CN101893884B - Soft measurement method of quality index data in rubber mixing process of internal mixer - Google Patents

Abstract

The invention discloses a soft measurement method of quality index data in the rubber mixing process of an internal mixer. The method is characterized by establishing a mixing process off-line model based on the historical data of the rubber mixing process, then acquiring the production data and the quality index data of the current mixing process as the current samples and projecting the current samples to high dimensional feature space, computing the linear relationship between the samples in the high dimensional feature space by the Kernel function, correcting the parameters and the samples of the model according to the linear similarity of the samples, eliminating the data samples with least contribution when the sample number in the model exceeds the set value, updating the mixing processing model on line and outputting the predicated value of the quality index of the mixed rubber in real time when the current production data are input, thus realizing soft measurement in the rubber mixing process. The method realizes effective online tracking of the rubber mixing process, is low in computation complexity, good in stability and accurate and reliable in measurement and has quite important practical value in pre-detection and system optimization control in the rubber mixing production process.

Description

The flexible measurement method of quality index data in the rubber mixing process of Banbury mixer

Technical field

The invention belongs to industrial control field, relate to detection and automatic control technology in the rubber manufacturing field, be specifically related to the online in real time flexible measurement method of quality index data in a kind of rubber mixing process of Banbury mixer.

Background technology

Compounding rubber is the first road master operation of rubber processing, and the processing characteristics and the end product quality of subsequent technique had very big influence, thereby the control of mixing process plays an important role to the raising of rubber total quality.Rubber mixing process is a typical batch process fast; Generally be to carry out under the transition state of stable operating point not having; It is dynamically more remarkable than continuous process with nonlinear characteristic, and a lot of significant variables usually can't on-line measurement, and less than mechanism model is not capable of using accurately.In addition, also have such as: often dimension is very big, sample number is less relatively for the modeling desired data, the institute's model complexity of setting up control difficulty and computation complexity be than problems such as height.Even more important a bit; Rubber mixing process is because uncontrollable factors such as the ageing equipment that takes place in the production run, catalyst structure are more; Model needs online updating to obtain stable valid model; And use traditional off-line method can not obtain desirable effect to the historical data analysis modeling, more than many reasons make traditional control method effectively to use.On the other hand; The quality index of glue stuff compounding, for example the measurement of mooney viscosity, sulphur variate etc. need be carried out in the laboratory in manual work, during need workman's hand sampling at the scene, cutting in the laboratory; The respective detection instrument is put in manual work; And wait for about 3 minutes time, and this process need consumes great amount of manpower and material resources, and soft-measuring technique is through setting up the relation that model embodies production data and quality index data; Under the situation of known current production data, effectively forecast the correlated quality achievement data; Can effectively reduce enterprise cost, therefore, the rubber mixing process online soft sensor technical method that the commercial Application requirement is satisfied in research has extremely important realistic meaning.

Owing to above each reason; Is to lag behind traditional manufacturingly as the automatic control level of typical semi-batch industrial process rubber mixing process with optimizing always, in have to realize the rubber mixing process of control automatically, do not carry out line modeling and soft measurement also all is to indulge in empty talk.Yet; In the last few years; Rubber mixing process progressively moves towards semi-automatic by initial manual control and controls with robotization; For example, above subsidiary engine is that the industrial control equipment of representative is popularized rapidly and made sizing material, carbon black, small powder weighing (can control automatically and mention or depress floating weight with feeding intake and the mixing process of Banbury mixer controlled; Can be by time, temperature, energy consumption, pressure and other parameters Combination Control binder removal etc.) realize robotization basically, also provide the foundation simultaneously for the online acquisition of mixing process modeling and the needed production process data of soft measurement.Along with manufacturing execution system (Manufacturing Execution System; Progressively popularizing MES); The automatization level of sizing material mixing process is further improved; Various production datas can obtain through field network easily, for the line modeling that realizes mixing process provides solid foundation.

Basic skills to the soft sensor modeling of mixing process can be divided into modelling by mechanism and data modeling, and modelling by mechanism is found out the rule of reflection mixing process according to the understanding to thing mechanism, is applicable to that structure is clear and definite, data integrity, and mechanism is system clearly.Because the influence factor of mixing process is many, the complicated this method of mechanism and inapplicable, thus data modeling adopted usually, promptly through the mixing process metric data is analyzed; Find out the model best with data fitting; The method is applicable to that structure is indeterminate, data deficiency, the system that mechanism is fuzzy.

For realizing soft sensor modeling to mixing process; The existing before soft-measuring modeling method based on data based on multiple regression, artificial neural network scheduling theory is suggested; Yet the former is based under the large sample assumed condition; The latter exists then that structure is difficult to be confirmed and problem such as over-fitting, and these methods all have that the high dimensional data of processing computation complexity is high, model can not online updating etc. shortcoming, can't satisfy in the commercial production that real-time is required than higher On-line Control requirement.In the last few years; Statistical learning and Kernel (Statistical Learning and Kernel, it is SLK) theoretical that (SupportVector Machine SVM) is suggested with SVMs; The SLK theory has solved the small sample problem concerning study on Fundamentals of Mathematics; The Kernel method that realizes as statistical learning algorithm is mapped to higher dimensional space with the inseparable sample point of lower dimensional space and tries to achieve the optimal classification face and distinguish, and can be used for the method for handling linear problem is generalized to non-linear field; But and have advantages such as pin-point accuracy small sample modeling, computation complexity is lower, the processing high dimensional data is effective, begun to be applied to various industrial circles.Particularly as Kernel method support vector machine method commonly used, because its superiority with respect to classic method has all obtained significant effect at numerous areas.Yet; Although the mixing process soft-measuring modeling method based on SVMs is suggested; But the support vector machine method of traditional off-line merges the production process data and the historical data of online acquisition, then it is carried out modeling again, and this method computation complexity is very high; And the effective time varying characteristic of on-line tracing rubber mixing process, thus current still lack feasible, effectively, mixing process soft-measuring modeling method accurately.

Summary of the invention

The invention provides the online in real time flexible measurement method and the system of the mixer mixing process of a kind of low complex degree and stabilizing effective high practicability.

The flexible measurement method of quality index data is characterized in that in the rubber mixing process of Banbury mixer, may further comprise the steps:

(1) carries out modeling according to the historical data of the rubber mixing process of Banbury mixer; Wherein, historical production data is as input feature vector, and historical quality index data is as output characteristic; Obtain reflecting the historical data model of the corresponding relation of production data and quality index data, as initial model; Historical production data and historical quality index data in the initial model constitute initial sample;

(2) production data of the current mixing process of collection and quality index data are as current sample; Use projection functions that current sample is projected the feature space of high dimension coordinate from low dimension coordinate space, and in the feature space of high dimension coordinate, calculate the linear relationship of existing sample in current sample and the model;

(3), judge whether current sample can be by existing sample approximately linear combination expression in the model according to result calculated in the step (2);

If, keep the existing sample of model constant, the adjustment model parameter is carried out model stability and is upgraded to absorb the information of current sample;

If not, current sample is added into model, and use the recursion computing formula to calculate the model parameter after current sample adds, model is revised renewal;

(4) after current sample was added in the model, whether sample number exceeded given maximum sample quantity in the judgment models; If, then take minimum contribution to eliminate method, with in the model the minimum sample of model contribution being deleted from model, stable to keep the model sample size;

(5) based on above step set up real-time update reflection production data and quality index data corresponding relation at line model;

(6) production data of setting up to step (5) in line model input mixing process, output obtains the predicted value of the quality index data of elastomeric compound, the soft measurement of quality index data in the rubber mixing process of realization Banbury mixer.

Among the present invention, described production data is by melting temperature, mixing time, mixing power and the vectors that information combination became such as sizing material and adjuvant; Described quality index data can be the combination of the one or more values in Mooney viscosity, glue burning, the sulphur variate;

Among the present invention, described projection functions is φ (x), satisfies k (x ₁, x ₂)=<φ (x ₁), φ (x ₂)>, wherein, k (x ₁, x ₂) be the Kernel function,<φ (x ₁), φ (x ₂)>Be projection functions φ (x ₁) and φ (x ₂) dot product, x ₁With x ₂It is real variable.

Among the present invention, the preferred gaussian kernel function of described Kernel function, its expression formula is suc as formula shown in (4):

K(x ₁，x ₂)＝exp[-||x ₁-x ₂|| ²/(2σ ²)] (4)

Wherein, σ representes kernel function width, x ₁With x ₂It is real variable.

Described Kernel function also can be the polynomial kernel function: K (x _i, x _j)=(x _iX _j+ 1) ^d, d is polynomial number of times.Select except passing through experience in the practical application; Generally through historical data being carried out cross validation (Cross Validation); Obtain the value of σ or d, described cross validation method has detailed description in 2002 46 volumes of Machine Learning (machine learning) 131-159 page or leaf Olivier Chappelle " Choosing multiple parameters for support vector machines ".

Among the present invention, the σ value adjusts according to sizing material Mooney initial value difference slightly, generally selects σ=120.

Among the present invention, the feature space of described high dimension coordinate be the reproducing kernel Hilbert space (Reproducing Kernel Hilbert Space, RKHS).When sample point projects to the reproducing kernel Hilbert space of higher-dimension from lower dimensional space, inseparable sample is realized and can be divided at higher dimensional space in lower dimensional space.About the reproducing kernel Hilbert space; In Conference board of the mathematicalsciences regional conference series in mathematics total the 71st phase H Dym in 1989 " J Contractive Matrix Functions, Reproducing Kernel Hilbert Spaces andInterpolation ", detailed description is arranged.

In the step (1), the process of described modeling is following:

(i) be non-linear multiple-input and multiple-output process by rubber mixing process, establish the rubber mixing process model as shown in the formula shown in (1):

$y_{t,b}=f({\mathrm{\&alpha;}}_{t,b},x_t)+{\mathrm{\&epsiv;}}_{t,b}={\mathrm{\&alpha;}}_{t,b}^T\mathrm{\&phi;}\left(x_t\right)+{\mathrm{\&epsiv;}}_{t,b}---\left(1\right)$

In the formula (1), functional f is present in the feature space of high dimension coordinate, is model to be asked; y _{T, b}Representation model is in t b output valve constantly, b=1 ..., B, wherein B is total output number of model; α _{T, b}And ε _{T, b}Model parameter vector and the noise vector of representing the b sub-systems respectively; x _tBe t input feature vector constantly;

(ii), find the solution functional f suc as formula the equality majorized function shown in (2) in the feature space foundation of high dimension coordinate to realize that soft measurement error value minimum is a target;

$\min J\left({\mathrm{\&alpha;}}_{t,b}\right)=\frac{1}{2}{\left|\right|{\mathrm{\&epsiv;}}_{t,b}\left|\right|}^2+\mathrm{c\&Omega;}\left[\right|\left|f\right|\left|\right]---\left(2\right)$

$\mathrm{st}:y_{t,b}-{\mathrm{\&alpha;}}_{t,b}^T\mathrm{\&phi;}\left(x_t\right)-{\mathrm{\&epsiv;}}_{t,b}=0$

ε in the formula (2) _{T, b}=[ε _{1, b}, ε _{2, b}..., ε _{T, b}] ^TC＞0 is the regularization parameter of the complexity that is used for controlling models, the ratio of the importance of its list of values representation model complexity relative error (that is model complexity weight); Ω [|| f||] be regularization term, be typically chosen in convex function and get final product, Ω [|| f||]=|| α _{T, b}|| ²/ 2; φ (x) is described projection functions;

(iii) convert the equality majorized function shown in the formula (2) into expression formula (3), introduce the Kernel function and find the solution functional f:

$\min J\left({\mathrm{\&beta;}}_{t,b}\right)=\frac{1}{2}{\left|\right|{\mathrm{\&epsiv;}}_{t,b}\left|\right|}^2+\frac{c}{2}{\left|\right|{\mathrm{\&beta;}}_{t,b}\left|\right|}^2---\left(3\right)$

st：y _t，b-K _tβ _t，b-ε _t，b＝0

In the formula (3), K _tSample is at the matrix of the similarity of the feature space of high dimension coordinate in the representation model, the element K of the capable j row of its i _t(i, j)=<φ (x _i), φ (x _j)>, be Kernel similarity calculated value, i, j=1 ..., t, β _{T, b}Be the model parameter vector after the conversion, ε _{T, b}Be noise vector;

(iv) with different mixing process production datas constantly in the historical data as input feature vector x _t, the quality index data of elastomeric compound is as output valve y _t, form mixing process data sample { (x ₁, y ₁) ..., (x _t, y _t), use projection functions that data sample is projected the feature space of high dimension coordinate from low dimension coordinate space, carry out Kernel at the feature space of high dimension coordinate and calculate formula (3) is found the solution, obtain initial model.

In the step (2), the described process of in the feature space of high dimension coordinate, calculating the linear relationship that has sample in current sample and the model is following:

1. confirm space similarity index s in (θ in the feature space of high dimension coordinate _t) computing formula be shown in the formula (5):

$\mathrm{Sin}\left({\mathrm{\&theta;}}_t\right)=\underset{a_t}{\min }\left|\right|\mathrm{\&phi;}\left(x_t\right)-\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_k\mathrm{\&phi;}\left({\tilde{x}}_k\right)\left|\right|/\left|\right|\mathrm{\&phi;}\left(x_t\right)\left|\right|---\left(5\right)$

In the formula (5), n is current sample number, φ (x _t) be the mapping of current sample in the feature space of high dimension coordinate, existing sample being mapped as in high-dimensional feature space in the model

a _kBe undetermined parameter, a _t=[a ₁..., a _n] ^T

2. formula (5) is found the solution, is obtained as shown in the formula the space similarity index expression formula shown in (6):

In the formula (6), k _Tt=<φ (x _t), φ (x _t), <math> <mrow> <msub> <mover> <mi>k</mi> <mo>~</mo> </mover> <mi>t</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&lt;;</mo> <mi>&amp;phi;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>&amp;phi;</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>></mo> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>,</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>;</mo> </mrow></math>

3. according to the Kernel function formula (6) is calculated, obtained the linearity of existing sample in current sample and the model, i.e. space similarity index.

In the step (3), judge whether current sample can be following by the process of existing sample approximately linear combination expression in the model:

As space similarity index s in (θ _t) less than predetermined threshold value, think that then current sample can be by existing sample approximately linear combination expression in the model; Otherwise current sample can not be by existing sample approximately linear combination expression in the model; Wherein, described predetermined threshold value gets 0.1～0.3 usually, is preferably 0.2.

In the step (3), during described model stability upgrades, do not have new sample to add, model structure remains unchanged, wherein,

Model sample more new formula is:

${\tilde{K}}_t={\tilde{K}}_{t-1}---\left(7\right)$

In the formula (7), K _tBe sample similarity matrix in the model, A _tBe transformation matrix,

Be sample similarity matrix in the model after the conversion;

Model parameter more new formula is:

${\widetilde{\mathrm{\&beta;}}}_{t,b}={\widetilde{\mathrm{\&beta;}}}_{t-1,b}+G_t(y_{t,b}-{\tilde{k}}_t^T{\widetilde{\mathrm{\&beta;}}}_{t-1,b})---\left(8\right)$

In the formula (8),

A _tBe transformation matrix, when i≤j, A (i, j)=a (i, j), the element of other positions is 0; β _{T, b}Be the model parameter vector after the conversion, Be the model parameter vector after the conversion;

is gain vector; Wherein, is scalar; is Kernel similarity compute matrix; The companion matrix that

derives for recursion, its inverse matrix is calculated by recursion computing formula

.

In the step (3), during described model correction is upgraded:

The model sample is new formula more:

${\tilde{K}}_t=\left[\begin{array}{cc}{\tilde{K}}_{t-1}& {\tilde{k}}_t\\ {\tilde{k}}_t^T& k_{\mathrm{tt}}\end{array}\right]---\left(9\right)$

In the formula (9), k _Tt=<φ (x _t), φ (x _t) be that current sample self similarity is calculated; <math> <mrow> <msub> <mover> <mi>k</mi> <mo>~</mo> </mover> <mi>t</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&lt;;</mo> <mi>&amp;phi;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>&amp;phi;</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>></mo> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>,</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>;</mo> </mrow></math>

Model parameter is new formula more:

${\widetilde{\mathrm{\&beta;}}}_{t,b}=P_t^{-1}\left[\begin{array}{c}{P}_{t-1}{\widetilde{\mathrm{\&beta;}}}_{t-1,b}+{\tilde{k}}_t{y}_{t,b}\\ {\tilde{k}}_t^T{\tilde{K}}_{t-1}^{-1}{P}_{t-1}{\widetilde{\mathrm{\&beta;}}}_{t-1,b}+k_{\mathrm{tt}}{y}_{t,b}\end{array}\right]---\left(10\right)$

Formula (10) in the <img file = "GDA0000136692370000073.GIF" he = "116" img-content = "drawing" img-format = "tif" inline = "yes" orientation = "portrait" wi = "700" /> where <img file = "GDA0000136692370000074.GIF" he = "61" img-content = "drawing" img-format = "tif" inline = "yes" orientation = "portrait" wi = "280" /> Matrix <img file = "GDA0000136692370000075.GIF" he = "182" img-content = "drawing" img-format = "tif" inline = "yes" orientation = "portrait" wi = "354" /> Matrix <maths num="0012"> <! [CDATA [<math> <mrow> <msubsup> <mi> P </ mi> <mi> t </ mi > <mrow> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msubsup> <mo> = </ mo> <mo> {</ mo> <mi> I </ mi> <mo> - </ mo> <msup> <mi> M </ mi> <mrow> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msup> <mfenced open = '[' close = ']'> <mtable> <mtr> <mtd> <msub> <mover> <mi> k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> </ msub> </ mtd> </ mtr> <mtr> <mtd> <msub> <mi> k </ mi> <mi> tt </ mi> </ msub> </ mtd> < / mtr> </ mtable> </ mfenced> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msubsup> <mover> <mi> k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> <mi> T </ mi> </ msubsup> </ mtd> <mtd> <msub> <mi> k </ mi> <mi> tt </ mi> </ msub> </ mtd> </ mtr> </ mtable> </ mfenced> <mo> / </ mo> <mo> {</ mo> <mn> 1 </ mn> < mo> + </ mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msubsup> <mover> <mi> k </ mi> <mo> ~ </ mo > </ mover> <mi> t </ mi> <mi> T </ mi> </ msubsup> </ mtd> <mtd> <msub> <mi> k </ mi> <mi> tt </ mi > </ msub> </ mtd> </ mtr> </ mtable> </ mfenced> <msup> <mi> M </ mi> <mrow> <mo> - </ mo> <mn> 1 </ mn > </ mrow> </ msup> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msubsup> <mover> <mi> k </ mi> <mo> ~ < / mo> </ mover> <mi> t </ mi> <mi> T </ mi> </ msubsup> </ mtd> <mtd> <msub> <mi> k </ mi> <mi> tt < / mi> </ msub> </ mtd> </ mtr> </ mtable> </ mfenced> <mo>} </ mo> <mo>} </ mo> <mo> × </ mo> <msup > <mi> M </ mi> <mrow> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msup> <mo>, </ mo> </ mrow> </ math>]]> </maths> transformation matrix <maths num="0013"> <! [CDATA [<math> <mrow> <msub> <mi> A </ mi> <mi> t </ mi> </ msub> <mo> = </ mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi> A </ mi> < mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msub> </ mtd> <mtd> <mn> 0 </ mn> < / mtd> </ mtr> <mtr> <mtd> <msup> <mn> 0 </ mn> <mi> T </ mi> </ msup> </ mtd> <mtd> <mn> 1 </ mn > </ mtd> </ mtr> </ mtable> </ mfenced> <mo>, </ mo> </ mrow> </ math>]]> </maths> Matrix <maths num = "0014"> <! [CDATA [<math> <mrow> <mi> M </ mi> <mo> = </ mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi> P </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msub> < / mtd> <mtd> <msub> <mover> <mi> K </ mi> <mo> ~ </ mo> </ mover> <mrow> <mi> t </ mi> <mo> - </ mo > <mn> 1 </ mn> </ mrow> </ msub> <mrow> <mo> (</ mo> <msubsup> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> <mi> T </ mi> </ msubsup> <msub> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msub> <mo>) </ mo> </ mrow> <msub> <mover> <mi> k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> </ msub> </ mtd> </ mtr> <mtr> <mtd> <msubsup> <mover> <mi > k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> <mi> T </ mi> </ msubsup> <mrow> <mo> (</ mo> < msubsup> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> <mi> T </ mi> < / msubsup> <msub> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msub> < mo>) </ mo> </ mrow> <msub> <mover> <mi> K </ mi> <mo> ~ </ mo> </ mover> <mrow> <mi> t </ mi> <mo > - </ mo> <mn> 1 </ mn> </ mrow> </ msub> </ mtd> <mtd> <mi> c </ mi> <mo> + </ mo> <msubsup> <mover > <mi> k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> <mi> T </ mi> </ msubsup> <mrow> <mo> (</ mo> <msubsup> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> <mi> T </ mi> </ msubsup> <msub> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msub> <mo>) </ mo> </ mrow> <msub> <mover> <mi> k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> </ msub> </ mtd> </ mtr> </ mtable> </ mfenced> <mo>. </ mo> </ mrow> </ math>]]> </maths>

In the step (4), method is eliminated in described minimum contribution, and (Least Contribution Eliminate LCE) is: the minimum sample of predicated error in the existing sample in the model is regarded as the minimum sample of final mask contribution rejects.Wherein the sample elimination method is with matrix

In with wait to reject corresponding row of sample and row deletion, with vectorial β _{T, b}With wait to reject sample row deletion accordingly.

Because the time complexity to the sample point forecast after the modelling is very low, be O (1), so this screening technique is that complexity is O (n) under the n situation at the model sample point, feasibility height very.

And at some real-time is required under the higher situation, use the method for directly rejecting sample the oldest in the model to reject sample to obtain better efficient.Because As time goes on; Early stage sample point more maybe be the good characteristic of descriptive system; Receive In-Process Factor to disturb less pattern to keep stable but can not get rid of some, though this method calculated amount is zero basically, effect is poorer than screening technique of the present invention in theory for it always; Because if disallowable sample point plays an important role to model, the model after rejecting so can not well be expressed mixing production run.

Among the present invention, space similarity index s in (θ _t) geometric meaning be i Feature Mapping φ (x constantly _i) and subspace F _I-1The sine of angle, embodiment be the fitting degree that existing sample point linear combination is expressed in rubber mixing process production data sample point and the model of current acquisition.Wherein, can not be explained that the pattern of current sample point representative is not held by model as yet by the sample of the existing effective match of sample point linear combination in the model, current model need absorb this sample point with better expression mixing process; Otherwise; Explain that the pattern that current sample point contains is grasped by current model with analysis through the study of sample point before; But a plurality of sample points repeat to occur explaining that the weight of this pattern is relatively large; So keeping following of the stable situation of model sample point to need its relevant parameter is done certain adjustment, the gain that embodies on this weight gets final product.

Among the present invention, line modeling process early stage, and when production run changes, need model structure to adjust adaptively; After model had fully been learnt the DYNAMIC PROCESS characteristic, then model structure kept stable, only need carry out coefficient adjustment and get final product.

Among the present invention, the iteration online according to production process data, the model f of mixing process is by the foundation of stepping type.Can implement control and application such as optimization on this basis, for example given f is established, and given mixing process is measured a certain group of data obtaining (temperature, energy consumption, consuming time etc.) as the input of f, then can obtain the model predication value etc. that glue burns degree.

The flexible measurement method of the rubber mixing process of Banbury mixer of the present invention is used for the quality index of the production data of real-time analysis rubber mixing process with the forecast elastomeric compound, realizes the soft measurement of rubber mixing process.The mooney viscosity of selected mixing colloid is during as output valve; System can be directly as the online Mooney forecast system of compounding rubber; The mixing process production data of given current point in time (temperature of sizing material hardness, different time points, pressure, energy consumption, consuming time etc. combination) as input feature vector, can obtain the input feature vector input model Mooney predicted value of current point in time glue stuff compounding in advance in the quality inspection process.Replace mooney viscosity as output other quality inspection values such as sulphur change, glue burning, can obtain forecast systems such as the online sulphur change of corresponding compounding rubber, glue burning.To be difficult for measuring or measure the cost higher data, and do to replace mooney viscosity as output, can obtain the corresponding soft measuring system of certain small powder dispersed homogeneous degree like certain small powder dispersed homogeneous degree through hardware.Further, the output valve Mooney viscosity of model, sulphur variate directly are used to control the binder removal control and pilot process control of compounding rubber production run as negative feedback, can obtain rubber mixing process optimal control system.

The flexible measurement method of the rubber mixing process of Banbury mixer of the present invention; With production data as sample; And it is projected high-dimensional feature space, at high-dimensional feature space through its linear relationship of Kernel function calculation, and according to the parameter and the sample of its linear similarity correction model; The online rubber mixing process controlling models of setting up, and when the model size surpasses given memory size, will reject the minimum production data sample of model contribution.

Therefore, compare prior art, the present invention has following beneficial technical effects:

The present invention is based on Statistical Learning Theory, derive, proposed online Kernel modeling method a kind of low complex degree, high practicability, that can satisfy requirement of real-time control to the mixing process modeling characteristic from the angle of linear model Kernelization; To inseparable input feature vector data in the input space of low dimension; Introduce the Kernel function it is projected high-dimensional feature space H, f is found the solution in the back in the high n-dimensional subspace n H that Feature Mapping φ (xi) opens, thus; Through the Kernel Function Mapping; Inseparable data always can be divided in H in the input space of low dimension, and the calculating in H can both not increase computation complexity in original input space realization; Well solved nonlinear problem again, and handled originally very effective with regard to high-dimensional data.

The present invention proposes space similarity index (Space Similarity Index, method SSI) is to before measuring sequence and carrying out modeling; Its similarity of input sample evidence is screened; Calculate through on-line recursive, the valid data of the production run of " absorption " current acquisition are in model, thus the linear dependence of elimination Feature Mapping in high-dimensional feature space; Rejecting by the sample of the approximate linear combination of existing sample in the model; Only remaining linear incoherent mapped sample, thus computation complexity reduced, and it is stable to keep the model complexity.

The present invention proposes minimum contribution and eliminate method (Least Contribution Eliminate; LCE) reject unnecessary sample; Reduced the complexity of method greatly; Combine the complexity of above-mentioned sample turnover method controlling models through the model of introducing " time window ", well satisfied the needs of production control modeling under the actual condition situation.

Description of drawings

Fig. 1 is the process flow diagram of the flexible measurement method of quality index data in the rubber mixing process of Banbury mixer;

Fig. 2 adopts flexible measurement method of the present invention to carry out the design sketch of field data online soft sensor;

Fig. 3 is flexible measurement method of the present invention online applicating flow chart in the rubber mixing process of Banbury mixer.

Embodiment

Specify the present invention below in conjunction with embodiment and accompanying drawing, but the present invention is not limited to this.

The production process data of rubber mixing process is various, comprises mixing time, temperature, energy consumption, pressure, rubber hardness, calendering process, prescription etc., and it is significant to modeling that rational and effective is chosen these characteristics composition input sample characteristics spaces.On the one hand, introduce too much characteristic and can increase the collection capacity of industrial production data, strengthen calculating strength and make model more complicated, and under some characteristic can be by other characteristic linear expression situation, this calculating was again redundant; On the other hand, when having key character not to be selected, can cause the out of true of modelling again.To above problem; When carrying out feature selecting; We use nuclear pivot constituent analysis (Kernel Principal Component Analysis, method KPCA) is analyzed the industrial production data that producer can provide, and extracts the pivot in these data; The principal character that promptly can reflect model is chosen these principal characters and is used for the actual production process modeling.To those skilled in the art; Nuclear pivot componential analysis is known and at Lecture notes incomputer science, specifies in 1997 1327 volume 583-589 page or leaf B Scholkopf " Kernel PrincipalComponent Analysis ".

What the method that the present invention proposes was taked is that many time points are chosen the method that different characteristic is formed sample point; When actual production, can determine according to the production process data actual conditions that each producer can provide, in the time of in applying to production; Because to various Banbury mixeies and calendering process; Model all is dynamically to set up, so constant factor (for example: type, female refining/whole sweetening process etc.) can not done consideration in this process, only considers the factor that in the middle of production run, possibly change.When this method was applied to certain rubber plant, our Feature Selection was selected as follows:

x _tForm as follows:

x _{T, 1}=rubber master batch hardness

x _{T, 2}=carry the floating weight time for the last time

x _{T, 3}=put forward the temperature of floating weight time for the last time

x _{T, 4}=carry the pressure of floating weight time for the last time

x _{T, 5}=put forward the energy consumption of floating weight time for the last time

x _{T, 6}=put forward the temperature after ten seconds floating weight time for the last time

x _{T, 7}=carry the pressure after ten seconds floating weight time for the last time

x _{T, 8}=put forward the energy consumption after ten seconds floating weight time for the last time

y _tForm as follows:

y _{T, 1}=Mooney Viscosity of Rubber Mix

y _{T, 2}=elastomeric compound sulphur variate

Form sample point (x thus _t, y _t), along with the increase of time t, constitute sample sequence successively.

The mixing process modeling is abstract to be based on sample sequence L={ (x ₁, y ₁) ..., (x _t, y _t), seek to reflect the Function Mapping f of the corresponding relation of production data and quality index data, that is, f:x → y makes it to each x _tTo y _tThe total error of mapping is minimum.

As shown in Figure 1, the flexible measurement method of quality index data in the rubber mixing process of Banbury mixer may further comprise the steps:

(1) carries out modeling according to the historical data of the rubber mixing process of Banbury mixer; Wherein, historical production data is as input feature vector, and historical quality index data is as output characteristic; Obtain reflecting production data and quality index data corresponding relation the historical data model, as initial model; Historical production data and historical quality index data in the initial model constitute initial sample;

The process of described modeling is following:

(i) be non-linear multiple-input and multiple-output process by rubber mixing process, establish the rubber mixing process model as shown in the formula shown in (1):

$y_{t,b}=f({\mathrm{\&alpha;}}_{t,b},x_t)+{\mathrm{\&epsiv;}}_{t,b}={\mathrm{\&alpha;}}_{t,b}^T\mathrm{\&phi;}\left(x_t\right)+{\mathrm{\&epsiv;}}_{t,b}---\left(1\right)$

In the formula (1), functional f is present in the feature space of high dimension coordinate, is model to be asked; y _{T, b}Representation model is in t b output valve constantly, b=1 ..., B, wherein B is total output number of model; α _{T, b}And ε _{T, b}Model parameter vector and the noise vector of representing the b sub-systems respectively; x _tBe t input feature vector constantly;

(ii), find the solution functional f suc as formula the equality majorized function shown in (2) in the feature space foundation of high dimension coordinate to realize that soft measurement error value minimum is a target;

$\min J\left({\mathrm{\&alpha;}}_{t,b}\right)=\frac{1}{2}{\left|\right|{\mathrm{\&epsiv;}}_{t,b}\left|\right|}^2+\mathrm{c\&Omega;}\left[\right|\left|f\right|\left|\right]---\left(2\right)$

$\mathrm{st}:y_{t,b}-{\mathrm{\&alpha;}}_{t,b}^T\mathrm{\&phi;}\left(x_t\right)-{\mathrm{\&epsiv;}}_{t,b}=0$

ε in the formula (2) _{T, b}=[ε _{1, b}, ε _{2, b}..., ε _{T, b}] ^TC＞0 is the regularization parameter of the complexity that is used for controlling models, and value is 0.1, and promptly the importance of representation model complexity relative error is 10%; Ω [|| f||] is a regularization term, get Ω [|| f||]=|| α _{T, b}|| ²/ 2; φ (x) is described projection functions;

(iii) convert the equality majorized function shown in the formula (2) into expression formula (3), introduce the Kernel function and find the solution functional f:

$\min J\left({\mathrm{\&beta;}}_{t,b}\right)=\frac{1}{2}{\left|\right|{\mathrm{\&epsiv;}}_{t,b}\left|\right|}^2+\frac{c}{2}{\left|\right|{\mathrm{\&beta;}}_{t,b}\left|\right|}^2---\left(3\right)$

st：y _t，b-K _tβ _t，b-ε _t，b＝0

In the formula (3), K _tSample is at the matrix of the similarity of the feature space of high dimension coordinate in the representation model, the element K of the capable j row of its i _t(i, j)=<φ (x _i), φ (x _j)>, be Kernel similarity calculated value, i, j=1 ..., t, β _{T, b}Be the model parameter vector after the conversion, ε _{T, b}Be noise vector;

(iv) with different mixing process production datas constantly in the historical data as input feature vector x _t, the quality index data of elastomeric compound is as output valve y _t, form mixing process data sample { (x ₁, y ₁) ..., (x _t, y _t), use projection functions that data sample is projected the feature space of high dimension coordinate from low dimension coordinate space, carry out Kernel at the feature space of high dimension coordinate and calculate formula (3) is found the solution, obtain initial model.

Wherein, described projection functions is φ (x), satisfies k (x ₁, x ₂)=<φ (x ₁), φ (x ₂)>, k (x ₁, x ₂) be the Kernel function,<φ (x ₁), φ (x ₂)>Be projection functions φ (x ₁) and φ (x ₂) dot product, x ₁With x ₂It is real variable.

Described Kernel function is a gaussian kernel function, and its expression formula is suc as formula shown in (4):

K(x ₁，x ₂)＝exp[-||x ₁-x ₂|| ²/(2σ ²)] (4)

Wherein, σ representes kernel function width, x ₁With x ₂It is real variable.The σ value adjusts according to sizing material Mooney initial value difference slightly, gets σ=120.

The feature space of described high dimension coordinate be the reproducing kernel Hilbert space (ReproducingKernel Hilbert Space, RKHS).When sample point projects to the reproducing kernel Hilbert space of higher-dimension from lower dimensional space, inseparable sample is realized and can be divided at higher dimensional space in lower dimensional space.

(2) production data of the current mixing process of collection and quality index data are as current sample; Use projection functions that current sample is projected the feature space of high dimension coordinate from low dimension coordinate space, and in the feature space of high dimension coordinate, calculate the linear relationship of existing sample in current sample and the model;

Adopt space similarity index s in (θ in the feature space of high dimension coordinate _t) calculate in current sample and the model linear relationship of existing sample, space similarity index s in (θ _t) computing formula be shown in the formula (5):

$\mathrm{Sin}\left({\mathrm{\&theta;}}_t\right)=\underset{a_t}{\min }\left|\right|\mathrm{\&phi;}\left(x_t\right)-\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_k\mathrm{\&phi;}\left({\tilde{x}}_k\right)\left|\right|/\left|\right|\mathrm{\&phi;}\left(x_t\right)\left|\right|---\left(5\right)$

In the formula (5), n is current sample number, φ (x _t) be the mapping of current sample in the feature space of high dimension coordinate, existing sample being mapped as in high-dimensional feature space in the model

a _kBe undetermined parameter, a _t=[a ₁..., a _n] ^T

Formula (5) is an expression formula, can't directly calculate, still formula (5) is done further derivation.Notice that minimizing of formula (5) is only relevant with minute subitem.The minimum value of remembering this quadratic sum for

suc as formula shown in (11):

Wherein,<img file="GDA0000136692370000125.GIF" he="77" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="471" />Be t node matrix equation constantly; k<sub >Tt</sub>=<φ (x<sub >t</sub>), φ (x<sub >t</sub>),<img file="GDA0000136692370000126.GIF" he="65" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="371" />With<img file="GDA0000136692370000127.GIF" he="67" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="318" />I=1 ..., t-1, k<sub >Tt</sub>,<img file="GDA0000136692370000128.GIF" he="60" img-content="drawing" img-format="GIF" inline="yes" orientation="portrait" wi="158" />Being corresponding kernel similarity calculates.The formula (6) of finding the solution <img file=" GDA0000136692370000131.GIF " he=" 48 " img-content=" drawing " img-format=" tif " inline=" yes " orientation=" portrait " wi=" 42 " /> but obtaining the recursion judgement and calculate.

In the formula (6), k _Tt=<φ (x _t), φ (x _t),

I=1 ..., t-1; k _Tt,

Being corresponding kernel similarity calculates.

According to the Kernel function formula (6) is calculated, obtained the linearity of existing sample in current sample and the model, i.e. space similarity index s in (θ _t).

(3), judge that whether current sample can make up expression by existing sample approximately linear in the model, and carry out model modification according to result calculated in the step (2):

As sin (θ _t) less than predetermined threshold value 0.2, think that then current sample is can be by existing sample approximately linear combination expression in the model.At this moment, keep the existing sample of model constant, the adjustment model parameter is carried out model stability and is upgraded to absorb the information of current sample.

Because do not have new sample to add, model structure remains unchanged, therefore, model sample more new formula is:

${\tilde{K}}_t={\tilde{K}}_{t-1}---\left(7\right)$

In the formula (7),

K _tBe sample similarity matrix in the model, A _tBe transformation matrix,

Be sample similarity matrix in the model after the conversion;

And model parameter more new formula be:

${\widetilde{\mathrm{\&beta;}}}_{t,b}={\widetilde{\mathrm{\&beta;}}}_{t-1,b}+G_t(y_{t,b}-{\tilde{k}}_t^T{\widetilde{\mathrm{\&beta;}}}_{t-1,b})---\left(8\right)$

In the formula (8),

A _tBe transformation matrix, when i≤j, A (i, j)=a (i, j), the element of other positions is 0; β _{T, b}Be the model parameter vector after the conversion, Be the model parameter vector after the conversion;

is gain vector; Wherein,

is scalar;

is Kernel similarity compute matrix; The companion matrix that derives for recursion, its inverse matrix is calculated by recursion computing formula

.

As sin (θ _t) being not less than predetermined threshold value 0.2, current sample can not be by existing sample approximately linear combination expression in the model.At this moment, current sample is added into model, and uses the recursion computing formula to calculate the model parameter after current sample adds, and model is revised renewal;

The model sample is new formula more:

${\tilde{K}}_t=\left[\begin{array}{cc}{\tilde{K}}_{t-1}& {\tilde{k}}_t\\ {\tilde{k}}_t^T& k_{\mathrm{tt}}\end{array}\right]---\left(9\right)$

In the formula (9), k _Tt=<φ (x _t), φ (x _t) be that current sample self similarity is calculated; <math> <mrow> <msub> <mover> <mi>k</mi> <mo>~</mo> </mover> <mi>t</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&lt;;</mo> <mi>&amp;phi;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>&amp;phi;</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>></mo> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>,</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>;</mo> </mrow></math>

Model parameter is new formula more:

${\widetilde{\mathrm{\&beta;}}}_{t,b}=P_t^{-1}\left[\begin{array}{c}{P}_{t-1}{\widetilde{\mathrm{\&beta;}}}_{t-1,b}+{\tilde{k}}_t{y}_{t,b}\\ {\tilde{k}}_t^T{\tilde{K}}_{t-1}^{-1}{P}_{t-1}{\widetilde{\mathrm{\&beta;}}}_{t-1,b}+k_{\mathrm{tt}}{y}_{t,b}\end{array}\right]---\left(10\right)$

Formula (10) in the <img file = "GDA0000136692370000144.GIF" he = "116" img-content = "drawing" img-format = "tif" inline = "yes" orientation = "portrait" wi = "700" /> where <img file = "GDA0000136692370000145.GIF" he = "61" img-content = "drawing" img-format = "tif" inline = "yes" orientation = "portrait" wi = "280" /> Matrix <img file = "GDA0000136692370000146.GIF" he = "182" img-content = "drawing" img-format = "tif" inline = "yes" orientation = "portrait" wi = "354" /> Matrix <maths num="0025"> <! [CDATA [<math> <mrow> <msubsup> <mi> P </ mi> <mi> t </ mi > <mrow> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msubsup> <mo> = </ mo> <mo> {</ mo> <mi> I </ mi> <mo> - </ mo> <msup> <mi> M </ mi> <mrow> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msup> <mfenced open = '[' close = ']'> <mtable> <mtr> <mtd> <msub> <mover> <mi> k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> </ msub> </ mtd> </ mtr> <mtr> <mtd> <msub> <mi> k </ mi> <mi> tt </ mi> </ msub> </ mtd> < / mtr> </ mtable> </ mfenced> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msubsup> <mover> <mi> k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> <mi> T </ mi> </ msubsup> </ mtd> <mtd> <msub> <mi> k </ mi> <mi> tt </ mi> </ msub> </ mtd> </ mtr> </ mtable> </ mfenced> <mo> / </ mo> <mo> {</ mo> <mn> 1 </ mn> < mo> + </ mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msubsup> <mover> <mi> k </ mi> <mo> ~ </ mo > </ mover> <mi> t </ mi> <mi> T </ mi> </ msubsup> </ mtd> <mtd> <msub> <mi> k </ mi> <mi> tt </ mi > </ msub> </ mtd> </ mtr> </ mtable> </ mfenced> <msup> <mi> M </ mi> <mrow> <mo> - </ mo> <mn> 1 </ mn > </ mrow> </ msup> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msubsup> <mover> <mi> k </ mi> <mo> ~ < / mo> </ mover> <mi> t </ mi> <mi> T </ mi> </ msubsup> </ mtd> <mtd> <msub> <mi> k </ mi> <mi> tt < / mi> </ msub> </ mtd> </ mtr> </ mtable> </ mfenced> <mo>} </ mo> <mo>} </ mo> <mo> × </ mo> <msup > <mi> M </ mi> <mrow> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msup> <mo>, </ mo> </ mrow> </ math>]]> </maths> transformation matrix <maths num="0026"> <! [CDATA [<math> <mrow> <msub> <mi> A </ mi> <mi> t </ mi> </ msub> <mo> = </ mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi> A </ mi> < mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msub> </ mtd> <mtd> <mn> 0 </ mn> < / mtd> </ mtr> <mtr> <mtd> <msup> <mn> 0 </ mn> <mi> T </ mi> </ msup> </ mtd> <mtd> <mn> 1 </ mn > </ mtd> </ mtr> </ mtable> </ mfenced> <mo>, </ mo> </ mrow> </ math>]]> </maths> Matrix <maths num = "0027"> <! [CDATA [<math> <mrow> <mi> M </ mi> <mo> = </ mo> <mfenced open='[' close=']'> <mtable> <mtr> <mtd> <msub> <mi> P </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msub> < / mtd> <mtd> <msub> <mover> <mi> K </ mi> <mo> ~ </ mo> </ mover> <mrow> <mi> t </ mi> <mo> - </ mo > <mn> 1 </ mn> </ mrow> </ msub> <mrow> <mo> (</ mo> <msubsup> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> <mi> T </ mi> </ msubsup> <msub> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msub> <mo>) </ mo> </ mrow> <msub> <mover> <mi> k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> </ msub> </ mtd> </ mtr> <mtr> <mtd> <msubsup> <mover> <mi > k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> <mi> T </ mi> </ msubsup> <mrow> <mo> (</ mo> < msubsup> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> <mi> T </ mi> < / msubsup> <msub> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msub> < mo>) </ mo> </ mrow> <msub> <mover> <mi> K </ mi> <mo> ~ </ mo> </ mover> <mrow> <mi> t </ mi> <mo > - </ mo> <mn> 1 </ mn> </ mrow> </ msub> </ mtd> <mtd> <mi> c </ mi> <mo> + </ mo> <msubsup> <mover > <mi> k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> <mi> T </ mi> </ msubsup> <mrow> <mo> (</ mo> <msubsup> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> <mi> T </ mi> </ msubsup> <msub> <mi> A </ mi> <mrow> <mi> t </ mi> <mo> - </ mo> <mn> 1 </ mn> </ mrow> </ msub> <mo>) </ mo> </ mrow> <msub> <mover> <mi> k </ mi> <mo> ~ </ mo> </ mover> <mi> t </ mi> </ msub> </ mtd> </ mtr> </ mtable> </ mfenced> <mo>. </ mo> </ mrow> </ math>]]> </maths>

(4) after current sample was added in the model, whether sample number exceeded given maximum sample quantity in the judgment models; If, then take minimum contribution to eliminate method, stable with in the model the minimum sample of model contribution being deleted from model to keep the model sample size, thus the complexity of controlling models.

Method is eliminated in minimum contribution, and (Least Contribution Eliminate LCE) is: the minimum sample of predicated error in the existing sample in the model is regarded as the minimum sample of final mask contribution rejects.The minimum choice of sample method of prediction error is: carry it into current model f to existing sample

in the model and calculate each predicted value y ' one by one; This predicted value and actual y are done comparison, and both differences (promptly | y-y ' |) reckling is selected.The sample delet method is with matrix

In with wait to reject corresponding row of sample and row deletion, with vectorial β _{T, b}With wait to reject sample row deletion accordingly.

(5) based on above step set up real-time update reflection production data and quality index data corresponding relation at line model;

(6) production data of setting up to step (5) in line model input mixing process, output obtains the predicted value of the quality index data of elastomeric compound, the soft measurement of quality index data in the rubber mixing process of realization Banbury mixer.

As shown in Figure 1, the soft sensor modeling initial stage since model in sample number less than given maximum sample quantity; And this moment, data were historical data; All data are added into model, and (among the present invention, maximum sample quantity is confirmed according to what that produce train number when sample number in the model during greater than designated value; Owing to produce train number generally between 50 to 150; The production train number selects smaller value when fewer but is not less than 10, and the production train number selects higher value when many but is no more than 50), whether can be divided into two kinds of situation according to current sample by existing sample approximately linear combination in the soft-sensing model; When current sample can not be had the combination of sample approximately linear in the model current sample is added model and correction model parameter; Further stable to keep the model size in the deletion model to the minimum sample of model contribution, otherwise, only the sample relevant parameter is adjusted to absorb the information of current model.

As shown in Figure 2; Adopt flexible measurement method of the present invention to carry out among the soft measured effect figure of field data, provided the soft measured value of Mooney coefficient and the correlation curve of actual measured value in the rubber mixing process, wherein; The data of preceding 10 train numbers only are used for modeling and are not used in soft measurement; The mooney viscosity of per car time is all by soft measurement afterwards, and a train number carries out a measuring at interval, and with the mooney viscosity of measuring as being used for the online updating soft-sensing model with production process data.Because the fitting degree of soft measured value and actual measured value is high; In this case; As long as through programmable logic controller (PLC) (Program Logic Control, PLC), the mixing process production data of the current train number of the quick online acquisition of device such as various electronic instruments, utilize real-time update among the present invention at line model; The Mooney point, sulphur that can forecast current train number become quality index datas such as appearance, dynamically to current and afterwards train number sizing material production process for milling be optimized adjustment.And Traditional use Mooney appearance, sulphur become quality inspection equipment such as appearance and need the corresponding quality inspection result that time of about 3 minutes just can obtain sizing material, so glue stuff compounding draws and needs certain delay from being sampled to the quality inspection result.Therefore, adopt flexible measurement method of the present invention, can save a large amount of measuring costs, and, also can be further used for on-line optimization control early than the mooney viscosity in measuring time (being generally 3 minutes) the acquisition quality index.

Fig. 3 is flexible measurement method of the present invention online applicating flow chart in the rubber mixing process of Banbury mixer.Set up both corresponding relations through using the corresponding mooney viscosity measured value of experiment of melting temperature, mixing time, mixing power, sizing material and adjuvant information; The former the information prediction latter through current acquisition; And predicted value is imported mixing process expert system auxiliary process personnel carry out production process optimization; Finally pass through manufacturing execution system control and go up subsidiary engine and feed proportioning system, finally go up subsidiary engine and feed proportioning system through automatic quality melting temperature, mixing time, mixing power of controlling original sizing material and each stage adjuvant such as industry spot computing machines.Use this online soft sensor method and utilize respective quality index predicted value On-line Control banburying process binder removal after the time; On-the-spot quality inspection cost savings about 60%; Use soft measurement data real-time optimization technological parameter, rubber mixing process quality (elastomeric compound qualification rate) improves about 5%, and along with mixing process modeling and application some rules that obtain are accumulated; These rules progressively are applied in process optimization, the formulation optimization and go, and enterprise will obtain more benefit.

Claims (5)

1. the flexible measurement method of quality index data in the rubber mixing process of Banbury mixer is characterized in that, may further comprise the steps:

(1) carries out modeling according to the historical data of the rubber mixing process of Banbury mixer; Wherein, historical production data is as input feature vector, and historical quality index data is as output characteristic; Obtain reflecting the historical data model of the corresponding relation of production data and quality index data, as initial model; Historical production data and historical quality index data in the initial model constitute initial sample;

(2) production data of the current mixing process of collection and quality index data are as current sample; Use projection functions that current sample is projected the feature space of high dimension coordinate from low dimension coordinate space, and in the feature space of high dimension coordinate, calculate the linear relationship of existing sample in current sample and the model; Described projection functions is φ (x), satisfies k (x ₁, x ₂)=<φ (x ₁), φ (x ₂)>, wherein, k (x ₁, x ₂) be the Kernel function,<φ (x ₁), φ (x ₂)>Be projection functions φ (x ₁) and φ (x ₂) dot product, x ₁With x ₂It is real variable; Described Kernel function is a gaussian kernel function, and its expression formula is suc as formula shown in (4):

k(x ₁，x ₂)＝exp[-||x ₁-x ₂|| ²/(2σ ²)](4)

Wherein, σ representes kernel function width, x ₁With x ₂It is real variable;

(3), judge whether current sample can be by existing sample approximately linear combination expression in the model according to result calculated in the step (2);

If, keep the existing sample of model constant, the adjustment model parameter is carried out model stability and is upgraded to absorb the information of current sample;

If not, current sample is added into model, and use the recursion computing formula to calculate the model parameter after current sample adds, model is revised renewal;

(4) after current sample was added in the model, whether sample number exceeded given maximum sample quantity in the judgment models; If; Then take minimum contribution to eliminate method; With in the model the minimum sample of model contribution being deleted from model; To keep the model sample size stable, the described minimum contribution method of eliminating is: the minimum sample of predicated error in the existing sample in the model is regarded as the minimum sample of final mask contribution deletes;

(5) based on above step set up real-time update reflection production data and quality index data corresponding relation at line model;

(6) production data of setting up to step (5) in line model input mixing process, output obtains the predicted value of the quality index data of elastomeric compound, the soft measurement of quality index data in the rubber mixing process of realization Banbury mixer.

2. flexible measurement method as claimed in claim 1 is characterized in that, in the step (1), the process of described modeling is following:

(i) establish the rubber mixing process model as shown in the formula shown in (1):

$y_{t,b}=f({\mathrm{\&alpha;}}_{t,b},x_t)+{\mathrm{\&epsiv;}}_{t,b}={\mathrm{\&alpha;}}_{t,b}^T\mathrm{\&phi;}\left(x_t\right)+{\mathrm{\&epsiv;}}_{t,b}---\left(1\right)$

In the formula (1), functional f is present in the feature space of high dimension coordinate, is model to be asked; y _{T, b}Representation model is in t b output valve constantly, b=1 ..., B, wherein B is total output number of model; α _{T, b}And ε _{T, b}Model parameter vector and the noise vector of representing the b sub-systems respectively; φ (x _t) be described projection functions, x _tBe t input feature vector constantly;

(ii), find the solution functional f suc as formula the equality majorized function shown in (2) in the feature space foundation of high dimension coordinate to realize that soft measurement error value minimum is a target;

$\min J\left({\mathrm{\&alpha;}}_{t,b}\right)=\frac{1}{2}{\left|\right|{\mathrm{\&epsiv;}}_{t,b}\left|\right|}^2+\mathrm{c\&Omega;}\left[\right|\left|f\right|\left|\right]---\left(2\right)$

$\mathrm{st}:y_{t,b}-{\mathrm{\&alpha;}}_{t,b}^T\mathrm{\&phi;}\left(x_t\right)-{\mathrm{\&epsiv;}}_{t,b}=0$

ε in the formula (2) _{T, b}=[ε _{1, b}, ε _{2, b}..., ε _{T, b}] ^TC＞0 is the regularization parameter of the complexity that is used for controlling models; Ω [|| f||] is a regularization term, for Ω [|| f||]=|| α _{T, b}|| ²/ 2; φ (x _t) be described projection functions, x _tBe t input feature vector constantly;

(iii) convert the equality majorized function shown in the formula (2) into expression formula (3), introduce the Kernel function and find the solution functional f:

$\min J\left({\mathrm{\&beta;}}_{t,b}\right)=\frac{1}{2}{\left|\right|{\mathrm{\&epsiv;}}_{t,b}\left|\right|}^2+\frac{c}{2}{\left|\right|{\mathrm{\&beta;}}_{t,b}\left|\right|}^2---\left(3\right)$

st：y _t，b-K _tβ _t，b-ε _t，b＝0

In the formula (3), K _tSample is at the matrix of the similarity of the feature space of high dimension coordinate in the representation model, the element K of the capable j row of its i _t(i, j)=<φ (x _i), φ (x _j)>, be Kernel similarity calculated value, i, j=1 ..., t, β _{T, b}Be the model parameter vector after the conversion, ε _{T, b}Be noise vector;

(iv) with different mixing process production datas constantly in the historical data as input feature vector x _t, the quality index data of elastomeric compound is as output valve y _t, form mixing process data sample { (x ₁, y ₁) ..., (x _t, y _t), use projection functions that data sample is projected the feature space of high dimension coordinate from low dimension coordinate space, carry out Kernel at the feature space of high dimension coordinate and calculate formula (3) is found the solution, obtain initial model.

3. flexible measurement method as claimed in claim 1 is characterized in that, the feature space of described high dimension coordinate is the reproducing kernel Hilbert space.

4. flexible measurement method as claimed in claim 1 is characterized in that, in the step (2), the described process of in the feature space of high dimension coordinate, calculating the linear relationship that has sample in current sample and the model is following:

1. confirm space similarity index s in (θ in the feature space of high dimension coordinate _t) computing formula be shown in the formula (5):

$\mathrm{Sin}\left({\mathrm{\&theta;}}_t\right)=\underset{a_t}{\min }\left|\right|\mathrm{\&phi;}\left(x_t\right)-\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{a}_k\mathrm{\&phi;}\left({\tilde{x}}_k\right)\left|\right|/\left|\right|\mathrm{\&phi;}\left(x_t\right)\left|\right|---\left(5\right)$

In the formula (5), n is current sample number, φ (x _t) be the mapping of current sample in the feature space of high dimension coordinate, existing sample being mapped as in high-dimensional feature space in the model

a _kBe undetermined parameter, a _t=[a ₁..., a _n] ^T

2. formula (5) is found the solution, is obtained as shown in the formula the space similarity index expression formula shown in (6):

$\mathrm{Sin}\left({\mathrm{\&theta;}}_t\right)=|k_{\mathrm{tt}}-a_t^T{\tilde{k}}_t|/k_{\mathrm{tt}}---\left(6\right)$

In the formula (6), k _Tt=<φ (x _t), φ (x _t), <math> <mrow> <msub> <mover> <mi>k</mi> <mo>~</mo> </mover> <mi>t</mi> </msub> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&lt;;</mo> <mi>&amp;phi;</mi> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>~</mo> </mover> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>&amp;phi;</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>t</mi> </msub> <mo>)</mo> </mrow> <mo>></mo> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>&amp;CenterDot;</mo> <mo>,</mo> <mi>t</mi> <mo>-</mo> <mn>1</mn> <mo>;</mo> </mrow></math>

3. according to the Kernel function formula (6) is calculated, obtained the linearity of existing sample in current sample and the model, i.e. space similarity index.

5. flexible measurement method as claimed in claim 4 is characterized in that, in the step (3), judges whether current sample can be following by the process of existing sample approximately linear combination expression in the model:

As space similarity index s in (θ _t) less than predetermined threshold value, think that then current sample can be by existing sample approximately linear combination expression in the model; Otherwise current sample can not be by existing sample approximately linear combination expression in the model; Wherein, described predetermined threshold value is 0.1～0.3.

Images