Pergamon Computers ind. Engng Vol. 33, Nos 3-4, pp. 453-456, 1997

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A H y b r i d Neural-Network/Mathematical P r e d i c t i o n M o d e l fo r T a n d e m Cold M i l l

Sungzoon Cho t ' t t , Min Jangt,Sungcheol Yoon t, Yongjoong Chott and Hyungsuk Cho t t t

t Dept. of Computer Science & Engineering, POSTECH, Pohang, 790-784, Korea tt Graduate School for Information and Technology, POSTECH, Pohang 7g0-784, Korea

tt~ Facilities Technology & Engineering Dept., POSCO, Pohang, Korea

Abstract

In tandem cold mill, a strip is flattened by stands of rolls to a desired thickness. At Pohang Iron and Steel Company (POSCO) in Pohang, Korea, precalculation determines the mill settings before a strip actually enters the mill and is done by an outdated mathematical model. A corrective neural network model is proposed to improve the accuracy of the roll force prediction. The network is fed not only the usual mathematical model's input but also a set of additional inputs such as the chemical composition of the coil, its coiling temperature and the aggregated amount of processed strips of each roll. The network was trained using a standard backpropagation with 4,944 process data collected at POSCO from March lCJ95 through December 1995, then was tested on the unseen 1,586 data from February 1996 through April 1996. The combined model reduced the prediction error by 33.88% on average. © 1997 Elsevier Science Ltd Keyboards : Roll Force, Mathematical Model, Corrective Neural Network Model

1 Introduction

In tandem cold mill, a strip is flattened by stands of rolls to a desired thickness. As passing through the stands of rolls, source strip coils are pressed (see the lower part of Figure 1).

j o ?.p£o% Figure 1: Cold mill process at POSCO

Cold mill process control (the upper part of Fig- ure 1) at Pohang Iron and Steel Company(POSCO) is divided into three phases, precalculation, real time control and postcalculation. Precalculation deter- mines initial settings of the mill before a source strip

coil is up-loaded into the mill. Real time control con- sists of four different kinds of control systems which, based on the preset values determined by precalcu- lation, continuously update the control commands. In particular, automatic gauge control system issues commands in order to meet the desired thickness of the strip. Thus, errors made in precalculation can be compensated if it is within a certain range. How- ever, large errors can not be handled by the real time control system. Postcalculation adjusts certain pa- rameter values used in the mathematical model for precalculation of future strips [3].

The goal of precalculation is a precise control of roll gap. The roll gap refers to the distance between the two adjacent rolls, one above and the other be- low the processed strip. The smaller the roll gap, the more milling is performed while the larger the roll gap, the less milling is done. Thus, the roll gap is the most important parameter that determines the precision of the thickness of the milling process. In most milling plants around the world, the roll gap is computed by a numerical or mathematical model. The "optimal" value of the roll gap for a particular situation is a complicated function of many variables among which the roll force to be applied in actual milling process is the single most important factor. So, the problem really turns into an accurate pre- diction of the roll force. The roll force is again a function of many variables. Currently, the mathe- matical model usually approximates those variables such as friction coefficients and deformation resis-

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tance of the coil. Because the exact values of these variables cannot be measured during processing of the coil, there is a lot to be desired in the accuracy of the mathematical model's roll force prediction. We can only "predict" the rolling force by approximat- ing from the historical information. The information consists in a number of tables specified according to the steel class of a coil. By referring to the tables, the mathematical model obtains values of variables and coefficients. But the values in the tables are discrete and even sparse at some ranges, thus the predicted rolling force can not but be poorly approx- imated. Another problem in the mathematical model is the fact that it is missing some important variables in rolling force precalculation, such as the coiling temperature at hot mill, the chemical compositions of the coil, the aggregated amount of processed strip at each stand and the roll type. These factors are well known to influence the rolling force prediction, but it is not clear how these factors could be incor- porated in the present mathematical model [5].

Recent efforts in improving the roll force predic- tion were made in two directions, first in improving the mathematical model and second in employing the neural network approach. In KSC steel works in Japan [6], the composition of a coil (silicon, man- ganese and carbon contents) and hot rolling tem- perature (coiling temperature and finishing delivery temperature) were used to calculate the deformation resistance. The accumulated amount of rolled coil length was used as well as the rolling speed to calcu- late the friction coefficient. They report an improve- ment in the accuracy of roll force prediction. Lee at POSCO also reported improvements by considering more variables that affect the deformation resistance and friction coefficients [2]. A more dramatic im- provement came from the neural network approach. In Westfallen steel works in Germany, neural net- works were used to calculate the roll force with the improved prediction accuracy in hot rolling process which is a previous process to cold rolling mill [5]. They proposed a corrective neural network model, where the network produces a corrective coefficient to be multiplied to the prediction made by the math- ematical model. Additional variables such as the composition of a coil and temperature variables were fed to the networks. Also at Sollac steel works in France, neural networks were used in work-hardening process to calculate the roll force [4]. They also in- troduced the concept "aberrant domain" which is an area in the input space that was not represented by the training patterns. A preprocessor is then used to detect if a new milling situation or input pattern

belongs to the aberrant domain. What we propose here is a hybrid approach, sim-

ilar to Portman's approach, where the mathemat- ical model's output is combined with a corrective neural network's output. Since there are a plenty of cold mill data available in the plant, the net- work can be trained to adjust the rolling force values calculated by the mathematical model. The hybrid NN/math model is described in the next section, fol- lowed by simulation results based on the real data from POSCO cold mill plant. Then we conclude with a summary and future work.

2 Corrective Neural Network

t Pact 7 =Pcal

Con'ective ~ Neural Network

X',Q,S

X={ro l l diameter(Di), coil width(W) forward and backward tension(Ty, Tb), initial and target thickness(H, h)}

Xl={aggegrated amount of coil processed, roll type }

Q={chemical composition (C, Mn, Si) } S={average coiling temperature at hot rolling

mill }

Figure 2: Hybrid NN/math model

Figure 2 shows a combination of mathematical model and a corrective neural network, originally proposed in [5]. The mathematical model on the left side calculates its prediction of rolling force Pcat based on input variables .~ as before. The neural network on the right side is a multilayer perceptron with a hidden layer of 12 nodes. The network's input includes not only the mathematical model's input .~" but also the additional input X ' , Q, and S (see Fig- ure 2). The network's target output is set to Zp, a

Proceedings of 1996 ICC&IC 455

corrective coefficient that is to be multiplied to the mathematical model's output /'cal to result in the hybrid model's final output ~'comb. The effect is to correct or modify the mathematical model's predic- tion by the multilayer perceptron neural network.

The input variables to the neural network have four parts. First, .~ contains the same inputs to the mathematical model. Second, .~t consists of two stand-oriented variables, the aggregated amount of processed coil in length and the roll type. Third,

represents the composition of C, Mn and Si in the coil. The chemical compositions are known to have to do with the deformation resistance. Lastly,

is the average coiling temperature from hot rolling mill, known to play an important role in determining deformation resistance.

The output of the corrective neural network is the corrective coefficient Zp, the ratio of the actual measured rolling force (Pact) to the predicted rolling force (/'cat) by the mathematical model. This cor- rective coefficient is multiplied to the rolling force calculated by the mathematical model to result in the combined rolling force (/'comb). A corrective neural network is built for each of the five milling stands.

3 Simulation Results

A total of 4,944 coil data were collected for the pur- pose of training the neural network at POSCO from March 1995 through December 1995. Each input variable was normalized as eq(1).

& _ x - ~ - - , (1)

fix

where #x and ax denote the average and standard deviation of variable x, respectively.

We built five networks, one for each stand. The networks were trained using a standard backprop- agation learning algorithm [1]. Both the learning rate and momentum were set to 0.05. The initial weights were randomly selected from [-0.01,0.01]. The number of hidden units was determined using a validation set, composed of randomly selected train- ing patterns, about 10% of the training set. The learning process converged in a relatively small num- ber of iterations, 200 epochs. It took less than 2 hours on a SPARC 20 workstation.

To evaluate the performance of the combined model, the unseen 1,586 coil data which were col- lected at POSCO during February 1996 and April 1996 were used for testing. The prediction error (E) was defined as the difference in ton between

the actual (/'act) and calculated (Pcat) or combined (/'comb) rolling forces. Formally, they are defined as eq(2).

Emath = IPa~ - P~ad (ton) E~omb = IPa~t - P~ombl (ton), (2)

where Emath and Ecomb are prediction errors of mathematical model and combined model, respec- tively.

Table 1: Comparison of the rolling force prediction

error both the mathematical and the hybrid models.

stand number

1 2 3 4 5

Average

average average Emath Ecomb 88.28 67.34 84.10 37.75 68.14 40.40 34.59 40.71 42.14 24.88 63.45 42.22

average error reduction(%)

23.72 55.11 40.71 8.88

40.96 33188

Table 1 shows the average prediction error of the two models. The combined model using the cor- rective neural network reduced the error 33.88% on average and up to 55.11% in stand No. 2.

The training and test patterns were collected re- gardless of steel class. Therefore, the result also shows that the proposed model reduce the predic- tion error for all steel classes, and this means that the chemical composition of a coil reflects its me- chanical characteristics, that is, friction coefficient and deformation resistance, better than steel class.

Figure 3 shows how well the two models can pre- dict the rolling force at stand No. 5. If the predicted rolling force (/'cal or /'comb) is same to the actual rolling force(Pact), the model's prediction is perfect and the dot will be placed on the line (y = x). The less perfect the model is, the farther the dot is placed from the line. The figure clearly shows that the com- bined model's predictions are placed more closely to the line than those of the mathematical model.

4 Conclusions

We proposed a hybrid Neural Net- work/Mathematical model for rolling force pre- diction in cold rolling mill process. Addition of a corrective neural network is especially advantageous in that it enables the model to take into account those variables which are known to be influential,

456 Proceedings of 1996 ICC&IC

m J m ¢ l l . ~ l ¢

j /

/ /

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[3] Hitachi Co Ltd. Guide Book for Mathematical Model of 1st Cold Mill. Japan, 1980.

[4] N. Pican and F. Alexandre. Artificial neural net- works for the presetting of a steel temper mill. IEEE Expert, pages 22-27, 1996.

[5] N. Portmann. Application of neural networks in rolling mill automation. Iron and Steel Engineer, pages 33-36, 1995.

[6] M. Yamashita, I. Yarita, H. Abe, T. Mikuriya, and F. Yanagishima. Technologies of flying gauge change in fully continuous cold rolling mill for thin gauge steel strips. IRSID Rolling Con- ference, 2(1), 1987.

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Figure 3: Comparison of the mathematical and the

hybrid models' predictions at stand No. 5

but whose mechanism not explicitly understood. In particular, we have incorporated such additional factors as the chemical composition of the coil, its hot coiling temperature, the aggregated amount of processed strips for each roll and the roll type. In the out of sample test, the proposed model reduced the prediction error by 32.8% on the average.

References

[1] D. Rumelhart G. Hinton and R. Williams. Learn- ing internal representation by error propagation. In D. Rumelhart, J. McCleliand, and the PDP Research Group, editors, Parallel Distributed Processing, Vol I : Foundations, pages 318-362. MIT Press, Cambridge, MA, 1986.

[2] W . Lee. Improvement of set-up model for tan- dem cold rolling mill. Technical report, RIST, 1994.