CN112051839A - Process monitoring and fault diagnosis method based on tree structure sparsity - Google Patents

Process monitoring and fault diagnosis method based on tree structure sparsity Download PDF

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CN112051839A
CN112051839A CN202010978981.2A CN202010978981A CN112051839A CN 112051839 A CN112051839 A CN 112051839A CN 202010978981 A CN202010978981 A CN 202010978981A CN 112051839 A CN112051839 A CN 112051839A
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fault
node
tree structure
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fault diagnosis
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曾九孙
陈薇
丁克勤
蔡晋辉
姚燕
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China Jiliang University
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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • 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
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    • G05B23/0213—Modular or universal configuration of the monitoring system, e.g. monitoring system having modules that may be combined to build monitoring program; monitoring system that can be applied to legacy systems; adaptable monitoring system; using different communication protocols
    • 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
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Abstract

The invention discloses a process monitoring and fault diagnosis method based on tree structure sparsity. Acquiring training data and test data, and analyzing and extracting principal components of the training data and process monitoring statistic control limits; calculating process monitoring statistics of the test data, and comparing and judging whether the process monitoring statistics of the test data fails or not; if a fault is monitored, a fault isolation model for processing a fault diagnosis problem is established, training data are converted into a tree structure, the weight of each node in the tree structure is established, and a fault diagnosis model based on tree structure sparsity is established according to the fault isolation model; and solving the fault diagnosis model based on the sparse tree structure to obtain an optimal fault amplitude, and positioning and separating the process variables of the fault by using the optimal fault amplitude. The invention can be conveniently expanded to a parallel or distributed version, can meet the requirements on the solving speed and precision of a large-scale data set in the industrial process, and provides effective support for industrial production control behaviors.

Description

Process monitoring and fault diagnosis method based on tree structure sparsity
Technical Field
The invention belongs to a monitoring method in the field of process monitoring and fault diagnosis in an industrial control system, and particularly relates to a process monitoring and fault diagnosis method based on tree structure sparsity.
Background
With the rapid development of sensing and instrumentation technologies, the amount of data collected and analyzed by modern industrial plants has grown exponentially. The rich data information greatly facilitates the process monitoring task, but also presents significant challenges due to problems such as high dimensions, multiple scales, inconsistent data quality, etc. In order to handle large data sets in large-scale processes, different distributed process monitoring methods, such as distributed Principal Component Analysis (PCA) and distributed Canonical Correlation Analysis (CCA), have been studied. The distributed process monitoring method carries out fault detection by decomposing a process into a group of sub-processes, and then carries out fault isolation and positioning by utilizing traditional methods such as a contribution diagram and the like. They have proven to be effective in fault detection. However, distributed methods have the same weaknesses as traditional methods in terms of fault isolation and localization, such as "smearing" and dilution effects of local and initial faults. This is especially true for large industrial processes where the increase in variables and data samples exacerbates the "smearing" and dilution effects, affecting the accuracy of fault isolation.
Therefore, in order to ensure reliability and safety of the industrial production process, and to improve isolation and diagnosis performance of faults, a method based on a process structure receives great attention. Also, by integrating structural information such as correlations and causal relationships into the model, the process structure based approach can produce fault isolation results that are more consistent with actual production conditions. Recently, it has been found that sparsity is commonly observed in fault structures of industrial production processes because most process faults are local, affecting only a subset of the process variables. This finding inspired the application of sparse methods in fault isolation, including shrinkage PCA based methods, LASSO (least absolute shrinkage and selection operator) and sparse specification variable analysis. By introducing sparse regularization conditions such as l into the fault isolation objective function1(sum of absolute values of all elements of the vector or matrix) and l2,1(the sum of the euclidean norms of each row of the matrix) the hidden fault structure can be better revealed, making the sparse method less prone to "smearing". However, as proved by research, the following two aspects are providedFor highly correlated process variables, the Lasso-like problem can lead to a reduction in isolation accuracy. To improve isolation accuracy, a natural extension is to combine sparsity with process structure to achieve structure sparsity.
When faults occur in the large industrial production process, the process monitoring and fault diagnosis method based on the sparse tree structure can make full use of tree structure information in the process, improve the sparsity of the structure, accurately estimate fault amplitude, separate out process variables of the faults and have very important practical value for diagnosing the faults in the large industrial production process.
Disclosure of Invention
In order to solve the technical problems in the background art, the invention provides a process monitoring and fault diagnosis method based on tree structure sparsity, which can fully utilize tree structure information in a process, improve the sparsity of a structure, estimate a fault amplitude and further realize the separation of fault variables. The method is suitable for fault diagnosis of large-scale industrial systems with a large number of variables, and has important significance for promoting process industrial knowledge automation and development of industrial big data technology.
The invention can be conveniently expanded to a parallel or distributed version, and can meet the requirements on the solving speed and precision of a large data set in an industrial process. The invention provides reliable and effective technical support for the evaluation of industrial production control behaviors and the diagnosis of fault variables.
The technical scheme adopted by the invention is as follows:
step 1, acquiring process variable data in the process industrial production process under normal working conditions by using a sensor as training data, and analyzing and extracting principal components in the training data and process monitoring statistic control limits by using the principal components of the training data; collecting data in the process industrial production process under a working condition to be tested as test data through a sensor, and calculating process monitoring statistics of the test data by using main components extracted from training data; comparing the process monitoring statistic of the test data with the process monitoring statistic control limit of the training data, and when the process monitoring statistic of the test data exceeds the process monitoring statistic control limit of the training data, determining that a fault is monitored, otherwise determining that the fault is not monitored;
the process variable refers to a variable detected by a sensor related to industrial production in the process of industrial production.
The training data is made up of data samples, each of which contains a respective process variable at the time of acquisition.
Step 2, if faults are monitored, the influence of each process variable on the faults is quantified, and a fault isolation model for processing the fault diagnosis problem is established to eliminate the influence caused by the faults in the test data, so that the process variables with the faults in the test data reach a normal state;
step 3, converting the training data into a tree structure, as shown in fig. 1, wherein the relation among the process variables in the process of the process industry production shows the relevant characteristics of the tree structure, the tree structure is provided with leaf nodes, intermediate nodes and root nodes, wherein the leaf nodes refer to the tail end of the tree structure, each leaf node correspondingly contains one process variable, the root node is the topmost node of the tree structure, the root node correspondingly contains all the process variables, other nodes between the leaf nodes and the root nodes are used as the intermediate nodes, and each intermediate node corresponds to the process variables containing all the sub-nodes under the intermediate nodes; setting the weight of each node in the tree structure, and establishing a fault diagnosis model based on tree structure sparsity by using the fault isolation model in the step 2;
and 4, solving the fault diagnosis model based on the sparse tree structure provided in the step 3 by adopting an alternative multiplier method (ADMM), obtaining an optimal estimation vector as an optimal fault amplitude, and positioning and separating the process variable of the fault by using the optimal fault amplitude to complete the monitoring and fault diagnosis of the process industrial production process.
In step 1, the process monitoring is specifically performed according to principal component analysis:
step 1.1: carrying out normalization processing on training data under a normal working condition to obtain a standard data set with zero mean and unit variance;
step 1.2: establishing a Principal Component Analysis (PCA) model by using the standard data set in the step 1.1, so as to reserve the variance of more than 85% in the standard data set and extract k Principal Components (PCs) in the standard data set under the condition of a significance level alpha;
step 1.3: normalizing each data sample in the test data to obtain a normalized data sample x;
then, calculating T of the normalized data sample x by using a principal component analysis model established by the standard data set2Statistics and SPE statistics, where T2The statistic represents the projected variation of the data sample x in a principal component space composed of k principal components, while the SPE statistic represents the projected variation of the data sample x in a residual space composed of other components, and the two statistics are represented as:
R＝xTMx
in the formula, R represents T2Or SPE; m is a symmetric positive semi-definite matrix. When the method is used for fault detection, training data acquired under normal working conditions can be analyzed through statistical theory or demonstration to obtain the sum T2And a control limit corresponding to the two statistics of SPE.
For a data sample x to be tested, violation of either statistic indicates that it is faulty.
In the step 2, each data sample x of the test data is monitored to determine whether a fault occurs, and if a fault is monitored, the data sample x is decomposed into data samples x without faults*And a sum of fault vectors f, establishing a fault isolation model for handling fault diagnosis problems:
Figure BDA0002686877920000031
in the formula (I), the compound is shown in the specification,
Figure BDA0002686877920000032
the method is characterized in that the method is an estimation vector of the influence of each process variable on the fault in the fault isolation model, f represents a fault vector, and T represents matrix transposition. The data sample x is fault isolated after being decomposed, and the purpose of fault isolation is to enable x to be*To reach fault-freeNormal state, which is expressed in x*Is as small as possible.
The step 3 comprises the following steps:
step 3.1: the mutual relation among the process variables in the process industrial production process is represented as a tree structure T, the number of all nodes of the tree structure T is N, and all nodes of the tree structure T are represented as v1,v2,…,vN。
For example, FIG. 1 shows a tree-structured system of four process variables, of which
Figure BDA0002686877920000033
Representing a process variable associated with a jth node, four leaf nodes each corresponding to a process variable, and each intermediate node being associated with a set of process variables that may overlap in the intermediate nodes; for a plurality of process variables, they are described as a tree structure like that of FIG. 1 based on correlations between the process variables;
step 3.2: applying the tree structure in a fault isolation processing model specifically comprises:
firstly, adding a penalty term into the fault isolation model in the step 2 is changed into:
Figure BDA0002686877920000041
in the formula (I), the compound is shown in the specification,
Figure BDA0002686877920000042
an estimate vector, W (v), representing the effect of each process variable on the faultroot) Representing a penalty term accumulated at the root node after recursion according to the tree structure;
W(vroot) Is a recursive traversal process, based on a tree structure, starting with leaf nodes, at each node vjWhere j denotes the serial number of the node, with
Figure BDA0002686877920000043
Representing a node vjThe process variable contained in (b) is calculated at node vjThe accumulated penalty W (v)j)：
Figure BDA0002686877920000044
In the formula, | | the luminance2Is represented by2Norm, which is the square of the sum of the squares of all elements in the vector;
Figure BDA0002686877920000045
is f in and
Figure BDA0002686877920000046
a set of coefficients corresponding to the process variable of (a); node c represents node vjChild node of vjRepresents the AND node v in the tree TjThe nodes of the next layer connected;
Figure BDA0002686877920000047
representing a node vjIndividually select child node weights, and
Figure BDA0002686877920000048
representing a node vjJointly select child node weights, and
Figure BDA0002686877920000049
Figure BDA00026868779200000410
and
Figure BDA00026868779200000411
and node vjIs closely related to the tree height, node vjThe tree height of (v) refers to the slave node vjThe number of edges of the longest path to a certain leaf node. Node vjThe height of the tree is standardized to obtain a node vjNormalized tree height
Figure BDA00026868779200000412
The normalization method is to make the tree height after the root node is normalized to 1. Node vjOf
Figure BDA00026868779200000413
And
Figure BDA00026868779200000414
the relationship between them is embodied as
Figure BDA00026868779200000415
Obtaining the punishment W (v) of each node from the leaf node through recursive traversal to the root nodej) When node vjRepresenting a root node vrootThe penalty term W (v) accumulated at the root node is obtainedroot) The fault diagnosis model based on the sparse tree structure is finally obtained by the expansion of (1):
Figure BDA00026868779200000416
Figure BDA00026868779200000417
wherein λ ≧ 0 is a regularization parameter;
Figure BDA00026868779200000418
representation and node vjAn associated set of process variables is then selected,
Figure BDA00026868779200000419
is f in and
Figure BDA00026868779200000420
a set of coefficients corresponding to the process variable of (a);
Figure BDA00026868779200000421
representing a node vjThe weight of (c); a denotes a node vjAncestor node of, node vjRepresents the slave node v according to the tree structurejAll nodes passed by up to the root node;
Figure BDA0002686877920000051
and representing an estimation vector of the optimal fault amplitude value for each process variable in the fault diagnosis model based on the sparse tree structure.
The method utilizes the known tree structure among the process variables as prior information to extract the relevant/causal characteristics among the process variables so as to construct a fault isolation model based on the sparse tree structure. And (3) converting the relevant/causal characteristics of the process variables in the tree structure into structured sparse constraint, analyzing the characteristics of the sparse constraint and giving description. And then, a fault positioning method is developed by introducing a tree-structured sparse constraint mode into the model, so that the processing scale of the fault positioning problem is reduced. And finally, solving and solving the optimal fault amplitude when the sample is closest to a normal value, so as to realize the separation of fault variables and obtain a fault detection result.
The process monitoring and fault diagnosis method based on the sparse tree structure is mainly based on the following consideration: in the process industrial process, all production links are closely related, the upstream and downstream processes are well-ordered, and the tree structured information can fully embody the process characteristics. The introduction of tree structured information can effectively utilize process information in production, and realize the remarkable improvement of fault positioning precision. In addition, the method effectively reduces the calculation load under a large sample, and is very suitable for large-scale industrial data application occasions.
The invention takes the tree structure as prior information, constructs a new penalty function to estimate the influence of the process variable on the fault, which is helpful to find out exact root cause, reduce the tailing effect and provide clear diagnosis information. Systematic weighting schemes are proposed for the case of overlapping groups in the tree, compensating each group in a balanced manner, avoiding diagnostic errors due to inter-group overlap.
Compared with the prior art, the invention has the following beneficial effects:
1. a tree structured sparse representation method is adopted to describe the structural characteristics such as process correlation, causality and the like and prior knowledge, a framework of the process characteristic tree structured sparse description is constructed, and innovation in the aspect of process industrial knowledge automation is realized;
2. developing a rapid parallel algorithm suitable for an industrial large-scale data set to improve the accuracy of fault location and realize innovation on a model structure and an algorithm;
3. the tailing effect of the fault process variable on the normal process variable is greatly reduced, and the method has good noise and interference resistance and is beneficial to engineering technicians to accurately and effectively confirm the fault variable.
4. The method has the advantages that precious and available process knowledge and production data are utilized more fully, more accurate fault positioning and diagnosis is realized, and reliable and effective technical support is provided for evaluation of industrial production control behaviors and diagnosis of fault variables.
Drawings
FIG. 1 is an exemplary tree structured system of four process variables according to the present invention;
FIG. 2 is a schematic diagram of a coal-fired power plant process according to the present invention;
FIG. 3 is a schematic illustration of the operation of a coal pulverizer to which the present invention relates;
FIG. 4 is a coal mill tree structure to which the present invention relates;
FIG. 5 is a PCA-based statistical monitoring of the present invention;
FIG. 6 is a fault isolation result of a fault isolation model according to the present invention;
FIG. 7 is a fault isolation result based on tree structure sparsity of the present invention;
FIG. 8 is a sample-by-sample fault isolation result of the present invention using tree structure sparseness;
FIG. 9 is a structure of a coal pulverizer fault diagnosed by the present invention.
Detailed Description
The invention is further illustrated by the following figures and examples.
The embodiment of the invention and the implementation process thereof are as follows:
the following describes in detail the method for diagnosing and isolating faults of process variables based on the real data recorded in the operation process, taking the actual working process of a coal pulverizer in a certain coal-fired power plant in southeast China as an example.
The coal-fired power plant generates electric energy by using heat energy, mainly generates high-temperature and high-pressure steam by burning coal and other fuels, the high-temperature and high-pressure steam pushes a steam turbine to operate, and the operated steam turbine drives a generator to generate electric energy. As shown in fig. 2, the operating principle is based on a rankine cycle, which is a closed cycle that uses the same fluid repeatedly. It is first necessary to inject water into the boiler until the entire heat exchange surface of the heat exchanger is filled, and to heat the water in the boiler by burning coal or other fuel with a coal mill to generate high-temperature and high-pressure steam. The generated steam is then passed through a turbine under high temperature and pressure conditions to generate mechanical power. The steam then needs to be recondensed by the condenser to water, which will be reused as boiler feed water. The above process will not be circulated until the power generation process is suspended. After mechanical power is generated, the rotation of the turbine drives the generator, producing electrical energy at the output of the generator. Coal fired power plants rely on a number of key components to convert the energy stored in coal mines into electricity, of which coal mills are one. The principle of operation of the coal mill is shown in fig. 3, in which coal enters the mill during operation, is crushed by the mill, and then a separator is used to ensure that only finely powdered coal particles are fed to the boiler for combustion. Coal mills are critical equipment in coal fired power plants and it is important to accurately detect and isolate faults in coal mills to ensure that operators have sufficient time to perform corrective actions.
TABLE 1
Figure BDA0002686877920000061
Figure BDA0002686877920000071
The coal mill involves a total of 46 process variables (denoted x)1To x46) The specific description is shown in table 1. The 46 process variables are divided into 7 blocks based on process knowledge, as shown in table 2, and the relationships between these 7 blocks can be summarized using the tree structure shown in fig. 4. The data set consisted of a training set of 3000 normal samples and a test set of 1000 samples. In the last 600 samples, the test unit operated abnormally due to the reduced outlet coal dust temperature, which caused the control system to close the cold primary air damper valve position in order to reduce the supply of cold air, which further resulted in reduced workload of the coal mill.
TABLE 2
Figure BDA0002686877920000072
In order to apply a process monitoring and fault diagnosis method based on tree structure sparsity to monitor, diagnose and separate the process of a coal mill in a coal-fired power plant, the following steps are made:
step 1, acquiring process variable data in the process industrial production process under normal working conditions by using a sensor as training data, and analyzing and extracting principal components in the training data and process monitoring statistic control limits by using the principal components of the training data; collecting data in the process industrial production process under a working condition to be tested as test data through a sensor, and calculating process monitoring statistics of the test data by using main components extracted from training data; comparing the process monitoring statistic of the test data with the process monitoring statistic control limit of the training data, and when the process monitoring statistic of the test data exceeds the process monitoring statistic control limit of the training data, determining that a fault is monitored, otherwise determining that the fault is not monitored;
to detect faults, a Principal Component Analysis (PCA) model was built using 3000 training data, and we found that retaining 5 Principal Components (PCs) could account for variances greater than 85%, so we set the number of PCs retained to 5. The significance level was set to 0.01 and the monitoring results are shown in fig. 5. It can be seen that after the 400 th sample point, at T2And SPE statisticsBy the time the monitored sample exceeds the control limit, a fault is detected.
And 2, if faults are monitored, quantifying the influence of each process variable on the faults, and establishing a fault isolation model for processing the fault diagnosis problem so as to eliminate the influence caused by the faults in the test data and enable the process variables with the faults in the test data to reach a normal state. The fault isolation results of the fault isolation model are shown in fig. 6.
As can be seen from fig. 6, the fault isolation result of the model determines a large number of process variables as faulty, which makes it difficult to locate the root cause of the fault, because the fault isolation model suffers from "smearing effect", which means that a fault of one process variable causes the influence of other fault-free process variables on the fault to increase, resulting in misjudgment.
Step 3, the relation among the process variables in the process industrial production process shows the relevant characteristics of a tree structure, the training data is converted into the tree structure, the tree structure among the process variables in the coal mill is shown in fig. 9, each leaf node correspondingly comprises a process variable, each root node correspondingly comprises all the process variables, and each intermediate node correspondingly comprises the process variables of all the sub-nodes under the root node; and setting the weight of each node in the tree structure, and establishing a fault diagnosis model based on the tree structure sparsity by using the fault isolation model in the step 2.
And 4, solving the fault diagnosis model based on the sparse tree structure provided in the step 3 by adopting an alternative multiplier method (ADMM), obtaining an optimal estimation vector as an optimal fault amplitude, and positioning and separating the process variable of the fault by using the optimal fault amplitude to complete the monitoring and fault diagnosis of the process industrial production process.
Setting the parameters λ 0.7 and ρ 1.2 involved in the ADMM algorithm, the diagnosis result is shown in fig. 7, comparing with fig. 6 and combining with table 2, the tree structured sparse model identifies 3 blocks as the failure group, and in addition, it identifies x in the output block16～x22X in primary windscreen panels23～x24And in the grinder blockX of38～x40Is faulty. That is, the fault affects the exit coal fines temperature, the control commands and valve positions of the cold primary air damper, and the oil temperature of the grinding roller bearings. This can be explained by the fact that the control system reduces the cold primary air flow as the pulverized coal outlet temperature decreases, while also reducing the workload of the grinding roller.
In order to have a clearer image of the fault, fig. 8 shows the fault isolation result of test data by test data obtained by using the fault diagnosis model based on the sparse tree structure. Process variable x16～x22First identified as a fault, after about 100 samples, the process variable x23～x24、x38～x40Identified as a fault variable, consistent with a series of faults caused by a reduction in outlet coal dust temperature resulting in an operational anomaly.
In addition, FIG. 9 shows the fault variables identified in the tree structure, which clearly identify the affected blocks and process variables. The clear tree structure is helpful for operators to identify the fault reason so as to carry out correction operation in time. This fully demonstrates the advantages of the proposed tree structure sparsity based fault diagnosis model.
In conclusion, the fault diagnosis and isolation method based on the tree structure sparsity can complete fault monitoring on the industrial process, realize positioning and isolation of process variables of faults, and effectively improve the sensitivity of fault monitoring and the accuracy of fault information positioning.

Claims (4)

1. A process monitoring and fault diagnosis method based on tree structure sparsity is characterized in that: the method comprises the following steps:
step 1, acquiring process variable data in the process industrial production process under normal working conditions by using a sensor as training data, and analyzing and extracting principal components in the training data and process monitoring statistic control limits by using the principal components of the training data; collecting data in the process industrial production process under a working condition to be tested as test data through a sensor, and calculating process monitoring statistics of the test data by using main components extracted from training data; comparing the process monitoring statistic of the test data with the process monitoring statistic control limit of the training data, and when the process monitoring statistic of the test data exceeds the process monitoring statistic control limit of the training data, determining that a fault is monitored, otherwise determining that the fault is not monitored;
step 2, if faults are monitored, the influence of each process variable on the faults is quantified, and a fault isolation model for processing the fault diagnosis problem is established to eliminate the influence caused by the faults in the test data, so that the process variables with the faults in the test data reach a normal state;
step 3, converting the training data into a tree structure, wherein the tree structure is provided with leaf nodes, intermediate nodes and root nodes, each leaf node correspondingly comprises a process variable, the root node correspondingly comprises all the process variables, other nodes between the leaf nodes and the root node are used as the intermediate nodes, and each intermediate node correspondingly comprises the process variables of all the sub-nodes under the intermediate node; setting the weight of each node in the tree structure, and establishing a fault diagnosis model based on tree structure sparsity by using the fault isolation model in the step 2;
and 4, solving the fault diagnosis model based on the sparse tree structure provided in the step 3 by adopting an alternative multiplier method (ADMM), obtaining an optimal estimation vector as an optimal fault amplitude, and positioning and separating the process variable of the fault by using the optimal fault amplitude to complete the monitoring and fault diagnosis of the process industrial production process.
2. The tree structure sparsity-based process monitoring and fault diagnosis method of claim 1, wherein: in step 1, the process monitoring is specifically performed according to principal component analysis:
step 1.1: carrying out normalization processing on training data under a normal working condition to obtain a standard data set with zero mean and unit variance;
step 1.2: establishing a Principal Component Analysis (PCA) model by using the standard data set in the step 1.1, so as to reserve the variance of more than 85% in the standard data set and extract k Principal Components (PCs) in the standard data set under the condition of a significance level alpha;
step 1.3: normalizing each data sample in the test data to obtain a normalized data sample x;
then, calculating T of the normalized data sample x by using a principal component analysis model established by the standard data set2Statistics and SPE statistics, where T2The statistic represents the projected variation of the data sample x in a principal component space composed of k principal components, while the SPE statistic represents the projected variation of the data sample x in a residual space composed of other components, and the two statistics are represented as:
R＝xTMx
in the formula, R represents T2Or SPE; m is a symmetric positive semi-definite matrix.
3. The tree structure sparsity-based process monitoring and fault diagnosis method of claim 1, wherein: in the step 2, each data sample x of the test data is monitored to determine whether a fault occurs, and if a fault is monitored, the data sample x is decomposed into data samples x without faults*And a sum of fault vectors f, establishing a fault isolation model for handling fault diagnosis problems:
Figure FDA0002686877910000021
in the formula (I), the compound is shown in the specification,
Figure FDA0002686877910000022
the method is characterized in that the method is an estimation vector of the influence of each process variable on the fault in the fault isolation model, f represents a fault vector, and T represents matrix transposition.
4. The tree structure sparsity-based process monitoring and fault diagnosis method of claim 3, wherein: the step 3 comprises the following steps:
step 3.1: correlation between process variables in a process industrial processThe system is represented as a tree structure T, the number of all nodes of the tree structure T is N, and all nodes of the tree structure T are represented as v1,v2,…,vN。
Step 3.2: applying the tree structure in a fault isolation processing model specifically comprises:
firstly, adding a penalty term into the fault isolation model in the step 2 is changed into:
Figure FDA0002686877910000023
in the formula (I), the compound is shown in the specification,
Figure FDA0002686877910000024
an estimate vector, W (v), representing the effect of each process variable on the faultroot) Representing a penalty term accumulated at the root node after recursion according to the tree structure;
based on the tree structure, starting from the leaf nodes, at each node vjWhere j denotes the serial number of the node, with
Figure FDA0002686877910000025
Representing a node vjThe process variable contained in (b) is calculated at node vjThe accumulated penalty W (v)j)：
Figure FDA0002686877910000026
In the formula, | | the luminance2Is represented by2A norm;
Figure FDA0002686877910000027
is f in and
Figure FDA0002686877910000028
a set of coefficients corresponding to the process variable of (a); node c represents node vjChild node of vjRepresents the AND node v in the tree TjThe nodes of the next layer connected;
Figure FDA0002686877910000029
representing a node vjIndividually select child node weights, and
Figure FDA00026868779100000210
representing a node vjJointly select child node weights, and
Figure FDA00026868779100000211
obtaining the punishment W (v) of each node from the leaf node through recursive traversal to the root nodej) When node vjRepresenting a root node vrootThe penalty term W (v) accumulated at the root node is obtainedroot) The fault diagnosis model based on the sparse tree structure is finally obtained by the expansion of (1):
Figure FDA0002686877910000031
Figure FDA0002686877910000032
wherein λ ≧ 0 is a regularization parameter;
Figure FDA0002686877910000033
representation and node vjAn associated set of process variables is then selected,
Figure FDA0002686877910000034
is f in and
Figure FDA0002686877910000035
a set of coefficients corresponding to the process variable of (a);
Figure FDA0002686877910000036
representing a node vjThe weight of (c); a denotes a node vjAncestor node of, node vjRepresents the slave node v according to the tree structurejAll nodes passed by up to the root node;
Figure FDA0002686877910000037
and representing an estimation vector of the optimal fault amplitude value for each process variable in the fault diagnosis model based on the sparse tree structure.
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