CN101872163A - Process monitoring method based on recursive non-linear partial least squares - Google Patents

Abstract

The invention relates to a 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. The method comprises the following steps: establishing a 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 process. When new data are obtained, the model and the control limits are updated in a recursive method so as to adapt to changes of the 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 data in order to adapt to changes of the process, thereby improving the monitoring performance.

Description

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

Technical field

The invention belongs to the information automation technical field, relate to a kind of course monitoring method based on recursive non-linear partial least square.

Background technology

Modern industrial process systems just develops towards direction extensive, complicacy, massive losses and environmental hazard that in a single day system breaks down and just may cause personnel and property.This just requires production run is monitored, thereby determines whether production status is normal, can in time take its corresponding measures when unusual service condition occurring, reduces and produces 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.A lot of actual industrial process have stronger non-linear, 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 course 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 course 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 the procedure of adaptation 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 based on non-linear partial least square (NLPLS) process monitoring model based on process database, and calculation control is limit simultaneously, and concrete grammar is:

A. gather the real-time process service data by data collector,, be expressed as { x (i), y (i) }, x (i) expression i group input data wherein, y (i) expression i group output data the real-time process service data of gathering sample set as data-driven; 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 input, output data, method is as follows:

Matrix X and Y are carried out normalized, and making it average is 0, and variance is 1; 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 wherein output of the latent node under the corresponding input vector effect of each row of G, the bias term coefficient of latent 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}:

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

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 formula (1) 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:

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

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 i value constantly, it portrayed this constantly measured value x (i) and y (i) to the departure degree of principal component model.After obtaining model with the PLS algorithm, the i value of SPE constantly is:

${\mathrm{SPE}\left(i\right)}_X={e\left(i\right)}_X^2=\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(x{\left(i\right)}_j-\hat{x}{\left(i\right)}_j)}^2)---\left(3\right)$

${\mathrm{SPE}\left(i\right)}_Y={e\left(i\right)}_Y^2=\underset{j=1}{\overset{p}{\mathrm{\Σ}}}{(y{\left(i\right)}_j-\hat{y}{\left(i\right)}_j)}^2)---\left(4\right)$

The Model Calculation value of representing i input sample,

The Model Calculation value of representing i output sample, SPE control limit Q _aBe calculated as follows:

$Q_a={\mathrm{\θ}}_1{[\frac{C_a\sqrt{{2\mathrm{\θ}}_2{h}_0^2}}{{\mathrm{\θ}}_1}+1+\frac{{\mathrm{\θ}}_2{h}_0(h_0-1)}{{\mathrm{\θ}}_1^2}]}^{\frac{1}{h_0}}---\left(5\right)$

Wherein:

${\mathrm{\θ}}_i=\underset{j=k+1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\λ}}_j^i(i=\mathrm{1,2,3})---\left(6\right)$

λ _j＝‖t _i‖ ² (7)

$h_0=1-\frac{{2\mathrm{\θ}}_1{\mathrm{\θ}}_3}{3{\mathrm{\θ}}_2^2}---\left(8\right)$

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 steps are as follows:

A. the data that newly obtain of note are X1 and Y1, adopt with step (1) in the same method new data is carried out the data pre-service;

B. judge whether to increase new latent node:

If the distance of the latent node center of new data X1 and existing RBF network then adds new latent node greater than setting value; Remember that new latent node center matrix is C _Gnew, the corresponding width vector is σ _Gnew, to original latent node center Matrix C _g, corresponding width vector σ _gCarry out following expansion with matrix of loadings P:

$C_g=\left[\begin{array}{c}{C}_g\\ C_{\mathrm{gnew}}\end{array}\right],$ ${\mathrm{\σ}}_g=\left[\begin{array}{c}{\mathrm{\σ}}_g\\ {\mathrm{\σ}}_{\mathrm{gnew}}\end{array}\right],$ $P=\left[\begin{array}{c}P\\ 0\end{array}\right]$

If the distance of the latent node center of X1 and existing RBF network does not then need to increase latent node, C smaller or equal to setting value _g, σ _gRemain unchanged with P;

C. X1 is expanded to X _E1=[1 X1 G1], wherein G1 is the output matrix of latent node for X1, order

To data to { X _E, Y} carries out PLS and returns, and obtains new NLPLS process monitoring model:

Then according to the step in the step (1) 3. method calculate weights coefficient matrices A, H and bias vector b;

D. calculate new control limit Q based on new NLPLS process monitoring model parameter _α, be used for new data, return step (2).

The course 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, problems such as effective deal with data amount is big, data dimension height, data collinearity, remedy traditional non-linear multivariate statistics course monitoring method and can not handle the deficiency of time variation, utilize new data to upgrade model parameter and control limit, thereby variation that can the procedure of adaptation has improved monitoring performance.

Embodiment

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

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

A. gather the real-time process service data by data collector,, be expressed as { x (i), y (i) }, x (i) expression i group input data wherein, y (i) expression i group output data the real-time process service data of gathering sample set as data-driven; 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 input, output data, method is as follows:

Matrix X and Y are carried out normalized, and making it average is 0, and variance is 1; 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 wherein output of the latent node under the corresponding input vector effect of each row of G, the bias term coefficient of latent node is 1; Following augmentation input matrix and output matrix are carried out partial least square (PLS) recurrence:

{[1 X G]，Y}

The NLPLS process monitoring model representation that obtains is:

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

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 i value constantly, it portrayed this constantly measured value x (i) and y (i) to the departure degree of principal component model.After obtaining model with the PLS algorithm, the i value of SPE constantly is:

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

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

The Model Calculation value of representing i input sample,

The Model Calculation value of representing i output sample, 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 steps are as follows:

A. the data that newly obtain of note are X1 and Y1, adopt with step (1) in the same method new data is carried out the data pre-service;

B. judge whether to increase new latent node:

If the distance of the latent node center of new data X1 and existing RBF network then adds new latent node greater than setting value; Remember that new latent node center matrix is C _Gnew, the corresponding width vector is σ _Gnew, to original latent node center Matrix C _g, corresponding width vector σ _gCarry out following expansion with matrix of loadings P:

$C_g=\left[\begin{array}{c}{C}_g\\ C_{\mathrm{gnew}}\end{array}\right],$ ${\mathrm{\σ}}_g=\left[\begin{array}{c}{\mathrm{\σ}}_g\\ {\mathrm{\σ}}_{\mathrm{gnew}}\end{array}\right],$ $P=\left[\begin{array}{c}P\\ 0\end{array}\right]$

If the distance of the latent node center of X1 and existing RBF network does not then need to increase latent node, C smaller or equal to setting value _g, σ _gRemain unchanged with P;

C. X1 is expanded to X _E1=[1 X1 G1], wherein G1 is the output matrix of latent node for X1, order

To data to { X _E, Y} carries out PLS and returns, and obtains new NLPLS process monitoring model:

Then according to the step in the step (1) 3. method calculate weights coefficient matrices A, H and bias vector b;

D. calculate new control limit Q based on new NLPLS process monitoring model parameter _α, be used for new data, return step (2).

Claims (1)

1. course 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 based on non-linear partial least square process monitoring model based on process database, and calculation control is limit simultaneously, and concrete grammar is:

A. gather the real-time process service data by data collector,, be expressed as { x (i), y (i) }, x (i) expression i group input data wherein, y (i) expression i group output data the real-time process service data of gathering sample set as data-driven; To import data constitutes input matrix X, output data is constituted output matrix Y;

B. set up based on non-linear partial least square process monitoring model based on input, output data, method is as follows:

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

What obtain based on non-linear partial least square process monitoring model representation is for [1 X G], Y}:

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

X in the formula _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;

Be latent node center vector c, respective width vector σ, weights coefficient matrices A and H, model bias vector b based on the unknown parameter in the non-linear partial least square process monitoring model, 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 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 i value constantly, it portrayed this constantly measured value x (i) and y (i) to the departure degree of principal component model; After obtaining model with the partial least square algorithm, the i value of SPE constantly is:

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

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

The Model Calculation value of representing i input sample,

The Model Calculation value of representing i output sample, 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;

What step (2) will be set up is applied to the real-time industrial process data of online acquisition based on non-linear partial least square process monitoring model, 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, and the method for utilizing step (3) is upgraded control limit Q simultaneously to upgrading based on non-linear partial least square process monitoring model _α

Step (3) utilize new data in conjunction with original based on non-linear partial least square process monitoring model, adopt the recursive non-linear partial least square algorithm that model is upgraded, upgrade control limit Q simultaneously _α, concrete steps are as follows:

A. the data that newly obtain of note are X1 and Y1, adopt with step (1) in the same method new data is carried out the data pre-service;

B. judge whether to increase new latent node:

If the distance of the latent node center of new data X1 and existing radial basis function neural network then adds new latent node greater than setting value; Remember that new latent node center matrix is C _Gnew, the corresponding width vector is σ _Gnew, to original latent node center Matrix C _g, corresponding width vector σ _gCarry out following expansion with matrix of loadings P:

$C_g=\left[\begin{array}{c}{C}_g\\ C_{\mathrm{gnew}}\end{array}\right],{\mathrm{\σ}}_g=\left[\begin{array}{c}{\mathrm{\σ}}_g\\ {\mathrm{\σ}}_{\mathrm{gnew}}\end{array}\right],P=\left[\begin{array}{c}P\\ 0\end{array}\right]$

If X1 and existing radial basis function neural network conceal the distance of node center smaller or equal to setting value, C _g, σ _gRemain unchanged with P;

C. X1 is expanded to X _E1=[1 X1 G1], wherein G1 is the output matrix of latent node for X1, order

To data to { X _E, Y} carries out partial least square and returns, and obtains new for non-linear partial least square process monitoring model:

Then according to the step in the step (1) 3. method calculate weights coefficient matrices A, H and bias vector b;

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