CN114995338A - Industrial process micro-fault detection method based on normative variable analysis and JS divergence fusion - Google Patents

Industrial process micro-fault detection method based on normative variable analysis and JS divergence fusion Download PDF

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CN114995338A
CN114995338A CN202210603724.XA CN202210603724A CN114995338A CN 114995338 A CN114995338 A CN 114995338A CN 202210603724 A CN202210603724 A CN 202210603724A CN 114995338 A CN114995338 A CN 114995338A
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divergence
data
variables
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variable
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朱健
商亮亮
丁晓星
王嘉
金伟俊
任学江
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Baokong Nantong Iot Technology Co ltd
Nantong University
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Nantong University
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B23/00—Testing or monitoring of control systems or parts thereof
    • G05B23/02—Electric testing or monitoring
    • G05B23/0205—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults
    • G05B23/0218—Electric testing or monitoring by means of a monitoring system capable of detecting and responding to faults characterised by the fault detection method dealing with either existing or incipient faults
    • G05B23/0224—Process history based detection method, e.g. whereby history implies the availability of large amounts of data
    • G05B23/024—Quantitative history assessment, e.g. mathematical relationships between available data; Functions therefor; Principal component analysis [PCA]; Partial least square [PLS]; Statistical classifiers, e.g. Bayesian networks, linear regression or correlation analysis; Neural networks
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract

The invention provides an industrial process micro fault detection method based on the fusion of canonical variable analysis and JS divergence, which comprises the steps of firstly, carrying out normalized preprocessing on training data to reduce the influence of data dynamic characteristics; secondly, calculating the JS divergence difference between normal variables corresponding to normal and fault data by introducing JS divergence which is sensitive to data distribution change and by means of a sliding window with the width of w; then, comparing the detected data with a detection control limit obtained by normalizing a variable sliding window according to normal data to judge whether the industrial process has a tiny fault; finally, the method is used for monitoring three different types of tiny faults in the Tennessman chemical process; the simulation result shows that T is equal to T of the traditional PCA and CVA 2 And Q statistic comparison is carried out, and the fault detection rate of the divergence index of the CVA-JS method is remarkably improved.

Description

Industrial process micro-fault detection method based on normative variable analysis and JS divergence fusion
Technical Field
The invention relates to the technical field of data-driven industrial process micro fault detection, in particular to a micro fault detection method based on canonical variable analysis and JS divergence.
Background
With the continuous improvement of the technological level, the industrial process or equipment is gradually complicated and large-sized. Once a tiny fault occurs in a production process or equipment, if the tiny fault cannot be found and effectively treated in time, the tiny fault gradually develops into a serious fault along with the lapse of time, even major safety accidents can be caused, casualties and huge economic losses can be caused, and meanwhile, irreversible influence can be caused on the ecological environment. A fault is an undesirable feature or any anomaly that occurs in a process. In modern industrial processes, fault detection is a necessary technique to improve system reliability and prevent system performance degradation. Fault detection and diagnosis are of great significance to ensure safe and reliable operation of modern industrial processes.
Most of the existing fault detection methods have better effect on sudden faults with larger amplitude. However, with the long-term operation of the production process, hidden tiny faults such as sensor drift, pipeline material leakage, equipment part abrasion and the like are inevitable, and huge hidden dangers are caused to the safe operation of the industrial process. Usually, the amplitude of the fault is smaller than the standard deviation of the corresponding variable under the normal working condition, and the fault is a minor fault. In recent years, tiny fault detection has become one of the research hotspots which are concerned by the scientific research field and the engineering community together, and the main purpose of the tiny fault detection is to detect and identify tiny faults at the early stage in time, eliminate potential safety hazards and avoid serious faults or accidents.
The traditional fault detection effect based on expert knowledge and analytical models is limited by the accuracy of established mathematical models of industrial processes, accurate modeling is difficult to realize for large complex processes, and a large amount of effective expert knowledge is difficult to obtain from industrial processes. For complex industrial processes with different data characteristics, the traditional fault detection method based on models and knowledge is often poor in effect; a highly automated and complicated industrial process accumulates a huge amount of data, and therefore, a fault detection method based on a data-driven method is in force. According to the method, an accurate mathematical model or knowledge of an industrial process is not needed, a detection model is established by utilizing collected sensor data based on a multivariate statistical theory, and micro fault detection of the industrial process is realized.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to solve the problems that the traditional data-driven fault detection method is insensitive to micro-fault detection and is easy to be submerged by noise, so that the detection rate is low, and provides an industrial process micro-fault detection method based on the combination of canonical variable analysis and JS divergence. When the method is used for detecting the tiny faults, the fault detection rate is high.
Divergence is more sensitive to small changes in data distribution. Can be used to determine the degree of similarity of the probability distributions of the two sets of data. Therefore, the detection of minor faults in the industrial process can be realized by means of the divergence index.
According to the technical scheme, the invention provides an industrial process micro fault detection method based on normative variable analysis and JS divergence fusion, which comprises the following steps of:
step one, off-line modeling:
dynamic data preprocessing and specification variable solving:
(1) utilizing historical data matrix Y epsilon R collected from industrial process m×l Wherein m is the number of variables in the data, and l is the sampling number of m variables;
(2) respectively combining the Hankel matrix Y of the past observation according to the formula p ＝[y p,p+1 y p,p+2 … y p,p+N ]∈R mp×N Hankel matrix Y of future observations f ＝[y f,p+1 y f,p+2 … y f,p+N ]∈R mp×N (ii) a Wherein, p is the number of past sampling moments taking the current sampling moment as a reference; n-l-2 p-1 is Hankel matrix Y p And Y f The number of columns;
Figure BDA0003669199080000021
wherein r is p-1, p-2, … … p-N;
the past observation vector y p,r And a future observation vector y f,r The measurement vectors of past sampling time and future sampling time in the data matrix Y are combined respectively;
(3) computing covariance of past and future observation vectors
Figure BDA0003669199080000022
Sum and mutual variance matrix
Figure BDA0003669199080000023
Wherein superscript T represents the transpose of the matrix;
(4) singular value decomposition of H matrix
Figure BDA0003669199080000024
V is a unitary matrix after singular value decomposition;
(5) determination of k main specification variables by cumulative contribution ratio method
Figure BDA0003669199080000025
Wherein k is 1, 2, 3 … … mp;
(II) calculating JS divergence between normative variables generated by normal data:
dividing the k main specification variables into a front part and a rear part, and respectively solving JS divergence values of the k main specification variables by using a sliding window with the width of w and combining a JS divergence calculation formula;
(III) determining a control limit:
respectively determining the control limit of JS divergence index of k main specification variables with confidence coefficient of alpha according to a nuclear density estimation method
Figure BDA0003669199080000026
Step two, on-line monitoring
1) After m observation values at the 2p sampling moment are acquired on line, assembling past observation vector y pp ；
2) Using formulas
Figure BDA0003669199080000031
Acquiring k main standard variables corresponding to fault measurement data;
3) respectively carrying out sliding windows with the width of w on k main specification variables obtained from the normal data and k main specification variables obtained from the fault data, and solving a JS divergence value between each pair of sliding windows;
4) if the JS divergence values of the k main specification variables corresponding to the fault data do not exceed the corresponding control limits thereof
Figure BDA0003669199080000032
Indicating that the process is operating normally; if it is not
Figure BDA0003669199080000033
Indicating that a minor fault was detected.
Further, the calculation of JS divergence between normative variables generated by the (second) normal data specifically includes: dividing the k main specification variables into a front part and a rear part respectively, and solving JS divergence values of the k main specification variables respectively by using a JS divergence formula; JS divergence is the symmetric operation of Kullback-Leibler (KL) divergence function, and is recorded as:
Figure BDA0003669199080000034
wherein
Figure BDA0003669199080000035
And
Figure BDA0003669199080000036
the first half and the second half of the kth main specification variable respectively;
Figure BDA0003669199080000037
is that
Figure BDA0003669199080000038
And
Figure BDA0003669199080000039
in the mixing ofDistributing;
Figure BDA00036691990800000310
indicating that a KL divergence value of a k main specification variable is calculated; the upper right marker KL indicates KL divergence;
Figure BDA00036691990800000311
is that
Figure BDA00036691990800000312
And
Figure BDA00036691990800000313
the mixing distribution of (a);
Figure BDA00036691990800000314
wherein the content of the first and second substances,
Figure BDA00036691990800000315
first half of k-th specification variable corresponding to normal data
Figure BDA00036691990800000316
The variance of (a);
Figure BDA00036691990800000317
wherein the content of the first and second substances,
Figure BDA00036691990800000318
the second half of the k-th specification variable corresponding to the normal data
Figure BDA00036691990800000319
The variance of (a); lambda [ alpha ] m As a canonical variable
Figure BDA00036691990800000320
And
Figure BDA00036691990800000321
mean of the variances of (a).
Compared with the prior art, the technical scheme of the invention hasThe following advantages are provided: a method for detecting micro faults in an industrial process based on the fusion of canonical variable analysis and JS divergence reduces the influence of data dynamic characteristics by carrying out normalized preprocessing on training data; by introducing JS divergence sensitive to data distribution change, calculating the difference JS divergence between the normal and fault data corresponding specification variables by means of a sliding window with the width of w; comparing the detected control limit to judge whether micro fault occurs in the industrial process; the method is used for monitoring three different types of tiny faults in the Tennessman chemical process; simulation results show that T is equal to T of traditional PCA and CVA 2 And Q statistic comparison is carried out, and the fault detection rate of the divergence index of the CVA-JS method is remarkably improved.
Drawings
FIG. 1 is a schematic diagram of the detection method of the present invention;
FIG. 2 is a schematic diagram illustrating determination of monitoring limits in offline modeling according to the present invention;
FIG. 3 is a schematic diagram of divergence calculation during online detection according to the present invention;
FIG. 4 is a simulation comparison of TE process fault 3 of the present invention;
FIG. 5 is a simulation comparison of TE process fault 9 of the present invention;
FIG. 6 is a simulation comparison of TE process fault 15 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by those skilled in the art without any creative work based on the embodiments of the present invention belong to the protection scope of the present invention.
FIG. 1 is a schematic diagram of the detection method of the present invention. It can be seen that the proposed detection method comprises two parts, off-line modeling and on-line detection. The off-line modeling mainly uses normal data to obtain a control limit, and how to determine a monitoring limit is shown in detail in fig. 2; the on-line detection part calculates divergence values between different standard variables generated by normal data and fault data respectively, compares the divergence values with control limits obtained in an off-line stage, and judges whether the process is normal in operation or has a tiny fault, wherein the divergence calculation method during on-line detection is shown in detail in fig. 3.
A method for detecting micro faults in an industrial process based on the fusion of normative variable analysis and JS divergence comprises the following steps: step one, off-line modeling:
dynamic data preprocessing and specification variable solving
Utilizing historical data matrix Y epsilon R collected from West Iseman chemical process of Tianna m×l Combining past observation vectors y p,r And a future observation vector y f,r The measurement values of past and future p sampling moments in the data matrix Y are combined:
Figure BDA0003669199080000041
wherein, y r Is a measurement from a training data set; r ═ p +1, p +2, …, p + N;
hankel matrix Y of past observation vectors p Hankel matrix Y of future observation vector f Are respectively defined as follows:
Y p ＝[y p,p+1 y p,p+2 … y p,p+N ]∈R mp×N
Y f ＝[y f,p+1 y f,p+2 … y f,p+N ]∈R mp×N
wherein, N ═ l-2p +1, namely Hankel matrix, contains N columns. The covariance and cross variance matrices of past and future observation vectors are calculated separately using the following equations:
Figure BDA0003669199080000051
Figure BDA0003669199080000052
Figure BDA0003669199080000053
the solution for the best linear combination can be obtained by singular value decomposition of the Hankel matrix H:
Figure BDA0003669199080000054
Figure BDA0003669199080000055
determination of k main specification variables by the criterion that the cumulative contribution of singular values reaches 90%
Figure BDA0003669199080000056
Where k is 1, 2, 3 … … mp.
(II) computation of JS divergence between canonical variables produced by Normal data
Dividing the k main specification variables into a front part and a rear part respectively, and solving JS divergence values of the k main specification variables respectively by using a JS divergence formula; JS divergence is the symmetric operation of Kullback-Leibler divergence function, and is recorded as:
Figure BDA0003669199080000057
wherein
Figure BDA0003669199080000058
And
Figure BDA0003669199080000059
the first half and the second half of the kth main specification variable respectively;
Figure BDA00036691990800000510
is that
Figure BDA00036691990800000511
And
Figure BDA00036691990800000512
the mixing distribution of (a);
Figure BDA00036691990800000513
wherein the content of the first and second substances,
Figure BDA00036691990800000514
first half of k-th specification variable corresponding to normal data
Figure BDA0003669199080000061
The variance of (a);
Figure BDA0003669199080000062
wherein the content of the first and second substances,
Figure BDA0003669199080000063
the second half of the k-th specification variable corresponding to the normal data
Figure BDA0003669199080000064
The variance of (a); lambda [ alpha ] m As a canonical variable
Figure BDA0003669199080000065
And
Figure BDA0003669199080000066
the mean of the variances of (a);
(III) determining control limits
Determining control limit of JS divergence index of k main specification variables with confidence coefficient alpha according to nuclear density estimation method
Figure BDA0003669199080000067
Step two, monitoring on line,
1) after m observation values of the first 2p sampling moments of the TE process fault test data are obtained on line, assembling past observation vector y pp ；
2) Using formulas
Figure BDA0003669199080000068
Acquiring k main standard variables corresponding to fault data;
3) respectively performing sliding windows with the width of w on k main specification variables obtained from the normal data and k main specification variables obtained from the fault data, and solving a JS divergence value between each pair of sliding windows, wherein the concrete implementation is shown in a schematic diagram 3, and a concrete calculation formula is as follows;
Figure BDA0003669199080000069
wherein z is k Is the k main specification variable of normal data and
Figure BDA00036691990800000610
k primary specification variable for fault data
Figure BDA00036691990800000611
Is z k And
Figure BDA00036691990800000612
the mixing distribution of (a);
Figure BDA00036691990800000613
wherein λ is k K specification variable z corresponding to normal data k The variance of (a);
Figure BDA00036691990800000614
wherein the content of the first and second substances,
Figure BDA00036691990800000615
the k specification variable corresponding to the fault data
Figure BDA00036691990800000616
The variance of (a); lambda [ alpha ] m As a canonical variable z k And
Figure BDA00036691990800000617
the mean of the variances of (a);
4) if no JS divergence value of k main specification variables corresponding to fault data exceeds the corresponding control limit
Figure BDA00036691990800000618
Indicating the normal operation of the TE chemical process; JS divergence value if there is one main specification variable
Figure BDA00036691990800000619
Indicating that a minor failure of the TE chemical process was detected.
Simulation verification
Three types of tiny fault data generated by a Tennessee Eastman (TE) chemical process simulation platform in Tennessee of Tennessee are utilized to verify the effectiveness and the detection performance of the algorithm. The TE process simulation platform can simulate the characteristics of non-linearity, non-Gaussian, time-varying, multi-modal and the like of the industrial process, and provides a standard simulation model for developing a process modeling and controlling method and a fault monitoring and diagnosing method. The TE procedure includes five main operating units: a reactor, a condenser, a compressor, a separator and a stripper; and also comprises 4 gas feeds, 2 main products generated by 2 gas-liquid exothermic reactions and 2 byproducts generated by two derived exothermic reactions; the process includes various types of faults, such as step, random variation, slow drift, stick, and constant position. The process contained 41 measured variables and 12 controlled variables. Each measured variable contains additive noise to simulate the noise in an actual industrial process. Each data set has 52 variables, and the sampling time of most variables is 3 minutes; the sampling time of 14 variables was 6 minutes and the sampling time of 5 variables was 15 minutes. The training and testing data set for the TE process may be downloaded from the network, with the data set including 1(Fault 0) normal operational data and 20(Fault 1-Fault 20) faulty operational data. Three types of tiny Fault data, namely step Fault 3, random variation Fault 9 and stuck Fault 15, are adopted in the simulation example.
In order to compare the detection performance of the PCA, the CVA and the CVA-JS on the tiny faults under the same condition, the lengths p of past observation windows and future observation windows of the CVA and the CVA-JS are set to be 3; the numbers of principal elements of PCA, CVA and CVA-JS are all set to 3, and the width w of the sliding window is set to 120.
FIGS. 4(a), 5(a) and 6(a) show the T of PCA-generated faults 3,9,15, respectively 2 And Q statistic monitoring graph. FIGS. 4(b), 5(b) and 6(b) show the T of faults 3,9,15 due to CVA, respectively 2 And Q statistic monitoring graph. Fig. 4(c), fig. 5(c) and fig. 6(c) are graphs showing the JS divergence index detection effect corresponding to the first two main normative variables of the CVA-JS faults 3,9 and 15, respectively, and the TE process fault occurs at 161 sampling moments, and occurs from 41 sampling moments as the sliding window of w ═ 120 is introduced, which is slightly different from the case of PCA and CVA without sliding windows.
As can be seen from the figure, in the case of faults 3,9,15, neither PCA nor CVA can effectively detect a minor fault because the fault is small in magnitude and is subject to noise interference. However, in three cases of faults 3,9 and 15 of CVA-JS, divergence indexes of two main specification variables can effectively detect the change trend of a tiny fault, which is similar to the traditional T 2 And compared with the fault detection rate, the Q statistic is obviously improved.
The above description is only an exemplary embodiment of the present invention, and not intended to limit the scope of the present invention, and all equivalent structures or equivalent processes that are transformed by the content of the present specification and the attached drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (2)

1. A method for detecting micro faults in an industrial process based on standard variable analysis and JS divergence fusion is characterized by comprising the following steps: the method comprises the following steps:
step one, off-line modeling:
dynamic data preprocessing and specification variable solving:
(1) utilizing historical data matrix Y ∈ R collected from industrial process m×l Where m is the number of variables in the data and l is m variablesThe number of samples;
(2) respectively combining the Hankel matrix Y of the past observation according to the formula p ＝[y p,p+1 y p,p+2 …y p,p+N ]∈R mp×N Hankel matrix Y of future observations f ＝[y f,p+1 y f,p+2 …y f,p+N ]∈R mp×N (ii) a Wherein, p is the number of past sampling moments taking the current sampling moment as a reference; n-l-2 p-1 is Hankel matrix Y p And Y f The number of columns;
Figure FDA0003669199070000011
wherein r is p-1, p-2, … … p-N;
the past observation vector y p,r And future observation vector y f,r The measurement vectors of past sampling time and future sampling time in the data matrix Y are combined respectively;
(3) computing covariance of past and future observation vectors
Figure FDA0003669199070000012
Sum and mutual variance matrix
Figure FDA0003669199070000013
Wherein superscript T represents the transpose of the matrix;
(4) singular value decomposition of H matrix
Figure FDA0003669199070000014
Wherein V is a unitary matrix after singular value decomposition;
(5) determination of k main specification variables by cumulative contribution ratio method
Figure FDA0003669199070000015
Wherein k is 1, 2, 3 … … mp;
(II) calculating JS divergence between normative variables generated by normal data:
dividing k main specification variables into a front part and a rear part, and respectively calculating JS divergence values of the k main specification variables by using a sliding window with the width of w and combining a JS divergence calculation formula;
(III) determining a control limit:
respectively determining the control limit of JS divergence index of k main specification variables with confidence coefficient of alpha according to a nuclear density estimation method
Figure FDA0003669199070000016
Step two, on-line monitoring
1) After m observation values at the 2p sampling moment are acquired on line, assembling past observation vector y pp ；
2) Using formulas
Figure FDA0003669199070000021
Acquiring k main standard variables corresponding to fault data;
3) respectively carrying out sliding windows with the width of w on k main standard variables obtained from the normal data and k main standard variables obtained from the fault data, and solving a JS divergence value between each pair of sliding windows;
4) if no JS divergence value of k main specification variables corresponding to the fault data exceeds the corresponding control limit
Figure FDA0003669199070000022
Indicating that the process is operating normally; if there is JS divergence value of a certain main specification variable
Figure FDA0003669199070000023
Indicating that a minor fault was detected.
2. The method for detecting the minor fault of the industrial process based on the fusion of the canonical variable analysis and the JS divergence, as recited in claim 1, wherein: and (II) calculating JS divergence among normative variables generated by normal data specifically comprises the following steps: dividing the k main specification variables into a front part and a rear part respectively, and solving JS divergence values of the k main specification variables respectively by using a JS divergence formula; JS divergence is the Kullback-Leibler (KL) divergence functionThe symmetric operation of (2) is noted as:
Figure FDA0003669199070000024
wherein
Figure FDA0003669199070000025
And
Figure FDA0003669199070000026
the first half and the second half of the kth main specification variable are respectively;
Figure FDA0003669199070000027
indicating that a KL divergence value of a k main specification variable is calculated; the upper right marker KL indicates KL divergence;
Figure FDA0003669199070000028
is that
Figure FDA0003669199070000029
And
Figure FDA00036691990700000210
the mixing distribution of (a);
Figure FDA00036691990700000211
wherein the content of the first and second substances,
Figure FDA00036691990700000212
first half of k-th specification variable corresponding to normal data
Figure FDA00036691990700000213
The variance of (a);
Figure FDA00036691990700000214
wherein the content of the first and second substances,
Figure FDA00036691990700000215
the second half of the k-th specification variable corresponding to the normal data
Figure FDA00036691990700000216
The variance of (a); lambda [ alpha ] m As a canonical variable
Figure FDA00036691990700000217
And
Figure FDA00036691990700000218
the mean of the variances of (c).
CN202210603724.XA 2022-05-30 2022-05-30 Industrial process micro-fault detection method based on normative variable analysis and JS divergence fusion Pending CN114995338A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117556202A (en) * 2023-11-09 2024-02-13 南通大学 Industrial process micro fault detection method based on probability correlation slow feature analysis

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117556202A (en) * 2023-11-09 2024-02-13 南通大学 Industrial process micro fault detection method based on probability correlation slow feature analysis
CN117556202B (en) * 2023-11-09 2024-06-11 南通大学 Industrial process micro fault detection method based on probability correlation slow feature analysis

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