CN105013832A - Hot rolled strip steel load distribution method giving consideration to rolling energy consumption and good strip shape - Google Patents

Abstract

The invention discloses a hot rolled strip steel load distribution method giving consideration to rolling energy consumption and good strip shape, and belongs to the fieldof control. The hot rolled strip steel load distribution method comprises the following steps: step I, carrying out off-line optimization on finish rolling load distribution coefficients; step II, carrying out off-line decision making on finish rolling load distribution coefficients; and step III, carrying out distribution computation and online control on rolling thickness for finish rolling of each rack strip steel. According to the hot rolled strip steel load distribution method, off-line optimization and online control are combined; an intelligent optimization method is utilized to carry out off-line optimization to obtain load distribution coefficients of typical strip steel stratification; by utilizing a rolling force mode load distribution coefficient method, online computation is carried out and real-time online control is realized; when the intelligent optimization method is adopted to determine finish rolling load distribution coefficients off-line, the rolling energy consumption and the good strip shape for finish-rolling strip steel are taken into consideration; and whiledefects in a method based on artificial experience are overcome, the purpose of improving strip shape control precision and rolling stability of the finish-rolling strip steel is achieved. The hot rolled strip steel load distribution method can be widely applied to thefields ofproduction process control of strip steel of a hot continuous rolling mill, and the finish-rolling strip steel product quality control.

Description

A kind of hot-strip load distribution method taking into account required power and good profile

Technical field

The invention belongs to control field, particularly relate to a kind of control method for band steel of hot strip mill production process.

Background technology

In Rolling production, blank, through the rolling of several frame (being also referred to as in the industry " passage "), produces plastic deformation, finally rolls out the product of requirement up to specification.This series of operation of rolling is that the production technology code of setting in advance before entering milling train according to blank is carried out, and this is the important process of band steel continuous rolling.Wherein sharing of load is prerequisite and the basis of setup algorithm, is the key link of setup algorithm.

Finish rolling sharing of load refers to the distribution system of each frame thickness of fine-rolling strip steel, it is the key technology that hot-strip production process controls, directly have influence on the product quality such as plate shape, thickness of slab precision, sharing of load also has material impact to item indexs such as required power, roller consumption, the stability of production process and operating rates.

From the empirical table method before the sixties in 20th century, the load distribution method of continuous hot-rolling mill mainly experienced by several stages such as energy consumption curve method, sharing of load Y-factor method Y, intelligent optimization method.

Sharing of load Y-factor method Y is the method that current modernization hot tandem sharing of load both at home and abroad generally adopts, and comprises 3 kinds of patterns: drafts pattern, roll-force pattern and power mode.Wherein roll-force and power mode (both can be of equal value) adopt Newton-Raphson method, but solve defect owing to existing, online calculated performance is poor, can not adapt to actual production process control in the requirement of " real-time ", therefore current in actual production process actual application on site be mainly drafts pattern.

Roll-force pattern sharing of load can keep the roll-force proportions constant of each frame of finish rolling, is conducive to the strip shape quality and the rolling stability that improve hot-strip, is therefore necessary to study the roll-force pattern sharing of load Y-factor method Y being used in line computation.

Realize the application on site of sharing of load Y-factor method Y, two aspects can be summed up as: one is how to determine suitable sharing of load coefficient; Two be how to realize sharing of load Y-factor method Y in line computation.

According to historical data and knowhow determine sharing of load coefficient be the most simply, the most direct method, although reasonable in most cases, and non-optimal.Application along with Intelligent Optimization Technique is deep into the every field of the operation of rolling, adopts intelligent optimization method determination sharing of load coefficient to be a technological trend.

Authorized announcement date is on 09 04th, 2013, Authorization Notice No. is disclose one in the Chinese invention patent of CN102489524B " to reduce the frame load distribution method of strip hot rolling process energy consumption ", and it comprises the following steps: step 1: the constraints determining initial control program; Step 2: determine the target controlled; Step 3: determine the machine parameter of control program and the parameter of rolled piece; Step 4: utilize the differential evolution algorithm improved to obtain each rack outlet thickness; Step 5: the exit thickness of each frame obtained according to step 4 determines threading speed, temperature, roll-force, rolling power, total energy consumption of each frame; Step 6: judge whether roll-force, roll torque, rolling power exceed the rated value of machine, exceeds and then repeats step 4, otherwise judge whether total energy consumption reaches minimum, is export end value, otherwise repeats step 4, until reach minimum of a value.

This technical scheme with the total energy consumption of each frame of finish rolling for object function, utilize the differential evolution algorithm (one of intelligent optimization algorithm) improved as optimized algorithm, optimize the drafts distributing each frame, determine that each frame is actual and shut out thickness, make total energy consumption reach minimum, directly carry out sharing of load in line computation by differential evolution algorithm, make total energy consumption reach minimum, decrease equipment damage, improve production efficiency and utilization rate of equipment and installations.Its deficiency is: one is that computing time is longer, is difficult to meet " real-time " requirement in line computation; Two each sub-distribution result fluctuations when being same specification rollings are comparatively large, are unfavorable for Strip Shape Control precision and the rolling stability of product in batch band steel production process.

Summary of the invention

Technical problem to be solved by this invention is to provide a kind of hot-strip load distribution method taking into account required power and good profile, " offline optimization+On-line Control " combines by it, intelligent optimization method offline optimization is utilized to obtain other sharing of load coefficient of typical case's band steel layer, roll-force pattern sharing of load Y-factor method Y is utilized to realize in line computation, the advantage of comprehensive two kinds of methods, both met line computation time/rate request, take into account again required power and Strip Shape Control requirement, reach the object improving fine-rolling strip steel rolling procedure setting accuracy and rolling stability.

Technical scheme of the present invention is: provide a kind of hot-strip load distribution method taking into account required power and good profile, comprise and determine finish rolling sharing of load coefficient, carry out the distribution of fine-rolling strip steel each frame rolling thickness and the On-line Control to each frame rolling thickness of fine-rolling strip steel accordingly, it is characterized in that described hot-strip load distribution method comprises the following steps:

The offline optimization of step one, finish rolling sharing of load coefficient:

First set up the Model for Multi-Objective Optimization of fine-rolling strip steel sharing of load, comprise the object function and optimized algorithm of determining finish rolling schedule model problem; Then calculated by offline optimization, obtain the Pareto optimal solution set of other finish rolling sharing of load scheme of typical case's band steel layer;

The off-line decision-making of step 2, finish rolling sharing of load coefficient:

Adopt the decision-making technique based on weighting polymerization, from the Pareto optimal solution set that step one obtains, select final Pareto optimization solution, be with other sharing of load coefficient of steel layer as typical case;

The Distribution Calculation of step 3, finish rolling each frame belt steel rolling thickness and On-line Control:

The typical case utilizing above-mentioned steps to obtain is with other sharing of load coefficient of steel layer, be rolled force mode sharing of load in line computation, obtain the final online hot-strip sharing of load scheme used, thus obtain drafts and the exit thickness thereof of each frame of finish rolling, according to drafts and the exit thickness thereof of each frame of above-mentioned finish rolling, on line real time control is carried out to the belt steel rolling thickness of each frame of finishing mill.

Described hot-strip load distribution method, " offline optimization+On-line Control " is combined, intelligent optimization method offline optimization is utilized to obtain other sharing of load coefficient of typical case's band steel layer, roll-force pattern sharing of load Y-factor method Y is utilized to realize in line computation and carry out real-time online control, when adopting intelligent optimization method off-line determination finish rolling sharing of load coefficient, take into account required power and the good profile of fine-rolling strip steel, while overcoming artificial experience method deficiency, reach the object improving fine-rolling strip steel Strip Shape Control precision and rolling stability.

Concrete, in described step one, determine Model for Multi-Objective Optimization and the optimized algorithm thereof of finish rolling sharing of load according to the following step:

S11, sets up the Model for Multi-Objective Optimization of finish rolling sharing of load:

Choose required power minimum target and the belt plate shape well-targeted object function as finish rolling schedule model problem:

(1) required power minimum target

Described required power minimum target adopts following expression formula to state:

$f_1=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{N}_i(h_{i-1},h_i)$ Formula (1)

Wherein: N _iit is the rolling power (kW) of the i-th frame; h _iit is the exit thickness (mm) of the i-th frame; N is finishing stand number;

(2) belt plate shape well-targeted

Described belt plate shape well-targeted adopts following expression formula to state:

$f_2=\underset{i=n-3}{\overset{n}{\mathrm{\Σ}}}{(C_h^i/h_i-C_h^{i-1}/h_{i-1}+{\mathrm{\Δ}}_i)}^2$ Formula (2)

Wherein, h _iit is the exit thickness (mm) of the i-th frame; it is the outlet convexity (μm) of the i-th frame; Δ _ifor optimizing regulation amount;

If $\mathrm{\δ}=C_h^i/h_i-C_h^{i-1}/h_{i-1},$ Then have

${\mathrm{\&Delta;}}_i=\left\{\begin{array}{cc}2a{(h_i/w)}^b& \mathrm{\&delta;}\&le;-2a{(h_i/w)}^b\\ -\mathrm{\&delta;}& -2a{(h_i/w)}^b<\mathrm{\&delta;}<a{(h_i/w)}^b\\ -a{(h_i/w)}^b& \mathrm{\&delta;}\&GreaterEqual;a{(h_i/w)}^b\end{array}\right.$ Formula (3)

Wherein, w is strip width (mm); A and b is model parameter;

Select the decision variable of exit thickness as schedule model of each frame of finish rolling:

H=(h ₁, h ₂..., h _n-2, h _n-1) formula (4)

Wherein, h is decision variable vector; N is finishing stand number;

The Model for Multi-Objective Optimization of described fine-rolling strip steel sharing of load adopts following expression formula to describe:

$\left\{\begin{array}{cc}\min & f_1=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i(h_{i-1},h_i)\\ \min & f_2=\underset{i=n-3}{\overset{n}{\mathrm{\&Sigma;}}}{(C_h^i/h_i-C_h^{i-1}/h_{i-1}+{\mathrm{\&Delta;}}_i)}^2\\ s.t.& 0\&le;P_i\&le;P_m\\ & 0\&le;I_i\&le;I_m\\ & h_n<h_{i+1}<h_i<h_0\end{array}\right.$ Formula (5)

Wherein, P _mfor maximum rolling force (kN); I _ifor electric current, I _mfor maximum current (A); h ₀for workpiece thickness, h _nfor product objective thickness (mm);

S12, determines the multi-objective optimization algorithm solving schedule model model:

Choose the non-dominated sorted genetic algorithm NSGA-II of band elitism strategy as the multi-objective optimization algorithm solving finish rolling sharing of load problem;

To any one, typically band steel layer is other, by the Model for Multi-Objective Optimization shown in formula (5), utilize NSGA-II algorithm to solve, the Pareto optimal solution set of this layer of other finish rolling sharing of load can be obtained, be i.e. the alternative schedule model solution of a sequence.

Further, in described step 2, adopt the decision-making technique based on weighting polymerization, select final Pareto optimization solution, the object function after weighting described in it adopts following expression formula to be described:

$\begin{array}{cc}\min & f={\mathrm{\&omega;}}_1\&CenterDot;\frac{f_1-f_{1,\min }}{f_{1,\max }-f_{1,\min }}+{\mathrm{\&omega;}}_2\&CenterDot;\frac{f_2-f_{2,\min }}{f_{2,\max }-f_{2,\min }}\end{array}$ Formula (6)

Wherein, ω ₁, ω ₂be respectively the weight of 2 object functions, and ω ₁+ ω ₂=1; f _{i, min}and f _{i, max}(i=1,2) represent minimum of a value and the maximum of i-th object function in Pareto optimal solution set respectively;

Determine weight { ω ₁, ω ₂value after, calculate the weighted target functional value f of all optimization solutions in Pareto optimal solution set, solution when selecting weighted target f to get minimum of a value, as final Pareto optimization solution;

After obtaining final Pareto optimization solution, obtain the proportionality coefficient of each frame roll-force of finish rolling of its correspondence further, it can be used as this typical case to be with other sharing of load coefficient of steel layer.

Further, in described step 3, the detailed process of described roll-force pattern sharing of load iterative computation each rack outlet thickness is as follows:

S31, determine the initial value of each rack outlet thickness of finish rolling:

Adopt following experience interpolation method:

$\left\{\begin{array}{c}{h}_i^0=\frac{h_0}{{\mathrm{\&lambda;}}_i^{\mathrm{KEY}}}(i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n)\\ {\mathrm{\&lambda;}}_i^{\mathrm{KEY}}={\left\{\frac{h_0/h_n}{h_0^{\mathrm{KEY}}/h_n^{\mathrm{KEY}}}\right\}}^{m_i}\&CenterDot;\left(\frac{h_0^{\mathrm{KEY}}}{h_i^{\mathrm{KEY}}}\right)\\ m_i=1-\frac{k_g}{n}\&CenterDot;{\left(\frac{n-i}{n-1}\right)}^2\end{array}\right.$ Formula (7)

In formula, n is finishing stand number; h ₀for workpiece thickness; h _nfor finish to gauge thickness; for the initial value of each rack outlet thickness; for the empirical table value that each frame thickness distributes; k _gfor gain coefficient, span 1≤k _g≤ n;

S32, the roll-force calculating each frame of finish rolling under current loads distributes and roll-force are to the derivative of drafts:

When other technological parameter is fixing, roll-force is the function of each frame inlet thickness and exit thickness; When finish rolling sharing of load scheme changes, need the roll-force recalculating each frame , it is the roll-force of the i-th frame jth time iteration; Meanwhile, need to calculate roll-force to the derivative of drafts , wherein it is the drafts of the i-th frame jth time iteration;

S33, according to the roll-force of above-mentioned each frame and roll-force to the result of calculation of drafts derivative, calculate the correction value of each frame drafts of finish rolling;

The expression formula that rolling described in it distributes iterative computation is:

$\mathrm{\&delta;}\left({\mathrm{\&Delta;h}}_i^j\right)=(\mathrm{\&Sigma;}{p}_i^j\&CenterDot;\frac{{\mathrm{\&alpha;}}_i}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}-p_i^j)/\frac{\&PartialD;p_i^j}{\&PartialD;\left({\mathrm{\&Delta;h}}_i^j\right)}-\mathrm{\&Sigma;}((\mathrm{\&Sigma;}{p}_i^j\&CenterDot;\frac{{\mathrm{\&alpha;}}_i}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}-p_i^j)/\frac{\&PartialD;p_i^j}{\&PartialD;\left(\mathrm{\&Delta;}{h}_i^j\right)})\&CenterDot;\frac{\mathrm{\&Delta;}{h}_i^j}{\mathrm{\&Sigma;\&Delta;}{h}_i^j}$ Formula (8)

Wherein, it is the correction value of the drafts of the i-th frame jth time iteration;

The correction value of S34, drafts after obtaining, calculate drafts and the exit thickness of each frame of finish rolling:

The renewal computing formula of each frame drafts of finish rolling is:

$\mathrm{\&Delta;}{h}_i^{j+1}=\mathrm{\&Delta;}{h}_i^j+{\mathrm{damp}}_j\&CenterDot;\mathrm{\&delta;}\left({\mathrm{\&Delta;h}}_i^j\right)$ Formula (9)

Wherein be the drafts of the i-th frame jth+1 iteration, damp _jfor damped coefficient, damp _j=β+(1-β) (1-e ^-j), β gets 0.6;

After the drafts of each frame obtains, the exit thickness of each frame can be calculated;

S35, judge whether the roll-force ratio of each frame of finish rolling meets the condition of convergence:

The condition of convergence that described roll-force distributes iterative computation is:

$|\frac{p_i^j}{\mathrm{\&Sigma;}{p}_i^j}-\frac{{\mathrm{\&alpha;}}_i}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}|\&le;\frac{\mathrm{\&tau;}}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}$ Formula (10)

Wherein, τ is positive number, desirable 0.01;

When formula (10) is set up, or when iterations j exceedes set point number, finishing iteration calculates, otherwise continues to perform S32 step, Simultaneous Iteration number of times j cumulative 1;

After above-mentioned iterative computation terminates, drafts and the exit thickness thereof of each frame of finish rolling can be obtained.

Further, in described step 3, the concrete computational process of described roll-force pattern sharing of load iterative computation each rack outlet thickness is as follows:

A, obtain for the sharing of load coefficient of roll-force pattern sharing of load in line computation according to step 2;

The initial value of each rack outlet thickness of B, rule of thumb interpolation method determination finish rolling;

C, the roll-force calculating each frame of finish rolling under current loads distributes, roll-force are to the derivative of drafts;

The correction value of D, each frame drafts of calculating finish rolling;

The updated value of E, the calculating each frame drafts of finish rolling and exit thickness;

F, judge whether the roll-force ratio of each frame meets the condition of convergence;

G, roll-force ratio as each frame meet the condition of convergence, then finishing iteration computational process; Otherwise, return and continue execution step C, Simultaneous Iteration number of times j cumulative 1;

After H, above-mentioned iterative computation terminate, drafts and the exit thickness thereof of each frame of finish rolling can be obtained.

Hot-strip load distribution method described in it, adopts intelligent optimization method determination sharing of load coefficient, with the defect avoiding Conventional wisdom method to need repeatedly trial and error, experimentation cost higher.

Compared with the prior art, advantage of the present invention is:

1. " offline optimization+On-line Control " combines by the technical program, intelligent optimization method offline optimization is utilized to obtain other sharing of load coefficient of typical case's band steel layer, roll-force pattern sharing of load Y-factor method Y is utilized to realize in line computation and carry out real-time online control, both the time requirement in line computation/control be can meet, required power and Strip Shape Control requirement taken into account again;

2. with intelligent optimization method determination sharing of load coefficient, carry out On-line Control with roll-force pattern sharing of load Y-factor method Y, while overcoming artificial experience method deficiency, reach the object improving fine-rolling strip steel rolling procedure setting accuracy and rolling stability.

Accompanying drawing explanation

Fig. 1 is method step block diagram of the present invention;

Fig. 2 is hot-strip load distribution method schematic diagram of the present invention;

Fig. 3 is roll-force pattern sharing of load computational process flow chart of the present invention;

Fig. 4 is the change schematic diagram of object function of the present invention with iterations;

Fig. 5 is the Pareto optimum forward position schematic diagram of typical carbon sharing of load of the present invention;

Fig. 6 is the roll-force distribution schematic diagram in each iterative process.

Detailed description of the invention

Below in conjunction with drawings and Examples, the present invention will be further described.

In Fig. 1 and Fig. 2, the Main process steps of the art of this patent scheme comprises: the Distribution Calculation of the offline optimization of finish rolling sharing of load coefficient, the off-line decision-making of finish rolling sharing of load coefficient and finish rolling each frame belt steel rolling thickness and On-line Control.

Concrete, technical scheme of the present invention provides a kind of hot-strip load distribution method taking into account required power and good profile, comprise and determine finish rolling sharing of load coefficient, carry out the distribution of fine-rolling strip steel each frame rolling thickness and the On-line Control to each frame rolling thickness of fine-rolling strip steel accordingly, it is characterized in that described hot-strip load distribution method comprises the following steps:

The offline optimization of step one, finish rolling sharing of load coefficient---first set up the Model for Multi-Objective Optimization of fine-rolling strip steel sharing of load, comprise the object function and optimized algorithm of determining finish rolling schedule model problem; Then calculated by offline optimization, obtain the Pareto optimal solution set of other finish rolling sharing of load scheme of typical case's band steel layer.

Adopt intelligent optimization method determination sharing of load coefficient, the defect that Conventional wisdom method needs repeatedly trial and error, experimentation cost higher can be avoided.

In production practices, a lot of engineering design and decision problem are all multi-objective problems, and are likely afoul mutually between each target, and each target namely cannot be made to reach optimum, and the improvement of a target is often to sacrifice another one target for cost simultaneously.

Usually, the method solving multi-objective problem is the single-object problem being translated into optimization method comparative maturity by weighted array, but the more difficult structure evaluation function of these class methods and once can only produce a solution, is difficult to the superiority-inferiority of the solution of objective evaluation gained multi-objective problem.

Multiple-objection optimization refers to that the optimization aim considered in optimizing process is not single, conflicting between each object function under normal circumstances, therefore do not exist " absolute optimal solution " that make all targets all reach optimum, can only try to achieve " being satisfied with disaggregation ", finally select some satisfactory solutions as final optimization pass solution by policymaker.

Multi-objective optimization question is different from the essence of single-object problem to be: the optimal solution of multi-objective optimization question is one and gathers, instead of a globally optimal solution, and we claim this disaggregation to be Pareto optimal solution set.Pareto disaggregation comprises a lot of and separates, and does not have dividing of quality between each solution.

Hot-strip sharing of load is a multi-objective optimization question, provides Model for Multi-Objective Optimization and the optimized algorithm thereof of finish rolling sharing of load below:

S11, sets up the Model for Multi-Objective Optimization of finish rolling sharing of load

Choose required power minimum target and the belt plate shape well-targeted object function as finish rolling schedule model problem:

(1) required power minimum target

Required power minimum target refers to when the mill speed of supplied materials and trimmed size size, rolling machine frame and final pass is given, by optimizing and revising the drafts of each frame of finish rolling, makes total required power of each frame of finish rolling reach minimum:

$f_1=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i(h_{i-1},h_i)$ Formula (1)

Wherein: N _iit is the rolling power (kW) of the i-th frame; h _iit is the exit thickness (mm) of the i-th frame; N is finishing stand number.

Along with the energy-saving and cost-reducing target becoming most iron and steel enterprise and pursue, required power minimum target becomes more meaningful.

(2) belt plate shape well-targeted

The change of finish rolling downstream frame ratio convexity will meet strip profile and flatness dead band condition, and to determine to obtain good belt plate shape between frame, this object function can be expressed as:

$f_2=\underset{i=n-3}{\overset{n}{\mathrm{\&Sigma;}}}{(C_h^i/h_i-C_h^{i-1}/h_{i-1}+{\mathrm{\&Delta;}}_i)}^2$ Formula (2)

Wherein, h _iit is the exit thickness (mm) of the i-th frame; it is the outlet convexity (μm) of the i-th frame; Δ _ifor optimizing regulation amount.

If $\mathrm{\&delta;}=C_h^i/h_i-C_h^{i-1}/h_{i-1},$ Then have

${\mathrm{\&Delta;}}_i=\left\{\begin{array}{cc}2a{(h_i/w)}^b& \mathrm{\&delta;}\&le;-2a{(h_i/w)}^b\\ -\mathrm{\&delta;}& -2a{(h_i/w)}^b<\mathrm{\&delta;}<a{(h_i/w)}^b\\ -a{(h_i/w)}^b& \mathrm{\&delta;}\&GreaterEqual;a{(h_i/w)}^b\end{array}\right.$ Formula (3)

Wherein, w is strip width (mm); A and b is model parameter.

In finish rolling schedule model problem, object function and constraints all have direct or indirect relation with the exit thickness of each frame, therefore select the decision variable of exit thickness as schedule model of each frame of finish rolling:

H=(h ₁, h ₂..., h _n-2, h _n-1) formula (4)

Wherein, h is decision variable vector; N is finishing stand number.

Based on above analysis, the Model for Multi-Objective Optimization of fine-rolling strip steel sharing of load can be described as:

$\left\{\begin{array}{cc}\min & f_1=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i(h_{i-1},h_i)\\ \min & f_2=\underset{i=n-3}{\overset{n}{\mathrm{\&Sigma;}}}{(C_h^i/h_i-C_h^{i-1}/h_{i-1}+{\mathrm{\&Delta;}}_i)}^2\\ s.t.& 0\&le;P_i\&le;P_m\\ & 0\&le;I_i\&le;I_m\\ & h_n<h_{i+1}<h_i<h_0\end{array}\right.$ Formula (5)

Wherein, P _mfor maximum rolling force (kN); I _ifor electric current, I _mfor maximum current (A); h ₀for workpiece thickness, h _nfor product objective thickness (mm).

S12, determines the multi-objective optimization algorithm solving schedule model model

In order to solve schedule model problem, need to determine multi-objective optimization algorithm.Non-dominated sorted genetic algorithm (NSGA-II) with elitism strategy is that the people such as Deb in 2002 are to the improvement of its algorithm NSGA, it is one of classic multi-objective Evolutionary Algorithm up to now, its essence is a kind of multi-objective genetic algorithm based on the optimum concept of Pareto, and the technical scheme of this patent chooses NSGA-II as the multi-objective optimization algorithm solving finish rolling sharing of load problem.

To any one, typically band steel layer is other, by the Model for Multi-Objective Optimization shown in formula (5), utilize NSGA-II algorithm to solve, the Pareto optimal solution set of this layer of other finish rolling sharing of load can be obtained, be i.e. the alternative schedule model solution of a sequence.

The off-line decision-making of step 2, finish rolling sharing of load coefficient---adopt the decision-making technique based on weighting polymerization, from the Pareto optimal solution set that step one obtains, selecting final Pareto optimization solution, is pick out final Pareto optimization solution from the sharing of load Pareto optimal solution set that step one obtains as the task of typical case with other this step of sharing of load coefficient of steel layer.

In multiple-objection optimization, policymaker selects final Pareto optimization solution according to the importance of each object function and certain preference usually.This patent provides a kind of decision-making technique based on weighting polymerization, and select final Pareto optimization solution, the object function after weighting is defined as:

$\begin{array}{cc}\min & f={\mathrm{\&omega;}}_1\&CenterDot;\frac{f_1-f_{1,\min }}{f_{1,\max }-f_{1,\min }}+{\mathrm{\&omega;}}_2\&CenterDot;\frac{f_2-f_{2,\min }}{f_{2,\max }-f_{2,\min }}\end{array}$ Formula (6)

Wherein, ω ₁, ω ₂be respectively the weight of 2 object functions, demand fulfillment relational expression ω ₁+ ω ₂=1; f _{i, min}and f _{i, max}(i=1,2) represent minimum of a value and the maximum of i-th object function in Pareto optimal solution set respectively, by the optimum forward position of Pareto obtains.

Policymaker can decide weight { ω according to the importance of each object function ₁, ω ₂value.

Determine weight { ω ₁, ω ₂value after, can calculate the weighted target functional value f of all optimization solutions in Pareto optimal solution set, solution when selecting weighted target f to get minimum of a value is as final Pareto optimization solution.

After obtaining final Pareto optimization solution, the proportionality coefficient of each frame roll-force of finish rolling of its correspondence can be obtained further, it can be used as this typical case to be with other sharing of load coefficient of steel layer.

The Distribution Calculation of step 3, finish rolling each frame belt steel rolling thickness and On-line Control---the typical case utilizing above-mentioned steps to obtain is with other sharing of load coefficient of steel layer, be rolled force mode sharing of load in line computation, obtain the final online hot-strip sharing of load scheme used, thus obtain drafts and the exit thickness thereof of each frame of finish rolling, according to drafts and the exit thickness thereof of each frame of above-mentioned finish rolling, on line real time control is carried out to the belt steel rolling thickness of each frame of finishing mill.

After typical case's band steel layer other sharing of load coefficient obtains, to each layer not under arbitrary hot-strip, can be rolled force mode sharing of load in line computation.Provide the detailed process of each rack outlet thickness of roll-force pattern sharing of load iterative computation below:

S31, determines the initial value of each rack outlet thickness of finish rolling

The convergence rate of quality to roll-force pattern load distribution algorithm of initial value has certain influence, and good initial value can make algorithm Fast Convergent.

The technical scheme of this patent proposes a kind of experience interpolation method:

$\left\{\begin{array}{c}{h}_i^0=\frac{h_0}{{\mathrm{\&lambda;}}_i^{\mathrm{KEY}}}(i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n)\\ {\mathrm{\&lambda;}}_i^{\mathrm{KEY}}={\left\{\frac{h_0/h_n}{h_0^{\mathrm{KEY}}/h_n^{\mathrm{KEY}}}\right\}}^{m_i}\&CenterDot;\left(\frac{h_0^{\mathrm{KEY}}}{h_i^{\mathrm{KEY}}}\right)\\ m_i=1-\frac{k_g}{n}\&CenterDot;{\left(\frac{n-i}{n-1}\right)}^2\end{array}\right.$ Formula (7)

In formula, n is finishing stand number; h ₀for workpiece thickness; h _nfor finish to gauge thickness; for the initial value of each rack outlet thickness; for the empirical table value that each frame thickness distributes; k _gfor gain coefficient, span 1≤k _g≤ n.

S32, to calculate under current loads distributes the roll-force of each frame of finish rolling and roll-force to the derivative of drafts:

When other technological parameter is fixing, roll-force is the function of each frame inlet thickness and exit thickness.When finish rolling sharing of load scheme changes, need the roll-force recalculating each frame , it is the roll-force of the i-th frame jth time iteration.Meanwhile, need to calculate roll-force to the derivative of drafts , wherein it is the drafts of the i-th frame jth time iteration.

S33, according to the roll-force of above-mentioned each frame and roll-force to the result of calculation of drafts derivative, calculates the correction value of each frame drafts of finish rolling.

Rolling distributes the formula of iterative computation:

$\mathrm{\&delta;}\left({\mathrm{\&Delta;h}}_i^j\right)=(\mathrm{\&Sigma;}{p}_i^j\&CenterDot;\frac{{\mathrm{\&alpha;}}_i}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}-p_i^j)/\frac{\&PartialD;p_i^j}{\&PartialD;\left({\mathrm{\&Delta;h}}_i^j\right)}-\mathrm{\&Sigma;}((\mathrm{\&Sigma;}{p}_i^j\&CenterDot;\frac{{\mathrm{\&alpha;}}_i}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}-p_i^j)/\frac{\&PartialD;p_i^j}{\&PartialD;\left(\mathrm{\&Delta;}{h}_i^j\right)})\&CenterDot;\frac{\mathrm{\&Delta;}{h}_i^j}{\mathrm{\&Sigma;\&Delta;}{h}_i^j}$ Formula (8)

Wherein, it is the correction value of the drafts of the i-th frame jth time iteration.

S34, the correction value of drafts after obtaining, calculate drafts and the exit thickness of each frame of finish rolling

The renewal computing formula of each frame drafts of finish rolling is:

$\mathrm{\&Delta;}{h}_i^{j+1}=\mathrm{\&Delta;}{h}_i^j+{\mathrm{damp}}_j\&CenterDot;\mathrm{\&delta;}\left({\mathrm{\&Delta;h}}_i^j\right)$ Formula (9)

Wherein be the drafts of the i-th frame jth+1 iteration, damp _jfor damped coefficient, damp _j=β+(1-β) (1-e ^-j), β gets 0.6.

After the drafts of each frame obtains, the exit thickness of each frame can be calculated.

and h ₀(workpiece thickness) is known quantity, according to , calculate from F1 frame the value that F7 frame can obtain the continuous renewal of each rack outlet thickness, this value will be used for next iteration and calculate roll-force use, wherein refer to the exit thickness of the i-th-1 frame jth+1 iteration;

Such as, to F1 frame, i=1, , no matter which time iteration, has constant;

To F2 frame, i=2, f1 exports and inputs as F2;

To F3 frame, i=3, successively recursion .....

So be summarized as , only as F1, , the input of all the other to be all the output of next frame be again next frames.

Wherein it is the exit thickness of the i-th frame jth+1 iteration.

S35, judges whether the roll-force ratio of each frame of finish rolling meets the condition of convergence.

The condition of convergence that roll-force distributes iterative computation is:

$|\frac{p_i^j}{\mathrm{\&Sigma;}{p}_i^j}-\frac{{\mathrm{\&alpha;}}_i}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}|\&le;\frac{\mathrm{\&tau;}}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}$ Formula (10)

Wherein, τ is very little positive number, desirable 0.01.

When formula (10) is set up, or when iterations j exceedes set point number, finishing iteration calculates, otherwise continues to perform S32 step, Simultaneous Iteration number of times j cumulative 1.

Such as, the set point number of iterations j is 6 times, and namely the span of j is 0≤j≤5, and the 1st time iterative computation j gets 0, and when formula (10) establishment or iterations j are more than 6 times, iterative computation terminates.

After above-mentioned iterative computation terminates, drafts and the exit thickness thereof of each frame of finish rolling can be obtained.

In Fig. 3, give the calculation flow chart of the step 3 of technical solution of the present invention, i.e. roll-force pattern sharing of load computational process flow chart.

In described step 3, the concrete computational process of described roll-force pattern sharing of load iterative computation each rack outlet thickness is as follows:

A, obtain for the sharing of load coefficient of roll-force pattern sharing of load in line computation according to step 2;

The initial value of each rack outlet thickness of B, rule of thumb interpolation method determination finish rolling;

C, the roll-force calculating each frame of finish rolling under current loads distributes, roll-force are to the derivative of drafts;

The correction value of D, each frame drafts of calculating finish rolling;

The updated value of E, the calculating each frame drafts of finish rolling and exit thickness;

F, judge whether the roll-force ratio of each frame meets the condition of convergence;

G, roll-force ratio as each frame meet the condition of convergence, then finishing iteration computational process; Otherwise, return and continue execution step C, Simultaneous Iteration number of times j cumulative 1;

After H, above-mentioned iterative computation terminate, drafts and the exit thickness thereof of each frame of finish rolling can be obtained.

The typical case utilizing above-mentioned steps to obtain is with other sharing of load coefficient of steel layer, be rolled force mode sharing of load in line computation, obtain the final online hot-strip sharing of load scheme used, by described hot-strip sharing of load scheme, obtain drafts and the exit thickness thereof of each frame of finish rolling, according to drafts and the exit thickness thereof of each frame of above-mentioned finish rolling, on line real time control is carried out to the belt steel rolling thickness of each frame of finishing mill.

Due to according to the drafts of each frame of finish rolling and exit thickness thereof, the specific implementation of on line real time control is carried out to the belt steel rolling thickness of each frame of finishing mill and control device belongs to prior art, therefore its concrete control method and realization means no longer describe at this.

Embodiment:

Select certain typical carbon as embodiment, steel grade is Q235B, and strip width is 1244mm, workpiece thickness h ₀for 42.6mm, finish to gauge target thickness h _nfor 3.38mm, target convexity is 40um, and finishing stand number n is 7.

Choosing of the middle model parameter of formula (3): a=40, b=1.86.

Model for Multi-Objective Optimization shown in formula (5) is carried out to this carbon steel, adopts the non-dominated sorted genetic algorithm (NSGA-II) of elitism strategy to solve.

In NSGA-II algorithm, population number is 100, and maximum iteration time is 40.After 40 iterative computation, can obtain the Pareto optimal solution set of this band steel finish rolling sharing of load, Fig. 4 is the change of object function with iterations.

As seen from the figure, after iteration 20 times, two object functions start to tend towards stability.

Fig. 5 optimizes the optimum forward position of the Pareto at the end of calculating, and it show that relation and the evolution trend of 2 object functions, f ₁with f ₂between there is obviously conflict, along with rolling power target f ₁increase (degenerating), plate shape target f ₂continuous reduction (improving).

Do not have between each Pareto optimal solution quality point, designer can attention degree rule of thumb with to each target, therefrom selects the most satisfied solution.Below according to the decision-making technique based on weighting polymerization, select final Pareto optimization solution.

According to the principle taking into account rolling rule target and belt plate shape target, choose ω ₁=0.65, ω ₂=0.35, calculate the f value that in Pareto optimal solution set, each optimization solution is corresponding, sort to all optimization solutions by f value incremental order, following table 1 lists 20 typical optimization solutions after sequence, picks out f value reckling as final optimization pass solution (corresponding No. 1 solution).

Table 1 is by the optimum forward position of the typical Pareto of overall goal function f ascending order arrangement and sharing of load coefficient thereof

Solution when selecting weighted target f to get minimum of a value is as final Pareto optimization solution, and No. No1 solution namely in table 1, is with other roll-force distribution coefficient of steel layer using the sharing of load coefficient of its correspondence as this typical case.

The sharing of load coefficient obtained according to offline optimization be below rolled force mode sharing of load Y-factor method Y in line computation.

Employing experience interpolation method determination initial value, get 45mm, k _gget 5.5.The calculating of finish rolling sharing of load is carried out to above-mentioned carbon steel band steel.

Table 2 fine-rolling strip steel sharing of load calculates relevant parameter

The initial value that can calculate finish rolling each frame sharing of load according to formula (7) is as shown in table 3:

The sharing of load initial value of each frame of table 3 finish rolling

With the result in table 3 for sharing of load initial value, by the absolute draft amount of each frame of roll-force pattern sharing of load Y-factor method Y iterative computation, until roll-force ratio meets target call.Condition of convergence ε _c=0.01, iterations is no more than 6 times.

Perform above-mentioned absolute draft amount iterative process (S32-S35), iterate to the 5th meet end condition terminate calculate, obtain result as shown in Figure 6, Fig. 6 be in each iterative process roll-force distribution.

Following table 4 gives the roll-force ratio situation of change of each iteration.

The roll-force ratio change of table 4 each iterative computation

Iterations	F1	F2	F3	F4	F5	F6	F7
								1	0.914	1.000	0.987	0.979	0.771	0.734	0.729
2	0.978	1.000	0.974	0.947	0.727	0.659	0.538
								3	1.000	0.975	0.932	0.887	0.668	0.588	0.428
4	1.000	0.951	0.896	0.843	0.632	0.557	0.404
								5	1.000	0.938	0.878	0.825	0.621	0.550	0.401
1 mark	1	0.93	0.87	0.82	0.62	0.55	0.40

From table 4, when iterating to the 5th, the roll-force ratio of each frame of finish rolling and target proportion closely, meet the condition of convergence shown in formula (10).

Following table 5, table 6 give drafts and the exit thickness of each frame in each iterative computation.

The drafts of each frame of table 5 each iterative computation

Iterations	F1	F2	F3	F4	F5	F6	F7
								1	17.1974	10.1035	5.4279	3.0704	1.7919	1.0608	0.5356
2	18.5824	9.8321	5.0721	2.7818	1.5967	0.9228	0.3995
								3	19.2263	9.6549	4.8702	2.6434	1.5236	0.8872	0.382
4	19.4772	9.5489	4.7809	2.5993	1.5109	0.8867	0.3835
								5	19.5558	9.4966	4.7526	2.5933	1.5138	0.8903	0.385

The exit thickness of each frame of table 6 each iterative computation

Iterations	F1	F2	F3	F4	F5	F6	F7
								1	27.2148	16.80021	0.9633	7.5386	5.4780	4.1927	3.3793
2	25.3693	15.2658	9.8379	6.7675	4.9756	3.9148	3.3793
								3	23.9843	14.1522	9.0801	6.2983	4.7016	3.7788	3.3793
4	23.3404	13.6856	8.8154	6.1720	4.6485	3.7612	3.3793
								5	23.0895	13.5406	8.7597	6.1603	4.6495	3.7628	3.3793

In table 6, last column data are final finish rolling sharing of load value, as shown in table 7 below:

The finish rolling sharing of load value that table 7 is final

F1	F2	F3	F4	F5	F6	F7
							23.0895	13.5406	8.7597	6.1603	4.6495	3.7628	3.3793

In summary, in the technical program, its " offline optimization " adopts Multipurpose Optimal Method, is calculated by offline optimization, the Pareto optimal solution set of other finish rolling sharing of load scheme of typical case's band steel layer can be obtained, for second step adopts the decision-making technique based on weighting polymerization to provide convenience.

Multi-target method is relative to the benefit of single object optimization:

1) single object optimization method (as weighting method) needs to determine target weight, requires that policymaker has enough prioris, otherwise is difficult to obtain desirable solution, and particularly when number of targets magnitude is different, target weight is just more difficult to be determined; And Multipurpose Optimal Method does not need priori, policymaker can select oneself satisfied solution by man-machine interaction mode from the Pareto optimal solution set obtained, and thus has the larger decision-making free degree.

2) the optimum forward position of the Pareto that obtains of Multipurpose Optimal Method can reflect the contradictory relation between different target, thus can the reasonability selected of test-target, makes policymaker do decision-making in " information security " situation simultaneously.

3) Multipurpose Optimal Method is once run and is just produced multiple Pareto optimal solution, and the operation of single object optimization method once only can produce an optimal solution, obtains multiple solution if want, need to run repeatedly, optimization efficiency is not high.

In addition, in the technical program, its " On-line Control " adopts roll-force pattern sharing of load Y-factor method Y, meets the requirement in line computation and control in real time: stable, have good convergence, and computational speed is very fast.

Because " offline optimization+On-line Control " combines by the present invention, adopt intelligent optimization method off-line determination finish rolling sharing of load coefficient, roll-force pattern sharing of load Y-factor method Y is adopted to realize in line computation and carry out real-time online control, combine the advantage of two kinds of methods, when adopting intelligent optimization method off-line determination finish rolling sharing of load coefficient, take into account required power and the good profile of fine-rolling strip steel, both the time requirement that real-time online calculates/controls had been met, required power and Strip Shape Control requirement are taken into account again, while overcoming artificial experience method deficiency, reach the object improving fine-rolling strip steel rolling procedure setting accuracy and rolling stability.

The production process that the present invention can be widely used in band steel of hot strip mill controls and fine-rolling strip steel control of product quality field.

Claims (7)

1. take into account the hot-strip load distribution method of required power and good profile for one kind, comprise and determine finish rolling sharing of load coefficient, carry out the distribution of fine-rolling strip steel each frame rolling thickness and the On-line Control to each frame rolling thickness of fine-rolling strip steel accordingly, it is characterized in that described hot-strip load distribution method comprises the following steps:

The offline optimization of step one, finish rolling sharing of load coefficient:

First set up the Model for Multi-Objective Optimization of fine-rolling strip steel sharing of load, comprise the object function and optimized algorithm of determining finish rolling schedule model problem; Then calculated by offline optimization, obtain the Pareto optimal solution set of other finish rolling sharing of load scheme of typical case's band steel layer;

The off-line decision-making of step 2, finish rolling sharing of load coefficient:

Adopt the decision-making technique based on weighting polymerization, from the Pareto optimal solution set that step one obtains, select final Pareto optimization solution, be with other sharing of load coefficient of steel layer as typical case;

The Distribution Calculation of step 3, finish rolling each frame belt steel rolling thickness and On-line Control:

The typical case utilizing above-mentioned steps to obtain is with other sharing of load coefficient of steel layer, be rolled force mode sharing of load in line computation, obtain the final online hot-strip sharing of load scheme used, thus obtain drafts and the exit thickness thereof of each frame of finish rolling, according to drafts and the exit thickness thereof of each frame of above-mentioned finish rolling, on line real time control is carried out to the belt steel rolling thickness of each frame of finishing mill.

2. according to the hot-strip load distribution method taking into account required power and good profile according to claim 1, it is characterized in that described hot-strip load distribution method, " offline optimization+On-line Control " is combined, intelligent optimization method offline optimization is utilized to obtain other sharing of load coefficient of typical case's band steel layer, roll-force pattern sharing of load Y-factor method Y is utilized to realize in line computation and carry out real-time online control, when adopting intelligent optimization method off-line determination finish rolling sharing of load coefficient, take into account required power and the good profile of fine-rolling strip steel, while overcoming artificial experience method deficiency, reach the object improving fine-rolling strip steel Strip Shape Control precision and rolling stability.

3. according to the hot-strip load distribution method taking into account required power and good profile according to claim 1, it is characterized in that in described step one, determine Model for Multi-Objective Optimization and the optimized algorithm thereof of finish rolling sharing of load according to the following step:

S11, sets up the Model for Multi-Objective Optimization of finish rolling sharing of load:

Choose required power minimum target and the belt plate shape well-targeted object function as finish rolling schedule model problem:

(1) required power minimum target

Described required power minimum target adopts following expression formula to state:

$f_1=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i(h_{i-1},h_i)$ Formula (1)

Wherein: N _iit is the rolling power (kW) of the i-th frame; h _iit is the exit thickness (mm) of the i-th frame; N is finishing stand number.

(2) belt plate shape well-targeted

Described belt plate shape well-targeted adopts following expression formula to state:

$f_2=\underset{i=n-3}{\overset{n}{\mathrm{\&Sigma;}}}{(C_h^i/h_i-C_h^{i-1}/h_{i-1}+{\mathrm{\&Delta;}}_i)}^2$ Formula (2)

Wherein, h _iit is the exit thickness (mm) of the i-th frame; it is the outlet convexity (μm) of the i-th frame; Δ _ifor optimizing regulation amount;

If $\mathrm{\&delta;}=C_h^i/h_i-C_h^{i-1}/h_{i-1}$ , then have

${\mathrm{\&Delta;}}_i=\left\{\begin{array}{cc}2a{(h_i/w)}^b& \mathrm{\&delta;}\&le;-2a{(h_i/w)}^b\\ -\mathrm{\&delta;}& -2a{(h_i/w)}^b<\mathrm{\&delta;}<a{(h_i/w)}^b\\ -a{(h_i/w)}^b& \mathrm{\&delta;}\&GreaterEqual;a{(h_i/w)}^b\end{array}\right.$ Formula (3)

Wherein, w is strip width (mm); A and b is model parameter;

Select the decision variable of exit thickness as schedule model of each frame of finish rolling:

H=(h ₁, h ₂..., h _n-2, h _n-1) formula (4)

Wherein, h is decision variable vector; N is finishing stand number;

The Model for Multi-Objective Optimization of described fine-rolling strip steel sharing of load adopts following expression formula to describe:

$\left\{\begin{array}{cc}\min & f_1=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i(h_{i-1},h_i)\\ \min & f_2=\underset{i=n-3}{\overset{n}{\mathrm{\&Sigma;}}}{(C_h^i/h_i-C_h^{i-1}/h_{i-1}+{\mathrm{\&Delta;}}_i)}^2\\ s.t.& 0\&le;P_i\&le;P_m\\ & 0\&le;I_i\&le;I_m\\ & h_n<h_{i+1}<h_i<h_0\end{array}\right.$ Formula (5)

Wherein, P _mfor maximum rolling force (kN); I _ifor electric current, I _mfor maximum current (A); h ₀for workpiece thickness, h _nfor product objective thickness (mm).

S12, determines the multi-objective optimization algorithm solving schedule model model:

Choose the non-dominated sorted genetic algorithm NSGA-II of band elitism strategy as the multi-objective optimization algorithm solving finish rolling sharing of load problem;

To any one, typically band steel layer is other, by the Model for Multi-Objective Optimization shown in formula (5), utilize NSGA-II algorithm to solve, the Pareto optimal solution set of this layer of other finish rolling sharing of load can be obtained, be i.e. the alternative schedule model solution of a sequence.

4. according to the hot-strip load distribution method taking into account required power and good profile according to claim 1, it is characterized in that in described step 2, adopt the decision-making technique based on weighting polymerization, select final Pareto optimization solution, the object function after weighting described in it adopts following expression formula to be described:

$\begin{array}{cc}\min & f={\mathrm{\&omega;}}_1\&CenterDot;\frac{f_1-f_{1,\min }}{f_{1,\max }-f_{1,\min }}+{\mathrm{\&omega;}}_2\&CenterDot;\frac{f_2-f_{2,\min }}{f_{2,\max }-f_{2,\min }}\end{array}$ Formula (6)

Wherein, ω ₁, ω ₂be respectively the weight of 2 object functions, and ω ₁+ ω ₂=1; f _{i, min}and f _{i, max}(i=1,2) represent minimum of a value and the maximum of i-th object function in Pareto optimal solution set respectively;

Determine weight { ω ₁, ω ₂value after, calculate the weighted target functional value f of all optimization solutions in Pareto optimal solution set, solution when selecting weighted target f to get minimum of a value, as final Pareto optimization solution;

After obtaining final Pareto optimization solution, obtain the proportionality coefficient of each frame roll-force of finish rolling of its correspondence further, it can be used as this typical case to be with other sharing of load coefficient of steel layer.

5. according to the hot-strip load distribution method taking into account required power and good profile according to claim 1, it is characterized in that in described step 3, the detailed process of described roll-force pattern sharing of load iterative computation each rack outlet thickness is as follows:

S31, determine the initial value of each rack outlet thickness of finish rolling:

Adopt following experience interpolation method:

$\left\{\begin{array}{c}{h}_i^0=\frac{h_0}{{\mathrm{\&lambda;}}_i^{\mathrm{KEY}}}(i=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,n)\\ {\mathrm{\&lambda;}}_i^{\mathrm{KEY}}={\left\{\frac{h_0/h_n}{h_0^{\mathrm{KEY}}/h_n^{\mathrm{KEY}}}\right\}}^{m_i}\&CenterDot;\left(\frac{h_0^{\mathrm{KEY}}}{h_i^{\mathrm{KEY}}}\right)\\ m_i=1-\frac{k_g}{n}\&CenterDot;{\left(\frac{n-i}{n-1}\right)}^2\end{array}\right.$ Formula (7)

In formula, n is finishing stand number; h ₀for workpiece thickness; h _nfor finish to gauge thickness; for the initial value of each rack outlet thickness; for the empirical table value that each frame thickness distributes; k _gfor gain coefficient, span 1≤k _g≤ n;

S32, the roll-force calculating each frame of finish rolling under current loads distributes and roll-force are to the derivative of drafts:

When other technological parameter is fixing, roll-force is the function of each frame inlet thickness and exit thickness; When finish rolling sharing of load scheme changes, need the roll-force recalculating each frame , it is the roll-force of the i-th frame jth time iteration; Meanwhile, need to calculate roll-force to the derivative of drafts , wherein it is the drafts of the i-th frame jth time iteration;

S33, according to the roll-force of above-mentioned each frame and roll-force to the result of calculation of drafts derivative, calculate the correction value of each frame drafts of finish rolling;

The expression formula that rolling described in it distributes iterative computation is:

$\mathrm{\&delta;}\left({\mathrm{\&Delta;h}}_i^j\right)=(\mathrm{\&Sigma;}{p}_i^j\&CenterDot;\frac{{\mathrm{\&alpha;}}_i}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}-p_i^j)/\frac{\&PartialD;p_i^j}{\&PartialD;\left({\mathrm{\&Delta;h}}_i^j\right)}-\mathrm{\&Sigma;}((\mathrm{\&Sigma;}{p}_i^j\&CenterDot;\frac{{\mathrm{\&alpha;}}_i}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}-p_i^j)/\frac{\&PartialD;p_i^j}{\&PartialD;\left(\mathrm{\&Delta;}{h}_i^j\right)})\&CenterDot;\frac{\mathrm{\&Delta;}{h}_i^j}{\mathrm{\&Sigma;\&Delta;}{h}_i^j}$ Formula (8)

Wherein, it is the correction value of the drafts of the i-th frame jth time iteration;

The correction value of S34, drafts after obtaining, calculate drafts and the exit thickness of each frame of finish rolling:

The renewal computing formula of each frame drafts of finish rolling is:

$\mathrm{\&Delta;}{h}_i^{j+1}=\mathrm{\&Delta;}{h}_i^j+{\mathrm{damp}}_j\&CenterDot;\mathrm{\&delta;}\left({\mathrm{\&Delta;h}}_i^j\right)$ Formula (9)

Wherein be the drafts of the i-th frame jth+1 iteration, damp _jfor damped coefficient, damp _j=β+(1-β) (1-e ^-j), β gets 0.6;

After the drafts of each frame obtains, the exit thickness of each frame can be calculated;

S35, judge whether the roll-force ratio of each frame of finish rolling meets the condition of convergence:

The condition of convergence that described roll-force distributes iterative computation is:

$|\frac{p_i^j}{\mathrm{\&Sigma;}{p}_i^j}-\frac{{\mathrm{\&alpha;}}_i}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}|\&le;\frac{\mathrm{\&tau;}}{\mathrm{\&Sigma;}{\mathrm{\&alpha;}}_i}$ Formula (10)

Wherein, τ is positive number, desirable 0.01;

When formula (10) is set up, or when iterations j exceedes set point number, finishing iteration calculates, otherwise continues to perform S32 step, Simultaneous Iteration number of times j cumulative 1;

After above-mentioned iterative computation terminates, drafts and the exit thickness thereof of each frame of finish rolling can be obtained.

6. according to the hot-strip load distribution method taking into account required power and good profile according to claim 1, it is characterized in that in described step 3, the concrete computational process of described roll-force pattern sharing of load iterative computation each rack outlet thickness is as follows:

A, obtain for the sharing of load coefficient of roll-force pattern sharing of load in line computation according to step 2;

The initial value of each rack outlet thickness of B, rule of thumb interpolation method determination finish rolling;

C, the roll-force calculating each frame of finish rolling under current loads distributes, roll-force are to the derivative of drafts;

The correction value of D, each frame drafts of calculating finish rolling;

The updated value of E, the calculating each frame drafts of finish rolling and exit thickness;

F, judge whether the roll-force ratio of each frame meets the condition of convergence;

G, roll-force ratio as each frame meet the condition of convergence, then finishing iteration computational process; Otherwise, return and continue execution step C, Simultaneous Iteration number of times j cumulative 1;

After H, above-mentioned iterative computation terminate, drafts and the exit thickness thereof of each frame of finish rolling can be obtained.

7. according to the hot-strip load distribution method taking into account required power and good profile according to claim 1, it is characterized in that described hot-strip load distribution method, adopt intelligent optimization method determination sharing of load coefficient, with the defect avoiding Conventional wisdom method to need repeatedly trial and error, experimentation cost higher.