CN111413931A - Self-adaptive industrial process monitoring method based on sliding window recursion principal component analysis - Google Patents

Self-adaptive industrial process monitoring method based on sliding window recursion principal component analysis Download PDF

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CN111413931A
CN111413931A CN202010199389.2A CN202010199389A CN111413931A CN 111413931 A CN111413931 A CN 111413931A CN 202010199389 A CN202010199389 A CN 202010199389A CN 111413931 A CN111413931 A CN 111413931A
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matrix
eigenvalues
data
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伊向良
江居传
郭伟
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China BlueChemical Ltd
CNOOC Fudao Ltd
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Abstract

The invention discloses a self-adaptive industrial process monitoring method for sliding window recursion principal component analysis, which uses the advantages of a sliding window and a recursion method for reference, adds forgetting factors in samples and covariance to retain useful information in historical data to a certain extent, and self-adaptively updates the number of principal components by combining a threshold method, overcomes the defect that the traditional principal component accumulative contribution rate cannot be updated in real time along with the change of the process, and finally completes model updating and carries out the next step of calculation through the steps; the method can effectively detect the process mode switching, can self-adapt to the learning process mode, updates the model and achieves the purpose of self-adapting monitoring.

Description

Self-adaptive industrial process monitoring method based on sliding window recursion principal component analysis
Technical Field
The invention belongs to the field of industrial process monitoring, relates to a self-adaptive industrial process monitoring method, and particularly relates to a self-adaptive industrial process monitoring method based on sliding window recursion principal component analysis.
Background
In the face of the current situation that the modern industrial process is increasingly complex, the maximum economic benefit can be obtained only by realizing safe and stable operation, so that the method for detecting whether the process breaks down in time and reasonably processing the process has important theoretical significance and engineering application value. In view of the fact that industrial process data reflect the internal changes and operating conditions of the system and the strong feature extraction capability of the multivariate statistical analysis method, in order to ensure manufacturing safety and production quality, multivariate statistical process monitoring draws high attention of researchers in academia and industry, and a series of multivariate statistical process monitoring methods based on data driving are formed. Among them, principal component analysis is widely used and in the field of process monitoring.
However, the actual production process has various modes and complex data components, and poses a small challenge to the establishment of a production condition monitoring model. The model established by the traditional principal component analysis method is fixed and non-time-varying, and is easy to generate model mismatching and false alarm phenomena when used for online monitoring of a real-time process, so that the effectiveness of a monitoring system is directly influenced. Aiming at the time-varying characteristic of the industrial process, the principal component model needs to be updated in real time, so that a recursion principal component analysis algorithm, sliding window principal component analysis and the like are provided by experts. The recursion principal component analysis algorithm recurrently updates the principal component analysis model by continuously collecting new data and then continuously recursively updating the old mean, variance and covariance matrix according to the new data. The sliding window principal component analysis adopts the window which slides backwards along with the time to continuously add newly acquired data, removes old data, continuously updates the data in the window, updates a principal component analysis model, and effectively overcomes the defect that the recursive principal component analysis is slow in recursive updating. Moreover, a common method for determining the number of the principal elements in the principal element analysis is a principal element accumulated contribution rate method, the method cannot be updated in real time along with process change, and the principal elements cannot be changed along with working condition change. Therefore, there is a limitation in adaptive modeling.
Disclosure of Invention
The invention aims to provide a self-adaptive industrial process monitoring method based on sliding window recursion principal component analysis, which aims at the time-varying characteristic of the current industrial process, combines a sliding window with recursion principal component analysis, introduces a threshold value method to determine the number of principal components in real time and realizes self-adaptive monitoring of the industrial process.
In order to achieve the purpose, the technical scheme of the invention is as follows: the self-adaptive industrial process monitoring method based on sliding window recursion principal component analysis comprises the following steps:
step one, collecting data X, X ∈ R of historical industrial processN×MN represents the number of samples and M represents the number of process variables, and assuming that the length of the sliding window is L, the k-th data matrix using the sliding window is Xk＝(xk-L+1,xk-L+2,...,xk)TThe next 1 data matrix is Xk+1＝(xk-L+2,xk-L+3,...,xk+1)TThe common intermediate data matrix of two adjacent windows:
Figure BDA0002418825510000021
step two: firstly, normalizing the k-th data matrix to obtain a mean value bkDetermining the number of principal elements by principal element analysis and a principal element cumulative contribution rate method to obtain a corresponding covariance matrix RkCalculating T from the F distribution2And control limit of SPE statistics at confidence level α:
Figure BDA0002418825510000022
Figure BDA0002418825510000023
wherein F (l, n-1, α) is the F distribution critical point corresponding to test level α, degree of freedom l and n-l;
Figure BDA0002418825510000024
λjis data
Figure BDA0002418825510000025
The jth eigenvalue of the covariance matrix of (1); c. CαIs a critical value for normal distribution at test level α;
and calculating the next data matrix to obtain T under the parameter2And SPE statistics, wherein the statistics at the moment i are defined as;
Figure BDA0002418825510000026
Figure BDA0002418825510000027
wherein, tiIs the ith row of the pivot score matrix, Λ is the eigenvalue λ corresponding to the first pivot1,λ2,...,λlA diagonal matrix of l × l is constructed,
Figure BDA0002418825510000028
a scoring matrix that is a pivot; e.g. of the typeiIs the ith row of the residual matrix,
Figure BDA0002418825510000029
is normalized data
Figure BDA0002418825510000031
Row i of (1), Pl＝[p1,p2,...,pl]Is the first l principal element load vectors, I is the identity matrix;
step three: by adding a forgetting factor, the mean and covariance of the (k + 1) th data matrix are found by the following formula:
Figure BDA0002418825510000032
Figure BDA0002418825510000033
wherein the content of the first and second substances,
Figure BDA0002418825510000034
derivation formula for the mean of the intermediate matrix:
Figure BDA0002418825510000035
bk+1mean of k +1 th data block:
Figure BDA0002418825510000036
step four: performing eigenvalue decomposition on the new covariance matrix to obtain a group of eigenvalues; firstly, extracting characteristic values which are not 0 from the characteristic values to form 1 new matrix eigenvalues, and sequencing the characteristic values after 0 is removed from the matrix eigenvalues from large to small, wherein the largest characteristic value is assumed to be maxEig, the smallest characteristic value is assumed to be mineiig, and the next largest characteristic value is secondEig; and (3) self-adaptively selecting the pivot element by a threshold value method:
a. when the number of elements in the eigenvalues is equal to the number of process variables M, a threshold is set at this time:
threshold＝(sum(eigenvalues)-maxEig-minEig)/numEig
b. when the number of elements in the eigenvalues is smaller than the number M of process variables, a threshold value is set:
threshold＝(sum(eigenvalues)-maxEig-secondEig)/numEig；
step five: comparing each eigenvalue in the eigenvalues with the threshold value determined in the fourth step, selecting eigenvalues larger than the threshold value by taking the threshold value as a threshold, wherein the number of the selected eigenvalues is the number of the newly determined principal elements, and the eigenvectors corresponding to the selected eigenvalues form a matrix load P;
step six: and (5) solving the control limit at the moment, solving the statistic of the next data matrix, and repeating the third step to the sixth step so as to realize the self-adaptive industrial process monitoring.
The self-adaptive industrial process monitoring method based on sliding window recursion principal component analysis has the following beneficial effects:
1. by adding forgetting factors into the samples and the covariance, the influence of the former data on the later newly acquired data is reduced, the new data can more effectively represent the current state characteristics, and useful information in the historical data is retained to a certain extent.
2. Compared with the traditional accumulated contribution rate method, the threshold value method adopted by the invention can adaptively update the number of the principal elements, overcomes the defect that the traditional principal element accumulated contribution rate cannot be updated in real time along with the change of the process, and finally completes the model updating and carries out the next calculation through the steps.
3. The method can effectively detect the process mode switching, can self-adapt to the learning process mode, and updates the model, thereby not only achieving the purpose of self-adapting monitoring, but also greatly improving the effectiveness and the safety of the monitoring system.
Drawings
FIG. 1 is a principal component scatter plot of data collected in accordance with the present invention;
FIG. 2 is a graph of the on-line adaptive monitoring results of sliding window recursive principal component analysis according to the present invention;
FIG. 3 is a pivot scatter plot of training data and test data in accordance with the present invention;
fig. 4 is a principal component analysis monitoring diagram of the present invention.
Detailed Description
The following describes a method for monitoring an adaptive industrial process based on sliding window recursive principal component analysis according to the present invention in detail with reference to the following embodiments.
The invention relates to a self-adaptive industrial process monitoring method based on sliding window recursion principal component analysis, which comprises the following steps of:
step one, collecting data X, X ∈ R of historical industrial processN×MN represents the number of samples, and M represents the number of process variables; the sliding window used here is 100 in length and the kth data matrix using the sliding window is Xk＝(xk-99,xk-98,...,xk)TThe next 1 data matrix is Xk+1＝(xk-98,xk-97,...,xk+1)TThe common intermediate data matrix of two adjacent windows:
Figure BDA0002418825510000041
step two: firstly, normalizing the k-th data matrix to obtain a mean value bkDetermining the number of principal elements by principal element analysis and a principal element cumulative contribution rate method to obtain a corresponding covariance matrix RkCalculating T from the F distribution2And the control limit of the SPE statistic at confidence α ═ 0.95:
Figure BDA0002418825510000042
Figure BDA0002418825510000051
and calculating the next data matrix to obtain T under the parameter2And SPE statistics, wherein the statistics at the moment i are defined as;
Figure BDA0002418825510000052
Figure BDA0002418825510000053
step three: by adding a forgetting factor, the mean and covariance of the (k + 1) th data matrix are found by the following formula:
Figure BDA0002418825510000054
Figure BDA0002418825510000055
step four: and carrying out eigenvalue decomposition on the new covariance matrix to obtain a group of eigenvalues. Determining a threshold value in two different modes through a threshold value method to select the pivot element;
step five: comparing each eigenvalue in the eigenvalues with the threshold value determined in the fourth step, selecting eigenvalues larger than the threshold value by taking the threshold value as a threshold, wherein the number of the selected eigenvalues is the number of the newly determined principal elements, and the eigenvectors corresponding to the selected eigenvalues form a matrix load P;
step six: and (5) solving the control limit at the moment, solving the statistic of the next data matrix, and repeating the third step to the sixth step so as to realize the self-adaptive process monitoring.
The performance of the sliding window recursive principal component analysis of the present invention is illustrated below in conjunction with a specific one-stage furnace unit example in a synthetic ammonia production process. The first-stage furnace unit is a conversion unit in the synthetic ammonia production process, is an important part of the synthetic ammonia production, and has the function of starting and stopping. In the conversion part, hydrocarbons and steam are converted by a catalyst through a pre-converter (03A-R001) and a primary converter (03B 001); after passing through a two-stage furnace (03R001) and air, the raw material gas with the components required by ammonia synthesis is generated through the reaction of the conversion by a catalyst.
For the process, 6953 process data were collected at a frequency of once per 1 minute, and the initial 2000 sample points were selected as the initial training data set for modeling and online anomaly detection. First, we perform principal component analysis dimension reduction on 6953 sample points of samples, and view the modal conditions presented by the data from the first and second principal components, and the principal component scatter diagram is shown in fig. 1. It is obvious from the figure that this section of sampled data presents 3 different modalities, and an adaptive model needs to be constructed to gradually learn the information of each modality and perform online monitoring.
The initial 2000 sample points are selected as the training data of the sliding window recursion principal component analysis model of the initial window, and the subsequent 4953 points are subjected to online adaptive modeling and monitoring. Fig. 2 shows the results of the online monitoring, respectively. The front 2500 points in the graph are stable in performance and do not significantly exceed the statistical limit, which indicates that modal switching does not occur in the 2500 points, and the mode switching occurs after a period of time after the 2500 points significantly exceed the statistical limit, and when the sliding window recursion principal component analysis model learns new information of the process mode, the monitoring statistics tend to be stable again, and then a second modal switching occurs near the 4000 th point. The monitoring result accords with the modal information of a given data set, and the method provided by the invention can effectively detect modal switching and realize self-adaptive modeling and process monitoring.
In order to further verify the feasibility of the adaptive monitoring of the invention, 12574 process data were newly collected, the former 10000 data were used as training samples, and the latter 2574 were used as test samples. Constructing a model by adopting a principal component analysis algorithm to obtain a principal component scatter diagram of a training sample and a test sample3, respectively. It can be seen that a significant portion of the principal elements of the test sample are in the operational mode of the training sample. But the pivot of another part of the test sample is outside the modal range of the training sample. The monitoring effect is shown in FIG. 4 from T2The statistics and the SPE statistics can also show that the test sample starts to change into another mode at the 1000 th sample and is consistent with the actual working condition change. When the working condition changes, a sliding window recursion principal component analysis algorithm is adopted for self-adaptive modeling so as to meet the monitoring requirement under a new mode.
The above disclosure is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the scope of the present invention, therefore, the present invention is not limited by the appended claims.

Claims (1)

1. A self-adaptive industrial process monitoring method based on sliding window recursion principal component analysis is characterized by comprising the following steps:
step one, collecting data X, X ∈ R of historical industrial processN×MN represents the number of samples and M represents the number of process variables, and assuming that the length of the sliding window is L, the k-th data matrix using the sliding window is Xk＝(xk-L+1,xk-L+2,...,xk)TThe next 1 data matrix is Xk+1＝(xk-L+2,xk-L+3,...,xk+1)TThe common intermediate data matrix of two adjacent windows:
Figure FDA0002418825500000011
step two: firstly, normalizing the k-th data matrix to obtain a mean value bkDetermining the number of principal elements by principal element analysis and a principal element cumulative contribution rate method to obtain a corresponding covariance matrix RkCalculating T from the F distribution2And control limit of SPE statistics at confidence level α:
Figure FDA0002418825500000012
Figure FDA0002418825500000013
wherein F (l, n-1, α) is the F distribution critical point corresponding to test level α, degree of freedom l and n-l;
Figure FDA0002418825500000014
i＝1,2,3，λjis data
Figure FDA0002418825500000015
The jth eigenvalue of the covariance matrix of (1); c. CαIs a critical value for normal distribution at test level α;
and calculating the next data matrix to obtain T under the parameter2And SPE statistics, wherein the statistics at the moment i are defined as;
Figure FDA0002418825500000016
Figure FDA0002418825500000017
wherein, tiIs the ith row of the pivot score matrix, Λ is the eigenvalue λ corresponding to the first pivot1,λ2,...,λlA diagonal matrix of l × l is constructed,
Figure FDA0002418825500000018
a scoring matrix that is a pivot; e.g. of the typeiIs the ith row of the residual matrix,
Figure FDA0002418825500000019
is normalized data
Figure FDA00024188255000000110
Row i of (1), Pl＝[p1,p2,...,pl]Is the first one principal elementLoad vector, I is identity matrix;
step three: by adding a forgetting factor, the mean and covariance of the (k + 1) th data matrix are found by the following formula:
Figure FDA0002418825500000021
Figure FDA0002418825500000022
wherein the content of the first and second substances,
Figure FDA0002418825500000023
derivation formula for the mean of the intermediate matrix:
Figure FDA0002418825500000024
bk+1mean of k +1 th data block:
Figure FDA0002418825500000025
step four: performing eigenvalue decomposition on the new covariance matrix to obtain a group of eigenvalues; firstly, extracting characteristic values which are not 0 from the characteristic values to form 1 new matrix eigenvalues, and sequencing the characteristic values after 0 is removed from the matrix eigenvalues from large to small, wherein the largest characteristic value is assumed to be maxEig, the smallest characteristic value is assumed to be mineiig, and the next largest characteristic value is secondEig; and (3) self-adaptively selecting the pivot element by a threshold value method:
a. when the number of elements in the eigenvalues is equal to the number of process variables M, a threshold is set at this time:
threshold＝(sum(eigenvalues)-maxEig-minEig)/numEig
b. when the number of elements in the eigenvalues is smaller than the number M of process variables, a threshold value is set:
threshold＝(sum(eigenvalues)-maxEig-secondEig)/numEig；
step five: comparing each eigenvalue in the eigenvalues with the threshold value determined in the fourth step, selecting eigenvalues larger than the threshold value by taking the threshold value as a threshold, wherein the number of the selected eigenvalues is the number of the newly determined principal elements, and the eigenvectors corresponding to the selected eigenvalues form a matrix load P;
step six: and (5) solving the control limit at the moment, solving the statistic of the next data matrix, and repeating the third step to the sixth step so as to realize the self-adaptive industrial process monitoring.
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112066724A (en) * 2020-08-18 2020-12-11 广东工业大学 Roller kiln energy consumption abnormity detection method based on self-adaptive principal component analysis
CN113485307A (en) * 2021-08-02 2021-10-08 天津大学 Gas-liquid two-phase flow state monitoring method based on multi-mode dynamic nuclear analysis

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
张媛媛: "自适应移动窗递推PCA过程监测方法研究", 《计算机与应用化学》 *
徐阳: "《中国科协振兴东北地区等老工业基地专家论坛暨首届沈阳科学学术年会论文选编》", 31 December 2004 *

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112066724A (en) * 2020-08-18 2020-12-11 广东工业大学 Roller kiln energy consumption abnormity detection method based on self-adaptive principal component analysis
CN113485307A (en) * 2021-08-02 2021-10-08 天津大学 Gas-liquid two-phase flow state monitoring method based on multi-mode dynamic nuclear analysis
CN113485307B (en) * 2021-08-02 2022-06-17 天津大学 Gas-liquid two-phase flow state monitoring method based on multi-mode dynamic nuclear analysis

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