Identification and Prediction of Temperature Difference Across Blast Furnace Bottom by AR Model for Control of Tapping Operation

Copyright © IF .\C Auto!llation in \Iillill~ . Mineral and ~Ietal Processing. Tok yo , Japan 1986

IDENTIFICATION AND PREDICTION OF TEMPERATURE DIFFERENCE ACROSS BLAST FURNACE BOTTOM BY AR MODEL FOR CONTROL OF TAPPING OPERATION K. Asano*, M. Kondo* and T. Sawada** */II.1'lr/llllmlalioll & COlllro! Rr;ra rrh DfparllllNII. Terhllira! Rl'.I'NlI'ch Dh 'i.l'ioll . Kawa;aki Slfe! Curpumlioll. Chiba. japall **lrolll/wkillg Dfpa rl III fII I. Chiha \\'urks. Kawa.w ki SIn'! Corporalioll, Chiba. japall

Abstract. The temperature difference through the bottom plate of a blast furnace is a performance criterion for tapping operations, because it is believed to be closely correlated with factors influencing slag drainage. A statistical model which represents dynamic behavior of the temperature difference is identified by applying a multivariable autoregressive model. It clarifies the relationship between the temperature difference and manipulated variables. The model is used to predict the temperature difference, showing that it can explain more than 80% of the variance of the temperature difference. Responses of the temperature difference are simulated in some t y pical cases of change of input variables which are probably adopted in actual operation. The model can guide realistic improvements of tapping operations. Keywords. Blast furnace; Identification; Modelling; Prediction; Steel industry; Tapping Operations; Temperature control

INTRODUCTION

variables of the BF are manipulated to control quality and quantity of liquid iron. Moreover, using physical considerations, quantitive evaluation of such operations is impossible, because phenomena in furnace bottoms are very complicated and fluctuation of DT is due to the accumulated results of daily operation of the BF. This paper sets forth a statistical model which represents dynamic behavior of DT by applying a multivariable autoregressive model. It clarifies relationships between DT and manipulated variables, such as blast volume, blast moisture, ore/coke ratio, slag basicity and so on. Data analysis was made for No.S blast furnace at Chiba Works.

Drainage of liquid iron and slag from the hearth of ironmaking blast furnaces (BF) is one of the major concerns of blast f urnace operators, because good drainage is needed for stable operation. Experimental and theoretical studies on fundamental mechanisms of drainage were carried out to improve drainage in recent operations(Fukutake 1976a, b; Burgess 1981; Ohno 1981) . But, process control aspects of this problem were not discussed sufficiently. According to our observations, with an increase in the temperature difference through the furnace bottom plate, the period of slag draining in one drainage becomes l onger, resulting in a lower level of residual liquids in the hearth.

TEMPERATURE DIFFERENCE THROUGH THE FURNACE BOTTOM AND TAPPING OPERATIONS

The temperature difference (DT) is physically equivalent to the downward heat flux flowing from the central core of the hearth, so it is affected by physical conditions of the furnace bottom, such as the amount of deadman, size of raceway, fluidity of iron and slag, temperature of fluid and raceway, wear of bottom refractories, and so on.

Temperature difference through the furnace bottom plate (DT) is the difference between temperatures measured by two thermocouples, one installed on the upper side of the bottom plate, and another installed on the underside. Figure 1 illustrates schematically a cross section of a blast furnace and the thermocouples used for measuring DT. Ohno, Nakamura and others (1981) studied the relation between iron flow and skull (solidified iron, coke and deposited graphite mixed layer) on the hearth brick. They reported that change of skull thickness was closely related to the iron flow in the hearth and caused large temperature fluctuation at the bottom of hearth. The iron flow was related not to draining but rather to wear of hearth brick .

Conversely, OT can be manipulated by changing conditions mentioned above. For example, in usual operation of a blast furnace, when condition of drainage becomes worse, ore/coke ratio is reduced and blast volume is increased to increase the temperature of the fluid and raceway, or slag basicity is decreased to increase fluidity of slag. Such operations may be effective to improve drainage, but they cannot always be taken, because the input

223

K. Asano, M. Kondo and T . Sawada

224

In each drainage. liquid iron flows out firstly and then slag begins to flow out with iron. If the start of slag tapping delays. residual liquids in the hearth increase at the end of drainage and the period of each drainage becomes short. which causes the increase in cost of tapping operations. Therefore. ratio of slag tapping period to the whole drainage is a performance index for tapping operations. According to our observations. DT has a positive correlation with the ratio. Figure 2 shows the relation between DT and the ratio. Figure 3 shows that the ratio increases with the increase of DT. which means that the tapping operation becomes stable. Therefore. DT can be an index of tapping operation. and controlling it can stabilize BF operation.

/tuyere ____ tap hole

AUTORECRESSIVE MODEL

r--~---I-===!:;;===t_/ a

pair of thermocouples used for measuring DT

Autoregressive model Autoregressive (AR) model is a method of describing characteristics of a time series {x(s); s-I. 2 ••• • • N} and has the form

Fig. I.

Cross sectional view of blast furnace

M

x(s) - L a(m)x(s-m) + e(s) m-I

1.0,...-----------::::r---,

(1)

where e(s) is normally independently distributed with mean of zero and variance of 0e 2 • And e(s) is independent of e(s-I). e(s-2) •..•• x(s-I). x(s-2). so e(s) is called a discrete white noise.

0 .9

0.8

The least squares estimates of a(m) are obtained by solving the Yu1e-Waker equation M L

0.7 Chiba 6BF

r(l-m)a(m) - r(l)

_I

(1 - I. 2 •••.• M)

(2)

where r(l) is the covariance of x(s-l) and x(s). A criterion called the Finite Prediction Error (FPE) is applicable to determine the order of an AR model. Le ••

°M2

Fig. 2.

Relation between DT and ratio of the slag tapping period to the whole drainage (R).

14r----------------~

where 0M2 is the variance of least squares estimate error e(s) when an AR model of the M-th order is adopted. The optimal value of M is that which minimizes the FPE (Akaike 1970). In the case of mu1tivariab1es. the AR model of the k-th dimension is described using a vector notation:

10 ~/+"V v'\JV' ~"§;J 10'[,,_ s: . ."&_...,._--_ . ...._~_~_CJ'_......... _ , , .. _~_=_=: : : :=-: . : : ! IJ

r

"[[_.".--""",..,:o..-_~-A..-:?-Jv "1_

0.5 M

x(s) - L A(m)x(s-m) + e(s) m-I

(4 )

o

where x(s) - (Xl (5). X (s) ••. • • 2

f:l1

A(m)

=

a

21

(m) (m)

u,.)

~(s»

,

a (m) 12 a (m) 22

alk(m)l a (m) 2k

a

,~,.,j

k2

(m)

e(s) - (e l (s). e 2 (s) •••.• ek(s»'

(S)

10

20

May

Fig. 3.

30

10 20 30 June

10

20

July

30

10

20

August

Transition of DT and performance criteria of drainage.

30

Identificalion and PrediClion of Temperalure Differance Across Blasl Furnace BOllom RESULTS OF IDENTIFICATION OF THE MODEL

x : BV 2 eO: residual

Data Used For Analysis

Model 11 was described by the following AR model:

Data used for analysis were gathered from No.5 blast furnace at Chiba Works. All data were gathered and averaged as data for every 10 days. The manipulated variables are as follows: ore/coke ratio (OC), blast volume (BV), blast moisture (BM), blast speed at the tuyere (BS), MgO content of slag (MgO), slag basicity (B2), and Al 0 content of slag (AI 2 0,)' 2 3 These variables can be dividea Into two groups, Group I and Group 11. Group I consists of variables concerning the charging conditions and the blast; i.e., OC, BV, BM and BS. Group 11 consists of variables concerning slag composition; i.e., MgO, B2 and A1 0 . Variables 2 3 of Group I are maneuverable in the usual BF operation in itself, but to manipulate variables of Group 11, operations in the sintering process are needed, so Group I variables allow easier manipulation. For this reason, three models were considered. In Model I, variables of Group I were considered as inputs. In Model 11, Group 11 variables were considered. In Model Ill, both Group 11 and Group III variables were considered. Data for 50 consecutive periods were used for identification of the models. Table 1 shows averages and variances of variables. TABLE 1

Average

xO(s) - 1.327x (s-1) - 0.449x (s-2) O O

+ 1.997x 1 (s-l) - 0.540x (s-2) 1 + 51.74x 2 (s-1) - 57.00x (s-2) 2 + 2.781x 3 (s-1) + 0.695x (s-2) 3

+ eO (s)

(22)

Model III was described by the following AR model: xO(s)

~

1.426x (s-1) - 0.653x (s-2) O O

+ 26.56x (s-l) - 50.56x (s-2) 1 1 - 0.028x (s-1) + 0.024x (s-2) 2 2 - 0.176x (s-1) + 0.438x (s-2) 3 3 - 0.060x (s-1) + 0.192x (s-2) 4 4

+ 4.735x (s-1) - 1.000x (s-2) 5

5

- 22.89x (s-1) - 11.22x (s-2) 6 6

Data Used for Anal;tsis

Unit

+ 2.382x (s-1) + 0.416x (s-2) 7 7

Mean dev.

+ eo(s) DT

·C

225

25.9

(23)

19.1 xl: OC

3.38

OC BV

Nm 3/min

3347.0

BM

g/Nm 3

28.9

BS

m/sec

255.7

A1 0 2 3

%

%

x

4

: IlS

x : MgO 7

267.0

Although the models were obtained in the form of (17), only the parts in which DT was considered as the output were shown.

8.46 16.2

14.6

B2 MgO

0.0735

0.448

Prediction of the Temperature Difference

1.17

0.0335

7.26

0.539

The models can be readily used to compute forecasts or predictions of DT. Figures 5, 6 and 7 show results of one step ahead prediction of 15 consecutive periods by each model.

Results of Identification In Model I, minimum MFPE was obtained when the order of the model, M, was 2. Minimum MFPE was obtained when M was 1 in Model 11 and Model Ill, but the MFPE scarcely increased when M was increased from 1 to 2 in both cases. So M = 2 was adopted as the order of each model, resulting in easy comparison of the three models.

Mean deviation of the prediction errors (measured value - predicted value) was 4.94 degrees in Model I, 3.49 degrees in Model 11, 4.54 degrees in Model Ill. Mean deviation of DT of these 15 periods is 13.2 degrees. Variance of DT can be divided into two parts, one is the part which the model can explain, the other is the part the model cannot explain. So, ratio of the former to the whole variance becomes 86.0% in the case of Model I, 93.0% in the case of Model 11, 88.2% in the case of Model Ill. Difference is small in the accuracy of the prediction by each model.

Model I was described by the following AR model: x (s) o

1.412x (s-1) O

0.641x (s-2) O

+ 5.880x (s-1) - 43.99x (s-2)

Noise Power Contribution Anal;tsis

- 0.020x (s-U + O.019x (s-2) 2 2

Figures 8, 9 and 10 show results of noise power contribution analysis. In Model I, the ratio of the noise of DT itself is relatively large especially in the medium frequency range. Manipulation of B5 and OC seems to be effective for long-term control of DT. In Model 11, the ratio of the noise of DT itself is larger than that in Model I, which means that changes of

1

1

- 0.361x (s-l) + 0.439x (s-2) 3 3 - 0.024x (s-1) + 0.090x (s-2) 4 4

+ eo(s)

(21)

K, Asano, M, Kondo and T. Sawada

226

Elements of e(s) are normally independently distributed white noises. Elements of A(m) are obtained by solvin~

M

u(s)

( (2)

L H(m)y(s-m) + w(s)

m-I L

(6 )

w(s)

L F(l)w(s-l) + n (s)

(13)

I-I

(h - I. 2 •...• k)

(1 - I. 2 •...• M)

where r (1) is the covariance of xj(s-l) and x (s). i to determine the order of tne model M. t~e Multidimensional Finite Prediction Error (MFPE) is available instead of FPE. i.e •• MFPE(M) _

1~~:~~:~lkdet

where n(s) is a vector whose elements are normally independently distributed white noises. Then, L M+L u(s) L F(l)u(s-l) + L B(m)y(s-m) + n(s) (14) I-I m-I holds, where

E(M)

(7)

B(I)

!N-(kM+I)

H(m)

m-I H(m) - L F(l)H(m-l) (m I-I 0 for m > M

F(l)

0

B(m)

where det E(M) is the dete~inant of the covariance matrix of e(s) (Akaike (971). If the process which is to be identified consists of a feedback system as shown in Fig. 4. the process is approximated by

HO)

Define (8)

"G(m)u(s-m) + v(s) m-I

ry(s) x(s)

1

I~

e(s)

~n

lu(s)J with a fairly good accuracy. when M is sufficiently large. If noise v(s) is not a vector whose elements are white noises. as is usually the case, ordinary least squares method is not applicable to obtain unbiased estimates of coefficients G(m). Noise v(s) is expressed by the AR model as "C(l)v(s-l) + I-I

(9)

~(s)

1

(s) (s)

(16)

A(s) -

[C(S)

G(S)]

B(s)

F(s)

the next expression is obtained as the AR model of the whole feedback system of Fig. 4,

L

v(s)

(15)

for 1 > L

M

yes)

2, 3, ... , M+L)

x(s)

M L A(m)x(m-s) + e(s)

(17)

m-I

where ~(s) is a vector whose elements are normally independently distributed white noises. Considering (9), (8) becomes M+l "C(l)y(s-l) + " D(m)u(s-m) + I-I m-I

As e(s) is a vector whose elements are normally independently distributed white noises, least squares analysis applied to the system (4) is applicable to get the optimal estimates of A(s) (Akaike (968).

L

yes)

~(s)

(10)

where D(I)

Noise Power Contribution Analysis GO)

m-I D(m) G(m) C(l)

G(m) - l: C(1)G(m-l) I-I for m > M 0 0

for

(m

2, 3, ... ,M+L)

Considering frequency analysis of the system (17), the frequency response function of x . (s) to x, (s) is described as: 1 J

(11 )

M

aiJ,(f) - L a ,(m)exp(-j2nfm) m-I i J

> l

As for the feedback loop, in the same way as above, describing as follows:

(18)

where a ,(m) is the ij-th element of A(m). Define !~e power spectral density function of x.(s) as p .. (x)(f), e , (s) as p .. (e)(f), and b~ (f) as rRe ij-th element ofJthe inverse ma~rix of (I - A(f)), where A(f) is a matrix whose ij-th element is a, ,(f), then. 1J

v (s) (19)

+

u (s)

y (s)

holds, because elements of e(s) are independent of one another. This implies that the power spectral density of x,(s) is given by the sum of contribution of e,(s)l to x,(s). Define J

1

(20)

w(s) Fig. 4.

Feedback system to be identified.

then ri,(f) represents the ratio of contribution of e,(s~ to the power spectrum density PH (t) (f).

Identification and Prediction of Temperature Differance Across Blast Furnace Bottom slag content was not very effective to change DT. In Model Ill, the ratio of the noise of DT itself is less than those in the case of Model I and I, but it is still large in the medium frequency range. Figure 10 also shows that changes of input variables of Group I were more effective than those of Group 11.

CONCLUSION A statistical model which represents dynamic behavior of DT was identified by applying a multivariable autoregressive model. Manipulated variables were divided into two groups, the first group consisted of variables concerning the solid charge and the blast, which were maneuverable in the usual BF operation in itself, the second group consisted of slag contents. Three models were identified, each with different inputs. Difference was small in the accuracy of the prediction by each model. Noise power contribution analysis showed that inputs of the first group were more effective than those of the second group. Responses of DT were simulated in some typical cases of changes of input variables which were probably adopted in actual operation. Results of these simulations indicated that increase in ore/coke ratio and in blast moisture were effective among various alternations of maneuverable input variables for the purpose of the increase in DT. The model could guide realistic improvement of tapping operations.

Response of DT to Manipulated Variables The model can be used to calculate the step response of DT to manipulated variables. In usual BF operation, inputs to BF are manipulated to control quantity and quality of liquid iron. Usually, several inputs are manipulated simultaneously in order to maintain the heat balance of BF. Therefore, typical eight patterns of manipulation of inputs were considered and response of DT in each case was calculated. Table 2 shows the eight patterns of operation. Normal operation conditions were assumed as follows: Iron production: 5400 t/day (Blast Volume): 3900 Nm 3/min. BV BT (Blast Temperature): 1100 °c BM (Blast Moisture): 30 g/Nm 3 (Ore/Coke ratio): 3.5 OC (Cokes ratio): 470 kg/t-pig iron CR (Blast Speed at the tuyere): 230 m/s BS

REFERENCES Akaike, H. (1970). Statistical predictor identification. Ann. Inst. Statist. Math., 22, 203-217. Akaike, H. (1971). Autoregressive model fitting for control. Ann. Inst. Statist. Math., 23, 163-180. -Akaike, H. (1968). On the use of a linear model for the identification of feedback systems. Ann. Inst. Statist. Math., 20, 425-439. Burgess, J. M., D. R. Jenkins, M: J. McCarthy, and others (1981). Mathematical and physical simulation of non-uniform liquid drainage in packed beds. Proceedings of International Blast Furnace Hearth & Raceway Symposium, 9-1 - 9-9. Fukutake, T., and K. Okabe (1976a). Experimental studies of slag flow in the blast furnace hearth during tapping operation. Trans. ISIJ, 16, 309-316. Fukutake, T., andlK. Okabe (1976b). Influences of slag tapping conditions on the amount of residual slag in the blast furnace hearth. Trans. ISIJ, ~, 317-323. Ohno, J., M. Nakamura, Y. Hara, and others (1981). Flow of iron in blast furnace hearth. Proceedings of International Blast Furnace Hearth & Raceway Symposium, 10-110-12.

In Case I and 11, OC is reduced by 0.1, and, to hold production rate constant, BV and BT or BM are manipulated, and BS is decreased as a result. In Case III and IV, OC is reduced by 0.1, but in order to reduce production rate, BV is not manipulated, but BT or BM is manipulated to keep the heat balance of BF, so BS is decreased in Case Ill. In Case V, BV is reduced by 195(Nm'/min.) in order to reduce production rate, which causes a decrease of BS. Case VI, VII and VIII are the converse operation of Case lIT, IV and V respectively. Figure 11 shows response of DT in each case. DT is increased in Case I, 11, III and IV, and decreased in Case VI and VII. And in Case V and VIII, DT is changed at most 3 degrees, when it settled. DT is increased most in Case 11, somewhat less in Case IV . These results indicate that increase of OC, BM and BS are effective for increasing DT. BS can be increased by increasing BV and BT or by decreasing tuyere diameter.

TABLE 2

Eight Patterns of Manipulated of Input Variables Blast Volume (Nm 3/min)

Blast Temperature (OC)

O.H

195t

l30.

Constant

O.H

195t

III

Decrease

O.H

IV

Decrease

O.H

V

Decrease

VI

Increase

0.1 t

VII

Increase

0.1t

VIII

Increase

Case

Production rate

I

Constant

II

Ore/Coke (-)

227

Blast Hoisture (g/Nm 3)

Blast Speed (m/sec) IH

9t

12t 22.

l30. 9t

12.

195.

22t

l30t 9t 195.

12t

228

K. Asano, M. Kondo and T. Sawada 60r-------------,

1.0

.------::::======-1 B2

~,

c: 0 .8 0 ~

"

.J:J

0. 6

~

~

c: 0

"

0.4

~

Cl>

20

"

0

DT

CL

10~~~-L~~~~-L~~~~

o

20

40

60 Time

80

100

120

0

Z

I

0 .0

60~-----------------------'

I

0

I

I

I

140

I

1' 20

Frequency ( / day) Fig. 9.

Noise power contribution analysis of Model II. MgO

1.0

50~., 40

,

"" ". ~r-

to-

••• .•

o

on

140

( days )

One step ahead prediction of DT by Model I (Full line is observed data, Broken line is prediction value).

Fig. 5.

P

0.2

Cl>

.

. .'" . ... .

0.8

c:

, '",

0

~

.,

::l .0

30

...

0.6

~

c: 0

20

<)

...Cl>

100_L-~~~~~~L-~~~~~

20

60 80 100 120 140 Time ( days ) One step ahead prediction of DT by Model 11 (Full line is observed data, Broken line is predicted value).

Fig. 6.

0.4

~ 0 CL

40

0.2

Cl> 11)

0

Z

0.0

60r---------------, Fig. 10.

Ui" Cl> Cl>

~ Cl>

20

(a)

10~~~~~~~~~L~I~ll~

o

20

60 80 100 120 140 Time ( days ) Fig. 7. One step ahead prediction of DT by Model III (Full line is observed data, Broken line is predicted value) . 1.0.-7=========-1

0

....0

-10

8. on

-20

...

Cl>

0

0 .6

~

0

U

....0

0

Cl>

, Case

IV

\. Case

0

40

80 120 160 Time ( days )

1[1

200

40 30

llD

Cl> Cl

c:

L-

-30

I[

Case

0

11)

Ui" Cl>

::l .J:J L-

10

Cl>

~

~

20

a::

BM

30

~

c:

c: 0.8

Frequency (/ day ) Noise power contribution analysis of Model Ill. 40

~

Cl>

40

0

(b)

0 .4

DT

" 0 .2

0 CL

8. Cl>

Fig. 8.

I 40

Frequency ( ,' day ) Noise power contribution analysis of Model I.

Fig. 11.

VI

,..Case VII

-20 -30

0

'- Case

Cl>

Z

00

Case VI[ I I'

c: -10

a::

0

10

on

11)

Cl>

11)

20

0

40

80 Time

120 160 ( days )

200

Responses o f DT to the manipulated variables (a) Case I ~ IV (b)Ca s e V ~ VIII.