CN108664706A - A kind of synthetic ammonia process primary reformer oxygen content On-line Estimation method based on semi-supervised Bayes's gauss hybrid models - Google Patents

A kind of synthetic ammonia process primary reformer oxygen content On-line Estimation method based on semi-supervised Bayes's gauss hybrid models Download PDF

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CN108664706A
CN108664706A CN201810338582.2A CN201810338582A CN108664706A CN 108664706 A CN108664706 A CN 108664706A CN 201810338582 A CN201810338582 A CN 201810338582A CN 108664706 A CN108664706 A CN 108664706A
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邵伟明
宋执环
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Zhejiang University ZJU
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Abstract

The present invention discloses a kind of synthetic ammonia process primary reformer oxygen content On-line Estimation method based on semi-supervised Bayes's gauss hybrid models, it designs a kind of new complete Bayesian model structure first, by all model parameter randomizations and so that Semi-Supervised Regression learns；Then under variation Framework for Reasoning, while excavation has exemplar and unlabeled exemplars information, establishes the learning procedure of model parameter.This method can provide the estimated value of synthetic ammonia process primary reformer oxygen content in real time online.With the application of the invention, the influence of over-fitting can be reduced effectively, to improve estimated accuracy, for reduce generate this, enhancing process operation stationarity, process monitoring and decision-making provide technical support and ensure.

Description

A kind of synthetic ammonia process primary reformer oxygen based on semi-supervised Bayes's gauss hybrid models Gas content On-line Estimation method
Technical field
The invention belongs to chemical process soft sensor modeling and application fields, and in particular to one kind is high based on semi-supervised Bayes The synthetic ammonia process primary reformer oxygen content On-line Estimation method of this mixed model.
Background technology
Ammonia is a kind of very important basic chemical industry product, and yield ranks first in all kinds of chemical products, in industry On be largely used to production urea, soda ash, ammonium fertilizer, nitric acid, and the organic syntheses industry production such as fiber, plastics, dyestuff is made Product.The raw material for synthesizing ammonia includes nitrogen and hydrogen, and wherein nitrogen can largely be obtained from air, and hydrogen needs to pass through specially Hydrogen producer produces.In most ammonia synthesis process, one-stage converter (abbreviation primary reformer) is the capital equipment for preparing hydrogen, In chemical reaction (catalyst is nickel) it is as follows：
Above-mentioned chemical reaction is the endothermic reaction, needs to provide heat to primary reformer.Therefore, it is anti-to be to maintain hydrogen manufacturing for reaction temperature An important factor for progress should be stablized.The mode of heating of primary reformer routine is to burn the useless of nozzle burning fuel gas and recycling in radiant section Gas.In order to maintain the reaction temperature of technique initialization, need to control the oxygen content in primary reformer in specified range.Oxygen Content (unit is molar percentage, mol%) can be measured by mass-synchrometer.But mass-synchrometer is not only at high price, Measurement period is longer, and is easy to be out of order.The measured value of oxygen content is lost, closed loop controller will be unable to work, may cause The problems such as a series of adverse consequences, environmental pollution and cost as caused by rejection rate increase, energy consumption increase etc. increase, very To leading to security risk.
The online real-time estimation of oxygen content may be implemented in the oxygen content soft-sensing model of data-driven, to make up quality The deficiency of analyzer.Its principle is in off-line phase according to oxygen content and the variable (such as temperature, the pressure that are easy measurement in the process Parameters such as power, flow, liquid level, and be referred to as auxiliary variable) between dependence founding mathematical models, it is then online using should Mathematical model estimates oxygen content, therefore has many advantages, such as that no measurement delay, at low cost, versatility is good, easy care.But Since primary reformer combustion process is sufficiently complex, and operating mode switching is frequent, and creation data presents uncertain, multi-modal, strong non-thread The features such as property so that traditional soft-sensing model (such as principal component model, partial least square model, neural network model, branch Hold vector machine model etc.) it is difficult to obtain satisfied estimated accuracy.On the other hand, since the measurement period of mass-synchrometer is longer, There is exemplar (i.e. sample known to oxygen content) quantity seldom, tradition is caused to have the modeling method of supervision due to " cross and learn " Or the reasons such as " owing study " are difficult to obtain accurate model parameter.The bad oxygen content soft-sensing model of training can not necessarily carry For satisfied estimated accuracy, and artificial setting parameter time and effort consuming, difficulty are very big.
Therefore, research and development can handle complicated uncertainty during primary reformer, strong nonlinearity, multi-modal simultaneously And have the oxygen content soft-sensing model for the problems such as exemplar is rare, the estimated accuracy of oxygen content is helped to improve, from And power-assisted ammonia enterprise realizes safety in production, energy conservation and environmental protection, the target of cost efficiency, is very necessary and urgent.
Invention content
In view of the deficiencies of the prior art, the present invention provides a kind of synthesis ammonia based on semi-supervised Bayes's gauss hybrid models Process primary reformer oxygen content On-line Estimation method is established oxygen content in the form of Bayes's gauss hybrid models and become with auxiliary Randomization mathematical model between amount, according to the contribution degree of operating mode switching self-adjusted block mixed model, effective solution uncertainty, The problems such as non-linear, multi-modal, and utilization has exemplar and unlabeled exemplars (i.e. oxygen content simultaneously by semi-supervised learning Unknown, only sample known to auxiliary variable), solve the problems, such as that model estimated accuracy caused by exemplar rareness is not high.Tool Body technique scheme is as follows：
A kind of synthetic ammonia process primary reformer oxygen content On-line Estimation side based on semi-supervised Bayes's gauss hybrid models Method, which is characterized in that include the following steps：
(1) selection and the associated auxiliary variables of primary reformer oxygen content yWherein d indicates auxiliary variable number；
(2) collect simultaneously that include auxiliary variable and oxygen content have exemplar collectionWith only wrap Unlabeled exemplars collection containing auxiliary variableWherein nlWith nuRespectively represent exemplar and unlabeled exemplars Quantity；
(3) to (Xl,Yl) and XuNondimensionalization processing is done, by the sample variance of auxiliary variable sample and oxygen content sample Be converted to unit variance；
(4) the cutoff level M of Di Li Cray processes, initialization model parameter are given Conjugate gradient descent method parameter a0、b0、c0、d0、e0、f0、β0、v0、m0、W0With Posterior distrbutionp parameter a, b, hk、lk、ck、dk、ek、 fk、βk、vk、mk、Wk、ωk、Ωk, wherein And
α indicates the concentration factor of Di Li Cray processes；
χkIndicate the parameter of k-th of mixed model coefficient；
μkAnd ΛkThe mean vector and concentration matrix of the distribution of auxiliary variable x in k-th of mixed model are indicated respectively；
Indicate the linear regression coeffficient between auxiliary variable x and oxygen content y in k-th of mixed model；
τkIt indicatesConcentration matrix parameter；
ηkIndicate the concentration matrix coefficient of measurement noise in k-th of mixed model.
The meaning of conjugate gradient descent method parameter and Posterior distrbutionp parameter is：
(a0,b0) and (a, b) respectively indicate α prior distribution parameter and Posterior distrbutionp parameter；
(hk,lk) indicate χkPosterior distrbutionp parameter；
(m0,β0,W0,v0) and (mk,βk,Wk,vk) (μ is indicated respectivelyk,Λk) prior distribution parameter and Posterior distrbutionp ginseng Number；
(c0,d0) and (ck,dk) τ is indicated respectivelykPrior distribution parameter and Posterior distrbutionp parameter；
(e0,f0) and (ek,fk) η is indicated respectivelykPrior distribution parameter and Posterior distrbutionp parameter；
ωkAnd ΩkIt indicatesPosterior distrbutionp parameter；
(5) it is built with exemplar (Xl,Yl) and unlabeled exemplars XuAnd its corresponding hidden variable Likelihood function, wherein zi=(zi1,…,ziM)TAnd zj=(zj1,…,zjM)TIt indicates to have exemplar (x i-th respectivelyi,yi) With j-th of unlabeled exemplars xjCorresponding binary system hidden variable, and meet
(6) by step (3) treated training sample set, in the original model parameter and step (5) in step (4) The likelihood function of structure inputs in semi-supervised Bayes's gauss hybrid models, learns each model parameter most by variation reasoning Excellent Posterior distrbutionp q (α) withHere q () indicate to dependent variable it is optimal after Test distribution.
(7) acquisition only includes the unknown sample of auxiliary variable, and the dimension of auxiliary variable is eliminated by step (3), utilizes step (6) the optimal Posterior distrbutionp of the model parameter obtained in, estimates oxygen content.
Further, what is built in the step (5) has exemplar (Xl,Yl) and unlabeled exemplars XuAnd its it is corresponding Hidden variable Zl、ZuLikelihood function be：
Wherein χ=(χ1,…,χM), μ=(μ1,…,μM), Λ=(Λ1,…,ΛM),η= (η1,…,ηM),Expression mean value is μk, covariance matrix beGaussian probability-density function,
Further, the parameter a, b, h of the optimal Posterior distrbutionp of the model parameter of the step (6)k, lk, ck, dk, ek, fk, βk, vk, mk, Wk, ωkAnd ΩkIterative formula have following form：
A=a0+M-1
ck=c0+(d+1)/2
Wherein, ψ () indicates that digamma functions, I indicate the unit matrix of corresponding dimension,1 arranges for complete 1 Vector, the mark of Tr () matrix, Indicate the evaluated error of k-th of mixed model, HereIndicate basisDistribution calculateExpectation；κikAnd κjkCalculating Mode is
Wherein
Further, the step (7) is specially：
According to the Posterior distrbutionp of the α calculated in step (6) and the property of Di Li Cray processes, each model mixed stocker Number π=(π1,…,πM) Posterior distrbutionp can be calculated as
Q (π)=Dir (π | φ1,…,φM)
Wherein Dir (π | φ1,…,φM) representation parameter be (φ1,…,φM) Di Li Crays distribution, and
Then, according to the Posterior distrbutionp of calculated model parameter in step (6), the auxiliary variable x after dimension must can be removedt Edge distribution be
Wherein Expression parameter is Xue Shengshi t distribution.And then x can be obtainedtCorresponding hidden variable zt=(zt1,…,ztM) Posterior distrbutionp be
Wherein zt1,…,ztMIt is 0-1 variables, and meets
Then the probability distribution that oxygen content can be acquired, to obtain the estimated value of oxygen content.
Further, the oxygen content ytProbability distribution be：
Wherein
Therefore, the estimated value that can obtain oxygen content is
Compared with prior art, beneficial effects of the present invention are as follows：
1, the mathematical model that oxygen content and auxiliary variable are established in the form of mixed model, can effectively solve the problem that by operating mode Multi-modal, strong nonlinearity problem caused by the combustion process of switching and complexity；
2, it can solve have exemplar insufficient simultaneously using having exemplar and unlabeled exemplars by semi-supervised learning Caused model parameter learns bad problem, to improve the estimated accuracy of oxygen content；
3, parameter learning and problem of model selection can be solved simultaneously in a wheel training, it is not necessary to traverse all candidate hybrid guided modes Type quantity, to improve training effectiveness.
Description of the drawings
Fig. 1 is that the synthetic ammonia process primary reformer oxygen content based on semi-supervised Bayes's gauss hybrid models of the present invention exists The flow chart of line method of estimation；
Fig. 2 is the process principle figure of certain synthesis ammonia factory primary reformer device；
Fig. 3 is estimated result schematic diagram of the present invention to oxygen content, wherein abscissa represents oxygen content, and unit is Molar percentage (mol%), ordinate represent test sample serial number, and solid line represents oxygen content actual value, and dotted line represents oxygen Content estimated value；
Fig. 4 is estimated result schematic diagram of the gauss hybrid models to oxygen content, wherein abscissa represents oxygen content, Unit is molar percentage (mol%), and ordinate represents test sample serial number, and solid line represents oxygen content actual value, dotted line generation Epoxy Gas content estimated value；
Fig. 5 is estimated result schematic diagram of the partial least square model to oxygen content, wherein abscissa represents oxygen and contains Amount, unit are molar percentage (mol%), and ordinate represents test sample serial number, and solid line represents oxygen content actual value, dotted line Represent oxygen content estimated value.
Specific implementation mode
With reference to specific embodiment to the synthesis ammonia mistake based on semi-supervised Bayes's gauss hybrid models of the present invention Journey primary reformer oxygen content On-line Estimation method is further elaborated.It should be pointed out that described embodiment is only intended to Reinforce the understanding of the present invention, any restriction effect is not played to the present invention.
A kind of synthetic ammonia process primary reformer oxygen content On-line Estimation side based on semi-supervised Bayes's gauss hybrid models Method, as shown in Figure 1, specifically comprising the following steps：
(1) selection and the associated auxiliary variables of oxygen content y in primary reformer production equipmentWherein d indicates auxiliary Variable number；
The present embodiment according to certain ICI-AMV techniques (yield 1000t/d) production of synthetic ammonia primary reformer device (such as Shown in Fig. 2) process mechanism analysis, select on maximum 13 variables of oxygen content influence as auxiliary variable, respectively：It arrives Fuel gas flow (the x of 03B0011, position number：FR03001.PV), to the exhaust combustion gases flow (x of 03B0012, position number： FR03002.PV), pressure (x of the exits 03E005 exhaust combustion gases3, position number：PC03002.PV), the exits 03B001 fuel gas Pressure (x4, position number：PC03007.PV), temperature (x of the exits 03E005 exhaust combustion gases5, position number：TI03001.PV)、 Temperature (the x of the exits 03B002E06 fuel gas6, position number：TI03009.PV), temperature (x of the inlet 03B001 Process Gas7, position Number：TR03012.PV), temperature (x of the upper left sides 03B001 fuel gas8, position number：TI03013.PV), the upper right side 03B001 fuel Temperature (the x of gas9, position number：TI03014.PV), temperature (x of the surfaces 03B001 gaseous mixture10, position number：TR03015.PV)、 03B001 left side outlets convert the temperature (x of gas11, position number：TR03016.PV), the temperature of 03B001 right-side outlets conversion gas (x12, position number：TR03017.PV), temperature (x of the outlets 03B001 conversion gas13, position number：TR03020.PV).Therefore auxiliary variable X=[x1,…,x13], i.e.,
(2) collect simultaneously that include auxiliary variable and oxygen content have exemplar collectionWith only wrap Unlabeled exemplars collection containing auxiliary variableWherein nlWith nuRespectively represent exemplar and unlabeled exemplars Quantity；
The present invention is collected from computer scattered control system database while having comprising auxiliary variable and oxygen content 2000 groups of exemplar collection (is denoted asWith 5000 groups of the unlabeled exemplars collection (note for only including auxiliary variable ForAs training dataset, wherein nl=2000 and nu=5000 have respectively represented exemplar and no label The quantity of sample.
(3) to (Xl,Yl) and XuNondimensionalization processing is done, by the sample variance of auxiliary variable sample and oxygen content sample Be converted to unit variance；
The method for wherein going dimension is：
In formula,Respectively Represent first of auxiliary variable and the sample standard deviation of oxygen content, xn(l) adopting for first of auxiliary variable of n-th of sample is indicated Sample value.
(4) the cutoff level M of Di Li Cray processes, initialization model parameter are given Conjugate gradient descent method parameter and Posterior distrbutionp parameter, the meaning of model parameter is：
α indicates the concentration factor of Di Li Cray processes；
χkIndicate the parameter of k-th of mixed model coefficient；
μkAnd ΛkThe mean vector and concentration matrix of the distribution of auxiliary variable x in k-th of mixed model are indicated respectively；
Indicate the linear regression coeffficient between auxiliary variable x and oxygen content y in k-th of mixed model；
τkIt indicatesConcentration matrix parameter；
ηkThe concentration matrix coefficient of measurement noise in k-th of mixed model of table.
In the present invention, the conjugate gradient descent method and Posterior distrbutionp of each model parameter are determined as：
The prior distribution p (α) and Posterior distrbutionp q (α) of α is that gamma is distributed, i.e. and p (α)=Gam (α | a0,b0), q (α)= Gam (α | a, b), wherein Gam (α | a0,b0) and Gam (α | a, b) expression parameter is distinguished for (a0,b0) and (a, b) gamma distribution；
χkPrior distribution p (χk) and Posterior distrbutionp q (χk) it is beta distribution, i.e. p (χk)=Beta (χk| 1, α), q (χk)=Beta (χk|hk,lk), wherein Beta (χk| 1, α) and Beta (χk|hk,lk) expression parameter is distinguished for (1, α) and (hk, lk) beta distribution；
μk,ΛkPrior distribution p (μk,Λk) and Posterior distrbutionp q (μk,Λk) be Gauss-prestige Saudi Arabia distribution, i.e., WhereinWithExpression parameter is (m respectively0, β0,W0,v0) and (mk,βk,Wk,vk) Gauss-prestige Saudi Arabia distribution；
Prior distributionAnd Posterior distrbutionpIt is Gaussian Profile, i.e., WhereinIndicate that mean vector is 0, covariance matrix isGaussian Profile,Expression mean vector is ωk, covariance matrix ΩkGaussian Profile, I indicates the unit square of corresponding dimension Battle array,；
τkPrior distribution p (τk) and Posterior distrbutionp q (τk) it is gamma distribution, i.e. p (τk)=Gam (τk|c0,d0), q (τk)=Gam (τk|ck,dk), wherein Gam (τk|c0,d0) and Gam (τk|ck,dk) expression parameter is distinguished for (c0,d0) and (ck,dk) Gamma distribution；
ηkPrior distribution p (ηk) and Posterior distrbutionp q (ηk) it is gamma distribution, i.e. p (ηk)=Gam (ηk|e0,f0), q (ηk)=Gam (ηk|ek,fk), wherein Gam (ηk|e0,f0) and Gam (ηk|ek,fk) expression parameter is distinguished for (e0,f0) and (ek,fk) Gamma distribution.
Therefore, in this step, need to initialize prior distribution parameter, including And Posterior distrbutionp parameter, including In this example, the parameter setting of prior distribution is a0=1, b0=1, c0=1, d0=1, e0=1, f0=1, β0=1, v0=1, m0=0, W0=I；The parameter a, b, h of Posterior distrbutionpk, lk, ck, dk, ek, fk, βk, vk, mk, Wk, ωk, Ωk's Initial value is random value.
(5) it is built with exemplar (Xl,Yl) and unlabeled exemplars XuAnd its corresponding hidden variable Likelihood function, wherein zi=(zi1,…,ziM)TAnd zj=(zj1,…,zjM)TIt indicates to have mark i-th respectively Signed-off sample sheet (xi,yi) and j-th of unlabeled exemplars xjCorresponding binary system hidden variable, and meetHave Following form：
(6) by step (3) treated training sample set, in the original model parameter and step (5) in step (4) The likelihood function of structure inputs in semi-supervised Bayes's gauss hybrid models, learns each model parameter most by variation reasoning Excellent Posterior distrbutionp q (α) andDetailed process include variation expectations section and Variation maximizes part.
In variation expectations section, need to calculate hidden variable ZlAnd ZuPosterior distrbutionp q (Zl) and q (Zu).According to variation reasoning Principle can obtain
WhereinIndicate basisDistribution calculateExpectation, χ=(χ1,…,χM), μ=(μ1,…, μM), Λ=(Λ1,…,ΛM),η=(η1,…,ηM),Expression mean value is μk, covariance Matrix isGaussian probability-density function,And
Wherein ψ () indicates digamma functions.Therefore,
WhereinFor during simplicity, constant term is omitted in formula (7)；After subsequently calculating each parameter Constant term is still omitted when testing distribution.
Similarly, Z can be obtaineduPosterior distrbutionp q (Zu) as follows：
Wherein
So as to
Wherein
Part is maximized in variation, needs computation model parameterPosterior distrbutionp q (Θ).Still the principle of variation reasoning is used.Specifically, the method for solving of q (α) is
Therefore, the parameter more new formula of Posterior distrbutionp q (α)=Gam (α | a, b) of α is
lnq(χk) can calculate according to the following formula
Therefore, χkPosterior distrbutionp q (χk)=Beta (χk|hk,lk) parameter more new formula be
lnq(μk,Λk) can calculate according to the following formula
Wherein
Above formula, that is, μk,ΛkPosterior distrbutionpParameter update Formula, the mark of Tr () matrix；
It can calculate according to the following formula
Wherein,1 is complete 1 column vector, It indicates to mix for k-th The evaluated error of molding type, therefore,Posterior distrbutionpParameter more new formula be
lnq(τk) can calculate according to the following formula
Therefore, τkPosterior distrbutionp q (τk)=Gam (τk|ck,dk) parameter more new formula be
lnq(ηk) can calculate according to the following formula
Therefore, ηkPosterior distrbutionp q (ηk)=Gam (ηk|ek,fk) parameter more new formula be
Variation expectations section is executed by iteration and variation maximizes part, and the Posterior distrbutionp of model parameter will restrain. Convergent criterion is that the relative increment of variation lower bound is less than given threshold (10 in this example-7)。
(7) on-line stage, acquisition only include the unknown sample x of auxiliary variablet, the amount of auxiliary variable is eliminated by step (3) Guiding principle estimates oxygen content using the optimal Posterior distrbutionp of the model parameter obtained in step (6).Specifically, according to The Posterior distrbutionp of the α calculated in step (6) and the property of Di Li Cray processes, each model mixed coefficint π=(π1,…, πM) Posterior distrbutionp can be calculated as
Q (π)=Dir (π | φ1,…,φM) (25)
Wherein Dir (π | φ1,…,φM) representation parameter be (φ1,…,φM) Di Li Crays distribution, and
Then, according to the Posterior distrbutionp of calculated model parameter in step (6), the auxiliary variable x after dimension must can be removedt Edge distribution be
Wherein Expression parameter is Xue Shengshi t distribution.And then x can be obtainedtCorresponding hidden variable zt=(zt1,…,ztM) Posterior distrbutionp be
Wherein zt1,…,ztMIt is 0-1 variables, and meets
Finally, oxygen content y can be obtainedtProbability distribution be
Wherein
Therefore, according to formula (29), the estimated value that can obtain oxygen content is
In order to verify effectiveness of the invention, received from the synthesis ammonia factory primary reformer device computer scattered control system Collection it is additional there is 4000 groups of exemplar to estimate oxygen content, averagely estimate according to step (7) as verification sample sets The results are shown in Figure 3 for meter.Meanwhile traditional gauss hybrid models are set forth with partial least square model to oxygen in Fig. 4 and Fig. 5 The averaged power spectrum result of Gas content.In gauss hybrid models, blending ingredients quantity is set as 12 by bayesian information criterion； In partial least square model, principal component quantity is set as 10 by cross-validation method.As can be seen that non-thread due to that cannot handle The estimated value of sex object, the oxygen content that partial least square model provides deviates significantly from true value；And traditional gauss hybrid models Although estimated result make moderate progress compared with partial least square model, but still it is unsatisfactory, especially in third and fourth operating space Domain (at the 2500-4000 sample).In contrast, the oxygen content that method provided by the invention is provided in all operating areas Estimated value substantially conforms to its true value.
Estimated with traditional gauss hybrid models, partial least square model using root-mean-square error (RMSE) the quantization present invention Precision is counted, is defined as follows
Wherein ytWithRespectively represent the true oxygen content and estimated value of t-th of verification sample.Method provided by the invention Estimation RMSE with gauss hybrid models, partial least square model is respectively 0.6933,1.1515,1.7143.As it can be seen that of the invention It is significantly increased to the estimated accuracy of oxygen content compared with gauss hybrid models, partial least square model, evaluated error reduces respectively About 40% and 60%.
Above-described embodiment is used for illustrating the present invention, rather than limits the invention, the present invention spirit and In scope of the claims, to any modifications and changes that the present invention makes, protection scope of the present invention is both fallen within.

Claims (5)

1. a kind of synthetic ammonia process primary reformer oxygen content On-line Estimation method based on semi-supervised Bayes's gauss hybrid models, It is characterized by comprising the following steps：
(1) selection and the associated auxiliary variables of primary reformer oxygen content yWherein d indicates auxiliary variable number；
(2) collect simultaneously that include auxiliary variable and oxygen content have exemplar collectionWith only include it is auxiliary Help the unlabeled exemplars collection of variableWherein nlWith nuRespectively represent the number of exemplar and unlabeled exemplars Amount；
(3) to (Xl,Yl) and XuNondimensionalization processing is done, the sample variance of auxiliary variable sample and oxygen content sample is converted For unit variance；
(4) the cutoff level M of Di Li Cray processes, initialization model parameter are givenBe total to Yoke prior distribution parameter a0、b0、c0、d0、e0、f0、β0、v0、m0、W0With Posterior distrbutionp parameter a, b, hk、lk、ck、dk、ek、fk、βk、 vk、mk、Wk、ωk、Ωk, wherein And
α indicates the concentration factor of Di Li Cray processes；
χkIndicate the parameter of k-th of mixed model coefficient；
μkAnd ΛkThe mean vector and concentration matrix of the distribution of auxiliary variable x in k-th of mixed model are indicated respectively；
Indicate the linear regression coeffficient between auxiliary variable x and oxygen content y in k-th of mixed model；
τkIt indicatesConcentration matrix parameter；
ηkIndicate the concentration matrix coefficient of measurement noise in k-th of mixed model.
The meaning of conjugate gradient descent method parameter and Posterior distrbutionp parameter is：
(a0,b0) and (a, b) respectively indicate α prior distribution parameter and Posterior distrbutionp parameter；
(hk,lk) indicate χkPosterior distrbutionp parameter；
(m0,β0,W0,v0) and (mk,βk,Wk,vk) (μ is indicated respectivelyk,Λk) prior distribution parameter and Posterior distrbutionp parameter；
(c0,d0) and (ck,dk) τ is indicated respectivelykPrior distribution parameter and Posterior distrbutionp parameter；
(e0,f0) and (ek,fk) η is indicated respectivelykPrior distribution parameter and Posterior distrbutionp parameter；
ωkAnd ΩkIt indicatesPosterior distrbutionp parameter；
(5) it is built with exemplar (Xl,Yl) and unlabeled exemplars XuAnd its corresponding hidden variable Likelihood function, wherein zi=(zi1,…,ziM)TAnd zj=(zj1,…,zjM)TIt indicates to have exemplar (x i-th respectivelyi,yi) With j-th of unlabeled exemplars xjCorresponding binary system hidden variable, and meet
(6) by step (3) treated training sample set, structure in the original model parameter and step (5) in step (4) Likelihood function input in semi-supervised Bayes's gauss hybrid models, by variation reasoning learn each model parameter it is optimal after Test distribution q (α) withHere q () indicates the optimal posteriority point to dependent variable Cloth.
(7) acquisition only includes the unknown sample of auxiliary variable, the dimension of auxiliary variable is eliminated by step (3), using in step (6) The optimal Posterior distrbutionp of the model parameter of acquisition, estimates oxygen content.
2. the synthetic ammonia process primary reformer oxygen according to claim 1 based on semi-supervised Bayes's gauss hybrid models contains Measure On-line Estimation method, which is characterized in that is built in the step (5) has exemplar (Xl,Yl) and unlabeled exemplars Xu And its corresponding hidden variable Zl、ZuLikelihood function be：
Wherein χ=(χ1,…,χM), μ=(μ1,…,μM), Λ=(Λ1,…,ΛM),η=(η1,…,ηM),Expression mean value is μk, covariance matrix beGaussian probability-density function,
3. the synthetic ammonia process primary reformer oxygen according to claim 1 or 2 based on semi-supervised Bayes's gauss hybrid models Gas content On-line Estimation method, which is characterized in that parameter a, the b of the optimal Posterior distrbutionp of the model parameter of the step (6), hk, lk, ck, dk, ek, fk, βk, vk, mk, Wk, ωkAnd ΩkIterative formula have following form：
A=a0+M-1
ck=c0+(d+1)/2
Wherein, ψ () indicates that digamma functions, I indicate the unit matrix of corresponding dimension,1 is complete 1 column vector, The mark of Tr () matrix,Indicate the evaluated error of k-th of mixed model, HereIndicate basisDistribution calculateExpectation；κikAnd κjkMeter Calculation mode is
Wherein
4. the synthetic ammonia process primary reformer oxygen according to claim 1 or 2 based on semi-supervised Bayes's gauss hybrid models Gas content On-line Estimation method, the step (7) are specially：
According to the Posterior distrbutionp of the α calculated in step (6) and the property of Di Li Cray processes, each model mixed coefficint π =(π1,…,πM) Posterior distrbutionp can be calculated as
Q (π)=Dir (π | φ1,…,φM)
Wherein Dir (π | φ1,…,φM) representation parameter be (φ1,…,φM) Di Li Crays distribution, and
Then, according to the Posterior distrbutionp of calculated model parameter in step (6), the auxiliary variable x after dimension must can be removedtSide Edge is distributed as
WhereinExpression parameter is Xue Shengshi t distribution.And then x can be obtainedtCorresponding hidden variable zt=(zt1,…,ztM) Posterior distrbutionp be
Wherein zt1,…,ztMIt is 0-1 variables, and meets
Then the probability distribution that oxygen content can be acquired, to obtain the estimated value of oxygen content.
5. the synthetic ammonia process primary reformer oxygen according to claim 4 based on semi-supervised Bayes's gauss hybrid models contains Measure On-line Estimation method, the oxygen content ytProbability distribution be：
Wherein
Therefore, the estimated value that can obtain oxygen content is
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