CN102662321A - Online updating method of principal component analysis monitoring model - Google Patents

Abstract

The invention relates to an online updating method of a principal component analysis monitoring model. The method comprises the following steps that: 1) A model online updating system comprising data acquisition equipment and a monitoring computer is arranged in industry field; 2) A traditional principal component analysis (PCA) modeling module uses historical data to establish a PCA initial monitoring model; 3) After the monitoring begins, a mean value variance updating module calculates a mean value and a standard deviation sigma' of a new model according to real-time process data and the current PCA model; 4) A projection point calculation module calculates a residual vector of a new sample and transmits to a residual determination module; 5) The residual determination module determines an updating method of a projection direction according to a size of a residual vector die; if the residual is large, a principal component space adjusting module is called; if the residual value is small, a principal component direction fine adjusting module is called; finally a load vector P' nk and a characteristic value matrix lambda' kk of the new model is obtained; 6) A control limit updating module carries out control limit and updating on statistical magnitude of the model; the system finally outputs the new model omega' which is used for online monitoring and fault diagnosis during an industrial process.

Description

A kind of online updating method of pivot analysis monitoring model

Technical field

The present invention relates to a kind of online updating method that is used for multivariate statistics process monitoring model, particularly about a kind of multivariate statistics process monitoring model online updating method based on the increment pca method.

Background technology

PCA (Principal Components Analysis; Pivot analysis) is a kind of multivariate statistics process monitoring modeling method; Through the linear dependence between the mining process variable; Set up the monitoring model of reflection system inherent law, offer the multivariate statistics PMS, thereby realize effective monitoring production run.Traditional monitoring model modeling process based on PCA at first need be collected a large amount of production datas that can represent the production run characteristic, sets up monitoring model based on these historical datas then.Yet in actual production process, external environment factors such as degradation of catalyst efficiency, ageing equipment dust stratification cause the slow drift phenomenon of process variable easily.The DATA DISTRIBUTION attributes such as average, standard deviation that this will change process variable make the PCA monitoring model of setting up based on historical data produce deviation gradually with the actual conditions of production run, cause monitoring model to lose efficacy, and cause a large amount of false-alarm of supervisory system generation.

The existing model online updating that can carry out roughly has two types with the PCA method for supervising that procedure of adaptation variable slowly drifts about.(Exponentially Weighted Moving Average, EWMA) wave filter combines with pca model first kind method, only the average and the standard deviation of process variable is upgraded with EWMA.The advantage of this method is that computing velocity is very fast, and storage demand is lower; Shortcoming is to upgrade pca model structural informations such as pivot projecting direction, makes still to have deviation between monitoring model and the actual production process.Second class methods can the whole pca model of online updating, comprises average, standard deviation, pivot projecting direction and the pivot number etc. of variable.Its advantage can guarantee the consistance of monitoring model and actual production process at any time, and shortcoming is the recursion of covariance matrix to be upgraded with " characteristic value decomposition " calculating will cause higher computation complexity, and higher storage demand.To sum up, existing adaptive model method for supervising or monitoring effect are accurate inadequately, or computational complexity is higher, all exist certain weak point.

In recent years, a kind of online data compression algorithm that is applied to area of pattern recognition being arranged---increment PCA (Incremental PCA) method has caused some scholars' concern.This method has the counting yield height, and need not the advantage of additional storage space, and average, standard deviation and pivot projecting direction that can the online updating model.But when this method is applied to the multivariate statistics process monitoring; The time variation of data will cause the continuous increase of the pivot number of monitoring model; Even level off to identical with the variable number; Make SPE (Squared Prediction Error, square prediction error) statistic be close to and lost efficacy, thereby can't be used for actual monitored.

Summary of the invention

To the problems referred to above; The purpose of this invention is to provide a kind of statistic processes monitoring model online updating method of using increment pivot analysis algorithm, average, standard deviation and pivot projecting direction that this method can the real-time update model have robustness to the slow drift phenomenon of the process variable in the industrial process; Also has the reliability height; Computing velocity is fast, to advantage such as the storage demand of system is low, is applicable to the model online updating of actual production process multivariate statistics supervisory system.

Be to realize above-mentioned purpose, the present invention takes following technical scheme: a kind of online updating method of pivot analysis monitoring model, it may further comprise the steps: 1) industry spot be provided with one comprise data acquisition equipment and supervisory control comuter model online updating system; Preset a conventional P CA MBM in the said supervisory control comuter, a mean variance update module, a subpoint computing module, a residual error determination module, a principal component space adjusting module, a pivot directional trim module and a control limit update module; 2) before the system start-up of model online updating; Data acquisition equipment is collected and can be represented the historical production data of production run characteristic to input to the conventional P CA MBM in the supervisory control comuter as training sample x; Set up the initial monitoring model Ω of PCA, and send the initial monitoring model of PCA to the mean variance update module; The initial monitoring model Ω of PCA is:

$\mathrm{\Ω}=(\stackrel{\‾}{x},\mathrm{\σ},P_{\mathrm{nk}},{\mathrm{\Λ}}_{\mathrm{kk}},N,{\mathrm{\δ}}_{\mathrm{\α}}^2,T_{\mathrm{\α}}^2)$

In the formula, $\stackrel{\‾}{x}={\mathrm{\Σ}}_{i=1}^N{x}_i/N$ The representation model average; $\mathrm{\σ}=\sqrt{{\mathrm{\Σ}}_{i=1}^N{(x_i-\stackrel{\‾}{x})}^2/(N-1)}$ The expression standard deviation; P _NkThe representation feature value is decomposed the pairing load vector of k maximum pivot score of back, i.e. pivot projection vector; Λ _KkThe representation feature value matrix, its diagonal element is made up of k pivot score of maximum; N representes the training sample number chosen;

The control limit of expression SPE statistic under level of significance α;

Expression T ²The control limit of statistic under level of significance α; x _iRepresent i training sample (i=1 ..., N); K representes the pivot number that keeps; N representes the dimension of process variable; 3) data acquisition equipment converts the real-time process variable in the industrial processes into real-time process data x _N+m, send the mean variance update module to; Simultaneously, model online updating system also sends required undated parameter to the mean variance update module; And the existing PCA monitoring model in the mean variance update module does

The mean variance update module is according to real-time process data x _N+mAnd undated parameter, calculate the PCA monitoring model that makes new advances

In the model average

And standard deviation sigma ', result of calculation is stored, and will have the PCA monitoring model now and correlation parameter sends the subpoint computing module to; 4) the subpoint computing module calculates real-time process data x _N+mThe coordinate of subpoint g on principal component space, and real-time process data x _N+mTo the distance of subpoint g, i.e. residual vector h, and send result of calculation, existing PCA monitoring model and correlation parameter to the residual error determination module, be used for the pivot projecting direction being adjusted at subsequent step; Concrete computing formula is following:

$g=P_{\mathrm{nk}}^T(x_{N+m}-{\stackrel{\‾}{x}}^{\′}){\mathrm{\Σ}}_{N+m}^{-1}$

$h=(x_{N+m}-{\stackrel{\‾}{x}}^{\′}){\mathrm{\Σ}}_{N+m}^{-1}-P_{\mathrm{nk}}g$

Wherein, ∑ _N+m=diag (σ ') is that the standard deviation vector σ ' of model is the diagonal matrix of diagonal element to upgrade afterwards; 5) the residual error determination module calls any model projection direction update method according to the size decision of the mould of the residual vector of subpoint: if residual values is bigger, then call the principal component space adjusting module, get into step 6); If residual values is less, then call pivot directional trim module, get into step 7); The principal component space adjusting module is identical with the output form of pivot directional trim module, is pivot projection vector and the eigenvalue matrix of upgrading the back model; The mould of residual error determination module through residual vector h relatively and the size of delta threshold η are selected the update method of current sample: 1. when the mould of residual error h greatly the time, promptly || h||＞η, and with the residual vector of optimization

Existing pca model and correlation parameter send the principal component space adjusting module to, get into step 6), and whole principal component space is adjusted calculating; 2. when the mould of residual error h hour, promptly || h||＜η, will have pca model and correlation parameter now and send pivot directional trim module to, get into step 7), carry out the fine setting calculating of pivot projecting direction; 6) the principal component space adjusting module is based on the constant thought of process variable correlativity essence; Utilize pca method that the pivot projection vector of expansion is carried out dimensionality reduction; Thereby when keeping the pivot number constant, existing pivot projecting direction is upgraded, obtain the load vector P ' of new model _NkWith eigenvalue matrix Λ ' _KkEigenvalue matrix Λ ' _KkSolution formula be:

$(\mathrm{\&mu;}\left[\begin{array}{cc}{\mathrm{\&Lambda;}}_{\mathrm{<figure-callout\; id="0"\; label="kk"\; filenames="HDA0000146315970000021.png,HDA0000146315970000022.png"\; state="\{\{state\}\}">kk</figure-callout>}}& \underset{\&OverBar;}{0}\\ {\underset{\&OverBar;}{0}}^{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000146315970000021.png,HDA0000146315970000022.png"\; state="\{\{state\}\}">T</figure-callout>}}& 0\end{array}\right]+(1-\mathrm{\&mu;})\left[\begin{array}{cc}{\mathrm{qq}}^T& \mathrm{\&rho;q}\\ {\mathrm{\&rho;q}}^T& {\mathrm{\&rho;}}^2\end{array}\right])\&ap;{\mathrm{R\&Lambda;}}_{\mathrm{kk}}^{\&prime;}{R}^T$

In the formula, $\mathrm{\&rho;}={\hat{h}}^T\left[{\mathrm{\&Sigma;}}_{N+m}^{-1}(x_{N+m}-\stackrel{\&OverBar;}{x})\right],$ $q=P_{\mathrm{Nk}}^T\left[{\mathrm{\&Sigma;}}_{N+m}^{-1}(x_{N+m}-\stackrel{\&OverBar;}{x})\right],$ R representes rotation matrix, and the matrix in the levoform is carried out characteristic value decomposition, and k maximum eigenwert constituted the eigenvalue matrix Λ ' after upgrading _Kk, its characteristic of correspondence value vector is exactly rotation matrix R; Because the vectorial P of existing load _NkIn each column vector and residual vector h orthogonal, constitute the pivot projection vector of expansion, then the load of new model vector P ' _NkBe the linear combination of the pivot projection vector of expansion; With the rotation matrix R substitution in the following formula, obtain the load vector P ' of new model _NkComputing formula be:

$P_{\mathrm{nk}}^{\&prime;}=[P_{\mathrm{nk}},\hat{h}]R$

This module is with the pivot projection vector P ' of the new model that calculates _NkStore, and with eigenvalue matrix Λ ' _KkBe sent to control and limit update module, get into step 8), continue to accomplish the adjustment of pivot score and the renewal work that control is limit; 7) pivot directional trim module is same utilizes result that existing pca model and step before obtain to the vectorial P ' of the load of new model _NkWith eigenvalue matrix Λ ' _KkCalculate; Owing to just the pivot projecting direction is finely tuned, only need carry out pivot analysis again in principal component space inside, the pivot projecting direction after promptly obtaining upgrading in principal component space inside; Eigenvalue matrix Λ ' _KkSolution formula be:

(λΛ _kk+(1-λ)qq ^T)≈RΛ′ _kkR ^T

Matrix in the levoform is carried out characteristic value decomposition, and all k eigenwert has constituted the eigenvalue matrix Λ ' after upgrading _Kk, its characteristic of correspondence value vector is exactly rotation matrix R; The pivot projection vector P ' of new model _NkBe by existing pivot projection vector P _NkIn the new linear combination that column vector constituted, calculate by following formula:

P′ _nk＝P _nkR

This module is with the pivot projection vector P ' of the new model that calculates _NkStore, and with eigenvalue matrix Λ ' _KkBe sent to control and limit update module, get into step 8), continue to accomplish the adjustment of pivot score and the renewal work that control is limit; 8) control limit update module based on the result of calculation of front to the eigenvalue matrix Λ ' after upgrading _KkStandardize, thereby accomplish control limit Model Monitoring statistic index

With

Renewal, the new model after finally being upgraded fully; Control limit update module is stored the aforementioned calculation result, with the new model after the renewal fully that finally obtains Export, be used for the on-line monitoring and the fault diagnosis of industrial process; To the eigenvalue matrix Λ ' after upgrading _KkCarrying out normalized method is: the eigenwert accumulation contribution rate of k pivot is Cum (Λ before in the existing model of definition _Kk), promptly before k reservation eigenwert add up and account for that all eigenwerts add up and ratio be Cum (Λ _Kk); Because new model only adjusts the eigenwert of a preceding k pivot, thus the eigenwert of preceding k pivot of note new model accumulate contribution rate be Cum (Λ ' _Kk), then new eigenvalue matrix Λ ' _KkEach diagonal line on element should be adjusted into:

Λ′ _i，i＝Λ′ _i，i×Cum(Λ)/Cum(Λ′)

In the formula, Λ ' _{I, i}Represent new eigenvalue matrix Λ ' _Kk(i, i) individual element; Through above adjustment, under the constant prerequisite of physical interconnection property, the SPE control limit of new model

Need not to upgrade adjustment and also can satisfy monitoring requirement in most cases; Therefore, the SPE of new model control limit

In the said step 3), model average of new PCA monitoring model

and standard deviation sigma ' more new formula following:

${\stackrel{\&OverBar;}{x}}^{\&prime;}=\mathrm{\&lambda;}\stackrel{\&OverBar;}{x}+(1-\mathrm{\&lambda;})x_{N+m}$

${\mathrm{\&sigma;}}^{\&prime;}=\sqrt{{\mathrm{\&lambda;\&sigma;}}^2+(1-\mathrm{\&lambda;}){(x_{N+m}-\stackrel{\&OverBar;}{x})}^2}$

In the formula, x _N+mBe illustrated in the real-time process data of m the real-time process variable that collects in the actual monitored process; M=1,2,3 In the definition monitor procedure, the existing PCA monitoring model in the mean variance update module does

When monitoring during first real-time process variable, promptly during m=1, the existing PCA monitoring model in the mean variance update module is exactly the initial monitoring model that conventional P CA MBM provides

λ is a forgetting factor, belongs to undated parameter, and its span is (0,1); Delta threshold η also belongs to undated parameter, span be (0, δ _α).

In the said step 8), the T of new PCA monitoring model ²The control limit

Adopt F to distribute and calculate, formula is:

$T_a^{2\&prime;}=\frac{k({(N+m)}^2-1)}{(N+m)(N+m-k)}{F}_{k,N+m-k;\mathrm{\&alpha;}}$

Wherein, the pivot number of k for keeping, N is the training sample sum that initial MBM is collected, m is the current total sample number that collects at monitor stages, F _{K, N+m-k; α}Corresponding to insolation level is α, and degree of freedom is k, and the F distribution critical value under the N+m-k condition obtains through tabling look-up, and therefore, the numerical value of the number of training N that only need upgrade in time promptly obtains the T of new PCA monitoring model ²The control limit

The present invention is owing to take above technical scheme; It has the following advantages: 1, the present invention upgrades through the projecting direction to model; Thereby guaranteed the consistance of model structure and real system; With only more the pca model update method of new model average, standard deviation compare, have lower false alarm rate and monitoring effect more accurately.2, the present invention is based on the constant thought of process variable correlativity essence, control pivot number remains unchanged, thereby need not to use whole data covariance matrix to upgrade, and only need finely tune the minority pivot projecting direction of the reflection property of system; Therefore in practical application, the present invention compares with the pca model update method that other need upgrade the The model structure, has computing velocity and lower storage demand faster, and can access similar even better monitoring effect.3, the present invention has robustness to the slow drift phenomenon of recurrent data in the industrial process, can in time report to the police to phenomenons such as variable that true fault causes sudden change and correlation of variables disappearances.The present invention is skillfully constructed, and is accurate and practical, can be widely used in the actual industrial process monitor procedure.

Description of drawings

Fig. 1 is a structural representation of the present invention

Fig. 2 is a modular structure synoptic diagram of the present invention

Fig. 3 is to use the embodiment monitored results synoptic diagram of conventional P CA monitoring model

Fig. 4 is an embodiment of the invention synoptic diagram as a result

Embodiment

Below in conjunction with accompanying drawing and embodiment the present invention is carried out detailed description.

The present invention is based on following thought: in the industrial system of normal operation, the physical interconnection property between process variable can be along with the time change, thereby the correlativity essence between variable can not change, and the pivot number should remain unchanged.The present invention is through the average and the standard deviation of real-time update model; And the pivot projecting direction of model adjusted; Only utilize the basic pivot information of pca model; Just can carry out fast and effectively upgrading, thereby when implementing the industrial system on-line monitoring, realize pca model being carried out the function of online updating according to the real-time process data to supervisory system.

The inventive method may be summarized to be: as shown in Figure 1, according to the industry spot actual conditions, be provided with one comprise data acquisition equipment 1, supervisory control comuter 2 model online updating system.Data acquisition equipment 1 converts real-time process variable in the industrial processes and historical process variable into digital signal, and sends supervisory control comuter 2 to; Supervisory control comuter 2 is set up initial p CA model through handling the historical process data, and carries out the online updating of monitoring model, the PCA monitoring model after output is upgraded in real time according to real-time process data and undated parameter.

The inventive method specifically may further comprise the steps:

1) as shown in Figure 1, according to the industry spot actual conditions, be provided with one comprise data acquisition equipment 1, supervisory control comuter 2 model online updating system.As shown in Figure 2, be provided with a conventional P CA MBM 21, one mean variance update module 22 in the supervisory control comuter 2; One subpoint computing module 23; One residual error determination module 24, one principal component space adjusting modules, 25, one pivot directional trim modules 26 and a control limit update module 27.

2) before the system start-up of model online updating; The historical data of at first data acquisition equipment 1 being collected is carried out artificial screening, picks out some abundant and representative historical datas according to certain industry spot experience and sends conventional P CA MBM 21 to as training sample.Conventional P CA MBM 21 only is called once before the system start-up of model online updating, sets up the initial monitoring model of PCA according to training sample, and sends the initial monitoring model of PCA to mean variance update module 22.After online updating begins, conventional P CA MBM 21 will be in dormant state, no longer participate in online updating work.After update calculation is accomplished for the first time, new monitoring model will be stored by system self, no longer need the external world to import.

Conventional P CA MBM 21 adopts traditional pivot analysis modeling method to set up pca model: the covariance matrix after the standardization is carried out characteristic value decomposition, to obtain the load vector sum pivot score of model.Through accumulation contribution rate threshold method, or the cross validation method confirms the pivot number that keeps, and calculates corresponding statistic control limit according to statistical formulas, finally obtains the initial monitoring model Ω of complete PCA:

$\mathrm{\&Omega;}=(\stackrel{\&OverBar;}{x},\mathrm{\&sigma;},P_{\mathrm{nk}},{\mathrm{\&Lambda;}}_{\mathrm{kk}},N,{\mathrm{\&delta;}}_{\mathrm{\&alpha;}}^2,T_{\mathrm{\&alpha;}}^2)$

In the formula, $\stackrel{\&OverBar;}{x}={\mathrm{\&Sigma;}}_{i=1}^N{x}_i/N$ The representation model average; $\mathrm{\&sigma;}=\sqrt{{\mathrm{\&Sigma;}}_{i=1}^N{(x_i-\stackrel{\&OverBar;}{x})}^2/(N-1)}$ The expression standard deviation; P _NkThe representation feature value is decomposed the pairing load vector of k maximum pivot score of back, i.e. pivot projection vector; Λ _KkThe representation feature value matrix, its diagonal element is made up of k pivot score of maximum; N representes the training sample number chosen;

The control limit of expression SPE (Squared Prediction Error, square prediction error) statistic under level of significance α;

Expression T ²The control limit of statistic (describing the sample changed situation on the pivot subspace) under level of significance α; x _iRepresent i training sample (i=1 ..., N); K representes the pivot number that keeps; N representes the dimension of process variable.

3) data acquisition equipment 1 converts the real-time process variable in the industrial processes into the real-time process data, sends the mean variance update module 22 in the supervisory control comuter 2 to.Simultaneously, model online updating system also sends required undated parameter to mean variance update module 22.Undated parameter comprises: forgetting factor λ, and span is (0,1); Delta threshold η, and span (0, δ _α), wherein, δ _αRadical sign value for SPE control limit among the initial monitoring model Ω of PCA.The initial value of above-mentioned undated parameter is generally by artificial setting, and can in the actual monitored process, carry out artificial based on concrete condition or machine is adjusted automatically.

The real-time process data of m the sample of supposing in the actual monitored process, to collect are x _N+m, m=1,2,3 ..., and be the more new technological process of example explanation PCA monitoring model with the monitor procedure of this sample.Existing PCA monitoring model in the definition monitor procedure does

So, as the real-time process data x that monitors first sample _N+1The time, existing PCA monitoring model is exactly the initial monitoring model that conventional P CA MBM 21 provides $\mathrm{\&Omega;}=(\stackrel{\&OverBar;}{x},\mathrm{\&sigma;},P_{\mathrm{Nk}},{\mathrm{\&Lambda;}}_{\mathrm{Kk}},N,{\mathrm{\&delta;}}_{\mathrm{\&alpha;}}^2,T_{\mathrm{\&alpha;}}^2).$

Mean variance update module 22 is according to the real-time process data x of the new samples that is collected _N+m, and required undated parameter, calculate the PCA monitoring model that makes new advances

In the model average

And standard deviation sigma ', result of calculation is stored, and send existing P CA monitoring model Ω and correlation parameter to subpoint computing module 23.Wherein, model average of new PCA monitoring model

and standard deviation sigma ' more new formula following:

${\stackrel{\&OverBar;}{x}}^{\&prime;}=\mathrm{\&lambda;}\stackrel{\&OverBar;}{x}+(1-\mathrm{\&lambda;})x_{N+m}$

${\mathrm{\&sigma;}}^{\&prime;}=\sqrt{{\mathrm{\&lambda;\&sigma;}}^2+(1-\mathrm{\&lambda;}){(x_{N+m}-\stackrel{\&OverBar;}{x})}^2}$

Model average and standard deviation are carried out the lasting effectiveness that real-time normalization can be guaranteed the PCA algorithm, and reduce the influence of dimension model accuracy.

4) subpoint computing module 23 is mainly used in and calculates new samples x _N+mThe coordinate of subpoint g on principal component space, and residual vector h (is used for describing x _N+mTo the distance of subpoint g), and send result of calculation, existing PCA monitoring model Ω and correlation parameter to residual error determination module 24, be used for the pivot projecting direction being adjusted at subsequent step.Concrete computing formula is following:

$g=P_{\mathrm{nk}}^T(x_{N+m}-{\stackrel{\&OverBar;}{x}}^{\&prime;}){\mathrm{\&Sigma;}}_{N+m}^{-1}$

$h=(x_{N+m}-{\stackrel{\&OverBar;}{x}}^{\&prime;}){\mathrm{\&Sigma;}}_{N+m}^{-1}-P_{\mathrm{nk}}g$

Wherein, ∑ _N+m=diag (σ ') is that the standard deviation vector σ ' of model is the diagonal matrix of diagonal element to upgrade afterwards.

5) residual error determination module 24 is according to the mould of residual vector || and any model projection direction update method is called in the size decision of h||: if residual values is bigger, then call principal component space adjusting module 25, get into step 6); If residual values is less, then call pivot directional trim module 26, get into step 7); Wherein, principal component space adjusting module 25 is identical with the output form of pivot directional trim module 26, is pivot projection vector and the eigenvalue matrix of upgrading the back model.Can avoid excessively being regulated by caused by noise according to residual vector decision control method, enhanced system is to the robustness of noise.

The size of mould and the delta threshold η of residual error determination module 24 through residual vector h is relatively selected the update method of current sample:

1. when the mould of residual error h is big; Promptly || h||＞η; It is far away to mean that new sample point arrives the distance of original pivot projector space; Need adjust the projecting direction of whole principal component space; Therefore send existing pca model of the residual vector of optimizing and correlation parameter to principal component space adjusting module 25, get into step 6), the projecting direction of whole principal component space is adjusted calculating;

2. when the mould of residual error h hour; Promptly || h||＜η; New sample meets the correlation of variables hypothesis of existing model basically, only need be existing pivot direction be finely tuned get final product in former principal component space inside, therefore with former data, have pca model now and correlation parameter sends pivot directional trim module 26 to; Get into step 7), carry out the fine setting of pivot projecting direction and calculate.

6) principal component space adjusting module 25 is based on the constant thought of process variable correlativity essence; Utilize pca method that the pivot projection vector of expansion is carried out dimensionality reduction; Thereby when keeping the pivot number to remain unchanged; Existing pivot projecting direction is upgraded, obtain the load vector P ' of new model _NkWith eigenvalue matrix Λ ' _Kk

Eigenvalue matrix Λ ' _KkSolution formula be:

$(\mathrm{\&mu;}\left[\begin{array}{cc}{\mathrm{\&Lambda;}}_{\mathrm{<figure-callout\; id="0"\; label="kk"\; filenames="HDA0000146315970000021.png,HDA0000146315970000022.png"\; state="\{\{state\}\}">kk</figure-callout>}}& \underset{\&OverBar;}{0}\\ {\underset{\&OverBar;}{0}}^{\mathrm{<figure-callout\; id="0"\; label="T"\; filenames="HDA0000146315970000021.png,HDA0000146315970000022.png"\; state="\{\{state\}\}">T</figure-callout>}}& 0\end{array}\right]+(1-\mathrm{\&mu;})\left[\begin{array}{cc}{\mathrm{qq}}^T& \mathrm{\&rho;q}\\ {\mathrm{\&rho;q}}^T& {\mathrm{\&rho;}}^2\end{array}\right])\&ap;{\mathrm{R\&Lambda;}}_{\mathrm{kk}}^{\&prime;}{R}^T---\left(1\right)$

In the formula, $\mathrm{\&rho;}={\hat{h}}^T\left[{\mathrm{\&Sigma;}}_{N+m}^{-1}(x_{N+m}-\stackrel{\&OverBar;}{x})\right],$ $q=P_{\mathrm{Nk}}^T\left[{\mathrm{\&Sigma;}}_{N+m}^{-1}(x_{N+m}-\stackrel{\&OverBar;}{x})\right],$ (k+1) * k dimension matrix R representes rotation matrix to be asked.Matrix in formula (1) levoform carries out characteristic value decomposition, selects k maximum eigenwert and constitutes the eigenvalue matrix Λ ' after upgrading _Kk, its characteristic of correspondence vector is exactly rotation matrix R.

Because the vectorial P of existing load _NkIn each column vector and residual vector h orthogonal, can constitute the pivot projection vector of expansion, then the load of new model vector P ' _NkBe the linear combination of the pivot projection vector of expansion.With the rotation matrix R substitution in the following formula, can obtain the load vector P ' of new model _NkComputing formula be:

$P_{\mathrm{nk}}^{\&prime;}=[P_{\mathrm{nk}},\hat{h}]R$

This module is with the load vector P ' of the new model that calculates _NkStore, and with eigenvalue matrix Λ ' _Kk, existing pca model and correlation parameter be sent to control limit update module 27, gets into step 8), continue to accomplish to the adjustment of pivot score and to the renewal work of control limit.

7) pivot directional trim module 26 is same utilizes result that existing pca model and step before obtain to the vectorial P ' of the load of new model _NkWith eigenvalue matrix Λ ' _KkCalculate.Owing to just the pivot projecting direction is finely tuned, only need carry out pivot analysis again in principal component space inside, the pivot projecting direction after just can obtaining upgrading in principal component space inside.

Eigenvalue matrix Λ ' _KkSolution formula be:

(λΛ _kk+(1-λ)qq ^T)≈RΛ′ _kkR ^T (2)

Matrix in formula (2) levoform carries out characteristic value decomposition, and all k eigenwert has constituted the eigenvalue matrix Λ ' after upgrading _Kk, its characteristic of correspondence vector is exactly rotation matrix R (R is that k * k ties up matrix).The load vector P ' of new model _NkShould be by the vectorial P of existing load _NkIn the new linear combination that column vector constituted, can calculate by following formula:

P′ _nk＝P _nkR

This module is with the pivot projection vector P ' of the new model that calculates _NkStore, and with eigenvalue matrix Λ ' _Kk, existing pca model and correlation parameter be sent to control limit update module 27, gets into step 8), continue to accomplish to the adjustment of pivot score and to the renewal work of control limit.

8) control limit update module 27 based on the result of calculation of front to the eigenvalue matrix Λ ' after upgrading _KkStandardize, thereby accomplish control limit Model Monitoring statistic index

With

Renewal, the new model after finally being upgraded fully.

To the eigenvalue matrix Λ ' after upgrading _KkCarrying out normalized method is: the eigenwert accumulation contribution rate of k pivot is Cum (Λ before in the existing model of definition _Kk), promptly before k reservation eigenwert add up and account for that all eigenwerts add up and ratio be Cum (Λ _Kk).Because new model only adjusts the eigenwert of a preceding k pivot, thus the eigenwert of preceding k pivot of note new model accumulate contribution rate be Cum (Λ ' _Kk), then new eigenvalue matrix Λ ' _KkEach diagonal line on element should be adjusted into:

Λ′ _i，i＝Λ′ _i，i×Cum(Λ)/Cum(Λ′)

In the formula, Λ ' _{I, i}Represent new eigenvalue matrix Λ ' _Kk(i, i) individual element.

Through above adjustment; The ratio in principal component space and residual error space will remain unchanged basically; Under the constant prerequisite of physical interconnection property, the SPE of new model control limit

need not to upgrade adjustment and also can satisfy monitoring requirement in most cases.Therefore, the SPE of new model control limit

On the other hand, the T of new PCA monitoring model ²The control limit

Can adopt traditional algorithm to calculate, for example can utilize F to distribute and calculate, formula is:

$T_a^{2\&prime;}=\frac{k({(N+m)}^2-1)}{(N+m)(N+m-k)}{F}_{k,N+m-k;\mathrm{\&alpha;}}$

Wherein, the pivot number of k for keeping, N is the training sample sum that initial MBM is collected, m is the current total sample number that collects at monitor stages, F _{K, N+m-k; α}Be to be α corresponding to level of significance, degree of freedom is k, the F distribution critical value under the N+m-k condition, and can table look-up obtains.Obviously, the present invention only need upgrade sample number that monitor stages collects in time to obtain the T of new PCA monitoring model ²The control limit

This module is with the new feature value matrix Λ ' that calculates _KkAnd T ²The control limit

Store, accomplished the update all work of new model, complete new model

Export, be used for the on-line monitoring and the fault diagnosis of industrial process.

Enumerating a specific embodiment below is described in detail application of the present invention.

This instance adopts one group of actual production data of northern Microtronic A/S plasma etching system as implementing sample.This experimental data comprises 339 samples, and the sample dimension is 16 dimensions, has contained the engineering variable of 16 non-setting values of reflection system normal variation characteristic, and all samples are normal sample originally, do not have fault sample.Owing to reasons such as equipment dust stratifications, experimental data has comparatively significantly data drift phenomenon.Adopt the monitored results of conventional P CA monitoring model on this data set as shown in Figure 3, modeling sample is preceding 100 groups of samples.Horizontal ordinate is sample sequence number (1～339) among the figure, arranges in strict accordance with the processing sequence of sample (wafer).Ordinate is represented the monitoring numerical value of each statistic, and solid line (figure medium blue colo(u)r streak) is the control limit of each statistic, and circle (red circle among the figure) is represented the actual count amount monitored value of each sample.In the ordinary course of things, if the circle of certain sample is positioned at (SPE or T more than the control limit in any control chart ²Statistic exceeds the control limit), then system should send warning.Observation can know that in whole monitor procedure, monitoring error constantly increases, and the SPE statistic exceeds control limit gradually, and false alarm rate is up to 64.02%, the monitoring model drift failure.

Use above-mentioned real data that the method among the present invention is carried out emulation, concrete simulation process and experimental result are following:

(1) sets SPE and T ²The level of significance of statistic control limit is 95%, specifies forgeing in the undated parameter

The factor is λ=0.95, and delta threshold is η=0.5.

(2) call 21 pairs of conventional P CA MBMs before 100 groups of samples carry out initial modeling, read all remaining normal samples successively and carry out the model online updating as the real-time process data.The monitoring model of model online updating system output is used to carry out on-line monitoring.

(3) provide that method comprises SPE control chart and T to the monitored results of all samples among the present invention ²Control chart,

(identical among mark implication and Fig. 3 among the figure) as shown in Figure 4.At whole monitor stages, the false alarm rate of method is merely 27.62% among the present invention, and monitoring effect is better.

Can know by embodiment, adopt the present invention to carry out the monitoring model that the model online updating obtains, have lower false alarm rate, the slow drift phenomenon of process variable that occurs easily in most of industrial processs is had robustness.

Above-mentioned each embodiment only is used to explain the present invention, and wherein the structure of each parts, connected mode etc. all can change to some extent, and every equivalents of on the basis of technical scheme of the present invention, carrying out and improvement all should not got rid of outside protection scope of the present invention.

Claims (3)

1. the online updating method of a pivot analysis monitoring model, it may further comprise the steps:

1) industry spot be provided with one comprise data acquisition equipment and supervisory control comuter model online updating system; Preset a conventional P CA MBM in the said supervisory control comuter, a mean variance update module, a subpoint computing module, a residual error determination module, a principal component space adjusting module, a pivot directional trim module and a control limit update module;

2) before the system start-up of model online updating; Data acquisition equipment is collected and can be represented the historical production data of production run characteristic to input to the conventional P CA MBM in the supervisory control comuter as training sample x; Set up the initial monitoring model Ω of PCA, and send the initial monitoring model of PCA to the mean variance update module;

The initial monitoring model Ω of PCA is:

$\mathrm{\&Omega;}=(\stackrel{\&OverBar;}{x},\mathrm{\&sigma;},P_{\mathrm{nk}},{\mathrm{\&Lambda;}}_{\mathrm{kk}},N,{\mathrm{\&delta;}}_{\mathrm{\&alpha;}}^2,T_{\mathrm{\&alpha;}}^2)$

In the formula, $\stackrel{\&OverBar;}{x}={\mathrm{\&Sigma;}}_{i=1}^N{x}_i/N$ The representation model average; $\mathrm{\&sigma;}=\sqrt{{\mathrm{\&Sigma;}}_{i=1}^N{(x_i-\stackrel{\&OverBar;}{x})}^2/(N-1)}$ The expression standard deviation; P _NkThe representation feature value is decomposed the pairing load vector of k maximum pivot score of back, i.e. pivot projection vector; Λ _KkThe representation feature value matrix, its diagonal element is made up of k pivot score of maximum; N representes the training sample number chosen;

The control limit of expression SPE statistic under level of significance α;

Expression T ²The control limit of statistic under level of significance α; x _iRepresent i training sample (i=1 ..., N); K representes the pivot number that keeps; N representes the dimension of process variable;

3) data acquisition equipment converts the real-time process variable in the industrial processes into real-time process data x _N+m, send the mean variance update module to; Simultaneously, model online updating system also sends required undated parameter to the mean variance update module; And the existing PCA monitoring model in the mean variance update module does

The mean variance update module is according to real-time process data x _N+mAnd undated parameter, calculate the PCA monitoring model that makes new advances

In the model average

And standard deviation sigma ', result of calculation is stored, and will have the PCA monitoring model now and correlation parameter sends the subpoint computing module to;

4) the subpoint computing module calculates real-time process data x _N+mThe coordinate of subpoint g on principal component space, and real-time process data x _N+mTo the distance of subpoint g, i.e. residual vector h, and send result of calculation, existing PCA monitoring model and correlation parameter to the residual error determination module, be used for the pivot projecting direction being adjusted at subsequent step;

Concrete computing formula is following:

$g=P_{\mathrm{nk}}^T(x_{N+m}-{\stackrel{\&OverBar;}{x}}^{\&prime;}){\mathrm{\&Sigma;}}_{N+m}^{-1}$

$h=(x_{N+m}-{\stackrel{\&OverBar;}{x}}^{\&prime;}){\mathrm{\&Sigma;}}_{N+m}^{-1}-P_{\mathrm{nk}}g$

Wherein, ∑ _N+m=diag (σ ') is that the standard deviation vector σ ' of model is the diagonal matrix of diagonal element to upgrade afterwards;

5) the residual error determination module calls any model projection direction update method according to the size decision of the mould of the residual vector of subpoint: if residual values is bigger, then call the principal component space adjusting module, get into step 6); If residual values is less, then call pivot directional trim module, get into step 7); The principal component space adjusting module is identical with the output form of pivot directional trim module, is pivot projection vector and the eigenvalue matrix of upgrading the back model;

The size of mould and the delta threshold η of residual error determination module through residual vector h is relatively selected the update method of current sample:

1. when the mould of residual error h is big; Promptly || h||＞η; Send existing pca model of the residual vector of optimizing

and correlation parameter to the principal component space adjusting module; Get into step 6), whole principal component space is adjusted calculating;

2. when the mould of residual error h hour, promptly || h||＜η, send former data, existing pca model and correlation parameter to pivot directional trim module, get into step 7), carry out the fine setting of pivot projecting direction and calculate;

6) the principal component space adjusting module is based on the constant thought of process variable correlativity essence; Utilize pca method that the pivot projection vector of expansion is carried out dimensionality reduction; Thereby when keeping the pivot number constant, existing pivot projecting direction is upgraded, obtain the load vector P ' of new model _NkWith eigenvalue matrix Λ ' _Kk

Eigenvalue matrix Λ ' _KkSolution formula be:

$(\mathrm{\&mu;}\left[\begin{array}{cc}{\mathrm{\&Lambda;}}_{\mathrm{kk}}& \underset{\&OverBar;}{0}\\ {\underset{\&OverBar;}{0}}^T& 0\end{array}\right]+(1-\mathrm{\&mu;})\left[\begin{array}{cc}{\mathrm{qq}}^T& \mathrm{\&rho;q}\\ {\mathrm{\&rho;q}}^T& {\mathrm{\&rho;}}^2\end{array}\right])\&ap;{\mathrm{R\&Lambda;}}_{\mathrm{kk}}^{\&prime;}{R}^T$

In the formula, $\mathrm{\&rho;}={\hat{h}}^T\left[{\mathrm{\&Sigma;}}_{N+m}^{-1}(x_{N+m}-\stackrel{\&OverBar;}{x})\right],$ $q=P_{\mathrm{Nk}}^T\left[{\mathrm{\&Sigma;}}_{N+m}^{-1}(x_{N+m}-\stackrel{\&OverBar;}{x})\right],$ R representes rotation matrix, and the matrix in the levoform is carried out characteristic value decomposition, and k maximum eigenwert constituted the eigenvalue matrix Λ ' after upgrading _Kk, its characteristic of correspondence value vector is exactly rotation matrix R;

Because the vectorial P of existing load _NkIn each column vector and residual vector h orthogonal, constitute the pivot projection vector of expansion, then the load of new model vector P ' _NkBe the linear combination of the pivot projection vector of expansion; With the rotation matrix R substitution in the following formula, obtain the load vector P ' of new model _NkComputing formula be:

$P_{\mathrm{nk}}^{\&prime;}=[P_{\mathrm{nk}},\hat{h}]R$

This module is with the pivot projection vector P ' of the new model that calculates _NkStore, and with eigenvalue matrix Λ ' _KkAnd correlation parameter is sent to control limit update module, gets into step 8), continues to accomplish to the adjustment of pivot score and to the renewal work of control limit;

7) pivot directional trim module is same utilizes result that existing pca model and step before obtain to the vectorial P ' of the load of new model _NkWith eigenvalue matrix Λ ' _KkCalculate; Owing to just the pivot projecting direction is finely tuned, only need carry out pivot analysis again in principal component space inside, the pivot projecting direction after promptly obtaining upgrading in principal component space inside;

Eigenvalue matrix Λ ' _KkSolution formula be:

(λΛ _kk+(1-λ)qq ^T)≈RΛ′ _kkR ^T

Matrix in the levoform is carried out characteristic value decomposition, and all k eigenwert has constituted the eigenvalue matrix Λ ' after upgrading _Kk, its characteristic of correspondence value vector is exactly rotation matrix R; The pivot projection vector P ' of new model _NkBe by existing pivot projection vector P _NkIn the new linear combination that column vector constituted, calculate by following formula:

P′ _nk＝P _nkR

This module is with the pivot projection vector P ' of the new model that calculates _NkStore, and with eigenvalue matrix Λ ' _KkAnd correlation parameter is sent to control limit update module, gets into step 8), continues to accomplish to the adjustment of pivot score and to the renewal work of control limit;

8) control limit update module based on the result of calculation of front to the eigenvalue matrix Λ ' after upgrading _KkStandardize, thereby accomplish control limit Model Monitoring statistic index With Renewal, the new model after finally being upgraded fully; Control limit update module is stored the aforementioned calculation result, with the new model after the renewal fully that finally obtains

Export, be used for the on-line monitoring and the fault diagnosis of industrial process;

To the eigenvalue matrix Λ ' after upgrading _KkCarrying out normalized method is: the eigenwert accumulation contribution rate of k pivot is Cum (Λ before in the existing model of definition _Kk), promptly before k reservation eigenwert add up and account for that all eigenwerts add up and ratio be Cum (Λ _Kk); Because new model only adjusts the eigenwert of a preceding k pivot, thus the eigenwert of preceding k pivot of note new model accumulate contribution rate be Cum (Λ ' _Kk), then new eigenvalue matrix Λ ' _KkEach diagonal line on element should be adjusted into:

Λ′ _i，j＝Λ′ _i，i×Cum(Λ)/Cum(Λ′)

In the formula, Λ ' _{I, i}Represent new eigenvalue matrix Λ ' _Kk(i, i) individual element; Through above adjustment, under the constant prerequisite of physical interconnection property, the SPE control limit of new model

Need not to upgrade adjustment and also can satisfy monitoring requirement in most cases; Therefore, the SPE of new model control limit

${\mathrm{\&delta;}}_{\mathrm{\&alpha;}}^{2^{\&prime;}}={\mathrm{\&delta;}}_{\mathrm{\&alpha;}}^2.$

2. the online updating method of a kind of pivot analysis monitoring model as claimed in claim 1; It is characterized in that: in the said step 3), model average of new PCA monitoring model

and standard deviation sigma ' more new formula following:

${\stackrel{\&OverBar;}{x}}^{\&prime;}=\mathrm{\&lambda;}\stackrel{\&OverBar;}{x}+(1-\mathrm{\&lambda;})x_{N+m}$

${\mathrm{\&sigma;}}^{\&prime;}=\sqrt{{\mathrm{\&lambda;\&sigma;}}^2+(1-\mathrm{\&lambda;}){(x_{N+m}-\stackrel{\&OverBar;}{x})}^2}$

In the formula, x _N+mBe illustrated in the real-time process data of m the real-time process variable that collects in the actual monitored process; M=1,2,3 In the definition monitor procedure, the existing PCA monitoring model in the mean variance update module does

When monitoring during first real-time process variable, promptly during m=1, the existing PCA monitoring model in the mean variance update module is exactly the initial monitoring model that conventional P CA MBM provides

λ is a forgetting factor, belongs to undated parameter, and its span is (0,1); Delta threshold η also belongs to undated parameter, and span is (0, δ α).

3. according to claim 1 or claim 2 a kind of online updating method of pivot analysis monitoring model is characterized in that: in the said step 8), and the T of new PCA monitoring model ²The control limit

Adopt F to distribute and calculate, formula is:

$T_a^{2\&prime;}=\frac{k({(N+m)}^2-1)}{(N+m)(N+m-k)}{F}_{k,N+m-k;\mathrm{\&alpha;}}$

Wherein, the pivot number of k for keeping, N is the training sample sum that initial MBM is collected, m is the current total sample number that collects at monitor stages, F _{K, N+m-k; α}Corresponding to insolation level is α, and degree of freedom is k, and the F distribution critical value under the N+m-k condition obtains through tabling look-up, and therefore, the numerical value of the number of training N that only need upgrade in time promptly obtains the T of new PCA monitoring model ²The control limit

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