A. E. TIRYAKI et al.: MATHEMATICAL MODELING OF A CEMENT RAW-MATERIAL BLENDING PROCESS ...
485–490
MATHEMATICAL MODELING OF A CEMENT RAW-MATERIAL
BLENDING PROCESS USING A NEURAL NETWORK
MATEMATI^NO MODELIRANJE POSTOPKA ME[ANJA SESTAVIN
CEMENTA S POMO^JO NEVRONSKE MRE@E
Aysun Egrisogut Tiryaki, Recep Kozan, Nurettin Gokhan Adar
Sakarya University, Department of Mechanical Engineering, 54187, Sakarya, Turkey
aysune@sakarya.edu.tr
Prejem rokopisa – received: 2014-08-01; sprejem za objavo – accepted for publication: 2015-06-30
doi:10.17222/mit.2014.156
Raw-material blending is an important process affecting cement quality. The aim of this process is to mix a variety of materials
such as limestone, shale, sandstone and iron to produce cement raw meal for the kiln. One of the fundamental problems in
cement manufacture is ensuring the appropriate chemical composition of the cement raw meal. A raw meal with a good fineness
and well-controlled chemical composition by a control system can improve the cement quality. The first step in designing a
control system for the process is obtaining an appropriate mathematical model. In this study, Linear and Nonlinear Neural
Network models were investigated for the raw-material blending process in the cement industry and their results were compared
with the experimental data. The results showed that the nonlinear model has a higher predictive accuracy.
Keywords: mathematical modeling, cement, raw material blending, neural network
Me{anje sestavin je pomemben postopek, ki vpliva na kvaliteto cementa. Naloga tega postopka je zme{ati razli~ne materiale, kot
so: apnenec, {krilavec, pe{~enjak, `elezo in drugi; da se dobi surovino za cement za rotacijsko pe~. Ena od osnovnih te`av pri
izdelavi cementa je zagotoviti primerno kemijsko sestavo surovine za cement. Kontrolni sistem za surovino z dobro zrnatostjo in
dobro kontrolirano kemijsko sestavo, lahko izbolj{a kvaliteto cementa. Prvi korak pri postavitvi kontrole procesa je postavitev
primernega matemati~nega modela procesa. V {tudiji sta bila preiskovana linearni in nelinearni model nevronske mre`e za
postopek me{anja v cementni industriji in rezultati so bili primerjani z eksperimentalnimi podatki. Rezultati so pokazali, da ima
nelinearni model ve~jo to~nost napovedovanja.
Klju~ne besede: matemati~no modeliranje, cement, me{anje surovin, nevronska mre`a
1 INTRODUCTION
Cement is the world’s most widely used construction
material and is a key ingredient in concrete. The cement
manufacturing process includes the raw-materials blend-
ing process as well as the burning process, the cement
clinker grinding process, and the packaging process. One
of the main processes that effects cement quality is the
raw-material blending process. The task of this process is
to mix a variety of materials such as limestone, shale,
sandstone, and iron, to produce cement raw meal for the
kiln. Raw meal mainly contains four oxides: calcium
oxide or lime (CaO), silica (SiO2), alumina (Al2O3) and
iron oxide (Fe2O3). The oxide compositions of the raw
meal significantly affect the quality and the properties of
cement clinker. On the other hand, the chemical
compositions of the raw materials vary from time to time
and the feeder tanks do not contain chemically homo-
geneous raw materials. That is why blend estimating
systems with computer control are needed to obtain the
correct composition of the blend.
The approaches to the solution of this fundamental
blending problem have varied widely. Stochastic model-
ing, which uses experimental process data and the
characteristics of the various disturbances, and self-
tuning control of a continuous cement raw-material
mixing system were presented in 1. A recursive estima-
tion of the cement raw-material feedstream oxide
concentrations was presented by using information from
the output raw meal X-ray analysis.2 L. Keviczky et al.3
modified the self-tuning (ST) minimum variance (MV)
regulator algorithm developed for a multiple input mul-
tiple output (MIMO) system presented with the required
average for finite time (RAFT). P. Lin et al.4 proposed a
two-level adaptive control policy combined with a heuri-
stic auxiliary system for the robustness of the raw mix
control system. A new generic optimal controller struc-
ture, which is equivalent to those used at internal model
principal or pole placement technique, was dealt with
in 5. C. Ozsoy et al.6 presented a constrained self-tuning
composition control algorithm for a MIMO system. The
identification and control of the cement raw-material
blending system in a cement factory were examined and
in the identification part of the studies, three different
linear multivariable stochastic time-series models (ARX)
in which the inputs are the feed ratios of the raw-material
components (low grade and iron ore) and the outputs are
the iron oxide and/or the lime module of the raw meal,
were constructed.7 K. Kizilaslan et al.8 modeled the raw-
material blending process in the cement industry using
intelligent techniques and the results are compared with
Materiali in tehnologije / Materials and technology 50 (2016) 4, 485–490 485
UDK 519.6:621.742.48:666.29.022.4:004.032.26 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 50(4)485(2016)
classic system-identification methods. A fuzzy controller
is proposed to improve the real-time performance in the
blending process.9 An adaptive control framework was
presented for the raw-material blending process, and the
corresponding optimal control structure was discussed
too.10 A fuzzy neural network with particle-swarm opti-
mization FNN-PSO methods was applied to establish
and optimize the cement raw-material blending process
in 11. The ingredient ratio optimization problem was
analyzed using the general nonlinear time-varying
(G-NLTV) model for the cement raw-material blending
process under various conditions by X. Li et al.12
The first step in applying an adaptive and dynamic
control strategy to this kind of process is obtaining an
appropriate mathematical model of the process. This
paper is concerned with modeling the raw-material
blending process in cement industry by using neural
networks. Linear and Nonlinear Neural Network models
were developed and the results were compared with the
experimental data.
2 CEMENT RAW-MATERIAL BLENDING
PROCESS
The cement -manufacturing process consists broadly
of mining, crushing and grinding, burning, and grinding
with gypsum. In the dry process of cement production,
the raw materials are proportioned, stored, ground,
mixed, pulverized, and fed into the kiln in a dry state.
Inside the kiln the raw mix will undergo a sequence of
reactions. Sintering takes place at the final stage of the
reaction, i.e., at 1400–1450 °C, and a substance called
clinker, having its own physical and chemical properties,
is formed. The clinker is cooled, crushed, and mixed
with a predetermined percentage of gypsum to regulate
the setting time of the cement. Finally, the finished pro-
duct, known as Portland cement, is stored in large sto-
rage bins called silos, from which it is fed to an auto-
matic packing machine.8
The original cement materials are obtained from a
natural mine, thus the chemical composition is time-
varying function. Composition fluctuation is inevitable
and it may contain randomness. Therefore, modeling of
the cement raw-material blending process becomes more
important and a challenge.
In this study, the raw material blending process in the
Nuh Cement Factory in Turkey was investigated. Here,
three different feed streams, which are low grade, high
grade and iron ore, are controlled by weigh feeders and,
after mixing on a conveyor belt, fed to the raw mill. A
simplified schematic diagram of the raw mill blending
process is shown in Figure 1.
Mixing on a conveyor belt is fed to the raw mill by
weight-feeders, before being thoroughly ground and
mixed in the raw mill. In this study, two feed streams
containing low grade and iron ore were modeled,
because the values of all the measurements are a per-
centage. A sample of this raw mix is collected at the
input of the raw mill grinder by an auto sampler and
analyzed every five seconds and the average of twelve
analyses is sent to the computer through a data-commu-
nication line by PGNAA (Prompt Gamma Neutron
Activation Analyzers). These data are utilized and mani-
pulated for the raw meal feed stream. Thus, the desired
blend is supplied continuously. The measurements con-
sist of the output concentrations of the four basic oxides
(CaO, SiO2, Fe2O3 and Al2O3). The raw meal is trans-
ferred to homogenization basins where further conti-
nuous mixing decreases the magnitude of the concen-
tration variations about the silo average values. The
complete filling of a basin requires a unit batch time of
16 h.
The quality of raw meal depends on the relative rates
of CaO, SiO2, Fe2O3 and Al2O3. The relative rates can be
expressed by the so-called modulus values:8,12
Lime standard (or modulus):
ML =
+ +
100CaO
2.8SiO 1.1Al O 0.8Fe O2 2 3 2 3
(1)
Aluminum modulus:
MA =
Al O
Fe O
2 3
2 3
(2)
Silica modulus:
MS =
+
SiO
Al O Fe O
2
2 3 2 3
(3)
A high ML requires a high heat consumption for the
clinker burning inside the kiln and thus gives more
strength to the cement. A higher MS decreases the
liquid-phase content, which impairs the burn ability of
the clinker and reduces the cement setting time. The
A. E. TIRYAKI et al.: MATHEMATICAL MODELING OF A CEMENT RAW-MATERIAL BLENDING PROCESS ...
486 Materiali in tehnologije / Materials and technology 50 (2016) 4, 485–490
Figure 1: Simple schema of the raw-material blending in the Nuh
Cement Factory
Slika 1: Preprosta shema me{anja surovin v tovarni cementa Nuh
value of MA determines the composition of the liquid
phase of the clinker. The goal is to achieve a desired
level of ML, MS and MA of the raw mix, to produce a
particular quality of the cement by controlling the mix
proportions of the raw materials. To achieve an appro-
priate raw mix proportion is very difficult due to the
inconsistencies in the chemical composition of the raw
material.8
3 ARTIFICIAL NEURAL NETWORK
APPROACH
The Artificial Neural Network (ANN) has been
developed by a generalization of the mathematical model
of the human brain’s ability and neural biology. The
ANN, which is relatively new modeling technique, has
shown remarkable performance when used to model
complex linear and non-linear relationships. Neural
Networks (NN) have been successfully applied to model
complicated processes in many engineering applications:
electronics, manufacturing, robotics, materials science
and physical metallurgy, automotive, defense, and tele-
communications. An ANN is a set of processing ele-
ments, or neurons, and connections with adjustable
weights. A multi-layer neural network consists of an
input layer, one or more hidden layers, and an output
layer. The input layer is the first layer and accepts sym-
ptoms, signs, and experimental data. The layers that are
placed between the input and output layers are called
hidden layers. The hidden layer processes the data it
receives from the input layer, and sends a response to the
output layer. The output layer accepts all the responses
from the hidden layer and produces an output vector.
Figure 2 shows the structure of the ANN.
Each layer has a certain number of processing ele-
ments that are connected by links with adjustable
weights. These weights are adapted during the training
process, most commonly through the backpropagation
algorithm, by presenting the neural network with exam-
ples of input-output pairs exhibiting the relationship the
network is attempting to learn.
The total input to the layer neuron i, xi, is the
summation of the weight (wij), which is associated with
the connection between the neuron i and the neuron j,
multiplied by the input value received from the
preceding layer neuron, xj, for each connection path:13
x w w xi i ij j
j
N
= + ×
=
∑0
1
(4)
where N is the number of inputs, wi0 is the bias of the
neuron.
The output from neuron i, Vi, is given by:
V f xi j= ( ) (5)
where f is the activation function.
During training, Q sets of input and output data are
given to the neural network. An iterative algorithm
adjusts the weights so that the outputs (yk) according to
the input patterns will be as close as possible to their
respective desired output patterns (dk). Considering a
neural network with K, which is the total number of out-
puts, the Mean Squared Error (MSE) function is to be
minimized:
[ ]MSE
Q K
d q y qk k
k
K
q
Q
=
⋅
⋅ −
==
∑∑1 2
11
( ) ( ) (6)
The backpropagation algorithm is the most widely
used to minimize MSE by adjusting the weights of the
connection links. The equation for calculating the up-
dated weights and bias is:
w w wij
t
ij
t
ij
t+ += +1 1Δ (7)
Where Δw ij
t+1 is the (±) incremental change in the
weight. The weight change is determined by an optimi-
zation method.13
A. E. TIRYAKI et al.: MATHEMATICAL MODELING OF A CEMENT RAW-MATERIAL BLENDING PROCESS ...
Materiali in tehnologije / Materials and technology 50 (2016) 4, 485–490 487
Figure 2: The structure of the ANN
Slika 2: Struktura ANN
Figure 3: The linear network structure14
Slika 3: Struktura linearne mre`e14
4 ANN MODEL
Linear and Nonlinear Neural Network models were
developed for the raw-material blending process in
cement manufacture. The inputs of both the models are
low grade and iron ore, and the outputs are Fe2O3 and
Lime Modulus.
4.1 Linear ANN
The linear network (ADALINE network) shown in
Figure 3 has one layer of S neurons connected to R
inputs through a matrix of weights W.14
The linear network has the same basic structure as
the perceptron network. The only difference is that the
linear neuron uses a linear transfer function. This trans-
fer function is shown in Figure 4. The linear transfer
function calculates the neuron’s output by simply return-
ing the value passed to it. This neuron can be trained to
learn an affine function of its inputs, or to find a linear
approximation to a nonlinear function. A linear network
cannot, of course, be made to perform a nonlinear com-
putation.14
A nonlinear relationships between the inputs and the
targets cannot be represented exactly by a linear net-
work. Under se circumstances, backpropagation might
be a good alternative.
4.2 Nonlinear ANN
The nonlinear network is shown in Figure 5.14 In this
study a feed-forward backpropagation network was
designed. A log-sigmoid transfer function was used in a
hidden layer and the output layer. Because, generally, a
natural incident resembles the structure of a log-sigmoid
function, using this function has given better results. A
log-sigmoid transfer function is shown in Figure 6.14
The inputs to the system determine the neuron number in
the input layer of the network and its outputs determine
the neuron number in output layer of network. Eight
neurons were used in the hidden layer of the model.
A neural network requires that the range of the both
input and output values should be between 0.1 and 0.9
due to the restriction of the sigmoid function, conse-
quently, the data must be unified.
Normalize data
Actual value Minimum value
Maximum v
=
−
alue Minimum value
(High Low) Low
−
×
× − +
is a widely employed method in unification.15
In this study, the backpropagation network training
function updates the weight and bias values according to
the Levenberg-Marquardt optimization. The performance
index was determined by the mean squared error. The
Levenberg-Marquardt algorithm is very well suited to
neural network training where the performance index is
the mean squared error.
5 RESULTS
The input-output data set for the neural network
training and testing were obtained from experiments in
the Nuh Cement Factory. A data set of 455 samples was
used to train the neural network model. A data set of 200
samples was utilized to test the network model.
The input and output data were used by the network
in the training stage and the network learned the process.
After the network was trained, the Fe2O3 and Lime
Modulus for different combinations of low grade and
A. E. TIRYAKI et al.: MATHEMATICAL MODELING OF A CEMENT RAW-MATERIAL BLENDING PROCESS ...
488 Materiali in tehnologije / Materials and technology 50 (2016) 4, 485–490
Figure 6: Log-Sigmoid transfer function 14
Slika 6: Log-Sigmoid prenosna funkcija 14
Figure 4: Linear transfer function 14
Slika 4: Linearna prenosna funkcija 14
Figure 5: The nonlinear network structure14
Slika 5: Struktura nelinearne mre`e14
iron ore from the test data set were predicted. Figures 7
and 8 show a comparison of the linear neural network
prediction with the experimental data. The comparison
of the nonlinear neural network prediction with the ex-
perimental data is shown in Figures 9 and 10.
During training, the mean squared errors were recom-
puted using next updated weights and the performance
graphic was obtained for the nonlinear network in
Figure 11. The goal in the figures is the target value of
the MSE and the performance is the MSE value obtained
from the ANN training result. As shown in Figure 11,
the error decreases rapidly in the next iterations.
The Fe2O3 prediction of the models indicated that the
maximum error between the linear neural network results
and desired outputs is about 7.5×10–3 and maximum
error between nonlinear neural network results and the
desired outputs is about 4×10–3. For the Lime Modulus
A. E. TIRYAKI et al.: MATHEMATICAL MODELING OF A CEMENT RAW-MATERIAL BLENDING PROCESS ...
Materiali in tehnologije / Materials and technology 50 (2016) 4, 485–490 489
Figure 11: Performance of the nonlinear neural network
Slika 11: Uspe{nost nelinearne nevronske mre`e
Figure 8: Comparison of the linear neural network prediction with
experimental data (for Lime Modulus)
Slika 8: Primerjava napovedi linearne nevronske mre`e z eksperimen-
talnimi podatki (za module z apnom)
Figure 7: Comparison of the linear neural network prediction with the
experimental data (for Fe2O3)
Slika 7: Primerjava napovedi linearne nevronske mre`e z eksperimen-
talnimi podatki (za Fe2O3)
Figure 10: Comparison of the nonlinear neural network prediction
with the experimental data (for Lime Modulus)
Slika 10: Primerjava napovedi nelinearne nevronske mre`e z eksperi-
mentalnimi podatki (za module z apnom)
Figure 9: Comparison of the nonlinear neural network prediction with
the experimental data (for Fe2O3)
Slika 9: Primerjava napovedi z nelinearno nevronsko mre`o z eksperi-
mentalnimi podatki (za Fe2O3)
output of the models, the maximum error of the linear
neural network is about –0.21 and the maximum error of
the nonlinear neural network is about 0.095. Further-
more, the training performance (MSE) of the nonlinear
neural network reached 3.00751×10–4 at 500 epochs. The
meaning of the MSE being very small is that the desired
outputs and the ANN’s outputs for the training set have
become very close to each other.
6 CONCLUSION
In this study the raw-material blending process in a
cement factory was examined and two different mathe-
matical models were developed using linear and non-
linear neural networks. In this modeling the experimental
data were used from a controlled process under varying
operating conditions in the Nuh Cement Factory in
Turkey. Good parametric multivariable models having
the minimum number of parameters were obtained. The
inputs are the feed ratios of the raw materials (low grade
and iron ore) and the outputs are iron oxide and/or the
lime module values of the raw meal.
The developed linear and nonlinear neural network
predictions were compared with the experimental results.
The network test showed that the nonlinear neural net-
work has a higher predictive accuracy and convergence
for the raw-material blending process. The linear-
model-based prediction shows a greater deviation than
the nonlinear model. The mathematical model that is
established by the nonlinear neural networkis a suitable
model for the blending process of cement raw material.
Finally, this multi-input, multi-output model has
made possible the control of the iron oxide and the lime
module together, instead of using parallel-working
single-loop controllers. In this case only the lime module
or the iron oxide could have been controlled, depending
on the choice in the Nuh Cement Factory with the avail-
able control package, designed models give the opportu-
nity for these outputs to be controlled together by using a
two-input, two-output process model. Furthermore,
stable operating conditions can predict the process with
these models.
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490 Materiali in tehnologije / Materials and technology 50 (2016) 4, 485–490