Development of bimetallic Ni-Cu/SiO2 catalysts for liquid phase selective hydrogenation of furfural to furfuryl alcohol

Article abstract of DOI:10.1016/j.catcom.2020.106221

Bimetallic Ni-Cu/SiO₂ catalysts with different Cu loading (2–5 wt%) were developed for liquid phase selective hydrogenation of furfural to furfuryl alcohol. Among these, bimetallic 2%Ni-X%Cu/SiO₂ (X = 2, 5) catalysts exhibited better

Full text of DOI:10.1016/j.catcom.2020.106221

Scientia Iranica E (2011) 18 (3), 722–730
Sharif University of Technology
Scientia Iranica
Transactions E: Industrial Engineering
www.sciencedirect.com
An enhanced neural network model for predictive control of granule
quality characteristics
N. Neshata, H. Mahloojib,∗, A. Kazemic
a Department of Industrial Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, P.O. Box 14155-143, Iran
b Department of Industrial Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-9414, Iran
c Department of Industrial Management, Faculty of Management, University of Tehran, Tehran, P.O. Box 14155-6311, Iran
Received 3 March 2010; revised 29 September 2010; accepted 6 December 2010
KEYWORDS
Abstract An integrated approach is presented for predicting granule particle size using Partial Correlation
(PC) analysis and Artificial Neural Networks (ANNs). In this approach, the proposed model is an abstract
form from the ANN model, which intends to reduce model complexity via reducing the dimension of
the input set and consequently improving the generalization capability of the model. This study involves
comparing the capability of the proposed model in predicting granule particle size with those obtained
from ANN and Multi Linear Regression models, with respect to some indicators. The numerical results
confirm the superiority of the proposed model over the others in the prediction of granule particle size.
In order to develop a predictive-control strategy, by employing the proposed model, several scenarios
are developed to identify the most suitable process settings with respect to the desired process response.
Utilization of these scenarios paves the way for decisions about spray drying to be made consistently and
correctly without any need for judgmental speculations or expensive trial-and-error tests.
Predictive control;
Artificial neural networks;
Partial correlation;
Particle size;
Modelling;
Spray drying.
© 2011 Sharif University of Technology. Production and hosting by Elsevier B.V.
Open access under CC BY-NC-ND license.
1. Introduction
to the upper part of the tower via a heat-insulated steel duct,
causes a constant suction pressure in the tower (9) and is set in
rotation by the annular distributor (10). Dried powder, i.e. the
granule, is unloaded via the outlet valve (5) onto a conveyor
belt. The fine powder residue that remains suspended in the air
is exhausted by the main fan (11) and is separated out, in part,
by the cyclones (6) and, in part, by the wet dust separator (12).
Then the exhausted air, at a constant temperature, leaves via
the stack (13) [1].
Granule particle (PS) size, as a quality characteristic, is
controlled by measurement during granule production. The
Weight of the Residual Granule (WRG) is the weight of the
output granule with a diameter greater than 300 µm in a
sample that weighs 0.1 kg. Hence diameters must be monitored
in order to control the PS quality. According to the spray
drying process diagram shown in Figure 2, the process response,
i.e. WRG, is considered in terms of its related variables. Such
variables usually have to do with either properties or operating
conditions, like slip viscosity (ν) and density (ρ). There are
also a few in-process variables, such as the hot air temperature
(Tin), air suction pressure (PS ) and fed slip pressure (Pp), to be
considered.
For over a century, spray drying, as a unique drying process
for powder production, has experienced extended applications
in the foodstuff, manufacturing and pharmaceutical industries.
A simplified description of the granule production process
is as follows (see Figure 1): The slip with specified density and
viscosity is fed at a constant pressure and temperature by the
pump (1), passes through the filters (2), reaches the distributor
ring (3), inside the tower (4). The finely atomized slip jet is
hit by a vortex of hot air at a fixed temperature produced by
natural gas (8), and an intake fan (7). The air, which is conveyed
∗
Corresponding author.
E-mail address: mahlooji@sharif.edu (H. Mahlooji).
1026-3098 © 2011 Sharif University of Technology. Production and hosting by
Elsevier B.V.
Open access under CC BY-NC-ND license.
Peer review under responsibility of Sharif University of Technology.
doi:10.1016/j.scient.2011.05.019
The exhausted air temperature (Tout), as an in-process
variable, is generated through internal treatment of the spray
drying process [1]. A few features of the input, in-process and
output variables of spray drying are summarized in Table 1.

N. Neshat et al. / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 722–730
723
Nomenclature
ANFIS
PSI
Adaptive Neuro-Fuzzy Inference System
Particle Size Index
ANN
Artificial Neural Network
absolute fraction of variance
Mean Absolute Percentage Error
Root Mean Square Error
Membership Function
inlet air temperature
R2
MAPE
RMSE
MFs
Tin
NN
Neural Network
Tout
PLS
WRG
Pp
exhausted air temperature
Partial Least Squares
Weight of Residual Granule
fed slip pressure
target value of output
air suction pressure
obtained value of output
ydm
PS
ym
Greek symbols
Figure 1: Schematic diagram of a spray drier.
ν
ρ
viscosity
density
γ
learning rate
1ψm
1ψj
1Wij
bias values of output layer to hidden layer
bias values of input layer to hidden layers
weighted value revising function between input
and hidden layer
weighted value revising function between hid-
den and output layers
1Wjm
Figure 2: Process diagram of spray drying.
Often, a full theoretical understanding of the mechanism of
a complex process such as spray drying may be lacking [2].
The lack of such understanding is directly attributed to the
complexity of the interdependent and correlated process
variables. Constructing a model of the process is a conventional
alternative for discovering the relationships between input and
output variables of the process with the aim of controlling the
process.
To judge by recent publications, conventional parametric
methods are not suitable for modelling complex manufacturing
processes [3–5] due to the great number of process variables
and the non-linear nature of their relations. In contrast,
Artificial Neural Networks (ANN) have been known to be
good candidate approaches for this purpose. Several successful
implementations of ANN have been reported recently. Su
and Hsieh [6] compared the reliability of the Taguchi
model with the ANN model for semiconductor manufacturing
processes and established the superiority of the ANN model.
Yimnirun et al. [7] studied the modelling of the synthesis
process of NiNb2O6 powder using ANN and multiple regression
models. In their investigation, ANN significantly outperformed
Multiple Regression. Furthermore, several studies investigated
the process mechanism and optimization of the manufacturing
process through neural network modelling [8–13].
Neural network modelling is an area with considerable
potential for improving quality control processes in the
ceramics industry as well. The literature on such applications
is more recent and less extensive. For instance, Lam et al. [14]
developed a prediction module to estimate two quality metrics
of slip-cast pieces through simultaneous execution of two
neural networks and a process improvement algorithm. Their
algorithm optimizes controllable process settings using the
neural network prediction module in the objective function.
Scott et al. [15] developed an ANN model in order to use
compositional information to predict the relative permittivity
and oxygen diffusion properties of ceramic materials. The
relevant results show that ANN is able to produce accurate
predictions of the properties of these ceramic materials.
Table 1: Characteristics of proposed variables of spray drying process.
Units
Type
Interval
Max
Mean value
Standard deviation
Min
−3
Slip density
kg
Input
1.66 × 103
1.70 × 103
1.68 × 103
57.02
0.01 × 103
9.04
Slip viscosity
S
Input
45.00
70.00
Inlet air temperature
Fed slip pressure
Air suction pressure
Exhausted air temperature
Weight of residual granule
°C
In-process
In-process
In-process
In-process
Output
540.00
555.00
549.12
2.94
N/m2
N/m2
°C
13.50 × 105
18.50 × 102
91.00
18.50 × 105
21.00 × 102
104.00
17.30 × 105
18.54 × 102
98.27
74.22 × 10
0.70 × 105
1.30 × 102
2.64
−3
−3
−3
−3
kg
68.10 × 10
77.00 × 10
3.68 × 10

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N. Neshat et al. / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 722–730
Dinh and Afzulpurkar [16] compared ANN and the Co-
Active Neuro-Fuzzy Inference System (CANFIS) in modeling the
real complicated Multi-Input–Multi-Output (MIMO) nonlinear
temperature process of a roller kiln used in the ceramic tile
manufacturing line. A three-layer Back Propagation Artificial
Neural Network (BPANN) was developed by Yu et al. [17]
for predicting the performance of porous Si3N4 ceramics. The
results indicated that BPANN is a very useful and accurate tool
for the prediction and optimization of porous Si3N4 ceramics
performance. However, earlier studies can be found for this
process in other industries [18–20] also. Since the most
popular application of ANN to spray drying is the prediction
of process parameters, citing the following works is in order:
Chegini et al. [21] predicted seven performance indices in an
orange juice spray drier using ANN. ANN and Response Surface
Methodology (RSM) were compared by Youssefi et al. [2] in
predicting the quality parameters of spray dried pomegranate
juice. The results showed that the ANN model outperforms RSM
for complex spray drying.
Ant studies published in the area of modelling complex
manufacturing processes can be categorized into two groups.
The first group includes those attempts to establish the
superiority of the ANN algorithm over parametric methods,
such as RSM and Multiple Linear Regression (MLR) analysis. The
second group consists of studies using an ANN algorithm or a
hybrid system of ANN along with other heuristic algorithms,
such as the Genetic Algorithm (GA), with the aim of predictive
control and optimization.
In this study, an integrated intelligent approach consisting
of Partial Correlation (PC) analysis (parametric approach) and
ANN (heuristic approach), code named PC-ANN, is used to
develop a reliable and accurate model for predicting the granule
PS. According to the proposed algorithm, initially, the PC
analysis is applied to process the actual data and provide the
necessary background to apply ANN. Based on the findings of
the PC analysis, at the next step, the PC-ANN model is developed
to predict the granule Particle Size Index (PSI). As a comparative
study, the performances of the PC-ANN and ANN models
are studied. Finally, based on the superior approach, several
scenarios are proposed in order to achieve predictive control of
the granule PS as accurate, fast running and inexpensive tools.
The remainder of this paper is organized as follows. Section 2
briefly describes artificial neural networks and modelling
with ANN. The proposed PC-ANN algorithm is introduced in
Section 3. Section 4 is devoted to experiments and the actual
case study of this work. Discussion and scenarios are included
in Section 5 and conclusions are presented in Section 6.
Figure 3: The network architecture of an ANN model consisting of one hidden
layer with S neurons, along with input and output layers, with R and one
neuron(s).
in-process variables, e.g. process settings, as well as process
responses/outputs, e.g. quality characteristics. The ANN then
‘learns’ the governing relationships in the input and output data
sets by modifying the weights between its nodes. In essence,
a trained ANN model can be considered a function that maps
input vectors to output vectors. Briefly, the intention is that the
network should behave exactly like the process, considering its
response to variables and conditions, hence providing a model
of the process which can be used for the prediction of output
properties.
The architecture of an ANN model usually consists of three
parts: an input layer, the hidden layers and an output layer.
The information contained in the input layer is mapped to the
output layer through the hidden layers. Each neuron can receive
its input only from the lower layer, and sends its output to the
neurons only on the higher layer.
Figure 3 illustrates the network architecture of an ANN
model consisting of one hidden layer with S neurons, along with
input and output layers with R and 1 neuron(s), respectively.
Here, input vector p with R input elements is represented by
a solid dark vertical bar on the left. Thus these inputs post
multiply the S-row, R-column matrix W. The quantity 1, as a
constant value, enters the neuron as an input and is multiplied
by vector bias b with S rows and a single column. The net input
to the transfer function, f , consists of n, the sum of bias b, and the
product Wp. This summation is passed to the transfer function,
f , to get the neuron’s output which in this case is a vector with
length S [23].
3. Methodology
Modelling complex and nonlinear manufacturing processes
that deal with noisy, limited and non-integrated data requires
methods that can alleviate these problems. Thus we propose
an integrated intelligent approach, code named PC-ANN, to
achieve this purpose. In this study, both ANN and PC-ANN
approaches are applied to predict granule PSI, in an attempt to
identify the superior approach.
2. Modeling with ANN
ANNs mimic the ability of biological neural systems in a
computerized way by resorting to the learning mechanism as
the basis of human behaviour [22]. Utilizing samples from pro-
cess outputs, ANN proposes an approximate model architecture
to fit the data. Therefore, ANN may be applied to problems with
a non-linear nature or with too complex algorithmic solutions.
Their ability to perform complex decision-making tasks without
prior programming makes ANNs more attractive and powerful
than parametric approaches, especially for complex problems.
Whereas the accurate prediction of a quality characteristic
is a key factor in the success of a manufacturing operation,
ANN can be deployed to model and predict the response
of a complex manufacturing process. In order to model the
process, the network must be trained based on input and
ANN and PC-ANN approaches are applied in order to develop
ANN and PC-ANN models for optimum prediction of the
granule, PSI. Although both these approaches take a similar set
of six phases (as follows) to develop the models, it should be
noted that their models are different, with regard to their input
set.
These six phases are described as follows:
Phase 1. Selection of neural network topology. At present,
there are about 31 different Neural Network (NN) topologies
being employed in research. The most common networks are:
Multi Layer Perceptrons (MLP), also called Multilayer Feed
Forward Networks, Adaptive Resonance Theory Models (ART),

N. Neshat et al. / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 722–730
725
Recurrent Associative Networks (RAN) and Self-Organizing
Maps (SOM) [24]. Each combination of an ANN type and
a training algorithm is selected for a different situation,
depending on the networks purpose of usage. For instance, the
MLP trained with a Back Propagation (BP) algorithm is suitable
as a black-box model of systems whose underlying relations are
vaguely known or are extremely complex. The most popular
algorithm in engineering applications is the standard Back
Propagation (BP) algorithm [25]. This algorithm is a widely used
iterative optimization technique that locates the minimum of a
function expressed as:
input layer and the hidden layer, as well as between the hidden
layer and the output layer, respectively.
In this phase, the topologies of the network and its training
algorithm, considering the nature of modelling the problem,
are chosen. The other decision to be made is defining how the
input variables and the process response are presented to the
network as input and output, respectively. One way is to present
all available process variables as network input, and then let
the network modify itself during training so that the connection
of any insignificant variables becomes weak. Another approach
that is more selective introduces as input only those variables
that are surely affecting the process output. The first approach
has been called the ‘‘global approach’’ while the second is
termed the ‘‘focused approach’’ [26].
−
1
E =
(ydm − ym)2,
(1)
2
m
Phase 2. Collection and preparation of training data set. In the data
collection stage, it is necessary to ensure the sufficiency and
integrity of the data used to train, validate and test the network.
As the performance of a network can be directly influenced by
the presented data, it is not simply possible to say how many
data sets are required, because this depends on the nature of the
modelling problem and the cost of providing data. The prepared
set of data is partitioned randomly into three sets: training,
validation and test data.
where ydm is the target output value of the output layer,
and ym is the obtained value of the output layer. Based on
the BP algorithm, during the training process, the deviation
between the network output and the desired output at each
presentation is computed as an error. This error, in quadratic
form, is then fed back (back propagated) to the network and is
used for modifying the weights by a gradient descent method,
as follows:
∂E
∂E ∂ym ∂netm
Training data can be provided in three ways [27].
1ωjm = −γ
= γ
.
.
,
(2)
(3)
(4)
∂Wjm
∂ym ∂netm ∂Wjm
1. Simulated data: The data in this category is replaced by
actual process data. Often, simulated data is generated
by statistical models (such as normal distribution) and
computational simulations (such as finite-element analysis
methods).
2. Actual process data: When randomly selected raw process
data is used for training NN, in fact, the actual data is
employed to construct NN model. Many manufacturing
companies have already provided both process variable data
and quality inspection/product test data in their databases.
3. Designed experiment data: This data is not collected directly
from normal production conditions, but is obtained from
designed experiments on the process, often using the
Taguchi or Design Of Experiment (DOE) approach.


−
∂E
∂ym
∂
1
2
=
(ydm − ym)2 = −(ydm − ym),
∂ym
m
∂ym
∂netm
′
= fo (netm),


−
∂netm
∂Wjm
∂
=
PjWjm = Pj,
(5)
(6)
∂Wjm
m
′
1Wjm = −γ [−(ydm − ym)]fo (netm)Pj = −γ θmPj,
′
θm = −(ydm − ym)f0(netm),
(7)
(8)
1ψm = −γ θm.
In order to enhance model fitness, several tasks for preparing
data may be performed, such as:
The weight change of the hidden layer to the input layer is
calculated s follows.
1. Data integrity check,
1Wij = −γ θjXi,
(9)
2. Extreme data removal,
3. Data pre-processing and post-processing,
4. Data coding.
−
−
∂E ∂Pj
∂E ∂ym ∂netj ∂Pj
θj =
=
∂Pj ∂netj
∂ym ∂netj ∂Pj ∂netj
′
m
m
−
×
[−(ydm − ym)] f0 (netm)
Phase 3. Constructing and fitting the neural network model. The
performance of the NN model depends on the fitness of the
network features. For instance, too few neurons may result
in under-fitting, but too many neurons may yield over-fitting,
which means that all the training data fit well, but the NN
model performance for the test data is mediocre. The optimal
configuration of the network is selected according to the value
of the training error function. So, various architectures with
different features of neural networks can be proposed. During
the training process, representative examples of inputs and
their corresponding outputs of process are presented to the
networks. Ultimately, the best network is chosen based on the
user-specified training error function.
m


−
∂
∂Pj
×
PjWjm
∂Pj
∂netj
j
−
′ 

= −
=
(ydm − ym) f0(netm)WjmfP netj
m
−


′ 

θmWjm fP netj
,
(10)
m
−


′
1Wij = −γ
θmWjm fP (netj)Xi = −γ θjXi,
(11)
(12)
m
1ψj = −γ θj,
where γ is the learning rate, 1ψm and 1ψj stand for the bias
values of the output layer to the hidden layer, as well as the
input layer to the hidden layers, respectively, and 1Wij and
1Wjm are the weighted value revising function between the
Phase 4. Model validation. The validation data set is used to
ensure that there is no over-fitting in the final result. In order
to validate the model, a data set is randomly selected from the
training data. When a significant over-fitting occurs, the error of

726
N. Neshat et al. / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 722–730
Figure 4: Effects of changing the number of neurons in the first and second hidden layers on the learning performance of the ANN model.
validation data starts to increase and the training process comes
to an end.
Phase 5. Selection of performance indicators. To determine the
reliability of a model, several performance indicators can be
used. The performance of the ANN model, based on model
reliability, is evaluated by a regression analysis between the
predicted and actual values.
Second, it is capable of handling the complexity of relations,
limitations and noise in the given data. Third, it improves
the predictive capability of the neural network via dimension
reduction operation.
4. The experiment
In order to develop the ANN and PC-ANN models for
predicting the granule PSI, a set of actual data consisting of 300
data vectors was collected under steady state conditions from
a real system. This data was collected from a large ceramic tile
factory in Yazd province in south Iran. The collected raw data
was provided randomly from the production database for the
period March 23rd, 2005 to September 22nd, 2006 (see the
Appendix). Then, 80% of the data set was randomly set aside
for training purposes, 10% as the validation, and the remaining
10% for testing the network. All the input and output values
were normalized by pre-processing, and checked for integrity
by histogram plots.
The indicators used for evaluation of the network perfor-
mance include mean relative error, root mean square error
and coefficient of determination [28]. The mean relative error
which shows the mean ratio between the error and the actual
values is calculated as:








m
−
ˆ
1
(yi − yi)
MRE (%) =
100
,
(13)
m
yi
i=1
ˆ
where yi is the estimated value by the ANN model, yi is the
actual value of the response process, and m is the number of
points in the data set. The root mean square error is calculated
as:

4.1. The ANN model

m
−


1
2
ˆ
RMSE =
(yi − yi) .
(14)
Taking a global approach in presenting data to the network,
the ANN model adopted for predicting the granule PSI was MLP,
trained by the BP algorithm, based on the Levenberg–Marquart
rule. The network includes five inputs, which consist of ρ, ν, PP ,
PS and Tin, while it has one output, which is WRG.
m
i=1
Finally, the coefficient of determination, a statistical criterion
that can be applied to multiple regression analysis, is calculated
as:
For choosing the optimal configuration of ANN for predicting
the granule PS via predicting the WRG, a number of different
network configurations consisting of one to three hidden layers
and different numbers of neurons in hidden layers with various
transfer functions were considered. The training process was
run in a MATLAB environment, so the minimum of a user-
specified error function, i.e. RMSE, was reached, while the
number of epochs (frequency of presenting training data to
the network) was less than 200, and the grad rate (deviation
of training error in each epoch) was greater than 1e−010.
The optimal configuration of each network was selected based
on values of its training and validation RMSE. As Figure 4
indicates, when the numbers of neurons in the first and second
hidden layers are equal to nine and ten, respectively, we get the
least training RMSE value for the training process in predicting
the granule PSI. However, in this network, selection of more
than three layers leads to a decrease in the network’s training
performance.


m
∑
2
ˆ
(yi − yi)






i=1
2
R = 1 −
.
(15)
m
∑
2
¯
(yi − y)
i=1
The coefficient of determination ranges between zero and one.
Ideally, R2 should be close to one, whereas a poor fit results in a
value near zero.
Phase 6. Model performance evaluation. By termination of
process training and validation, the network is ready for
prediction. Hence, input vectors from separate test data are
introduced to the trained network, and the responses of the
network, i.e. the predicted outputs, are compared with the
actual ones using the performance indicators.
The significance of the integrated PC-ANN approach for
optimum prediction of the granule PSI is threefold. First, it
normalizes all input and output values by pre-processing and
post-processing, respectively, to eliminate all possible noise.
The optimum network architecture of the ANN model for
predicting the granule PSI is given in Figure 5. This figure shows

N. Neshat et al. / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 722–730
727
Figure 5: The network architecture of the ANN model for predicting the granule PSI.
Table 2: The detailed information of optimum configuration and the results of performance evaluation of the PC-ANN, ANN and the MLR models for predicting
the grannule PSI.
Optimum configuration
Training
Validation RMSE
Performance evaluation
Training RMSE
R2 (%)
MRE (%)
RMSE (kg)
−3
−3
−3
PC-ANN model
NN model
MLR model
3-6-8-1
6-7-10-1
5.82358e−005
2.37658e−004
3.2451e−004
8.10037e−004
88.16
82.32
68.09
5.582
8.945
15.67
1.014 × 10
1.784 × 10
4.056 × 10
Table 3: The PC analysis between the process response and the other process variables.
WRG, PS
WRG, Tin
WRG, Pp
WRG, Tout
WRG, ν
WRG, ρ
PC coefficient
Pvalue
Status
−0.055
0.111
0.002
0.249
0.567
0.316
0.002
Correlated
0.601
0.497
0.983
0.017
0.000
Not correlated
Not correlated
Not correlated
Correlated
Correlated
that the network including two hidden layers with nine and ten
neurons is the preferred network. The activation functions in
the layers of this network were chosen as the purline (which
generates output the same value of input), tangent sigmoid
(which generates output between −1 and 1 as the neuron’s
net input goes from negative to positive infinity) and purline
transfer functions, respectively.
Table 4: The PC analysis of pair interactions of input and in-process
variables of spray drying.
PS , Tout
PP , Tout
T
in, Tout
ν, ρ
PC coefficient
Pvalue
0.31
0.003
−0.324
0.354
0.001
0.477
0.000
0.035
The ANN model for predicting the granule PSI was validated
by a stopping rule after 87 epochs when the error due to the
validation data started to increase. Detailed information for
optimum configuration and the results of the training of the
ANN model for predicting the granule PSI are given in Table 2.
The ANN model predictions for granule PSI resulted in an MRE
of the other variables were calculated, and the correlation status
of each pair was determined. The results indicate that only ρ,
ν and Tout are evidently correlated with the process response,
considering that the Pvalue for these tests is larger than the
selected value of the level of significance (0.025). Evidently,
the other four variables, PP , Tin, PS and TS , are not significantly
correlated to WRG.
−3
of 8.945%, an RMSE of 1.784 × 10 kg and an R2 of 82.32% in
comparison to the actual values for the test data set.
To provide a better insight, the correlation analysis was
applied to input and in-process variables and the results
are illustrated in Table 4 (for cases with considerable linear
correlation). It should be noted that the availability of nonlinear
relations between variables that were not linearly correlated
was also investigated. Our investigation failed to register any
significant non-linear relation either.
4.2. PC analysis
In order to discover how the input and in-process variables
influence the process response and discover pair interactions
between process variables, a PC analysis was applied to the
process variables. The PC produces coefficients that describe
the relationship between two variables while adjusting for
the effects of one or more additional variable. In fact, the PC
coefficient measures the degree of association between two
random variables, with the effect of a set of controlling random
variables removed [29]. In order to calculate the PC coefficient,
a statistical test whose null hypothesis is ‘‘two variables are
correlated’’ must be conducted. The null hypothesis will be
rejected if the Pvalue (the probability of observing data at least
as extreme as that observed) for these tests is smaller than the
selected value of the level of significance.
The following conclusions can be drawn, based on the results
displayed in Table 4.
1. ρ and ν are positively related, which is reasonable because
as the density, i.e. the water percentage of slip, decreases,
the viscosity of slip also decreases.
2. PP , Tin and PS are pair wise independent, while they all are
correlated to Tout
.
The concurrent analysis of the results contained in Tables 2 and
3 implies that PP , Tin and PS have directly influenced Tout, which
means that they are indirectly related to WRG. Thus Tout, as an
As illustrated in Table 3, using SPSS software, the partial
correlation coefficients between the process response and each

728
N. Neshat et al. / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 722–730
Figure 6: Network architecture of the PC-ANN model for predicting the granule PSI.
explanatory variable for the process response, is dependent on
PP , Tin and PS . Also within the neural network training process,
Tout can incorporate some additional information in predicting
the granule PSI.
PC-ANN model for predicting the granule PSI are given in
Table 2. The PC-ANN model predictions for the WRG led to an
MRE of 5.582%, an RMSE of 1.014×10−3 kg and an R2 of 88.16%,
when compared to the actual values for the set of the test data.
4.3. The PC-ANN model
4.4. Multi linear regression model
The PC-ANN model was developed considering the findings
of the PC analysis presented in the previous section. First, we
used ANN to estimate Tout in terms of PP , Tin and PS . Second,
we constructed the PC-ANN model for estimating the WRG
in terms of the estimated Tout as a hint [10], as well as two
input variables, i.e. ν and ρ. According to the six stages of ANN
modelling, the PC-ANN model was constructed.
In order to compare the performance of the proposed ANN
model and the PC-ANN model of spray drying, the same test
data vectors were used to evaluate the performance of the PC-
ANN model.
To identify the optimal configuration of the PC-ANN model
for predicting the granule PSI via predicting WRG, all plausible
PC-ANN models were run and estimated with regard to various
network features. Based on different numbers of hidden layers
and neurons, as well as various transfer functions, a number
of different network configurations were considered. The
computer code for solving the BP algorithm (MATLAB 7, Release
14, The Mathworks Inc., MA, USA) was implemented. Training
information and the results of the PC-ANN model are shown in
Table 2.
The training process was run, and led to the minimum value
of the RMSE function, while the number of epochs was less than
200 and the grad rate was greater than 1e−010. The optimal
configuration of the network was determined based on the
value of training and validation, RMSE. The sensitivity analysis
of the RMSE value showed that when the number of neurons
in the first and second hidden layers are equal to six and
nine, respectively, it assumes its smallest value in predicting
the granule PSI. However, when the number of hidden layers
exceeds three, the performance of the training process starts to
deteriorate.
Multi Linear Regression (MLR) estimates the coefficients
of a linear equation involving two or more independent
variables that best predict the value of the dependent variable.
Considering the fact that Tout is correlated to Tin, PS and Pp, the
MLR model for predicting the granule PSI via estimating the
WRG is illustrated by the following equations:
Tout = 0.249Tin − 0.541 × 10−2PS
+ 0.090 × 10−5PP − 30.302,
(16)
WRG = 1.93 × 10−3ρ − 0.011ν + 0.292Tout − 281.11. (17)
According to the outcomes of the following hypothesis tests, the
MLR model for predicting the WRG is validated.
1. Analysis-of-variance test: F0 = 24.105 and the correspond-
ing Pvalue = 0.000.
2. Individual coefficient test: Pvalue < 0.05 (defined level of
significance) for t0 statistics of ρ, ν and Tout
.
3. Non-multi colinearity test; variance inflation factors of ρ, ν
and Tout < 4.
4. Durbin–Watson test: D0 = 2.247 > D = 1.74.
α,u
Based on the outcomes of these tests of hypothesis, the validity
of the MLR model in predicting Tout was accepted. The results
of the performance evaluation of the MLR model in predicting
the granule PSI, based on the set of the test data, are given in
Table 2.
5. Discussion and scenarios
The indicators used for evaluation of the model performance
are MRE, RMSE and R2. The comparison of numerical results
for performance evaluation shows that the ANN model has
an improvement in R2 of 14.23%, a decrease in MRE of 6.72%
The optimum network architecture of the PC-ANN model
for predicting the granule PSI is given in Figure 6. This figure
shows that the network consisting of two hidden layers with
six and nine neurons is the most preferred network. Activation
functions in the layers of this network were chosen as the tan
sigmoid, log sigmoid and pure line transfer functions.
The ANN model for predicting the granule PSI was validated
by a stopping rule after 240 epochs when the error due to the
validation data started to increase. Detailed information about
the optimum configuration and the results of training of the
−3
and a decrease in RMSE of 2.27 × 10 kg when compared to
the MLR model. These results indicate that the complexity and
nonlinearity of the spray drying treatment may hardly allow
a parametric model to discover and capture the relationships
between the input and output variables.
In addition, according to the results of Table 2, the PC-
ANN model has an improvement in R2 of 5.84%, a decrease
−3
in MRE of 3.36% and a decrease in RMSE of 0.77 × 10 kg
when compared to the ANN model. These results demonstrate

N. Neshat et al. / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 722–730
729
Figure 7: Comparison of predicted values of PC-ANN (ꢀ) and ANN models (×)
versus actual values (•) for the set of the test data.
Figure 9: An illustration of several scenarios using predictions of the PC-ANN
model for the process response as a function of the slip viscosity and the air
suction pressure.
9 report the predictions not only in the normal range of inputs
considered in the study, but also beyond the normal range.
Figure 8 depicts the changes in the predicted values of WRG,
with respect to ν and Pp, when the other three input variables
are kept constant at the values shown (ρ = 1.68, PS = 18.54
and Tin
=
549.12). As can be seen, in spite of what one
expects to observe, WRG decreases, while Pp is more than 21.
This abnormal behaviour can be interpreted as follows. When
Pp increases significantly, a cloud of slip particles forms due
to excessive height of spraying, which in turn, causes the slip
particles to stick together. However, there is little exclusion,
considering the interactive effects among variables.
Figure 9 reports the changes in the predicted values of
WRG, with respect to ν and PS , when the other three input
variables are kept constant at the values shown (ρ = 1.68,
Pp
=
17.30 and Tin
=
549.12). It can be seen that WRG
Figure 8: An illustration of several scenarios using predictions of the PC-ANN
model for the process response as a function of the slip viscosity and the fed slip
pressure.
increases, while PS decreases with any increase in ν, because of
a greater chance of particles sticking together. However, several
exclusions considering the interactive effects among variables
can be observed.
that a proper dimension reduction in the input set, based on
the findings of the PC analysis, leads to an improvement in
the performance indicators of the PC-ANN model. In other
words, the generalization capability of the PC-ANN model, via
eliminating redundant inputs, tends to increase.
In order to compare the predicted values rendered by ANN
and PC-ANN models versus the actual values of test data on an
individual basis, one can refer to Figure 7. This figure shows that
the PC-ANN predictions have a distinct visual correlation with
actual values, even when the samples are selected beyond the
normal range of actual values. For instance, even though the 3rd,
13th, 18th, 26th and 27th observations have been gathered out
of the normal range of operating conditions, the PC-ANN model
is capable of extrapolating them properly.
An important feature in modeling the spray drying mech-
anism is that the superior model, i.e. the PC-ANN model, can
also be used to accurately investigate the effects of the input
variables on the output. In order to visualize this capability, the
PC-ANN model predictions of granule PSI, as a function of input
variable, ν, for instance, are shown in Figures 8 and 9. These
figures illustrate several scenarios for predictive process con-
trol when two input variables vary and the other input variables
are kept constant. In fact, first, the values of Tout are calculated
in terms of Tin, PS and Pp, and then, they are used for prediction
of WRG values via the PC-ANN model. Note that Figures 8 and
6. Conclusions
This study has been undertaken to present an integrated
approach for prediction of granule particle size using Partial
Correlation (PC) analysis and Artificial Neural Networks (ANN).
According to the proposed algorithm, initially, a PC analysis
is used to process actual data and to provide the necessary
background for applying ANN. Next, with respect to the findings
of the PC analysis, the PC-ANN model is developed for predicting
the granule PSI. The performance of both models, based on
their predictive capability, was evaluated, using such indicators
as the coefficient of determination (R2), Mean Relative Error
(MRE) and Root Mean Square Error (RMSE). Comparing the
performance of both models reveals that the PC-ANN model
outperforms the ANN model in terms of an improvement in R2
of 5.84%, a decrease in MRE of 3.36% and a decrease in RMSE of
−3
0.77 × 10 kg. In fact, a proper reduction in the dimension of
the input data set, based on a PC analysis, leads to improving
the performance of the PC-ANN model. Besides, a comparison
of the predictions of both models versus the actual values for a
set of test data demonstrates that the PC-ANN model, not only
interpolates more accurately than the ANN model, but also can
extrapolate more satisfactorily.

730
N. Neshat et al. / Scientia Iranica, Transactions E: Industrial Engineering 18 (2011) 722–730
Table A.1: A sample of raw data of spray drying in a large ceramic tile manufactory in Yazd province in south Iran.
Data number
1
2
3
4
5
6
7
· · ·
292
293
294
295
296
297
298
299
300
ρ(×103)
1.66
60
555
18.7
19
98
72
1.68
65
543
21.2
18.5
96
1.69
59
549
20.1
19
98
69.5
1.69
58
547
17.9
19.5
91
1.66
70
551
19.6
20
92
72.1
1.67
65
552
21.3
19
95
63.1
1.67
58
· · ·
· · ·
· · ·
· · ·
· · ·
· · ·
· · ·
1.67
60
547
18.8
20.5
97
1.68
61
550
20.3
20.05
97
1.68
58
1.67
59
551
18.7
21
98
69.5
1.66
66
549
17.9
21
96
72.8
1.68
58
547
20.9
20.5
93
1.68
64
540
20.8
20
93
76.6
1.67
64
552
19.7
19
98
64.3
1.69
66
548
19.6
19
97
74.5
ν
Tin
550
20.3
19.5
101
63.4
549
21.3
19.5
102
69.4
−5
−2
Pp(×10
PS (×10
Tout
)
)
−3
WRG (×10
)
69.2
69.9
67.9
68.6
74.6
Finally, deploying the superior model, several scenarios, as
accurate, fast running and inexpensive tools, are presented
to identify the optimal process settings based on the desired
process response. Production engineers employing the PC-ANN
model, as a reliable model for predictive control of complex
processes, can save both engineering effort and funds.
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Appendix
The sample of spray drying raw data which was utilized in
this experiment is presented in Table A.1. This set of actual
data was gathered from one spray drier in a large ceramic tile
manufactory in Yazd province, Iran.
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Najmeh Neshat received her B.S. and M.S. Degrees in Industrial Engineering
from the Departments of Industrial Engineering at Yazd University, Iran, in 2001
and Sharif University of Technology, in Tehran, in 2008, respectively. Currently
she is a Ph.D. student of Industrial Engineering in the Department of Industrial
Engineering at Tarbiat Modares University in Tehran, Iran. She has worked in the
ceramic industry as consultant for over 6 years. Her current research interests
are in Artificial Intelligence.
Aliyeh Kazemi was born in Iran, in 1980. She received her B.S. Degree
in Industrial Management from the Department of Industrial Management,
Faculty of Administrative Science and Economics, Isfahan University, in 2002,
and her M.S. degree in Operations Research Management from the Department
of Industrial Management, Faculty of Management, Tehran University, in
2005. Currently she is a Ph.D. student of Operations Research Management
at the Department of Industrial Management, Faculty of Management, Tehran
University.
Her employment experience includes the National Iranian Oil Refining and
Distribution Company, Tehran, Iran (2004–2006) and the Petroleum Ministry,
Tehran, Iran (2006–2009). Her current research interests include Operations
Research, Energy Models and Artificial Intelligence.