CN103823925A - Blast furnace top pressure control nonlinear mathematical modeling method - Google Patents

Abstract

The invention discloses a blast furnace top pressure control nonlinear mathematical modeling method. Mechanism analysis is performed on the blast furnace top pressure control process, influences on the blast furnace top pressure by changes in factors such as turbine stationary blade opening, blast furnace gas flow, and blast furnace production physical process are comprehensively considered, accordingly the blast furnace top pressure control process is described accurately and effectively through a mathematical model, and important significance is provided to blast furnace top pressure control scheme optimization, blast furnace stable production, and yield increase and quality improvement of blast furnace production.

Description

A kind of blast furnace top pressure control nonlinear mathematical modeling method

Technical field

The present invention relates to blast furnace top pressure control field, particularly a kind of blast furnace top pressure control nonlinear mathematical modeling method.

Background technology

Top gas pressure recovery turbine electricity generation system (TRT) is a kind of pressure energy and heat energy that utilizes top gas, the system that drives generator or miscellaneous equipment to carry out energy recovery by turbine expansion, as shown in Figure 1, blast furnace gas by gravitational dust collection and dry method dust after, enter TRT system and reduction valve group (TRT system is relation in parallel with reduction valve group), finally enter gas main road.System, to reducing blast furnace energy consumption, improves capacity usage ratio significant, also plays the effect of stablizing blast furnace top pressure simultaneously.System is as the efficient secondary energy retracting device of one, and the prerequisite of its operation is to guarantee the stability of blast furnace top pressure.Setting up blast furnace top pressure control system mathematical model is accurately the necessary condition of the blast furnace top pressure control program of excellent in design, it to stablize blast furnace top pressure, improve blast furnace produce output and quality significant.

As shown in Figure 2, when nominal situation, blast furnace gas enters blast furnace top pressure system to blast furnace top pressure system, enters turbine expansion acting by variable stator vane angle, and the gas after expansion enters gas main.Valve shield (closing when nominal situation, when press or front pressure is just opened with relief pressure during higher than certain threshold value on top) is left on quick-opening valve and side.

The mathematical model that research is set up for this object both at home and abroad is at present all to obtain by each blast furnace system process model binding analysis, complex structure, and often fail to react intuitively blast furnace top pressure control procedure; Research does not both at home and abroad take the method for parameter identification to carry out determining of model parameters to blast furnace top pressure model, and model is often difficult to have practicality.

Summary of the invention

Technical matters to be solved by this invention is, for prior art deficiency, provides a kind of blast furnace top pressure control nonlinear mathematical modeling method,

For solving the problems of the technologies described above, the technical solution adopted in the present invention is: a kind of blast furnace top pressure control nonlinear mathematical modeling method, and the method is:

1) determine the relation between blast furnace top pressure system stator blade circulation area F and stator blade aperture L:

F=K _fL+k ₀；

Wherein, K _f, k ₀be constant;

2) determine described stator blade gas flow Q ₂with top gas flow Q ₁between relation:

$Q_2=\frac{\sqrt{2}\mathrm{AF}}{\sqrt{\mathrm{\ξ}}}\sqrt{\frac{\mathrm{\Δp}}{\mathrm{\ρ}}};$

Wherein, A is constant; ρ is coal gas density; ξ is the resistance coefficient of stator blade to Gas Flow; △ p=p ₁-p ₂, p ₁for blast furnace top pressure actual value; p ₂for coal gas is by the pressure of blast furnace gas main pipe after blast furnace top pressure system;

3) utilize stator blade gas flow Q ₂with top gas flow Q ₁obtain blast furnace top pressure actual value p ₁differential expressions:

$\frac{{\mathrm{dp}}_1}{\mathrm{dt}}=K(Q_1-Q_2);$

Wherein, K is constant;

4) by step 2) the formula of formula substitution step 3) in, obtain: $\frac{{\mathrm{dp}}_1}{\mathrm{dt}}=-K\frac{\sqrt{2}\mathrm{AF}}{\sqrt{\mathrm{\ξ}}}\sqrt{\frac{p_1-p_2}{\mathrm{\ρ}}}+{\mathrm{KQ}}_1;$

5) by the formula of the formula substitution step 4) of step 1), obtain:

$\frac{{\mathrm{dp}}_1}{\mathrm{dt}}=-K\frac{\sqrt{2}A}{\sqrt{\mathrm{\ξ}}}(K_{f}L+k_0)\sqrt{\frac{p_1-p_2}{\mathrm{\ρ}}}+{\mathrm{KQ}}_1;$

6), by the formula discretize of step 5), obtain the discrete expression of blast furnace top pressure actual value:

$p_1\left(k\right)=p_1(k-1)+\mathrm{aL}\left(k\right)\·\sqrt{p_1\left(k\right)-15}+{\mathrm{bQ}}_1\left(k\right)+c\sqrt{p_1\left(k\right)-15}+d;$

Wherein, a, b, c, d are constant, utilize least square method to determine a, b, c, d; p ₁(k) be k moment blast furnace top pressure actual value; L (k) is k moment stator blade aperture; Q ₁(k) be k moment top gas flow.

Coal gas is by the pressure p of blast furnace gas main pipe after blast furnace top pressure system ₂span be 10KPa-15KPa.

Utilize least square method to determine that the concrete steps of a, b, c, d are as follows:

1) set up following criterion function

$J\left(\widehat{\mathrm{\θ}}\right)=\frac{1}{2}\underset{k=1}{\overset{2000}{\mathrm{\Σ}}}{(Y\left(k\right)-p_1\left(k\right))}^2;$

Wherein, Y (k) is k moment blast furnace top pressure measured value; θ is the procedure parameter vector that needs identification, θ=[a, b, c, d];

2) use simplicial method to try to achieve and make criterion function minimum procedure parameter vector estimator

Compared with prior art, the beneficial effect that the present invention has is: the present invention carries out Analysis on Mechanism to blast furnace top pressure control procedure, the impact of the variation that has considered the factors such as turbine stator blade aperture, blast furnace gas flow, blast furnace production physical process on blast furnace top pressure, thereby describe accurately and efficiently blast furnace top pressure control procedure by mathematical model, thereby had great importance along output and the quality of producing, improve blast furnace production for optimizing the steady of blast furnace top pressure control program assurance blast furnace; The present invention carries out Analysis on Mechanism to blast furnace top pressure system, has set up the mathematical model of simplifying, and can reflect intuitively the relation of blast furnace top pressure and stator blade aperture; Take least square method to carry out identification of Model Parameters, this mechanism model has practicality, for blast furnace top pressure control program provides good theoretical foundation.

Accompanying drawing explanation

Fig. 1 is TRT blast furnace system process flow diagram of the present invention;

Fig. 2 is stock gas path schematic diagram of the present invention;

Fig. 3 is mode input of the present invention (turbine stator blade aperture) change curve;

Fig. 4 is model disturbance input (blast furnace gas flow) change curve of the present invention;

Fig. 5 is blast furnace top pressure mechanism model simulation data of the present invention and actual output comparison diagram.

Embodiment

For being greater than 2000m ³large blast furnace, the present invention, by the Analysis on Mechanism to blast furnace top pressure control procedure, sets up Nonlinear Mechanism model, adopts least square method to carry out parameter identification to model, utilize the reliability of the method validation model of data detection, realize the quantitative description to blast furnace top pressure control.

(1) blast furnace top pressure control procedure Analysis on Mechanism

According to the Ideal-Gas Equation: PV=nRT

Volume and gaseous tension one timing, closed container pressure is directly proportional to other amount of substances in container, so can obtain:

$\mathrm{\ΔP}=\frac{\mathrm{RT}}{V}\mathrm{\Δn};$

Obtain for blast furnace top pressure p ₁with coal gas by the pressure p of blast furnace gas main pipe after blast furnace top pressure system ₂dynamic equation:

$\frac{{\mathrm{dp}}_1}{\mathrm{dt}}=K(Q_1-Q_2)---\left(1\right)$

Wherein, K is the constant relevant with system of units calculating according to volume, temperature, gas law constant; Q ₁for blast furnace top pressure gas flow, Q ₂for by the gas flow of stator blade, Q ₁can regard the disturbance input of blast furnace top pressure system as;

From conservation of energy principle, the pressure loss on variable valve (stator blade) is:

$h=\frac{p_1-p_2}{\mathrm{\ρg}}=\mathrm{\ξ}\frac{{\mathrm{\ω}}^2}{2g}$

According to the relation of valve and gas differential pressure

can obtain regulating valve flow equation:

$Q=\frac{\mathrm{AF}}{\sqrt{{\mathrm{\ξ}}_v}}\sqrt{\frac{p_1-p_2}{\mathrm{\ρ}}}---\left(2\right)$

If stator blade circulation area is F, stator blade aperture is L, by blast furnace top pressure system, as shown in Figure 2, can establish:

F=f（L），P ₁=f（F）；

According to the linear structure characteristic of stator blade, can obtain the linear relation of F and L:

$\frac{\mathrm{dF}}{\mathrm{dL}}=K_f$

Integration obtains:

F=K _fL+k ₀ (3)

Derive and obtain by (2): $Q_2=\frac{\sqrt{2}\mathrm{AF}}{\sqrt{\mathrm{\ξ}}}\sqrt{\frac{\mathrm{\Δp}}{\mathrm{\ρ}}}---\left(4\right)$

Through type (1) is derived, and has: $\frac{{\mathrm{dp}}_1}{\mathrm{dt}}=K(Q_1-Q_2)---\left(5\right)$

(4) substitution (5) is obtained: $\frac{{\mathrm{dp}}_1}{\mathrm{dt}}=-K\frac{\sqrt{2}\mathrm{AF}}{\sqrt{\mathrm{\ξ}}}\sqrt{\frac{p_1-p_2}{\mathrm{\ρ}}}+{\mathrm{KQ}}_1---\left(6\right)$

Again (3) substitution (6) is obtained: $\frac{{\mathrm{dp}}_1}{\mathrm{dt}}=-K\frac{\sqrt{2}A}{\sqrt{\mathrm{\ξ}}}(K_{f}L+k_0)\sqrt{\frac{p_1-p_2}{\mathrm{\ρ}}}+{\mathrm{KQ}}_1---\left(7\right)$ (2) mechanism model parameter identification pre-service

Because mechanism model form is continuous, it is the discrete data in interval 1s sampling time that data are pressed on top, thus model is carried out to discretize, and the each parameter of definite model:

$\frac{p_1\left(k\right)-p_1(k-1)}{1}=\mathrm{aL}\left(k\right)\·\sqrt{p_1\left(k\right)-p_2}+{\mathrm{bQ}}_1\left(k\right)+c\sqrt{p_1\left(k\right)-p_2}+d---\left(8\right)$

In formula (8), Q ₁(k) regard the disturbance input of model as, due to p ₂for gas main pressure, change very littlely, fluctuation range is 10KPa-15KPa, gets 15KPa, so model can be rewritten into:

$p_1\left(k\right)=p_1(k-1)+\mathrm{aL}\left(k\right)\·\sqrt{p_1\left(k\right)-15}+{\mathrm{bQ}}_1\left(k\right)+c\sqrt{p_1\left(k\right)-15}+d---\left(9\right)$

Wherein, a, b, c, d are constant.

(3) mechanism least square identification

Choose near 2000 groups of continuous input vector U working point _k=[L (k), Q ₁(k)] (k=1,2 ... 2000), by input vector substitution discriminant equation:

$J\left(\widehat{\mathrm{\θ}}\right)=\frac{1}{2}\underset{k=1}{\overset{2000}{\mathrm{\Σ}}}{(Y\left(k\right)-p_1\left(k\right))}^2;$

Wherein, Y (k) is k moment blast furnace top pressure measured value; θ is the procedure parameter vector that needs identification, θ=[a, b, c, d]; for the estimator of procedure parameter vector θ.

Use simplicial method to try to achieve and make criterion function value

minimum parameter estimation vector

Parameter estimation vector

be the nonlinear least-square estimated value of model parameter, try to achieve model least square method estimate vector and be through deriving:

[a,b,c,d]=[-0.0176,5.0789·10 ^-5,-46.1392,671.4824]

By a, b, c, the value of d can obtain in blast furnace top pressure modular form (7):

K=5.0789×10 ^-5， $\frac{{\mathrm{<figure-callout\; id="0"\; label="K\; f\; k"\; filenames="HDA0000462238190000021.png,HDA0000462238190000022.png"\; state="\{\{state\}\}">K</figure-callout>}}_f}{k_{}}=3.8\&times;{10}^{-4},\frac{A}{\sqrt{\mathrm{\&xi;\&rho;}}}\&times;K_f=220,\frac{A}{\sqrt{\mathrm{\&xi;\&rho;}}}\&times;{\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HDA0000462238190000021.png,HDA0000462238190000022.png"\; state="\{\{state\}\}">k</figure-callout>}}_0=576740$

(4) model emulation

Determine that mechanism model detailed process is as follows:

(1) utilize priori and blast furnace top pressure technique to derive the mathematical model expression formula that contains undetermined parameter;

(2) 2000 of collection site actual motion groups of data, set undetermined parameter a, b, c, the initial value of d;

(3) by on-the-spot actual operating data, use simplicial method, utilize formula (12) training data, according to the condition of convergence, obtain the minimum value of criterion function value J;

(4) determine parameter a, b, c, the approximate optimal solution of d.

(5) reliability of the method validation mechanism model of employing data detection: choose at random not 2000 group data sets from collection in worksite for modeling, comprise mode input amount: turbine stator blade aperture (%), blast furnace gas flow (m ³); Model output quantity: blast furnace top pressure (KPa), build emulation platform, by turbine stator blade aperture (cut select 200 groups of data) (Fig. 3), blast furnace gas flow (Fig. 4) data and curves inputting mathematical model obtains the analogous diagram of blast furnace top pressure, the accuracy of the contrast verification model by blast furnace top pressure actual curve and simulation curve tendency.

As seen from Figure 5, blast furnace top pressure simulation curve and actual curve tendency are substantially identical, and fitting effect is more satisfactory, and surperficial mechanism model has higher fitting precision.

Claims (5)

1. a blast furnace top pressure control nonlinear mathematical modeling method, is characterized in that, the method is:

1) determine the relation between blast furnace top pressure system stator blade circulation area F and stator blade aperture L:

F=K _fL+k ₀；

Wherein, K _f, k ₀be constant;

2) determine described stator blade gas flow Q ₂with top gas flow Q ₁between relation:

$Q_2=\frac{\sqrt{2}\mathrm{AF}}{\sqrt{\mathrm{\&xi;}}}\sqrt{\frac{\mathrm{\&Delta;p}}{\mathrm{\&rho;}}};$

Wherein, A is constant; ρ is coal gas density; ξ is the resistance coefficient of stator blade to Gas Flow; △ p=p ₁-p ₂, p ₁for blast furnace top pressure actual value; p ₂for coal gas is by the pressure of blast furnace gas main pipe after blast furnace top pressure system;

3) utilize stator blade gas flow Q ₂with top gas flow Q ₁obtain blast furnace top pressure actual value p ₁differential expressions:

$\frac{{\mathrm{dp}}_1}{\mathrm{dt}}=K(Q_1-Q_2);$

Wherein, K is constant;

4) by step 2) the formula of formula substitution step 3) in, obtain: $\frac{{\mathrm{dp}}_1}{\mathrm{dt}}=-K\frac{\sqrt{2}\mathrm{AF}}{\sqrt{\mathrm{\&xi;}}}\sqrt{\frac{p_1-p_2}{\mathrm{\&rho;}}}+{\mathrm{KQ}}_1;$

5) by the formula of the formula substitution step 4) of step 1), obtain:

$\frac{{\mathrm{dp}}_1}{\mathrm{dt}}=-K\frac{\sqrt{2}A}{\sqrt{\mathrm{\&xi;}}}(K_{f}L+k_0)\sqrt{\frac{p_1-p_2}{\mathrm{\&rho;}}}+{\mathrm{KQ}}_1;$

6), by the formula discretize of step 5), obtain the discrete expression of blast furnace top pressure actual value:

$p_1\left(k\right)=p_1(k-1)+\mathrm{aL}\left(k\right)\&CenterDot;\sqrt{p_1\left(k\right)-15}+{\mathrm{bQ}}_1\left(k\right)+c\sqrt{p_1\left(k\right)-15}+d;$

Wherein, a, b, c, d are constant, utilize least square method to determine a, b, c, d; p ₁(k) be k moment blast furnace top pressure actual value; L (k) is k moment stator blade aperture; Q ₁(k) be k moment top gas flow.

2. blast furnace top pressure control nonlinear mathematical modeling method according to claim 1, is characterized in that described step 2) in, coal gas is by the pressure p of blast furnace gas main pipe after blast furnace top pressure system ₂span be 10KPa-15KPa.

3. blast furnace top pressure control nonlinear mathematical modeling method according to claim 2, is characterized in that, coal gas is by the pressure p of blast furnace gas main pipe after blast furnace top pressure system ₂for 15KPa.

4. according to the blast furnace top pressure control nonlinear mathematical modeling method one of claim 1～3 Suo Shu, it is characterized in that, in described step 6), utilize least square method to determine that the concrete steps of a, b, c, d are as follows:

1) set up following criterion function

$J\left(\widehat{\mathrm{\&theta;}}\right)=\frac{1}{2}\underset{k=1}{\overset{2000}{\mathrm{\&Sigma;}}}{(Y\left(k\right)-p_1\left(k\right))}^2;$

Wherein, Y (k) is k moment blast furnace top pressure measured value; θ is the procedure parameter vector that needs identification, θ=[a, b, c, d];

for the estimator of procedure parameter vector θ;

2) use simplicial method to try to achieve and make criterion function

minimum procedure parameter vector estimator

5. blast furnace top pressure control nonlinear mathematical modeling method according to claim 4, is characterized in that

[a,b,c,d]=[-0.0176,5.0789×10 ^-5,-46.1392,671.4824]。

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