are process monitoring curves, T in FIG. 8, obtained using a nonlinear dynamic pivot analysis method2The statistic and the SPE statistic in FIG. 9 both exceed the control limit, the process monitoring system gives a fault alarm, but cannot judge whether the product quality is affected; FIGS. 10 to 12 are non-linear dynamic process monitoring curves for mass, and in FIG. 10 it can be seen that T is associated with mass after a fault has occurreds 2The statistic exceeds the control limit, but returns to the control limit after a period of time, and the quality is inferred to be abnormal, but is finally adjusted and restored to the normal state; in FIG. 11
Figure BDA0001644322770000181
Statistics and SPE in FIG. 12exThe statistics all exceed the control limit indicating that a process not related to quality has failed.
The quality-oriented nonlinear dynamic process monitoring method is applied to the Tennessee-Iseman process, and can judge the change trend of the product quality according to the process data when the fault 2 occurs, compared with a nonlinear dynamic principal component analysis method.
The failure 3 related to the present embodiment is that the reaction dynamic generates slow offset at the 160 th sampling time, and the process monitoring results are shown in fig. 13-17; FIGS. 13 and 14 are process monitoring curves, T in FIG. 13, obtained using a nonlinear dynamic pivot analysis method2Both the statistic and the SPE statistic in FIG. 14 exceed the control limit, and the process monitoring system gives a fault alarm but cannot judge whether the product quality is affected; FIGS. 15 to 17 are non-linear dynamic process monitoring curves for quality, and FIG. 15 shows T associated with quality after a fault occurss 2And if the statistic exceeds the control limit, indicating that the process has a fault, causing the product quality to be abnormal, and giving an alarm.
Compared with a nonlinear dynamic principal component analysis method, the quality-oriented nonlinear dynamic process monitoring can not only detect process faults, but also further judge whether the process faults affect the product quality.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (4)

1. A quality-oriented nonlinear dynamic process monitoring method is characterized in that: the method comprises the following steps:
(1) setting process variable and quality variable in nonlinear dynamic process, collecting process data and quality data of nonlinear continuous process under normal working condition, respectively mapping phi with unknown nonlinearity according to nonlinear characteristics of processx(x) And phiy(y) projecting the process augmentation vector x and the mass vector y into a high-dimensional linear feature space, where u is an m-dimensional process vector and y is an n-dimensional mass vector, and then phix(x) Is a m-dimensional vector, phiy(y) is an n-dimensional vector; sampling time i, i ═ h +1, h + 2.., h + N, constructing a process augmentation vector according to the dynamic characteristics of the nonlinear dynamic process
Figure FDA0002780165120000011
Wherein h represents the hysteresis order; acquiring process data and quality data at h + N sampling moments under normal working conditions, and if the sampling rate of the quality data is low, filling up missing quality data; constructing process augmentation data matrix X belongs to RN×(h+1)mAnd the quality data matrix Y is belonged to RN×n(ii) a Calculating the standard deviation sigma corresponding to n quality variablesrR is 1,2, …, n; standardizing the matrix X and the matrix Y respectively to ensure that each column of data is uniformThe value is 0 and the variance is 1.
(2) Performing subspace decomposition by utilizing nonlinear typical variable analysis, extracting process characteristics related to quality, and calculating standard square sum of typical vectors related to quality
Figure FDA0002780165120000012
And its control limit;
(3) performing subspace decomposition by utilizing nonlinear principal component analysis, extracting process features irrelevant to quality, and calculating standard square sum of principal component vectors irrelevant to quality
Figure FDA0002780165120000013
Sum squared prediction error SPEexAnd its control limit;
(4) and monitoring the process: real-time monitoring of process and quality variable data in a nonlinear dynamic process, calculation using process data
Figure FDA0002780165120000014
And SPEexAnd (5) statistics, namely judging whether the nonlinear dynamic process fails or not and whether the process failure affects the product quality or not.
2. A quality-oriented nonlinear dynamic process monitoring method as recited in claim 1, further comprising: the step (2) specifically comprises the following steps: extracting the maximum phi in a high-dimensional linear characteristic space by utilizing linear typical variable analysisx(x) And phiy(y) typical variables of relevance; finding projection vectors
Figure FDA0002780165120000015
And
Figure FDA0002780165120000016
maximizing the following correlation coefficient
Figure FDA0002780165120000017
Wherein, the matrix
Figure FDA0002780165120000018
Is indicative of phix(x) And phiy(y) a cross-covariance matrix of (y),
Figure FDA0002780165120000019
is indicative of phix(x) The covariance matrix of (a) is determined,
Figure FDA00027801651200000110
is indicative of phiy(y) a covariance matrix; due to the non-linear mapping phix(x) And phiy(y) difficult to determine, unable to directly perform linear typical variable analysis in a high-dimensional linear feature space, and extract process features related to quality;
projection vectors alpha and beta are present such that
Figure FDA0002780165120000021
Conversion of formula (1) to
Figure FDA0002780165120000022
Wherein, the kernel matrix [ Kx]i,j＝kx(xi,xj)＝<φx(xi)·φx(xj)>Kernel matrix [ K ]y]i,j＝ky(yi,yj)＝<φy(yi)·φy(yj)>，kx(xi,xj) And ky(yi,yj) Is a kernel function, i 1., N, j 1., N; typically using a Gaussian kernel function k (x)1,x2)＝exp(-||x1-x2||2C); the optimization problem of equation (2) can be transformed into a generalized eigenvalue solution problem:
Figure FDA0002780165120000023
wherein λ is a characteristic value, [ α ]T βT]TIs a feature vector corresponding to lambda; to avoid the ill-conditioned matrix solving problem, K is used separatelyxKx+ η I and KyKy+ η I instead of KxKxAnd KyKyIs obtained by
Figure FDA0002780165120000024
Wherein η represents a regularization constant, and I represents an identity matrix having dimensions N × N; obtaining k maximum eigenvalues λ from equation (4)1≥λ2≥…≥λkCorresponding projection vector alpha1,α2,…,αkAnd beta1,β2,…,βk；
The eigenvalue lambda represents a correlation coefficient of the process augmentation vector and the quality vector, and the larger the eigenvalue lambda is, the stronger the correlation is;
determining a parameter k according to the magnitude of the correlation coefficient;
constructing a projection matrix Ak＝[α1,α2,…,αk]For process-augmented vector sample x, the corresponding low-dimensional process-representative vector is
c＝Ak TKx(X,x) (5)；
Wherein the kernel vector Kx(X,x)＝[kx(x1,x),kx(x2,x),…,kx(xN,x)]T；
The correlation between the process typical vector c and the quality vector is strongest, and the process typical vector is used as the characteristic of a process subspace related to the quality; under the condition of quality data missing, if the process typical vector c is abnormal, the quality vector can be deduced to be abnormal; construct statistics
Figure FDA0002780165120000031
Monitoring a quality-related process subspace variation;
data calculation using normal operating conditions
Figure FDA0002780165120000032
Statistics calculated by a kernel density estimation method
Figure FDA0002780165120000033
A control limit for the statistic.
3. A quality-oriented nonlinear dynamic process monitoring method as recited in claim 2, further comprising: the step (3) specifically comprises the following steps:
projecting the process subspace characteristic c which is calculated by the formula (5) and is related to the quality back to a high-dimensional linear characteristic space to obtain phix(x) Is estimated value of
Figure FDA0002780165120000034
Estimating residual error
Figure FDA0002780165120000035
Information is described that is not related to the quality vector due to the non-linear mapping phix(x) Difficult to determine, unable to calculate the estimated residual
Figure FDA0002780165120000036
Linear principal component analysis and extraction of process features irrelevant to quality cannot be directly carried out in a residual error space, namely a process subspace irrelevant to quality;
estimated value
Figure FDA0002780165120000037
Is a function of a process representative vector c, the process dictionaryType vector c is a function of process augmentation vector x; thus, the estimated value
Figure FDA0002780165120000038
Is a non-linear function of the process-augmented vector x, estimates the residual error
Figure FDA0002780165120000039
Is also a non-linear function of the process spread vector x
Figure FDA00027801651200000310
In the process subspace irrelevant to the quality, converting the principal component feature extraction problem into a feature value solving problem:
λexvex＝CFvex (8)；
wherein, the matrix CFIs indicative of phiex(x) Of the covariance matrix, λexRepresenting a characteristic value, vexDenotes λexA corresponding feature vector; presence of projection vector alphaexSo that v isex＝φex(X)TαexConversion of equation (8) to
Figure FDA00027801651200000311
Wherein, the matrix
Figure FDA00027801651200000312
Core matrix
Figure FDA00027801651200000313
j ═ 1.., N; the kernel function can be derived from equation (7)
Figure FDA0002780165120000041
Expression (c):
Figure FDA0002780165120000042
according to the formula (10),
Figure FDA0002780165120000043
is a kernel function kx(xi,xj) In a high-dimensional linear and mass-dependent process subspace, selecting a kernel function kx(xi,xj) Then, no kernel function needs to be selected
Figure FDA0002780165120000044
But a kernel function is calculated using equation (10)
Figure FDA0002780165120000045
Obtaining k from formula (9)exA maximum eigenvalue
Figure FDA0002780165120000046
Corresponding projection vector
Figure FDA0002780165120000047
In order to ensure that the feature vector satisfies | | | vex||2For projection vector α of 1exThe following normalization was performed:
Figure FDA0002780165120000048
characteristic value lambdaexInformation representing the variance of a subspace not related to the quality, the eigenvalues lambdaexThe larger the process change corresponding to the pivot feature description is, the stronger the parameter k is determined according to the accumulated sum of the variancesex；
Constructing a projection matrix
Figure FDA0002780165120000049
For process-augmented vector sample x, corresponding and primeThe principal component of which the quantity is irrelevant is characterized by
Figure FDA00027801651200000410
Wherein the kernel vector
Figure FDA00027801651200000411
Principal component texReflecting the main change of the process subspace irrelevant to the quality, taking the principal element as the characteristic of the subspace, and constructing
Figure FDA00027801651200000412
Statistics and SPEexStatistics
Figure FDA00027801651200000413
Figure FDA00027801651200000414
Wherein, the diagonal matrix
Figure FDA00027801651200000415
Respectively calculating by using data of normal working conditions
Figure FDA00027801651200000416
Statistics and SPEexStatistics calculated by the kernel density estimation method respectively
Figure FDA0002780165120000051
Statistics and SPEexA control limit for the statistic.
4. A quality oriented nonlinear dynamic process monitoring method as recited in claim 3, further comprising: the step (4) specifically comprises the following steps:
(4.1) acquiring data of a process variable and a quality variable at the current moment, constructing a process augmentation vector x and carrying out standardization processing on the process augmentation vector x;
(4.2) computing the feature c of the process subspace relating to the mass using equation (5), then computing it according to equation (6)
Figure FDA0002780165120000052
Statistics; judgment of
Figure FDA0002780165120000053
Whether the statistic exceeds the control limit; if the process exceeds the control limit, the process is abnormal, the product quality is abnormal, and the step (4.1) is returned to after the alarm is given; otherwise, performing the step (4.3);
(4.3) calculating the feature t of the quality-independent process subspace by using the formula (12)exThen, it is calculated from the equations (13) and (14)
Figure FDA0002780165120000054
Statistics and SPEexStatistics; judgment of
Figure FDA0002780165120000055
Statistics and SPEexWhether the statistic exceeds the control limit; if it is
Figure FDA0002780165120000056
Statistics or SPEexIf the statistic exceeds the control limit, the process is abnormal but the product quality is not influenced or the influence is small, and the step (4.1) is returned to be executed after prompting; otherwise, performing the step (4.4);
(4.4) judging whether the quality data y is collected at the current moment; if the quality data are collected, standardizing the quality data, and performing the step (4.5); otherwise, returning to execute the step (4.1);
(4.5) judging whether the quality data exceeds the control limit, and if the quality data exceeds the control limit, judging whether the quality data exceeds the control limit or not, and if the quality data exceeds the control limit, judging whether the quality data exceeds the control limit, and if the quality data exceeds the control limit, judging the quality data tor|＞3σr，r＝1,2,.., n, indicating that the r-th quality variable is abnormal, and returning to the step (4.1) after alarming; otherwise, directly returning to the step (4.1).
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CN109613891B (en) * 2018-11-06 2020-07-14 北京航空航天大学 Method, device and equipment for identifying key parameters in numerical control machining process
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CN101446831B (en) * 2008-12-30 2011-05-25 东北大学 Decentralized process monitoring method
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US20150206727A1 (en) * 2014-01-17 2015-07-23 Rudjer Boskovic Institute Method and apparatus for underdetermined blind separation of correlated pure components from nonlinear mixture mass spectra
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CN105955241B (en) * 2016-06-03 2018-09-14 北京科技大学 A kind of quality fault localization method based on joint data-driven production process
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