CN117605667A - Compressed air system fault detection algorithm based on random projection T-PLS - Google Patents
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Abstract
The application discloses a compressed air system fault detection algorithm based on random projection T-PLS, and relates to the field of fault detection based on data driving. The specific implementation scheme is as follows: acquiring training sample data, and sequentially carrying out data standardization, random projection and data dimension reduction on the training sample data; decomposing training sample data subjected to data dimension reduction into principal elements and residual errors by using a PLS model; establishing a T-PLS model by using the principal component and the residual error and calculating statistics; according to F distribution and χ 2 And distributing the control limit of the calculation statistic to realize fault detection. According to the method, the data space is primarily decomposed by utilizing the PLS model, the principal component subspace and the residual subspace of the PLS are further decomposed by utilizing the T-PLS, the change orthogonal to the quality variable in the projection subspace is separated, and the residual subspace is separatedThe change of larger variance in the space is distinguished from noise, so that the detection rate of quality-related faults is further improved, and the false alarm rate of quality-unrelated faults is reduced.
Description
Technical Field
The application relates to the technical field of fault detection based on data driving, in particular to a compressed air system fault detection algorithm based on random projection T-PLS.
Background
Compressed air systems refer to air at atmospheric pressure that is compressed and delivered to a pneumatic system at a higher pressure. A typical compressed air system consists of the following components: air compressor (possibly with cooler), air storage tank, dryer (frozen or adsorbed), filter (including oil-water separator, deoiling filter, deodorizing filter, sterilizing filter, etc.), pressure stabilizing air storage tank, automatic water and sewage draining device, gas pipeline, pipeline valve, control instrument, pneumatic tool, pneumatic power machine, process flow using compressed air, etc. With the development of modern industry, a compressed air system has become an indispensable fourth large energy system, and thus, the compressed air system has been widely adopted. Because of the specificity of the industrial environment, various faults of equipment often occur, if the equipment cannot be timely processed, economic loss can be caused, and serious safety accidents can be possibly caused, wherein the fault problem of the electrical equipment is particularly prominent, a complete fault detection system needs to be established, the faults can be timely found, and the faults can be solved as soon as possible.
Disclosure of Invention
Based on the problem, the compressed air system fault detection algorithm based on the random projection T-PLS is provided for solving the problem of high fault detection false alarm rate.
The application provides a compressed air system fault detection algorithm based on random projection T-PLS, which comprises the following steps:
acquiring training sample data, and sequentially carrying out data standardization, random projection and data dimension reduction on the training sample data;
decomposing training sample data subjected to data dimension reduction into principal elements and residual errors by using a PLS model;
establishing a T-PLS model by using the principal component and the residual error and calculating statistics;
according to F distribution and χ 2 And distributing the control limit of the calculation statistic to realize fault detection.
The training sample data are process variable data and quality variable data of the target industrial process under normal working conditions; setting the process variable data as a matrix containing m-dimensional process variables, n samples, denoted as X 0 ＝[x 1 ,x 2 ,…,x n ]∈R n×m The quality variable data is a matrix of n samples containing p-dimensional process variables, denoted as Y 0 ＝[y 1 ,y 2 ,…,y n ]∈R n×p 。
The operation of normalizing the training sample data includes,
for a pair ofPerforming data dimension reduction by random projection to obtain processed process variable data X,
wherein,intermediate variable, X, representing process variable data mean X represents 0 Mean value of X std X represents 0 X represents the processed process variable data, H.epsilon.R m×r Belonging to a random matrix, Y mean Represents Y 0 Mean value of Y std Represents Y 0 And Y represents the processed process variable data.
The operation of decomposing the training sample data subjected to the data dimension reduction into principal elements and residuals by using the PLS model includes,
taking training sample data subjected to data dimension reduction as input of a PLS model, and projecting (X, Y) to a model formed by a few latent variables (t 1 ,...,t A ) In the defined low-dimensional space, A is the number of main components, and after decomposition, the method comprises the following steps:
X＝TP T +E
Y＝TQ T +F
wherein T= [ T ] 1 ,...,t A ]Represents a scoring matrix, p= [ P ] 1 ,...,p A ]Load matrix representing X, q= [ Q ] 1 ,...,q A ]The load matrix of Y is represented, and E and F respectively represent matrices obtained by normalizing X and Y;
T＝XR
R＝W(P T W) -1 。
operations for building a T-PLS model using principal elements and residuals include,
according to the data space obtained after decomposition by using the PLS model, the following model is obtained by combining a T-PLS algorithm:
wherein T is y 、T o 、T r A scoring matrix representing the directly related part of the quality variable, the orthogonal part of the quality variable and the part of the original residual with larger variance change respectively,P y 、P o 、P r separate tableLoad matrix showing the direct correlation part of quality variable, the orthogonal part of quality variable and the larger variance variation part of the original residual error,/for>Q y The representation corresponds to T y Is a new load matrix for Y of (c),representing a new residual matrix, A y Represents the number of principal components related to Y, A r The number of principal components independent of Y is represented.
Also included is a method of manufacturing a semiconductor device,
calculated by PCA algorithmThe number of main components is A y ＝rank(Q)；
Calculation of
Calculated by PCA algorithmThe number of main components is (A-A) y )；
Calculated by PCA algorithmThe number of main components is A r Wherein T is r Representing the main part of E r Representing the residual portion of E.
The step of calculating the statistics includes,
for a variable sample x, statistics of directly related parts of quality variables are calculated by using a T-PLS modelStatistics of orthogonal parts of quality variable->Statistics of larger variance variation part in original residual +.>And statistics of the final residual portion Q r ；
Wherein t is y Representing the score of a variable sample x in the directly related part of the quality variable, t o Representing the score of the variable sample x in the orthogonal part of the quality variable, t r A score representing the larger variance variation portion of the variable sample x in the original residual,representing the residual of the variable sample x in the final residual portion, Λ y 、Λ o 、Λ t All represent intermediate variables in the calculation process.
According to F distribution and χ 2 The control limits of the distribution calculation statistics include, in particular,
wherein,representation->Control limit of->Representation->Control limit of->Representation->Control limit of J (Q) r ) Represents Q r α represents confidence, S represents sample variance of Q, and μ represents sample mean of Q.
In the process of real-time detection, for a newly acquired process sample x new After normalization and random projection, statistics of directly related parts of the newly acquired process sample quality variables are respectively calculated through PLS model decompositionStatistics of orthogonal parts of quality variable->Statistics of larger variance variation part in original residual +.>Statistics of the final residual part +.>
Wherein t is y，new Representing a newly acquired process sample x new Score in directly related part of quality variable, t o，new Representing a newly acquired process sample x new Score in orthogonal part of quality variable, t r，new Representing a newly acquired process sample x new The score of the larger variance variation part in the original residual,representing a newly acquired process sample x new Is a residual of (c).
The fault detection determination includes that,respectively with control limitsComparison, if->And->Then it is indicated that a fault associated with the quality variable data Y was detected; if->And->It is indicated that a fault is detected that is independent of the quality variable data Y.
The beneficial effects are that: according to the method, the data space is initially decomposed by using the PLS model, the principal component subspace and the residual subspace of the PLS are further decomposed by using the T-PLS, the change orthogonal to the quality variable in the projection subspace is separated, and the change of the larger variance in the residual subspace is distinguished from noise, so that the detection rate of quality-related faults is further improved, and the false alarm rate of quality-independent faults is reduced.
It should be understood that the description of this section is not intended to identify key or critical features of the embodiments of the application or to delineate the scope of the application. Other features of the present application will become apparent from the description that follows.
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The drawings are for better understanding of the present solution and do not constitute a limitation of the present application. Wherein:
FIG. 1 is a flow chart according to a specific embodiment provided herein;
fig. 2 is a schematic illustration of simulation results on a published tennessee-eastman (Tennessee Eastman, TE) dataset according to a particular embodiment provided herein.
Detailed Description
Exemplary embodiments of the present application are described below in conjunction with the accompanying drawings, which include various details of the embodiments of the present application to facilitate understanding, and should be considered as merely exemplary. Accordingly, one of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the present application. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.
The application provides a compressed air system fault detection algorithm based on random projection T-PLS (Total Partial Least Squares, full-latent structure projection model), comprising:
as shown in fig. 1, a flow chart of a compressed air system fault detection algorithm based on random projection T-PLS provided in the present application specifically includes:
offline modeling: acquiring training sample data, and sequentially carrying out data standardization, random projection and data dimension reduction on the training sample data;
decomposing training sample data subjected to data dimension reduction into principal elements and residual errors by using a PLS model;
establishing a T-PLS model by using the principal component and the residual error and calculating statistics;
on-line monitoring: according to F distribution and χ 2 And distributing the control limit of the calculation statistic to realize fault detection.
The training sample data are process variable data and quality variable data of the target industrial process under normal working conditions; setting the process variable data as a matrix containing m-dimensional process variables, n samples, denoted as X 0 ＝[x 1 ,x 2 ,…,x n ]∈R n×m The quality variable data is a matrix of n samples containing p-dimensional process variables, denoted as Y 0 ＝[y 1 ,y 2 ,…,y n ]∈R n×p 。
The operation of normalizing the training sample data includes,
for a pair ofPerforming data dimension reduction by random projection to obtain processed process variable data X,
wherein,intermediate variable, X, representing process variable data mean X represents 0 Mean value of X std X represents 0 X represents the processed process variable data, H.epsilon.R m×r Belongs to the followingMatrix of machines, Y mean Represents Y 0 Mean value of Y std Represents Y 0 And Y represents the processed process variable data.
The operation of decomposing the training sample data subjected to the data dimension reduction into principal elements and residuals by using the PLS model includes,
taking training sample data subjected to data dimension reduction as input of a PLS model, and projecting (X, Y) to a model formed by a few latent variables (t 1 ,...,t A ) In the defined low-dimensional space, A is the number of main components, and after decomposition, the method comprises the following steps:
X＝TP T +E
Y＝TQ T +F
wherein T= [ T ] 1 ,...,t A ]Represents a scoring matrix, p= [ P ] 1 ,...,p A ]Load matrix representing X, q= [ Q ] 1 ,...,q A ]The load matrix of Y is represented, and E and F respectively represent matrices obtained by normalizing X and Y;
in PLS processes, the weight matrix W is used to calculate the scoring matrix T, however W cannot relate T to the original process data X, but can use the original weight matrix R, which can be used to calculate the scoring matrix T directly from X:
T＝XR
R＝W(P T W) -1 。
operations for building a T-PLS model using principal elements and residuals include,
according to the data space obtained after decomposition by using the PLS model, the following model is obtained by combining a T-PLS algorithm:
wherein T is y 、T o 、T r Representing the quality variable directly related part, quality variable orthogonal part and original residue respectivelyThe scoring matrix for the larger variance variant of the difference,P y 、P o 、P r load matrix representing the directly related part of the quality variable, the orthogonal part of the quality variable and the larger variance variation part of the original residual, respectively,>Q y the representation corresponds to T y Is a new load matrix for Y of (c),representing a new residual matrix, A y Represents the number of principal components related to Y, A r The number of principal components independent of Y is represented.
Also included is a method of manufacturing a semiconductor device,
calculated by PCA algorithmThe number of main components is A y ＝rank(Q)；
Calculation of
Calculated by PCA algorithmThe number of main components is (A-A) y )；
Calculated by PCA algorithmThe number of main components is A r Wherein T is r Representing the main part of E r Representing the residual portion of E.
The step of calculating the statistics includes,
for a variable sample x, statistics of directly related parts of quality variables are calculated by using a T-PLS modelQuality variable orthogonalityStatistics of parts->Statistics of larger variance variation part in original residual +.>And statistics of the final residual portion Q r ；
Wherein t is y Representing the score of a variable sample x in the directly related part of the quality variable, t o Representing the score of the variable sample x in the orthogonal part of the quality variable, t r A score representing the larger variance variation portion of the variable sample x in the original residual,representing the residual of the variable sample x in the final residual portion, Λ y 、Λ o 、Λ t All represent intermediate variables in the calculation process, +.>And Q r Detecting Y-related faults, whereas +.>And->Faults independent of Y are detected.
According to F distribution and χ 2 The control limits of the distribution calculation statistics include, in particular,
wherein,representation->Control limit of->Representation->Control limit of->Representation->Control limit of J (Q) r ) Represents Q r α represents confidence, S represents sample variance of Q, and μ represents sample mean of Q.
In the process of real-time detection, for a newly acquired process sample x new After normalization and random projection, statistics of directly related parts of the newly acquired process sample quality variables are respectively calculated through PLS model decompositionStatistics of orthogonal parts of quality variable->Statistics of larger variance variation part in original residual +.>Statistics of the final residual part +.>
Wherein t is y，new Representing a newly acquired process sample x new Score in directly related part of quality variable, t o，new Representing a newly acquired process sample x new Score in orthogonal part of quality variable, t r，new Representing a newly acquired process sample x new The score of the larger variance variation part in the original residual,representing a newly acquired process sample x new Is a residual of (c).
The fault detection judgment comprises the following steps ofRespectively with control limitsComparison, if->And->Then it is indicated that a fault associated with the quality variable data Y was detected; if->And->It is indicated that a fault is detected that is independent of the quality variable data Y.
As shown in fig. 2, the simulation results of the random projection T-PLS-based fault detection algorithm of the present application on the published tennessee-eastmann (Tennessee Eastman, TE) dataset are shown, and the simulation is performed on MATLAB. TE data is generated by an open and challenging chemical model simulation platform developed by Eastman chemical company in the united states, with time-varying, strongly coupled and nonlinear features, and is widely used to test control and fault diagnosis models of complex industrial processes. The number of process variables in TE data set is up to 41, the number of process variables can be reduced to more than 30 through random projection dimension reduction, and then the result is obtained after detection by using a PLS model and a T-PLS model. In fig. 2, the solid line is the statistic calculated according to the new process sample, the dotted line is the control limit of the statistic, wherein the first 160 samples of the data set are normal samples, and the 160 th and later samples are fault samples; statistics starting from sample 160Are significantly higher than the respective control limits and the statistics Q r,new Below its control limit, this indicates that the detected fault is a fault independent of the quality variable Y; statistics starting from sample 160And Q r,new Are significantly above the respective control limits, which indicates that the detected fault is a fault associated with the quality variable Y.
The foregoing is merely a specific embodiment of the present application, but the protection scope of the present application is not limited thereto, and any changes or substitutions within the technical scope of the present disclosure should be covered in the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (10)
1. A compressed air system fault detection algorithm based on random projection T-PLS, comprising:
acquiring training sample data, and sequentially carrying out data standardization, random projection and data dimension reduction on the training sample data;
decomposing training sample data subjected to data dimension reduction into principal elements and residual errors by using a PLS model;
establishing a T-PLS model by using the principal component and the residual error and calculating statistics;
according to F distribution and χ 2 And distributing the control limit of the calculation statistic to realize fault detection.
2. A compressed air system fault detection algorithm based on random projection T-PLS according to claim 1, wherein: the training sample data are process variable data and quality variable data of the target industrial process under normal working conditions; setting the process variable data as a matrix containing m-dimensional process variables, n samples, denoted as X 0 ＝[x 1 ,x 2 ,…,x n ]∈R n×m The quality variable data is a matrix of n samples containing p-dimensional process variables, denoted as Y 0 ＝[y 1 ,y 2 ,…,y n ]∈R n×p 。
3. A compressed air system fault detection algorithm based on random projection T-PLS according to claim 2, wherein: the operation of normalizing the training sample data includes,
for a pair ofPerforming data dimension reduction by random projection to obtain processed process variable data X,
wherein,intermediate variable, X, representing process variable data mean X represents 0 Mean value of X std X represents 0 X represents the processed process variable data, H.epsilon.R m×r Belonging to a random matrix, Y mean Represents Y 0 Mean value of Y std Represents Y 0 And Y represents the processed process variable data.
4. A compressed air system fault detection algorithm based on random projection T-PLS according to claim 3, wherein: the operation of decomposing the training sample data subjected to the data dimension reduction into principal elements and residuals by using the PLS model includes,
taking training sample data subjected to data dimension reduction as input of a PLS model, and projecting (X, Y) to a model formed by a few latent variables (t 1 ,...,t A ) In the defined low-dimensional space, A is the number of main components, and after decomposition, the method comprises the following steps:
X＝TP T +E
Y＝TQ T +F
wherein T= [ T ] 1 ,...,t A ]Represents a scoring matrix, p= [ P ] 1 ,...,p A ]Load matrix representing X, q= [ Q ] 1 ,...,q A ]The load matrix of Y is represented, and E and F respectively represent matrices obtained by normalizing X and Y;
T＝XR
R＝W(P T W) -1 。
5. a compressed air system fault detection algorithm based on random projection T-PLS according to claim 4, wherein: operations for building a T-PLS model using principal elements and residuals include,
according to the data space obtained after decomposition by using the PLS model, the following model is obtained by combining a T-PLS algorithm:
wherein T is y 、T o 、T r A scoring matrix representing the directly related part of the quality variable, the orthogonal part of the quality variable and the part of the original residual with larger variance change respectively,P y 、P o 、P r the load matrix respectively represents a quality variable direct correlation part, a quality variable orthogonal part and a larger variance variation part in the original residual,Q y the representation corresponds to T y Is a new load matrix for Y of (c),representing a new residual matrix, A y Represents the number of principal components related to Y, A r The number of principal components independent of Y is represented.
6. A compressed air system fault detection algorithm based on random projection T-PLS according to claim 5, wherein: also included is a method of manufacturing a semiconductor device,
calculated by PCA algorithmThe number of main components is A y ＝rank(Q)；
Calculation of
Calculated by PCA algorithmThe number of main components is (A-A) y )；
Calculated by PCA algorithmThe number of main components is A r Wherein T is r Representing the main part of E r Representing the residual portion of E.
7. A compressed air system fault detection algorithm based on random projection T-PLS according to claim 6, wherein: the step of calculating the statistics includes,
for a variable sample x, statistics of directly related parts of quality variables are calculated by using a T-PLS modelStatistics of orthogonal parts of quality variable->Statistics of larger variance variation part in original residual +.>And statistics of the final residual portion Q r ；
Wherein t is y Representing the score of a variable sample x in the directly related part of the quality variable, t o Representing the score of the variable sample x in the orthogonal part of the quality variable, t r A score representing the larger variance variation portion of the variable sample x in the original residual,representing the residual of the variable sample x in the final residual portion, Λ y 、Λ o 、Λ t All represent intermediate variables in the calculation process.
8. A compressed air system fault detection algorithm based on random projection T-PLS according to claim 7, wherein: according to F distribution and χ 2 The control limits of the distribution calculation statistics include, in particular,
wherein,representation->Control limit of->Representation->Control limit of->Representation->Control limit of J (Q) r ) Represents Q r α represents confidence, S represents sample variance of Q, and μ represents sample mean of Q.
9. A compressed air system fault detection algorithm based on random projection T-PLS according to claim 7, wherein: in the process of real-time detection, for a newly acquired process sample x new After normalization and random projection, statistics of directly related parts of the newly acquired process sample quality variables are respectively calculated through PLS model decompositionStatistics of orthogonal parts of quality variable->Statistics of larger variance variation part in original residual +.>Statistics of the final residual part +.>
Wherein t is y，new Representing a newly acquired process sample x new Score in directly related part of quality variable, t o，new Representing newly acquired oversubscriptionCheng Yangben x new Score in orthogonal part of quality variable, t r，new Representing a newly acquired process sample x new The score of the larger variance variation part in the original residual,representing a newly acquired process sample x new Is a residual of (c).
10. The compressed air system fault detection algorithm based on the random projection PLS method of claim 9, wherein: the fault detection determination includes that,
will beRespectively +.>Comparison, if->And->Then it is indicated that a fault associated with the quality variable data Y was detected; if it isAnd->It is indicated that a fault is detected that is independent of the quality variable data Y.
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