CN107272655B - Batch process fault monitoring method based on multistage ICA-SVDD - Google Patents
Batch process fault monitoring method based on multistage ICA-SVDD Download PDFInfo
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Abstract
The invention discloses a kind of batch process fault monitoring methods based on multistage ICA-SVDD.For process mechanism complexity and there are the batch processes of multiple operational phases.The multistage negotiation and data distribution non-Gaussian system problem having for some batch processes, using a kind of improved divided stages and fault monitoring method.Divided stages are carried out according to the similarity of each timeslice and K mean algorithm first, then the characteristic information that Independent Component Analysis extracts non-gaussian is utilized respectively to each stage, it is finally introducing Support Vector data description algorithm and Statistic analysis models is established respectively to independent element and remaining Gauss residual error space, realize the malfunction monitoring to whole process.Malfunction monitoring applied to an actual conductor etching process, the results showed that this method has more preferably monitoring effect to multistage batch process.
Description
Technical field
The present invention relates to the batch process fault monitoring methods based on multistage ICA-SVDD, belong to industrial process failure and examine
Disconnected and hard measurement field.
Background technique
Batch process is a kind of important industrial mode of production, and process mechanism is complicated and there are multiple operation ranks
Section, and influence of the product quality vulnerable to uncertain factor.In order to guarantee batch production process safe and reliable operation and
The high quality of product is pursued, and is needed to establish effective process monitoring system and is carried out failure monitoring to batch production process.Polynary system
Meter course control method for use has been widely applied in Batch process monitoring, such as multidirectional pivot analysis (multiway
Principal component analysis, MPCA) and multidirectional partial least squares analysis (multiway partial least
Squares, MPLS).But most of data description method relevant to principal component analysis and partial least squares analysis have number
It is linear limitation according to the relationship met between Gaussian Profile and different variables.
For the non-Gaussian feature of batch process data, independent component analysis (independent component
Analysis, ICA) it is introduced in process monitoring field, in order to adapt to the malfunction monitoring to batch process, some scholars are ICA
Method is extended to multidirectional independent component analysis (multiway ICA, MICA) method.Although can handle non-gaussian data,
It is to be based on Density Estimator method calculating process complexity in the confidence limit of determination process monitoring statisticss amount and parameter can not
It is accurate to obtain, when dimension is larger, the problems such as not can avoid Density Estimator bring " dimension disaster ".In addition, for
The monitoring of nonlinear batch process, traditional MPCA/MPLS method also extend to its non-linear form, such as multidirectional core PCA and more
To core PLS, however, the course monitoring method based on these nonlinear methods is also required to Gaussian distributed.
The multioperation stage is an inherent characteristic of many batch processes, if realizing entire batch using single modeling pattern
It is bad to will lead to monitoring effect of the model in different phase for the monitoring of secondary process.For this characteristic, domestic and foreign scholars are
Done a large amount of research, by batch process carry out reasonable divided stages and in sub-stage establishment process monitoring
Model, to improve Monitoring Performance.
Process monitoring may be considered a monodrome classification problem, because the task of monitoring is by normal data and number of faults
According to separation.Support Vector data description (Support vector data description, SVDD) algorithm is a kind of initial
The monodrome classification method proposed by Tax and Duin.Normal data sample space is mapped to high dimensional feature by nonlinear transformation
A model is simultaneously established in space, so that normal data be separated with fault data, achievees the purpose that procedure fault monitors.It uses
SVDD algorithm carry out malfunction monitoring can handle simultaneously do not meet be between Gaussian Profile and variable non-linear relation data.
SVDD has been used for the fields such as damage check, image classification, pattern-recognition, and the application in process monitoring field also starts
Paid attention to.
A kind of fault monitoring method of the multistage batch process based on independent component analysis and Support Vector data description,
It can effectively improve the malfunction monitoring performance of batch process.Due to most of with principal component analysis and partial least squares analysis phase
It is linear limitation that the data description method of pass, which has the relationship between data fit Gaussian Profile and different variables,.The party
Method can solve process data non-gaussian and nonlinear monitoring problem simultaneously, have more preferably malfunction monitoring effect.
Summary of the invention
It is directed to multistage, non-Gaussian system and non-linear, the process mechanism complexity of batch process presentation, and product quality
Vulnerable to the influence of uncertain factor, in order to improve the malfunction monitoring performance to multistage batch process, the present invention provides one kind
Batch process fault monitoring method based on multistage ICA-SVDD.
Three-dimensional data is unfolded along batch direction first, fuzzy divided stages are carried out according to the similarity of each timeslice,
Available initial cluster number carries out accurate divided stages will pass through K mean algorithm；After determining the stage, then
Three-dimensional data is unfolded along variable direction, is then utilized respectively ICA method to each stage and carries out feature extraction, extracts corresponding
Non-gaussian characteristic information and residual information；Finally the non-gaussian space of independent element and remaining residual error space are passed through respectively
SVDD algorithm establishes Statistic analysis models, realizes the on-line fault monitoring to whole process.
The purpose of the present invention is what is be achieved through the following technical solutions:
Batch process fault monitoring method based on multistage ICA-SVDD, the method includes following procedure: being directed to
The multioperation stage feature of batch process needs to carry out reasonable divided stages to production process, to establish multiple submodels
Carry out malfunction monitoring.Fuzzy divided stages are carried out to production process according to the similarity of the mean vector of each timeslice first,
Obtain preliminary number of stages.Then it is classified as one kind at the time of by K mean algorithm that data characteristics is similar, and then is obtained more
Accurate divided stages.
The characteristic information that Independent Component Analysis extracts non-gaussian is utilized respectively to each stage, when using ICA algorithm
It after extracting whole independent elements, is rearranged according to non-gaussian degree size, the stronger independent element of d independence before choosing
Obtain homographyDue to having carried out multistage division to batch process, so will carry out ICA to each stage
Analysis is to carry out feature extraction.And then corresponding non-gaussian characteristic information of each stage and residual information can be extracted, so as to
Monitoring and statistics model is established to carry out malfunction monitoring.
It is finally introducing Support Vector data description algorithm and system is established respectively to independent element and remaining Gauss residual error space
Analysis model is counted, realizes the malfunction monitoring to whole process.Normal data sample space is mapped to height by nonlinear transformation
Dimensional feature space simultaneously establishes a model, so that normal data be separated with fault data, reaches the mesh of procedure fault monitoring
's.Carrying out malfunction monitoring using SVDD algorithm can handle that not meet be non-linear relation between Gaussian Profile and variable simultaneously
Data.
Detailed description of the invention
Fig. 1 is the Batch process monitoring method flow diagram based on multistage ICA-SVDD；
The expansion of Fig. 2 batch process data；
Fig. 3 multistage division result；
The normal batch monitoring result of Fig. 4；
Fig. 5 failure TCP+50 batch monitoring result；
Specific embodiment
Below with reference to shown in Fig. 1, the present invention is further described:
The data used is collected during an actual semiconductor etch processes, is half-and-half led respectively
The normal data and fault data of body etching carry out malfunction monitoring.
Step 1: the 3-D data set X (I × J × K) of batch process carries out two-dimensional development, wherein I represents lot number, J generation
Table variable number, K represent sampling number.Using along batch direction and the data processing method combined along variable direction, first by three
The data X (I × J × K) of dimension form is converted into two-dimensional matrix X (I × KJ) along batch direction, then standardizes two-dimensional matrix；Again
It is reconfigured according to variable direction, forms new two-dimensional matrix X (KI × J).Two step data method of deploying are as shown in Figure 2.
Step 2: reasonable divided stages being carried out to production process, carry out malfunction monitoring to establish multiple submodels.It is first
Fuzzy divided stages are first carried out to production process according to the similarity of the mean vector of each timeslice, obtain the preliminary stage
Number.Then it is classified as one kind at the time of by K mean algorithm that data characteristics is similar, and then obtains more accurate divided stages.
Step1: first it is unfolded three dimensional process data X (I × J × K) to obtain two-dimensional matrix X (I × KJ) by batch direction, so
The 2-D data timeslice matrix X that temporally axis direction is cut into batch afterwards and variable formsk(I × J), k=1,2 ..., K.
Step2: each timeslice matrix X is soughtkThe mean vector of (I × J), is denoted asThese mean values
Vector represents the characteristic information of each timeslice, carries out initial stage division to timeslice using these characteristic informations, goes forward side by side
The identification in row each stage, with first timeslice X1Benchmark X as first stagebase, then according to similarity calculation
Formula:
Successively calculate XbaseSubsequent timeslice and its similarity, and similarity threshold α is set, if X2And XbasePhase
It is greater than threshold alpha like degree, then it is assumed that X2Present period is also belonged to, then proceedes to calculate next timeslice and XbaseSimilarity；
Otherwise it is assumed that X2Belong to next stage, and enables Xbase=X2, continue by above-mentioned steps.
Similar timeslice is connected to form a period according to similarity, obtains preliminary fuzzy division.It can obtain
To corresponding stage number P, this provides foundation to choose cluster numbers with clustering algorithm below, still, this fuzzy division method
Will appear certain points or few continuity point can not accurately be divided into some stage.
Step3: being clustered by mean vector of the K-means clustering algorithm to timeslice, algorithm input be mean value to
Duration setAnd cluster number P, P cluster centre is arbitrarily selected, successive ignition calculating is carried out, when algorithm is full
When the sufficient condition of convergence, the cluster centre of available P subclass calculates each mean vectorTo all cluster centres away from
From, so that it may it obtainsFor the membership of P subclass, since the input of clustering algorithm arranges sequentially in time
Timeslice mean vector, therefore sequentially in time, the point in affiliated stage can will can not be determined in fuzzy division, be divided into
In one corresponding stage, so that it may obtain more accurate divided stages.The multistage division result of conductor etching process is shown in
Fig. 3.
Step 3: carrying out feature letter using independent component analysis (independent component analysis, ICA)
Breath extracts, and data higher-order statistics are more fully utilized in ICA, and can further extract phase from observation data
Mutual independent latent variable, these latent variables can more constitutionally extraction reaction process features.
ICA model is defined as
X=AS+E (2)
Wherein X=[x (1), x (2) ..., x (n)] ∈ Rm×nIt is observation data matrix, A=[a1,a2,...,ad]∈Rm×d
It is unknown hybrid matrix, S=[s (1), s (2) ..., s (n)] ∈ Rd×nIt is hiding independent element matrix, E ∈ Rm×nIt is
Residual matrix.N is the number of samples of acquisition, by d≤m it is found that a kind of ICA and data compression technique similar with PCA in fact,
Information as much as possible is described by data as few as possible.
The purpose of ICA is to estimate hybrid matrix W and independent element S from observation data X, therefore, ICA target: is found
One solves mixed matrix W, source signal can be isolated from observation signal, i.e.,
As d=m, that is, the inverse time that mixed matrix W is hybrid matrix A is solved,It is exactly the best estimate of independent element S.
It after extracting whole independent elements using ICA algorithm, is rearranged according to non-gaussian degree size, d before choosing
The stronger independent element of independence obtains homographyDue to having carried out multistage division to batch process, so wanting
To the X in each stagep(KpI × J) ICA analysis is carried out to carry out feature extraction, wherein p indicates corresponding pth stage, XpTable
Show the two-dimensional matrix that the pth stage is unfolded along variable direction, KpIt indicates pth stage corresponding number of samples, and then can extract
Each stage corresponding non-gaussian characteristic information and residual information carry out malfunction monitoring to establish monitoring and statistics model.
Step 4: being carried out using Support Vector data description (Support vector data description, SVDD)
The on-line monitoring of batch process, SVDD are a kind of monodrome sorting algorithms, and basic thought is for training dataset X={ xi,i
=1 ..., N }, by Φ: X → F of non-linear transfer by luv space data projection to feature space { Φ (xi), i=1 ...,
N }, the suprasphere that may include the minimum volume of all data samples then can be found in feature space, SVDD passes through core
The input space is mapped to higher dimensional space to learn to obtain flexible and accurate data descriptive model, obtained hypersphere by function
Volume data, which describes boundary, to be indicated by the supporting vector of sub-fraction.
In order to construct such minimal hyper-sphere, SVDD needs to solve following optimization problem:
In formula (4), a be suprasphere the centre of sphere, R be suprasphere radius, penalty coefficient C weighed suprasphere volume and
The false segmentation rate of training sample, slack variable ξiIntroducing represent penalty term accidentally point generated to i-th training sample, it is above-mentioned excellent
Change problem, which can be converted into, solves corresponding dual problem:
It is to introduce kernel function K (x hereini,xj) replace interior Product function (xi,xj), using quadratic programming, a can be found outi, such as
Fruit x0An arbitrary supporting vector is represented, then the centre of sphere of suprasphere and radius may be expressed as:
For new sample xnew, its available distance for arriving the suprasphere centre of sphere:
If DistnewThen the sample is normal by≤R；Conversely, the sample is exceptional sample.
After carrying out feature extraction using each stage of the ICA to batch process, the non-height of independent element can be respectively obtained
The data in this space and remaining residual error space, by SVDD method to the independent element extractedIt is established with residual matrix E
Statistic analysis models, first against independent elementIt is as follows to establish SVDD model:
In formula:Indicate k-th of sample, αkFor the Lagrange multiplier of corresponding sample, K () indicates Gaussian kernel letter
Number, available independent elementThe centre of sphere and radius for being formed by SVDD suprasphere are as shown in (9) formula:
Equally, then to residual matrix E it is as follows to establish SVDD model:
So, the centre of sphere and radius that residual matrix E is formed by SVDD suprasphere are as shown in (11) formula:
For each stage of batch process, the suprasphere radius R in corresponding stage, online process monitoring can be respectively obtained
When, as the sampled data x for obtaining current timenewWhen, after data prediction and ICA feature extraction, independence is sought respectively
IngredientWith residual matrix EnewTo the distance of the corresponding centre of sphereAnd DistE_new, therefore as Dist≤R, it can recognize
Sample for current time is normal, and works as Dist > R, then it represents that the sample at current time is fault data.
After carrying out divided stages and pretreatment to process data, for the failure of relatively simple modeling and multi-stage modeling
Monitoring effect establishes the Statistical monitor model of single and multistage PCA, ICA, ICA-SVDD respectively, all statistics
Statisti-cal control limit is set as 99%.Fig. 4 gives six kinds of methods to the monitored results of normal batch, it can be seen that six kinds of sides
Method can obtain good monitored results to normal batch.Wherein (a), (b), the event that (c) is the normal batch of single modeling method
Barrier monitoring figure, (d), (e), (f) be the normal batch of multi-stage modeling method malfunction monitoring figure.Fig. 5 gives TCP+50 failure
Malfunction monitoring figure, wherein (a), (b), (c) be single modeling method failure batch monitoring figure, (d), (e), (f) be it is multistage
The monitoring figure of section modeling method failure batch.From figure 5 it can be seen that either single model is still for TCP+50 failure
The malfunction monitoring of multiphase confinement, ICA-SVDD are to be substantially better than other two methods.
Claims (2)
1. the method for the batch process malfunction monitoring based on multistage ICA-SVDD, which is characterized in that this method step are as follows:
Step 1: the 3-D data set X (I × J × K) of batch process carries out two-dimensional development, wherein I represents lot number, and J, which is represented, to be become
Number is measured, K represents sampling number；Using along batch direction and the data processing method combined along variable direction, first by three-dimensional shaped
The data X (I × J × K) of formula is converted into two-dimensional matrix X (I × KJ) along batch direction, then standardizes two-dimensional matrix；According still further to
Variable direction reconfigures, and forms new two-dimensional matrix X (KI × J)；
Step 2: reasonable divided stages being carried out to production process, carry out malfunction monitoring to establish multiple submodels；Root first
Fuzzy divided stages are carried out to production process according to the similarity of the mean vector of each timeslice, obtain preliminary number of stages；
Then it is classified as one kind at the time of by K mean algorithm that data characteristics is similar, and then obtains more accurate divided stages；
Step1: first it is unfolded three dimensional process data X (I × J × K) to obtain two-dimensional matrix X (I × KJ) by batch direction, then press
Time-axis direction is cut into the 2-D data timeslice matrix X of batch and variable compositionk(I × J), k=1,2 ..., K；
Step2: each timeslice matrix X is soughtkThe mean vector of (I × J), is denoted asThese mean vectors
The characteristic information of each timeslice is represented, initial stage division is carried out to timeslice using these characteristic informations, and carry out each
The identification in a stage, with first timeslice X1Benchmark X as first stagebase, then according to calculating formula of similarity:
Successively calculate XbaseSubsequent timeslice and its similarity, and similarity threshold α is set, if X2And XbaseSimilarity
Greater than threshold alpha, then it is assumed that X2Present period is also belonged to, then proceedes to calculate next timeslice and XbaseSimilarity；Otherwise,
Think X2Belong to next stage, and enables Xbase=X2, continue by above-mentioned steps；
Similar timeslice is connected to form a period according to similarity, obtains preliminary fuzzy division；It is available right
The stage number P answered, this provides foundation to choose cluster numbers with clustering algorithm below, and still, this fuzzy division method can go out
Existing certain points or few continuity point can not accurately be divided into some stage；
Step3: being clustered by mean vector of the K-means clustering algorithm to timeslice, and algorithm input is mean vector collection
It closesAnd cluster number P, P cluster centre is arbitrarily selected, successive ignition calculating is carried out, is restrained when algorithm meets
When condition, the cluster centre of available P subclass calculates each mean vectorTo the distance of all cluster centres, so that it may
To obtainFor the membership of P subclass, since the input of clustering algorithm is that the timeslice that arranges sequentially in time is equal
Be worth vector, therefore sequentially in time, can will can not be determined in fuzzy division belonging to the stage point, be divided into one it is corresponding
In stage, so that it may obtain more accurate divided stages；
Step 3: carrying out characteristic information using independent component analysis (independent component analysis, ICA) and mention
It takes, data higher-order statistics are more fully utilized in ICA, and can further extract from observation data mutually indepedent
Latent variable, these latent variables can more constitutionally extract reaction process feature；
ICA model is defined as
X=AS+E (2)
Wherein X=[x (1), x (2) ..., x (n)] ∈ Rm×nIt is observation data matrix, A=[a1,a2,...,ad]∈Rm×dIt is
Unknown hybrid matrix, S=[s (1), s (2) ..., s (n)] ∈ Rd×nIt is hiding independent element matrix, E ∈ Rm×nIt is residual error
Matrix；N be acquisition number of samples, by d≤m it is found that ICA in fact it is similar with PCA be also a kind of data compression technique, by use up
May data less information as much as possible described；
The purpose of ICA is to estimate hybrid matrix A and independent element S from observation data X, therefore, ICA target: finds one
Mixed matrix W is solved, source signal can be isolated from observation signal, i.e.,
As d=m, that is, the inverse time that mixed matrix W is hybrid matrix A is solved,It is exactly the best estimate of independent element S；
It after extracting whole independent elements using ICA algorithm, is rearranged according to non-gaussian degree size, selection first d independent
The stronger independent element of property obtains homographyDue to having carried out multistage division to batch process, so will be to every
The X in a stagep(KpI × J) ICA analysis is carried out to carry out feature extraction, wherein p indicates corresponding pth stage, XpIndicate pth
The two-dimensional matrix that stage is unfolded along variable direction, KpIt indicates pth stage corresponding number of samples, and then each rank can be extracted
The corresponding non-gaussian characteristic information of section and residual information carry out malfunction monitoring to establish monitoring and statistics model；
Step 4: interval is carried out using Support Vector data description (Support vector data description, SVDD)
The on-line monitoring of process, SVDD are a kind of monodrome sorting algorithms, and basic thought is for training dataset X={ xi, i=
1 ..., N }, by Φ: X → F of non-linear transfer by luv space data projection to feature space { Φ (xi), i=1 ..., N },
Then the suprasphere that may include the minimum volume of all data samples can be found in feature space, SVDD passes through kernel function
The input space is mapped to higher dimensional space to learn to obtain flexible and accurate data descriptive model, obtained hypersphere volume data
Describing boundary is indicated by the supporting vector of sub-fraction, and in order to construct such minimal hyper-sphere, SVDD needs
Solve following optimization problem:
In formula (4), a is the centre of sphere of suprasphere, and R is the radius of suprasphere, and penalty coefficient C has weighed the volume and training of suprasphere
The false segmentation rate of sample, slack variable ξiIntroducing represent penalty term accidentally point, above-mentioned optimization problem generated to i-th training sample
It can be converted into and solve corresponding dual problem:
Wherein, αiRepresent the Lagrange multiplier of corresponding i-th of training sample, αjThe glug for representing corresponding j-th of training sample is bright
Day multiplier；
It is to introduce kernel function K (x hereini,xj) replace interior Product function (xi,xj), using quadratic programming, a can be found outiIf x0
An arbitrary supporting vector is represented, then the centre of sphere of suprasphere and radius may be expressed as:
For new sample xnew, its available distance for arriving the suprasphere centre of sphere:
If DistnewThen the sample is normal by≤R；Conversely, the sample is exceptional sample；
After carrying out feature extraction using each stage of the ICA to batch process, the non-gaussian that can respectively obtain independent element is empty
Between and remaining residual error space data, by SVDD method to the independent element extractedIt establishes and counts with residual matrix E
Analysis model, first against independent elementIt is as follows to establish SVDD model:
In formula:Indicate k-th of sample, αkFor the Lagrange multiplier of corresponding sample, K () indicates gaussian kernel function, can
To obtain independent elementThe centre of sphere and radius for being formed by SVDD suprasphere are as shown in (9) formula:
Equally, then to residual matrix E it is as follows to establish SVDD model:
Wherein, βkRepresent the Lagrange multiplier of corresponding k-th of training sample；
So, the centre of sphere and radius that residual matrix E is formed by SVDD suprasphere are as shown in (11) formula:
For each stage of batch process, the suprasphere radius R in corresponding stage can be respectively obtained, when online process monitoring,
As the sampled data x for obtaining current timenewWhen, after data prediction and ICA feature extraction, independent element is sought respectivelyWith residual matrix EnewTo the distance of the corresponding centre of sphereAnd DistE_new, therefore as Dist≤R, it is believed that when
The sample at preceding moment is normal, and works as Dist > R, then it represents that the sample at current time is fault data.
2. the method for the batch process malfunction monitoring according to claim 1 based on multistage ICA-SVDD, feature exist
In, the problem of there is multistage negotiation and data distribution non-Gaussian system due to batch process, based on independent component analysis and support to
The fault monitoring method for measuring the multistage batch process of data description, can solve process data non-gaussian and nonlinear simultaneously
Monitoring problem.
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