CN103336880A - Efficient method for solving model modification problem of operation-oriented optimization - Google Patents

Abstract

The invention discloses an efficient method for solving a model modification problem of operation-oriented optimization. The method comprises the steps of analyzing sensitivity of a model to model parameters and measuring variables firstly, designing subproblems based on the measuring variables and the model parameters respectively according to a sensitivity analysis result, decomposing the model modification problem under the operation optimization into the subproblems from low complexity to high complexity, solving the subproblems, taking an optimum solution of each solved subproblem as an initial value point of calculation of the next to-be-solved subproblem, solving step by step, and finally achieving convergence of solving the model modification problem under the operation optimization on the basis of the better initial value point to obtain accurate parameter values of a strict mechanism model according to structural characteristics of the model modification problem under the process system operation optimization. Since the modified model is adopted to perform the operation optimization, the production efficiency of a process system can be improved remarkably.

Description

A kind of be used to finding the solution the model correction problem high efficiency method that oriented manipulation is optimized

Technical field

The present invention relates to model correction field and operation optimization method research field in the complex process system, especially, relate to a kind of be used to finding the solution the model correction problem high efficiency method that oriented manipulation is optimized.

Background technology

At present China's flow industry enterprise exists energy consumption height, cost height, labour productivity is low, resource utilization is low characteristics to some extent.Therefore adopt simulation and the optimisation technique of flow process, real time operation optimizing is carried out in process units, production procedure, the key variables of production run are carried out online adjustment, process units is moved under optimum state, the high efficiency and the economy that keep flow process to produce are of great practical significance.It is relevant with the levels of precision of process object model that process operation is optimized effect, if process object model and realistic model deviation are bigger, can cause that then the optimal result of optimizing result and process reality is inconsistent, thereby cause optimizing the reduction of precision.Therefore must the application model correction technique, the model parameter of adjustment process object makes the output of model consistent with on-the-spot actual measurement data or deviation is minimum.

In the building method research about model correction problem, Deming has at first proposed the model correction problem based on implicit function, and adopts EVM (error-in-variable) method construct model correction proposition.The modal building method of model correction problem is to carry out data according to the strict mechanism model of simple parts earlier to proofread and correct the corrected value that obtains measurand, obtain the parameter value of complicated strict mechanism model then according to the correction value of measurand, as Marlin and Hrymak, the method that the paper that Perkins etc. deliver is mentioned.The inefficiency of the method impels a lot of scholars that the simultaneous method of model correction problem is studied, and mainly contains Bard, Kim, Tjoa, Gau, Arora and Biegler etc.The simultaneous method of model correction problem is exactly all strict mechanism models of simultaneous, under the prerequisite that satisfies strict mechanism model equation, minimize the correction error weighted sum of squares of measurand, thereby obtain the corrected value of measurand, the not estimated value of measurand and model parameter synchronously.The method is high-efficiency method during process operation is optimized, and therefore uses very extensive.

On the method for solving of model correction problem, domestic scholars has been carried out a large amount of research.Mainly contain Chen Xiao, Wang Ning etc. at the model correction problem of chemical process, proposed a kind of new DNA genetic algorithm and be applied on this problem solving.Yu Huanjun, a beautiful equality are applied to finding the solution of model correction problem with the composite particle colony optimization algorithm.Wang Junyan, Huang Dexian carry out algorithm based on mixing difference, and soft measurement time delay model correction problem is studied.Wei Long, Gu Baiqin etc. have introduced and have adopted the square estimation technique, the maximum likelihood estimation technique and linear regression analysis method that the model correction problem based on the Reliability of Mechanical Seal data is studied.Liu Yijian, Zhang Jianming etc. are applied to particle swarm optimization on the model correction problem solving of nonlinear system.Yu Longwen, Liu Guozhi then are applied to improved particle swarm optimization on the nonlinear system model correction problem solving.Li Wei, Su Hongye are applied to particle swarm optimization algorithm in the model correction of catalytic cracking system.Yan Xuefeng, Yu Juan, Qian Feng etc. study the dynamic (dynamical) model correction of supercritical water oxidation problem based on improving differential evolution algorithm.Li Binbin, Wang Ling, Zheng Dazhong etc. study genetic algorithm and the application in model correction problem thereof based on the interpolation evaluation.Foreign scholars have also carried out continuous research and improvement to model correction problem solving method.Britt and Luecke adopt the method for solving of linear iteration that model correction problem has been carried out effectively finding the solution.Peneloux, Reilly and Patino-Leal etc. have developed the method based on linear iteration solving model correction problem.Schwetlick and Tiller, Valko and Vadja have proposed the two-step approach of solving model correction problem, be the parameter estimation problem of computation model after the first computational data correction problem, carry out iteratively then, up to the corrected value of the estimated value of parameter and measurand change very little till.Liebman and Edgar have improved the high efficiency of model correction problem calculating and result's accuracy by adopting nonlinear optimization method.Along with the nonlinear optimization algorithm fast development, can adopt the problem of the direct computation model correction of nonlinear optimization algorithm efficiently.Tjoa and Biegler adopt the SQP method of global convergence that model correction problem is found the solution.Kim has proposed in computation model correction problem two-step approach, calculates and adopts nonlinear optimization algorithm to replace the linear iteration algorithm, can obtain result more accurately.

The applied research of model correction technique on process industry mainly contains: Hu Haijun, Cheng Guangxu etc. adopt the failure process of model description refining device time delay, use the maximal possibility estimation that genetic algorithm obtains model parameter time delay, with the correctness of method for numerical simulation verification algorithm code.Mantenance data with 39 heat interchanger of certain refinery is that example is analyzed, to its time delay model revise.Zheng Qifu, Zhou Zhaoliang etc. have proposed a kind of improved genetic algorithm, and it is applied on cyclohexanol/cyclohexanone nitration oxidation reaction Kinetics Model correction problem.Xue Yaoyu, Wang Jianlin, Yu Tao etc. have proposed a kind of based on the sweat model modification method that improves particle swarm optimization algorithm, and this method is used for the penicillin fermentation process modeling ^[28]Hardin was applied to the model correction technique on the industrial process operation optimization in nineteen ninety-five.In recent years mainly can be with reference to Yip and Marlin with application about the research of model correction technique, Schwaab and Biscaia, Creveling and Gill, the document of Zavala and Laird etc.

The research that above-mentioned Chinese scholars are based on simple procedures system or carry out based on the mechanism model of simplifying the research major part of model correction.When the complex process system was carried out modelling by mechanism, because the flow process complexity, strict mechanism model generally all had in large scale and is characteristic such as non-linear.The running operating point of industrial processes is more, and way commonly used during construction problem is all operating modes of simultaneous, and structure is based on the model correction proposition of full simultaneous model equation.This model correction problem generally has characteristics such as large-scale nonlinear and degree of freedom are big, and the scale of problem is along with the increase of operating mode number is the linear relation that increases.Adopt above-mentioned method for solving about model correction problem, if directly find the solution, because the equation dimension is big and be non-linear, find the solution the difficulty height, be easy to cause the convergence of solution procedure to fail.Along with the modern production scale enlarges day by day, technology and equipment complexity are more and more higher, and production run model forward both macro and micro both direction is expanded.Based on simple procedures system or be difficult to satisfy the needs of modern production based on the mechanism model operation optimization of simplifying.Yip and Marlin point out that by numerical experiment the precision of operation optimization is along with the resolution (fine degree, resolution) of model increases and increases.Advantage based on strict mechanism model operation optimization is that the optimization result is more accurate, and it is higher to optimize efficient.Therefore, be the demand of modern production development based on the operation optimization of high resolving power or high-res mechanism model, also be the trend of Future Development.In the face of new challenge, need be research object with the complex process system, be driving with a large amount of measurement data, from the strict mechanism model of the inherence of flow process production run, realize the real time operation optimizing of high precision, high-performance, high availability.Yet cohesive process mechanism is carried out high-res, high resolving power modeling, wherein can introduce deviation and the mismatch of model unavoidably, adding the important model parameter of part may not directly obtain, and therefore need adopt model correction technique efficiently, obtains the strict mechanism model of process accurately.Therefore the mechanism model of complex process system presents very significantly extensive, non-linear, multiple dimensioned feature, and is very difficult based on the model correction problem solving of this model, presses for efficiently method for solving as support technology.How design efficiency height and the good method for solving of convergence are the challenges that the model correction technique of complex process system faces.

Summary of the invention

The objective of the invention is the deficiency at the model correction problem solving method of existing oriented manipulation optimization in the procedures system, provide a kind of be used to finding the solution the model correction problem high efficiency method that oriented manipulation is optimized.

The objective of the invention is to be achieved through the following technical solutions: a kind of this method is applied in the PTA oxidation reaction process system be used to finding the solution the model correction problem high efficiency method that oriented manipulation is optimized, and this method may further comprise the steps:

(1) according to the characteristic of PTA oxidation reaction process system model correction problem, the corresponding reaction power mathematic(al) constant of balance equation of relative ten reaction kineticses of model that analysis is to be revised and the sensitivity of seven measurands, and model parameter and measurand are respectively parameter p=[p by the level of sensitivity ordering ₁, p ₂..., p ₁₀], measurand X=[x ₁, x ₂..., x ₇]; Seven measurands are respectively: per hour in phthalic acid output, the product to carboxyl benzaldehyde concentration, the per hour oxygen concentration, the carbonomonoxide concentration of tail gas, the gas concentration lwevel of tail gas, the oxygen concentration of crystallizer tail gas of acetic acid consumption amount, tail gas;

(2) according to the sensitivity analysis result, design is based on the subproblem of measurand and model parameter.Thereby the model correction PROBLEM DECOMPOSITION of complex process system is the subproblem of the progressive complexity of cluster, and subproblem is expressed as follows:

$\underset{X,U,p_1}{\min }{J}_{\mathrm{nk}}(X,Y)=\underset{j=1}{\overset{5}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{\mathrm{nk}}{\mathrm{\&Sigma;}}}{(x_{\mathrm{ij}}-y_{\mathrm{ij}})}^2/{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA00003008052400021.png"\; state="\{\{state\}\}">i</figure-callout>}}^2$

s.t.F(X,U,p ₁,p ₂,...,p _pk)=0

P _nk,pk:lx _i≤x _i≤ux _ii=1,2,...,7

lu _j≤u _j≤uu _jj=1,2,...,21711

lp _k≤p _k≤up _kk=1,2,...,pk

nk=1,2,3,...,7，pk=1,2,3,...,10；

Wherein, J _Nk(X Y) is least square function based on correction error, Y=[y ₁, y ₂..., y _n] be the measured value of measurand, X=[x ₁, x ₂..., x _n] be the corrected value of measurand, ux _i=[ux _I1, ux _I2..., ux _IM] ^T, lx _i=[lx _I1, lx _I2..., lx _IM] ^TBe respectively the bound of measurand, U=[u ₁, u ₂..., u _m] be measurand not, y _i=[y _I1, y _I2..., y _IM] ^T, x _i=[x _I1, x _I2..., x _IM] ^T, u _j=[u _J1, u _J2..., u _JM] ^T, uu _j=[uu _J1, uu _J2..., uu _JM] ^T, lu _i=[lu _J1, lu _J2..., lu _JM] ^TBe respectively the not bound of measurand, σ _iStandard deviation for measurand.M is the operating mode number,

Be the model parameter that to estimate, lp _k, up _kBe respectively the bound of model parameter, (X, U p)=0 are the mechanism model equation of procedures system to F.Total n * the n of the subproblem of dividing _pIndividual and nk=1,2,3 ..., n, pk=1,2,3 ..., n _p

(3) adopt above-mentioned subproblem based on measurand and model parameter, use quadratic programming optimization algorithm and find the solution these subproblems, the initial value point that the subproblem optimum solution found the solution is calculated as next one subproblem to be found the solution, find the solution down length by length, on better initial point basis, reach the convergence of solving model correction problem at last.

(4) find the solution result of calculation according to subproblem planning method for solving, obtained model parameter p=[p accurately ₁, p ₂..., p ₁₀], the corrected value of measurand and the estimated value of measurand not.Revised model further is applied to improved the production efficiency of this procedures system significantly in the operation optimization and process control of this process.

The invention has the beneficial effects as follows:

1, the efficient method for solving of model correction problem of oriented manipulation optimization of the present invention, sensitivity analysis by model, be the complex model correction PROBLEM DECOMPOSITION of procedures system cluster complicacy subproblem from low to high, abbreviate, the model correction that not only can solve effectively under the procedures system operation optimization restrains difficult problem in finding the solution computation process, also will provide a kind of new research method for extensive optimization method field.

2, the efficient method for solving of model correction problem of oriented manipulation optimization of the present invention, by finding the solution these subproblems, easy first and difficult later, the initial value point that the subproblem optimum solution found the solution is calculated as next one subproblem to be found the solution, find the solution down length by length, on better initial point basis, improved and found the solution efficient and constringency performance at last.

3, the efficient method for solving of model correction problem of oriented manipulation optimization of the present invention, can use in the different complex process system on the model correction problem under the operation optimization, can combine with the Different Optimization algorithm, method has versatility, use very flexibly, realize simple.

Description of drawings

Fig. 1 is of the present invention be used to finding the solution the model correction problem high efficiency method synoptic diagram that oriented manipulation is optimized;

Fig. 2 is the structural map of subproblem.

Embodiment

Following reference accompanying drawing of the present invention is for a more detailed description to the present invention.The present invention also can be with many multi-form enforcements, therefore should not think that it is confined to the listed embodiment of instructions, on the contrary, it is for enforcement of the present invention and fully is described that this embodiment is provided, and can describe specific implementation process of the present invention to those skilled in the relevant art.

Fig. 1 is of the present invention be used to finding the solution the model correction problem high efficiency method synoptic diagram that oriented manipulation is optimized.As shown in Figure 1, this method mainly comprises the sensitivity analysis of model, and the structure of subproblem reaches to be optimized effectively respectively set by step and finds the solution, and is easy first and difficult later by finding the solution subproblem, on better initial point basis, improved and found the solution efficient and constringency performance.The efficient method for solving of model correction problem of oriented manipulation optimization of the present invention specifically comprises following implementation step:

1, according to procedures system model correction problem characteristics, analyze model relative model parameter to be revised and the sensitivity of measurand, and model parameter and measurand are respectively parameter by the level of sensitivity ordering

Measurand X=[x ₁, x ₂..., x _n];

2, according to the sensitivity analysis result, design is based on the subproblem of measurand and model parameter.In the subproblem based on measurand, the correction error of measurand is incorporated in the measurand of problem singly, the sensitivity that the precedence of introducing is pressed measurand is order from big to small, has therefore reduced the complexity of problem.In the subproblem based on model parameter, to the most influential parameter of finding the solution of problem, i.e. the preferential relieving of the sensitivity maximum of parameter relative model, and those less parameters of sensitivity are fixed earlier, decontrol parameter from big to small by sensitivity length by length then.Thereby the model correction PROBLEM DECOMPOSITION of complex process system is cluster complicacy subproblem from low to high, and subproblem is expressed as follows:

$\underset{X,U,{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00003008052400021.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00003008052400021.png"\; state="\{\{state\}\}">p</figure-callout>}}_2,\&CenterDot;\&CenterDot;\&CenterDot;p_{\mathrm{pk}}}{\min }{J}_{\mathrm{nk}}(X,Y)=\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{\mathrm{nk}}{\mathrm{\&Sigma;}}}{(x_{\mathrm{ij}}-y_{\mathrm{ij}})}^2/{\mathrm{\&sigma;}}_i^2$

s.t.F(X,U,p ₁,p ₂,...,p _pk)=0

P _nk,pk:lx _i≤x _i≤ux _ii=1,2,...,n

lu _j≤u _j≤uu _jj=1,2,...,m

lp _k≤p _k≤up _kk=1,2,...,pk

Wherein, J _Nk(X Y) is least square function based on correction error, Y=[y ₁, y ₂..., y _n] be the measured value of measurand, X=[x ₁, x ₂..., x _n] be the corrected value of measurand, ux _i=[ux _I1, ux _I2..., ux _IM] ^T, lx _i=[lx _I1, lx _I2..., lx _IM] ^TBe respectively the bound of measurand, U=[u ₁, u ₂..., u _m] be measurand not, y _i=[y _I1, y _I2..., y _IM] ^T, x _i=[x _I1, x _I2..., x _IM] ^T, u _j=[u _J1, u _J2..., u _JM] ^T, uu _j=[uu _J1, uu _J2..., uu _JM] ^T, lu _i=[lu _J1, lu _J2..., lu _JM] ^TBe respectively the not bound of measurand, σ _iStandard deviation for measurand.M is the operating mode number,

Be the model parameter that to estimate, lp _k, up _kBe respectively the bound of model parameter, (X, U p)=0 are the mechanism model equation of procedures system to F.Total n * the n of the subproblem of dividing _pIndividual and nk=1,2,3 ..., n, pk=1,2,3 ..., n _p

The subproblem of structure supposes that the number of above-mentioned model correction problem measurand is n as shown in Figure 2, and model parameter number to be estimated is n _pThen She Ji subproblem increases measurand and model parameter number from less to more from both direction, wherein laterally from left to right increase direction for the measurand number, be from the bottom up that vertically the model parameter number increases direction, each model parameter and the precedence that measurand increases press relative their the descending order arrangement of sensitivity of model.Make scale and the degree of freedom of problem change from small to large like this.When adopting all measurands and estimating all model parameters, problem

Be the model correction problem under the procedures system operation optimization.

3, employing is based on the subproblem of measurand and model parameter, the optimizing application algorithm is found the solution these subproblems, and the subproblem optimum solution that will find the solution is as the initial value point of next one subproblem calculating to be found the solution, find the solution down length by length, on better initial point basis, reach the convergence of the model correction problem under the solution procedure system operation optimization at last.

4, according to the result of calculation of finding the solution of efficient method for solving, obtain the optimum solution of each subproblem, thereby obtain strict mechanism model model parameter p accurately, the corrected value X of measurand, the estimated value U of measurand does not return the model correction result.These results further are applied to significantly improve the production efficiency of procedures system in operation optimization and the process control.

Pure terephthalic acid (PTA) oxidation reaction process system embodiment

Can be applied in PTA oxidation reaction process system be used to the model correction problem high efficiency method of finding the solution oriented manipulation optimization and implement of the present invention.In the present embodiment, 7 measurands per hour are respectively in phthalic acid output, the product carboxyl benzaldehyde concentration, the per hour oxygen concentration, the carbonomonoxide concentration of tail gas, the gas concentration lwevel of tail gas, the oxygen concentration of crystallizer tail gas of acetic acid consumption amount, tail gas.Its measured value is the data that industry spot is gathered, and by to Field Production Data analysis and processing, the difference according to load obtains 5 kinds of stable state production datas under the operating mode.The model equation of system mainly is based on the balance equation of reaction kinetics.Model parameter is the corresponding reaction power mathematic(al) constant of the balance equation of ten reaction kineticses p=[p ₁, p ₂..., p ₁₀].It is that 21718(comprises the variable that some is fixing that the model correction problem of this embodiment contains the variable dimension), and the equation number is 18488, it is non-linear that model equation is.According to the model correction problem characteristics of PTA oxidation reaction process system, embodiment is included in computer system and carries out following steps:

1, according to the characteristics of PTA oxidation reaction process system model correction problem, analyze model relative response kinetic constant to be revised and the sensitivity of seven measurands, and model parameter and measurand are respectively parameter p=[p by the level of sensitivity ordering ₁, p ₂..., p ₁₀], measurand X=[x ₁, x ₂..., x ₇];

2, according to the sensitivity analysis result, design is based on the subproblem of measurand and model parameter.Thereby the model correction PROBLEM DECOMPOSITION of complex process system is the subproblem of the progressive complexity of cluster, and subproblem is expressed as follows:

$\underset{X,U,p_1}{\min }{J}_{\mathrm{nk}}(X,Y)=\underset{j=1}{\overset{5}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{\mathrm{nk}}{\mathrm{\&Sigma;}}}{(x_{\mathrm{ij}}-y_{\mathrm{ij}})}^2/{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA00003008052400021.png"\; state="\{\{state\}\}">i</figure-callout>}}^2$

s.t.F(X,U,p ₁,p ₂,...,p _pk)=0

P _nk,pk:lx _i≤x _i≤ux _ii=1,2,...,7

lu _j≤u _j≤uu _jj=1,2,...,21711

lp _k≤p _k≤up _kk=1,2,...,pk

nk=1,2,3,...,7，pk=1,2,3,...,10

3, adopt above-mentioned subproblem based on measurand and model parameter, use quadratic programming optimization algorithm and find the solution these subproblems, the initial value point that the subproblem optimum solution found the solution is calculated as next one subproblem to be found the solution, find the solution down length by length, on better initial point basis, reach the convergence of solving model correction problem at last.

4, find the solution result of calculation according to subproblem planning method for solving, obtained model parameter p=[p accurately ₁, p ₂..., p ₁₀], the corrected value of measurand and the estimated value of measurand not.Revised model further is applied to improved the production efficiency of this procedures system significantly in the operation optimization and process control of this process.

Model correction problem in the present embodiment, if directly find the solution, because the equation dimension is big and be non-linear, the problem degree of freedom is big, and it is higher to find the solution difficulty, and convergence is failed when causing optimizing algorithm and finding the solution.Restrain to make this problem solving be used to the model correction problem high efficiency method of finding the solution oriented manipulation optimization the time by embodiment result is of the present invention as can be known.Therefore, method of the present invention can make the convergence of the correction problem solving under the optimization of procedures system model manipulation further improve.

Method simple and clear principle of the present invention is convenient to realize on computers, and dirigibility is fine, can combine with the Different Optimization algorithm.The present invention is fit to be applied to the model correction problem under the solution procedure system operation optimization very much, makes the model correction result accurately and reliably.Revised model further is applied to improve the production efficiency of this procedures system significantly in the operation optimization and process control of this process.

Claims (1)

1. one kind is used for finding the solution the model correction problem high efficiency method that oriented manipulation is optimized, and this method is applied to it is characterized in that this method may further comprise the steps in the PTA oxidation reaction process system:

(1) according to the characteristic of PTA oxidation reaction process system model correction problem, the corresponding reaction power mathematic(al) constant of balance equation of relative ten reaction kineticses of model that analysis is to be revised and the sensitivity of seven measurands, and model parameter and measurand are respectively parameter p=[p by the level of sensitivity ordering ₁, p ₂..., p ₁₀], measurand X=[x ₁, x ₂..., x ₇]; Seven measurands are respectively: per hour in phthalic acid output, the product to carboxyl benzaldehyde concentration, the per hour oxygen concentration, the carbonomonoxide concentration of tail gas, the gas concentration lwevel of tail gas, the oxygen concentration of crystallizer tail gas of acetic acid consumption amount, tail gas;

(2) according to the sensitivity analysis result, design is based on the subproblem of measurand and model parameter.Thereby the model correction PROBLEM DECOMPOSITION of complex process system is the subproblem of the progressive complexity of cluster, and subproblem is expressed as follows:

$\underset{X,U,p_1}{\min }{J}_{\mathrm{nk}}(X,Y)=\underset{j=1}{\overset{5}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{\mathrm{nk}}{\mathrm{\&Sigma;}}}{(x_{\mathrm{ij}}-y_{\mathrm{ij}})}^2/{\mathrm{\&sigma;}}_i^2$

s.t.F(X,U,p ₁,p ₂,...,p _pk)=0

P _nk,pk:lx _i≤x _i≤ux _ii=1,2,...,7

lu _j≤u _j≤uu _jj=1,2,...,21711

lp _k≤p _k≤up _kk=1,2,...,pk

nk=1,2,3,...,7，pk=1,2,3,...,10；

Wherein, J _Nk(X Y) is least square function based on correction error, Y=[y ₁, y ₂..., y _n] be the measured value of measurand, X=[x ₁, x ₂..., x _n] be the corrected value of measurand, ux _i=[ux _I1, ux _I2..., ux _IM] ^T, lx _i=[lx _I1, lx _I2..., lx _IM] ^TBe respectively the bound of measurand, U=[u ₁, u ₂..., u _m] be measurand not, y _i=[y _I1, y _I2..., y _IM] ^T, x _i=[x _I1, x _I2..., x _IM] ^T, u _j=[u _J1, u _J2..., u _JM] ^T, uu _j=[uu _J1, uu _J2..., uu _JM] ^T, lu _i=[lu _J1, lu _J2..., lu _JM] ^TBe respectively the not bound of measurand, σ _iStandard deviation for measurand.M is the operating mode number, p=[p ₁, p ₂..., p _Np] be the model parameter that will estimate, lp _k, up _kBe respectively the bound of model parameter, (X, U p)=0 are the mechanism model equation of procedures system to F.Total n * the n of the subproblem of dividing _pIndividual and nk=1,2,3 ..., n, pk=1,2,3 ..., n _p

(3) adopt above-mentioned subproblem based on measurand and model parameter, use quadratic programming optimization algorithm and find the solution these subproblems, the initial value point that the subproblem optimum solution found the solution is calculated as next one subproblem to be found the solution, find the solution down length by length, on better initial point basis, reach the convergence of solving model correction problem at last.

(4) find the solution result of calculation according to subproblem planning method for solving, obtained model parameter p=[p accurately ₁, p ₂..., p ₁₀], the corrected value of measurand and the estimated value of measurand not.Revised model further is applied to improved the production efficiency of this procedures system significantly in the operation optimization and process control of this process.

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