CN101872182A - Batch process monitoring method based on recursive non-linear partial least square - Google Patents

Abstract

The invention relates to a batch process monitoring method based on recursive non-linear partial least squares. The traditional method adopts the fixed statistical model and control limits, and the model can not be updated promptly to track process changes, thereby resulting in failure and errors in reporting. The method comprises the following steps: establishing a batch process monitoring model based on the non-linear partial least squares according to a process database, calculating control limits, and applying the established model to industrial process data collected on-line to monitor a batch process. When a new batch of data is obtained, the model and the control limits are updated in a recursive method so as to adapt to changes of the batch process. The method provided by the invention overcomes the defect of the traditional nonlinear multivariable statistical process monitoring method that the time varying problem can not be dealt with, and the model parameters and control limits can be updated with the new batch of data in order to adapt to changes of the batch process, thereby improving the monitoring performance.

Description

A kind of batch process monitoring method based on recursive non-linear partial least square

Technical field

The invention belongs to areas of information technology, relate to a kind of batch process monitoring method based on recursive non-linear partial least square.

Background technology

Along with the popularization of quick manufacturing technology, be applicable to that the batch process of production short run high value added product more and more comes into one's own.In batch process, a lot of quality index can not on-line measurement, normally after a batch of end, judges last product quality quality according to product sampling analysis value.In order better to control product quality, need set up the process monitoring model to batch process, control operation variable according to on-line measurement is monitored product quality, thereby determine whether production status is normal, can in time take its corresponding measures when unusual service condition occurring, reduce and produce down time, the security of safeguards system and reliability to greatest extent.Along with robotization, computer network and development of database, factory can directly obtain a large amount of real-time running datas from production run.But to from observation data, realize assessment, exceed slip-stick artist or operator's limit of power the process operation situation.Do not rely on the analytic model of object based on the multivariate statistics process monitoring technique of data-driven, and make full use of factory's rich data resource, effectively problems such as big, the data dimension height of deal with data amount, data collinearity are used widely industrial.Batch process has stronger non-linear usually, and as time passes, Properties of Objects and working point all may change.Traditional non-linear multivariate statistics course monitoring method all is to adopt fixing statistical model and control limit, thereby when process feature or operating conditions change, can not in time carry out the variation of model modification tracing process, thereby produce the situation of failing to report and reporting by mistake.Therefore, press for a kind of can the non-linear batch process monitoring method that can handle time variation again of processing procedure.

Summary of the invention

Purpose of the present invention is exactly the weak point at the existing process monitoring technique, and a kind of batch process monitoring method based on recursive non-linear partial least square is provided.This method has remedied the deficiency that traditional non-linear multivariate statistics course monitoring method can not be handled time variation, can utilize new data to upgrade model parameter and control limit, thereby the variation of procedure of adaptation characteristic has improved monitoring performance.

The inventive method adopts means such as data acquisition, process identification, data-driven, at first based on the process monitoring model of process database foundation based on non-linear partial least square, calculation control is limit simultaneously, then the model of setting up is applied to the real-time industrial process data of online acquisition, process is monitored.After obtaining new data, adopt recurrence method that model and control limit are upgraded, thus the variation of the procedure of adaptation.

The concrete steps of the inventive method are:

Step (1) is set up non-linear partial least square (NLPLS) process monitoring model based on process database, simultaneously the calculation control limit.Concrete grammar is:

A. by data collector gatherer process service data,, be used to set up model with the process operation data of gathering sample set as data-driven.In the batch process, each batch process repeatedly repeatability is produced, its data acquisition than the continuous process data acquisition many one dimension " batch " element, have sequential property.Therefore the data acquisition of batch production process is with three-dimensional data formation formula (batch * time * variable) expression, and X (all process datas that the expression of I * J * K) collects, wherein, I represents a batch number, and J represents the sample number, and K represents the process variable number; Quality variable generally obtains by off-line analysis when process finishes, and each batch obtains M quality variable assay value, and I batch quality variable formation matrix Y (I * M).

During modeling, at first with three-dimensional data piece X along time-axis direction cutting batch and variable data piece, each data block is horizontal to the right successively, regards the data of each batch as a data sample, forms a new two-dimensional matrix X (I * JK).Then with matrix X as input matrix, Y is used to set up model as output matrix.Wherein, the data of each batch are to being expressed as { x (i) } and { y (i) }, and x (i) expression is imported data for i batch, and y (i) represents i batch of output data.To import data constitutes input matrix X, output data is constituted output matrix Y;

B. set up the non-linear partial least square model based on inputoutput data, method is:

Matrix X and Y are carried out normalized, and making it average is 0, and variance is 1; Then input matrix is listed as expansion, the expansion item is 1 column vector 1 entirely for the latent node output matrix G of radial basis function (RBF) neural network and element, the output g of the corresponding input vector effect of each row latent node down of G wherein, the bias term coefficient that conceals node is 1; Following augmentation input matrix and output matrix are carried out partial least square (PLS) recurrence:

The NLPLS process monitoring model representation that obtains is for [1 X G], Y}:

$\hat{Y}=\mathrm{XA}+\mathrm{GH}+1b^T=\left[1\mathrm{X\; G}\right]\left[\begin{array}{c}{b}^T\\ A\\ H\end{array}\right]=X_E\mathrm{\β}$

In the formula, X _EExpression augmentation input matrix, A and H are respectively the weights matrix of coefficients of corresponding original input vector and the latent node output vector of corresponding RBF network, and b is the output offset vector, and T represents transposition.

Unknown parameter in the NLPLS process monitoring model is latent node center vector c, respective width vector σ, weights coefficient matrices A and H, model bias vector b, and these parameters are determined as follows:

1. with the k-means clustering algorithm input data are carried out cluster, obtain latent node center c; This algorithm can be determined optimum cluster centre number, can make cluster centre reasonably be distributed in the data space simultaneously;

2. adopt p neighbour rule to calculate latent node width:

${\mathrm{\σ}}_j=\sqrt{\frac{1}{p}\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{\left|\right|c_i-c_j\left|\right|}^2},j=1,\·\·\·,N$

Wherein N is the number of latent node center, c _iBe p nearest latent node center of j latent node center of distance.

3. adopt PLS to return and determine weights coefficient matrices A, H and bias vector b:

Calculate latent node output matrix G according to latent node center that obtains and width, then input matrix is expanded, obtain augmentation input matrix [1 X G].To data to { [1 X G], Y} carry out PLS and return, and obtain PLS model parameter matrix { T, W, P, B, Q}.In order in the model modification of back, to keep all information, extract the order that the characteristic variable number equals augmentation input matrix [1 X G], and the proper vector number a that model kept that finally is used to predict adopts cross validation method to determine, the parameter matrix that obtains is designated as { Ta, Wa, Pa, Ba, Qa} calculates PLS regression coefficient matrix β by them, thereby obtain A, H and b.

C. the control of compute statistics SPE is limit.SPE is a scalar in the value of each batch, and it has portrayed this batch measured value x (i) and y (i) departure degree to principal component model.After obtaining model, be to i batch of its SPE value with the PLS algorithm:

${\mathrm{SPE}\left(i\right)}_X={e\left(i\right)}_X^2=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(x{\left(i\right)}_j-\hat{x}{\left(i\right)}_j)}^2)$

${\mathrm{SPE}\left(i\right)}_Y={e\left(i\right)}_Y^2=\underset{j=1}{\overset{p}{\mathrm{\Σ}}}{(y{\left(i\right)}_j-\hat{y}{\left(i\right)}_j)}^2)$

The Model Calculation value of representing i batch process variable, The Model Calculation value of representing i batch quality variable, SPE control limit Q _aBe calculated as follows:

$Q_a={\mathrm{\θ}}_1{[\frac{C_a\sqrt{{2\mathrm{\θ}}_2{h}_0^2}}{{\mathrm{\θ}}_1}+1+\frac{{\mathrm{\θ}}_2{h}_0(h_0-1)}{{\mathrm{\θ}}_1^2}]}^{\frac{1}{h_0}}$

Wherein:

${\mathrm{\θ}}_i=\underset{j=k+1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_j^i(i=\mathrm{1,2,3})$

λ _j＝‖t _i‖ ²

$h_0=1-\frac{{2\mathrm{\θ}}_1{\mathrm{\θ}}_3}{3{\mathrm{\θ}}_2^2}$

t _iBe i the proper vector that keeps, C _αBe normal distribution at insolation level be critical value under the α, C _αWith h ₀The pivot number that jack per line, k are in the principal component model to be kept, n is whole pivot numbers.

Step (2) is applied to the real-time industrial process data of online acquisition with the NLPLS process monitoring model of setting up, and calculates the SPE value of the data of newly arriving, and limits Q with control _αCompare: if SPE 〉=Q _α, declarative procedure has occurred unusually; If SPE＜Q _α, declarative procedure is normal, utilizes the method for step (3) that NLPLS process monitoring model is upgraded, and upgrades control limit Q simultaneously _α

Step (3) utilizes new data in conjunction with original NLPLS process monitoring model, adopts the recursive non-linear partial least square algorithm that model is upgraded, and upgrades control limit Q simultaneously _α, concrete grammar is:

If pass through in the NLPLS process monitoring model that obtains after k-1 batch, the latent node center matrix of RBF network is

The corresponding center vector of each row, the respective width vector is

The width of the corresponding latent node of each element, { W (k-1), P (k-1), B (k-1), Q (k-1) } is PLS model parameter matrix, after k batch end, obtains new input/output variable x (k) and y (k);

A. adopt with step (1) in identical method new data is carried out the data pre-service.Calculate the output vector of the latent node of former NLPLS model, be designated as g (k) for new samples x (k).

B. judge whether to increase new latent node:

If all elements of g (k) all less than setting value, then adds new latent node.New latent node center is taken as x (k), and corresponding width σ adopts the arest neighbors rule to calculate:

σ＝z _c-ησ _c

Wherein, z _cBe the distance of x (k) to nearest latent node center, η is overlapping parameter, and span is [0,1], σ _cBe width, thereby obtain new latent node center matrix and width vector from the nearest latent node of x (k):

$C_g^{\left(k\right)}=\left[\begin{array}{c}{C}_g^{(k-1)}\\ x^{\left(k\right)T}\end{array}\right],$ ${\mathrm{\σ}}_g^{\left(k\right)}=\left[\begin{array}{c}{\mathrm{\σ}}_g^{(k-1)}\\ \mathrm{\σ}\end{array}\right]$

As follows to parameter matrix P (k-1) and vectorial g (k) expansion simultaneously:

$P(k-1)=\left[\begin{array}{c}P(k-1)\\ 0\end{array}\right],$ $g\left(k\right)=\left[\begin{array}{c}g\left(k\right)\\ 1\end{array}\right]$

In the formula, 0 is that whole elements all are 0 row vector.

If all elements of g (k) all more than or equal to setting value, does not then need to increase latent node, C _g, σ _g, P, g remain unchanged.

C. x (k) is expanded, obtain augmentation input vector: x _E(k) ^T=[1x (k) ^TG (k) ^T].

D. with new data x _E(k) and y (k) combine with old PLS model parameter matrix, carry out PLS then and return, form is as follows:

$X\left(k\right)=\left[\begin{array}{c}{P(k-1)}^T\\ x_E{\left(k\right)}^T\end{array}\right],$ $Y\left(k\right)=\left[\begin{array}{c}{B(k-1)Q(k-1)}^T\\ {y\left(k\right)}^T\end{array}\right]$

According to 3. method of step in the step (1), calculate PLS regression parameter A (k), H (k) and b (k).Preserve new model parameter

For prediction with use during model modification next time.

Step (4) is calculated new control limit Q based on new NLPLS process monitoring model parameter _α, be used for new data, return step (2).

The batch process monitoring method that the present invention proposes based on recursive non-linear partial least square, do not rely on the analytic model of object, make full use of factory's rich data resource, effectively the deal with data amount is big, data dimension height, problems such as data collinearity, this method has remedied the problem of failing to report and reporting by mistake that traditional non-linear multivariate statistics course monitoring method adopts fixing statistical model and control limit to be produced, can utilize new data to upgrade model parameter and control limit, thereby the variation of procedure of adaptation characteristic, can processing procedure is non-linear can handle time variation again, improve monitoring performance.

Embodiment

A kind of batch process monitoring method based on recursive non-linear partial least square, concrete steps are:

Step (1) is set up non-linear partial least square (NLPLS) process monitoring model based on process database, simultaneously the calculation control limit.Concrete grammar is:

A. by data collector gatherer process service data,, be used to set up model with the process operation data of gathering sample set as data-driven.In the batch process, each batch process repeatedly repeatability is produced, its data acquisition than the continuous process data acquisition many one dimension " batch " element, have sequential property.Therefore the data acquisition of batch production process is with three-dimensional data formation formula (batch * time * variable) expression, and X (all process datas that the expression of I * J * K) collects, wherein, I represents a batch number, and J represents the sample number, and K represents the process variable number; Quality variable generally obtains by off-line analysis when process finishes, and each batch obtains M quality variable assay value, and I batch quality variable formation matrix Y (I * M).

During modeling, at first with three-dimensional data piece X along time-axis direction cutting batch and variable data piece, each data block is horizontal to the right successively, regards the data of each batch as a data sample, forms a new two-dimensional matrix X (I * JK).Then with matrix X as input matrix, Y is used to set up model as output matrix.Wherein, the data of each batch are to being expressed as { x (i) } and { y (i) }, and x (i) expression is imported data for i batch, and y (i) represents i batch of output data.To import data constitutes input matrix X, output data is constituted output matrix Y;

B. set up the non-linear partial least square model based on inputoutput data, method is:

Matrix X and Y are carried out normalized, and making it average is 0, and variance is 1; Then input matrix is listed as expansion, the expansion item is 1 column vector 1 entirely for the latent node output matrix G of radial basis function (RBF) neural network and element, the output g of the corresponding input vector effect of each row latent node down of G wherein, the bias term coefficient that conceals node is 1; Following augmentation input matrix and output matrix are carried out partial least square (PLS) recurrence:

The NLPLS process monitoring model representation that obtains is for [1 X G], Y}:

$\hat{Y}=\mathrm{XA}+\mathrm{GH}+1b^T=\left[1\mathrm{X\; G}\right]\left[\begin{array}{c}{b}^T\\ A\\ H\end{array}\right]=X_E\mathrm{\β}$

In the formula, X _EExpression augmentation input matrix, A and H are respectively the weights matrix of coefficients of corresponding original input vector and the latent node output vector of corresponding RBF network, and b is the output offset vector, and T represents transposition.

Unknown parameter in the NLPLS process monitoring model is latent node center vector c, respective width vector σ, weights coefficient matrices A and H, model bias vector b, and these parameters are determined as follows:

1. with the k-means clustering algorithm input data are carried out cluster, obtain latent node center c;

2. adopt p neighbour rule to calculate latent node width:

${\mathrm{\σ}}_j=\sqrt{\frac{1}{p}\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{\left|\right|c_i-c_j\left|\right|}^2},j=1,\·\·\·,N$

Wherein N is the number of latent node center, c _iBe p nearest latent node center of j latent node center of distance.

3. adopt PLS to return and determine weights coefficient matrices A, H and bias vector b:

Calculate latent node output matrix G according to latent node center that obtains and width, then input matrix is expanded, obtain augmentation input matrix [1 X G].To data to { [1 X G], Y} carry out PLS and return, and obtain PLS model parameter matrix { T, W, P, B, Q}.Extract the order that the characteristic variable number equals augmentation input matrix [1 X G], and the proper vector number a that model kept that finally is used to predict adopts cross validation method to determine, the parameter matrix that obtains is designated as { Ta, Wa, Pa, Ba, Qa}, calculate PLS regression coefficient matrix β by them, thereby obtain A, H and b.

C. the control of compute statistics SPE is limit.SPE is a scalar in the value of each batch, and it has portrayed this batch measured value x (i) and y (i) departure degree to principal component model.After obtaining model, be to i batch of its SPE value with the PLS algorithm:

${\mathrm{SPE}\left(i\right)}_X={e\left(i\right)}_X^2=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(x{\left(i\right)}_j-\hat{x}{\left(i\right)}_j)}^2)$

${\mathrm{SPE}\left(i\right)}_Y={e\left(i\right)}_Y^2=\underset{j=1}{\overset{p}{\mathrm{\Σ}}}{(y{\left(i\right)}_j-\hat{y}{\left(i\right)}_j)}^2)$

The Model Calculation value of representing i batch process variable,

The Model Calculation value of representing i batch quality variable, SPE control limit Q _aBe calculated as follows:

$Q_a={\mathrm{\θ}}_1{[\frac{C_a\sqrt{{2\mathrm{\θ}}_2{h}_0^2}}{{\mathrm{\θ}}_1}+1+\frac{{\mathrm{\θ}}_2{h}_0(h_0-1)}{{\mathrm{\θ}}_1^2}]}^{\frac{1}{h_0}}$

Wherein:

${\mathrm{\θ}}_i=\underset{j=k+1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_j^i(i=\mathrm{1,2,3})$

λ _j＝‖t _i‖ ²

$h_0=1-\frac{{2\mathrm{\θ}}_1{\mathrm{\θ}}_3}{3{\mathrm{\θ}}_2^2}$

t _iBe i the proper vector that keeps, C _αBe normal distribution at insolation level be critical value under the α, C _αWith h ₀The pivot number that jack per line, k are in the principal component model to be kept, n is whole pivot numbers.

Step (2) is applied to the real-time industrial process data of online acquisition with the NLPLS process monitoring model of setting up, and calculates the SPE value of the data of newly arriving, and limits Q with control _αCompare: if SPE 〉=Q _α, declarative procedure has occurred unusually; If SPE＜Q _α, declarative procedure is normal, utilizes the method for step (3) that NLPLS process monitoring model is upgraded, and upgrades control limit Q simultaneously _α

Step (3) utilizes new data in conjunction with original NLPLS process monitoring model, adopts the recursive non-linear partial least square algorithm that model is upgraded, and upgrades control limit Q simultaneously _α, concrete grammar is:

If pass through in the NLPLS process monitoring model that obtains after k-1 batch, the latent node center matrix of RBF network is

The corresponding center vector of each row, the respective width vector is The width of the corresponding latent node of each element, { W (k-1), P (k-1), B (k-1), Q (k-1) } is PLS model parameter matrix, after k batch end, obtains new input/output variable x (k) and y (k);

A. adopt with step (1) in identical method new data is carried out the data pre-service.Calculate the output vector of the latent node of former NLPLS model, be designated as g (k) for new samples x (k).

B. judge whether to increase new latent node:

If all elements of g (k) all less than setting value, then adds new latent node.New latent node center is taken as x (k), and corresponding width σ adopts the arest neighbors rule to calculate:

σ＝z _c-ησ _c

Wherein, z _cBe the distance of x (k) to nearest latent node center, η is overlapping parameter, and span is [0,1], σ _cBe width, thereby obtain new latent node center matrix and width vector from the nearest latent node of x (k):

$C_g^{\left(k\right)}=\left[\begin{array}{c}{C}_g^{(k-1)}\\ x^{\left(k\right)T}\end{array}\right],$ ${\mathrm{\σ}}_g^{\left(k\right)}=\left[\begin{array}{c}{\mathrm{\σ}}_g^{(k-1)}\\ \mathrm{\σ}\end{array}\right]$

As follows to parameter matrix P (k-1) and vectorial g (k) expansion simultaneously:

$P(k-1)=\left[\begin{array}{c}P(k-1)\\ 0\end{array}\right],$ $g\left(k\right)=\left[\begin{array}{c}g\left(k\right)\\ 1\end{array}\right]$

In the formula, 0 is that whole elements all are 0 row vector.

If all elements of g (k) is all more than or equal to setting value, C _g, σ _g, P, g remain unchanged.

C. x (k) is expanded, obtain augmentation input vector: x _E(k) ^T=[1x (k) ^TG (k) ^T].

D. with new data x _E(k) and y (k) combine with old PLS model parameter matrix, carry out PLS then and return, form is as follows:

$X\left(k\right)=\left[\begin{array}{c}{P(k-1)}^T\\ x_E{\left(k\right)}^T\end{array}\right],$ $Y\left(k\right)=\left[\begin{array}{c}{B(k-1)Q(k-1)}^T\\ {y\left(k\right)}^T\end{array}\right]$

According to 3. method of step in the step (1), calculate PLS regression parameter A (k), H (k) and b (k).Preserve new model parameter For prediction with use during model modification next time.

Step (4) is calculated new control limit Q based on new NLPLS process monitoring model parameter _α, be used for new data, return step (2).

Claims (1)

1. batch process monitoring method based on recursive non-linear partial least square is characterized in that the concrete steps of this method are:

Step (1) is set up non-linear partial least square process monitoring model based on process database, simultaneously the calculation control limit; Concrete grammar is:

A. by data collector gatherer process service data, with the process operation data of gathering sample set, be used to set up model as data-driven, represent X (all process datas that the expression of I * J * K) collects with three-dimensional data formation formula; Wherein I represents that a batch number, J represent that sample number, K represent the process variable number; Each batch obtains M quality variable assay value, and I batch quality variable formation matrix Y (I * M);

During modeling, at first with three-dimensional data piece X along time-axis direction cutting batch and variable data piece, each data block is horizontal to the right successively, regards the data of each batch as a data sample, forms a new two-dimensional matrix X (I * JK); Then with matrix X as input matrix, Y is used to set up model as output matrix; Wherein, the data of each batch are to being expressed as { x (i) } and { y (i) }, and x (i) expression is imported data for i batch, and y (i) represents i batch of output data; To import data constitutes input matrix X, output data is constituted output matrix Y;

B. set up the non-linear partial least square model based on inputoutput data, method is:

Matrix X and Y are carried out normalized, and making it average is 0, and variance is 1; Then input matrix is listed as expansion, the expansion item is 1 column vector 1 entirely for the latent node output matrix G of radial basis function neural network and element, the output g of the corresponding input vector effect of each row latent node down of G wherein, the bias term coefficient that conceals node is 1; Following augmentation input matrix and output matrix are carried out the partial least square recurrence:

The non-linear partial least square process monitoring model representation that obtains is for [1 X G], Y}:

$\hat{Y}=\mathrm{XA}+\mathrm{GH}+1b^T=\left[\begin{array}{ccc}1& X& G\end{array}\right]\left[\begin{array}{c}{b}^T\\ A\\ H\end{array}\right]=X_E\mathrm{\β}$

In the formula, X _EExpression augmentation input matrix, A and H are respectively the weights matrix of coefficients of corresponding original input vector and the latent node output vector of corresponding radial basis function neural network, and b is the output offset vector, and T represents transposition;

Unknown parameter in the non-linear partial least square process monitoring model is latent node center vector c, respective width vector σ, weights coefficient matrices A and H, model bias vector b, and these parameters are determined as follows:

1. with the k-means clustering algorithm input data are carried out cluster, obtain latent node center c;

2. adopt p neighbour rule to calculate latent node width:

${\mathrm{\σ}}_i=\sqrt{\frac{1}{p}\underset{i=1}{\overset{p}{\mathrm{\Σ}}}{\left|\right|c_i-c_j\left|\right|}^2},j=1,\·\·\·,N$

Wherein N is the number of latent node center, c _iBe p nearest latent node center of j latent node center of distance;

3. adopt partial least square to return and determine weights coefficient matrices A, H and bias vector b:

Calculate latent node output matrix G according to latent node center that obtains and width, then input matrix is expanded, obtain augmentation input matrix [1 X G]; To data to { [1 X G], Y} carry out partial least square and return, and obtain partial least square model parameter matrix { T, W, P, B, Q}; Extract the order that the characteristic variable number equals augmentation input matrix [1 X G], and the proper vector number a that model kept that finally is used to predict adopts cross validation method to determine, the parameter matrix that obtains is designated as { Ta, Wa, Pa, Ba, Qa}, calculate partial least square regression coefficient matrix β by them, thereby obtain A, H and b;

C. the control of compute statistics SPE is limit; SPE is a scalar in the value of each batch, and it has portrayed this batch measured value x (i) and y (i) departure degree to principal component model; After obtaining model, be to i batch of its SPE value with the partial least square algorithm:

$\mathrm{SPE}{\left(i\right)}_X=e{\left(i\right)}_X^2=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(x{\left(i\right)}_j-\hat{x}{\left(i\right)}_j)}^2)$

$\mathrm{SPE}{\left(i\right)}_Y=e{\left(i\right)}_Y^2=\underset{j=1}{\overset{p}{\mathrm{\Σ}}}{(y{\left(i\right)}_j-\hat{y}{\left(i\right)}_j)}^2)$

The Model Calculation value of representing i batch process variable,

The Model Calculation value of representing i batch quality variable, SPE control limit Q _aBe calculated as follows:

$Q_a={\mathrm{\θ}}_1{[\frac{C_a\sqrt{2{\mathrm{\θ}}_2{h}_0^2}}{{\mathrm{\θ}}_1}+1+\frac{{\mathrm{\θ}}_2{h}_0(h_0-1)}{{\mathrm{\θ}}_1^2}]}^{\frac{1}{h_0}}$

Wherein:

${\mathrm{\θ}}_i=\underset{j=k+1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_j^i,(i=\mathrm{1,2,3})$

λ _j＝‖t _i‖ ²

$h_0=1-\frac{2{\mathrm{\θ}}_1{\mathrm{\θ}}_3}{3{\mathrm{\θ}}_2^2}$

t _iBe i the proper vector that keeps, C _αBe normal distribution at insolation level be critical value under the α, C _αWith h ₀The pivot number that jack per line, k are in the principal component model to be kept, n is whole pivot numbers;

Step (2) is applied to the real-time industrial process data of online acquisition with the non-linear partial least square process monitoring model of setting up, and calculates the SPE value of the data of newly arriving, and limits Q with control _αCompare: if SPE 〉=Q _α, declarative procedure has occurred unusually; If SPE＜Q _α, declarative procedure is normal, utilizes the method for step (3) that non-linear partial least square process monitoring model is upgraded, and upgrades control limit Q simultaneously _α

Step (3) utilizes new data in conjunction with original non-linear partial least square process monitoring model, adopts the recursive non-linear partial least square algorithm that model is upgraded, and upgrades control limit Q simultaneously _α, concrete grammar is:

If pass through in the non-linear partial least square process monitoring model that obtains after k-1 batch, the latent node center matrix of radial basis function neural network is The corresponding center vector of each row, the respective width vector is

The width of the corresponding latent node of each element, { W (k-1), P (k-1), B (k-1), Q (k-1) } is partial least square model parameter matrix, after k batch end, obtains new input/output variable x (k) and y (k);

A. adopt with step (1) in identical method new data is carried out the data pre-service; Calculate the output vector of the latent node of former non-linear partial least square process monitoring model, be designated as g (k) for new samples x (k);

B. judge whether to increase new latent node:

If all elements of g (k) all less than setting value, then adds new latent node; New latent node center is taken as x (k), and corresponding width σ adopts the arest neighbors rule to calculate:

σ＝z _c-ησ _c

Wherein, z _cBe the distance of x (k) to nearest latent node center, η is overlapping parameter, and span is [0,1], σ _cBe width, thereby obtain new latent node center matrix and width vector from the nearest latent node of x (k):

$C_g^{\left(k\right)}=\left[\begin{array}{c}{C}_g^{(k-1)}\\ x^{\left(k\right)T}\end{array}\right],{\mathrm{\σ}}_g^{\left(k\right)}=\left[\begin{array}{c}{\mathrm{\σ}}_g^{(k-1)}\\ \mathrm{\σ}\end{array}\right]$

As follows to parameter matrix P (k-1) and vectorial g (k) expansion simultaneously:

$P(k-1)=\left[\begin{array}{c}P(k-1)\\ 0\end{array}\right],g\left(k\right)=\left[\begin{array}{c}g\left(k\right)\\ 1\end{array}\right]$

In the formula, 0 is that whole elements all are 0 row vector;

If all elements of g (k) is all more than or equal to setting value, C _g, σ _g, P, g remain unchanged;

C. x (k) is expanded, obtain augmentation input vector: x _E(k) ^T=[1x (k) ^TG (k) ^T];

D. with new data x _E(k) and y (k) divide least square model parameter matrix to combine with former subordinates, carry out partial least square then and return, form is as follows:

$X\left(k\right)=\left[\begin{array}{c}P{(k-1)}^T\\ x_E{\left(k\right)}^T\end{array}\right],Y\left(k\right)=\left[\begin{array}{c}B(k-1)Q{(k-1)}^T\\ y{\left(k\right)}^T\end{array}\right]$

According to 3. method of step in the step (1), calculate partial least square regression parameter A (k), H (k) and b (k); Preserve new model parameter A (k), H (k), b (k), P (k), B (k), Q (k),

For prediction with use during model modification next time;

Step (4) is calculated new control limit Q based on new non-linear partial least square process monitoring model parameter _α, be used for new data, return step (2).