CN106270438A - A kind of shell thickness Forecasting Methodology and system - Google Patents

Abstract

The invention discloses a kind of shell thickness Forecasting Methodology and system, belong to steel-making and continuous casting technology field.In order to solve shell thickness Forecasting Methodology, to there is data precision ratio relatively low, the problem of waste material.Including: obtain the steel grades of the steel billet entering two cold-zones, the first information of steel billet, according to formula (1), determine the steel billet equation of heat conduction in two cold-zones；According to the equation of heat conduction and the boundary condition of the equation of heat conduction, determine that the coefficient of heat transfer of two cold-zones determines formula；The coefficient of heat transfer according to two cold-zones determines the first information of formula and steel billet, determines the gradient formula of object function；When determining that gradient determines the parameter of formula equal to zero, determined the minima of object function by formula (2)；Work as stopping criterion | | J (α_k)‑J(α_k‑1) | | ＞ ε or iterative step k ＜ N_maxTime, determine direction of search d by formula (3)_k；When direction of search d_kMeet and decline criterion | | J (α_k+d_k)||≤η||J(α_k) | | time, determine new conticaster parameter by formula (4), determine steel billet thickness according to new conticaster parameter and the equation of heat conduction.

Description

A kind of shell thickness Forecasting Methodology and system

Technical field

The invention belongs to steel-making and continuous casting technology field, more particularly relate to a kind of shell thickness Forecasting Methodology and system.

Background technology

Conticaster has been the main tool that slab produces, and Secondary Cooling Zone of Continuous Caster is the important step that strand produces.Slab Production is that molten steel forms initial green shell through crystallizer, is then passed through two cold-zone water-spraying control, constantly solidifies, the thickness of green shell Degree constantly increases, and ultimately forms slab.Importance based on secondary cooling area for continuous casting, measures the shell thickness obtaining slab accurately Cause and pay close attention to widely.

Owing to, in slab production process, production environment is severe, is difficult to use physical method and carries out on-line checking, therefore can only Shell thickness is predicted.The method of prediction shell thickness mainly includes testing measurement method and method for numerical simulation two is big at present Class.Experimental technique is mainly shoot-pin test method.Shoot-pin test method mainly uses the steel nail containing FeS to inject slab, root According to the fusing situation of steel nail in sufur printing and the distribution situation of S, determine the thickness of green shell；Owing to casting process is the mistake of a heat release Journey, therefore can use heat conduction model to describe, and uses heat conduction model can calculate the profiling temperatures of slab, permissible The shell thickness of prediction slab；Above two method, experimental technique can only carry out in limited position, thus obtain shell thickness Data are limited, and waste product；The accurate ratio of method for numerical simulation is relatively low.

In sum, it is limited to there is estimation range in present shell thickness Forecasting Methodology, and data precision ratio is relatively low, waste The problem of material.

Summary of the invention

The embodiment of the present invention provides a kind of shell thickness Forecasting Methodology and system, in order to solve the prediction of existing shell thickness It is limited to there is estimation range in method, and data precision ratio is relatively low, the problem of waste material.

The embodiment of the present invention provides a kind of shell thickness Forecasting Methodology, including:

Obtaining the steel grades of the steel billet entering two cold-zones, the first information of described steel billet, according to described steel grades, institute State the first information and the formula (1) of steel billet, determine the described steel billet equation of heat conduction in two cold-zones；

According to the described equation of heat conduction and the boundary condition of the described equation of heat conduction, determine that the coefficient of heat transfer of two cold-zones determines Formula；The coefficient of heat transfer according to described two cold-zones determines formula and the first information of described steel billet, determines the gradient of object function Formula；

When determining the first parameter of described gradient formula equal to zero, determine that described object function is by formula (2) Little value；

Work as stopping criterion | | J (α_k)-J(α_k-1) | | ＞ ε or iterative step k ＜ N_maxTime, determine search by formula (3) Direction d_k；

When described direction of search d_kMeet and decline criterion | | J (α_k+d_k)||≤η||J(α_k) | | time, determined by formula (4) New conticaster parameter, according to described new conticaster parameter and described steel billet at the equation of heat conduction of two cold-zones, determines green shell Thickness；

Formula (1) is as follows:

$\mathrm{\ρ}\left(T\right)c\left(T\right)V_{cast}\frac{\∂T}{\∂z}=\mathrm{\λ}\left(T\right)\frac{{\∂}^{2}T}{\∂x^2}+Q\left(T\right)$

The coefficient of heat transfer determines that formula is as follows:

$h_{s,i}=\frac{1570.0{\mathrm{\ω}}_i^{0.55}\[1.0-0.0075\]}{{\mathrm{\α}}_i}$

Target function gradient formula is as follows:

$\▿J\left(\mathrm{\α}\right)=\underset{n=1}{\overset{N}{\Σ}}\frac{\∂T_c^n\left(\mathrm{\α}\right)}{\∂\mathrm{\α}}\[T_c^n\left(\mathrm{\α}\right)-T_e^n\left(\mathrm{\α}\right)\]$

Formula (2) is as follows:

$\underset{\mathrm{\α}}{min}J\left(\mathrm{\α}\right)=\frac{1}{2}min\underset{n=1}{\overset{N}{\Σ}}{\[T_c^n\left(\mathrm{\α}\right)-T_e^{\mathrm{\δ},n}\left(\mathrm{\α}\right)\]}^2$

Formula (3) is as follows:

d_k=-M (α_k)▽J(α_k)^TJ(α_k)

Formula (4) is as follows:

α_k+1=α_k+d_k

Wherein, V_castBeing the pulling rate of slab, ρ (T), c (T) and λ (T) represent the density of steel grade, specific heat and heat conduction system respectively Number, Q (T) represents latent heat of solidification item, and T is temperature, h_s,iFor the coefficient of heat transfer, α_iFor the parameter of conticaster, ω_iIt is the water yield of i-th section, J (α) is the gradient of object function,It is the measured value of steel slab surface temperature, T_c(α) it is the value of calculation of surface temperature,For the minima of described object function, M (α_k)=(J (α_k)^T▽J(α_k)+μ_kI), J (α_k)^TIt it is object function The transposition of gradient, μ_kLM parameter when kth step iteration, I is a unit matrix, α_k+1For conticaster during kth+1 step iteration Parameter, α_kFor the parameter of conticaster during kth step iteration, d_kFor the direction of search, η ∈ (0,1).

Preferably, described before determining that described gradient determines that the parameter of formula is equal to zero, also include:

The matrix expression of described target function gradient is determined by following equation:

$\▿J\left(\mathrm{\α}\right)=\mathrm{\φ}\left[\begin{array}{c}{T}_c^1\left(\mathrm{\α}\right)-T_e^1\left(\mathrm{\α}\right)\\ T_c^2\left(\mathrm{\α}\right)-T_e^2\left(\mathrm{\α}\right)\\ \·\\ \·\\ \·\\ T_c^N\left(\mathrm{\α}\right)-T_e^N\left(\mathrm{\α}\right)\end{array}\right]$

Wherein,

Preferably, after the described gradient formula determining object function, also include:

When determining that described gradient determines that the parameter of formula, more than zero or stopping criterion ε ＞ 0, determines initial iterative steps K=1, and iteration have maximum iterative step N_max。

Preferably, described when described direction of search d_kIt is unsatisfactory for declining criterion | | J (α_k+d_k)||≤η||J(α_k) | | time, can To determine new conticaster parameter by formula (5)；

Formula (5) is as follows:

α_k+1=α_k+γ_kd_k

Wherein,γ_kFor the iteration step length of kth step, γ is iteration step length.

The embodiment of the present invention also provides for a kind of shell thickness prognoses system, including:

First determines unit, for obtaining the steel grades of the steel billet entering two cold-zones, the first information of described steel billet, root According to described steel grades, the first information of described steel billet and formula (1), determine the described steel billet conduction of heat side in two cold-zones Journey；

Second determines unit, for according to the described equation of heat conduction and the boundary condition of the described equation of heat conduction, determines two The coefficient of heat transfer of cold-zone determines formula；The coefficient of heat transfer according to described two cold-zones determines formula and the first information of described steel billet, Determine the gradient formula of object function；

3rd determines unit, during for being equal to zero when the first parameter determining described gradient formula, is determined by formula (2) The minima of described object function；

4th determines unit, for working as stopping criterion | | J (α_k)-J(α_k-1) | | ＞ ε or iterative step k ＜ N_maxTime, logical Cross formula (3) and determine direction of search d_k；

5th determines unit, for when described direction of search d_kMeet and decline criterion | | J (α_k+d_k)||≤η||J(α_k)|| Time, determine new conticaster parameter by formula (4), the heat in two cold-zones according to described new conticaster parameter and described steel billet Diffusivity equation, determines shell thickness；

Formula (1) is as follows:

$\mathrm{\ρ}\left(T\right)c\left(T\right)V_{cast}\frac{\∂T}{\∂z}=\mathrm{\λ}\left(T\right)\frac{{\∂}^{2}T}{\∂x^2}+Q\left(T\right)$

The coefficient of heat transfer determines that formula is as follows:

$h_{s,i}=\frac{1570.0{\mathrm{\ω}}_i^{0.55}\[1.0-0.0075\]}{{\mathrm{\α}}_i}$

Target function gradient formula is as follows:

$\▿J\left(\mathrm{\α}\right)=\underset{n=1}{\overset{N}{\Σ}}\frac{\∂T_c^n\left(\mathrm{\α}\right)}{\∂\mathrm{\α}}\[T_c^n\left(\mathrm{\α}\right)-T_e^n\left(\mathrm{\α}\right)\]$

Formula (2) is as follows:

$\underset{\mathrm{\α}}{min}J\left(\mathrm{\α}\right)=\frac{1}{2}min\underset{n=1}{\overset{N}{\Σ}}{\[T_c^n\left(\mathrm{\α}\right)-T_e^{\mathrm{\δ},n}\left(\mathrm{\α}\right)\]}^2$

Formula (3) is as follows:

d_k=-M (α_k)▽J(α_k)^TJ(α_k)

Formula (4) is as follows:

α_k+1=α_k+d_k

Wherein, V_castBeing the pulling rate of slab, ρ (T), c (T) and λ (T) represent the density of steel grade, specific heat and heat conduction system respectively Number, Q (T) represents latent heat of solidification item, and T is temperature, h_s,iFor the coefficient of heat transfer, α_iFor the parameter of conticaster, ω_iIt is the water yield of i-th section, J (α) is the gradient of object function,It is the measured value of steel slab surface temperature, T_c(α) it is the value of calculation of surface temperature,For the minima of described object function, M (α_k)=(J (α_k)^T▽J(α_k)+μ_kI), J (α_k)^TIt it is object function The transposition of gradient, μ_kLM parameter when kth step iteration, I is a unit matrix, α_k+1For conticaster during kth+1 step iteration Parameter, α_kFor the parameter of conticaster during kth step iteration, d_kFor the direction of search, η ∈ (0,1).

Preferably, the described 3rd determines that unit is additionally operable to:

The matrix expression of described target function gradient is determined by following equation:

$\▿J\left(\mathrm{\α}\right)=\mathrm{\φ}\left[\begin{array}{c}{T}_c^1\left(\mathrm{\α}\right)-T_e^1\left(\mathrm{\α}\right)\\ T_c^2\left(\mathrm{\α}\right)-T_e^2\left(\mathrm{\α}\right)\\ \·\\ \·\\ \·\\ T_c^N\left(\mathrm{\α}\right)-T_e^N\left(\mathrm{\α}\right)\end{array}\right]$

Wherein,

Preferably, described second determines that unit is additionally operable to:

When determining that described gradient determines that the parameter of formula, more than zero or stopping criterion ε ＞ 0, determines initial iterative steps K=1, and iteration have maximum iterative step N_max。

Preferably, the described 5th determines unit, is additionally operable to:

When described direction of search d_kIt is unsatisfactory for declining criterion | | J (α_k+d_k)||≤η||J(α_k) | | time, formula can be passed through (5) new conticaster parameter is determined；

Formula (5) is as follows:

α_k+1=α_k+γ_kd_k

Wherein,γ_kFor the iteration step length of kth step, γ is iteration step length.

In the embodiment of the present invention, it is provided that a kind of shell thickness Forecasting Methodology, including: obtain the steel billet of entrance two cold-zones Steel grades, the first information of described steel billet, according to described steel grades, the first information of described steel billet and formulaDetermine the described steel billet equation of heat conduction in two cold-zones；According to described conduction of heat Equation and the boundary condition of the described equation of heat conduction, determine that the coefficient of heat transfer of two cold-zones determines formula；According to described two cold-zones The coefficient of heat transfer determines formula and the first information of described steel billet, determines the gradient formula of object function；When determining that described gradient is public When first parameter of formula is equal to zero, pass through formulaDetermine described target letter The minima of number；Work as stopping criterion | | J (α_k)-J(α_k-1) | | ＞ ε or iterative step k ＜ N_maxTime, by formula d_k=-M (α_k)▽J(α_k)^TJ(α_k) determine direction of search d_k；When described direction of search d_kMeet and decline criterion | | J (α_k+d_k)||≤η||J (α_k) | | time, formula α can be passed through_k+1=α_k+d_kDetermine new conticaster parameter, according to described new conticaster parameter and described Steel billet, at the equation of heat conduction of two cold-zones, determines shell thickness；Wherein, V_castIt is the pulling rate of slab, ρ (T), c (T) and λ (T) point Not representing the density of steel grade, specific heat and heat conductivity, Q (T) represents latent heat of solidification item, and T is temperature, h_s,iFor the coefficient of heat transfer, α_iFor The parameter of conticaster, ω_iBeing the water yield of i-th section, J (α) is the gradient of object function,It it is the survey of steel slab surface temperature Value, T_c(α) it is the value of calculation of surface temperature,For the minima of described object function, M (α_k)=(J (α_k)^T ▽J(α_k)+μ_kI), J (α_k)^TIt is the transposition of target function gradient, μ_kLM parameter when kth step iteration, I is a unit square Battle array, α_k+1For the parameter of conticaster during kth+1 step iteration, α_kFor the parameter of conticaster during kth step iteration, d_kFor searcher To, η ∈ (0,1).In actual applications, owing to the parameter of some conticasters in heat conduction model is difficult to determine, therefore Need these parameters of identification.The surface temperature obtained by data acquisition module, can obtain these conticasters by optimized algorithm Parameter.Owing to there are some measurement error during surface temperature measurement, again due to this process exist be not qualitative, at this Ill-posedness in bright embodiment, during using Levenberg-Marquardt (LM) algorithm to overcome above-mentioned calculating.Pass through Heat conduction model after above calculating, it may be determined that the parameter of conticaster, and rectification can be used to predict that the green shell of strand is thick Degree.The method provided by the embodiment of the present invention, can be calculated the shell thickness of prediction more accurately, thus be conducive to connecting Cast the control of the two cold-zone water yields, improve the quality of slab.

Accompanying drawing explanation

In order to be illustrated more clearly that the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing In having technology to describe, the required accompanying drawing used is briefly described, it should be apparent that, the accompanying drawing in describing below is only this Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, it is also possible to Other accompanying drawing is obtained according to these accompanying drawings.

Fig. 1 provides a kind of shell thickness Forecasting Methodology flow chart for the embodiment of the present invention；

A kind of shell thickness prognoses system structural representation that Fig. 2 provides for the embodiment of the present invention.

Detailed description of the invention

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Describe, it is clear that described embodiment is only a part of embodiment of the present invention rather than whole embodiments wholely.Based on Embodiment in the present invention, it is every other that those of ordinary skill in the art are obtained under not making creative work premise Embodiment, broadly falls into the scope of protection of the invention.

A kind of shell thickness Forecasting Methodology schematic flow sheet that Fig. 1 provides for the embodiment of the present invention, as it is shown in figure 1, this A kind of shell thickness Forecasting Methodology that bright embodiment provides comprises the following steps:

Step 101, obtains the steel grades of the steel billet entering two cold-zones, and the first information of described steel billet, according to described steel Plant composition, the first information of described steel billet and formula (1), determine the described steel billet equation of heat conduction in two cold-zones；

Step 102, according to the described equation of heat conduction and the boundary condition of the described equation of heat conduction, determines the heat exchange of two cold-zones Coefficient determines formula；The coefficient of heat transfer according to described two cold-zones determines formula and the first information of described steel billet, determines target letter The gradient formula of number；

Step 103, when the first parameter determining described gradient formula is equal to zero, determines described target by formula (2) Functional minimum value；

Step 104, works as stopping criterion | | J (α_k)-J(α_k-1) | | ＞ ε or iterative step k ＜ N_maxTime, by formula (3) Determine direction of search d_k；

Step 105, when described direction of search d_kMeet and decline criterion | | J (α_k+d_k)||≤η||J(α_k) | | time, by public affairs Formula (4) determines new conticaster parameter, the equation of heat conduction in two cold-zones according to described new conticaster parameter and described steel billet, Determine shell thickness；

Formula (1) is as follows:

$\mathrm{\ρ}\left(T\right)c\left(T\right)V_{cast}\frac{\∂T}{\∂z}=\mathrm{\λ}\left(T\right)\frac{{\∂}^{2}T}{\∂x^2}+Q\left(T\right)$

The coefficient of heat transfer determines that formula is as follows:

$h_{s,i}=\frac{1570.0{\mathrm{\ω}}_i^{0.55}\[1.0-0.0075\]}{{\mathrm{\α}}_i}$

Target function gradient formula is as follows:

$\▿J\left(\mathrm{\α}\right)=\underset{n=1}{\overset{N}{\Σ}}\frac{\∂T_c^n\left(\mathrm{\α}\right)}{\∂\mathrm{\α}}\[T_c^n\left(\mathrm{\α}\right)-T_e^n\left(\mathrm{\α}\right)\]$

Formula (2) is as follows:

$\underset{\mathrm{\α}}{min}J\left(\mathrm{\α}\right)=\frac{1}{2}min\underset{n=1}{\overset{N}{\Σ}}{\[T_c^n\left(\mathrm{\α}\right)-T_e^{\mathrm{\δ},n}\left(\mathrm{\α}\right)\]}^2$

Formula (3) is as follows:

d_k=-M (α_k)▽J(α_k)^TJ(α_k)

Formula (4) is as follows:

α_k+1=α_k+d_k

Wherein, V_castBeing the pulling rate of slab, ρ (T), c (T) and λ (T) represent the density of steel grade, specific heat and heat conduction system respectively Number, Q (T) is latent heat item, and T is temperature, h_s,iFor the coefficient of heat transfer, α_iFor the parameter of conticaster, ω_iIt is the water yield of i-th section, J (α) For the gradient of object function,It is the measured value of steel slab surface temperature, T_c(α) it is the value of calculation of surface temperature,For the minima of described object function, M (α_k)=(J (α_k)^T▽J(α_k)+μ_kI), J (α_k)^TIt it is object function The transposition of gradient, μ_kLM parameter when kth step iteration, I is a unit matrix, α_k+1For conticaster during kth+1 step iteration Parameter, α_kFor the parameter of conticaster during kth step iteration, d_kFor the direction of search, η ∈ (0,1).

Before step 101, need advanced row data acquisition, wherein it is desired to the data gathered include the steel billet of two cold-zones Steel grades, the first information of steel billet.

The most right, in actual applications, the first information of steel billet includes one or more combinations in following information: tie The height of brilliant device, physical dimension, the position of meniscus, the speed of throwing, the temperature of cooling water, metallurgical length two cold-zone of continuous casting The distribution of the water yield, the injection flow rate that two cold-zones are each section, use the testing temperature metrical information to the surface temperature of slab production process Deng.

It should be noted that the above-mentioned first information includes being not limited to listed information.

Determining the steel grades of steel billet, after the first information of steel billet, can be according to above-mentioned steel grades, the of steel billet One information, determines the temperature of solid-liquid phase line, heat conductivity, density, the parameter such as specific heat and latent heat of solidification successively.

Specifically:

(1) determination of solid, liquid liquidus temperature, the solid, liquid liquidus temperature of steel depends primarily on the chemical composition contained by steel, and one As be the content of carbon, silicon, manganese, phosphorus, sulfur, nickel, chromium and aluminum etc., can determine with following equation (6) and formula (7) respectively:

$\begin{array}{c}{T}_l=1536-(90\[\%C\]+6.2\[\%Si\]+1.7\[\%Mn\]+28\[\%P\]+40\[\%S\]+2.9\[\%Ni\]\\ +1.8\[\%Cr\]+5.1\[\%Al\]\end{array}---\left(6\right)$

$\begin{array}{c}{T}_s=1536-(415.3\[\%C\]+12.3\[\%Si\]+6.8\[\%Mn\]+124.5\[\%P\]+183.9\[\%S\]+\\ 4.3\[\%Ni\]+1.4\[\%Cr\]+4.1\[\%Al\]\end{array}---\left(7\right)$

Wherein, in above-mentioned formula, T_lFor the liquidus temperature of steel, unit is DEG C；T_sFor the solidus temperature of steel, unit is ℃。

(2) determination of density, the solid, liquid liquidus temperature of steel is closely related with the chemical composition steel of steel, and the density of steel is then Depend primarily on temperature and the phase of steel, so just with the solid, liquid liquidus temperature of steel as boundary, the density of steel being processed into one point Section constant, its more than liquidus curve, subsolidus and solid-liquid two-phase region take different numerical value respectively, specifically, density is really Determine formula as follows:

$\mathrm{\ρ}=\left\{\begin{array}{cc}{\mathrm{\ρ}}_s& T(x,t)\≤T_s\\ {\mathrm{m\ρ}}_s+(1-m){\mathrm{\ρ}}_l& T_s\≤T(x,t)\≤T_l\\ {\mathrm{\ρ}}_l& T_s\≤T(x,t)\end{array}\right.---\left(8\right)$

Wherein, ρ_sFor the density of steel during solid-state, unit is kg/m³；ρ_lFor the density of steel during liquid, unit is kg/m³；m∈ (0,1)。

(3) determination of heat conductivity, the same with the density of steel, the heat conductivity of steel is also relevant with the temperature of steel, according to same The way of sample is pressed solid, liquid phase line segment processing, and different and steel density is piecewise constant, and the heat conductivity of steel is one point Section function, concrete, heat conductivity is determined by following equation:

$\mathrm{\λ}\left(u\right)=\left\{\begin{array}{cc}{\mathrm{\λ}}^{\′}\left(T\right)& T(x,t)\≤T_s\\ {\mathrm{m\λ}}^{\′}\left(T\right)& T_s\≤T(x,t)\≤T_l\\ \mathrm{\γ}\left(T\right){\mathrm{\λ}}^{\′}\left(T\right)+(1-\mathrm{\γ}(T)){\mathrm{m\λ}}^{\′}\left(T\right)& T_s\≤T(x,t)\end{array}\right.---\left(9\right)$

$\mathrm{\γ}\left(T\right)=\frac{T_l-T(x,t)}{T_l-T_s}---\left(10\right)$

Wherein, (x, t) is the temperature of strand to T, and unit is DEG C；λ (T) is effective thermal conductivity, and unit is W/ (m K)；λ′ U () is the heat conductivity of solid-state steel grade, unit is W/ (m K)；M is normal number, and square billet takes 1～4, and strand takes 4～7；γ(T) For solid rate.

(4) determination of latent heat of solidification, molten steel, during the phase transition from liquid to solid-state, is different from and typically solidifies biography Thermal process, will discharge latent heat of solidification.Specifically, latent heat of solidification refers to that the molten steel of unit mass is cooled to solid from liquidus temperature Liquidus temperature institute liberated heat.Influence of Temperature Field when molten steel is cooled down by latent heat of solidification is very big, frequently with way have temperature Rise method, Enthalpy method, source item facture and equivalent specific heat hold method.Wherein, temperature recovery method and the error calculated of Enthalpy method Slightly larger, more accurately but the process of calculating is relative complex for source item facture, so, in embodiments of the present invention, in order to simplify calculating Amount, uses equivalent specific heat to hold method equivalent set latent heat.

In a step 101, according to steel grades, the temperature of the solid-liquid phase line that the first information of steel billet determines, heat conductivity, Density, after the parameter such as specific heat and latent heat of solidification, can pass through formula (1) and determine the steel billet equation of heat conduction in two cold-zones:

$\mathrm{\ρ}\left(T\right)c\left(T\right)V_{cast}\frac{\∂T}{\∂z}=\mathrm{\λ}\left(T\right)\frac{{\∂}^{2}T}{\∂x^2}+Q\left(T\right)---\left(1\right)$

Wherein, ρ (T), c (T) and λ (T) represent the density of steel grade, specific heat and heat conductivity respectively, and T is temperature, V_castIt is The pulling rate of slab, Q (T) is latent heat item.

Further, heat conductivity is determined by following equation:

K=f_sk_s+m(1-f_s)k_l (11)

Wherein, k_lAnd k_sIt is convection conduct heat coefficient respectively, and liquid phase heat conductivity, m is a factor, and T is temperature (unit For K), f_sBeing fraction solid, it is the function of temperature T, and t is the time (s) and Q (T) is the latent heat item produced due to phase transformation.

In embodiments of the present invention, replace owing to latent heat of solidification item Q (T) uses equivalent specific heat to hold method, i.e. can pass through Following equation determines:

$c_{eff}=c-L(\∂f_s/\∂T)---\left(12\right)$

Wherein, L is latent heat (unit is J/kg), andIt is pseudo-specific heat.

In a step 102, the equation of heat conduction determined according to formula (1), determine this equation of heat conduction boundary condition and Initial condition:

Specifically, initial condition can be determined by following equation:

T_begin=T_cast (13)

Wherein, T_castIt it is cast temperature.

Further, boundary condition can be determined by following equation:

$-k\frac{\∂T}{\∂n}=h(T-T_w)---\left(14\right)$

Wherein, h=[h_mold,h_s,h_e], h_moldRepresent the coefficient of heat transfer of crystallizer, h_sRepresent the heat exchange system of secondary cooling area for continuous casting Number, h_eRepresent that radiation is changed.The coefficient of heat transfer h of secondary cooling area for continuous casting_sCan be determined by following equation:

$h_{s,i}=\frac{1570.0{\mathrm{\ω}}_i^{0.55}\[1.0-0.0075\]}{{\mathrm{\α}}_i}.---\left(15\right)$

Wherein, α_iFor the parameter of conticaster, i represents i-th section of secondary cooling area for continuous casting, ω_iIt it is the water yield of i-th section.

It should be noted that in actual applications, conticaster parameter alpha_iIt is difficult to determine, but it can affect the calculating of model Precision, in embodiments of the present invention, it is thus necessary to determine that this parameter, and according to the parameter after determining, it was predicted that the shell thickness of slab.

Further, by the surface temperature of the slab that the first information, the coefficient of heat transfer and temperature measurer measurement obtain, Ke Yijian Object function described in Liru formula (2):

$\underset{\mathrm{\α}}{min}J\left(\mathrm{\α}\right)=\frac{1}{2}min\underset{n=1}{\overset{N}{\Σ}}{\[T_c^n\left(\mathrm{\α}\right)-T_e^{\mathrm{\δ},n}\left(\mathrm{\α}\right)\]}^2---\left(2\right)$

Wherein,For the minima of object function, T_c(α) it is the value of calculation of model,It it is steel slab surface temperature The measured value of degree, the error level that this measured value contains is δ.

It should be noted that in embodiments of the present invention, when object function minimizes value, just may determine that conticaster Parameter alpha_i。

In embodiments of the present invention, in order to make object function (2) that value can be minimized, by following non-linear side Journey determines:

J (α)=0 (16)

Further, the gradient of object function is determined by following equation:

$\▿J\left(\mathrm{\α}\right)=\underset{n=1}{\overset{N}{\Σ}}\frac{\∂T_c^n\left(\mathrm{\α}\right)}{\∂\mathrm{\α}}\[T_c^n\left(\mathrm{\α}\right)-T_e^n\left(\mathrm{\α}\right)\]---\left(17\right)$

Wherein, J (α) is target function gradient,It is the measured value of steel slab surface temperature, T_c(α) it is to surface temperature The value of calculation of degree.

In actual applications, because α=[α₁,α₂,…,α_M], so Jacobian matrix J (α) can be expressed as follows Form:

$\▿J\left(\mathrm{\α}\right)=\mathrm{\φ}\left[\begin{array}{c}{T}_c^1\left(\mathrm{\α}\right)-T_e^1\left(\mathrm{\α}\right)\\ T_c^2\left(\mathrm{\α}\right)-T_e^2\left(\mathrm{\α}\right)\\ \·\\ \·\\ \·\\ T_c^N\left(\mathrm{\α}\right)-T_e^N\left(\mathrm{\α}\right)\end{array}\right]---\left(18\right)$

Further, the φ in formula (18) can be represented by following equation:

In embodiments of the present invention, the method using the numerical derivative of approximation, formula (19) determines that φ can be further Expressed by following equation:

It should be noted that Δ α is a positive number the least.

In embodiments of the present invention, formula (16) mainly introduces the meter of gradient J (α) of object function to formula (20) Calculation method.On the basis of determining J (α), just may determine that the value of conticaster parameter alpha.In embodiments of the present invention, Ke Yitong Cross the value of Levenberg-Marquard (LM) Algorithm for Solving conticaster parameter alpha.

In step 103, the initial value α of given conticaster parameter_intial∈Rⁿ, when the first parameter determined in formula (20) Δ α ＞ 0, stopping criterion ε ＞ 0, the most initial iterative steps k=1 and maximum iterative step N_max。

It should be noted that here, the first parameter is the parameter, Δ α of conticaster, when the initial value of parameter, Δ α, for positive number Time, stopping criterion ε, initial iterative steps k=1 and maximum iterative step N_maxIt is all that operator runs in actual algorithm Initial period gives.Wherein, the initial value of conticaster parameter is that operator is given at random, and positive number Δ α is that operator is given, It may only provide a number more than zero, and typically this number is little, between 1 to 10.Stopping criterion ε ＞ 0 and greatest iteration step Rapid N_maxAll operator oneself to.

When reaching stopping criterion, after stopping, it is possible to determining the parameter alpha of conticaster, wherein the coefficient of heat transfer just can root Obtain according to formula (15).In formula (15), water yield ω_iCan be by water meter to find the flow of water and obtain, therefore ω_iIt is Know.

It should be noted that k is here an iterative step, owing to LM algorithm is the algorithm of a loop iteration, its During iteration, owing to, in subsequent calculations, iterative step the most constantly increases, until arriving stopping criterion.But work as nothing When method reaches stopping criterion, this iterative cycles will go on always, not the not completeest.Arise that showing of endless loop As.In embodiments of the present invention, in order to avoid the generation of this phenomenon of endless loop, this iterative step is arranged maximum changing Ride instead of walk rapid N_max, when iterative step k reaches this maximum N_maxTime, algorithm will stop, to avoid being absorbed in endless loop.

When determining the first parameter of described gradient formula equal to zero, the object function that formula (2) provides can be passed through true The minima of this object function fixed.

At step 104, after the minima determining object function, further, K+1 is determined by formula (2) The minima of the object function of step, i.e. determines J (α_k+1), when determining | | J (α_k)-J(α_k-1) | | ＜ ε or k ＞ N_maxTime, pass through Following equation (3) determines direction of search d_k:

d_k=-M (α_k)▽J(α_k)^TJ(α_k) (3)

Wherein, M (α_k)=(J (α_k)^T▽J(α_k)+μ_kI), J (α_k)^TIt is the transposition of target function gradient, α_kWalk for kth The parameter of conticaster during iteration, d_kFor the direction of search.

It should be noted that in formula (15), discharge ω_iKnown, then the coefficient of heat transfer h in formula (15)_s,i With conticaster parameter alpha_iIt is functional relationship, only it is to be understood that α_iValue, it is possible to determine coefficient of heat transfer h_s,i。

At step 104, the direction of search determined when step 103 meets decline criterion | | J (α_k+d_k)||≤η||J(α_k)| | time, following equation (4) can be passed through and determine new conticaster parameter, specifically, formula (4) is as follows:

α_k+1=α_k+d_k (4)

Further, when direction of search d_kIt is unsatisfactory for declining criterion | | J (α_k+d_k)||≤η||J(α_k) | | time, can pass through Formula (5) determines new conticaster parameter, and specifically, formula (5) is as follows:

α_k+1=α_k+γ_kd_k (5)

Wherein,γ_kFor the iteration step length of kth step, γ is iteration step length.

It should be noted that in actual applications, after determining conticaster parameter, both can dope the heat after correction Conduction model can be used to predict the shell thickness of strand, can be demonstrated in the picture by the shell thickness of the strand of prediction Come, specifically, the display secondary cooling area for continuous casting process of setting of image conversion, it was predicted that go out the shell thickness curve of strand.

In order to clearly introduce the said method that the embodiment of the present invention provides, having carried out the experiment of thermometric in certain steel mill it is Example, is discussed in detail the shell thickness Forecasting Methodology that the embodiment of the present invention provides.

Specifically include the following step:

Step 201: gather the initial information of data.The composition of steel grade, the height of crystallizer, physical dimension, meniscus Position, the speed of throwing, the temperature of cooling water, the distribution of the metallurgical length two cold-zone water yield of continuous casting, the spray that two cold-zones are each section The water yield at table 1, is given in 2,3,4 respectively.In experimentation, use color comparison temperature measurement instrument along the center of the width of slab even The exit casting the 2nd, 3,4,5,6,7 and 8 section, two cold-zone measures.This temperature measurer be noncontact be temperature measurer, its thermometric is by mistake Difference is 7 DEG C.

Step 202: according to the composition of the steel grade in step 201, calculated the temperature of solid-liquid phase line by formula (6)-(10), Heat conductivity, density, specific heat and latent heat of solidification.Table 1 is the parameter of continuous casting machine, and table 2 is the major parameter of steel grade, and table 3 is Main technical parameter and thermal physical property parameter.

The parameter of table 1 continuous casting machine

Parameter	Value
		Metallurgical length (m)	31.5
Casting speed (m/min)	1.1
		The effective length (m) of crystallizer	0.9
The segments of two cold-zones	8

The major parameter of table 2 steel grade

[%C]	[Si%]	[Mn%]	[S%]	[P%]	[Al%]	[N%]
							0.15	0.15	0.25	0.015	0.02	0.002	0.016

Technical parameter that table 3 is main and thermal physical property parameter

Step 203: according to the information in step 201 and step 202, uses LM algorithm to calculate conticaster parameter；First make With finite difference method, heat conduction model (1) and boundary condition thereof are solved.Secondly, for the metrical information of surface temperature Process.Oxide-film is an obstacle of surface temperature measurement.Oxide-film will make temperature drastically reduce.For the thermometric value with reality Unanimously, use the method for peak value for reducing the oxidation mould worth impact on thermometric.The meansigma methods of peak value is used for actual temperature Measured value.Finally, LM algorithm inverting is used to obtain conticaster parameter alpha.Its solution procedure by the agency of in upper joint.Table 4 is segmentation situation and the injection flow rate of whole two cold-zones, and table 5 is that the result of the bound of parameter of conticaster compared with original being worth.Will Calculated conticaster parameter is given in Table 5.

The segmentation situation of whole two cold-zones of table 4 and injection flow rate

The result of the bound of parameter of table 5 conticaster compared with original being worth

Conticaster parameter	Empirical value (W/ (m2K))	The result of inverting
			α1	4	---
α2	5	4.0
			α3	5	4.83
α4	5	3.78
			α5	5	4.2
α6	5	3.8
			α7	4	2.88
α8	2	1.5

Step 204: the display of result.

Based on same inventive concept, embodiments provide a kind of shell thickness prognoses system, due to this Solutions of Systems Certainly the principle of technical problem is similar with a kind of shell thickness Forecasting Methodology, and therefore the enforcement of this system may refer to the reality of method Execute, repeat no more in place of repetition.

A kind of shell thickness prognoses system structural representation that Fig. 2 provides for the embodiment of the present invention, specifically, such as Fig. 2 institute Showing, this system includes: first determines unit 21, and second determines unit 22, and the 3rd determines unit 23, and the 4th determines unit 24 and Five determine unit 25.

First determines unit 21, for obtaining the steel grades of the steel billet entering two cold-zones, and the first information of described steel billet, According to described steel grades, the first information of described steel billet and formula (1), determine the described steel billet conduction of heat side in two cold-zones Journey；

Second determines unit 22, for according to the described equation of heat conduction and the boundary condition of the described equation of heat conduction, determines The coefficient of heat transfer of two cold-zones determines formula；The coefficient of heat transfer according to described two cold-zones determines the first letter of formula and described steel billet Breath, determines the gradient formula of object function；

3rd determines unit 23, during for being equal to zero when the first parameter determining described gradient formula, true by formula (2) The minima of fixed described object function；

4th determines unit 24, for working as stopping criterion | | J (α_k)-J(α_k-1) | | ＞ ε or iterative step k ＜ N_maxTime, Direction of search d is determined by formula (3)_k；

5th determines unit 25, for when described direction of search d_kMeet and decline criterion | | J (α_k+d_k)||≤η||J(α_k)| | time, determine new conticaster parameter by formula (4), according to described new conticaster parameter and described steel billet in two cold-zones The equation of heat conduction, determines shell thickness；

Formula (1) is as follows:

$\mathrm{\ρ}\left(T\right)c\left(T\right)V_{cast}\frac{\∂T}{\∂z}=\mathrm{\λ}\left(T\right)\frac{{\∂}^{2}T}{\∂x^2}+Q\left(T\right)$

The coefficient of heat transfer determines that formula is as follows:

$h_{s,i}=\frac{1570.0{\mathrm{\ω}}_i^{0.55}\[1.0-0.0075\]}{{\mathrm{\α}}_i}$

Target function gradient formula is as follows:

$\▿J\left(\mathrm{\α}\right)=\underset{n=1}{\overset{N}{\Σ}}\frac{\∂T_c^n\left(\mathrm{\α}\right)}{\∂\mathrm{\α}}\[T_c^n\left(\mathrm{\α}\right)-T_e^n\left(\mathrm{\α}\right)\]$

Formula (2) is as follows:

$\underset{\mathrm{\α}}{min}J\left(\mathrm{\α}\right)=\frac{1}{2}min\underset{n=1}{\overset{N}{\Σ}}{\[T_c^n\left(\mathrm{\α}\right)-T_e^{\mathrm{\δ},n}\left(\mathrm{\α}\right)\]}^2$

Formula (3) is as follows:

d_k=-M (α_k)▽J(α_k)^TJ(α_k)

Formula (4) is as follows:

α_k+1=α_k+d_k

Wherein, V_castBeing the pulling rate of slab, ρ (T), c (T) and λ (T) represent the density of steel grade, specific heat and heat conduction system respectively Number, Q (T) represents latent heat of solidification item, and T is temperature, h_s,iFor the coefficient of heat transfer, α_iFor the parameter of conticaster, ω_iIt is the water yield of i-th section, J (α) is the gradient of object function,It is the measured value of steel slab surface temperature, T_c(α) it is the value of calculation of surface temperature,For the minima of described object function, M (α_k)=(J (α_k)^T▽J(α_k)+μ_kI), J (α_k)^TIt it is object function The transposition of gradient, μ_kLM parameter when kth step iteration, I is a unit matrix, α_k+1For conticaster during kth+1 step iteration Parameter, α_kFor the parameter of conticaster during kth step iteration, d_kFor the direction of search, η ∈ (0,1).

Preferably, the described 3rd determines that unit 23 is additionally operable to:

The matrix expression of described target function gradient is determined by following equation:

$\▿J\left(\mathrm{\α}\right)=\mathrm{\φ}\left[\begin{array}{c}{T}_c^1\left(\mathrm{\α}\right)-T_e^1\left(\mathrm{\α}\right)\\ T_c^2\left(\mathrm{\α}\right)-T_e^2\left(\mathrm{\α}\right)\\ \·\\ \·\\ \·\\ T_c^N\left(\mathrm{\α}\right)-T_e^N\left(\mathrm{\α}\right)\end{array}\right]$

Wherein,

Preferably, described second determines that unit 22 is additionally operable to:

When determining that described gradient determines that the parameter of formula, more than zero or stopping criterion ε ＞ 0, determines initial iterative steps K=1, and iteration have maximum iterative step N_max。

Preferably, the described 5th determines unit 25, is additionally operable to:

When described direction of search d_kIt is unsatisfactory for declining criterion | | J (α_k+d_k)||≤η||J(α_k) | | time, formula can be passed through (5) new conticaster parameter is determined；

Formula (5) is as follows:

α_k+1=α_k+γ_kd_k

Wherein,γ_kFor the iteration step length of kth step, γ is iteration step length.

Should be appreciated that the merit that according to unit that one of the above shell thickness prognoses system includes is only, this apparatus realizes The logical partitioning that can carry out, in actual application, can carry out superposition or the fractionation of said units.And the one of the offer of this embodiment Function and a kind of shell thickness Forecasting Methodology one_to_one corresponding of above-described embodiment offer that shell thickness prognoses system is realized are provided, The more detailed handling process realized for this device, is described in detail, the most not in said method embodiment one Describe in detail again.

Those skilled in the art are it should be appreciated that embodiments of the invention can be provided as method, system or computer program Product.Therefore, the reality in terms of the present invention can use complete hardware embodiment, complete software implementation or combine software and hardware Execute the form of example.And, the present invention can use at one or more computers wherein including computer usable program code The upper computer program product implemented of usable storage medium (including but not limited to disk memory, CD-ROM, optical memory etc.) The form of product.

The present invention is with reference to method, equipment (system) and the flow process of computer program according to embodiments of the present invention Figure and/or block diagram describe.It should be understood that can the most first-class by computer program instructions flowchart and/or block diagram Flow process in journey and/or square frame and flow chart and/or block diagram and/or the combination of square frame.These computer programs can be provided Instruction arrives the processor of general purpose computer, special-purpose computer, Embedded Processor or other programmable data processing device to produce A raw machine so that the instruction performed by the processor of computer or other programmable data processing device is produced for real The system of the function specified in one flow process of flow chart or multiple flow process and/or one square frame of block diagram or multiple square frame now.

These computer program instructions may be alternatively stored in and computer or other programmable data processing device can be guided with spy Determine in the computer-readable memory that mode works so that the instruction being stored in this computer-readable memory produces and includes referring to Make the manufacture of system, this instruction system realize at one flow process of flow chart or multiple flow process and/or one square frame of block diagram or The function specified in multiple square frames.

These computer program instructions also can be loaded in computer or other programmable data processing device so that at meter Perform sequence of operations step on calculation machine or other programmable devices to produce computer implemented process, thus at computer or The instruction performed on other programmable devices provides for realizing at one flow process of flow chart or multiple flow process and/or block diagram one The step of the function specified in individual square frame or multiple square frame.

Although preferred embodiments of the present invention have been described, but those skilled in the art once know basic creation Property concept, then can make other change and amendment to these embodiments.So, claims are intended to be construed to include excellent Select embodiment and fall into all changes and the amendment of the scope of the invention.

Obviously, those skilled in the art can carry out various change and the modification essence without deviating from the present invention to the present invention God and scope.So, if these amendments of the present invention and modification belong to the scope of the claims in the present invention and equivalent technologies thereof Within, then the present invention is also intended to comprise these change and modification.

Claims (8)

1. a shell thickness Forecasting Methodology, it is characterised in that including:

Obtaining the steel grades of the steel billet entering two cold-zones, the first information of described steel billet, according to described steel grades, described steel The first information of base and formula (1), determine the described steel billet equation of heat conduction in two cold-zones；

According to the described equation of heat conduction and the boundary condition of the described equation of heat conduction, determine that the coefficient of heat transfer of two cold-zones determines public affairs Formula；The coefficient of heat transfer according to described two cold-zones determines formula and the first information of described steel billet, determines that the gradient of object function is public Formula；

When the first parameter determining described gradient formula is equal to zero, determined the minima of described object function by formula (2)；

Work as stopping criterion | | J (α_k)-J(α_k-1) | | ＞ ε or iterative step k ＜ N_maxTime, determine the direction of search by formula (3) d_k；

When described direction of search d_kMeet and decline criterion | | J (α_k+d_k)||≤η||J(α_k) | | time, determine new by formula (4) Conticaster parameter, according to described new conticaster parameter and described steel billet at the equation of heat conduction of two cold-zones, determines shell thickness；

Formula (1) is as follows:

$\mathrm{\ρ}\left(T\right)c\left(T\right)V_{cast}\frac{\∂T}{\∂z}=\mathrm{\λ}\left(T\right)\frac{{\∂}^{2}T}{\∂x^2}+Q\left(T\right)$

The coefficient of heat transfer determines that formula is as follows:

$h_{s,i}=\frac{1570.0{\mathrm{\ω}}_i^{0.55}\[1.0-0.0075\]}{{\mathrm{\α}}_i}$

Target function gradient formula is as follows:

$\▿J\left(\mathrm{\α}\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\frac{\∂T_c^n\left(\mathrm{\α}\right)}{\∂\mathrm{\α}}\[T_c^n\left(\mathrm{\α}\right)-T_e^n\left(\mathrm{\α}\right)\]$

Formula (2) is as follows:

$\underset{\mathrm{\α}}{\min }J\left(\mathrm{\α}\right)=\frac{1}{2}\min \underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\[T_c^n\left(\mathrm{\α}\right)-T_e^{\mathrm{\δ},n}\left(\mathrm{\α}\right)\]}^2$

Formula (3) is as follows:

$d_k=-M\left({\mathrm{\α}}_k\right)\▿J{\left({\mathrm{\α}}_k\right)}^{T}J\left({\mathrm{\α}}_k\right)$

Formula (4) is as follows:

α_k+1=α_k+d_k

Wherein, V_castBeing the pulling rate of slab, ρ (T), c (T) and λ (T) represent the density of steel grade, specific heat and heat conductivity, Q respectively (T) representing latent heat of solidification item, T is temperature, h_s,iFor the coefficient of heat transfer, α_iFor the parameter of conticaster, ω_iIt is the water yield of i-th section,For the gradient of object function, T_c(α) it is the value of calculation of surface temperature,Minimum for described object function Value,It is the measured value of steel slab surface temperature, d_kFor the direction of search, It is the transposition of target function gradient, μ_kLM parameter when kth step iteration, I is a unit matrix, α_k+1For kth+ The parameter of conticaster during 1 step iteration, α_kFor the parameter of conticaster during kth step iteration, η ∈ (0,1).

2. the method for claim 1, it is characterised in that described when determining that described gradient determines that the parameter of formula is equal to zero Before, also include:

The matrix expression of described target function gradient is determined by following equation:

$\▿J\left(\mathrm{\α}\right)=\mathrm{\φ}\left[\begin{array}{c}{T}_c^1\left(\mathrm{\α}\right)-T_e^1\left(\mathrm{\α}\right)\\ T_c^2\left(\mathrm{\α}\right)-T_e^2\left(\mathrm{\α}\right)\\ \·\\ \·\\ \·\\ T_c^N\left(\mathrm{\α}\right)-T_e^N\left(\mathrm{\α}\right)\end{array}\right]$

Wherein,

3. the method for claim 1, it is characterised in that after the described gradient formula determining object function, also include:

When determining that described gradient determines that the parameter of formula, more than zero or stopping criterion ε ＞ 0, determines initial iterative steps k= 1, and iteration have maximum iterative step N_max。

4. the method for claim 1, it is characterised in that when described direction of search d_kIt is unsatisfactory for declining criterion | | J (α_k+ d_k)||≤η||J(α_k) | | time, formula (5) can be passed through and determine new conticaster parameter；

Formula (5) is as follows:

α_k+1=α_k+γ_kd_k

Wherein,γ_kFor the iteration step length of kth step, γ is iteration step length.

5. a shell thickness prognoses system, it is characterised in that including:

First determines unit, and for obtaining the steel grades of the steel billet entering two cold-zones, the first information of described steel billet, according to institute State steel grades, the first information of described steel billet and formula (1), determine the described steel billet equation of heat conduction in two cold-zones；

Second determines unit, for according to the described equation of heat conduction and the boundary condition of the described equation of heat conduction, determines two cold-zones The coefficient of heat transfer determine formula；The coefficient of heat transfer according to described two cold-zones determines formula and the first information of described steel billet, determines The gradient formula of object function；

3rd determines unit, during for being equal to zero when the first parameter determining described gradient formula, is determined described by formula (2) The minima of object function；

4th determines unit, for working as stopping criterion | | J (α_k)-J(α_k-1) | | ＞ ε or iterative step k ＜ N_maxTime, by public affairs Formula (3) determines direction of search d_k；

5th determines unit, for when described direction of search d_kMeet and decline criterion | | J (α_k+d_k)||≤η||J(α_k) | | time, logical Cross formula (4) and determine new conticaster parameter, the conduction of heat in two cold-zones according to described new conticaster parameter and described steel billet Equation, determines shell thickness；

Formula (1) is as follows:

$\mathrm{\ρ}\left(T\right)c\left(T\right)V_{cast}\frac{\∂T}{\∂z}=\mathrm{\λ}\left(T\right)\frac{{\∂}^{2}T}{\∂x^2}+Q\left(T\right)$

The coefficient of heat transfer determines that formula is as follows:

$h_{s,i}=\frac{1570.0{\mathrm{\ω}}_i^{0.55}\[1.0-0.0075\]}{{\mathrm{\α}}_i}$

Target function gradient formula is as follows:

$\▿J\left(\mathrm{\α}\right)=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}\frac{\∂T_c^n\left(\mathrm{\α}\right)}{\∂\mathrm{\α}}\[T_c^n\left(\mathrm{\α}\right)-T_e^n\left(\mathrm{\α}\right)\]$

Formula (2) is as follows:

$\underset{\mathrm{\α}}{\min }J\left(\mathrm{\α}\right)=\frac{1}{2}\min \underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\[T_c^n\left(\mathrm{\α}\right)-T_e^{\mathrm{\δ},n}\left(\mathrm{\α}\right)\]}^2$

Formula (3) is as follows:

$d_k=-M\left({\mathrm{\α}}_k\right)\▿J{\left({\mathrm{\α}}_k\right)}^{T}J\left({\mathrm{\α}}_k\right)$

Formula (4) is as follows:

α_k+1=α_k+d_k

Wherein, V_castBeing the pulling rate of slab, ρ (T), c (T) and λ (T) represent the density of steel grade, specific heat and heat conductivity, Q respectively (T) representing latent heat of solidification item, T is temperature, h_s,iFor the coefficient of heat transfer, α_iFor the parameter of conticaster, ω_iIt is the water yield of i-th section,For the gradient of object function,It is the measured value of steel slab surface temperature, T_c(α) it is the value of calculation of surface temperature,For the minima of described object function, It it is object function ladder The transposition of degree, μ_kLM parameter when kth step iteration, I is a unit matrix, α_k+1For conticaster during kth+1 step iteration Parameter, α_kFor the parameter of conticaster during kth step iteration, d_kFor the direction of search, η ∈ (0,1).

6. system as claimed in claim 5, it is characterised in that the described 3rd determines that unit is additionally operable to:

The matrix expression of described target function gradient is determined by following equation:

$\▿J\left(\mathrm{\α}\right)=\mathrm{\φ}\left[\begin{array}{c}{T}_c^1\left(\mathrm{\α}\right)-T_e^1\left(\mathrm{\α}\right)\\ T_c^2\left(\mathrm{\α}\right)-T_e^2\left(\mathrm{\α}\right)\\ \·\\ \·\\ \·\\ T_c^N\left(\mathrm{\α}\right)-T_e^N\left(\mathrm{\α}\right)\end{array}\right]$

Wherein,

7. system as claimed in claim 5, it is characterised in that described second determines that unit is additionally operable to:

When determining that described gradient determines that the parameter of formula, more than zero or stopping criterion ε ＞ 0, determines initial iterative steps k= 1, and iteration have maximum iterative step N_max。

8. system as claimed in claim 5, it is characterised in that the described 5th determines unit, is additionally operable to:

When described direction of search d_kIt is unsatisfactory for declining criterion | | J (α_k+d_k)||≤η||J(α_k) | | time, formula (5) can be passed through true Fixed new conticaster parameter；

Formula (5) is as follows:

α_k+1=α_k+γ_kd_k

Wherein,γ_kFor the iteration step length of kth step, γ is iteration step length.