CN108171002A - A kind of polypropylene melt index Forecasting Methodology based on semi-supervised mixed model - Google Patents
A kind of polypropylene melt index Forecasting Methodology based on semi-supervised mixed model Download PDFInfo
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Abstract
The invention discloses a kind of polypropylene melt index Forecasting Methodologies based on semi-supervised mixed model, it considers by separated processing auxiliary variable and melt index and explicitly the dependence between melt index and auxiliary variable first, establishes the mathematical model of randomization；Then excavating simultaneously has exemplar and unlabeled exemplars information, and carry out automodel parameter learning using expectation-maximization algorithm and bayesian information criterion selects with model.This method can provide the predicted value of melt index in real time online, and assess its confidence level.Using the present invention, the accuracy of model parameter study and model selection can be improved and all parameters are without manually setting, the precision of prediction of melt index can be effectively improved, technical support is provided with ensureing to improve product quality, reducing cost, process monitoring and decision-making.
Description
Technical field
The invention belongs to procedures system soft sensor modeling and application fields, and in particular to one kind is based on semi-supervised mixed model
Polypropylene melt index Forecasting Methodology.
Background technology
Acrylic resin due to proportion is small, nontoxic, tasteless, easy processing, it is excellent in cushion effect, buckling good and
The advantages that electrical insulating property is good obtains very extensive application in numerous industrial circles of national economy.Melt index is weighing apparatus
The important indicator of polypropylene product quality is measured, is usually measured in a manner that laboratory assay is analyzed, the period is 2-4 hours.So
Big measurement delay can significantly reduce the dynamic and stability of closed-loop control system, and bounder control is not known where to begin more, causes to gather
Production of propylene process variation is strong, product waste material is more, not only increases the production cost of enterprise, also exacerbates environmental pollution.
The soft-sensing model of melt index can realize the online real-time prediction of melt index.The hard measurement of melt index at present
Modeling method can be summarized as two major class.The first kind is to establish mechanism model according to the mechanism of polymerisation, and another kind of is to utilize life
Production process data establishes the model of data-driven.Accurate mechanism model dynamic is good, and precision of prediction is high, applied widely, so
And since polypropylene production process mechanism is extremely complex and is not yet fully apparent from, melt index mechanism model usually requires a large amount of strong
Strong assumed condition is general to be relatively suitable for bistable design.In comparison, the model of data-driven is directly established using process data
Model, can more reflect the real-time of actual production situation, therefore be more suitable for the on-line prediction of melt index.
The melt index soft-sensing model of data-driven is established mainly there are two difficult point.First, due to the market demand, poly- third
Alkene production process operation operating mode is numerous, and product usually has multiple trades mark (up to dozens of) so that polypropylene production process
The characteristics such as strong nonlinearity, non-Gaussian system are presented in data.Single world model (such as partial least square model, neural network model, branch
Hold vector machine model etc.) it is difficult to provide satisfied precision of prediction in the range of all trades mark.Second, the prediction of current melt index
Method is usually supervised learning method, that is, rely only on has exemplar with melt index laboratory values.However, as melting
The index chemical examination period is long, and the quantity for having exemplar is generally seldom so that melt index soft-sensing model due to " cross learn " or
Reasons such as " owing study " are difficult to obtain accurate model parameter.The bad soft-sensing model of training can not necessarily provide satisfied pre-
Precision is surveyed, and artificial setting parameter time and effort consuming, difficulty are very big.On the other hand, only comprising auxiliary variable without label sample
This largely exists, but existing melt index soft-sensing model can not excavate the significant process letter that these unlabeled exemplars contain
Breath.In addition, soft-sensing model provide melt index predicted value after, it is also desirable that know the predicted value reliability have it is more
Greatly, i.e., the precision of prediction of melt index is assessed.Regrettably, most melt index soft-sensing models do not have this at present
One function.Therefore, research and development has the functions such as more trade mark processing, unlabeled exemplars information excavating and precision of prediction assessment
Melt index soft-sensing model, help to improve the precision of prediction of melt index, power-assisted manufacturing enterprise realizes energy conservation and environmental protection, drop
The target of this synergy is very necessary and urgent.
Invention content
In view of the deficiencies of the prior art, it is pre- to provide a kind of polypropylene melt index based on semi-supervised mixed model by the present invention
Survey method establishes the non-linear relation of auxiliary variable and melt index in the form of mixed model, can adaptively cope with the trade mark
Switching effectively solves the problems, such as product grade numerous caused strong nonlinearity, non-Gaussian systems, and passes through semi-supervised learning and excavate simultaneously
There is the information that exemplar and unlabeled exemplars contain so that model training is more reliable.Specific technical solution is as follows：
A kind of polypropylene melt index Forecasting Methodology based on semi-supervised mixed model, which is characterized in that including following step
Suddenly：
(1) selection and the associated auxiliary variable x ∈ R of polypropylene melt index ym, wherein m expression auxiliary variable numbers；
(2) collect has exemplar collection comprising auxiliary variable and melt index simultaneouslyWith only wrapping
Unlabeled exemplars collection containing auxiliary variableWherein n1With n2Representing respectively has exemplar and unlabeled exemplars
Quantity；
(3) to [XL,YL] and XUNondimensionalization processing is done, by the sample variance of auxiliary variable sample and melt index sample
Be converted to unit variance；
(4) the gauss component number K of semi-supervised mixed model, random initializtion model parameter are givenWherein, αkFor the prior probability of k-th of gauss component,WithIt is respectively k-th high
The mean value and covariance matrix of the marginal probability density of x, ω in this ingredientkAnd ωkX and y in respectively k-th of gauss component
Regression coefficient,Represent the measurement noise variance of melt index y in k-th of gauss component；
(5) by step (3), treated has initial model in exemplar collection, unlabeled exemplars collection and step (4) to join
Number is inputted in semi-supervised mixed model, by maximizing semi-supervised object function L (ΘK) learning model parameter ΘK；
(6) K=K is traversedmin,Kmin+1,…,Kmax, step (4) and (5) is repeated, is calculated most using bayesian information criterion
Excellent gauss component number, is denoted as Kopt, and fromThe middle corresponding model parameter collection of selection
(7) acquisition only includes the unknown sample of auxiliary variable, and the dimension of auxiliary variable is eliminated by step (3), utilizes step
(6) the optimal gauss component number K obtained inoptAnd corresponding model parameter collectionPolyacrylic melt index is carried out pre-
It surveys, and the confidence interval of the predicted value is provided.
Further, the object function L (Θ of the semi-supervised mixed model built in the step (5)K) be：
Wherein, Pk(yi|xi) to give x in k-th of gauss componentiThe conditional probability density of melt index y, Pk(xi) and Pk
(xj) it is respectively x in k-th of gauss componentiAnd xjMarginal probability density, RikFor [xi,yi] k-th of gauss component is subordinate to
Degree, RjkFor xjTo the degree of membership of k-th of gauss component, their calculation formula is as follows：
In formula, N (；μ, Σ) represent mean value be μ, the normal distribution that covariance matrix is Σ；
WithThe mean vector and covariance matrix of the joint probability density of x and y are represented respectively, wherein,
Further, the model parameterIterative formula have following form：
In formula1 for complete 1 arrange to
Amount.
Further, in the step (5), optimal gauss component number KoptCalculation formula it is as follows：
Wherein, the value of bayesian information criterion when BIC (K) represents Gauss gauss component number as K, calculation formula
It is as follows：
Compared with prior art, beneficial effects of the present invention are as follows：
1st, the non-linear relation of auxiliary variable and melt index is established in the form of mixed model, can adaptively cope with board
Number switching, effectively solves the problems, such as product grade numerous caused strong nonlinearity, non-Gaussian systems；
2nd, the information for having exemplar and unlabeled exemplars to contain is excavated by semi-supervised learning simultaneously, makes model training more
Reliably；
3rd, all model parameters can adaptive learning, without manual intervention, without additional verification data collection, greatly save
The time and efforts for putting into model development is saved；
4th, in addition to the predicted value for providing melt index, the present invention may also provide the confidence interval of the predicted value, for pre-
Survey precision discrimination, exceptional sample classification and the newer reliability of assurance model etc..
Description of the drawings
Fig. 1 is the flow chart of the polypropylene melt index Forecasting Methodology based on semi-supervised mixed model of the present invention；
Fig. 2 is the process principle figure of certain petroleum chemical enterprise Spheripol-II Liquid-Phase Bulk Polypropylene process units；
Fig. 3 is polypropylene melt index on-line prediction result and its confidence interval signal based on semi-supervised mixed model
Figure；
Fig. 4 is prediction result schematic diagram of the partial least square model to melt index.
Specific embodiment
The polypropylene melt index based on semi-supervised mixed model of the present invention is predicted with reference to specific embodiment
Method is further elaborated.It should be pointed out that described embodiment is only intended to strengthen the understanding of the present invention, it is not right
The present invention plays any restriction effect.
A kind of polypropylene melt index Forecasting Methodology based on semi-supervised mixed model, as shown in Figure 1, specifically including as follows
Step：
(1) selection and the associated auxiliary variable x ∈ R of polypropylene melt index ym, wherein m expression auxiliary variable numbers；
The present embodiment according to certain petro-chemical corporation Spheripol-II Liquid-Phase Bulk Polypropylenes production technology (such as Fig. 2 institutes
Show) Analysis on Mechanism, select to influence melt index 8 maximum variables as auxiliary variable, in respectively reactor R201
Hydrogen/density of propylene ratio (x1), catalyst/density of propylene ratio (x in reactor R2012), the reaction heat (x of reactor R2013)、
Reaction density (the x of reactor R2014), hydrogen/density of propylene ratio (x in reactor R2025), catalyst/the third in reactor R202
Alkene concentration ratio (x6), the reaction heat (x of reactor R2027) and reactor R202 reaction density (x8), therefore auxiliary variable x
=[x1,x2,…,x8], i.e. x ∈ Rm, m=8.
(2) collect has exemplar collection comprising auxiliary variable and melt index simultaneouslyWith only wrapping
Unlabeled exemplars collection containing auxiliary variableWherein n1With n2Representing respectively has exemplar and unlabeled exemplars
Quantity；
The present invention collects having comprising auxiliary variable and melt index simultaneously from computer scattered control system database
200 groups of exemplar collection (is denoted as), 200 groups of the unlabeled exemplars collection with only including auxiliary variable (is denoted as), as training dataset, wherein n1=200 and n2=200 respectively represent have exemplar and no label sample
This quantity.
(3) to [XL,YL] and XUNondimensionalization processing is done, by the sample variance of auxiliary variable sample and melt index sample
Be converted to unit variance；
The method for wherein going dimension is：
In formula,Respectively
Represent the sample standard deviation of l-th of auxiliary variable and melt index, xn(l) adopting for l-th of auxiliary variable of n-th of sample is represented
Sample value.
(4) the gauss component number K of semi-supervised mixed model, random initializtion model parameter are givenWherein, αkFor the prior probability of k-th of gauss component,WithIt is respectively k-th high
The mean value and covariance matrix of the marginal probability density of x, ω in this ingredientkAnd ωkX and y in respectively k-th of gauss component
Regression coefficient,Represent the measurement noise variance of melt index y in k-th of gauss component；
(5) by step (3), treated has initial model in exemplar collection, unlabeled exemplars collection and step (4) to join
Number is inputted in semi-supervised mixed model, by maximizing semi-supervised object function L (ΘK) learning model parameter ΘK；It is i.e. given mixed
During molding type gauss component quantity K, the prior probability of each gauss component, the marginal probability density of x, the functional relation of x and y with
And noise variance.Detailed process is：
In kth (k=1,2 ..., K) a gauss component, the marginal probability density P of auxiliary variable xk(x), the function of x and y
Relationship y=fk(x) it is defined as
N in formula (；μ, Σ) expression mean value be μ, covariance matrix be Σ normal distribution；
Linear Gauss operation is carried out to formula (2), the conditional probability density P of melt index y can be obtainedk(y | x) and x and
The joint probability density P of yk(x, y) is shown below：
According to the definition of covariance and the Adding law of probability, the complete of the global probability density P (x) of x, x and y can be obtained
Office joint probability density P (x, y) has following form：
In formula,WithThe joint probability density of x and y is represented respectively
Mean vector and covariance matrix；αkRepresent the prior probability of k-th of gauss component in mixed model；
In semi-supervised mixed model, parameter to be estimated given gauss component number K includes
Since by probability learning Method Modeling, EM algorithm learning model parameters Θ can be usedK.In E steps, after each hidden variable
Probability is tested to be calculated as follows：
Z in formulaiAnd zjIt is represented respectively with having exemplar and the corresponding hidden change of discrete type of j-th of unlabeled exemplars for i-th
Amount；
In M steps, it is first determined the log-likelihood function of partial data is shown below：
WhereinWithIt is represented respectively with having exemplar and the corresponding hidden variable of unlabeled exemplars
Set.Lagrange multiplier β is introduced, with reference to constraintBuild following Lagrangian；
It willTo αkDerivation, and β is eliminated, and can obtain αkStudy formula, be shown below：
By L (ΘK) to right respectivelyWithDerivation can obtain
In formula1 for complete 1 arrange to
Amount.
By above-mentioned derivative zero setting, can obtainWithStudy formula, i.e.,
(6) K=K is traversedmin,Kmin+1,…,Kmax, step (4) and (5) is repeated, is calculated most using bayesian information criterion
Excellent gauss component number, is denoted as Kopt, and fromThe middle corresponding model parameter collection of selection
Wherein, the value of bayesian information criterion when BIC (K) represents gauss component number as K, calculation formula is such as
Under：
(7) acquisition only includes the unknown sample x of auxiliary variableq, the dimension of auxiliary variable is eliminated by step (3), utilizes step
Suddenly the optimal gauss component number K obtained in (6)optAnd corresponding model parameter collectionPolyacrylic melt index is carried out
Prediction, and the confidence interval of the predicted value is provided, it is specific as follows：
Melt index y is calculated as followsqConditional probability density P (yq|xq)：
In formulazqRepresent with it is unknown
Sample xqCorresponding hidden variable.
According to formula (19), to melt index yqPredicted value be
In addition, the variance of the predicted value is calculated as follows
According to formula (20) and formula (21), melt index yqThe calculation formula of confidence interval (three times standard deviation) be
In order to verify effectiveness of the invention, what collection was additional from petro-chemical corporation's computer scattered control system has mark
148 groups of signed-off sample sheet according to step (7), predicted melt index as verification sample sets, prediction result and is put accordingly
Believe that section is as shown in Figure 3.Meanwhile Fig. 4 gives prediction result of traditional partial least square model to melt index.Using square
The precision of prediction of root error (RMSE) the quantization present invention and partial least square model, are defined as follows
Wherein ytWithThe laboratory values and predicted value of t-th of verification sample are represented respectively.Method provided by the invention with partially most
The small two prediction RMSE for multiplying model are respectively 0.3233 and 0.4097.As it can be seen that the partial least square model pair that the present invention is more traditional
The precision of prediction of melt index is significantly improved, and prediction error reduces 21%.In addition, Fig. 3 is shown, confidence provided by the invention
Section can provide the true distribution that suitable width covers melt index, and traditional method is that do not have this function.
Above-described embodiment be used for illustrate the present invention rather than limit the invention, the present invention spirit and
In scope of the claims, to any modifications and changes that the present invention makes, protection scope of the present invention is both fallen within.
Claims (4)
1. a kind of polypropylene melt index Forecasting Methodology based on semi-supervised mixed model, which is characterized in that include the following steps：
(1) selection and the associated auxiliary variable x ∈ R of polypropylene melt index ym, wherein m expression auxiliary variable numbers；
(2) collect has exemplar collection comprising auxiliary variable and melt index simultaneouslyIt is auxiliary with only including
Help the unlabeled exemplars collection of variableWherein n1With n2The number for having exemplar and unlabeled exemplars is represented respectively
Amount；
(3) to [XL,YL] and XUNondimensionalization processing is done, the sample variance of auxiliary variable sample and melt index sample is converted
For unit variance；
(4) the gauss component number K of semi-supervised mixed model, random initializtion model parameter are givenWherein, αkFor the prior probability of k-th of gauss component,WithIt is respectively k-th high
The mean value and covariance matrix of the marginal probability density of x, ω in this ingredientkAnd ωkX and y in respectively k-th of gauss component
Regression coefficient,Represent the measurement noise variance of melt index y in k-th of gauss component；
(5) by step (3), treated has the original model parameter in exemplar collection, unlabeled exemplars collection and step (4) defeated
Enter in semi-supervised mixed model, by maximizing semi-supervised object function L (ΘK) learning model parameter ΘK；
(6) K=K is traversedmin,Kmin+1,…,Kmax, step (4) and (5) is repeated, optimal height is calculated using bayesian information criterion
This ingredient number, is denoted as Kopt, and fromThe middle corresponding model parameter collection of selection
(7) acquisition only includes the unknown sample of auxiliary variable, the dimension of auxiliary variable is eliminated by step (3), using in step (6)
The optimal gauss component number K obtainedoptAnd corresponding model parameter collectionPolyacrylic melt index is predicted, and
The confidence interval of the predicted value is provided.
2. the polypropylene melt index Forecasting Methodology according to claim 1 based on semi-supervised mixed model, feature exist
In the object function L (Θ of the semi-supervised mixed model built in the step (5)K) be：
Wherein, Pk(yi|xi) to give x in k-th of gauss componentiMelt index yiConditional probability density, Pk(xi) and Pk(xj)
X in respectively k-th of gauss componentiAnd xjMarginal probability density, RikFor [xi,yi] to the degree of membership of k-th of gauss component,
RjkFor xjTo the degree of membership of k-th of gauss component, their calculation formula is as follows：
In formula, N (；μ, Σ) expression mean value be μ, covariance matrix be Σ normal distribution；
WithThe mean vector and covariance matrix of the joint probability density of x and y are represented respectively, wherein,
3. the polypropylene melt index Forecasting Methodology according to claim 1 or 2 based on semi-supervised mixed model, feature
It is, the model parameterIterative formula have following form：
In formula1 is complete 1 column vector.
4. the polypropylene melt index prediction side according to any one of claim 1-3 based on semi-supervised mixed model
Method, which is characterized in that in the step (5), optimal gauss component number KoptCalculation formula it is as follows：
Wherein, the value of bayesian information criterion when BIC (K) represents gauss component number as K, calculation formula are as follows：
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