CN106569982A - GPR online soft measurement method and system with singular point detection compensation function - Google Patents

Abstract

The invention relates to a GPR online soft measurement method and system with a singular point detection compensation function. The problem that during practical application of a soft measurement method, singular points may affect a prediction result in respect of query samples is solved. According to the method, first, a Gaussian process regression (GPR) method is utilized to perform modeling on a training sample to obtain a GPR soft measurement model; second, the Pauta criterion is adopted to perform singular point detection on a new query sample; when a singular value of the new query sample is determined, an auxiliary model is utilized to repair the singular value, and then the GPR soft measurement model is utilized to predict a query sample point obtained after repairing; or else, the GPR soft measurement model is directly used for predicting a new query sample point. The GPR online soft measurement method and system are used for realizing online estimation of important indicators in the chemical process eventually, and the stability of an industrial system during operation is improved.

Description

GPR online soft sensor method and system with inflection point detection compensation

Technical field

The present invention relates to a kind of be related to the GPR online soft sensor method and system with inflection point detection compensation, belong to complicated Industrial process modeling and hard measurement field.

Background technology

Science and technology it is growing cause industrial processes become to become increasingly complex with finely, while to industrial process Index monitoring and control requirement it is higher.But it is extremely difficult that current these indexs carry out On-line sampling system.Therefore it is soft E measurement technology is arisen at the historic moment and greatlys save manual analyses time and equipment cost.

At present, the common modeling method based on data mainly have offset minimum binary (partial least squares, PLS), artificial neural network (artificial neural networks, ANN), least square method supporting vector machine (least Squares support vector machine, LSSVM) and Gaussian process recurrence (gaussian process Regression, GPR) etc..It is a kind of brand-new machine grown up based on Bayesian statistical theory that wherein Gaussian process is returned Learning method.It has good adaptability on the challenge such as some small samples, high dimension, non-linear is processed.Except this it Outward, which also has the advantages that model parameter is few, parameter optimization is relatively easy, output is with probability meaning.

A class problem can be run in production application in view of soft-sensing model, i.e., when collecting a new inquiry sample When this, it is impossible to ensure that adopted sample point is accurate.But traditional flexible measurement method seldom notes such in research application Problem, it is general that singular value process is carried out to training sample in the off-line modeling stage only, in actual applications directly to query sample Point is predicted, and actual production process is instructed with this result.But, when query sample point has singular value, blindly Which is predicted and will necessarily obtain a wrong predictive value.Actual production process is fed back using this error prediction value When instructing, the stability and effect of optimization of actual industrial production system is would necessarily affect, or even system crash can be caused.

In view of above-mentioned defect, the positive in addition research and innovation of the design people is mended to founding a kind of band inflection point detection The GPR online soft sensor method and system repaid so as to more the value in industry.

The content of the invention

To solve above-mentioned technical problem, it is an object of the invention to provide it is strange that a kind of effective detection goes out new query sample point Dissimilarity, and singular point is compensated, the accuracy of online soft sensor prediction is improve, and then industrial system is improved in operation The stability of period.

GPR online soft sensor method of the present invention with inflection point detection compensation, including：

GPR soft-sensing models are set up using Gaussian process homing method；

Improvement is adopted to draw to carry out inflection point detection to new query sample point up to criterion；

If query sample point is normal, the query sample point is predicted using GPR soft-sensing models, is predicted As a result；

If query sample point is singular point, training sample is processed using singular point information, after being processed Training sample set simultaneously sets up submodel, singular point xq is repaired followed by submodel, sample is inquired about after being compensated This pointThen the query sample point is predicted using GPR soft-sensing models, is predicted the outcome；

Wherein, Pauta criterion is specially：

If training dataset X={ x_i|x_i∈R^m}_{I=1 ... n}, m is the dimension of process variable, and n is the individual of training data Number, X is the matrix of a n × m, for each column data obtains its average according to following formulaAnd mean square deviation S_j：

As a new collecting sample point x_qγ is calculated by Pauta criterion per one-dimensional element to which during arrival_j, wherein

If meeting arbitrary γ_j＞ 3, then show that this sample point belongs to unusual sample point, while obtaining this sample point singular value Present position；

Submodel is repaired to be included：Assume that unusual query sample point present position is sample point x_qJth is tieed up, with this to training Sample set X process, the process include：

By x_qObtain x_q'={ x_q,1,x_q,2…x_q,j-1,x_q,j+1…x_q,m, X ' is obtained with reason X, be shown below：

Y'=[x_1,j,x_2,j,……x_n,j]^T

Simultaneously to query sample point x_qProcessed, be shown below：

X ', Y ' and x are obtained by above-mentioned process_q', wherein X ' is the former training sample X new inputs of gained after treatment Training sample set, Y ' arrange the new output training sample set for constituting residing for singular value in former training sample X, and x_q' it is then x_qJing Cross the new query sample point of gained after process.Finally X ' and Y ' are reconfigured as a new training sample set, using Gauss mistake Journey homing method is trained to which and obtains submodel；

Using gained submodel to x_q' be predicted and obtain singular value x_q,jPredictive value x '_q,j, using gained x '_q,jIt is right x_qMiddle singular value x_q,jIt is replaced and is compensated rear query sample point

Further, also include that the query sample to being judged to singular point carries out secondary detection, specifically include：

Chosen and x from training sample using the method for Euclidean distance_qMost like sample point, such as formula under specific formula for calculation It is shown：

d_i(x_q,x_i)=| | x_q,x_i| |, i=1 ..., n

In formula, x_i、d_iAnd s_iEuclidean distance and coefficient of similarity between training sample point, sample point is represented respectively；

As in singular point, singular value can produce interference to asking for similar sample point, thus it is right before similar sample point is asked for Unusual sample point is processed.By singular point x_qObtain x '_q={ x_q,1,x_q,2…x_q,j-1,x_q,j+1…x_q,m, X ' is obtained with reason X, such as Shown in following formula：

In the middle acquisition x ' of X '_qMost like sample point x '_p, so as to obtain x '_pIn the middle position information of X ', finally according to institute Obtain positional information and obtain x_qThe most like sample point x in X_p.Obtain error vector x_eSuch as following formula：

x_e={ x_q,1-x_p,1,x_q,2-x_p,2,…,x_q,m-x_p,m}

By error vector x_e：

IfThen query sample point x_qFor unusual sample point；

Otherwise, x_qNormal queries sample point is to report unusual sample point by mistake, wherein α is predetermined threshold value.

Further, predetermined threshold value α is set to 0.9.

Further, GPR soft-sensing models model is as follows：

Given training sample set is input into X={ x_i|x_i∈R^m}_{I=1 ... n}With output Y={ y_i∈R}_{I=1 ... n}, it is input into and exports it Between relation be shown below：

Y=f (x)+ε

Wherein f (x) is unknown functional form, and ε is that average is 0, and variance isGaussian noise；

Gaussian process regression model is limited f (x_i) stochastic variable constituted multivariate Gaussian distribution：f(x₁),…,f (x_n) ∝ N (0, Σ), wherein covariance matrix ask for used radial direction base covariance function, be shown below：

Wherein v represents the overall tolerance of priori；

Represent the variance of the noise of Gaussian distributed；

δ_ijIt is Kronecher operators；

ω_tRepresent the relative importance of each auxiliary variable；

For described radial direction base covariance function, shown in its log-likelihood function equation below：

Wherein hyper parameterC is corresponding covariance matrix, and then log-likelihood function enters Row derivation is obtained：

The hyper parameter θ of optimum is obtained by conjugate gradient method；

For the test sample point x that newly arrives_q, it is assumed which belongs to a joint normal distribution with the data of training sample, obtains Average and prediction variance are predicted to which：

y_q(x_q)=c^T(x_q)C^-1Y

Wherein c (x_q) for the covariance vector between test sample and each training sample, c (x_q,x_q) for test sample with The covariance value of itself, covariance matrixes of the C for training sample.

GPR online soft sensor system of the present invention with inflection point detection compensation, including：

Model sets up unit, for setting up GPR soft-sensing models, GPR submodels；

Inflection point detection unit, draws for adopting to improve to carry out singular point inspection to new query sample point up to criterion Survey；

If query sample point is normal, the GPR soft-sensing models of unit foundation are set up to the query sample using model Point is predicted, and is predicted the outcome；

If query sample point is singular point, training sample is processed using singular point information, after being processed Training sample set, model are set up unit and set up GPR submodels, followed by the GPR submodels to singular point x_qRepaiied Mend, be compensated rear query sample pointThe GPR soft-sensing model of unit foundation is set up using model then to inquiring about after the compensation Sample pointIt is predicted, is predicted the outcome；

Wherein, Pauta criterion is specially：

If training dataset X={ x_i|x_i∈R^m}_{I=1 ... n}, m is the dimension of process variable, and n is the individual of training data Number, X is the matrix of a n × m, for each column data obtains its average according to following formulaAnd mean square deviation S_j：

As a new collecting sample point x_qγ is calculated by Pauta criterion per one-dimensional element to which during arrival_j, wherein

If meeting arbitrary γ_j＞ 3, then show that this sample point belongs to unusual sample point, while obtaining this sample point singular value Present position；

Submodel method for repairing and mending includes：Assume that unusual query sample point present position is sample point x_qJth is tieed up, right with this Training sample set X process, the process include：

By x_qObtain x '_q={ x_q,1,x_q,2…x_q,j-1,x_q,j+1…x_q,m, X ', Y ' are obtained with reason X, be shown below：

Y'=[x_1,j,x_2,j,……x_n,j]^T

Simultaneously to query sample point x_qProcessed, be shown below：

X ', Y ' and x ' are obtained by above-mentioned process_q, wherein X ' is the former training sample X new inputs of gained after treatment Training sample set, Y ' arrange the new output training sample set for constituting residing for singular value in former training sample X, and x '_qIt is then x_qJing Cross the new query sample point of gained after process.Finally X ' and Y ' are reconfigured as a new training sample set, using Gauss mistake Journey homing method is trained to which and obtains submodel；

Using gained submodel to x '_qIt is predicted and obtains singular value x_q,jPredictive value x '_q,j, using gained x '_q,jIt is right x_qMiddle singular value x_q,jIt is replaced and is compensated rear query sample point

Further, also include query unit secondary to singular point, carry out for the query sample to being judged to singular point Secondary detection, specifically includes：

Chosen and x from training sample using the method for Euclidean distance_qMost like sample point, such as formula under specific formula for calculation It is shown：

d_i(x_q,x_i)=| | x_q,x_i| |, i=1 ..., n

In formula, x_i、d_iAnd s_iEuclidean distance and coefficient of similarity between training sample point, sample point is represented respectively；

As in singular point, singular value can produce interference to asking for similar sample point, thus it is right before similar sample point is asked for Unusual sample point is processed.By singular point x_qObtain x '_q={ x_q,1,x_q,2…x_q,j-1,x_q,j+1…x_q,m, X ' is obtained with reason X, such as Shown in following formula：

In the middle acquisition x ' of X '_qMost like sample point x '_p, so as to obtain x '_pIn the middle position information of X ', finally according to institute Obtain positional information and obtain x_qThe most like sample point x in X_p.Obtain error vector x_eSuch as following formula：

x_e={ x_q,1-x_p,1,x_q,2-x_p,2,…,x_q,m-x_p,m}

By error vector x_e：

IfThen query sample point x_qFor unusual sample point；

Otherwise, x_qNormal queries sample point is to report unusual sample point by mistake, wherein α is predetermined threshold value.

By such scheme, the present invention at least has advantages below：

The present invention is returned using Gaussian process to original training data first and carries out off-line modeling；Secondly using improve draw according to Inflection point detection is carried out to query sample point of newly arriving up to criterion.If query sample of newly arriving point is confirmed to be singular point, using auxiliary Help model method to repair this singular point, then query sample point after repairing is carried out using offline soft-sensing model pre- Survey；Otherwise, directly query sample point is predicted using offline soft-sensing model.Finally realize to chemical process important indicator On-line Estimation, and substantially increase the stability of system.

Described above is only the general introduction of technical solution of the present invention, in order to better understand the technological means of the present invention, And can be practiced according to the content of description, below with presently preferred embodiments of the present invention and coordinate accompanying drawing describe in detail as after.

Description of the drawings

Fig. 1 is the modeling procedure figure of the GPR online soft sensor methods with inflection point detection compensation；

Fig. 2 sulfur recovery unit flow processs；

Fig. 3 predicts the outcome without inflection point detection compensation method；

Fig. 4 is without inflection point detection compensation method forecast error；

Fig. 5 inflection point detection performance comparisons；

Fig. 6 predicts the outcome with inflection point detection compensation method；

Fig. 7 is with inflection point detection compensation method forecast error.

Specific embodiment

With reference to the accompanying drawings and examples, the specific embodiment of the present invention is described in further detail.Hereinafter implement Example is for illustrating the present invention, but is not limited to the scope of the present invention.

Embodiment 1

The GPR online soft sensor methods that the present embodiment is compensated with inflection point detection, by an actual sulfur recovery industry mistake Number of passes is demonstrated institute's extracting method of the present invention with stronger singular point capacity of resisting disturbance according to emulating.

Step 1：The input of gatherer process and output data composition soft sensor modeling data base.

Step 2：Training sample is standardized, normalization and the pretreatment such as singular point is gone.

Step 3：Input data after process and output data are constituted into training sample set and corresponding GPR hard measurements mould is set up Type.The GPR models of foundation are：

Given training sample set is input into X={ x_i|x_i∈R^m}_{I=1 ... n}With output Y={ y_i∈R}_{I=1 ... n}.It is generally defeated Shown in relation between entering and exporting such as formula (1)：

Y=f (x)+ε (1)

Wherein f (x) is unknown functional form, and ε is that average is 0, and variance isGaussian noise.Gaussian process returns mould Type is limited f (x_i) stochastic variable constituted multivariate Gaussian distribution：f(x₁),…,f(x_n)∝N(0,Σ).Wherein covariance The asking for of matrix has used covariance function, and the present invention chooses radial direction base covariance function, such as shown in formula (2)：

Wherein v represents the overall tolerance of priori, can control the degree of local correlations.Represent and obey Gauss point The variance of the noise of cloth, δ_ijIt is Kronecher operators, ω_tRepresent the relative importance of each auxiliary variable.For above-mentioned association side Difference function, shown in its log-likelihood function such as formula (3)：

Wherein hyper parameterC is corresponding covariance matrix.Then to formula (3) logarithm seemingly Right function carries out derivation and can obtain：

The hyper parameter θ of optimum is obtained by conjugate gradient method.

For the test sample point x that newly arrives_q, it is assumed which belongs to a joint normal distribution with the data of training sample, can Obtain its prediction average and prediction variance：

y_q(x_q)=c^T(x_q)C^-1Y (5)

C (x in formula (5), (6)_q) for the covariance vector between test sample and each training sample, c (x_q,x_q) be Test sample and the covariance value of itself, covariance matrixes of the C for training sample.

Step 4：As any one query sample point x_qDuring arrival, inflection point detection is carried out to which using Pauta criterion. If query sample point normally if go to step 6；Otherwise, 5 are gone to step.Pauta criterion method is：

If training dataset X={ x_i|x_i∈R^m}_{I=1 ... n}, m is the dimension of process variable, and n is the individual of training data Number.Apparent X is the matrix of a n × m.For each column data, we can obtain its average and according to formula (7), (8) Variance：

As a new collecting sample point x_qγ is calculated by formula (9) per one-dimensional element to which during arrival_j：

If meeting arbitrary γ_j＞ 3, then show that this sample point belongs to unusual sample point, while it is unusual that this sample point is obtained Value present position.Discriminant (9) is Pauta criterion.

But we can have found that some normal queries sample point can be detected as unusual sample among practical application Point.For this problem, further query sample point is analyzed with reference to similarity based method, the mistake of Pauta criterion is reduced with this Report rate.

When Pauta criterion detects singular point x_qWhen, it will be assumed that singular value present position is sample point x_qJth is tieed up.Then Choose and x from training sample using the method for similarity criteria_qMost like sample point.Similarity criteria of the present invention selects Europe The method of family name's distance, shown in specific formula for calculation such as formula (10), (11)：

d_i(x_q,x_i)=| | x_q,x_i| |, i=1 ..., n (10)

In formula, x_i、d_iAnd s_iEuclidean distance and coefficient of similarity between training sample point, sample point is represented respectively.

As in singular point, singular value can produce interference to asking for similar sample point, thus it is right before similar sample point is asked for Unusual sample point is processed.First by x_qX ' can be obtained_q={ x_q,1,x_q,2…x_q,j-1,x_q,j+1…x_q,m, X ' can be obtained with reason X, As shown in formula (12)：

By formula (10), (11) can be in the middle acquisition x ' of X '_qMost like sample point x '_p, so as to obtain x '_pIn the middle institutes of X ' In positional information, x can be obtained finally according to gained positional information_qThe most like sample point x in X_p..Therefore be obtained error to Amount x_eSuch as formula (13)

x_e={ x_q,1-x_p,1,x_q,2-x_p,2,…,x_q,m-x_p,m} (13)

By error vector x_eCan obtain：

If(α is predetermined threshold value, specifically can be obtained according to experiment simulation analysis), then query sample point x_qFor unusual Sample point；Otherwise, x_qNormal queries sample point is to report unusual sample point by mistake.

Step 5：Original training sample is processed first with singular point information, the training sample set after being processed And set up submodel.Followed by submodel to singular point x_qRepaired, be compensated rear query sample pointAuxiliary Model method is：

As new collection query sample point x_qDuring arrival, singular values standard form is carried out to which first with Pauta criterion.If inspection Survey result and show query sample point x_qBelong to normal queries sample point, then directly which be predicted using GPR soft-sensing models, Simultaneously actual industrial production control process is instructed；Otherwise, to query sample point x_qRepaiied using auxiliary model identification algorithm Mend, detailed process is as follows：

May be assumed that singular value present position is sample point x first_qJth is tieed up, with this to training sample set X process, such as Shown in formula (12), (15)：

Y'=[x_1,j,x_2,j,……x_n,j]^T (15)

Simultaneously to query sample point x_qProcessed, as shown in formula (16)：

Then X ', Y ' and x ' are obtained by above-mentioned process_q, wherein X ' is that gained is new after treatment for former training sample X Input training sample set, Y ' arranges the new output training sample set for constituting residing for singular value in former training sample X, and x '_qThen It is x_qNew query sample point obtained by after treatment.Finally X ' and Y ' are reconfigured as a new training sample set, utilization Gaussian process homing method is trained to which and obtains submodel.Modeling detailed process refers to step 3.

Using gained submodel to x '_qIt is predicted and obtains singular value x_q,jPredictive value x '_q,j, using gained x '_q,jIt is right x_qMiddle singular value x_q,jIt is replaced and is compensated rear query sample point

Step 6：Using gained GPR soft-sensing models to query sample point after compensationOr x_q(query sample point non-singular point When) be predicted and predicted the outcomeActual industrial production control process is instructed with this.

Can be seen that for the test sample collection that there is singular point from Fig. 3, Fig. 4, if without process directly to test Sample point is predicted, and can produce predicting the outcome for substantial deviation true value in singular point position, as circle chooses an institute in Fig. 3 Show.If predict the outcome using this rashly instructed to actual industrial process, greater impact is produced to control system inherently, Production system collapse is even resulted in, a large amount of economic losses are caused.

As predetermined threshold value α is related to the quality of singular values standard form result, therefore the present invention enters when arranging different value to threshold alpha The detection that row compares.Can find that when taking 0.9 can be to prevent singular point wrong report completely from Fig. 5 contrasts, therefore predetermined threshold value of the present invention It is set to 0.9.

By predicting the outcome in singular point position after inflection point detection with compensation is can be seen that shown in Fig. 6, Fig. 7 Put and can be good at tracking practical situation.Compared to result shown in Fig. 3, Fig. 4, the method can produce higher supporting to singular point Anti- ability, provides more accurately tutorial message to actual industrial process.

Embodiment 2

GPR online soft sensor system of the present embodiment based on submodel, including：

Model sets up unit, for setting up GPR soft-sensing models, submodel；

Inflection point detection unit, draws for adopting to improve to carry out singular point inspection to new query sample point up to criterion Survey；

If query sample point is normal, the GPR soft-sensing models of unit foundation are set up to the query sample using model Point is predicted, and is predicted the outcome；

If query sample point is singular point, training sample is processed using singular point information, after being processed Training sample set, model are set up unit and set up submodel, followed by the submodel to singular point x_qRepaired, obtained Query sample point after compensationThen the GPR soft-sensing models of unit foundation are set up to query sample point after the compensation using modelIt is predicted, is predicted the outcome；

Wherein, Pauta criterion is specially：

If training dataset X={ x_i|x_i∈R^m}_{I=1 ... n}, m is the dimension of process variable, and n is the individual of training data Number, X is the matrix of a n × m, for each column data obtains its average according to following formulaAnd mean square deviation S_j：

As a new collecting sample point x_qγ is calculated by Pauta criterion per one-dimensional element to which during arrival_j, wherein

If meeting arbitrary γ_j＞ 3, then show that this sample point belongs to unusual sample point, while it is unusual that this sample point is obtained Value present position；

Submodel method for repairing and mending includes：Assume that unusual query sample point present position is sample point x_qJth is tieed up, right with this Training sample set X process, the process include：

By x_qX ' can be obtained_q={ x_q,1,x_q,2…x_q,j-1,x_q,j+1…x_q,m, X ' can be obtained with reason X, be shown below：

Y'=[x_1,j,x_2,j,……x_n,j]^T

Simultaneously to query sample point x_qProcessed, be shown below：

Then X ', Y ' and x ' are obtained by above-mentioned process_q, wherein X ' is that gained is new after treatment for former training sample X Input training sample set, Y ' arranges the new output training sample set for constituting residing for singular value in former training sample X, and x '_qThen It is x_qNew query sample point obtained by after treatment.Finally X ' and Y ' are reconfigured as a new training sample set, utilization Gaussian process homing method is trained to which and obtains submodel.

Using gained submodel to x '_qIt is predicted and obtains singular value x_q,jPredictive value x '_q,j, using gained x '_q,jIt is right x_qMiddle singular value x_q,jIt is replaced and is compensated rear query sample point

The present embodiment also includes query unit secondary to singular point, carries out two for the query sample to being judged to singular point Secondary detection, specifically includes：

Chosen and x from training sample using the method for Euclidean distance_qMost like sample point, such as formula under specific formula for calculation It is shown：

d_i(x_q,x_i)=| | x_q,x_i| |, i=1 ..., n

In formula, x_i、d_iAnd s_iEuclidean distance and coefficient of similarity between training sample point, sample point is represented respectively；

As in singular point, singular value can produce interference to asking for similar sample point, thus it is right before similar sample point is asked for Unusual sample point is processed.By singular point x_qObtain x '_q={ x_q,1,x_q,2…x_q,j-1,x_q,j+1…x_q,m, X ' is obtained with reason X, such as Shown in following formula：

In the middle acquisition x ' of X '_qMost like sample point x '_p, so as to obtain x '_pIn the middle position information of X ', finally according to institute Obtain positional information and can obtain x_qThe most like sample point x in X_p.Obtain error vector x_eSuch as following formula：

x_e={ x_q,1-x_p,1,x_q,2-x_p,2,…,x_q,m-x_p,m}

By error vector x_e：

IfThen query sample point x_qFor unusual sample point；

Otherwise, x_qNormal queries sample point is to report unusual sample point by mistake, wherein α is predetermined threshold value.

The GPR soft-sensing models set up in the various embodiments described above may be replaced by：Offset minimum binary (partial Least squares, PLS), artificial neural network (artificial neural networks, ANN), least square support Vector machine (least squares support vector machine, LSSVM).

The above is only the preferred embodiment of the present invention, is not limited to the present invention, it is noted that for this skill For the those of ordinary skill in art field, on the premise of without departing from the technology of the present invention principle, can also make it is some improvement and Modification, these improve and modification also should be regarded as protection scope of the present invention.

Claims (6)

1. it is a kind of with inflection point detection compensation GPR online soft sensor methods, it is characterised in that include：

GPR soft-sensing models are set up using Gaussian process homing method；

Adopt improvement to draw to reach criterion to new query sample point x_qCarry out inflection point detection；

If query sample point is normal, the query sample point is predicted using GPR soft-sensing models, obtains prediction knot Really；

If query sample point is singular point, training sample is processed using singular point information, the training after being processed Sample set simultaneously sets up submodel, followed by submodel to query sample point x_qRepaired, after being compensated, inquired about sample This pointFinally the query sample point is predicted using soft-sensing model, is predicted the outcome；

Wherein, Pauta criterion is specially：

There are training dataset X={ x_i|x_i∈R^m}_{I=1 ... n}, m is the dimension of process variable, and n is the number of training data, and X is one The matrix of n × m, for each column data obtains its average according to following formulaAnd mean square deviation S_j：

As a new query sample point x_qγ is calculated by Pauta criterion per one-dimensional element to which during arrival_j, wherein γ_j For：

If meeting arbitrary γ_j＞ 3, then show that this sample point belongs to unusual sample point, while being obtained residing for this sample point singular value Position；

Submodel is repaired to be included：Assume that unusual query sample point present position is query sample point x_qJth is tieed up, with this to training Sample set X process, the process include：

By query sample point x_qX can be obtained_q'={ x_q,1,x_q,2…x_q,j-1,x_q,j+1…x_q,m, X ' and Y ' can be obtained with reason X, it is as follows Shown in formula：

Y'=[x_1,j,x_2,j,……x_n,j]^T

X ', Y ' and x ' are obtained by above-mentioned process_q, wherein X ' is the former training sample X new input training samples of gained after treatment This collection, Y ' arrange the new output training sample set for constituting residing for singular value in former training sample X, and x '_qIt is then x_qThrough processing The new query sample point of gained afterwards, is finally reconfigured X ' and Y ' for a new training sample set, is returned using Gaussian process Method is trained to which and obtains submodel；

Using gained submodel to x '_qIt is predicted and obtains singular value x_q,jPredictive value x '_q,j, using gained x '_q,jTo x_qIn Singular value x_q,jIt is replaced and is compensated rear query sample point

2. it is according to claim 1 with inflection point detection compensation GPR online soft sensor methods, it is characterised in that also wrap Including the query sample to being judged to singular point carries out secondary detection, specifically includes：

Chosen from training sample and singular point x using the method for Euclidean distance_qMost like sample point, specific formula for calculation following formula It is shown：

d_i(x_q,x_i)=| | x_q,x_i| |, i=1 ..., n

In formula, x_i、d_iAnd s_iEuclidean distance and coefficient of similarity between training sample point, sample point is represented respectively；

As in singular point, singular value can produce interference to asking for similar sample point, therefore to unusual before similar sample point is asked for Sample point is processed, by singular point x_qObtain x '_q={ x_q,1,x_q,2…x_q,j-1,x_q,j+1…x_q,m}。

In the middle acquisition x ' of X '_qMost like sample point x '_p, so as to obtain x '_pIn the middle position information of X ', finally according to gained position Put information acquisition x_qThe most like sample point x in X_p, obtain error vector x_eSuch as following formula：

x_e={ x_q,1-x_p,1,x_q,2-x_p,2,…,x_q,m-x_p,m}

By error vector x_e：

IfThen query sample point x_qFor unusual sample point；

Otherwise, query sample point x_qNormal queries sample point is to report unusual sample point by mistake, wherein α is predetermined threshold value.

3. GPR online soft sensor methods with inflection point detection compensation according to claim 2, it is characterised in that default Threshold alpha is set to 0.9.

4. it is according to claim 1 with inflection point detection compensation GPR online soft sensor methods, it is characterised in that GPR is soft Measurement model model is as follows：

Given training sample set is input into X={ x_i|x_i∈R^m}_{I=1 ... n}With output Y={ y_i∈R}_{I=1 ... n}, the pass between input and output System is shown below：

Y=f (x)+ε

Wherein f (x) is unknown functional form, and ε is that average is 0, and variance isGaussian noise；

Gaussian process regression model is limited f (x_i) stochastic variable constituted multivariate Gaussian distribution：f(x₁),…,f(x_n)∝ The asking for of N (0, Σ), wherein covariance matrix has used radial direction base covariance function, is shown below：

Wherein v represents the overall tolerance of priori；

Represent the variance of the noise of Gaussian distributed；

δ_ijIt is Kronecher operators；

ω_tRepresent the relative importance of each auxiliary variable；

For described radial direction base covariance function, shown in its log-likelihood function equation below：

Wherein hyper parameterC is corresponding covariance matrix, and then log-likelihood function is asked Lead：

The hyper parameter θ of optimum is obtained by conjugate gradient method；

For the test sample point x that newly arrives_q, it is assumed which belongs to a joint normal distribution with the data of training sample, obtains which pre- Survey average and prediction variance：

y_q(x_q)=c^T(x_q)C^-1Y

Wherein c (x_q) for the covariance vector between test sample and each training sample, c (x_q,x_q) for test sample and itself Covariance value, C for training sample covariance matrix.

5. it is a kind of with inflection point detection compensation GPR online soft sensor systems, it is characterised in that include：

Model sets up unit, for setting up GPR soft-sensing models, GPR submodels；

Inflection point detection unit, for adopting improvement Pauta criterion to carry out inflection point detection to new query sample point；

If query sample point is normal, the GPR soft-sensing models for setting up unit foundation using model are clicked through to the query sample Row prediction, is predicted the outcome；

If query sample point is singular point, training sample is processed using singular point information, the training after being processed Sample set, model are set up unit and set up GPR submodels, followed by the GPR submodels to singular point x_qRepaired, obtained The query sample point to after compensationThen the GPR soft-sensing models of unit foundation are set up to query sample after the compensation using model PointIt is predicted, is predicted the outcome；

Wherein, Pauta criterion is specially：

If training dataset X={ x_i|x_i∈R^m}_{I=1 ... n}, m is the dimension of process variable, and n is the number of training data, and X is The matrix of one n × m, for each column data obtains its average according to following formulaAnd mean square deviation S_j：

As a new collecting sample point x_qγ is calculated by Pauta criterion per one-dimensional element to which during arrival_j, wherein ${\mathrm{\γ}}_j=\frac{|x_{q,j}-{\stackrel{\‾}{x}}_j|}{S_j},j=1...m$

If meeting arbitrary γ_j＞ 3, then show that this sample point belongs to unusual sample point, while obtaining this position residing for sample point singular value Put；

Submodel method for repairing and mending includes：Assume that unusual query sample point present position is sample point x_qJth is tieed up, with this to training Sample set X process, the process include：

By x_qObtain x '_q={ x_q,1,x_q,2…x_q,j-1,x_q,j+1…x_q,m, X ', Y ' are obtained with reason X, be shown below：

Y'=[x_1,j,x_2,j,……x_n,j]^T

Simultaneously to query sample point x_qProcessed, be shown below：

X ', Y ' and x ' are obtained by above-mentioned process_q, wherein X ' is the former training sample X new input training samples of gained after treatment This collection, Y ' arrange the new output training sample set for constituting residing for singular value in former training sample X, and x '_qIt is then x_qThrough processing New query sample point obtained by afterwards.Finally X ' and Y ' are reconfigured as a new training sample set, is returned using Gaussian process Method is trained to which and obtains submodel；

Using gained submodel to x '_qIt is predicted and obtains singular value x_q,jPredictive value x '_q,j, using gained x '_q,jTo x_qIn Singular value x_q,jIt is replaced and is compensated rear query sample point

6. it is according to claim 5 with inflection point detection compensation GPR online soft sensor methods, it is characterised in that also wrap Query unit secondary to singular point is included, and for secondary detection being carried out to the query sample for being judged to singular point, is specifically included：

Chosen and x from training sample using the method for Euclidean distance_qMost like sample point, under specific formula for calculation as shown in formula：

d_i(x_q,x_i)=| | x_q,x_i| |, i=1 ..., n

In formula, x_i、d_iAnd s_iEuclidean distance and coefficient of similarity between training sample point, sample point is represented respectively；

As in singular point, singular value can produce interference to asking for similar sample point, therefore to unusual before similar sample point is asked for Sample point is processed, by singular point x_qObtain x '_q={ x_q,1,x_q,2…x_q,j-1,x_q,j+1…x_q,m, X ' is obtained with reason X, such as following formula It is shown：

In the middle acquisition x ' of X '_qMost like sample point x '_p, so as to obtain x '_pIn the middle position information of X ', finally according to gained position Confidence ceases to obtain x_qThe most like sample point x in X_p, obtain error vector x_eSuch as following formula：

x_e={ x_q,1-x_p,1,x_q,2-x_p,2,…,x_q,m-x_p,m}

By error vector x_e：

IfThen query sample point x_qFor unusual sample point；

Otherwise, query sample point x_qNormal queries sample point is to report unusual sample point by mistake, wherein α is predetermined threshold value.