CN111880090B - Online fault detection method for million-kilowatt ultra-supercritical unit - Google Patents

Online fault detection method for million-kilowatt ultra-supercritical unit Download PDF

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CN111880090B
CN111880090B CN201910579518.8A CN201910579518A CN111880090B CN 111880090 B CN111880090 B CN 111880090B CN 201910579518 A CN201910579518 A CN 201910579518A CN 111880090 B CN111880090 B CN 111880090B
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赵春晖
张淑美
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Zhejiang University ZJU
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Abstract

The invention discloses a distribution layering type online fault detection method for a million kilowatt ultra-supercritical unit. Aiming at the problems of numerous process variables and complex changing conditions of a million-kilowatt ultra-supercritical unit, comprehensively considering the correlation among the variables and the distribution condition of the variables in the sample direction, blocking the variables by using a multi-layer information theory decomposition method, and establishing a multi-layer distributed monitoring algorithm facing the million-kilowatt ultra-supercritical unit based on a blocking result and combining a Gaussian mixture model method and a Bayesian theory. The method fully explores relevant information among process variables, is beneficial to understanding the complex process characteristics of the million kilowatt ultra-supercritical unit, can effectively excavate local information of the process, can analyze the relevant relation among different variable subblocks, and greatly improves the fault detection performance of the million kilowatt ultra-supercritical unit in the complex process, thereby ensuring the safe and reliable operation of a large coal-fired generator set.

Description

Online fault detection method for million-kilowatt ultra-supercritical unit
Technical Field
The invention belongs to the field of thermal power process fault detection, and particularly relates to a distributed layered online process monitoring method for a million-kilowatt ultra-supercritical unit with a plurality of heavy-faced variables and frequent fluctuation of working conditions.
Background
The power industry is an important basic industry of national economy and is a key project in the national economic development strategy. With the rapid development of economy, the demand for electricity is also rapidly increasing. Coal resources are the main energy in China, so that the energy structure mainly based on coal is difficult to change fundamentally in a long period in the future. As a main power source in China, the installed capacity of coal-fired power generation is always over 70 percent. According to statistics, under the promotion of vigorous electricity demand, the total electricity consumption of the whole society in 1-8 months in 2018 is up to 45296 hundred million kilowatt hours, and the electricity consumption is increased by 9.0 percent on a same scale. Wherein, the accumulated power generation amount of the thermal power is 33103 hundred million kilowatts, which accounts for 73.1 percent of the total power generation amount of the whole country and is increased by 7.2 percent on a par. In recent years, in order to realize sustainable development of electric power, structural adjustment is actively carried out in the thermal power generation industry, the upper large pressure is small, a high-energy-consumption small thermal power generating unit is replaced by a high-capacity and low-energy-consumption supercritical (supercritical) unit, and an electric power energy structure mainly comprising a large coal-fired generating unit such as a million-kilowatt supercritical unit is basically formed. Therefore, the method has great practical significance and application value for the analysis and research of the million-kilowatt ultra-supercritical unit.
Compared with the traditional generator set, the million kilowatt ultra-supercritical generator set has the advantages of large scale, various devices, numerous parameters and mutual influence, long industrial process, multiple unit devices, wide spatial distribution and high safety requirement in the whole power generation process, and brings difficulty to state monitoring and fault diagnosis of the million kilowatt ultra-supercritical generator set. In addition, due to different reasons such as environmental conditions, fuel characteristics and load, the million kilowatt ultra-supercritical unit can operate under different working conditions. Especially, in recent years, due to the fact that new energy such as wind power, photoelectricity and the like are connected to the power grid, the load fluctuation of the power grid, the peak-valley difference is increased, and the requirement of a user side changes, the unit is in a full-working-condition operation mode with different working conditions switched frequently due to new normality such as frequent deep peak regulation and the like. And the large coal-fired power generation process has complex environment and long industrial process, and a plurality of variables still present different data distribution characteristics even under the same working condition. These all present significant challenges to fault detection and diagnosis for large coal-fired power generating units.
For the problem of fault detection of the thermal generator set, the predecessors have made corresponding research and discussion from different angles, and a corresponding online process monitoring method is provided. However, most of the existing methods are mainly centralized single-working-condition monitoring methods. The centralized single-working-condition monitoring method cannot obtain a good monitoring effect in the face of the characteristics of long flow, numerous variables, complex correlation and dynamic working conditions of the million-kilowatt ultra-supercritical unit. The invention further considers the complex correlation among a plurality of variables of the million kilowatt ultra-supercritical unit and the multi-distribution condition of the variables in the sample direction, and provides a novel multi-layer distributed online fault detection method for the million kilowatt ultra-supercritical unit.
Disclosure of Invention
The invention aims to provide a multi-layer distributed monitoring algorithm for million-kilowatt ultra-supercritical units, aiming at the problem that the existing fault detection method for the million-kilowatt ultra-supercritical units cannot accurately describe local information. The method comprehensively considers the correlation among the variables and the distribution condition of the variables in the sample direction, blocks the variables by using a multi-layer information theory decomposition method, fully explores the process information among the process variables, and is beneficial to understanding the complex process characteristics of the million kilowatt ultra-supercritical unit. The multilayer distributed monitoring method can effectively mine local information of the process, can analyze the correlation among different variable subblocks, and greatly improves the fault detection performance of the million-kilowatt ultra-supercritical unit in the complex process, thereby ensuring the safe and reliable operation of the large coal-fired generator set.
The purpose of the invention is realized by the following technical scheme: a distribution layered online fault detection method for a million kilowatt ultra-supercritical unit comprises the following steps:
(1) acquiring normal data to be analyzed: a million-kilowatt ultra-supercritical unit is provided with J measurement variables and operation variables, a vector of 1 XJ can be obtained by sampling every time, and data acquired after sampling N times is expressed as a two-dimensional matrix X ═ X1,X2,...,XJ]∈RN×JThe measured variables are state parameters which can be measured in the normal operation process of the unit, and comprise flow, voltage, current, temperature, speed and the like; the operation variables comprise air intake, feeding amount, valve opening and the like;
(2) the process variable is divided into different sub-blocks by using a spectral clustering method based on mutual information, the variable in the same sub-block has stronger correlation, and the correlation between different sub-blocks is weaker. This step is realized by the following substeps:
(2.1) obtaining mutual information among variables:
I(Xi，Xj)＝H(Xi)+H(Xj)-H(Xi，Xj) (1)
wherein, Xi(i ═ 1, 2.., J) denotes the second groupi variables, H (X)i) Is a variable XiThe information entropy of (2):
H(Xi)＝-∫xp(Xi)log p(Xi)dx (2)
H(Xi，Xj) Is a variable XiAnd XjJoint information entropy of (a):
Figure GDA0003008268680000034
p(Xi) And p (X)j) Represents variable XiAnd XjP (X) is a probability density function ofi，Xj) Is a joint probability density function.
(2.2) solving the generalized correlation coefficient between every two variables based on the mutual information solved by the formula (1):
Figure GDA0003008268680000031
wherein r isij∈[0，1]。
(2.3) based on equation (4), a correlation matrix of the variables is found:
Figure GDA0003008268680000032
(2.4) solving a diagonal matrix D based on the correlation matrix R defined by the formula (5):
D＝diag{Dii} (6)
wherein D isiiIs the sum of all elements in row i in equation (5):
Figure GDA0003008268680000033
(2.5) solving Laplace matrix of diagonal matrix D
L＝D-1/2RD-1/2 (8)
(2.6) spectral decomposition of Laplace matrix
L＝PAPT (9)
Wherein, P ═ P1，P2，...，PJ]Are orthogonal eigenvectors.
(2.7) selecting the eigenvectors corresponding to the k maximum eigenvalues to form a matrix E ═ P1，P2，...，Pk]∈RJ×kNormalizing each row in the matrix E to obtain a matrix Y
Figure GDA0003008268680000041
(2.8) clustering Y by using a kmeans clustering algorithm, and if the ith row belongs to the b-th class, carrying out variable XiDivision into sub-block b Xb. Thus, a plurality of operation variables of the million-kilowatt ultra-supercritical unit are divided into B variable blocks according to the degree of correlation.
X＝[X1 X2 … XB] (11)
Wherein,
Figure GDA00030082686800000412
is the (B ═ 1, 2.., B) th variable block, JbRepresents XbThe number of variables contained in (1).
(3) Further decomposing the variables in the variable block according to the distribution situation in the sample direction by using an information theory decomposition method based on a Gaussian mixture model, wherein the step is realized by the following sub-steps:
(3.1) randomly dividing the variable block into WbIndividual block:
Figure GDA0003008268680000042
(3.2) using gaussian mixture model method to obtain W (W1, 2.., W)b) Probability density of individual variable subblocks:
Figure GDA0003008268680000043
wherein,
Figure GDA0003008268680000044
is the number of sub-gaussian components;
Figure GDA0003008268680000045
is the prior probability of the mth sub-Gaussian component, satisfies
Figure GDA0003008268680000046
And
Figure GDA0003008268680000047
is a mean value containing sub-Gaussian components
Figure GDA0003008268680000048
Sum covariance matrix
Figure GDA0003008268680000049
Of the parameter set (c).
Figure GDA00030082686800000410
Is a multivariate gaussian probability density:
Figure GDA00030082686800000411
wherein, Jb，wIs composed of
Figure GDA0003008268680000051
The number of medium variables.
(3.3) solving probability density distribution functions of all variables in the sub-blocks:
Figure GDA0003008268680000052
wherein the variable
Figure GDA0003008268680000053
i＝1，2，...，Jb，w，w＝1，2，...，Wb，Jb，wIs a variable block
Figure GDA0003008268680000054
The number of the medium variables is equal to or greater than the total number of the medium variables,
Figure GDA0003008268680000055
represents Xb，iBelonging to sub-blocks
Figure GDA0003008268680000056
When Xb，iThe conditional probability density of (2).
(3.4) solving variable subblocks
Figure GDA0003008268680000057
And
Figure GDA0003008268680000058
KL divergence of (W, v ∈ [1, W ]b])：
Figure GDA0003008268680000059
Wherein,
Figure GDA00030082686800000510
and
Figure GDA00030082686800000511
are respectively
Figure GDA00030082686800000512
And
Figure GDA00030082686800000513
the probability density function of (2) can be calculated by using the formula (13).
(3.5) optimizing the random partitions of step (3.1) using an ant colony algorithm such that the following objective function is maximized:
Figure GDA00030082686800000514
(3.6) each variable block (B ═ 1, 2.., B) is further divided into sub-blocks by repeating steps (3.2) - (3.5). The original data set X is divided into different sub-blocks:
Figure GDA00030082686800000515
wherein, the variable block
Figure GDA00030082686800000516
All variables in the system have strong correlation, and variable sub-blocks
Figure GDA00030082686800000517
The variables in (a) have both strong correlations and similar data distributions.
(4) Based on the variable block result obtained in the steps (2) and (3), firstly, describing the variable sub-block by using a Principal Component Analysis (PCA)
Figure GDA00030082686800000518
Correlation of each variable in the
Figure GDA00030082686800000519
Wherein, Pb，wIs a load matrix, Tb，wIs a principal component matrix.
(5) Principal component matrix T established by Gaussian Mixture Model (GMM) methodb，wThe distribution of (c):
Figure GDA0003008268680000061
wherein,
Figure GDA0003008268680000062
is the number of gaussian components;
Figure GDA0003008268680000063
the weight of the m-th component is represented,
Figure GDA0003008268680000064
is a mean value containing sub-Gaussian components
Figure GDA0003008268680000065
Sum covariance matrix
Figure GDA0003008268680000066
Of the parameter set (c).
(6) For each variable sub-block
Figure GDA0003008268680000067
Establishing BIP statistics
Figure GDA0003008268680000068
Wherein,
Figure GDA0003008268680000069
to represent
Figure GDA00030082686800000610
Belonging to the m-th component
Figure GDA00030082686800000611
The probability of (a) of (b) being,
Figure GDA00030082686800000612
as a principal component matrix Tb，wAn nth (N ═ 1, 2.., N) row vector.
Figure GDA00030082686800000613
Is based on the probability of local Mahalanobis distance, which is defined as
Figure GDA00030082686800000614
Wherein,
Figure GDA00030082686800000615
is composed of
Figure GDA00030082686800000616
Mahalanobis distance to mth gaussian component, T being Tb，wAny one of the rows.
(7) The relationship between each sub-block in each variable block is monitored by a Gaussian Mixture Model (GMM) method, which is implemented by the following sub-steps.
(7.1) blocking each variable block XbThe first columns of the pivot matrices of the respective sub-blocks are combined together:
Figure GDA00030082686800000617
wherein, tb，w(w＝1，2，...，Wb) As a principal component matrix Tb，wThe 1 st column vector.
(7.2) describing principal metadata with GMM
Figure GDA00030082686800000618
The distribution of (c):
Figure GDA00030082686800000619
wherein,
Figure GDA00030082686800000620
the number of Gaussian components in the b variable sub-block is shown;
Figure GDA00030082686800000621
the weight of the m-th component is represented,
Figure GDA00030082686800000622
to be composed ofMean value of Gaussian components
Figure GDA00030082686800000623
Sum covariance matrix
Figure GDA00030082686800000624
Of the parameter set (c).
(7.3) Main metadata for each variable Block
Figure GDA00030082686800000625
Establishing BIP statistic:
Figure GDA0003008268680000071
wherein,
Figure GDA0003008268680000072
as a principal component matrix
Figure GDA0003008268680000073
An nth (N ═ 1, 2.., N) row vector.
Figure GDA0003008268680000074
Is based on the probability of the local mahalanobis distance.
Figure GDA0003008268680000075
Is based on the probability of the local mahalanobis distance,
Figure GDA0003008268680000076
is composed of
Figure GDA0003008268680000077
Mahalanobis distance to the mth gaussian component,
Figure GDA0003008268680000078
is composed of
Figure GDA0003008268680000079
Any one of the rows.
(8) During online fault detection, the process is monitored from three levels of variable subblocks, variable blocks and the whole unit. This step is realized by the following substeps.
(8.1) acquiring new data: and (4) collecting the variable values of the measuring points according to the step (1) and recording as z (1 multiplied by J).
(8.2) according to the variable blocking results obtained in the step (2) and the step (3), carrying out sub-block decomposition on the new data:
z＝[z1 z2 … zb ... zB] (26)
Figure GDA00030082686800000710
wherein z isb(B ═ 1, 2.., B) is the B variable sub-block.
(8.3) at the bottom layer, i.e., variable sub-block layer, each sub-block
Figure GDA00030082686800000711
(b＝1，2，...，B；w＝1，2，...，Wb) The data of (2) are projected to the principal element direction of the corresponding sub-block:
Figure GDA00030082686800000712
wherein
Figure GDA00030082686800000713
Is a load matrix.
(8.4) obtaining each sub-block
Figure GDA00030082686800000714
The online statistic index of (1):
Figure GDA00030082686800000715
wherein, the meaning of each parameter in the above formula is similar to that in the formula (22).
Figure GDA00030082686800000716
To represent
Figure GDA00030082686800000717
Belonging to the m-th component
Figure GDA00030082686800000718
The probability of (c).
Figure GDA00030082686800000719
Is based on the probability of the local mahalanobis distance,
Figure GDA00030082686800000720
is composed of
Figure GDA00030082686800000721
Mahalanobis distance to mth gaussian component, T being Tb，wAny one of the rows.
(8.5) at the variable block level, z is first putbThe main elements of each variable sub-block are combined together:
Figure GDA0003008268680000081
(8.6) obtaining each variable block zbThe online statistic index of (1):
Figure GDA0003008268680000082
wherein, the meaning of each parameter of the above formula is similar to that in the formula (25).
Figure GDA0003008268680000083
To represent
Figure GDA0003008268680000084
Belonging to the m-th component
Figure GDA0003008268680000085
The probability of (c).
Figure GDA0003008268680000086
Is based on the probability of the local mahalanobis distance,
Figure GDA0003008268680000087
is composed of
Figure GDA0003008268680000088
Mahalanobis distance to the mth gaussian component,
Figure GDA0003008268680000089
is composed of
Figure GDA00030082686800000810
Any one of the rows.
(8.7) in order to analyze the relation between different variable subblocks, the operation condition of the million kilowatt ultra-supercritical unit is monitored from the whole unit level, and the BIP index of each variable block is firstly converted into the probability of normal (marked as 'N') and fault (marked as 'F'):
Figure GDA00030082686800000811
Figure GDA00030082686800000812
wherein BIPb，lmtA control limit for the statistical BIP indicator;
Figure GDA00030082686800000813
representing the normal conditional probability of the b variable block;
Figure GDA00030082686800000814
indicating the conditional probability of the failure of the b-th variable block.
(8.8) calculating the posterior probability of the b variable block failing by the Bayes rule
Figure GDA00030082686800000815
Wherein, Pb(F)＝α；Pb(N) ═ 1- α represents the prior probability of the process failing or being normal, respectively, at a level of significance α.
(8.9) comprehensively considering the fault probability of all variable blocks and calculating the global monitoring statistic
Figure GDA00030082686800000816
(9) Judging the running state of the process: and analyzing the process state from three levels of the variable subblocks, the variable blocks and the whole unit. Three levels of statistics are compared with the control limits in real time:
(a) at each variable sub-block
Figure GDA0003008268680000091
In, if BIPb，w1-alpha, in sub-blocks
Figure GDA0003008268680000092
The variable in (b) fails, otherwise the variable in the sub-block is considered to be operating within the normal range.
(b) At the variable block level, if BIPbIf the value is more than 1-alpha, the related relation of each variable sub-block in the variable block is abnormal, otherwise, all the variables in the b-th sub-block are normally operated.
(c) At the unit level, if PFZIf the measured value is more than alpha, the abnormal condition or the fault occurs in the running process of the million kilowatt ultra-supercritical unit, otherwise, the whole unit runs normally.
Compared with the prior art, the invention has the beneficial effects that: the invention aims to provide a multi-layer distributed monitoring algorithm for million-kilowatt ultra-supercritical units, aiming at the characteristics that million-kilowatt ultra-supercritical units are large in scale, various in equipment, numerous in parameters and mutually influenced, and the whole power generation process is long in industrial process, multiple in unit devices, wide in spatial distribution and frequent in working condition switching. The method comprehensively considers the correlation among the variables and the distribution condition of the variables in the sample direction, blocks the variables by using a multi-layer information theory decomposition method, fully explores the process information among the process variables, and is beneficial to understanding the complex process characteristics of the million kilowatt ultra-supercritical unit. The multilayer distributed monitoring method can effectively mine local information of the process, can analyze the correlation among different variable subblocks, and greatly improves the fault detection performance of the million-kilowatt ultra-supercritical unit in the complex process, thereby ensuring the safe and reliable operation of the large coal-fired generator set.
Description of the drawings:
FIG. 1 is an explanatory diagram of a distributed hierarchical online fault detection method for a million kilowatt ultra-supercritical unit according to the invention;
fig. 2 shows the monitoring results of the variable sub-blocks in the specific embodiment of the method of the present invention, (a) shows the monitoring results of two variable sub-blocks in the 5 th variable block, (b) shows the monitoring results of three variable sub-blocks in the 7 th variable block, and (c) shows the monitoring results of three variable sub-blocks in the 9 th variable block.
Fig. 3 shows the monitoring results in the variable layer of the method of the present invention in a specific embodiment, (a) is the monitoring result in the 5 th variable block, (b) is the monitoring result in the 7 th variable block, and (c) is the monitoring result in the 9 th variable block.
Fig. 4 shows the unit level monitoring result of the method according to the present invention in an embodiment.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific examples.
The invention takes the unit of Zhe energy group subordinate Jiahua power plant No. 3 as an example, the unit is a million kilowatt ultra-supercritical unit, the power of the unit is 600MW, the unit totally comprises 154 process variables, and the variables relate to pressure, temperature, flow rate and the like.
As shown in figure 1, the invention discloses an online monitoring method for the dynamic and static characteristic collaborative analysis of a million kilowatt ultra-supercritical unit, which comprises the following steps:
(1) acquiring normal data to be analyzed: a million-kilowatt ultra-supercritical unit is provided with J measurement variables and operation variables, a vector of 1 XJ can be obtained by sampling every time, and data acquired after sampling N times is expressed as a two-dimensional matrix X ═ X1，X2，...，XJ]∈RN×J. In this example, the sampling period is 1 minute, 2940 sample data in the normal operation process of the thermal power generating unit are collected for variable blocking and offline modeling, and 154 process variables, namely, the modeling data is X (2940 × 154). The measurement variables are state parameters which can be measured in the normal operation process of the unit, and comprise flow, voltage, current, temperature, speed and the like; the operation variables comprise air intake, feeding amount, valve opening and the like;
(2) the process variable is divided into different sub-blocks by using a spectral clustering method based on mutual information, the variable in the same sub-block has stronger correlation, and the correlation between different sub-blocks is weaker. This step is realized by the following substeps:
(2.1) obtaining mutual information among variables:
I(Xi，Xj)＝H(Xi)+H(Xj)-H(Xi，Xj) (1)
wherein, Xi(i ═ 1, 2.., J) denotes the ith variable, H (X)i) Is a variable XiThe information entropy of (2):
H(Xi)＝-∫xp(Xi)log p(Xi)dx (2)
H(Xi，Xj) Is a variable XiAnd XjJoint information entropy of (a):
Figure GDA0003008268680000101
p(Xi) And p (X)j) Represents variable XiAnd XjP (X) is a probability density function ofi，Xj) Is a joint probability density function.
(2.2) solving the generalized correlation coefficient between every two variables based on the mutual information solved by the formula (1):
Figure GDA0003008268680000111
wherein r isij∈[0，1]。
(2.3) based on the formula (4), obtaining a correlation matrix of the variables:
Figure GDA0003008268680000112
(2.4) solving a diagonal matrix D based on the correlation matrix R defined by the formula (5):
D＝diag{Dii} (6)
wherein D isiiIs the sum of all elements in the ith row in formula (5)
Figure GDA0003008268680000113
(2.5) solving Laplace matrix of diagonal matrix D
L＝D-1/2RD-1/2 (8)
(2.6) spectral decomposition of Laplace matrix
L＝PAPT (9)
Wherein, P ═ P1，P2，...，PJ]Are orthogonal eigenvectors.
(2.7) selecting the eigenvectors corresponding to the k maximum eigenvalues to form a matrix E ═ P1，P2，...，Pk]∈RJ×kNormalizing each row in the matrix E to obtain a matrix Y
Figure GDA0003008268680000114
(2.8) clustering on Y by using kmeans algorithmClustering is performed, if the ith row belongs to the b-th class, the variable XiDivision into sub-block b Xb. Thus, a plurality of operation variables of the million-kilowatt ultra-supercritical unit are divided into B variable blocks according to the degree of correlation.
X＝[X1 X2 … XB] (11)
Wherein,
Figure GDA0003008268680000124
is the (B ═ 1, 2.., B) th variable block, JbRepresents XbThe number of variables contained in (1).
In this example, 154 process variables are divided into 11 sub-blocks according to the correlation, as shown in table 1, the variables in each sub-block have a strong correlation, and the correlation between different sub-blocks is weak.
TABLE 1 variable blocking in megawatt ultra supercritical units
Figure GDA0003008268680000121
(3) Further decomposing the variables in the 11 variable blocks according to the distribution situation in the sample direction by using an information theory decomposition method based on a Gaussian mixture model, wherein the step is realized by the following sub-steps
(3.1) randomly dividing the variable block into WbIndividual block:
Figure GDA0003008268680000122
(3.2) using gaussian mixture model method to obtain W (W1, 2.., W)b) Probability density of individual variable subblocks:
Figure GDA0003008268680000123
wherein,
Figure GDA0003008268680000131
is the number of sub-gaussian components;
Figure GDA0003008268680000132
is the prior probability of the mth sub-Gaussian component, satisfies
Figure GDA0003008268680000133
And
Figure GDA0003008268680000134
is a mean value containing sub-Gaussian components
Figure GDA0003008268680000135
Sum covariance matrix
Figure GDA0003008268680000136
Of the parameter set (c).
Figure GDA0003008268680000137
Is a multivariate gaussian probability density:
Figure GDA0003008268680000138
wherein, Jb，wIs composed of
Figure GDA0003008268680000139
The number of medium variables.
(3.3) solving probability density distribution functions of all variables in the sub-blocks:
Figure GDA00030082686800001310
wherein the variable
Figure GDA00030082686800001311
i＝1，2，...，Jb，w，w＝1，2，...，Wb，Jb，wIs a variable block
Figure GDA00030082686800001312
The number of the medium variables is equal to or greater than the total number of the medium variables,
Figure GDA00030082686800001313
represents Xb，iBelonging to sub-blocks
Figure GDA00030082686800001314
When Xb，iThe conditional probability density of (2).
(3.4) solving variable subblocks
Figure GDA00030082686800001315
And
Figure GDA00030082686800001316
KL divergence of (W, v ∈ [1, W ]b])：
Figure GDA00030082686800001317
Wherein,
Figure GDA00030082686800001318
and
Figure GDA00030082686800001319
are respectively
Figure GDA00030082686800001320
And
Figure GDA00030082686800001321
the probability density function of (2) can be calculated by using the formula (13).
(3.5) optimizing the random partitions of step (3.1) using an ant colony algorithm such that the following objective function is maximized:
Figure GDA00030082686800001322
(3.6) each variable block (B ═ 1, 2.., B) is further divided into sub-blocks by repeating steps (3.2) - (3.5). The original data set X is divided into different sub-blocks:
Figure GDA00030082686800001323
wherein, the variable block
Figure GDA00030082686800001324
All variables in the system have strong correlation, and variable sub-blocks
Figure GDA00030082686800001325
The variables in (a) have both strong correlations and similar data distributions.
In this example, the 11 variable blocks obtained in step (2) are further divided into 27 variable sub-blocks according to the distribution of the variables, and the variables in each sub-block have both strong correlation and the same distribution.
TABLE 2 partitioning of variable sub-blocks in megawatt-hour ultra-supercritical units
Figure GDA0003008268680000141
(4) Based on the variable block result obtained in the steps (2) and (3), firstly, describing the variable sub-block by using a Principal Component Analysis (PCA)
Figure GDA0003008268680000142
Correlation of each variable in the
Figure GDA0003008268680000143
Wherein, Pb，wIs a load matrix, Tb，wIs a principal component matrix.
(5) Principal component matrix T established by Gaussian Mixture Model (GMM) methodb，wThe distribution of (c):
Figure GDA0003008268680000144
wherein,
Figure GDA0003008268680000145
is the number of gaussian components;
Figure GDA0003008268680000146
the weight of the m-th component is represented,
Figure GDA0003008268680000147
is a mean value containing sub-Gaussian components
Figure GDA0003008268680000151
Sum covariance matrix
Figure GDA0003008268680000152
Of the parameter set (c).
(6) For each variable sub-block
Figure GDA0003008268680000153
(b＝1，2，...，B；w＝1，2，...，Wb) Establishing BIP statistics
Figure GDA0003008268680000154
Wherein,
Figure GDA0003008268680000155
to represent
Figure GDA0003008268680000156
Belonging to the m-th component
Figure GDA0003008268680000157
The probability of (a) of (b) being,
Figure GDA0003008268680000158
as a principal component matrix Tb，wAn nth (N ═ 1, 2.., N) row vector.
Figure GDA0003008268680000159
Is based on the probability of local Mahalanobis distance, which is defined as
Figure GDA00030082686800001510
Wherein,
Figure GDA00030082686800001511
is composed of
Figure GDA00030082686800001512
Mahalanobis distance to mth gaussian component, T being Tb，wAny one of the rows.
(7) The relationship between each sub-block in each variable block is monitored by a Gaussian Mixture Model (GMM) method, which is implemented by the following sub-steps.
(7.1) blocking each variable block XbThe first columns of the pivot matrices of the respective sub-blocks are combined together:
Figure GDA00030082686800001513
wherein, tb，w(w＝1，2，...，Wb) As a principal component matrix Tb，wThe 1 st column vector.
(7.2) describing principal metadata with GMM
Figure GDA00030082686800001514
The distribution of (c):
Figure GDA00030082686800001515
wherein,
Figure GDA00030082686800001516
the number of Gaussian components in the b variable sub-block is shown;
Figure GDA00030082686800001517
the weight of the m-th component is represented,
Figure GDA00030082686800001518
is a mean value containing sub-Gaussian components
Figure GDA00030082686800001519
Sum covariance matrix
Figure GDA00030082686800001520
Of the parameter set (c).
(7.3) Main metadata for each variable Block
Figure GDA00030082686800001521
Establishing BIP statistic:
Figure GDA00030082686800001522
wherein,
Figure GDA00030082686800001523
as a principal component matrix
Figure GDA00030082686800001524
An nth (N ═ 1, 2.., N) row vector.
Figure GDA00030082686800001525
Is based on the probability of the local mahalanobis distance.
Figure GDA0003008268680000161
Is based on the probability of the local mahalanobis distance,
Figure GDA0003008268680000162
is composed of
Figure GDA0003008268680000163
Mahalanobis distance to the mth gaussian component,
Figure GDA0003008268680000164
is composed of
Figure GDA0003008268680000165
Any one of the rows.
(8.1) fault data preparation: here, the collected fault data contains 460 samples in total, and the data is recorded as Z (460 × 154), the fault is the increase of the circulating water pump outlet pressure, and the fault occurs at the 121 th sampling point.
(8.2) according to the variable blocking results obtained in the steps (2) and (3), new data is recorded as z (1 × 154), and sub-block decomposition is performed, wherein in the present example, B is 11:
z＝[z1 z2 … zb ... zB] (26)
Figure GDA0003008268680000166
wherein z isb(B ═ 1, 2.., B) is the B variable sub-block.
(8.3) at the bottom layer, i.e., variable sub-block layer, each sub-block
Figure GDA0003008268680000167
(b＝1，2，...，B；w＝1，2，...，Wb) The data of (2) are projected to the principal element direction of the corresponding sub-block:
Figure GDA0003008268680000168
(8.4) obtaining each sub-block
Figure GDA0003008268680000169
The online statistic index of (1):
Figure GDA00030082686800001610
wherein, the meaning of each parameter in the above formula is similar to that in the formula (22).
Figure GDA00030082686800001611
To represent
Figure GDA00030082686800001612
Belonging to the m-th component
Figure GDA00030082686800001613
The probability of (c).
Figure GDA00030082686800001614
Is based on the probability of the local mahalanobis distance,
Figure GDA00030082686800001615
is composed of
Figure GDA00030082686800001616
Mahalanobis distance to mth gaussian component, T being Tb，wAny one of the rows.
(8.5) at the variable block level, z is first putbThe main elements of each variable sub-block are combined together:
Figure GDA00030082686800001617
(8.6) obtaining each variable block zbThe online statistic index of (1):
Figure GDA00030082686800001618
wherein, the meaning of each parameter of the above formula is similar to that in the formula (25).
Figure GDA00030082686800001619
To represent
Figure GDA00030082686800001620
Belonging to the m-th component
Figure GDA0003008268680000171
The probability of (c).
Figure GDA0003008268680000172
Is based on the probability of the local mahalanobis distance,
Figure GDA0003008268680000173
is composed of
Figure GDA0003008268680000174
Mahalanobis distance to the mth gaussian component,
Figure GDA0003008268680000175
is composed of
Figure GDA0003008268680000176
Any one of the rows.
(8.7) in order to analyze the relation between different variable subblocks, the operation condition of the million kilowatt ultra-supercritical unit is monitored from the whole unit level, and the BIP index of each variable block is firstly converted into the probability of normal (marked as 'N') and fault (marked as 'F'):
Figure GDA0003008268680000177
Figure GDA0003008268680000178
wherein BIPb，lmtFor the control limit of the statistic BIP, 0.5 is taken in the specific embodiment;
Figure GDA0003008268680000179
representing the normal conditional probability of the b variable block;
Figure GDA00030082686800001710
indicating the conditional probability of the failure of the b-th variable block.
(8.8) calculating the posterior probability of the b variable block failing by the Bayes rule
Figure GDA00030082686800001711
Wherein, Pb(F)＝α；Pb1- α represents the prior probability of the process failing or being normal, respectively, at a significance level α, which in this example is 0.5.
(8.9) comprehensively considering the fault probability of all variable blocks and calculating the global monitoring statistic
Figure GDA00030082686800001712
(9) Judging the running state of the process: and analyzing the process state from three levels of the variable subblocks, the variable blocks and the whole unit. Three levels of statistics are compared with the control limits in real time:
(a) at each variable sub-block
Figure GDA00030082686800001713
In, if BIPb，w1-alpha, in sub-blocks
Figure GDA00030082686800001714
The variable in (b) fails, otherwise the variable in the sub-block is considered to be operating within the normal range.
(b) At the variable block level, if BIPbIf the value is more than 1-alpha, the related relation of each variable sub-block in the variable block is abnormal, otherwise, all the variables in the b-th sub-block are normally operated.
(c) At the unit level, if PFzIf the measured value is more than alpha, the abnormal condition or the fault occurs in the running process of the million kilowatt ultra-supercritical unit, otherwise, the whole unit runs normally.
The thermal power process is monitored on line by using the monitoring method disclosed by the invention, and the results are shown in fig. 2-4. FIG. 2 shows the monitoring results of the method of the present invention in 8 variable sub-blocks. As can be seen from fig. 2(a), the statistics of the two variable sub-blocks of the fifth variable block are basically below the control limit, which indicates that the current fault does not affect the variables in the variable block #5, and these variables are all operating normally. As can be seen from fig. 2(b), in the first 120 samples, the statistics of the first two sub-blocks of variable block #7 are basically below the control limit, indicating that the process is operating normally. Starting from the 121 th sample, the variable sub-block statistic BIPsub7,1And BIPsub7,2The control limit is quickly exceeded and a fault occurrence is detected, indicating that the fault significantly affects the variables in both sub-blocks. Also, analyzing the monitoring results of fig. 2(c), it can be found that the variables in the first two sub-blocks of variable block #9 operate substantially normally, but BIPsub9,3The occurrence of the failure is effectively detected.
Fig. 3 shows the partial monitoring results of the method of the invention in the variable layer. As can be seen in fig. 3(a), the fifth variable block is substantially below the control limit, indicating that the correlation between the two variable sub-blocks in variable block #5 is not affected by a fault and the process variable in variable block #5 is operating normally. The monitoring results of fig. 3(b) and 3(c) show that the correlation between the variable subblocks in the variable block #7 and the variable block #9 is affected by a failure and an abnormality occurs. Fig. 4 shows the monitoring results of the inventive method at the stack level. It can be seen that the statistics of the first 120 samples are basically operated below the control limit, which indicates that the megawatt ultra-supercritical unit is operated under the normal working condition. Starting from the 121 th sample, the statistic PFzAnd immediately exceeding the control limit, and effectively detecting the occurrence of the fault. Generally speaking, the layered distributed fault detection method has excellent fault detection performance when monitoring a typical large-scale multi-working-condition process of million kilowatt ultra-supercritical, and the blocking result effectively analyzes the complex correlation among a plurality of variables, thereby not only deepening the understanding of an operator to the process, but also providing a high-precision online process monitoring result for the technical management department of the actual industrial field of the thermal power plantThe method provides a reliable basis for judging the process running state in real time and identifying whether a fault occurs, and further improves the safety, reliability and effectiveness of running of the million-kilowatt ultra-supercritical unit.

Claims (1)

1. A distribution layered online fault detection method for a million kilowatt ultra-supercritical unit is characterized by comprising the following steps:
(1) acquiring normal data to be analyzed: a million-kilowatt ultra-supercritical unit is provided with J measurement variables and operation variables, a vector of 1 XJ can be obtained by sampling every time, and data acquired after sampling N times is expressed as a two-dimensional matrix X ═ X1,X2,...,XJ]∈RN×JThe measured variables are state parameters which can be measured in the normal operation process of the unit, and comprise flow, voltage, current, temperature and speed; the operation variables comprise air intake, feeding amount and valve opening;
(2) dividing process variables into different sub-blocks by using a spectral clustering method based on mutual information, wherein the variables in the same sub-block have stronger correlation, and the correlation among different sub-blocks is weaker; this step is realized by the following substeps:
(2.1) obtaining mutual information among variables:
I(Xi,Xj)＝H(Xi)+H(Xj)-H(Xi,Xj) (1)
wherein, XiDenotes the ith variable, H (X)i) Is a variable XiThe information entropy of (2): 1,2, J
H(Xi)＝-∫xp(Xi)logp(Xi)dx (2)
H(Xi,Xj) Is a variable XiAnd XjJoint information entropy of (a):
Figure FDA0003008268670000011
p(Xi) And p (X)j) Represents variable XiAnd XjP (X) is a probability density function ofi,Xj) Is a joint probability density function;
(2.2) solving the generalized correlation coefficient between every two variables based on the mutual information solved by the formula (1):
Figure FDA0003008268670000012
wherein r isij∈[0,1]；
(2.3) based on equation (4), a correlation matrix of the variables is found:
Figure FDA0003008268670000021
(2.4) solving a diagonal matrix D based on the correlation matrix R defined by the formula (5):
D＝diag{Dii} (6)
wherein D isiiIs the sum of all elements in row i in equation (5):
Figure FDA0003008268670000022
(2.5) solving a Laplace matrix of the diagonal matrix D:
L＝D-1/2RD-1/2 (8)
(2.6) performing spectral decomposition on the Laplace matrix:
L＝PΛPT (9)
wherein, P ═ P1,P2,...,PJ]Is an orthogonal eigenvector;
(2.7) selecting the eigenvectors corresponding to the k maximum eigenvalues to form a matrix E ═ P1,P2,...,Pk]∈RJ×kNormalizing each row in the matrix E to obtain a matrix Y:
Figure FDA0003008268670000023
(2.8) clustering Y by using a kmeans clustering algorithm, and if the ith row belongs to the b-th class, carrying out variable XiDivision into sub-block b Xb(ii) a Thus, a plurality of operation variables of the million-kilowatt ultra-supercritical unit are divided into B variable blocks according to the correlation degree:
X＝[X1 X2...XB] (11)
wherein,
Figure FDA0003008268670000024
is the B-th variable block, B1, 2bRepresents XbThe number of variables contained in (1);
(3) further decomposing the variables in the variable block according to the distribution situation in the sample direction by using an information theory decomposition method based on a Gaussian mixture model, wherein the step is realized by the following substeps;
(3.1) randomly dividing the variable block into WbIndividual block:
Figure FDA0003008268670000031
(3.2) solving the probability density of the W-th variable sub-block by using a Gaussian mixture model method, wherein W is 1,2b：
Figure FDA0003008268670000032
Wherein,
Figure FDA0003008268670000033
is the number of sub-gaussian components;
Figure FDA0003008268670000034
is the prior probability of the mth sub-Gaussian component, satisfies
Figure FDA0003008268670000035
And
Figure FDA0003008268670000036
Figure FDA0003008268670000037
is a mean value containing sub-Gaussian components
Figure FDA0003008268670000038
Sum covariance matrix
Figure FDA0003008268670000039
A set of parameters of;
Figure FDA00030082686700000310
is a multivariate gaussian probability density:
Figure FDA00030082686700000311
wherein, Jb,wIs composed of
Figure FDA00030082686700000312
The number of the medium variables;
(3.3) solving probability density distribution functions of all variables in the sub-blocks:
Figure FDA00030082686700000313
wherein the variable
Figure FDA00030082686700000314
i＝1,2,...,Jb,w，w＝1,2,...,Wb，Jb,wIs a variable block
Figure FDA00030082686700000315
The number of the medium variables is equal to or greater than the total number of the medium variables,
Figure FDA00030082686700000316
represents Xb,iBelonging to sub-blocks
Figure FDA00030082686700000317
When Xb,iThe conditional probability density of (a);
(3.4) solving variable subblocks
Figure FDA00030082686700000318
And
Figure FDA00030082686700000319
KL divergence of (1, W), W, v ∈ 1, Wb]：
Figure FDA00030082686700000320
Wherein,
Figure FDA00030082686700000321
and
Figure FDA00030082686700000322
are respectively
Figure FDA00030082686700000323
And
Figure FDA00030082686700000324
can be calculated by using formula (13);
(3.5) optimizing the random partitions of step (3.1) using an ant colony algorithm such that the following objective function is maximized:
Figure FDA00030082686700000325
(3.6) by repeating the steps (3.2) - (3.5), each variable block is further divided into a plurality of sub-blocks; the original data set X is divided into different sub-blocks:
Figure FDA0003008268670000041
wherein, the variable block
Figure FDA0003008268670000042
(4) Based on the variable block result obtained in the steps (2) and (3), firstly, describing the variable sub-block by using a Principal Component Analysis (PCA)
Figure FDA0003008268670000043
The correlation relationship of each variable in (1):
Figure FDA0003008268670000044
wherein, Pb,wIs a load matrix, Tb,wIs a principal component matrix;
(5) principal component matrix T established by Gaussian Mixture Model (GMM) methodb,wThe distribution of (c):
Figure FDA0003008268670000045
wherein,
Figure FDA0003008268670000046
is the number of gaussian components;
Figure FDA0003008268670000047
the weight of the m-th component is represented,
Figure FDA0003008268670000048
is a mean value containing sub-Gaussian components
Figure FDA0003008268670000049
Sum covariance matrix
Figure FDA00030082686700000410
A set of parameters of;
(6) for each variable sub-block
Figure FDA00030082686700000312
，b＝1,2,...,B；w＝1,2,...,WbEstablishing BIP statistics
Figure FDA00030082686700000412
Wherein,
Figure FDA00030082686700000413
to represent
Figure FDA00030082686700000414
Belonging to the m-th component
Figure FDA00030082686700000415
The probability of (a) of (b) being,
Figure FDA00030082686700000416
as a principal component matrix Tb,wAn nth row vector, N being 1,2,., N;
Figure FDA00030082686700000417
is based on the probability of local Mahalanobis distance, which is defined as
Figure FDA00030082686700000418
Wherein,
Figure FDA00030082686700000419
is composed of
Figure FDA00030082686700000420
Mahalanobis distance to mth gaussian component, T being Tb,wAny one row in the row;
(7) monitoring the relation between each sub-block in each variable block by using a Gaussian mixture model method, wherein the step is realized by the following substeps;
(7.1) blocking each variable block XbThe first columns of the pivot matrices of the respective sub-blocks are combined together:
Figure FDA0003008268670000051
wherein, tb,wAs a principal component matrix Tb,wThe 1 st column vector, W1, 2b；
(7.2) describing principal metadata with GMM
Figure FDA0003008268670000052
The distribution of (c):
Figure FDA0003008268670000053
wherein,
Figure FDA0003008268670000054
the number of Gaussian components in the b variable sub-block is shown;
Figure FDA0003008268670000055
the weight of the m-th component is represented,
Figure FDA0003008268670000056
is a bagMean value of sub-Gaussian components
Figure FDA0003008268670000057
Sum covariance matrix
Figure FDA0003008268670000058
A set of parameters of;
(7.3) Main metadata for each variable Block
Figure FDA0003008268670000059
Establishing BIP statistic:
Figure FDA00030082686700000510
wherein,
Figure FDA00030082686700000511
as a principal component matrix
Figure FDA00030082686700000512
An nth row vector, N being 1,2,., N;
Figure FDA00030082686700000513
to represent
Figure FDA00030082686700000514
Belonging to the m-th component
Figure FDA00030082686700000515
The probability of (d);
Figure FDA00030082686700000516
is based on the probability of the local mahalanobis distance,
Figure FDA00030082686700000517
is composed of
Figure FDA00030082686700000518
Mahalanobis distance to the mth gaussian component,
Figure FDA00030082686700000519
is composed of
Figure FDA00030082686700000520
Any one row in the row;
(8) during online fault detection, the process is monitored from three levels of variable subblocks, variable blocks and the whole unit; this step is achieved by the following sub-steps:
(8.1) acquiring new data: collecting the variable values of the measuring points according to the step (1) and recording as z (1 multiplied by J);
(8.2) according to the variable blocking results obtained in the step (2) and the step (3), carrying out sub-block decomposition on the new data:
z＝[z1 z2…zb…zB](26)
Figure FDA00030082686700000521
wherein z isbIs the b variable sub-block;
(8.3) at the bottom layer, i.e., variable sub-block layer, each sub-block
Figure FDA00030082686700000522
Is projected in the direction of the principal element of the corresponding subblock, B1, 2b：
Figure FDA0003008268670000061
Wherein
Figure FDA0003008268670000062
Is a load matrix;
(8.4) obtaining each seedBlock
Figure FDA0003008268670000063
The online statistic index of (1):
Figure FDA0003008268670000064
wherein, the meaning of each parameter in the above formula is similar to that in the formula (22);
Figure FDA0003008268670000065
to represent
Figure FDA0003008268670000066
Belonging to the m-th component
Figure FDA0003008268670000067
The probability of (d);
Figure FDA0003008268670000068
is based on the probability of the local mahalanobis distance,
Figure FDA0003008268670000069
is composed of
Figure FDA00030082686700000610
Mahalanobis distance to mth gaussian component, T being Tb,wAny one row in the row;
(8.5) at the variable block level, z is first putbThe main elements of each variable sub-block are combined together:
Figure FDA00030082686700000611
(8.6) obtaining each variable block zbThe online statistic index of (1):
Figure FDA00030082686700000612
wherein, the meaning of each parameter in the above formula is similar to that in the formula (25);
Figure FDA00030082686700000613
to represent
Figure FDA00030082686700000614
Belonging to the m-th component
Figure FDA00030082686700000615
The probability of (d);
Figure FDA00030082686700000616
is based on the probability of the local mahalanobis distance,
Figure FDA00030082686700000617
is composed of
Figure FDA00030082686700000618
Mahalanobis distance to the mth gaussian component,
Figure FDA00030082686700000619
is composed of
Figure FDA00030082686700000620
Any one row in the row;
(8.7) marking the normal as 'N', marking the fault as 'F', converting the BIP indexes of the variable blocks into the probabilities of normal and fault:
Figure FDA00030082686700000621
Figure FDA00030082686700000622
wherein BIPb,lmtA control limit for the statistical BIP indicator;
Figure FDA00030082686700000623
representing the normal conditional probability of the b variable block;
Figure FDA00030082686700000624
representing the conditional probability of the b variable block failing;
(8.8) calculating the posterior probability of the b variable block failing by the Bayes rule
Figure FDA0003008268670000071
Wherein, Pb(F)＝α；Pb(N) ═ 1- α represents the prior probability of the process failing or being normal, respectively, at a level of significance α;
(8.9) comprehensively considering the fault probability of all variable blocks and calculating the global monitoring statistic
Figure FDA0003008268670000072
(9) Judging the running state of the process: analyzing the process state from three levels of variable subblocks, variable blocks and the whole unit; three levels of statistics are compared with the control limits in real time:
(a) at each variable sub-block
Figure FDA0003008268670000073
In, if BIPb,w1-alpha, in sub-blocks
Figure FDA0003008268670000074
If the variable in the sub-block fails, the variable in the sub-block is considered to be in a normal range;
(b) at variable block levelNoodle if BIPbIf the value is more than 1-alpha, the correlation relation of each variable sub-block in the variable block is abnormal, otherwise, all the variables in the b-th sub-block operate normally;
(c) at the unit level, if PFzIf the measured value is more than alpha, the abnormal condition or the fault occurs in the running process of the million kilowatt ultra-supercritical unit, otherwise, the whole unit runs normally.
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