Content uploaded by Bin Chen
Author content
All content in this area was uploaded by Bin Chen on Mar 03, 2017
Content may be subject to copyright.
166 Int. J. Materials and Product Technology, Vol. 46, Nos. 2/3, 2013
Copyright © 2013 Inderscience Enterprises Ltd.
Application of back-propagation neural network for
controlling the front end bending phenomenon in
plate rolling
Bin Chen
School of Materials Science and Engineering,
Shanghai Jiao Tong University,
Shanghai-200240, China
E-mail: steelboy@sjtu.edu.cn
Xiao Ru Cheng*, Yan Sheng Hu and
Yong Ren
School of Materials and Metallurgy,
Wuhan University of Science and Technology,
Wuhan-430081, China
E-mail: xrcheng@mail.wust.edu.cn
E-mail: pjxwh@126.com
E-mail: renyong5800@163.com
*Corresponding author
Abstract: In this paper, a new method of controlling the front end bending in
plate rolling is introduced. In this method, the back-propagation neural network
with three layers is designed. The input layer has three inputs of temperature,
entry thickness, and parameter of deformation zone. The hidden layer has seven
neurons. The only value of the output layer is the front end bending value. The
optimised rolling schedule at different conditions is obtained after training and
calculating. Its application to a plate rolling mill shows that the method solves
the problem of the front end bending successfully.
Keywords: back-propagation neural network; front end bending; plate rolling.
Reference to this paper should be made as follows: Chen, B., Cheng, X.R.,
Hu, Y.S. and Ren, Y. (2013) ‘Application of back-propagation neural network
for controlling the front end bending phenomenon in plate rolling’, Int. J.
Materials and Product Technology, Vol. 46, Nos. 2/3, pp.166–176.
Biographical notes: Bin Chen is an Associate Professor at the School of
Materials Science and Engineering, Shanghai Jiao Tong University in
Shanghai, China. His major research interest includes optimisation of process
parameters, advanced processing technology of materials, microstructure
observation, and electron microscopy of materials. He received his PhD from
Shanghai Jiao Tong University. He received his ME in Materials Processing
Engineering and his BE in Material Forming and Control Engineering, both
from Wuhan University of Science and Technology, China. He has published
more than 40 research papers in reputed international and national journals or
conferences.
Application of back-propagation neural network 167
Xiao Ru Cheng is a Professor at the School of Materials and Metallurgy,
Wuhan University of Science and Technology, Wuhan, China. She obtained
her BE and ME from Wuhan University of Science and Technology. Her areas
of interest include steel rolling, computer aided manufacturing, mathematical
modelling, and computer control technology. The technologies developed by
her research group had been applied in some Chinese steel industries.
Yan Sheng Hu is Associate Professor and Head of Experimental Center of
Materials Processing and Engineering at the School of Materials and
Metallurgy, Wuhan University of Science and Technology, Wuhan, China. His
research focus is the application of computer in metal forming process. He has
rich experience in the areas of steel rolling.
Yong Re is an Associate Professor at the School of Materials and Metallurgy,
Wuhan University of Science and Technology, Wuhan, China. His major
research interest includes control of microstructure, mechanical property, and
surface quality during metal forming process. His research focus is also on the
new technologies and new methods on metal forming process. He received his
Bachelors from Wuhan University of Science and Technology.
1 Introduction
The front end bending is a common phenomenon in plate rolling. It is one of serious
problems in rolling field. The front end bending decreases productivity, causes
deterioration in product quality, and damages to the equipment. It may result in the
impact of plate on work rolls or baffles, and shortens the service life of work rolls and
baffles. The excessive upward bending may cause damage to water cooling equipment.
The downward bending, however, may result in folding defects on plate surface (Song et
al., 2001a) and cause plate get into underside work roll table (Song et al., 2001b).
Consequently, an uncontrolled front end bending in plate rolling may lead to losses in
product quality and severe damage of the system components. So the front end bending is
a serious problem should be solved. The front end bending is related to many influencing
factors such as temperature, diameter proportion of work rolls, work roll speed ratio,
surface roughness of work rolls, parameter of deformation zone, plate thickness as well
as bite angle.
To improve the control ability of the front end bending, various methods have been
studied by many researchers. Johnson and Needham (1966) carried out a few experiments
using lead as a model material to study curvature. Buxton and Browning (1972)
investigated the turn-up and turn-down in hot rolling by using plasticine. Pan and
Sansome (1982) derived a uniaxial analytical model to explore the characteristics of
asymmetrical sheet rolling and compared it to experimental data. An analytical approach
for capturing the rolling asymmetries by means of the slab method had been used to
quantify rolling pressure, forces, torques and shear stresses (Hwang and Tzou, 1993;
Hwang and Tzou, 1995). The slab method was extended to predict the curvature of the
rolled strip (Salimia and Sassani, 2002). A detailed finite element based elastic-plastic
analysis of the stress and strain distributions in the slab subjected to asymmetric rolling
conditions was performed (Richelsen, 1997). Jeswiet and Greene (1998) employed
two-dimensional finite element simulations in order to quantify front end bending in
168 B. Chen et al.
dependence of the roll surface speed. The finite-element simulations were made to
simulate ski-end behaviour and the experiments were performed to study how different
parameters influence front end bending in plate rolling (Nilsson A. et al., 2001). The
comparison between experimental results and simulations was made. Harrer et al. (2003)
used finite element analysis to characterise asymmetric effects in plate rolling. A
pass-to-pass control concept based on a physical model for asymmetrical rolling was
presented in order to minimise the occurrence of the front end bending in the hot rolling
process of heavy plates (Kiefer and Kugi, 2000). Three methods based on the theorem of
the upper bound of total power were discussed (Pawelski, 2000). Kiefer and Kugi (2008)
developed a semi-analytical approach utilising the upper bound theorem in order to
extract an efficient mathematical model for online execution in process control. As
discussed above, the conventional way of controlling the front end bending is via
experimental methods and mathematical model. However, the fitting ability of the
mathematical model is limited because the model cannot describe all the physical
phenomena perfectly because of the very nonlinear, complex, and unmeasurable data
such as friction, yield stress, and system disturbances. And experimental results in lab are
difficult to be applied in the rolling mill. Due to the complex influencing factors, the front
end bending still exists in many steel rolling mills. By comparison, the modelling process
in the artificial neural network (ANN) is much easier and effective.
ANN is first introduced as a mathematical aid by McCulloch and Pitts (1943). It has
seen an explosion of interest and has been successfully applied in all fields over the last
two decades (Patterson, 1998; Meireles et al., 2003). It has been widely used for many
different industrial areas such as prediction, control, identification, classification, pattern
recognition, speech and vision. ANN has been trained to solve nonlinear and complex
problems that are not exactly modelled mathematically. The wide applicability of ANN
stems from their flexibility and ability to model linear and nonlinear systems without
prior knowledge of an empirical model. This gives ANN an advantage over traditional
fitting methods for some industrial applications. Many different types of ANN have been
developed. The back-propagation artificial neural network (BP-ANN) which developed
by Rumelhart is the most representative learning model for the ANN and also is the most
popular network type (Zárate and Dias, 2009). In steel rolling fields, the application of
ANN is becoming popular. Particularly attention has been given to how to build a
suitable ANN model to resolve the actual problems of rolling (Rumelhart, et al., 1986;
Zárate and Bittencout, 2008; Ai et al., 2003; Larkiola et al., 1996; Peng et al., 2008;
Shahani et al., 2009; Lee and Choi, 2004; Lee and Lee, 2002; Son et al., 2005). However,
very little work has been reported on the application of ANN techniques to the control of
front end bending in plate rolling. In this work, we introduce a successful industrial
example for prediction and reducing the front end bending in hot rolling of Q235 carbon
steel plate by application of the BP-ANN. With this method, there is no necessity to
specify a mathematical relationship between the front end bending and its influencing
factors.
2 Network architecture
According to actual condition of a plate rolling mill, a BP-ANN with three layers is
chosen to solve the problem of the front end bending. Figure 1 shows the typical
BP-ANN used in this study, which consists of a number of neuron-containing layers
Application of back-propagation neural network 169
interconnected in a particular topology. It consists of three kinds of layers classified as
input layer, hidden layer, and output layer. Each layer includes one or more neurons.
Neighbouring layers are joined by interconnections. The lines between the neurons
indicate the flow of information from one neuron to the next, as shown in Figure 1. Each
neuron in a layer is connected to all of the neurons in adjacent layers. Hecht-Nielsen
rediscovered the importance of the Kolmogorov theorem (1957) for the theoretical
understanding of the abilities of neural networks in 1987, exactly 30 years after
Kolmogorov’s theorem has been published. Hecht-Nielsen (1987)suggested that a three
layer neural network, having n input neurons in the input layer, upper limit of (2n + 1)
processing neurons in the hidden layer, and m processing neurons in the output layer
ensure that ANN are able to approximate any continuous function.
Figure 1 Topology of the BP-ANN
Output layer
Hidden layer
Input layer
In present work, three key influencing factors, temperature, entry thickness of plate, and
parameter of deformation zone are selected as inputs in the input layer. Correspondingly,
the hidden layer has seven neurons. In the output layer, only one neuron is used for the
output variable of the front end bending. A tan-sigmoid function is used in the hidden
layer, while a linear transfer function is used in the output layer. The BP-ANN
calculations are carried out using MATLAB mathematical software with ANN toolbox.
The working principle of the BP-ANN lies in its learning ability. The sample data are
inputted to the input layer and propagated to the output layer through the hidden layer via
the interconnections, which is called training process. At the beginning of the learning
step, random values are chosen to initialise weight data. During the learning step, the
weights of the network are continuously adjusted, based on the error signal generated by
the deviation between the output data computed through the network and the data from
the database used in the training. The errors are back-propagated and the weights of each
layer are modified accordingly, so that the errors are gradually minimised during training
process. The training process will be stopped until the error becomes small enough after
propagating forward and backward repeatedly. The popular criteria used to stop training
are small mean-square training error or slight changes in network weights. Definition of
the criteria is usually in accordance with the desired accuracy level of the ANN. In this
research, the front end bending of 30 mm is selected as training stopping criteria. If
training failed, it needs to check up the network and to improve the initial settings, such
170 B. Chen et al.
as the number of neurons in the hidden layer, learning rate, target error, even the number
of layers. The network extracts useful information from data and store information
implicitly in the connections in form of weights. A weight matrix is obtained after
training. The trained network can then be used for prediction. The flow of the BP-ANN
for controlling the front end bending in plate rolling is shown in Figure 2.
Figure 2 Flow chart of the BP-ANN for controlling the front end bending (see online version
for colours)
3 Results and discussion
3.1 Training
In our experiments, 489 sets of representative sample data have been collected in the
rolling mill for training, including influencing factors and corresponding front end
bending values. Then, the front end bending values at different conditions are obtained.
The contour map of the front end bending at rolling temperature of 1,100°C after training
is shown in Figure 3. As can be seen from the figure, the predicted bending value at
1,100°C by different parameter of deformation zone and thickness of plate is displayed in
the contour map, contour line ‘0’ represents flat, contour line ‘1’ represents bending
value of 300 mm, contour line ‘2’ represents bending value of 600 mm, and so on.
Simultaneously, the results of the predicted bending value at temperature from 1,050°C
to 1,200°C are also obtained. According to the experience, flat or minor positive end
bending is favourable state for rolling. Therefore, the regions between contours ‘0’ and
‘1’ should be chosen. On the other hand, the allowable rolling conditions based on
practical production process of the rolling mill fall in the areas marked I, II, and III in
Figure 3. Therefore the regions should be selected in these areas. Once the bending value
Application of back-propagation neural network 171
is selected, the ordinate value of parameter of deformation zone and abscissa value of
thickness is determined accordingly.
Figure 3 Contour map of front end bending (T = 1,100°C) (see online version for colours)
3.2 Calculation
Based on the results obtained in the training procedure, the optimised parameters of
deformation zone are determined accordingly. Then they are used to calculate the plate
exit thickness by the following improved formula of deformation parameter (Ginzburg,
1989) as
hH
hHR
2
)(3
+
−×
=
α
(1)
where α is parameter of deformation zone, h is exit thickness, H represents entry
thickness, and R corresponds to work roll radius.
By the formula (1), we can calculate the thickness of each pass. Accordingly,
thickness reduction of each pass also can be worked out. In some cases, however, the
optimised rolling schedules may add extra passes to the original rolling schedule. If this
addition of passes should be avoided considering the rolling efficiency, an alternative
schedule is offered at the cost of decreasing the bending control effect. In order to solve
the complicated process, a programme code is employed to obtain appropriate deforming
parameters in each pass by multiply a constant coefficient, such as 1.05. Smaller variation
172 B. Chen et al.
in parameters in each pass by calculating iteratively is found to be better than an
excessive front end bending occurred in one pass of rolling. It distributes the change to
the all passes and avoids an excessive front end bending at one pass. Sometimes,
coefficient multiplication may repeat several times in order to obtain an optimised rolling
schedule. Figure 4 is the flow chart of the calculation of the optimised rolling schedule.
Figure 4 Flow chart of the calculation of the optimised rolling schedule (see online version
for colours)
Application of back-propagation neural network 173
3.3 Application
To verify the optimised rolling schedule, the method is applied in a plate rolling mill. The
plates under the same heat treatment process in same batch are divided into two parts
randomly which are rolled by the original rolling schedule or by the optimised rolling
schedule respectively. The comparison of front end bending between the original rolling
and the optimised rolling schedule is listed in Table 1.
Table1 The comparison between rolling schedules without and with the optimisation
The rolling schedule before optimisation
Pass Thickness (mm) Parameter of deformation zone Front end bending (mm)
1 180.75 0.462 √
2 161.74 0.511 √
3 144.58 0.543 √
4 129.56 0.567 √
5 115.63 0.611 √
6 99.37 0.758 √
7 82.78 0.909 √
8 67.32 1.069 250~350
9 53.20 1.279 550~650
10 40.55 1.565 50~100
11 31.42 1.727 250~350
12 24.08 2.012 √
13 21.40 1.447 √
14 19.72 1.255 √
The rolling schedule after optimisation
Pass Thickness (mm) Parameter of deformation zone Front end bending (mm)
1 180.75 0.462 √
2 161.74 0.511 √
3 144.58 0.543 √
4 129.56 0.567 √
5 115.63 0.611 √
6 90 1.012 √
7 70 1.149 √
8 59 1.042 √
9 51 1.038 √
10 45 1.027 √
11 40 1.057 √
12 29.5 1.934 √
13 22 2.202 √
14 19.73 1.449 √
Notes: The signal ‘√’ means that there is no bending or slim bending.
174 B. Chen et al.
As can be seen from Table 1, no front end bending can be observed from pass one to pass
seven in both experiments. This may be attributed to the high thickness of the plates at
early stages. But from pass eight to pass eleven, the front end bending of plate rolled by
the original processing is serious, as shown in Figure 5(a). On the other hand, the
downward and the excessive upward bending do not happen by applying the optimised
rolling schedule, as shown in Figure 5(b). Obviously, the application of the BP-ANN
successfully solves the front end bending in plate rolling.
Figure 5 The comparison of the frond end bending by rolling schedule (a) before optimisation
and (b) after optimisation (see online version for colours)
(a)
(b)
4 Conclusions
This paper has provided a new method of controlling the front end bending in plate
rolling. The results obtained in the present paper can be summarised briefly as follows.
Application of back-propagation neural network 175
1 A BP-ANN network with three layers is designed. The input layer has three inputs,
namely, temperature, entry thickness, parameter of deformation zone. The hidden
layer has seven neurons. The output layer has only one neuron. Its input value during
training is the front end bending value. A tan-sigmoid function is used in the hidden
layer, while a linear transfer function is used in the output layer.
2 The optimised rolling schedule at different conditions is obtained after training and
calculating. Its application to a plate rolling mill shows that the method solves the
problem of the front end bending successfully.
References
Ai, J.H., Xu, J., Gao, H.J., Hu, Y.H. and Xie, X.S. (2003) ‘Artificial neural network prediction of
the microstructure of 60Si2MnA rod based on its controlled rolling and cooling process
parameters’, Materials Science and Engineering A, Vol. 344, Nos. 1–2, pp.318–322.
Buxton, S.A, and Browning, S.C. (1972) ‘Turn-up and turn-down in hot rolling: a study on a model
mill using plasticine’, Journal Mechanical Engineering Science, Vol. 14, No. 4, p.245.
Ginzburg, V.B. (1989) ‘Steel-Rolling Technology: Theory and Practice’, Publisher: Marcel Dekker.
Harrer,O., Philipp, M. and Pokorny, I. (2003) ‘Numerical simulation of asymmetric effects in plate
rolling’, Acta Metallurgica Slovaca, Vol. 9, No. 4, pp.306–313.
Hecht-Nielsen, R. (1987) ‘Kolmogorov’s mapping neural network existence theorem’, in
Proceedings of the First International Conference on Neural Networks, Volume III., IEEE
Press, New York, pp.11–13.
Hwang, Y.M. and Tzou, G.Y. (1993) ‘An analytical approach to asymmetrical cold strip rolling
using the slab method’, Journal of Engineering and Performance, Vol. 2, No. 4, pp.597–606.
Hwang, Y.M. and Tzou, G.Y. (1995) ‘An analytical approach to asymmetrical hot-sheet rolling
considering the effects of the shear stress and internal moment at the roll gap’, Journal of
Materials Processing Technology, Vol. 52, Nos. 2–4, pp.399–424.
Jeswiet, J. and Greene, P.G. (1998) ‘Experimental measurement of curl in rolling’, Journal of
Materials Processing Technology, Vol. 84, Nos. 1–3, pp.202–209.
Johnson, W. and Needham, G. (1966) An Experimental Study of Asymmetrical Rolling, Applied
Mechanics Convention Institute of Mechanical Engineers, Cambridge, UK
Kiefer, T. and Kugi, A. (2007) ‘Modeling and control of front end bending in heavy plate mills’,
IFAC Symp. on Automation in Mining, Mineral and Metal Processing – MMM ‘07, Quebec,
pp.231–236.
Kiefer, T. and Kugi, A. (2008) ‘Model-based control of front-end bending in hot rolling processes’,
Vortrag: 17th World Congress, The International Federation of Automatic Control,
06.07.2008-11.07.2008, in Proceedings of the 17th World Congress, The International
Federation of Automatic Control, Seoul, Korea, 6–11 July, ISSN: 1474-6670, pp.1645–1650.
Kolmogorov, A.N. (1957) ‘On the representation of continuous functions of several variables by
superpositions of continuous functions of one variable and addition’, Doklady Akademii Nauk
SSSR, Vol. 114, pp.67–681 (in Russian).
Larkiola, J., Myllykoski, P., Nylander, J. and Korhonen, A.S. (1996) ‘Prediction of rolling force in
cold rolling by using physical models and neural computing’, Journal of Materials Processing
Technology, Vol. 60, Nos. 1–4, pp.381–386.
Lee, D.M. and Choi, S.G. (2004) ‘Application of on-line adaptable neural network for the rolling
force set-up of a plate mill’, Engineering Applications of Artificial Intelligence, Vol. 17, No. 5,
pp.557–565.
Lee, D.M. and Lee, Y. (2002) ‘Application of neural-network for improving accuracy of roll-force
model in hot-rolling mill’, Control Engineering Practice, Vol. 10, No. 4, pp.473–478.
176 B. Chen et al.
McCulloch, W.S. and Pitts, W. (1943) ‘A logical calculus of the ideas imminent in nervous
activity’, Bulletin of Mathematical Biophysics, Vol. 5, No. 4, pp.115–133.
Meireles, M.R.G., Almeida P.E.M. and Simoes M.G. (2003) ‘A comprehensive review for
industrial applicability of artificial neural networks’, IEEE Transactions on Industrial
Electronics, Vol. 50, No. 3, pp.585–601.
Nilsson, A. (2001) ‘Front-end bending in plate rolling’, Scandinavian Journal of Metallurgy,
Vol. 30, No. 5, pp.337–344.
Pan, D. and Sansome, D.H. (1982) ‘An experimental study of the effect of roll-speed mismatch on
the rolling load during the cold rolling of thin strip’, Journal of Mechanical Working
Technology, Vol. 6, No. 4, pp.361–377.
Patterson, D.W. (1998) Artificial Neural Networks-Theory and Applications, Prentice Hall, USA.
Pawelski, H. (2000) ‘Comparison of methods for calculating influence of asymmetry in plate
rolling’, Steel Research, Vol. 71, No. 12, pp.490–497.
Peng, Y., Liu, H.M. and Du, R. (2008) ‘A neural network-based shape control system for
cold rolling operations’, Journal of Materials Processing Technology, Vol. 202, Nos. 1–3,
pp.54–60.
Richelsen, A.B. (1997) ‘Elastic-plastic analysis of the stress and strain distributions in asymmetric
rolling’, International Journal of Mechanical Sciences, Vol. 39, No. 11, pp.1199–1211.
Rumelhart, D.E., Hinton G.E. and Williams, R.J. (1986) ‘Learning representations by back-
propagating errors’, Nature, Vol. 323, No. 6088, pp.533–536.
Salimia, M. and Sassani, F. (2002) ‘Modified slab analysis of asymmetrical plate rolling’,
International Journal of Mechanical Sciences, Vol. 44, No. 9, pp.1999–2023.
Shahani, A.R., Setayeshi, S., Nodamaie, S.A., Asadic, M.A. and Rezaiec, S. (2009) ‘Prediction of
influence parameters on the hot rolling process using finite element method and neural
network’, Journal of Materials Processing Technology, Vol. 209, No. 4, pp.1920–1935.
Son, J.S., Lee, D.M., Kim, I.S. and Choib, S.G. (2005) ‘A study on on-line learning neural network
for prediction for rolling force in hot-rolling mill’, Journal of Materials Processing
Technology, Vol. 164–165, pp.1612–1617.
Song, Y.H., Zhang, X., Zhou, P., Zhang, G. X., Cheng X.R., Hu, Y.S. and Li, H.X. (2001)
‘Discussion on the prevention measures of the head down-bending of plate’, Steel Rolling,
Vol. 18, No. 1, pp.19–22 (in Chinese).
Song, Y.H., Zhou, P., Zhang, G.X., Han, G.Y. and Cheng X.R. (2001) ‘Origin of folding defects
in steel plate of WISCO and control approach’, Wisco Technology, Vol. 39, No. 4, pp.1–5
(in Chinese).
Zárate, L.E. and Bittencout, F.R. (2008) ‘Representation and control of the cold rolling process
through artificial neural networks via sensitivity factors’, Journal of Materials Processing
Technology, Vol. 197, Nos. 1–3, pp.344–362.
Zárate, L.E. and Dias, S.M. (2009) ‘Qualitative behavior rules for the cold rolling process extracted
from trained ANN via the FCANN method’, Engineering Applications of Artificial
Intelligence, Vol. 22, Nos. 4–5, pp.718–731.
