CN110634198B - Industrial system layered fault diagnosis method based on regular polycell filtering - Google Patents

Industrial system layered fault diagnosis method based on regular polycell filtering Download PDF

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CN110634198B
CN110634198B CN201910904643.1A CN201910904643A CN110634198B CN 110634198 B CN110634198 B CN 110634198B CN 201910904643 A CN201910904643 A CN 201910904643A CN 110634198 B CN110634198 B CN 110634198B
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王子赟
徐桂香
王艳
纪志成
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Jiangnan University
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Abstract

The invention relates to an industrial system hierarchical fault diagnosis method based on regular multicellular filtering, which comprises the steps of obtaining a CSTR system model and a fault library thereof, enveloping a feasible parameter set by using the regular multicellular filtering method, judging whether the CSTR system has faults or not by detecting whether the feasible parameter set is empty or not, carrying out hierarchical clustering analysis on the fault library if the system has faults, carrying out layer-by-layer discriminant analysis according to clustering results, finally carrying out model matching, determining the fault type, considering the fault type in the neighborhood of a sample if the fault type is not matched within a certain time, indicating that the CSTR system has a new fault type if the fault type is not matched within the whole simulation duration, adding the new fault type into the fault library, and carrying out hierarchical clustering analysis again when the type of faults occur again. Compared with the fault diagnosis method for directly carrying out model matching, the method has the advantages of reducing the complexity of calculation time, reducing the calculation load and increasing the fault diagnosis efficiency.

Description

Industrial system layered fault diagnosis method based on regular polycell filtering
Technical Field
The invention relates to the technical field of fault diagnosis, in particular to an industrial system layered fault diagnosis method based on positive multi-cell filtering.
Background
The Continuous Stirred Tank Reactor (CSTR) is a complex non-linear chemical reactor, is a core device for producing polymers, has the characteristics of strong heat exchange capacity, low investment, stable product quality and the like, and is widely applied to industrial production processes of chemical industry, petroleum production, fermentation, biopharmaceutical industry and the like. The key variables in the CSTR are typically reactor temperature, product concentration, etc., so that online estimation and fault diagnosis of the key variables will facilitate control of the entire reaction process, thereby improving product quality.
Generally, the failure cause is composed of three situations, i.e., lumped parameter change, structural change and sensor/actuator failure, and since the performance of the chemical process is more reduced and is represented by the change of the parameter rather than the change of the structure or state, the failure diagnosis of the chemical process usually searches for the specific source of the process failure by identifying unknown process parameters. For fault diagnosis with fewer fault types, a model matching method is generally directly adopted for realizing the fault diagnosis, but for a more complex chemical process, the fault types are more, and the fault diagnosis efficiency is reduced and the time complexity is increased by directly applying the model matching method.
Disclosure of Invention
The applicant provides an industrial system layered fault diagnosis method based on regular multicellular filtering aiming at the defects in the prior art, adopts the regular multicellular filtering technology and is matched with a diagnosis algorithm with reasonable complexity, avoids high calculation load and low diagnosis efficiency caused by directly carrying out model matching by a traditional detection method, and can realize rapid and stable fault diagnosis.
The technical scheme adopted by the invention is as follows:
a hierarchical fault diagnosis method for an industrial system based on positive multilocular filtering comprises the following steps:
firstly, acquiring a CSTR system model and a fault library;
secondly, determining a positive multicellular body at the k-1 moment according to a CSTR system model;
thirdly, determining a measurement set at the moment k;
step four, detecting whether the intersection of the positive multicellular body at the moment k-1 and the measurement set at the moment k is an empty set, if the intersection is the empty set, judging that the system has a fault and skipping to the step five, and if the intersection is not the empty set, judging that the system has no fault, updating related data information and skipping to the step twelfth;
fifthly, initializing a positive multicellular body O (k) and recording fault information;
sixthly, performing hierarchical clustering analysis on the fault library obtained in the first step;
seventhly, updating related data information;
eighthly, performing discriminant analysis layer by taking the result of the sixth step as priori knowledge, and skipping to the ninth step after the eighth step is repeated until the number of samples of each layer is less than three;
the ninth step: identifying the fault type through model matching, recording fault information and skipping to the twelfth step if matching is successful within a certain time, and skipping to the tenth step if matching is failed within a certain time;
tenth step, carrying out model matching in the neighborhood of the sample, recording fault information and skipping to the twelfth step if matching is successful in the simulation duration, and skipping to the tenth step if matching is failed in the simulation duration;
eleventh, judging that a new fault type occurs in the system, adding the fault type into a fault library, and jumping to the twelfth step;
twelfth, if a fault is detected, jumping to the seventh step; and if the fault is not detected, jumping to the fourth step, and circularly jumping until k is larger than N, wherein N is the data length.
The further technical scheme is as follows:
the first step of obtaining the CSTR system model further comprises the following steps of A-C:
A. creating a state space model according to the concentration of the substances in the reactor and the reaction temperature;
B. performing finite difference discretization processing on a continuous differential equation of the CSTR system based on the established state space model;
C. converting the linearized CSTR model into a recursive model;
the process of determining the polypody and measurement set in the second and third steps further includes steps D to F:
D. defining a feasible parameter set at time k and defining a parallel hyperplane for the feasible parameter set;
E. defining a eupolyposome;
F. defining a measurement set;
the process of detecting whether the intersection of the positive multicellular body and the measurement collection is an empty collection in the fourth step further comprises the following steps G-I:
G. determining the vertex of the positive polycell body;
H. creating position variables of the vertexes relative to the two hyperplanes;
I. converting whether the intersection of the detected positive multicellular body and the measurement collection is an empty set into whether the vertex of the detected positive multicellular body is between two hyperplanes or not;
the hierarchical clustering analysis process in the sixth step further includes steps J to L:
J. defining the square distance between classes;
K. constructing a recurrence formula of the inter-class square clustering according to the inter-class square distance;
l. performing cluster analysis.
The invention has the following beneficial effects:
the invention provides a hierarchical fault diagnosis method of an industrial system based on positive multicellular filtering, aiming at the diagnosis problem that more fault types occur in the complex chemical process of CSTR, wherein a positive multicellular enveloping feasible parameter set is applied, and whether the CSTR system has faults or not is judged by detecting whether the feasible parameter set is empty or not; hierarchical clustering analysis is carried out on the fault library by using a hierarchical clustering method, discriminant analysis is carried out layer by layer, fault identification is carried out by using a model matching method, and new fault types can be automatically added. According to the invention, during layer-by-layer discriminant analysis, the fault types which do not meet the discriminant conditions are directly discarded, compared with the fault diagnosis method based on model matching which is usually applied, the calculation time complexity is reduced, the fault diagnosis efficiency is increased, and the more the fault types are contained in the fault library, the more the beneficial effect of the fault diagnosis method is obvious.
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FIG. 1 is a schematic flow chart of the present invention.
FIG. 2 is a detailed flow chart of the present invention.
FIG. 3 is a schematic diagram of hierarchical clustering analysis according to the present invention.
FIG. 4 is a schematic diagram of layer-by-layer discriminant analysis according to the present invention.
Detailed Description
The following describes embodiments of the present invention with reference to the drawings.
As shown in FIGS. 1-2, the present invention comprises the following steps:
the method comprises the following steps of firstly, obtaining a CSTR system model and a fault library, wherein the step of obtaining the CSTR system model comprises the following steps:
A. creating a state space model from the concentration of the species in the reactor and the reaction temperature:
Figure BDA0002212915920000031
Figure BDA0002212915920000032
wherein C isAIs the concentration of the reactant, CA0Is the feed liquid concentration, CpIs the specific heat of the components, T is the reaction temperature, TcIs the coolant temperature, T0Is the temperature of the feed liquid, q is the feed flow, UA is the composite number, rho is the component density, E/R is the composite number, k0Is the reaction constant, V is the reactor volume, Δ H is the latent heat of vaporization, Δ t is the time span between simulation time steps;
B. carrying out finite difference discretization processing on a continuous differential equation of the CSTR system based on the established state space model to obtain the following model:
Figure BDA0002212915920000041
yk＝xk+vk
wherein xk,ykRespectively representing an input variable and an output variable, w being process noise and v being measurement noise;
C. the linearized CSTR model is converted into a recursive model of the form:
Figure BDA0002212915920000042
wherein
Figure BDA0002212915920000043
And the regression vector is represented, y (k) represents output data at the moment k, and theta represents a parameter vector to be estimated of the CSTR system and represents a known noise boundary.
Since the performance degradation of the chemical process is mainly manifested as parameter variation, the fault diagnosis of the chemical process usually searches for a specific source of a process fault by identifying unknown process parameters, and thus the fault library obtained in the first step is composed of faults caused by the parameter variation of the CSTR system.
Step two, determining a positive multicellular body at the k-1 moment according to a CSTR system model, comprising the following steps of:
D. defining a feasible parameter set for time k and a parallel hyperplane defining the feasible parameter set:
first define the feasible parameter set Θ (k):
Figure BDA0002212915920000044
from the feasible parameter set Θ (k), a definition of k pairs of parallel hyperplanes is determined, denoted as:
Figure BDA0002212915920000045
Figure BDA0002212915920000046
E. define the eupolyposome as:
Figure BDA0002212915920000047
where diag (d) denotes a diagonal matrix with diagonal values equal to d, d denotes the interval length for parameter estimation,
Figure BDA0002212915920000048
the center of the euploid is shown,
Figure BDA0002212915920000049
as a parameter estimation value, ω denotes a matrix with an infinite norm of not more than 1,
Figure BDA00022129159200000410
d∈Rn，ω∈Rn，Rnis an n-dimensional real number set.
Thirdly, determining a measurement set at the moment k:
Figure BDA00022129159200000411
(claim step F).
And step four, detecting whether the intersection of the positive multicellular body at the moment k-1 and the measurement set at the moment k is an empty set, if the intersection is the empty set, judging that the system has a fault and jumps to the step five, and if the intersection is not the empty set, judging that the system has no fault, updating related data information and jumping to the step twelfth, wherein the process of judging whether the intersection of the positive multicellular body and the measurement set at the moment k is the empty set comprises the following steps of G-I:
G. determining vertex V of polyploidm(k-1)(m＝1,…2n)：
Set C (k-1) consisting of a constrained subset of Θ (k-1), i.e., set C (k-1), is set under the condition that the orthopolysoma O (k-1) at time k-1 is known
Figure BDA0002212915920000051
Is known at time k-1 and is satisfied
Figure BDA0002212915920000052
Let v(j)(k-1)∈C(k-1)∩Fj(k-1), (j ═ 1, …,2n), i.e.:
Figure BDA0002212915920000053
wherein Fj(k-1) is the plane of time O (k-1) at k-1, v(j)The maximum value and the minimum value of each parameter estimation range are shown,
Figure BDA0002212915920000054
the maximum value of the ith parameter estimate is indicated,
Figure BDA0002212915920000055
is the minimum value of the ith parameter estimate,v(j)and
Figure BDA0002212915920000056
and
Figure BDA0002212915920000057
the relationship between them is:
Figure BDA0002212915920000058
v(j)(k-1) vertex V of the regular multicellular body constituting the time k-1m(k-1)(m＝1,…,2n)；
H. Establishing two hyperplanes H relative to the vertex1(k) And H2(k) Position variable of (2):
Figure BDA0002212915920000059
Figure BDA00022129159200000510
I. converting whether the intersection of the detected positive multicellular body and the measurement collection is an empty set into a mode of detecting whether the vertex of the positive multicellular body is positioned on two hyperplanes H1(k) And H2(k) The method comprises the following steps:
when V is presentm(k-1) so that Bm,1Not less than 0 or Bm,2Not less than 0, judging that the existence intersection of the positive polycyte O (k-1) at the k-1 moment and the measurement set S (k) at the k moment, namely
Figure BDA00022129159200000511
At the moment, the system has no fault;
when for any Vm(k-1) are all such that Bm,1<0 and Bm,2<0, judging that the intersection of the positive multicellular body O (k-1) at the k-1 moment and the measurement set S (k) at the k moment is an empty set, namely
Figure BDA00022129159200000512
At this time, the systemThere is a fault.
In the process of solving the linear programming equation, whether the fault occurs can be judged by detecting whether the parameter feasible set is empty, namely, the consistency of the positive multicellular body O (k-1) and the measurement set is judged, so that the fault detection criterion adopted in the invention is as follows:
Figure BDA00022129159200000513
and fifthly, initializing the positive multicellular bodies O (k) and recording fault information, wherein the fault information mainly comprises fault detection time k. After the fault is detected, the parameter estimation process is stopped, parameters in the fault state need to be estimated for fault identification, and at the moment, system estimation parameters are reinitialized, namely O (k) is reinitialized, and meanwhile, the fault detection time k is recordedd＝k。
Sixthly, performing hierarchical clustering analysis on the fault library obtained in the first step, wherein the hierarchical clustering analysis comprises the following steps:
J. defining class squared distance:
Figure BDA0002212915920000061
where G represents a class and s samples in G are represented by a column vector xi(i is 1, …, s) and d isijDenotes xiAnd xjDistance of (D)KLRepresents class GKAnd GLDistance between, nKAnd nLRespectively represent class GKAnd GLThe number of samples in (1);
K. constructing a recurrence formula of the inter-class square clustering:
Figure BDA0002212915920000062
performing cluster analysis:
and taking the p samples as one class respectively, defining the distance between the samples and the clustering parameters between the classes, combining the two classes with the closest distance into a new class, calculating the distance between the new class and the other classes, and repeating the combination calculation process, wherein one class is reduced each time until all the samples are combined into one class or the set condition is reached.
The clustering parameters between classes are suitable for the calculation formula of the square distance between classes in the step J and the recursion formula of the square clustering between classes in the step K.
Seventhly, updating the related data information, wherein the updating operation comprises the following steps of M-O:
m. update v(j)(k) The value of (c) includes the following two cases:
the first condition is as follows: if it is not
Figure BDA0002212915920000063
Order:
Figure BDA0002212915920000064
where the flag max (min) indicates the operator of taking the maximum value max for j 1, …, and the operator of taking the minimum value min for j n +1, …,2 n. Ci(k)＝Ai(k) Wherein A isi(k) Is a set of binding constraints.
Case two: if v is(j)(k-1) e S (k), let:
v(j)(k)＝v(j)(k-1),
Cj(k)＝Cj(k-1).
updating the polyposome:
Figure BDA0002212915920000065
Figure BDA0002212915920000066
Figure BDA0002212915920000067
update set c (k):
Figure BDA0002212915920000068
and eighthly, performing discriminant analysis layer by taking the result of the sixth step as priori knowledge, and jumping to the ninth step after the eighth step is repeated until the number of samples of each layer is less than three, wherein the method for discriminant analysis layer by layer comprises the following steps:
calculating estimated parameters
Figure BDA0002212915920000071
And D, when the distance between the parameter estimation values of the continuous L data lengths and the subclasses meets the condition: d ≦ α · β (α ═ α - γ Δ α, γ initial value is 0, and 1 is added to the value of γ every time the number of analysis layers increases by 1), the failure type belongs to the subclass, the other subclass is discarded, and by analogy, discriminant analysis is performed on the next layer in the retained subclass until the number of samples in the subclass to be analyzed is less than three. Because the hierarchical clustering method is a binary tree structure, a part which does not meet the judgment condition is discarded when each layer is judged, thereby reducing the complexity of calculation time and improving the efficiency of fault diagnosis.
The ninth step: identifying fault types through model matching, recording fault information and skipping to the twelfth step if matching is successful within a certain time, and skipping to the tenth step if matching is failed within a certain time, wherein the model matching method comprises the following steps:
defining residual errors
Figure BDA0002212915920000072
When the parameter estimation values of the continuous Q data lengths satisfy
Figure BDA0002212915920000073
When the fault is always established, the fault identification process is judged to be completed, and the fault identification time is recorded as kIAnd displaying the fault type by using a filter, wherein theta0Fault samples for model matching of the last layer, threshold values selected。
Tenth step, carrying out model matching in the neighborhood of the sample, recording fault information and skipping to the twelfth step if the matching is successful in the simulation duration, and skipping to the tenth step if the matching is failed in the simulation duration, wherein the method for matching the neighborhood of the sample model comprises the following steps:
if to N-TN(TNSelected time threshold) time is not matched with the fault type, the fault type with the similarity sim more than or equal to sigma (sigma is the similarity threshold) of the current matched fault type is considered, model matching is carried out at the same time until the fault type is identified, and the fault identification time is recorded as kIAnd a filter is used to display the fault type.
The calculation formula of the similarity is as follows:
Figure BDA0002212915920000074
where sim (x, y) is the similarity between sample x and sample y, dmaxIs the maximum of the distance between sample x and the samples in the sample library, and d (x, y) is the distance between sample x and sample y.
The recording method of the fault information comprises the following steps:
recording the time k at which a fault is detecteddK and failure recognition time kIAnd a filter is used for displaying the fault type. In the process, the recorded fault time is kdThe assignment is carried out in a fifth step, recording the time k of the fault recognitionIAnd the type of failure is indicated by a filter in the ninth or tenth step. Considering that the failure does not occur again in a short time, the twelfth step is directly skipped after the recording step is completed when the system failure is detected.
And eleventh, judging that a new fault type occurs in the system, adding the fault type into a fault library, and jumping to the twelfth step, wherein after the new fault type is added, if the fault type occurs again in the system, hierarchical clustering analysis needs to be carried out on the fault library again.
And if the fault types are not matched in the simulation time length, the system generates new fault types, numbers the new fault types and adds the new fault types into a fault library.
Twelfth, if a fault is detected, jumping to the seventh step; and if the fault is not detected, jumping to the fourth step, and circularly jumping until k is larger than N, wherein N is the data length.
Because the system can not be failed again in a short time, the fault identification process is directly executed without executing a fault detection step after the system is detected to be failed.
By executing the method in a loop, the fault diagnosis process is completed without interruption.
The above description is intended to be illustrative and not restrictive, and the scope of the invention is defined by the appended claims, which may be modified in any manner within the scope of the invention.
An embodiment of the method for fault detection according to the present invention is as follows:
if a CSTR system may have 25 fault types due to parameter changes, the fault library consists of the 25 fault types. Sequentially executing the first step to the third step, detecting whether the intersection of the positive multicellular body at the k-1 moment and the measurement set at the k moment is an empty set or not in the fourth step, if the intersection is an empty set, judging that the system has a fault and jumps to the fifth step, if the intersection is not an empty set, judging that the system has no fault, updating related data information and jumping to the twelfth step, initializing the positive multicellular body O (k) in the fifth step, recording fault information, namely fault detection moment, performing hierarchical clustering analysis on the fault library obtained in the first step in the sixth step, obtaining a hierarchical clustering analysis result of the fault library shown in figure 3 through the hierarchical clustering analysis, updating the related data information in the seventh step, performing layer-by-layer discriminant analysis by layer by taking the sixth step result as prior knowledge in the eighth step, circulating the eighth step until the number of samples in each layer is less than three, jumping to the ninth step, and assuming that a fault type with the label of 15 occurs in the running process of the system, discriminant analysis is performed layer by layer until the number of remaining fault types in the fourth layer is less than 3, and the analysis process is as shown in fig. 4 (the dotted line portion is the fault type discarded in the layer-by-layer discriminant analysis process).
Identifying the fault type through model matching in the ninth step, recording fault information and skipping to the twelfth step if matching is successful within a certain time, and skipping to the tenth step if matching is failed within a certain time, wherein the model matching method comprises the following steps: defining residual errors
Figure BDA0002212915920000081
When the parameter estimation values of the continuous Q data lengths satisfy
Figure BDA0002212915920000082
When the fault is always established, the fault identification process is judged to be completed, and the fault identification time is recorded as kIAnd displaying the fault type by using a filter, wherein theta0The fault sample for the last layer for model matching is the selected threshold. When the discrimination analysis of the fourth layer is completed as shown in fig. 4, the remaining fault types are only fault types 15 and 16, and the model matching step is entered, where θ0Indicating fault types 15 and 16, and the filter shows that the fault type is fault type number 15.
And in the tenth step, performing model matching in a sample neighborhood, recording fault information and skipping to the twelfth step if the matching is successful in the simulation duration, and skipping to the tenth step if the matching is failed in the simulation duration, wherein the method for matching the sample neighborhood model comprises the following steps: if to N-TN(TNSelected time threshold) time is not matched with the fault type, the fault type with the similarity sim more than or equal to sigma (sigma is the similarity threshold) of the current matched fault type is considered, model matching is carried out at the same time until the fault type is identified, and the fault identification time is recorded as kIAnd using filters to indicate the type of fault, when N-TNAnd if the fault type 15 is not matched at the moment, performing model matching according to the similarity by considering the fault types in the neighborhood of the fault types 15 and 16.
And judging that a new fault type occurs in the system in the eleventh step, adding the fault type into the fault library, and jumping to the twelfth step, wherein after the new fault type is added, if the fault type occurs again in the system, hierarchical clustering analysis needs to be carried out on the fault library again, if the fault type is not matched in the simulation duration, the new fault type occurs in the system, is numbered as 26, and is added into the fault library.
If the fault is detected in the twelfth step, jumping to the seventh step; and if the fault is not detected, jumping to the fourth step, and circularly jumping until k is larger than N, wherein N is the data length, and the fault does not occur again in a short time, so that the fault detection step is not required to be executed after the fault of the system is detected, and the fault identification process is directly executed.
By executing the method in a loop, the fault diagnosis process is completed without interruption.
The above description is intended to be illustrative and not restrictive, and the scope of the invention is defined by the appended claims, which may be modified in any manner within the scope of the invention.

Claims (5)

1. A hierarchical fault diagnosis method for an industrial system based on positive multilocular filtering is characterized by comprising the following steps:
firstly, acquiring a CSTR system model and a fault library;
secondly, determining a polyploid O (k-1) at the moment of k-1 according to a CSTR system model;
thirdly, determining a measurement set S (k) at the moment k;
step four, detecting whether the intersection of the positive multicellular body O (k-1) at the moment k-1 and the measurement set S (k) at the moment k is an empty set, if the intersection is the empty set, judging that the system has a fault and skipping to the step five, and if the intersection is not the empty set, judging that the system has no fault, updating related data information and skipping to the step twelfth;
fifthly, initializing a positive multicellular body O (k) and recording fault information;
sixthly, performing hierarchical clustering analysis on the fault library obtained in the first step;
seventhly, updating related data information;
eighthly, performing discrimination analysis layer by taking the result of the sixth step as priori knowledge, and skipping to the ninth step after the number of samples on the layer is less than three in the eighth step;
the ninth step: identifying the fault type through model matching, recording fault information and skipping to the twelfth step if matching is successful within a certain time, and skipping to the tenth step if matching is failed within a certain time;
tenth step, carrying out model matching in the neighborhood of the sample, recording fault information and skipping to the twelfth step if matching is successful in the simulation duration, and skipping to the tenth step if matching is failed in the simulation duration;
eleventh, judging that a new fault type occurs in the system, adding the fault type into a fault library, and jumping to the twelfth step;
and twelfth, if the fault is detected, jumping to the seventh step, and if the fault is not detected, jumping to the fourth step, and circularly jumping until k is larger than N, wherein N is the data length.
2. The method according to claim 1, wherein the step of obtaining the CSTR system model in the first step further comprises steps A-C:
A. creating a state space model according to the concentration of the substances in the reactor and the reaction temperature;
B. performing finite difference discretization processing on a continuous differential equation of the CSTR system based on the established state space model;
C. and converting the linearized CSTR model into a recursive model.
3. The method according to claim 1, wherein the determining of the positive multicellular bodies and the measurement set in the second and third steps further comprises steps D-F:
D. defining a feasible parameter set at time k and defining a parallel hyperplane for the feasible parameter set;
E. defining a eupolyposome;
F. a set of measurements is defined.
4. The method for diagnosing hierarchical failure of industrial system based on positive multicellular filtering as recited in claim 1 wherein said step four of detecting whether the intersection of the positive multicellular body and the measurement collection is an empty set further comprises steps G to I:
G. determining the vertex of the positive polycell body;
H. creating position variables of the vertexes relative to the two hyperplanes;
I. whether the intersection of the detection positive multicellular body and the measurement collection is an empty set is converted into whether the vertex of the positive multicellular body is between two hyperplanes.
5. The method according to claim 1, wherein the hierarchical clustering analysis process in the sixth step further comprises steps J to L:
J. defining the square distance between classes;
K. constructing a recurrence formula of the inter-class square clustering according to the inter-class square distance;
l. performing cluster analysis.
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