CN107451102A - A kind of semi-supervised Gaussian process for improving self-training algorithm returns soft-measuring modeling method - Google Patents
A kind of semi-supervised Gaussian process for improving self-training algorithm returns soft-measuring modeling method Download PDFInfo
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Abstract
Soft-measuring modeling method is returned based on the semi-supervised Gaussian process for improving self-training algorithm the invention discloses a kind of.Chemical process soft sensor modeling for the training dataset with missing leading variable.The leading variable sample that this method is lacked using the estimation of self-training algorithm, and according to influence of the obtained sample estimates to original training data, filter out the strong sample of generalization ability and be added to original sample concentration, so as to which the training sample set for forming new is modeled.On the one hand this method realizes the Effective selection of sample estimates, improve semi-supervised model accuracy；Another aspect filter criteria is simple, it is not necessary to divides complete data set, and is not limited by model structure.This method can improve product quality, reduce production cost.
Description
Technical field
The present invention relates to soft-measuring modeling method is returned based on the semi-supervised Gaussian process for improving self-training algorithm, belong to multiple
Miscellaneous industrial process modeling and hard measurement field.
Background technology
At present, the complexity of chemical process increasingly increases, and the requirement to product quality is also improving constantly, modern work
Industry generally requires to equip some advanced monitoring systems.Yet with some Key Quality variables sensor it is expensive, can
By property difference or there is very big measurement delay, cause some important process variables to survey effectively in real time
Amount.
In order to solve these problems, soft-measuring technique receives more and more extensive concern in industrial process field.In mistake
The more than ten years gone, the soft sensor modeling technology based on data-driven obtained it is widely studied, for improving the quality of product, reduce
Influence to environment.The method of some conventional linear regressions such as pivot returns (principal component
Regression, PCR), offset minimum binary (partial least squares, PLS), etc. can handle well input become
Linear relationship between amount and output variable.However, nonlinear relation, linear modelling side is usually presented between input and output
Method is no longer applicable, and non-linear modeling method such as artificial neural network (artificial neural networks, ANN), is supported
Vector machine (support vector machine, SVM), least square method supporting vector machine (least squares support
Vector machine, LS-SVM) good precision of prediction can be obtained.
Although these methods can obtain good global Generalization Capability, industrial process usually present the multistage, when
The dynamic characteristic of change, prediction effect tend not to be guaranteed.Gaussian process returns (Gaussian process
Regression, GPR) a kind of nonparametric density estimation can be used as, predicted value can be not only provided, predicted value can also be obtained
To the trust value of model.Therefore, selection GPR establishes soft-sensing model.
For leading variable in actual industrial process acquisition frequency well below auxiliary variable, cause training sample to be concentrated
Only a fraction sample has label, be more only input variable and lack the unlabeled exemplars of output variable.From instruction
It is simple to practice method computing, it is workable, and be easy to same soft-sensing model and combine, the present invention estimates the master of missing using self-training
Lead variate-value.
Traditional self-training algorithm only realizes the estimation of missing leading variable sample, can not but distinguish the quality of estimate.
Because self-training model according to similarity estimates missing leading variable, and the non-linear and nonparametric feature of GPR methods, the two
The phenomenon of easy generation model over-fitting is simply combined, therefore the present invention establishes a kind of criterion for screening sample estimates, rejects letter
The sample of redundancy is ceased, the strong sample of generalization ability is added into partial data concentrates, and realizes the reconstruct of training sample to improve mould
Type precision of prediction.
The content of the invention
For leading variable in actual industrial process acquisition frequency well below auxiliary variable, cause training sample to be concentrated
Only a fraction sample has label, and directly data set as use, which is modeled, can cause model prediction performance not high.
Using the leading variable sample of self-training algorithm estimation missing, and according to obtained sample estimates to original training number
According to influence, filter out the strong sample of generalization ability and be added to original sample concentration, carried out so as to form new training sample set
Modeling.
The purpose of the present invention is achieved through the following technical solutions：
Based on the semi-supervised GPR soft sensor modelings for improving self-training algorithm, methods described includes procedure below：Supervised for half
Data set is superintended and directed, estimates missing leading variable value with self-training algorithm, and uses a kind of Variable Selection method, picks out generalization ability
Strong sample reconstruct training sample set.
Finally according to the training sample set after reconstruct, the query sample newly to arrive is predicted.
Brief description of the drawings
Fig. 1 is the semi-supervised GPR modeling procedures of improved self-training algorithm；
Fig. 2 is the RMSE of the various method predictions under different label rates；
Embodiment
With reference to shown in Fig. 1, the present invention is further described：
By common chemical process --- exemplified by debutanizing tower process.Experimental data comes from debutanizing tower E processes, to fourth
Alkane concentration is predicted.
Step 1：Collection has exemplar collection { XL,YL, L indicates label；With unlabeled exemplars collection { XU, U indicates no mark
Label, and for each sample x of unlabeled exemplars concentrationi∈{XU, it is calculated with there is exemplar to concentrate each sample xj∈
{XL, j=1,2 ..., NLSimilarity, NLExemplar number is indicated, index of similarity Sim calculating such as formula (1) institute
Showing, and the similarity arranged in descending order is designated as RSim, wherein γ ∈ (0,1) are similarity parameters, | | xi-xj| |, cos ＜ xi,
xj＞ represents vector x respectivelyi,xjBetween Euclidean distance and folder cosine of an angle.
Simj=γ exp (- | | xi-xj| |)+(1- γ) cos ＜ xi,xj＞ (1)
Step 2：Current unlabeled exemplars are estimated using formula (2), whereinRepresent k-th and current unlabeled exemplars
The label value of most like exemplar, w are the most like number of samples set.
Step 3：Step 1 and Step 2 is repeated, until the estimate of unlabeled exemplars collection all obtains, obtains estimating sample
This collection
Step 4：Establish withCorresponding GPR models, and calculate the mould
Type is to legacy data collection { XL,YLPrediction error, computational methods are formula (3).
Step 5：Repeat Step4 until corresponding to all sample estimateses predict error all calculate, that is, obtain error to
ERR (i), i=1,2 are measured ... nU, and the error vector arranged in descending order is designated as RERR.
Step 6：The maximum preceding k sample of error will be predicted as exptended sample collection [Xadd；Yadd] it has been added to label sample
This concentration, composing training sample set { Xtrain,Ytrain}={ [XL；Xadd],[YL；Yadd], wherein, RERR (k) is expressed as resetting
The error vector RERR of row preceding k element, Xadd=XU[RERR (k)],
Step 7：Using the training sample after reconstruct, final GPR models are established, model is used when query sample arrives
It is predicted.
Assuming that there are the training sample set X=[x that n sample is formed1,x2,...,xn]TWith Y=[y1,y2,...,yn]T, wherein
xi∈Rm(i=1,2 ..., n) be m dimension input vector, yi∈ R (i=1,2 ..., n) it is output.Gaussian process, which returns, to be assumed
The Gaussian prior that regression function y=f (x) has zero-mean is distributed, and obeys specific descriptions and sees (4) formula：F~N (μ, ∑) expressions f~
N(μ,∑)
Y={ f (x1),f(x2),...,f(xn)~N (0, K) (4)
Wherein, f~N (μ, ∑) represents that f is obeyed with μ, and ∑ is the normal distribution of average and variance
F is unknown functional form in formula (4), and K is covariance matrix, and its i-th row jth column element is defined as kij=k
(xi,xj), wherein k () is kernel function, chooses conventional square exponential kernel functions herein, and its definition is provided by (5) formula：
Wherein δij=1 only sets up in i=j, otherwise δij=0.M=l-2I, l are variance measures,WithIt is signal side respectively
Difference and noise variance.
Hyper parameter setValue have a great impact to last prediction result, therefore suitable super ginseng
Several performances to GPR models serve key.Optimal hyper parameter Θ is typically solved using Maximum Likelihood Estimation Method*, such as (6)
Shown in formula.
The closed form of parameters optimal solution is tried to achieve by conjugate gradient decent
Once obtaining optimal hyper parameter, GPR models can determine that.As new query sample xnewAfter arrival, according to multidimensional
The property of Gaussian Profile, can obtain be all the leading variable of Gaussian Profile posterior probability (ynew|X,y,xnew)~N (mean
(ynew),var(ynew)), the last prediction output valve using desired value as model, wherein mean (ynew) and var (ynew) respectively
It is (ynew|X,Y,xnew) distribution expectation and variance, computational methods such as formula (7) and (8)：
Output is the predicted value of butane concentration
Fig. 2 is the RMSE of the various method predictions under different label rates；As seen from the figure, based on the height for improving self-training algorithm
This process, which returns semi-supervised soft-measuring modeling method, can effectively predict butane concentration.
Claims (2)
1. soft-measuring modeling method is returned based on the semi-supervised Gaussian process for improving self-training algorithm, it is characterised in that this method
Step is：
Step 1：Collection has exemplar collection { XL,YL, L indicates label；With unlabeled exemplars collection { XU, U indicates no label,
And for each sample x of unlabeled exemplars concentrationi∈{XU, it is calculated with there is exemplar to concentrate each sample xj∈{XL,j
=1,2 ..., NLSimilarity, NLExemplar number is indicated, shown in index of similarity Sim calculating such as formula (1), and
The similarity arranged in descending order is designated as RSim, wherein γ ∈ (0,1) are similarity parameters, | | xi-xj| |, cos ＜ xi,xj＞
Vector x is represented respectivelyi,xjBetween Euclidean distance and folder cosine of an angle.
Simj=γ exp (- | | xi-xj| |)+(1- γ) cos ＜ xi,xj＞ (1)
Step 2：Current unlabeled exemplars are estimated using formula (2), whereinRepresent k-th and current unlabeled exemplars most phase
As exemplar label value, w be set most like number of samples.
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Step 3：Step 1 and Step 2 is repeated, until the estimate of unlabeled exemplars collection all obtains, obtains sample estimates collection
Step 4：Establish withI=1,2 ..., nUCorresponding soft-sensing model, and calculate and be somebody's turn to do
Model is to legacy data collection { XL,YLPrediction error, computational methods are formula (3).
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Step 5：Step4 is repeated until predicting that error all calculates corresponding to all sample estimateses, that is, obtains error vector ERR
(i), i=1,2 ... nU, and the error vector arranged in descending order is designated as RERR.
Step 6：The maximum preceding k sample of error will be predicted as exptended sample collection [Xadd；Yadd] it has been added to exemplar collection
In, composing training sample set { Xtrain,Ytrain}={ [XL；Xadd],[YL；Yadd], wherein, RERR (k) is expressed as permutatation
Error vector RERR preceding k element, Xadd=XU[RERR (k)],
Step 7：Using the training sample after reconstruct, final soft-sensing model is established, model is used when query sample arrives
It is predicted.
2. according to claim 1 return soft sensor modeling side based on the semi-supervised Gaussian process for improving self-training algorithm
Method, it is characterised in that the leading variable value of missing is estimated using self-training algorithm, and it is accurate to establish the screening of estimation label value
Then, the generalization ability of model is improved.
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