CN102489524A - Machine frame load distribution method for decreasing energy consumption of rolling process of hot rolled strip steel - Google Patents

Abstract

A machine frame load distribution method for decreasing energy consumption of a rolling process of hot rolled strip steel includes the following steps: step 1 determining constraint conditions of an initial control scheme, step 2 determining a control target, step 3 determining parameters of a machine and parameters of rolled pieces of the control scheme, step 4 obtaining thickness of an outlet of each machine frame through improved differential evolution algorithm, step 5 determining strip threading speed, temperature, rolling force, rolling power and total energy consumption of each machine frame based on the thickness of the outlet of each machine frame obtained in step 4, and step 6 judging whether rolling force, roll torque and rolling power exceed rated values of the machine or not. If the values exceed the rated values, repeat step 4, and if not, judge whether total energy consumption reaches the minimum value or not. If the total energy consumption reaches the minimum value, output the final value, and if not, repeat step 4 until the minimum value is reached. Through the improved differential evolution algorithm, load of each machine frame is optimally set, rolling reduction of each machine frame is optimally distributed, and actual rolled thickness of each machine frame is determined so that total energy consumption reaches the minimum value, device damage is reduced, and production efficiency and device utilization ratio are improved.

Description

A kind of frame load distribution method that reduces the strip hot rolling process energy consumption

Technical field

The invention belongs to steel plate rolling process control technology field, be specifically related to a kind of frame load distribution method that reduces the strip hot rolling process energy consumption.

Background technology

When hot rolling strip steel, steel billet comes out in heating furnace, through rolling (n is frame number or road number of times) of n frame or passage; Roll out the finished strip that meets quality standard; These a series of operations of rolling are to carry out according to the rolling procedure that sets in advance, and are as shown in Figure 1.The central issue of formulating rolling procedure is the exit thickness that how to distribute the drafts of each frame, confirms each frame; Just confirm the sharing of load of depressing of each frame; In essence; Sharing of load has determined the state characteristic of the operation of rolling, and end product quality requirement, equipment adjustment are all had significant effects.Formulate sharing of load; The restrictive condition that needs to consider has the overload of equipment intensity, motor and the restriction of heating, process conditions, plate shape and speed etc.; These factors are conflicting often, and under different rolling conditions, the limiting factor of each rolling mill also is different; Interact again between each factor, relation is very complicated.Therefore, can reach production increases with quality up and cost of production down, just need the drafts of each frame of optimized distribution for making the production of band steel.

For a long time, Chinese scholars has been carried out number of research projects to the precision aspect that improves mm finishing mill unit sharing of load model.But still be based on the experiential operating method in essence; Rule of thumb distribute earlier each frame load; Calculate then reach the finish to gauge target temperature required wear tape speed; Confirm the temperature of rolled piece,, carry out the limit and check with mathematical model prediction resistance of deformation, roll-force, rolling power, and other parameters in each frame; If the rolling power of a certain frame surpasses the main motor current limit, just utilize correction algorithm to redistribute the drafts of each frame, to adjust each frame load, constantly adjustment is checked, and does not transfinite up to the rolling power of institute's organic frame.Check through after calculate roll gap, speed dispatch control system setting value again, accomplish the setting of parameter.

This method is easy, reliable, can guarantee device security, and little to the automation degree of equipment dependence, but need constantly check and repair the worker, is prone to cause each frame load uneven, causes load to side arm or to the phenomenon of after-frame accumulation.The computation model of this method generally can not online adaptive, and can not guarantee in each passage in process of production or each frame can both be rolled under the load that allows, let alone energy-conservation with consider belt plate shape.And when production description or rolling condition change, accumulate experience again again, could make sharing of load again.So not only influence the performance of whole unit capacity, and the quality of influence band steel.This method does not too much consider to carry out the production process operation optimization from the optimal design of production process.

In addition, the scholar who has proposes the thickness allocation optimized method based on related algorithm, as waiting methods such as sharing of load, the combination of plurality of target function; These methods are from the angle of balanced load, minimizing energy consumption, because the load (roll-force, power etc.) in this method is complicated non-linear relation with drafts; And roll-force; Parameters such as power are to depress the result of generation, are difficult to obtain relatively good separating, and can not well satisfy the needs that hot rolling is produced.

In steel rolling was produced, blank was rolling through number frame (passage), produced plastic deformation, finally rolled out the product of requirement up to specification.The operation of rolling that these are a series of is to get into the rules of setting in advance before the milling train according to blank to carry out, and this is the important process of band steel continuous rolling.Wherein sharing of load is the prerequisite and the basis of set-up and calculated, is the key link of set-up and calculated.In steel rolling was produced, energy consumption was one of key factor that influences production cost always.Therefore the synergy that lowers consumption also is the target that the producer pursues.

Summary of the invention

To the deficiency of prior art, the present invention provides a kind of frame load distribution method that reduces the strip hot rolling process energy consumption, and the drafts of each frame of optimized distribution is confirmed the actual thickness that shuts out of each frame, makes total energy consumption reach minimum.

Technical scheme of the present invention: a kind of frame load distribution method that reduces the strip hot rolling process energy consumption specifically comprises the steps:

Step 1: confirm the constraints of initial control scheme, comprising:

(1) bite condition

Bite condition guarantees nipping smoothly of band steel, nips smoothly to guarantee that the band steel can get into mill milling, if the thickness of rolled piece is big, temperature is high, drafts is big, just can not guarantee nipping smoothly with steel.In order to guarantee to guarantee bite condition with the nipping smoothly of steel with drafts, promptly rolling each reduction in pass should allow drafts less than maximum, and computing formula is suc as formula shown in (1)

$\mathrm{\&Delta;}{h}_i<\mathrm{\&Delta;}{h}_{\max }=D(1-\frac{1}{\sqrt{1+f^2}}),i=\mathrm{1,2},...,n---\left(1\right)$

Δ h wherein _iThe drafts of representing i frame; Δ h _MaxFor maximum allows drafts; F is the coefficient of friction between roll and rolled piece; D representes the diameter of roll.

(2) roll strength condition

When maximum pressure that draught pressure can bear greater than roll, the roll part possibly destroyed.For guaranteeing roll strength, reply draught pressure and roll torque limit, and guarantee can not surpass maximum roll-force and roll torque in the operation of rolling, and computing formula is suc as formula shown in (2) formula (3):

P _i＜P _imax i＝1，2，...，n (2)

M _i＜M _imax i＝1，2，...，n (3)

P wherein _iIt is the roll-force of i frame; P _ImaxIt is the maximum rolling force that i frame allows; M _iIt is the roll torque of i frame; M _ImaxIt is the maximum rolling force square that i frame allows.

(3) motor ability condition

The motor ability is the restrictive condition of motor overload, and rolling power should satisfy the loading condiction of milling train master motor, requires rolling power must not surpass its rated power, and computing formula is suc as formula shown in (4)

N _i＜N _imax i＝1，2，...，n (4)

N wherein _iIt is the rolling power of i frame; N _ImaxIt is the maximum rolling power that i frame allows.

(4) strip shape quality restrictive condition

In order to keep strip shape quality to reach customer requirement, optimize the drafts of arranging several of backs, making between its corresponding roll-force has certain ratio, prevents to be with steel the limit wave to occur, and computing formula is suc as formula shown in (5)

$-40{\left(\frac{h_i}{b}\right)}^{1.86}<\mathrm{\&Delta;}{\mathrm{CR}}_i<80{\left(\frac{h_i}{b}\right)}^{1.86},i=n-3,n-2,n-1,n---\left(5\right)$

Δ CR wherein _iInlet convexity when passing through i frame for slab is poor with the outlet convexity; h _iIt is the exit thickness of i frame; B is the width of slab.

Step 2: the target of confirming control.The target of this method control is to make rolling total energy consumption reach minimum, and the energy consumption calculation formula is shown in (6) formula:

$\min \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i,i=\mathrm{1,2},...,n---\left(6\right)$

Wherein: n-mm finishing mill unit frame number;

N _i-Di i frame power of motor, computing formula is suc as formula shown in (7):

$N_i=\frac{2\mathrm{\&pi;}*{10}^3}{60*102}{c}_i*M_i,i=\mathrm{1,2},...,n---\left(7\right)$

C in the formula (7) _iBe revolution;

M _iBe the moment of the horizontal roller of i frame, computing formula is suc as formula shown in (8):

Wherein, is arm of force coefficient;

P _iThe roll-force computing formula that is horizontal roller is suc as formula shown in (9):

$P_i=B{l}_c^{/}{Q}_{p}K,i=\mathrm{1,2},...,n---\left(9\right)$

B is the width of blank in the formula (9);

is contact arc length, and computing formula is suc as formula shown in (10):

$l_c^{/}=\sqrt{R^{/}\mathrm{\&Delta;}{h}_i},i=\mathrm{1,2},...,n---\left(10\right)$

In the formula (5), R ' is the roller radius after flattening, and computing formula is suc as formula shown in (11):

$R_i^{\&prime;}=R_i\&CenterDot;(1+2.2\&times;{10}^{-5}\frac{P_i}{\mathrm{B\&Delta;}{h}_i}),i=\mathrm{1,2},...,n---\left(11\right)$

R _iIt is the radius of the working roll of i frame;

Δ h _iExpression drafts computing formula is suc as formula shown in (12):

Δh _i＝h _i-1-h _i i＝1，2，...，n (12)

H in the formula _I-1It is the inlet thickness of i frame; h _iIt is the exit thickness of i frame;

Q _PBe external friction stress state coefficient, computing formula is suc as formula shown in (13):

Q _p＝0.8206+0.2376l _c/h _c+0.1006εl _c/h _c-0.3768ε i＝1，2，...，n(13)

ε is that the relative reduction computing formula is suc as formula shown in (14) in the formula

$\mathrm{\&epsiv;}=\frac{h_{i-1}-h_i}{h_{i-1}},i=\mathrm{1,2},...,n---\left(14\right)$

l _cBe the floor projection length of contact arc, computing formula is suc as formula shown in (15):

$l_c=\sqrt{R_i\mathrm{\&Delta;}{h}_i},i=\mathrm{1,2},...,n---\left(15\right)$

h _cThe mean value of the inlet thickness of rolled piece and exit thickness when being rolling, computing formula is suc as formula shown in (16)

$h_c=\frac{h_{i-1}+h_i}{2},i=\mathrm{1,2},...,n---\left(16\right)$

Deformation drag under the K plane deformation, computing formula are formula (17) formula (18)

K＝1.15σ (17)

$\mathrm{\&sigma;}={\mathrm{\&sigma;}}_0\exp (a_{1}T+a_2){\left(\frac{u_m}{10}\right)}^{(a_{3}T+a_4)}[a_6{\left(\frac{e}{0.4}\right)}^{a_5}-(a_6-1)\left(\frac{e}{0.4}\right)]---\left(18\right)$

The temperature of steel plate when wherein, T is rolling;

E is the actual texturing process degree, and computing formula is suc as formula shown in (19)

$e=\ln \frac{h_{i-1}}{h_i},i=\mathrm{1,2},...,n---\left(19\right)$

u _mBe average deformation speed, computing formula is suc as formula shown in (20)

$u_m=\frac{v_i}{l_c}e,i=\mathrm{1,2},...,n---\left(20\right)$

v _iBe the mill speed of i frame, computing formula is suc as formula shown in (21)

$v_i=\frac{v_n{h}_n}{h_i},i=\mathrm{1,2},...,n---\left(21\right)$

v _nRoll linear velocity for last milling train;

h _nExit thickness for last milling train;

σ ₀, a ₁～a ₆Be regression coefficient.

T _iBe the rolling temperature of i milling train, computing formula is suc as formula shown in (22)

$\frac{T_i-T_W}{T_{F0}-T_W}=\exp (-K_a\frac{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{L}_i}{h_n{v}_n}),i=\mathrm{1,2},...,n---\left(22\right)$

L ₁-finish rolling inlet point for measuring temperature is to F ₁Distance;

L _i-i-1 frame is to the distance (i=2～7) of i frame; m

L _n-finish rolling end frame is to the distance of finish rolling outlet temperature measurer loca; m

T _WThe water temperature of spraying water between-frame;

K _a-comprehensive convection current cooling ratio;

T _F0-mm finishing mill unit porch estimated temperature, computing formula is suc as formula shown in (23)

${\mathrm{<figure-callout\; id="0"\; label="T\; F"\; filenames="HDA0000114341500000021.png,HDA0000114341500000022.png"\; state="\{\{state\}\}">T</figure-callout>}}_F=100{(\frac{6\mathrm{\&epsiv;\&sigma;}}{100\mathrm{\&gamma;}{\mathrm{<figure-callout\; id="0"\; label="c\; p\; h"\; filenames="HDA0000114341500000021.png,HDA0000114341500000022.png"\; state="\{\{state\}\}">c</figure-callout>}}_p{h}_{}{}_0}\mathrm{\&tau;}+{\left(\frac{T_{\mathrm{Rc}}}{100}\right)}^{-3})}^{-\frac{1}{3}}---\left(23\right)$

σ is this graceful constant of Si Difen-bohr;

ε is a blackness;

C _pBe specific heat capacity;

γ is a density;

τ is for exporting to the band steel run duration of finishing mill inlet from roughing mill;

h ₀Be roughing unit exit actual measurement thickness;

T _RCBe roughing unit exit observed temperature.

Step 3: confirm the parameter of the machine parameter and the rolled piece of control scheme, machine parameter comprises running time, the rated power of the work roll diameter of mm finishing mill unit, backing roll diameter, motor, the rated speed of motor, maximum rolling force and maximum rolling force square; The parameter of rolled piece comprises the width B of rolled piece, the supplied materials thickness H of rolled piece, the finished product thickness h of rolled piece, the outlet temperature TFC of roughing mill, finish rolling outlet temperature T.

Step 4: utilize improved differential evolution algorithm to obtain each frame exit thickness, concrete steps are following:

Step 4.1: the structure initial population, and population scale and iterations are set.Initial population of the present invention adopts real coding, and the step that initial population produces is following:

If have N n dimension individual in the population, each individual vectorial X _iRepresentation be X _i=[x _I1, x _I2, L, x _In].

Step 4.1.1: make x ₀₁=500, x _0n=-500,

Step 4.1.2: utilize formula (24) to calculate x _0j, obtain X ₀, X ₀=[x ₀₁, x ₀₂, L, x _0n].

x _0j＝x _0j-Slot，j＝2，3，L，n-1 (24)

Step 4.1.3: make i=1.

Step 4.1.4: utilize formula (25), with X ₀Be template, produce the individual X in the population _i, i=1,2, L, N.x _i1＝500，x _in＝-500，

x _ij＝x _0j+f·Slot，j＝2，3，L，n-1 (25)

In the formula, f is a random number, f ∈ (1,1).

Step 4.1.5:i=i+1.

Step 4.1.6: if i=N, then the initial population structure finishes; Otherwise, change step 4.1.4 over to.

Step 4.2: the individual vector of improved differential evolution algorithm is mapped to the solution vector space from real number space, and concrete steps are following:

Step 4.2.1: find out the maximum and the minimum of a value of each component among the individual vectorial X, be designated as x _MaxAnd x _Min, make v _Max=h ₀, v _Min=h _n, v wherein _MaxAnd v _MinBe respectively x _MaxWith x _MinThe corresponding component in decoding back; h ₀Be mm finishing mill unit strip steel at entry thickness; h _nBe mm finishing mill unit outlet belt steel thickness.For other component among the X, be mapped to solution space with formula (26):

$v_i=v_{\max }-\frac{(x_{\max }-x_i)}{(x_{\max }-x_{\min })}*(v_{\max }-v_{\min }),i=\mathrm{1,2},L,n,$

$i\&NotEqual;\max ,\min ---\left(26\right)$

Step 4.2.2: with the component (v of decoded intermediate vector V ₁, v ₂, L, v _n) by arranging from big to small.

Step 4.2.3: with the component v after arranging _iUpgrade solution vector U:u ₁=v _Max, L, u _n=v _Min

Step 4.3: for the solution vector after the decoding, if do not satisfy constraints, carry out and repair strategy, concrete steps are following:

Step 4.3.1:, then get into step 4.3.2 if decoded solution vector does not satisfy constraints; Otherwise, preserve current solution vector, finish to repair strategy.

Step 4.3.2: the drafts Δ h that calculates each corresponding frame of solution vector _i, and these drafts are arranged from big to small: Δ h ₁=Δ h _Max..., Δ h _n=Δ h _Min

Step 4.3.3: the drafts of redistributing for each frame, and recomputate the exit thickness of each frame, upgrade solution vector.x ₁＝h ₀+Δh ₁，x ₂＝x ₁+Δh ₂，......，x _n＝x _n-1+Δh _n。

Step 4.3.4: if the solution vector after upgrading can satisfy constraints, preserve current solution vector, finish to repair strategy; Otherwise, get into step 4.3.5.

Step 4.3.5: make i=n.

Step 4.3.6: the component x of inspection solution vector _iWhether satisfy constraints.If x _iDo not satisfy constraint, get into step 4.3.7, otherwise, step 4.3.9 got into.

Step 4.3.7:x _i=x _i-0.1, i=1,2, L, n.

Step 4.3.8: if x _i≤x _I+1(i=1,2, L n), changes step 4.3.11 over to; If x _iSatisfy constraint, then keep x _i, get into step 4.3.9; Otherwise, continue step 4.3.7.

Step 4.3.9:, finish to repair strategy if i=1 preserves current solution vector; Otherwise, get into step 4.3.10.

Step 4.3.10:i=i-1 gets into step 4.3.6.

Step 4.3.11: repairing failure, add a big penalty value to object function, abandon current separating.

Step 4.4: calculate each the individual fitness value in the population.The present invention will control target as the fitness function that calculates ideal adaptation degree value.

Step 4.5: inspection algorithm end condition.See whether fitness value reaches minimum, and satisfy the constraints that the present invention considers.If satisfy the algorithm end condition, then stop and export the optimum individuality of fitness value in the population; Otherwise, continue next step.

Step 4.6: the population to algorithm carries out mutation operation.For individual X _{I, G}: i=1,2, L, N, a new individual V _{I, G+1}But through type (27) produces:

$V_{i,G+1}={\mathrm{<figure-callout\; id="1"\; label="X\; r"\; filenames="HDA0000114341500000021.png,HDA0000114341500000022.png"\; state="\{\{state\}\}">X</figure-callout>}}_{r_{}}+F*({\mathrm{<figure-callout\; id="2"\; label="X\; r"\; filenames="HDA0000114341500000021.png,HDA0000114341500000022.png"\; state="\{\{state\}\}">X</figure-callout>}}_{r_{}}-{\mathrm{<figure-callout\; id="3"\; label="X\; r"\; filenames="HDA0000114341500000021.png,HDA0000114341500000022.png"\; state="\{\{state\}\}">X</figure-callout>}}_{r_{}})---\left(27\right)$

Wherein, r ₁, r ₂And r ₃Be to go up the mutually different integer of picked at random from interval [1, N], and be different from subscript index i, mutagenic factor F value is between [0,1].

Step 4.7: the population to algorithm carries out interlace operation.Interlace operation is suc as formula shown in (28).

$v_{i,j}^{G+1}=\left\{\begin{array}{c}{u}_{i,j}^{G+1},\mathrm{if}\left((\mathrm{randb}\left(j\right)\&le;\mathrm{CR})\mathrm{or}(j=\mathrm{mbr}\left(i\right))\right)\\ x_{i,j}^G,\mathrm{if}\left((\mathrm{randb}\left(j\right)>\mathrm{CR})\mathrm{and}(j\&NotEqual;\mathrm{mbr}\left(i\right))\right)\end{array}\right.,---\left(28\right)$

i＝1，2，L，N，j＝1，2，L，Dv

In the formula, the j dimension component that

is

; The j dimension component that

is

, the individuality that

produces for variation; The j dimension component that

is

,

is that parent is individual; Randb (j) is an equally distributed probability between [0,1]; An integer that generates at random between mbr (i) expression [1, Dv], CR is a crossover probability, generally gets the number between [0,2].Here

$\mathrm{CR}={\mathrm{CR}}_{\min }+\frac{g}{G}(1-{\mathrm{CR}}_{\min }\&CenterDot;\frac{F\left(X_i\right)}{F\left(U_i\right)+F\left(X_i\right)})---\left(29\right)$

In the formula, F (X _i) the individual fitness value of i parent of expression; F (U _i) fitness value of the variation individuality that i parent of expression is corresponding; CR _MinBe minimum crossover probability; G is a current iteration algebraically; G is an algorithm greatest iteration algebraically.

Step 4.8: selection operation is carried out in the filial generation in the population.The selection operation of differential evolution algorithm is between parent colony and progeny population, the individual and man-to-man competition of offspring individual of parent.The selection operation of algorithm is suc as formula shown in (30).

$X_i^{G+1}=\left\{\begin{array}{cc}{V}_i^{G+1},& \mathrm{if}(F\left(V_i^{G+1}\right)\&le;F\left(X_i^G\right))\\ X_i^G,& \mathrm{otherwise}\end{array}\right.,i=\mathrm{1,2},L,N---\left(30\right)$

Step 4.9: return step 4.2.

Step 5: what the exit thickness of each frame that obtains according to step 4 was confirmed each frame wears tape speed, temperature, roll-force, rolling power, total energy consumption.

Step 6: judge whether roll-force, roll torque, rolling power exceed the rated value of machine, exceed, and then repeating step 4, otherwise judge whether total energy consumption reaches minimum, is then to export end value, otherwise repeating step 4, up to reaching minimum of a value.

Beneficial effect: the present invention is optimized setting through improved differential evolution algorithm to the load of each frame of hot rolling production process; Reach the purpose that cuts down the consumption of energy; According to frame load distribution method of the present invention, the exit thickness of each frame, its result of rolling power are better than experience sharing of load result, simultaneously because the rolling power optimized distribution; Reduce equipment damage, improved production efficiency and utilization rate of equipment and installations.

Description of drawings

Sketch map is produced in the hot rolling of Fig. 1 iron and steel;

Fig. 2 embodiment of the invention frame load distribution method flow chart;

The rolling power of two kinds of each frames of method of Fig. 3 embodiment of the invention seven frames distributes contrast;

The rolling power of two kinds of each frames of method of Fig. 4 embodiment of the invention six frames distributes contrast.

The specific embodiment

Below in conjunction with embodiment and accompanying drawing the present invention is further specified.

Embodiment 1

With seven frame hot fine rolling unit production lines is example.Steel plate material is Q235, strip width B ₀Be 1535mm, belt steel thickness H ₀Be 36.7mm, finished product thickness h _nBe 5.7mm, roughing outlet temperature t _RCBe 1067 ℃, finish rolling outlet temperature t _FCBe 891 ℃, be 21s running time, the distance L=5.5m between frame, L ₁=14.5m, L ₈=8.5m, the coefficient of friction f=0.45 between roll and rolled piece, density γ=7800kg/m ³, this graceful constant σ=5.6662J/m of Si Difen-bohr ²SK ⁴, last frame is worn tape speed v ₇=10m/s, the machinery and the technological parameter of other capital equipments are seen table 1.

Table 1 mm finishing mill unit major parameter

Carry out the inventive method, specific as follows:

Step 1: confirm the constraints of control, constraints is shown below:

$\mathrm{\&Delta;}{h}_i<\mathrm{\&Delta;}{h}_{\max }=D(1-\frac{1}{\sqrt{1+f^2}}),i=1,...,7$

P _i＜P _imax i＝1，...，7

M _i＜M _imax i＝1，...，7

N _i＜N _imax i＝1，...，7

$-40{\left(\frac{h}{b}\right)}^{1.86}<\mathrm{\&Delta;}{\mathrm{CR}}_i<80{\left(\frac{h}{b}\right)}^{1.86},i=4,L,N$

Step 2: the target of confirming control.The target of the present invention control is to make total energy consumption reach minimum, the energy consumption calculation formula as shown in the formula:

$\min \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i,i=1,...,7,n=7$

Step 3: the parameter of confirming the machine parameter and the rolled piece of control scheme.Width B=the 1535mm that comprises rolled piece, the supplied materials thickness H=36.7mm of rolled piece, the finished product thickness h=5.7mm of rolled piece, the outlet temperature T of roughing mill _FC=1067 ℃, T=891 ℃ of finish rolling outlet temperature, running time τ=21s, the work roll diameter of mm finishing mill unit, the backing roll diameter, the rated power of motor, the rated speed of motor, maximum rolling force, the maximum rolling force square is as shown in table 1.

Step 4: utilize improved differential evolution algorithm to obtain the exit thickness of each frame, concrete steps are following:

Step 4.1: the structure initial population, and population scale and maximum iteration time are set.Population of the present invention is 60, and maximum iteration time is 1000, and initial population adopts real coding, and the step that initial population produces is following:

If have 60 7 dimensions individual in the population, each individual vectorial X _iRepresentation be X _i=[x _I1, x _I2, L, x _I7].

Step 4.1.1: make x ₁=500, x ₇=-500,

Step 4.1.2: utilize formula (24) to calculate x _j, obtain X ₀: X ₀=[x ₀₁, x ₀₂, L, x ₀₇].

x _j＝x _j-1-Slot，j＝2，3，L，6 (24)

Step 4.1.3: make i=1.

Step 4.1.4: utilize formula (25), with X ₀Be template, produce the individual X in the population _i, i=1,2, L, N.x _i1＝500，x _i7＝-500，x _ij＝x _0j+f·Slot，j＝2，3，L，6 (25)

In the formula, f is a random number, f ∈ (1,1).

Step 4.1.5:i=i+1.

Step 4.1.6: if i=N, then the initial population structure finishes; Otherwise, change step 4.1.4 over to.

Step 4.2: the individual vector of adaptive differential descent algorithm is mapped to the solution vector space from real number space.Concrete steps are following:

Step 4.2.1: find out the maximum and the minimum of a value of each component among the individual vectorial X, be designated as x _MaxAnd x _Min, make v _Max=h ₀, v _Min=h ₇(v _MaxAnd v _MinBe respectively x _MaxWith x _MinThe corresponding component in decoding back; h ₀Be mm finishing mill unit strip steel at entry thickness; h ₇Be mm finishing mill unit outlet belt steel thickness).For other component among the X, be mapped to solution space with formula (26):

$v_i=v_{\max }-\frac{(x_{\max }-x_i)}{(x_{\max }-x_{\min })}*(v_{\max }-v_{\min }),i=\mathrm{1,2},L,7,i\&NotEqual;\max ,\min ---\left(26\right)$

Step 4.2.2: with the component (v of decoded intermediate vector V ₁, v ₂, L, v ₇) by arranging from big to small.

Step 4.2.3: with the component v after arranging _iUpgrade solution vector U:u ₁=v _Max, L, u ₇=v _Min

Step 4.3: for the solution vector after the decoding, if do not satisfy constraints, the reparation strategy below adopting, concrete steps are following:

Step 4.3.1:, then get into step 4.3.2 if decoded solution vector does not satisfy constraints; Otherwise, preserve current solution vector, finish to repair strategy.

Step 4.3.2: the drafts Δ h that calculates each corresponding frame of solution vector _i, and these drafts are arranged from big to small: Δ h ₁=Δ _Max..., Δ h ₇=Δ h _Min

Step 4.3.3: the drafts of redistributing for each frame, and recomputate the exit thickness of each frame, upgrade solution vector.x ₁＝h ₀+Δh ₁，x ₂＝x ₁+Δh ₂，......，x ₇＝x ₆+Δh ₇。

Step 4.3.4: if the solution vector after upgrading can satisfy constraints, preserve current solution vector, finish to repair strategy; Otherwise, get into step 4.3.5.

Step 4.3.5: make i=7.

Step 4.3.6: the component x of inspection solution vector _iWhether satisfy constraints.If x _iDo not satisfy constraint, get into step 4.3.7, otherwise, step 4.3.9 got into.

Step 4.3.7:x _i=x _i-0.1.

Step 4.3.8: if x _i≤x _I+1, change step 4.3.11 over to; If x _iSatisfy constraint, then keep x _i, get into step 4.3.9; Otherwise, continue step 4.3.7.

Step 4.3.9:, finish to repair strategy if i=1 preserves current solution vector; Otherwise, get into step 4.3.10.

Step 4.3.10:i=i-1 gets into step 4.3.6.

Step 4.3.11: repairing failure, add a big penalty value to object function, abandon current separating.

Step 4.4: be each the individual fitness value that calculates in the population.The present invention adopts the fitness value function of control target as the adaptive differential descent algorithm; According to formula (6), calculate fitness value

Step 4.5: inspection algorithm end condition.See whether fitness value F reaches minimum, and satisfy the constraints that the present invention considers.If satisfy the algorithm end condition, then stop and export the optimum individuality of fitness value in the population; Otherwise, continue next step.

Step 4.6: the population to algorithm carries out mutation operation.For individual X _{I, G}: i=1,2, L, 60, one new individual V _{I, G+1}But through type (27) produces:

$V_{i,G+1}={\mathrm{<figure-callout\; id="1"\; label="X\; r"\; filenames="HDA0000114341500000021.png,HDA0000114341500000022.png"\; state="\{\{state\}\}">X</figure-callout>}}_{r_{}}+F*({\mathrm{<figure-callout\; id="2"\; label="X\; r"\; filenames="HDA0000114341500000021.png,HDA0000114341500000022.png"\; state="\{\{state\}\}">X</figure-callout>}}_{r_{}}-{\mathrm{<figure-callout\; id="3"\; label="X\; r"\; filenames="HDA0000114341500000021.png,HDA0000114341500000022.png"\; state="\{\{state\}\}">X</figure-callout>}}_{r_{}})---\left(27\right)$

Here r ₁, r ₂And r ₃Be to go up the mutually different integer of picked at random from interval [1, N], and be different from subscript index i, mutagenic factor F value is between [0,1].

Step 4.7: the population to algorithm carries out interlace operation.Interlace operation is suc as formula shown in (28).

$v_{i,j}^{G+1}=\left\{\begin{array}{c}{u}_{i,j}^{G+1},\mathrm{if}\left((\mathrm{randb}\left(j\right)\&le;0.4+\frac{g}{1000}(1-0.4\&CenterDot;\frac{F\left(X_i\right)}{F\left(U_i\right)+F\left(X_i\right)}))\mathrm{or}(j=\mathrm{mbr}\left(i\right))\right)\\ x_{i,j}^G,\mathrm{if}\left((\mathrm{randb}\left(j\right)>0.4+\frac{g}{1000}(1-0.4\&CenterDot;\frac{F\left(X_i\right)}{F\left(U_i\right)+F\left(X_i\right)}\left)\right)\mathrm{and}(j\&NotEqual;\mathrm{mbr}\left(i\right))\right)\end{array}\right.$

$i=\mathrm{1,2},L,60,j=\mathrm{1,2},L,7---\left(28\right)$

Step 4.8: selection operation is carried out in the filial generation in the population.The selection operation of differential evolution algorithm is between parent colony and progeny population, the individual and man-to-man competition of offspring individual of parent.The selection operation of algorithm is suc as formula shown in (30).

$X_i^{G+1}=\left\{\begin{array}{cc}{V}_i^{G+1},& \mathrm{if}(F\left(V_i^{G+1}\right)\&le;F\left(X_i^G\right))\\ X_i^G,& \mathrm{otherwise}\end{array}\right.,i=\mathrm{1,2},L,60---\left(30\right)$

Step 4.7: return step 4.2.

What the exit thickness of step 5, each frame of obtaining according to step 4 was confirmed each frame wears tape speed v, temperature T, roll-force P, rolling power N, total energy consumption F.

Step 4: judge whether roll-force, roll torque, rolling power exceed the rated value of machine, exceed, and then repeating step 4, otherwise judge whether total energy consumption reaches minimum, is then to export end value, otherwise repeating step 4, up to reaching minimum of a value.The sharing of load result of each frame that empirical method and the inventive method obtain is as shown in table 3.

Table 3 empirical method and the inventive method comparative result

From table 3 and Fig. 3; More reasonable than the sharing of load that obtains with empirical method with the inventive method, the general power of consumption also descends to some extent, and the object function that obtains with empirical method is 20992.55KW; Object function with the inventive method is 17825KW; Save energy consumption 3167.55KW, thereby method of the present invention is adopted in explanation, can reach the purpose of saving energy consumption.

Embodiment 2

If the milling train of hot fine rolling unit is not seven frames, the present invention also is suitable for.With six frame hot fine rolling unit production lines is example.Concrete steps change n into 6 with embodiment 1, each frame exit thickness, rolling power, roll-force, object function such as table 4 that sharing of load obtains, and the rolling power contrast that empirical method and the inventive method obtain is as shown in Figure 4.

Table 4 empirical method and improved difference algorithm comparative result

From table 4 and Fig. 4, more reasonable than the sharing of load that obtains with empirical method with the inventive method, the general power of consumption also descends to some extent; The object function that empirical method obtains is 22457.7KW; Object function with the inventive method is 18189.6KW, saves energy consumption 4268.1KW, and energy consumption reduces by 19%; Thereby explain and adopt method of the present invention, can reach the purpose of saving energy consumption.

Claims (5)

1. a frame load distribution method that reduces the strip hot rolling process energy consumption is characterized in that: specifically comprise the steps:

Step 1: confirm the constraints of initial control scheme, comprising:

(1) bite condition

Bite condition guarantees nipping smoothly of band steel, and rolling each reduction in pass should allow drafts less than maximum, and computing formula is suc as formula shown in (1)

$\mathrm{\&Delta;}{h}_i<\mathrm{\&Delta;}{h}_{\max }=D(1-\frac{1}{\sqrt{1+f^2}}),i=\mathrm{1,2},...,n---\left(1\right)$

Δ h wherein _iThe drafts of representing i frame; Δ h _MaxFor maximum allows drafts; F is the coefficient of friction between roll and rolled piece; D representes the diameter of roll;

(2) roll strength condition

For guaranteeing roll strength, draught pressure and roll torque are limited, guarantee can not surpass in the operation of rolling maximum roll-force and roll torque computing formula suc as formula shown in (2) formula (3):

P _i＜P _imax i＝i＝1，2，...，n (2)

M _i＜M _imax i＝1，2，...，n (3)

P wherein _iIt is the roll-force of i frame; P _ImaxIt is the maximum rolling force that i frame allows; M _iIt is the roll torque of i frame; M _ImaxIt is the maximum rolling force square that i frame allows;

(3) motor ability condition

The motor ability is the restrictive condition of motor overload, and rolling power must not surpass its rated power, and computing formula is suc as formula shown in (4)

N _i＜N _imax i＝1，2，...，n (4)

N wherein _iIt is the rolling power of i frame; N _ImaxIt is the maximum rolling power that i frame allows;

(4) strip shape quality restrictive condition

In order to keep strip shape quality to reach customer requirement, optimize the drafts of arranging several of backs, making between its corresponding roll-force has certain ratio, prevents to be with steel the limit wave to occur, and computing formula is suc as formula shown in (5)

$-40{\left(\frac{h_i}{b}\right)}^{1.86}<\mathrm{\&Delta;}{\mathrm{CR}}_i<80{\left(\frac{h_i}{b}\right)}^{1.86},i=n-3,n-2,n-1,n---\left(5\right)$

Δ CR wherein _iInlet convexity when passing through i frame for slab is poor with the outlet convexity; h _iIt is the exit thickness of i frame; B is the width of slab;

Step 2: confirming the target of control, is to make rolling total energy consumption reach minimum, and the energy consumption calculation formula is shown in (6) formula:

$\min \underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{N}_i,i=\mathrm{1,2},...,n---\left(6\right)$

Wherein: n-mm finishing mill unit frame number;

N _i-Di i frame power of motor;

Step 3: confirm the parameter of the machine parameter and the rolled piece of control scheme, machine parameter comprises running time, the rated power of the work roll diameter of mm finishing mill unit, backing roll diameter, motor, the rated speed of motor, maximum rolling force and maximum rolling force square; The parameter of rolled piece comprises the width B of rolled piece, the supplied materials thickness H of rolled piece, the finished product thickness h of rolled piece, the outlet temperature TFC of roughing mill, finish rolling outlet temperature T;

Step 4: utilize improved differential evolution algorithm to obtain each frame exit thickness;

Step 5: what the exit thickness of each frame that obtains according to step 4 was confirmed each frame wears tape speed, temperature, roll-force, rolling power, total energy consumption;

Step 6: judge whether roll-force, roll torque, rolling power exceed the rated value of machine, exceed, and then repeating step 4, otherwise judge whether total energy consumption reaches minimum, is then to export end value, otherwise repeating step 4, up to reaching minimum of a value.

2. the frame load distribution method of reduction strip hot rolling process energy consumption according to claim 1 is characterized in that: said step 4 utilizes improved differential evolution algorithm to obtain each frame exit thickness, and concrete steps are following:

Step 4.1: the structure initial population, and population scale and iterations are set;

Step 4.2: the individual vector of improved differential evolution algorithm is mapped to the solution vector space from real number space;

Step 4.3:,, carry out and repair strategy if do not satisfy constraints for the solution vector after the decoding;

Step 4.4: calculate each the individual fitness value in the population, with the fitness function of control target as calculating ideal adaptation degree value;

Step 4.5: inspection algorithm end condition, see whether fitness value reaches minimum, and satisfy constraints; If satisfy the algorithm end condition, then stop and export the optimum individuality of fitness value in the population; Otherwise, continue next step;

Step 4.6: the population to algorithm carries out mutation operation;

For individual X _{I, G}: i=1,2, L, N, a new individual V _{I, G+1}But through type (27) produces:

$V_{i,G+1}=X_{r_1,G}+F*(X_{r_2,G}-X_{r_3,G})---\left(27\right)$

Wherein, r ₁, r ₂And r ₃Be to go up the mutually different integer of picked at random from interval [1, N], and be different from subscript index i, mutagenic factor F value is between [0,1];

Step 4.7: the population to algorithm carries out interlace operation; Interlace operation is suc as formula shown in (28),

$v_{i,j}^{G+1}=\left\{\begin{array}{c}{u}_{i,j}^{G+1},\mathrm{if}\left((\mathrm{randb}\left(j\right)\&le;\mathrm{CR})\mathrm{or}(j=\mathrm{mbr}\left(i\right))\right)\\ x_{i,j}^G,\mathrm{if}\left((\mathrm{randb}\left(j\right)>\mathrm{CR})\mathrm{and}(j\&NotEqual;\mathrm{mbr}\left(i\right))\right)\end{array}\right.,---\left(28\right)$

i＝1，2，L，N，j＝1，2，L，Dv

In the formula, the j dimension component that is

; The j dimension component that is

, the individuality that

produces for variation; The j dimension component that

is

,

is that parent is individual; Randb (j) is an equally distributed probability between [0,1]; An integer that generates at random between mbr (i) expression [1, Dv], CR is a crossover probability, generally gets the number between [0,2]; Here

$\mathrm{CR}={\mathrm{CR}}_{\min }+\frac{g}{G}(1-{\mathrm{CR}}_{\min }\&CenterDot;\frac{F\left(X_i\right)}{F\left(U_i\right)+F\left(X_i\right)})---\left(29\right)$

In the formula, F (X _i) the individual fitness value of i parent of expression; F (U _i) fitness value of the variation individuality that i parent of expression is corresponding; CR _MinBe minimum crossover probability; G is a current iteration algebraically; G is an algorithm greatest iteration algebraically;

Step 4.8: selection operation is carried out in the filial generation in the population;

The selection operation of differential evolution algorithm is between parent colony and progeny population, parent individual with the man-to-man competition of offspring individual, the selection operation of algorithm is suc as formula shown in (30),

$X_i^{G+1}=\left\{\begin{array}{cc}{V}_i^{G+1},& \mathrm{if}(F\left(V_i^{G+1}\right)\&le;F\left(X_i^G\right))\\ X_i^G,& \mathrm{otherwise}\end{array}\right.,i=\mathrm{1,2},L,N---\left(30\right)$

Step 4.9: return step 4.2.

3. the frame load distribution method of reduction strip hot rolling process energy consumption according to claim 2 is characterized in that: the step that the said initial population of step 4.1 produces is following:

If have N n dimension individual in the population, each individual vectorial X _iRepresentation be X _i=[x _I1, x _I2, L, x _In],

Step 4.1.1: make x ₀₁=500, x _0n=-500,

Step 4.1.2: utilize formula (24) to calculate x _0j, obtain X ₀, X ₀=[x ₀₁, x ₀₂, L, x _0n];

x _0j＝x _0j-Slot，j＝2，3，L，n-1 (24)

Step 4.1.3: make i=1;

Step 4.1.4: utilize formula (25), with X ₀Be template, produce the individual X in the population _i, i=1,2, L, N, x _I1=500, x _In=-500,

x _ij＝x _0j+f·Slot，j＝2，3，L，n-1 (25)

In the formula, f is a random number, f ∈ (1,1);

Step 4.1.5:i=i+1;

Step 4.1.6: if i=N, then the initial population structure finishes; Otherwise, change step 4.1.4 over to.

4. the frame load distribution method of reduction strip hot rolling process energy consumption according to claim 2 is characterized in that: the individual vector of said step 4.2 evolution algorithm is mapped to the solution vector space from real number space, and concrete steps are following:

Step 4.2.1: find out the maximum and the minimum of a value of each component among the individual vectorial X, be designated as x _MaxAnd x _Min, make v _Max=h ₀, v _Min=h _n, v wherein _MaxAnd v _MinBe respectively x _MaxWith x _MinThe corresponding component in decoding back; h ₀Be mm finishing mill unit strip steel at entry thickness; h _nBe mm finishing mill unit outlet belt steel thickness; For other component among the X, be mapped to solution space with formula (26):

$v_i=v_{\max }-\frac{(x_{\max }-x_i)}{(x_{\max }-x_{\min })}*(v_{\max }-v_{\min }),i=\mathrm{1,2},L,n,$

$i\&NotEqual;\max ,\min ---\left(26\right)$

Step 4.2.2: with the component (v of decoded intermediate vector V ₁, v ₂, L, v _n) by arranging from big to small;

Step 4.2.3: with the component v after arranging _iUpgrade solution vector U:u ₁=v _Max, L, u _n=v _Min

5. the frame load distribution method of reduction strip hot rolling process energy consumption according to claim 2 is characterized in that: the described reparation strategy of step 4.3, and concrete steps are following:

Step 4.3.1:, then get into step 4.3.2 if decoded solution vector does not satisfy constraints; Otherwise, preserve current solution vector, finish to repair strategy;

Step 4.3.2: the drafts Δ h that calculates each corresponding frame of solution vector _i, and these drafts are arranged from big to small: Δ h ₁=Δ h _Max..., Δ h _n=Δ h _Min

Step 4.3.3: the drafts of redistributing for each frame, and recomputate the exit thickness of each frame, upgrade solution vector; x ₁=h ₀+ Δ h ₁, x ₂=x ₁+ Δ h ₂..., x _n=x _N-1+ Δ h _n

Step 4.3.4: if the solution vector after upgrading can satisfy constraints, preserve current solution vector, finish to repair strategy; Otherwise, get into step 4.3.5;

Step 4.3.5: make i=n;

Step 4.3.6: the component x of inspection solution vector _iWhether satisfy constraints, if x _iDo not satisfy constraint, get into step 4.3.7, otherwise, step 4.3.9 got into;

Step 4.3.7:x _i=x _i-0.1, i=1,2, L, n;

Step 4.3.8: if x _i≤x _I+1(i=1,2, L n), changes step 4.3.11 over to; If x _iSatisfy constraint, then keep x _i, get into step 4.3.9; Otherwise, continue step 4.3.7;

Step 4.3.9:, finish to repair strategy if i=1 preserves current solution vector; Otherwise, get into step 4.3.10;

Step 4.3.10:i=i-1 gets into step 4.3.6;

Step 4.3.11: repairing failure, add a big penalty value to object function, abandon current separating.

Images