CN103488091A - Data-driving control process monitoring method based on dynamic component analysis - Google Patents

Abstract

The invention provides a data-driving control process monitoring method based on dynamic component analysis. The method comprises the steps of (1) establishing ICA and DICA process statistics models according to multiple detection variables obtained from continuous detection, and defining statistics I2 relevant to independent variables belonging to non-Gaussian distribution in measured variables according to the DICA process statistics model; (2) establishing PCA and DPCA process statistics models for a process information matrix E left over after non-Gaussian distribution measured variable extraction, and defining statistics T2 and SPE of the detected variables in pivot element space and residual space; (3) obtaining similarity indexes ISM to serve as monitoring indexes through training by means of the support vector data description algorithm which is input by the performance indexes Lambda = (I2, T2, SPE); (4) comparing actual monitoring indexes ISM with IMAX and getting the conclusion that faults appear in the current control process if ISM>IMAX. According to the data-driving control process monitoring method based on dynamic component analysis, the number of monitoring diagrams can be reduced, and monitoring efficiency can be improved. The data-driving control process monitoring method based on dynamic component analysis can be widely used for multivariable control system monitoring such as industrial process control.

Description

A kind of control procedure method for supervising of analyzing based on dynamic element of data-driven

Technical field

The present invention relates to the control system technical field, be in particular the technical field that relates to the control system monitoring, be specially a kind of control procedure method for supervising of analyzing based on dynamic element of data-driven.

Background technology

Nowadays industrial processes scale is day by day huge, especially for most chemistry and biological factory, in order to improve product yield, guarantee product quality, guarantee factory safety simultaneously, production run is carried out to on-line monitoring, provide control procedure information timely and effectively just to seem particularly important.At present, the control procedure method for supervising is mainly method based on mathematical model and the method for data-driven.Owing to there being various unknown disturbances in actual production process, be difficult to obtain accurate mathematical model, the method for supervising based on mathematical model is subject to restriction to a certain extent.On the other hand, the method of data-driven does not need the accurate mathematical model of control procedure, directly utilize on-the-spot image data to set up statistical model, extracted valid data information and then control procedure is carried out to Supervision and Evaluation, can be applied to fast, in practice, has become one of process monitoring area research focus.In the method for data-driven, multivariate statistics process control (multivariate statistical process control, MSPC) be subject to the extensive attention of academia and industry member as a kind of process performance based on multivariate statistical projection method theory monitoring and fault diagnosis technology, and beginning is applied in process of production.But in MSPC, usually suppose the complete Gaussian distributed of control procedure measurand or obey non-Gaussian distribution fully, yet in fact, most industry process variable composition is more complicated all generally, except mixing various noises, often comprise Gaussian-distributed variable and non-Gaussian-distributed variable, this makes traditional MSPC be subject in actual applications restriction to a certain extent simultaneously.

Through the retrieval of the open source literature to prior art, find, Z.Q.Ge, Z.H.Song.Process monitoring based on independent component analysis-principle component analysis (ICA-PCA) and Similarity Factors[J] .Industrial and Engineering Chemistry Research, 2007, 46 (7): 2054-2063.(course monitoring method based on ICA-PCA and similar factor, International Periodicals: industry and engineering chemistry research periodical, 2007, 46 (7): 2054-2063), the author proposes a kind of based on the ICA-PCA method for supervising, the method combines ICA and PCA, the non-Gaussian distribution of leaching process control survey variable and Gaussian distribution information, choosing respectively statistic is monitored, reached the purpose that the non-Gaussian-distributed variable of process and Gaussian-distributed variable are monitored simultaneously, but the author does not consider the dynamic perfromance of control procedure, if the dynamic change of control procedure is considered in model, and adopt unified statistical variable to be monitored, can reach more excellent monitoring effect.

Summary of the invention

The shortcoming of prior art in view of the above, the object of the present invention is to provide a kind of control procedure method for supervising of analyzing based on dynamic element of data-driven, the variable that simultaneously contains Gaussian distribution and non-Gaussian distribution for the most industry process, under the prerequisite of taking into account system dynamic behaviour, ICA is combined with PCA, a kind of course monitoring method based on DICA-DPCA is proposed, and adopt the algorithm based on Support Vector data description to be monitored, to improve the monitoring accuracy rate and to enlarge the scope of application.

Reach for achieving the above object other relevant purposes, the invention provides a kind of control procedure method for supervising of analyzing based on dynamic element of data-driven, comprise the following steps:

1) set up ICA process statistics model: X=A * S+E according to a plurality of detection variable of continuous detecting; X ∈ R ^{n * m}for sample matrix, S ∈ R ^{r * m}for extracted process independent component matrix, A ∈ R ^{n * r}for unknown hybrid matrix; N is the process sample number, and m is the detection variable number, and r is extracted non-Gauss's independent component variable number; E is residual matrix; X in ICA process statistics model is used replace, obtain DICA process statistics model; K means k constantly, and l is Delay Parameters, and l ∈ 1,2,3; Statistic I by DICA process statistics model definition detection variable in principal component space and residual error space ², wherein,

for belonging to the independent variable of non-Gaussian distribution in detection variable;

2) for procedural information matrix E remaining after non-gaussian distribution characteristic signal extraction, the statistical model of setting up the PCA process is:

wherein, t _k∈ R ^m(k ∈ 1,2 ... n}) be the score vector of principal component space, p _k∈ R ^m(k ∈ 1,2 ... n}) be principal component space load vector; N is the process sample number, and m is the observational variable number, and k is the pivot number; E ' is the residual error space matrix; E in PCA process statistics model is used

replace, obtain DPCA process statistics model; K means k constantly, and l is Delay Parameters, l ∈ 1,2; The definition detection variable is in the statistic T in principal component space and residual error space ²and SPE,

the estimate covariance matrix that Λ is the principal component space score matrix;

3) adopt the algorithm of Support Vector data description, with performance index λ=(I ², T ², SPE) the input algorithm, obtain similar index I through training _sMas monitoring index,

r is the super spheroid radius of gained after the SVDD training; Wherein, $D^2\left(\mathrm{\Φ}\left(\mathrm{\λ}\right)\right)=K(\mathrm{\λ},\mathrm{\λ})-2\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K({\mathrm{\λ}}_i,\mathrm{\λ})+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_{j}K({\mathrm{\λ}}_i,{\mathrm{\λ}}_j);$ In above formula: α _i, α _jfor Lagrange multiplier, the function that Φ (λ) is feature λ, K is that kernel function changes, and meets K (λ _i, λ _j)=Φ (λ _i) * Φ (λ _j); Determine monitoring index I _sMcontrol limit I _mAX, by I _mAXas performance reference;

4) by actual monitoring index I _sMwith I _mAXrelatively, if I _sM>I _mAX, illustrate that fluctuation has appearred in current control procedure.

Preferably, in step 1), the definition detection variable is at the statistic I in principal component space and residual error space ²process also comprise: right carry out Independent component analysis and obtain split-matrix W, and W is continued to be decomposed into W _dand W _e; Build the independent variable that belongs to non-Gaussian distribution in measurand

${\hat{S}}_d\left(k\right)=W_d\×\stackrel{-}{X}\left(k\right).$

Preferably, W, W _dand W _eacquisition process as follows: split-matrix W=A ^-1; Right

while carrying out the DICA analysis, it is bleached, had

albefaction matrix Q=Λ wherein ^-1/2u ^t, Λ is by covariance matrix

the diagonal matrix that forms of eigenwert, U is the matrix that corresponding proper vector forms; $Z\left(k\right)=Q\stackrel{-}{X}\left(k\right)=\mathrm{QAS}\left(k\right)=\mathrm{BS}\left(k\right),$ $\hat{S}\left(k\right)=B^{T}Z\left(k\right)=B^{T}Q\stackrel{-}{X}\left(k\right),$ W=B ^tq; Based on square coefficient with on the principle of vectorial independent component impact, the d row of choosing the W matrix form matrix W _d, residual matrix is W from group _e.

Preferably, in step 2) in, in identical average and variance situation, the measurand of Gaussian distributed has maximum differential entropy, by the size that compares differential entropy, carries out the extraction of the non-gaussian distribution characteristic signal of process.

Preferably, the method for employing negentropy is extracted the characteristic variable of non-Gaussian distribution.

Preferably, in step 2) in, for the vector of samples x of any time _new, it is decomposed into to two parts by following formula:

$x_{\mathrm{new}}={\stackrel{-}{x}}_{\mathrm{new}}+e_{\mathrm{new}}=t_{\mathrm{new}}{P}^T+e_{\mathrm{new}}=x_{\mathrm{new}}{\mathrm{PP}}^T+e_{\mathrm{new}};$ Wherein, x _newthe row vector of the measurand that comprises n Gaussian distributed, and e _newbe respectively x _newpredicted value in principal component space and the error space; t _new=x _new* P, P is the principal component space matrix of loadings.

Preferably, in step 3), the algorithm of support vector data model specifically comprises: the distributed areas that obtain data by calculating the minimal hyper-sphere border that comprises the target class mapping (enum) data in higher dimensional space, thereby realize target class and all non-target classes are separated, with an as far as possible little suprasphere of radius, training sample is described for data field; If be that X is the sample matrix of a m * n, wherein each is listed as a corresponding measurand, and the corresponding collecting sample of a line, by kernel function K (x _i, x _j)=(Φ (x _i) * Φ (x _j)) mapping, the data-mapping in original sample space to feature space; The arthmetic statement of support vector data model is as follows: s.t.|| Φ (x _i)-a|| ²≤ r ²+ ξ _i, ξ _i>=0; Wherein, ξ _ithe>=0th, slack variable; C is penalty coefficient, by formula C=1 (fN), is calculated, and f is that the user defines for meaning that training data exceeds the parameter of the part of determining area, and N is the training data number; A is the center of suprasphere in feature space; r ²the distance of the suprasphere centre of sphere to border; Introduce Lagrange factor α _i, can further describe into:

$\underset{a_{\text{i}}}{\min }\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K(x_i,x_j)-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_{j}K(x_i,x_j);s.t.0\≤a_i\≤C,\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i=1;$

Above-mentioned formula is solved, for x _newif meet D ²(Φ (x _new))≤r ²think that control procedure is normal; Wherein, $D^2\left(\mathrm{\Φ}\left(x_{\mathrm{new}}\right)\right)=K(x_{\mathrm{new}},x_{\mathrm{new}})-2\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K(x_i,x_{\mathrm{new}})+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_{j}K(x_i,x_j).$

As mentioned above, the control procedure method for supervising of analyzing based on dynamic element of a kind of data-driven of the present invention has following beneficial effect:

The present invention can realize the performance monitoring of the control system to contain Gaussian distribution and non-Gaussian-distributed variable simultaneously, thereby improved the broad applicability of policing algorithm, in addition, the present invention adopts and obtains similar index I based on holding vector data description (SVDD) Algorithm for Training _sMreplace performance index in the past, reduced monitoring figure, improved monitoring efficiency.Institute of the present invention extracting method is applicable to the multivariable control system monitoring such as industrial process control.

The accompanying drawing explanation

Fig. 1 is shown as the process flow diagram of the control procedure method for supervising of analyzing based on dynamic element of a kind of data-driven of the present invention.

Fig. 2 is shown as Nahsi-Yi Siman process schematic diagram.

Fig. 3 is shown as the monitoring effect figure based on PCA.

Fig. 4 is shown as the monitoring effect figure based on ICA.

Fig. 5 is shown as the monitoring effect figure based on ICA-PCA.

Fig. 6 is shown as this monitoring effect figure based on DPCA.

Fig. 7 is shown as the monitoring effect figure based on DICA.

Fig. 8 is shown as the monitoring effect figure based on DICA-DPCA in the control procedure method for supervising of analyzing based on dynamic element of a kind of data-driven of the present invention.

Embodiment

Below, by specific instantiation explanation embodiments of the present invention, those skilled in the art can understand other advantages of the present invention and effect easily by the disclosed content of this instructions.The present invention can also be implemented or be applied by other different embodiment, and the every details in this instructions also can be based on different viewpoints and application, carries out various modifications or change not deviating under spirit of the present invention.

The present invention is achieved by the following technical solutions, the present invention gathers the measurand data under industrial processes works fine situation, under the prerequisite of taking into account system dynamic behaviour, first adopt Independent Component Analysis (ICA) to extract characteristic signal the structural behavior index of non-Gaussian distribution from procedural information, and then the process variable of extracting the polynary Gaussian distribution of obedience remaining after non-gaussian distribution characteristic variable is carried out to pivot analysis (PCA) to extract pivot structural behavior index, finally utilize the algorithm implementation procedure monitoring of Support Vector data description (SVDD).The method is specifically wrapped the foundation of DICA-DPCA model, the foundation of Support Vector data description model (SVDD), the performance monitoring based on the SVDD algorithm, wherein the coupling system dynamic change proposes the DICA-DPCA method, and it is innovation of the present invention that employing is carried out performance monitoring based on the SVDD algorithm.

The DICA-DPCA model is set up: the data under acquisition system works fine situation are set up the DICA-DPCA model, calculate its performance index I ², T ², SPE and corresponding performance reference.The foundation of Support Vector data description model (SVDD): adopt the SVDD algorithm, with performance index λ=(I ², T ², SPE), as the input algorithm, through training, obtain similar index I _sM, as monitoring index, and the method for estimating by the guiding figure place is calculated this index control limit I _mAX, as performance reference.Performance monitoring based on the SVDD algorithm: gather the measurand data under the control procedure practical working situation, calculate actual similar index I _sM, and by itself and performance reference to recently judging system operation situation.

Refer to Fig. 1, be shown as the process flow diagram of the control procedure method for supervising of analyzing based on dynamic element of a kind of data-driven of the present invention.As shown in Figure 1, method of the present invention specifically comprises the following steps:

S1, set up ICA and DICA process statistics model according to a plurality of detection variable of continuous detecting; The statistic I relevant to the independent variable that belongs to non-Gaussian distribution in measurand by DICA process statistics model definition ².

Be specially, according to a plurality of detection variable of continuous detecting, set up ICA process statistics model: X=A * S+E; X ∈ R ^{n * m}for sample matrix, S ∈ R ^{r * m}for extracted process independent component matrix, A ∈ R ^{n * r}for unknown hybrid matrix; N is the process sample number, and m is the detection variable number, and r is extracted non-Gauss's independent component variable number; E is residual matrix; X in ICA process statistics model is used

replace, obtain DICA process statistics model; K means k constantly, and l is Delay Parameters, and l ∈ 1,2,3; Statistic I by DICA process statistics model definition detection variable in principal component space and residual error space ², wherein,

for belonging to the independent variable of non-Gaussian distribution in detection variable.

S2, the procedural information matrix E for remaining after non-gaussian distribution characteristic signal extraction, set up PCA and DPCA process statistics model, and the definition detection variable is in the statistic T in principal component space and residual error space ²and SPE.

Be specially, for procedural information matrix E remaining after non-gaussian distribution characteristic signal extraction, the statistical model of setting up the PCA process is:

wherein, t _k∈ R ^m(k ∈ 1,2 ... n}) be the score vector of principal component space, p _k∈ R ^m(k ∈ 1,2 ... n}) be principal component space load vector; N is the process sample number, and m is the observational variable number, and k is the pivot number; E ' is the residual error space matrix; E in PCA process statistics model is used replace, obtain DPCA process statistics model; K means k constantly, and l is Delay Parameters, l ∈ 1,2; The definition detection variable is in the statistic T in principal component space and residual error space ²and SPE,

the estimate covariance matrix that Λ is the principal component space score matrix;

S3, the algorithm of employing Support Vector data description, with performance index λ=(I ², T ², SPE) the input algorithm, obtain similar index as monitoring index through training.

Be specially, adopt the algorithm of Support Vector data description, with performance index λ=(I ², T ², SPE) the input algorithm, obtain similar index I through training _sMas monitoring index,

r is the super spheroid radius of gained after the SVDD training; Wherein, $D^2\left(\mathrm{\Φ}\left(\mathrm{\λ}\right)\right)=K(\mathrm{\λ},\mathrm{\λ})-2\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K({\mathrm{\λ}}_i,\mathrm{\λ})+\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_{j}K({\mathrm{\λ}}_i,{\mathrm{\λ}}_j);$ In above formula: α _i, α _jfor Lagrange multiplier, the function that Φ (λ) is feature λ, K is that kernel function changes, and meets K (λ _i, λ _j)=Φ (λ _i) * Φ (λ _j); Determine monitoring index I _sMcontrol limit I _mAX, by I _mAXas performance reference;

S4, by actual monitoring index I _sMwith I _mAXrelatively, if I _sM>I _mAX, illustrate that fluctuation has appearred in current control procedure.

Below specific implementation of the present invention is described.

1) foundation of DICA statistical model

Independent component analysis (ICA) is a kind of statistic algorithm that extracts the data centralization independent component, is mainly used in the process variable of non-Gaussian distribution, and concrete mathematical description is as follows:

Get the process observation signal X of one section nominal situation ^{n * m}, suppose to pass through standardization, set up ICA process statistics model:

X＝A×S+E

Wherein, n is the process sample number, and m is the observational variable number, and r is extracted non-Gauss's independent component variable number, X ∈ R ^{n * m}for sample matrix, S ∈ R ^{r * m}for extracted process independent component matrix, A ∈ R ^{n * r}for unknown hybrid matrix.Therefore, separate hybrid matrix W=A if try to achieve ^-1, just can utilize formula

decompose the independent variable that obtains in measurand belonging to non-Gaussian distribution.Due in identical average and variance situation, the variable of Gaussian distributed has maximum differential entropy, so can carry out the extraction of the non-gaussian distribution characteristic signal of process by the size that compares differential entropy, extract in the present invention the characteristic variable of non-Gaussian distribution with regard to the method that adopts negentropy.

Further, we are decomposed into W with the SCREE test by matrix W _dand W _e, matrix A is decomposed into to A _dand A _e.Then choose statistic I ²,

the SPE(squared prediction error), as performance index, monitored parameters is in the variation in principal component space and residual error space, to obtain the real-time information of whole process operation situation.I ²,

sPE is defined as follows respectively:

${\mathrm{<figure-callout\; id="2"\; label="I"\; filenames="HDA0000388941990000011.png"\; state="\{\{state\}\}">I</figure-callout>}}^2={\hat{S}}_d{\left(k\right)}^T\&times;{\hat{S}}_d\left(k\right);$

${\mathrm{<figure-callout\; id="2"\; label="I\; e"\; filenames="HDA0000388941990000011.png"\; state="\{\{state\}\}">I</figure-callout>}}_e^{}={\hat{S}}_e{\left(k\right)}^T\&times;{\hat{S}}_e\left(k\right);$

$\mathrm{SPE}\left(k\right)={(x\left(k\right)-\hat{x}\left(k\right))}^T\&times;(x\left(k\right)-\hat{x}\left(k\right));$

Wherein,

adopt Density Estimator (KDE) method to try to achieve the control limit of above performance index, as performance reference.

With ICA, compare, the DICA model has been considered the dynamic perfromance of control procedure, increases l the moment in past measured value of measurand and obtains being augmented matrix, is about to X (k) and is rewritten as

so just successfully built an autoregressive model with the outside input, according to priori, l ∈ 1,2,3 has been arranged.

2) foundation of DPCA statistical model

Pivot analysis (PCA) is as a kind of polytomy variable statistical method, its main thought is, by linear transformation, a plurality of relevant original variable of process is converted into to incoherent pivot variable, makes these pivot variablees can reflect as much as possible the model information that original correlated variables provides simultaneously.PCA is a kind of Data Dimensionality Reduction Algorithm, is mainly used in the variable of Gaussian distribution, and concrete mathematical description is as follows:

Get the process observation signal X of one section nominal situation ^{m * n}, suppose to pass through standardization, through pivot analysis, set up PCA process statistics model, X is written as to following form:

$X=\underset{i=1}{\overset{k<n}{\mathrm{\&Sigma;}}}{t}_k\&times;p_k^T+E$

Wherein, n is the process sample number, and m is the observational variable number, t _k∈ R ^m(k ∈ 1,2 ... n}) be separate artificial variables, be called the score vector of principal component space; p _k∈ R ^m(k ∈ 1,2 ... n}) be the proper vector of principal component space covariance matrix, be called principal component space load vector; K is the pivot number.

Vector of samples x for any time _new, it is decomposed into to two parts by following formula:

$x_{\mathrm{new}}={\stackrel{-}{x}}_{\mathrm{new}}+e_{\mathrm{new}}=t_{\mathrm{new}}{P}^T+e_{\mathrm{new}}=x_{\mathrm{new}}{\mathrm{PP}}^T+e_{\mathrm{new}}$

Wherein, x _newthe row vector of the measurand that comprises n Gaussian distributed,

and e _newbe respectively x _newpredicted value in principal component space and the error space.Choose statistic T ²with SPE, as performance index, monitored parameters is in the variation in pivot and residual error space, to obtain the real-time information of whole process operation situation.T ²with SPE, be defined as follows respectively:

${\mathrm{<figure-callout\; id="2"\; label="T"\; filenames="HDA0000388941990000011.png"\; state="\{\{state\}\}">T</figure-callout>}}^2=t_{\mathrm{new}}{\mathrm{\&Lambda;}}^{-1}{t}_{\mathrm{new}}^T;$

$\mathrm{SPE}=e_{\mathrm{new}}\&times;e_{\mathrm{new}}^T;$

Wherein, the estimate covariance matrix that Λ is the principal component space score matrix, t _new=x _new* P.

With PCA, compare, the DPCA model has been considered the dynamic perfromance of system, increases l past measured value constantly of measurand and obtains being augmented matrix, is about to X (k) and is rewritten as so just successfully built an autoregressive model with the outside input, according to priori, l ∈ 1,2 has been arranged.

3) foundation of Support Vector data description (SVDD) model

Support Vector data description (SVDD) combines support vector machine (SVM) and data description method, its main thought is to obtain the distributed areas of data by calculating the minimal hyper-sphere border that comprises the target class mapping (enum) data in higher dimensional space, thereby realizes target class and all non-target classes are separated.The thought with an as far as possible little suprasphere of radius, training sample comprised is wherein described for data field, namely single class classification.Suppose that X is the sample matrix of a m * n, wherein each is listed as a corresponding measurand, and the corresponding collecting sample of a line, by kernel function K (x _i, x _j)=(Φ (x _i) Φ (x _j)) mapping, the data-mapping in original sample space to feature space.The SVDD arthmetic statement is as follows:

$\underset{r,a,\mathrm{\&xi;}}{\min }{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="HDA0000388941990000011.png"\; state="\{\{state\}\}">r</figure-callout>}}^2+C\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_i$

s.t.||Φ(x _i)-a|| ²≤r ²+ξ _i,ξ _i≥0

Wherein, ξ _ithe>=0th, slack variable; C is penalty coefficient, for controlling minimum of surrounding the radius of a ball and wrong branch, trades off, and can be calculated by formula C=1 (fN), and f is user-defined parameter, is used for meaning that training data exceeds the part of determining area, and N is the training data number; A is the center of suprasphere in feature space; r ²the distance of the suprasphere centre of sphere to border.Introduce Lagrange factor α _i, the problems referred to above can further describe into:

$\underset{a_{\text{i}}}{\min }\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{i}K(x_i,x_j)-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_{j}K(x_i,x_j);$

$s.t.0\&le;a_i\&le;C,\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i=1;$

Solve the problems referred to above, for x _newif meet D ²(Φ (x _new))≤r ²think that control procedure is normal.Wherein,

$D^2\left(\mathrm{\&Phi;}\left(x_{\mathrm{new}}\right)\right)=K(x_{\mathrm{new}},x_{\mathrm{new}})-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{i}K(x_i,x_{\mathrm{new}})+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_{j}K(x_i,x_j).$

Method for monitoring performance based on DICA-DPCA proposed by the invention, obtain being augmented matrix by increasing l the moment in past value of measurand, and the method that adopts ICA and PCA to combine is extracted respectively non-Gaussian distribution and Gaussian-distributed variable in measurand, the similar index I of last SVDD study proposition _sM, and the method for estimating by the guiding figure place is calculated this index control limit I _mAX, as performance reference, control procedure is monitored, not only reduce control chart, improve monitoring efficiency, and can process the variable of non-gaussian sum Gaussian distribution simultaneously, very strong practicality is arranged.

For making those skilled in the art further understand method of the present invention, the concrete implementation step of following simple declaration the inventive method.

A, off-line training

Step1, acquisition system be measurand data set X ∈ R under the works fine situation ^{m * n}.

Step2, determine the l value, X (k) is rewritten $\hat{X}\left(k\right)=[X\left(k\right),X(k-1),...,X(k-l)].$

Step3, right

carrying out standardization and bleaching obtains

right carry out Independent component analysis (ICA), obtain split-matrix W, use the SCREE method to obtain Wd and Ad, and then can obtain the independent pivot of reconstruct sum test statistics $I^2\left(k\right)=\hat{S}{\left(k\right)}^T\&times;\hat{S}\left(k\right)(k=\mathrm{1,2},...,m).$

Step4, calculate remaining matrix

it is carried out to pivot analysis (PCA), obtain score matrix and matrix of loadings, compute statistics T ²and SPE.

Step5, utilization SVDD algorithm, with statistic λ=(I ², T ², SPE), as the algorithm input, through training, obtain radius r and similar index

using this index as monitoring index, wherein

$D^2\left(\mathrm{\&Phi;}\left(\mathrm{\&lambda;}\right)\right)=K(\mathrm{\&lambda;},\mathrm{\&lambda;})-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{i}K({\mathrm{\&lambda;}}_i,\mathrm{\&lambda;})+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_{j}K({\mathrm{\&lambda;}}_i,{\mathrm{\&lambda;}}_j).$

Step6, employing guiding figure place method of estimation are determined statistic I _sMcontrol limit I _mAX, as performance reference.

B, on-line evaluation

Step1, obtain system actual measurement variable x _new, determine the l value, vector is expanded and obtained being augmented vector and it is carried out to standardization and bleaching obtains

Step2, the W that utilizes off-line training to obtain _dand A _d, real data is carried out to independent component analysis (ICA), calculate independent pivot ${\hat{S}}_{\mathrm{new}}=W_d^T\&times;{\stackrel{-}{x}}_{\mathrm{new}}\left(k\right)$ Sum test statistics $I_{\mathrm{new}}^2={\hat{s}}_{\mathrm{new}}^T\&times;{\hat{S}}_{\mathrm{new}}.$

Step3, calculate remaining matrix $e_{\mathrm{new}}={\stackrel{-}{x}}_{\mathrm{new}}\left(k\right)-A_d\&times;{\hat{S}}_{\mathrm{new}}.$

Step4, to matrix e _newcarry out pivot analysis (PCA), vectorial t counts the score _new=e _new* P, residual error r _new=e _new-e _new* P * P ^t, statistic $T_{\mathrm{new}}^2=t_{\mathrm{new}}\&CenterDot;{\mathrm{\&Lambda;}}^{-1}\&CenterDot;t_{\mathrm{new}}^T$ With $\mathrm{SPE}=e_{\mathrm{new}}\&times;e_{\mathrm{new}}^T.$

Step5, employing SVDD algorithm obtain actual monitoring index I _sM, by I _sMwith I _mAXrelatively, if I _sM>I _mAX, mean that fluctuation has appearred in active procedure, need further diagnosis and repair.

For the validity of technical scheme of the present invention is described better, below in conjunction with Tennessee-Yi Siman process (TEP), the implementation process of this method is described.As shown in Figure 2, TEP consists of five formants, be respectively: reactor, condenser, compressor, separation vessel and stripping tower, this system has contained the unit operation of transport comprehensively, utilize the data that gather in the TEP process simulation to carry out the validity of more various fault detection methods, be widely used at process control field.Tennessee-Yi Siman process comprises 22 continuous process variablees, 19 component variables and 12 controlled variables.

The method that proposes in the present invention and traditional method are applied to respectively in TEP, analyze relatively.Because 19 component variables are difficult to measure, stirring rate is restive, does not consider in this example, and we choose 22 process continuous variables and 11 controlled variables as research object.Under the system normal operative condition, emulation produces standard data set, introduces fault (random variation of the cooling air inlet temperature of reactor) emulation the 160th sampling instant and produces the fault data collection.Validity for comparative descriptions institute of the present invention extracting method, adopt respectively ICA, PCA, and ICA-PCA, DICA, DPCA, the DICA-DPCA method is carried out emulation experiment to TEP.Parameter designing is l=2, and independent pivot number and pivot number are made as respectively 9 and 15, SVDD parameter f=0.01, confidence level α=0.01.

Based on ICA, PCA, the monitoring effect figure of ICA-PCA as shown in Fig. 3, Fig. 4, Fig. 5, based on DICA, DPCA, the monitoring effect figure of DICA-DPCA is as shown in Fig. 6, Fig. 7, Fig. 8.The Monitoring Performance index is respectively, PCA:T ², SPE, ICA:I ², SPE, ICA-PCA:T ², I ², SPE, DPCA:T ², SPE, DICA:

sPE, DICA-DPCA:I _sM.As shown in Fig. 3～Fig. 8, dotted line is separatrix, and its following part means that control procedure is in good condition, and its above part means that performance index surpass the control limit, and control procedure goes wrong; Fork is illustrated in this and fault constantly detected; Therefore, if the number that the part fork occurs more than dotted line is more, illustrate that monitoring effect is better.By analyzing comparison diagram 3, Fig. 4, Fig. 5, according to, the number that the above part fork of dotted line occurs, we are easy to observe, and the monitoring effect of ICA is better than PCA but both inferior to ICA-PCA; Same methods analyst comparison diagram 3,6, and 4,7, observe DICA and DPCA and be better than respectively ICA and PCA; Comparison diagram 6, Fig. 7, Fig. 8, can be observed DICA-DPCA and be better than DICA and DPCA, so we can reach a conclusion: than above method for supervising, method DICA-DPCA monitoring effect the best that the present invention carries.

In sum, the control procedure method for supervising of analyzing based on dynamic element of a kind of data-driven of the present invention has reached following beneficial effect:

The present invention proposes the DICA-DPCA method, and the method is considered measurand information constantly in the past, and has merged the information of Gaussian distribution of process variable and the information of non-Gaussian distribution, utilizes the method for SVDD to realize performance monitoring.The present invention can realize the monitoring of the control procedure to containing Gaussian distribution and non-Gaussian-distributed variable, there is applicability widely, owing to having considered the measurand information in the moment in the past in algorithm, improved the accuracy of monitoring, in addition, employing is carried out performance monitoring based on the SVDD algorithm, has reduced monitoring figure, has improved monitoring efficiency.This method for supervising is applicable to the performance monitoring of various multivariate industrial process control systems.So the present invention has effectively overcome various shortcoming of the prior art and the tool high industrial utilization.

Above-described embodiment is illustrative principle of the present invention and effect thereof only, but not for limiting the present invention.Any person skilled in the art scholar all can, under spirit of the present invention and category, be modified or be changed above-described embodiment.Therefore, such as in affiliated technical field, have and usually know that the knowledgeable, not breaking away from all equivalence modifications that complete under disclosed spirit and technological thought or changing, must be contained by claim of the present invention.

Claims (7)

1. the control procedure method for supervising of analyzing based on dynamic element of a data-driven, is characterized in that, comprises the following steps:

1) set up ICA process statistics model: X=A * S+E according to a plurality of detection variable of continuous detecting;

X ∈ R ^{n * m}for sample matrix, S ∈ R ^{r * m}for extracted process independent component matrix, A ∈ R ^{n * r}for unknown hybrid matrix; N is the process sample number, and m is the detection variable number, and r is extracted non-Gauss's independent component variable number; E is residual matrix;

X in ICA process statistics model is used

replace, obtain DICA process statistics model; K means k constantly, and l is Delay Parameters, and l ∈ 1,2,3;

Statistic I by DICA process statistics model definition detection variable in principal component space and residual error space ², wherein,

for belonging to the independent variable of non-Gaussian distribution in detection variable;

2) for procedural information matrix E remaining after non-gaussian distribution characteristic signal extraction, the statistical model of setting up the PCA process is: wherein, t _k∈ R ^m(k ∈ 1,2 ... n}) be the score vector of principal component space, p _k∈ R ^m(k ∈ 1,2 ... n}) be principal component space load vector; N is the process sample number, and m is the observational variable number, and k is the pivot number; E ' is the residual error space matrix;

E in PCA process statistics model is used

replace, obtain DPCA process statistics model; K means k constantly, and l is Delay Parameters, l ∈ 1,2;

The definition detection variable is in the statistic T in principal component space and residual error space ²and SPE,

the estimate covariance matrix that Λ is the principal component space score matrix;

3) adopt the algorithm of Support Vector data description, with performance index λ=(I ², T ², SPE) the input algorithm, obtain similar index I through training _sMas monitoring index,

r is the super spheroid radius of gained after the SVDD training;

Wherein, $D^2\left(\mathrm{\&Phi;}\left(\mathrm{\&lambda;}\right)\right)=K(\mathrm{\&lambda;},\mathrm{\&lambda;})-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{i}K({\mathrm{\&lambda;}}_i,\mathrm{\&lambda;})+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_{j}K({\mathrm{\&lambda;}}_i,{\mathrm{\&lambda;}}_j);$

In above formula: α _i, α _jfor Lagrange multiplier, the function that Φ (λ) is feature λ, K is that kernel function changes, and meets K (λ _i, λ _j)=Φ (λ _i) * Φ (λ _j);

Determine monitoring index I _sMcontrol limit I _mAX, by I _mAXas performance reference;

4) by actual monitoring index I _sMwith I _mAXrelatively, if I _sM>I _mAX, illustrate that fluctuation has appearred in current control procedure.

2. the control procedure method for supervising of analyzing based on dynamic element of data-driven according to claim 1, is characterized in that, in step 1), the definition detection variable is at the statistic I in principal component space and residual error space ²process also comprise: right

carry out Independent component analysis and obtain split-matrix W, and W is continued to be decomposed into W _dand W _e; Build the independent variable that belongs to non-Gaussian distribution in measurand

${\hat{S}}_d\left(k\right)=W_d\&times;\stackrel{-}{X}\left(k\right).$

3. the control procedure method for supervising of analyzing based on dynamic element of data-driven according to claim 2, is characterized in that W, W _dand W _eacquisition process as follows:

Split-matrix W=A ^-1; Right

while carrying out the DICA analysis, it is bleached, had

albefaction matrix Q=Λ wherein ^-1/2u ^t, Λ is by covariance matrix

the diagonal matrix that forms of eigenwert, U is the matrix that corresponding proper vector forms;

w=B ^tq; Based on square coefficient with on the principle of vectorial independent component impact, the d row of choosing the W matrix form matrix W _d, residual matrix is W from group _e.

4. the control procedure method for supervising of analyzing based on dynamic element of data-driven according to claim 2, it is characterized in that, in step 2) in, in identical average and variance situation, the measurand of Gaussian distributed has maximum differential entropy, by the size that compares differential entropy, carries out the extraction of the non-gaussian distribution characteristic signal of process.

5. the control procedure method for supervising of analyzing based on dynamic element of data-driven according to claim 4, is characterized in that, the method for employing negentropy is extracted the characteristic variable of non-Gaussian distribution.

6. the control procedure method for supervising of analyzing based on dynamic element of data-driven according to claim 1, is characterized in that, in step 2) in, for the vector of samples x of any time _new, it is decomposed into to two parts by following formula:

$x_{\mathrm{new}}={\stackrel{-}{x}}_{\mathrm{new}}+e_{\mathrm{new}}=t_{\mathrm{new}}{P}^T+e_{\mathrm{new}}=x_{\mathrm{new}}{\mathrm{PP}}^T+e_{\mathrm{new}};$

Wherein, x _newthe row vector of the measurand that comprises n Gaussian distributed,

and e _newbe respectively x _newpredicted value in principal component space and the error space; t _new=x _new* P, P is the principal component space matrix of loadings.

7. the control procedure method for supervising of analyzing based on dynamic element of data-driven according to claim 1, it is characterized in that, in step 3), the algorithm of Support Vector data description specifically comprises: the distributed areas that obtain data by calculating the minimal hyper-sphere border that comprises the target class mapping (enum) data in higher dimensional space, thereby realize target class and all non-target classes are separated, with an as far as possible little suprasphere of radius, training sample is described for data field;

If be that X is the sample matrix of a m * n, wherein each is listed as a corresponding measurand, and the corresponding collecting sample of a line, by kernel function K (x _i, x _j)=(Φ (x _i) * Φ (x _j)) mapping, the data-mapping in original sample space to feature space; The arthmetic statement of support vector data model is as follows:

$\underset{r,a,\mathrm{\&xi;}}{\min }{r}^2+C\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&xi;}}_i;$

s.t.||Φ(x _i)-a|| ²≤r ²+ξ _i,ξ _i≥0；

Wherein, ξ _ithe>=0th, slack variable; C is penalty coefficient, by formula C=1 (fN), is calculated, and f is that the user defines for meaning that training data exceeds the parameter of the part of determining area, and N is the training data number; A is the center of suprasphere in feature space; r ²the distance of the suprasphere centre of sphere to border; Introduce Lagrange factor α _i, can further describe into:

$\underset{a_{\text{i}}}{\min }\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{i}K(x_i,x_j)-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_{j}K(x_i,x_j);$

$s.t.0\&le;a_i\&le;C,\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i=1;$

Above-mentioned formula is solved, for x _newif meet D ²(Φ (x _new))≤r ²think that control procedure is normal; Wherein,

$D^2\left(\mathrm{\&Phi;}\left(x_{\mathrm{new}}\right)\right)=K(x_{\mathrm{new}},x_{\mathrm{new}})-2\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{i}K(x_i,x_{\mathrm{new}})+\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_{j}K(x_i,x_j).$

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