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CN108664002B - A Quality-Oriented Nonlinear Dynamic Process Monitoring Method - Google Patents

A 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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    • G05B19/00—Programme-control systems
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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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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
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Abstract

本发明涉及一种面向质量的非线性动态过程监控方法，包括以下步骤：(1)、采集非线性过程在正常工况下的过程数据和质量数据，构造建模数据并进行标准化；(2)、计算与质量相关的典型向量的标准平方和

Figure DDA0001644322790000011
及其控制限；(3)、计算与质量不相关的主元向量的标准平方和
Figure DDA0001644322790000012
和平方预测误差SPEex及其控制限；(4)、实时监控非线性动态过程中的过程变量和质量变量的数据，计算
Figure DDA0001644322790000013
和SPEex统计量，判断是否发生故障、过程故障是否影响产品质量。本发明能够有效过滤掉不影响产品质量的过程故障报警，提高过程监控的可信度，增强了实时过程监控系统的逻辑完整性和实用性，适应非线性动态化工过程实时过程监控的需求；过程故障判断准确，实时过程监控效率高，适应范围广。

Figure 201810394768

The invention relates to a quality-oriented nonlinear dynamic process monitoring method, comprising the following steps: (1) collecting process data and quality data of the nonlinear process under normal working conditions, constructing modeling data and standardizing; (2) , computes the standard sum of squares of typical vectors related to mass

Figure DDA0001644322790000011
and its control limit; (3), calculate the standard sum of squares of the pivot vector that is not related to quality
Figure DDA0001644322790000012
sum squared prediction error SPE ex and its control limit; (4), real-time monitoring of process variables and quality variables in nonlinear dynamic process data, calculation
Figure DDA0001644322790000013
and SPE ex statistics to judge whether there is a failure and whether the process failure affects the product quality. The invention can effectively filter out process fault alarms that do not affect product quality, improve the reliability of process monitoring, enhance the logical integrity and practicability of the real-time process monitoring system, and adapt to the needs of real-time process monitoring in nonlinear dynamic chemical processes; Accurate fault judgment, high efficiency of real-time process monitoring, and wide adaptability.

Figure 201810394768

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)

1.一种面向质量的非线性动态过程监控方法，其特征在于：包括以下步骤：1. a quality-oriented nonlinear dynamic process monitoring method, is characterized in that: comprise the following steps: (1)、设置非线性动态过程中的过程变量和质量变量，采集非线性连续过程在正常工况下的过程数据和质量数据，根据过程的非线性特征，分别利用未知非线性映射φx(x)和φy(y)将过程增广向量x和质量向量y投影到高维线性特征空间，设u为m维过程向量，y为n维质量向量，则φx(x)为m维向量，φy(y)为n维向量；采样时刻i，i＝h+1,h+2,...,h+N，根据非线性动态过程的动态特性，构造过程增广向量
Figure FDA0002780165120000011
其中h表示滞后阶次；采集正常工况下h+N个采样时刻的过程数据和质量数据，若质量数据的采样速率较低，则补齐缺失的质量数据；构造过程增广数据矩阵X∈RN×(h+1)m和质量数据矩阵Y∈RN×n；计算n个质量变量对应的标准差σr，r＝1,2,…,n；分别对矩阵X和Y进行标准化处理，使各列数据的均值为0，方差为1。(1) Set the process variables and quality variables in the nonlinear dynamic process, collect the process data and quality data of the nonlinear continuous process under normal operating conditions, and use the unknown nonlinear mapping φ x ( x) and φ y (y) project the process augmentation vector x and mass vector y into the high-dimensional linear feature space, let u be the m-dimensional process vector, y be the n-dimensional quality vector, then φ x (x) is the m-dimensional vector, φ y (y) is an n-dimensional vector; sampling time i, i=h+1, h+2,...,h+N, according to the dynamic characteristics of the nonlinear dynamic process, construct the process augmentation vector
Figure FDA0002780165120000011
where h represents the lag order; collect process data and quality data at h+N sampling times under normal conditions, if the sampling rate of quality data is low, then fill in the missing quality data; construct the process augmented data matrix X∈ R N×(h+1)m and quality data matrix Y∈R N×n ; calculate the standard deviation σ r corresponding to n quality variables, r=1,2,…,n; standardize the matrices X and Y respectively Process so that the mean of each column of data is 0 and the variance is 1. (2)、利用非线性典型变量分析进行子空间分解，提取与质量相关的过程特征，计算与质量相关的典型向量的标准平方和
Figure FDA0002780165120000012
及其控制限；(2) Use nonlinear canonical variable analysis for subspace decomposition, extract quality-related process features, and calculate the standard sum of squares of quality-related canonical vectors
Figure FDA0002780165120000012
and its control limits; (3)、利用非线性主元分析进行子空间分解，提取与质量不相关的过程特征，计算与质量不相关的主元向量的标准平方和
Figure FDA0002780165120000013
和平方预测误差SPEex及其控制限；(3) Use nonlinear principal component analysis to decompose the subspace, extract the process features that are not related to quality, and calculate the standard sum of squares of the principal component vectors that are not related to quality.
Figure FDA0002780165120000013
sum squared prediction error SPE ex and its control limits; (4)、过程监控：实时监控非线性动态过程中的过程变量和质量变量的数据，利用过程数据计算
Figure FDA0002780165120000014
和SPEex统计量，判断非线性动态过程是否发生故障、过程故障是否影响产品质量。(4) Process monitoring: monitor the data of process variables and quality variables in the nonlinear dynamic process in real time, and use the process data to calculate
Figure FDA0002780165120000014
and SPE ex statistics to judge whether the nonlinear dynamic process fails and whether the process failure affects the product quality. 2.根据权利要求1所述的一种面向质量的非线性动态过程监控方法，其特征在于：步骤(2)具体包括：在高维线性特征空间，利用线性典型变量分析提取最大化φx(x)和φy(y)相关性的典型变量；寻找投影向量
Figure FDA0002780165120000015
和
Figure FDA0002780165120000016
最大化下述相关系数2. a kind of quality-oriented nonlinear dynamic process monitoring method according to claim 1, is characterized in that: step (2) specifically comprises: in high-dimensional linear feature space, utilizes linear typical variable analysis to extract and maximize φ x ( Typical variables for the correlation of x) and φ y (y); find the projection vector
Figure FDA0002780165120000015
and
Figure FDA0002780165120000016
Maximize the following correlation coefficient
Figure FDA0002780165120000017
Figure FDA0002780165120000017
 其中，矩阵
Figure FDA0002780165120000018
表示φx(x)和φy(y)的交叉协方差矩阵，
Figure FDA0002780165120000019
表示φx(x)的协方差矩阵，
Figure FDA00027801651200000110
表示φy(y)的协方差矩阵；由于非线性映射φx(x)和φy(y)难以确定，无法直接在高维线性特征空间进行线性典型变量分析、提取与质量相关的过程特征；Among them, the matrix
Figure FDA0002780165120000018
represents the cross-covariance matrix of φ x (x) and φ y (y),
Figure FDA0002780165120000019
represents the covariance matrix of φ x (x),
Figure FDA00027801651200000110
Represents the covariance matrix of φ y (y); since the nonlinear mappings φ x (x) and φ y (y) are difficult to determine, it is impossible to directly perform linear canonical variable analysis in high-dimensional linear feature space and extract quality-related process features ; 存在投影向量α和β，使得
Figure FDA0002780165120000021
利用核函数技术，式(1)转化为There exist projection vectors α and β such that
Figure FDA0002780165120000021
Using the kernel function technique, Equation (1) is transformed into
Figure FDA0002780165120000022
Figure FDA0002780165120000022
 其中，核矩阵[Kx]i,j＝kx(xi,xj)＝<φx(xi)·φx(xj)>，核矩阵[Ky]i,j＝ky(yi,yj)＝<φy(yi)·φy(yj)>，kx(xi,xj)和ky(yi,yj)为核函数，i＝1,...,N，j＝1,...,N；一般采用高斯核函数k(x1,x2)＝exp(-||x1-x2||2/c)；式(2)的优化问题可以转化为广义特征值求解问题：Among them, the kernel matrix [K x ] i,j =k x (x i ,x j )=<φ x (x i )·φ x (x j )>, the kernel matrix [K y ] i,j =k y (y i , y j )=<φ y (y i )·φ y (y j )>, k x (x i , x j ) and k y (y i , y j ) are kernel functions, i=1 ,...,N, j=1,...,N; Gaussian kernel function k(x 1 , x 2 )=exp(-||x 1 -x 2 || 2 /c) is generally used; formula ( The optimization problem of 2) can be transformed into a generalized eigenvalue solution problem:
Figure FDA0002780165120000023
Figure FDA0002780165120000023
 其中，λ为特征值，[αT βT]T为λ对应的特征向量；为了避免病态矩阵求解问题，分别利用KxKx+ηI和KyKy+ηI代替KxKx和KyKy，可得Among them, λ is the eigenvalue, [α T β T ] T is the eigenvector corresponding to λ; in order to avoid the problem of ill-conditioned matrix solution, K x K x +ηI and K y K y +ηI are used to replace K x K x and K respectively y K y , we can get
Figure FDA0002780165120000024
Figure FDA0002780165120000024
 其中，η表示正则化常数，I表示维数为N×N的单位矩阵；由式(4)获得k个最大特征值λ1≥λ2≥…≥λk对应的投影向量α1,α2,…,αk和β1,β2,…,βk；Among them, η represents the regularization constant, and I represents the unit matrix with dimension N×N; the projection vectors α 1 , α 2 corresponding to the k largest eigenvalues λ 1 ≥λ 2 ≥...≥λ k are obtained from equation (4). ,…,α k and β 1 ,β 2 ,…,β k ; 特征值λ表示过程增广向量和质量向量的相关系数，特征值λ越大，相关性越强；The eigenvalue λ represents the correlation coefficient between the process augmentation vector and the quality vector, the larger the eigenvalue λ, the stronger the correlation; 根据相关系数的大小确定参数k；Determine the parameter k according to the size of the correlation coefficient; 构造投影矩阵Ak＝[α1,α2,…,αk]，对于过程增广向量样本x，对应的低维过程典型向量为Construct the projection matrix A k =[α 1 ,α 2 ,...,α k ], for the process augmentation vector sample x, the corresponding low-dimensional process typical vector is c＝Ak TKx(X,x) (5)；c=A k T K x (X,x) (5); 其中，核向量Kx(X,x)＝[kx(x1,x),kx(x2,x),…,kx(xN,x)]T；Wherein, the kernel vector K x (X,x)=[k x (x 1 ,x),k x (x 2 ,x),…,k x (x N ,x)] T ; 过程典型向量c与质量向量的相关性最强，将过程典型向量作为与质量相关的过程子空间的特征；在质量数据缺失的情况下，若过程典型向量c发生异常，可推理得到质量向量发生异常；构造统计量The process typical vector c has the strongest correlation with the quality vector, and the process typical vector is used as the feature of the process subspace related to quality; in the case of missing quality data, if the process typical vector c is abnormal, it can be inferred that the quality vector occurs. exception; construction statistic
Figure FDA0002780165120000031
Figure FDA0002780165120000031
 监控与质量相关的过程子空间的变化；Monitor changes in quality-related process subspaces; 利用正常工况的数据计算
Figure FDA0002780165120000032
统计量，通过核密度估计方法计算出
Figure FDA0002780165120000033
统计量的控制限。Calculated using data from normal operating conditions
Figure FDA0002780165120000032
statistic, calculated by kernel density estimation method
Figure FDA0002780165120000033
The control limit for the statistic. 3.根据权利要求2所述的一种面向质量的非线性动态过程监控方法，其特征在于：步骤(3)具体包括：3. a kind of quality-oriented nonlinear dynamic process monitoring method according to claim 2 is characterized in that: step (3) specifically comprises: 将式(5)计算的与质量相关的过程子空间特征c返回投影到高维线性特征空间，可得φx(x)的估计值The quality-related process subspace feature c calculated by equation (5) is projected back to the high-dimensional linear feature space, and the estimated value of φ x (x) can be obtained
Figure FDA0002780165120000034
Figure FDA0002780165120000034
 估计残差
Figure FDA0002780165120000035
描述了与质量向量不相关的信息，由于非线性映射φx(x)难以确定，无法计算估计残差
Figure FDA0002780165120000036
无法直接在残差空间即与质量不相关的过程子空间中进行线性主元分析、提取与质量不相关的过程特征；Estimated residuals
Figure FDA0002780165120000035
Describes information that is not related to the quality vector, since the nonlinear mapping φ x (x) is difficult to determine, the estimated residual cannot be calculated
Figure FDA0002780165120000036
It is impossible to directly perform linear principal component analysis in the residual space, that is, the process subspace that is not related to quality, and extract process features that are not related to quality; 估计值
Figure FDA0002780165120000037
是过程典型向量c的函数，过程典型向量c是过程增广向量x的函数；因此，估计值
Figure FDA0002780165120000038
是过程增广向量x的非线性函数，估计残差
Figure FDA0002780165120000039
也是过程增广向量x的非线性函数，设
Figure FDA00027801651200000310
与质量不相关的过程子空间中，主元特征提取问题转化为特征值求解问题：estimated value
Figure FDA0002780165120000037
is a function of the process canonical vector c, which is a function of the process augmentation vector x; therefore, the estimated value
Figure FDA0002780165120000038
is a nonlinear function of the process augmentation vector x, estimating the residual
Figure FDA0002780165120000039
is also a nonlinear function of the process augmentation vector x, let
Figure FDA00027801651200000310
In the quality-independent process subspace, the problem of feature extraction of principal components is transformed into the problem of eigenvalue solution: λexvex＝CFvex (8)；λ ex v ex =C F v ex (8); 其中，矩阵CF表示φex(x)的协方差矩阵，λex表示特征值，vex表示λex对应的特征向量；存在投影向量αex使得vex＝φex(X)Tαex，利用核函数技术，式(8)转化为Among them, the matrix CF represents the covariance matrix of φ ex (x), λ ex represents the eigenvalue, and v ex represents the eigenvector corresponding to λ ex ; there is a projection vector α ex such that v ex =φ ex (X) T α ex , Using the kernel function technique, Equation (8) is transformed into
Figure FDA00027801651200000311
Figure FDA00027801651200000311
 其中，矩阵
Figure FDA00027801651200000312
核矩阵
Figure FDA00027801651200000313
j＝1,...,N；根据式(7)可推导得到核函数
Figure FDA0002780165120000041
的表达式：Among them, the matrix
Figure FDA00027801651200000312
Kernel matrix
Figure FDA00027801651200000313
j=1,...,N; according to formula (7), the kernel function can be deduced
Figure FDA0002780165120000041
expression:
Figure FDA0002780165120000042
Figure FDA0002780165120000042
 根据式(10)，
Figure FDA0002780165120000043
是核函数kx(xi,xj)的函数，在高维线性与质量相关的过程子空间中选择核函数kx(xi,xj)之后，不需要再选择核函数
Figure FDA0002780165120000044
而是利用式(10)计算核函数
Figure FDA0002780165120000045
According to formula (10),
Figure FDA0002780165120000043
is the function of the kernel function k x (x i ,x j ), after selecting the kernel function k x (x i ,x j ) in the high-dimensional linear and quality-related process subspace, there is no need to select the kernel function again
Figure FDA0002780165120000044
Instead, use equation (10) to calculate the kernel function
Figure FDA0002780165120000045
 由式(9)获得kex个最大特征值
Figure FDA0002780165120000046
对应的投影向量
Figure FDA0002780165120000047
The k ex largest eigenvalues are obtained by formula (9)
Figure FDA0002780165120000046
Corresponding projection vector
Figure FDA0002780165120000047
 为了保证特征向量满足||vex||2＝1，对投影向量αex进行如下归一化：In order to ensure that the feature vector satisfies ||v ex || 2 =1, the projection vector α ex is normalized as follows:
Figure FDA0002780165120000048
Figure FDA0002780165120000048
 特征值λex表示与质量不相关的子空间的方差信息，特征值λex越大，对应主元特征描述的过程变化越强，根据方差累积和大小确定参数kex；The eigenvalue λ ex represents the variance information of the subspace that is not related to the quality. The larger the eigenvalue λ ex is, the stronger the process change of the corresponding pivot feature description is, and the parameter k ex is determined according to the cumulative sum of the variance; 构造投影矩阵
Figure FDA0002780165120000049
对于过程增广向量样本x，对应的与质量不相关的主元特征为Construct the projection matrix
Figure FDA0002780165120000049
For the process augmented vector sample x, the corresponding quality-independent pivot feature is
Figure FDA00027801651200000410
Figure FDA00027801651200000410
 其中，核向量
Figure FDA00027801651200000411
主元tex反应了与质量不相关的过程子空间的主要变化，将主元作为该子空间的特征，构造
Figure FDA00027801651200000412
统计量和SPEex统计量Among them, the kernel vector
Figure FDA00027801651200000411
The pivot element tex reflects the main changes in the mass-independent process subspace, and the pivot element is used as the feature of this subspace to construct
Figure FDA00027801651200000412
Statistics and SPE ex statistics
Figure FDA00027801651200000413
Figure FDA00027801651200000413
Figure FDA00027801651200000414
Figure FDA00027801651200000414
 其中，对角矩阵
Figure FDA00027801651200000415
Among them, the diagonal matrix
Figure FDA00027801651200000415
 利用正常工况的数据分别计算
Figure FDA00027801651200000416
统计量和SPEex统计量，通过核密度估计方法分别计算
Figure FDA0002780165120000051
统计量和SPEex统计量的控制限。Calculated separately using data from normal operating conditions
Figure FDA00027801651200000416
Statistics and SPE ex statistics, calculated separately by kernel density estimation method
Figure FDA0002780165120000051
Control limits for the statistic and the SPE ex statistic. 4.根据权利要求3所述的一种面向质量的非线性动态过程监控方法，其特征在于：步骤(4)具体包括：4. a kind of quality-oriented nonlinear dynamic process monitoring method according to claim 3 is characterized in that: step (4) specifically comprises: (4.1)、采集当前时刻的过程变量和质量变量的数据，构造过程增广向量x并对其进行标准化处理；(4.1) Collect the data of the process variables and quality variables at the current moment, construct the process augmentation vector x and standardize it; (4.2)、利用式(5)计算与质量相关的过程子空间的特征c，然后根据式(6)计算
Figure FDA0002780165120000052
统计量；判断
Figure FDA0002780165120000053
统计量是否超出控制限；若超出控制限，表明过程发生异常，将导致产品质量发生异常，进行报警后返回执行步骤(4.1)；否则进行步骤(4.3)；(4.2), use formula (5) to calculate the feature c of the process subspace related to quality, and then calculate according to formula (6)
Figure FDA0002780165120000052
statistic; judgment
Figure FDA0002780165120000053
Whether the statistic exceeds the control limit; if it exceeds the control limit, it indicates that the process is abnormal, which will lead to abnormal product quality. After alarming, return to step (4.1); otherwise, go to step (4.3); (4.3)、利用式(12)计算与质量不相关的过程子空间的特征tex，然后根据式(13)和式(14)计算
Figure FDA0002780165120000054
统计量和SPEex统计量；判断
Figure FDA0002780165120000055
统计量和SPEex统计量是否超出控制限；若
Figure FDA0002780165120000056
统计量或SPEex统计量超出控制限，表明过程发生异常，但不会影响产品质量或影响较小，进行提示后返回执行步骤(4.1)；否则进行步骤(4.4)；(4.3), use the formula (12) to calculate the characteristic tex of the process subspace that is not related to the quality, and then calculate according to the formula (13) and the formula (14)
Figure FDA0002780165120000054
Statistics and SPE ex statistics; judgment
Figure FDA0002780165120000055
Whether the statistic and the SPE ex statistic exceed the control limits; if
Figure FDA0002780165120000056
If the statistic or SPE ex statistic exceeds the control limit, it indicates that the process is abnormal, but it will not affect the product quality or the impact is small, and return to step (4.1) after prompting; otherwise, go to step (4.4); (4.4)、判断当前时刻是否采集到质量数据y；若采集到质量数据，对质量数据进行标准化，进行步骤(4.5)；否则返回执行步骤(4.1)；(4.4), determine whether the quality data y is collected at the current moment; if the quality data is collected, standardize the quality data, and go to step (4.5); otherwise, return to step (4.1); (4.5)、判断质量数据是否超出控制限，若第r个质量变量|yr|＞3σr，r＝1,2,...,n，则表明第r个质量变量发生异常，进行报警后返回执行步骤(4.1)；否则直接返回执行步骤(4.1)。(4.5) Judging whether the quality data exceeds the control limit, if the rth quality variable |y r |＞3σ r , r=1,2,...,n, it means that the rth quality variable is abnormal and an alarm will be issued Then return to execution step (4.1); otherwise, return directly to execution step (4.1).
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