An Intelligent Model to Predict Breaking Strength of Rotor Spun Yarns Using Gene Expression Programming

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Journal of Engineered Fibers and Fabrics 1
Volume 7, Issue 2 – 2012

An Intelligent Model to Predict Breaking Strength of Rotor
Spun Yarns Using Gene Expression Programming

Abdolrasool Moghassem, Ph.D.
, Alireza Fallahpour
, Mohsen Shanbeh

Department of Textile Engineering, Qaemshahr Branch, Islamic Azad University, Qaemshahr, IRAN

Department of Management, Firoozkooh Branch, Islamic Azad University, Firoozkooh, IRAN

Department of Textile Engineering, Isfahan University of Technology, Isfahan, IRAN

Correspondence to:
Abdolrasool Moghassem email:
Exploring relationships between characteristics of a
yarn and influencing factors is momentous subject to
optimize the selection of the variables. Different
modelling methodologies have been used to predict
spun yarn properties. Developing a prediction
approach with higher degree of precision is a subject
that has received attention by the researchers. In the
last decade, Artificial Neural Network (ANN) has
been developed successfully for textile nonlinear
processes. In spite of the precision, ANN is a black
box and does not indicate inter-relationship between
input and output parameters. Hence, Gene Expression
Programming (GEP) is presented here as an
intelligent algorithm to predict breaking strength of
rotor spun yarns based on draw frame parameters as
one of the most important stages in spinning line.
Forty eight samples were produced and different
models were evaluated. Prediction performance of
the GEP was compared with that of ANN using Mean
Square Error (MSE) and correlation coefficient (R
Value) parameters on test data. The results showed a
better capability of the GEP model in comparison to
the ANN model. The R
-value and MSE were 97%
and 0.071 respectively which means desirable
predictive power of GEP algorithm. Finally, an
equation was extracted to predict breaking strength of
the yarns with a high degree of accuracy using GEP

Keywords: Rotor spun yarn – Gene expression
programming – Artificial neural network – Draw
frame – Production speed – Break draft – Breaking

Breaking strength of a yarn is an important quality
parameter that affects determination of its application
possibilities [1]. This property is related to raw
materials factors, process variables, machine

parameters and machine parts selection [2]. A survey
of the literature reveals that, there has been a great
deal of research done on roller drafting of staple fiber
assemblies such as sliver

[2]. The purpose of the draw
frame is to attenuate the sliver to the desired linear
density. It also reduces irregularity by the process of
doubling [3]. Drafting quality affects fiber
arrangement, fiber parallelization and fiber
distribution in a sliver. The effect of the drafting
quality may transmit up to the fibrous assembly in
spun yarn, affecting its structure and properties
consecutively [2].

Drafting quality is governed by process variables
such as break draft, roller setting, delivery speed and
top arm pressure. There is a high degree of
interaction between these variables and quality of the
product in this step [4-6]. The complexity of a fiber-
to-yarn process is very high and models that consider
all the variables are not available for such kind of the
problems [7].

A model can be defined as the group of expressions
that determines the relationship between the elements
in order to examine the behavior of a system under
changing conditions, to control it, and to make
assumptions about the future [8].

Statistical models were the first that used in textile
disciplines to explore relationships between variables
and characteristics of product and to optimize
processing parameters [9]. The prediction ability of
regression analysis may be limited for highly non-
linear problems [10].

As a nonlinear problem, predicting breaking strength
of a yarn can be realized by using an alternative
modelling method that is an artificial neural network
(ANN) of soft computing approaches. ANN models
are called as "black box" as they simply connect the
Journal of Engineered Fibers and Fabrics 2
Volume 7, Issue 2 – 2012

inputs and outputs without understanding any
physical information about the process [11, 12]. On
the other hand, it is not easy to relate inputs of ANN
with its outputs in an analytical equation form.

A new soft computing approach from the family of
evolutionary programming that is known as Gene
Expression Programming (GEP) (Ferreira, 2001) is
also a promising candidate for complex prediction
problems. GEP is able to provide prediction
equations without requiring a cast equation as in the
case of regression analysis [10, 13].

This paper makes an attempt by using GEP for
predicting breaking strength of rotor spun yarns
based on the draw frame variables of break draft,
production speed, and distance between back and
middle rolls.

An artificial neural network is an information-
processing system that has certain performance
characteristics in common with biological neural
networks. This technique is useful when there are a
large number of effective factors on the specific
process [12, 14].

A neural network consists of a large number of
simple processing elements called neurons, units,
cells, nodes. Each neuron receives connections from
other neurons and/or itself, each with an associated
weight. The interconnectivity defines the topology of
the ANN. The weights represent information being
used by the neural network model to solve a problem.
One of the central issues in neural network design is
to utilize systematic procedures (a training algorithm)
to modify the weights directly from the training data
without any assumptions about the data's statistical
distribution [14, 15].

There are different kinds of topologies and training
algorithms but the feed forward neural network with
back-propagation learning algorithms is more
popular. In this structure, the neurons are located in
layers and from one layer to another one connected
with each other with links to carry the signals
between them. There is a weight for each connection
link which acts as a multiplication factor to the
transmitted signal. An activation function such as
linear or sigmoid. is applied to each neuron’s input to
determine the output signal. Usually a feed forward
neural network consists of several layers of nodes,
one input layer, one output layer and some hidden
layers in between.

The training of a neural network by back-propagation
involves three stages: the feed-forward of the input
training pattern, the calculation and back-propagation
of the associated error, and the adjustment of the
weights [14]. The calculation of error vector to adjust
the weights is done according to the calculated mean
square error (MSE) form the difference between
actual and predicted outputs according to the
following relationship.

 

0 0


are the target output and predicted
output respectively for
th training pattern at
output neuron.
is the total number of output
neurons and
indicates the number of training

In the backward pass, this error signal is propagated
backwards to the neural network and the synaptic
weights are adjusted in such a manner that the error
signal decreases with each iteration process. Thus,
the neural network model approaches closer and
closer to producing the desired output. The
corrections necessary in the synaptic weights are
carried out by a delta rule, which is expressed by the
following equation.

)()( njinji


is the weight connecting the
at the
th iteration;
, the
correction applied to
at the
th iteration; and


䅎丠桡猠扥敮⁥e灬潹敤⁥硴e湳nv敬y⁩n⁶ 物ou猠
牥獥慲rh映䉥汴牡渠 (2005) on the pilling
tendency of wool knits [18]. The performance of
ANN model was compared with statistical regression
and fuzzy regression to develop the predictive models
for polyester dyeing [19]. The ANN model has also
been used to predict cotton yarn hairiness [20].
Bursting strength of cotton plain knitted fabrics was
predicted using ANN and neuro-fuzzy approaches by
Ertugrul and Ucar [21]. They used a total of 62 data
pairs. Three pairs were reserved for testing and 59
pairs for training.
Journal of Engineered Fibers and Fabrics 3
Volume 7, Issue 2 – 2012

Genetic algorithm (GA) (Goldberg, 1989) is another
component of soft computing methods. This method
has different domains of applications in various
engineering fields [26]. Nonetheless, offshoots of
GA, namely, gene expression programming (Ferreira,
2001), a natural development of Genetic algorithm
(GA), and Genetic programming (GP) have not
received attention by the researchers.

Similarly to GA, GP needs only the problem to be
defined. Then the program searches for a solution in
a problem-independent manner. The process begins
with the random generation of the chromosomes of
each of the initial population. Then the chromosomes
are expressed and the fitness of each individual is
assessed. The individuals are then selected on the
basis of fitness to reproduce with modification,
leaving progeny with new train. The individuals of
the new generation are subjected to the same
developmental process until a solution has been

GEP is a genetic algorithm that consists of mainly
five components; the function set, terminal set,
fitness function, control parameters and stop
condition. In GEP, the individuals are encoded as
linear strings of fixed length (the genome or
chromosomes) which are afterwards expressed as
non-linear entities of different sizes and shapes
(simple diagram representations or expression trees
(ET)). A chromosome might be modified by one or
several operators at a time or not be modified at all.
The advantages of GEP are: first, the chromosomes
are simple entities: linear, compact, relatively small,
easy to genetically manipulate (replicate, mutate,
recombine, transpose) and second, the expression
trees are exclusively the expression of the respective

GEP genes are composed of a head and a tail. The
head contains symbols that represent both functions
and terminals, whereas the tail contains only
terminals. For each problem, the length of the head is
chosen, whereas the length of the tail is a function of
the length of the head and the number of arguments
of the function with more arguments.

A typical GEP gene with the given function and
terminal sets can be Eq. (3).



Where ‘.’ is used to separate elements for easy
reading, Sqrt is the square-root function; 2 is a
constant and a, b, c, d are variable names. The above-
mentioned equation is known as Karva or K-
expression. For a detailed explanation of GEP, refer
to reference No 27.

Sample Yarn Production and Experiment
The data used in the GEP and ANN models were
collected from 48 rotor spun yarn samples. Cotton
fiber with 27 mm mean fiber length, 3.6 micronaire
fineness and 0.85 fiber maturity index were furnished
as a second draw frame sliver with linear density of
5.2 ktex. The 30Ne yarn was spun on a Rieter RU04
rotor spinning machine with 900 tpm. The opening
roller speed was 8200 t.min
. The 35mm diameter
rotor worked at a speed of 75000 t.min

The effect of three main variable parameters in draw
frame (passage No.1) namely, production speed,
break draft and distance between back and middle
rolls on breaking strength of rotor spun yarn was
studied. Production speed was changed in four levels:
550, 650, 700, and 750 m.min
. The distance
between back and middle rolls was set in four values:
8, 10, 12, and 14mm. Break draft was selected 1.14,
1.41 and 1.70. Based on a full factorial design, forty-
eight different yarn samples were produced according
to the above-mentioned variables as shown in Table
I. Tensile characteristics of the rotor spun yarns were
examined with a Uster Tesorapid3. A test specimen
of 500mm was elongated at an extension rate of
. Each sample was tested 15 times. The
average values of the experiments are shown in Table

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TABLE I. Specifications of the cotton rotor-spun-yarn samples.

TABLE II. Quality parameters of the sample yarns.

A one-way ANOVA test was applied to determine
the effect of the parameters on the breaking strength
of rotor spun yarns. Average breaking strength values
(Table II) were compared at the 5% significance level
and grouped according to the Duncan Multiple Range
Test. Results of the Univariate analysis are
summarized in Table III. Duncan Multiple Range
Test results cannot be shown due to space limitation.
Statistical analysis confirmed that, main effect and
interactive effect of the three variables on yarn
strength were statistically significant. In this study,
the effect of draw frame parameters on the breaking
strength of rotor spun yarns was evaluated and fiber
qualities were the same in all the samples. Although
the fiber parameters interact with draw frame
parameters in general, the effect of fiber properties on
draw frame parameters and breaking strength of rotor
spun yarns is beyond the scope of this research.

TABLE III. Results of the statistical analysis to show the effect of the factors on samples properties.

Journal of Engineered Fibers and Fabrics 5
Volume 7, Issue 2 – 2012

Model Construction and Analysis Using GEP
Forty eight pairs of input-output patterns were
available from the experiments. These patterns were
randomly divided into training and testing sets. It
should be noted that the testing data are those that are
different from training data in at least one of the input
parameters. This means that the data sets used are not
the same as ones used in training. Besides, the range of
each independent parameter (break draft, distance
between middle and back rolls and production speed)
was selected in such a way that covers all possible
ranges of practical variations on the draw frame which
is one of the main criteria to develop predictive
models. Thirty-eight data pairs were selected as
training set and 10 data pairs as testing set. In the
proposed models, the input units were break draft,
production speed, distance between back and middle
rolls and the output unit was the breaking strength of
spun yarns.

The major task is to define the hidden function
connecting the input variables (X
, X
, X
) and output
variable (Y). In this study, Y is the breaking strength
(cN/tex); X
is the break draft; X
is the distance
between back and middle rolls (mm); and X
is the
production speed (m.min
). This can be written in the
form of the Y = f (X
, X
, X
). The function developed
by GEP can be used to predict the breaking strength of
rotor spun yarns. The parameters used in the GEP
algorithm are summarized in Table IV. There were
many different combinations of the parameters which
means several GEP models. Since running the GEP for
all of them requires a long computational time, a subset
of these combinations was selected to investigate the
performance of the GEP in predicting the breaking
strength of rotor spun yarns.

TABLE IV. Parameters of the GEP algorithm.

Model Construction and Analysis Using Artificial
Neural Network
The artificial neural network parameters were adapted
by applying the same data sets used in GEP algorithm.
The number of hidden neurons and the number of
hidden layers are usually adjusted by trial and error.
The studies of various researchers have shown that,
neural networks with one hidden layer are suitable for
majority of applications and the second hidden layer
can improve the performance of the network, if there is
a complex relationship between input and output
parameters. In order to obtain the best topology and to
evaluate the capability of ANN algorithm, 12
topologies with different numbers of hidden layers and
different numbers of hidden neurons (processing
elements) were used. Therefore, 8 different network
structures with only one hidden layer consisting of 3 to
10 neurons and four architectures with two hidden
layers were used in this study. All the designed
networks had three input units and one output neuron
in output layer as explained in the prior section.

One of the important parameters in back-propagation
algorithms is learning rate. Choosing a large learning
rate value accelerates the training but cause big errors
at the output or unstable the training cycles, but small
values provide convergence with smaller errors and
prolong training time. Therefore using an adaptive
learning rate enhances the training performance. In this
study, the adaptive learning rate with momentum
training algorithm was used to enhance the training
performance. Momentum rate was optimized at 0.90.
The testing and training data were normalized in such a
way that they got zero mean and unit standard
deviation. After some trials the hyperbolic tangent and
linear function were applied for hidden neurons and
output neuron respectively.

Artificial Neural Network Model
Table V shows the training results of ANN models after
1000 epochs. The mean square error (MSE) and
correlation coefficient (R
-value) of testing data were
used to judge the performance of different models. The
results showed that, the ANN model with two hidden
layers and 4 processing elements into first and second
hidden layers gives the best performance and the least
MSE for predicting the breaking strength of rotor spun
yarns on testing data. The MSE of testing and training
data was 0.106 and 0.052 respectively. The R
-value of
testing and training data was 0.93 and 0.97

Details of testing data are presented in Table VI. The
ability of the best model to predict the testing data are
shown in Table VII and Figure 1 respectively. Table
VII reveals that, minimum and maximum prediction is
0.247% and 5.167%. Figure 1 shows the predictive
performance of obtained model schematically.
According to this figure, the prediction errors of the
test data were comparable with each other.

Journal of Engineered Fibers and Fabrics 6
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TABLE V. The performance of different ANN architectures on training and testing data sets.

TABLE VI. Specifications of the yarn samples selected for testing set.

TABLE VII. The prediction error of testing samples using ANN model with 3-4-4-1 architecture.

Journal of Engineered Fibers and Fabrics 7
Volume 7, Issue 2 – 2012

FIGURE 1. Evaluation of the ANN model to predict the yarn
breaking strength.

GENE Expression Programming Algorithm
In Table VIII, the 10 best solutions obtained from the
tests are presented. As can be seen in this table, the
best result obtained from the GEP algorithm has a
0.97 R
-value. The MSE of the test data was 0.071.
Equation (4) represents mathematical function
generated by the best structure of the GEP approach
to predict the breaking strength (BS) of rotor spun
yarns based on three independent variables namely,
distance between back and middle rolls (DBBMR),
production speed (PS), and break draft (BD).
TABLE VIII. The performance of different GEP architectures on training and testing data sets.


The performance of the best gene expression
programming architecture (equation 4) on the same
test data as used in the ANN model is shown in
Figure 2 and Table IX. According to Figure 2, there
was a closer match between the actual and predicted
yarn strength values than with ANN model. The
average absolute error of the yarn breaking strength
prediction was as low as 1.90%. According to Table
IX, the minimum and maximum error for the best
GEP model for the test data was 0.202% and 2.979%
respectively. Therefore, the GEP function was able to
closely follow the trend of the actual data.

FIGURE 2. Evaluation of GEP model to predict the yarn breaking
Journal of Engineered Fibers and Fabrics 8
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TABLE IX. Comparison between experimental and predicted values for testing data set in GEP model.

Table X shows a comparison of the prediction
performance of ANN and GEP models. The
difference between the MSE values for predicting the
breaking strength of test data was 0.035 or 33.02%,
although the difference between the R
-value of these
two models was as low as 4.30%. The maximum
error of ANN model for predicting testing data was
5.167% and belonged to sample 7. That was 2.970%
for the GEP model. In addition, the ANN model
exhibited a minimum error of 0.247% compared to
0.202% for the GEP model, which indicates the
margin difference between two models.

TABLE X. Comparison between the prediction power of two
models on testing data.

The difference between the maximum prediction
errors of two models was 42.34%, which again
confirmed the excellent capability of GEP model in
predicting breaking strength of cotton rotor spun
yarns compared to ANN model. As shown in Table
X, the standard deviation of prediction error of GEP
model was 0.859 and this value was obtained 1.625
for ANN model that again confirms the better
capability of GEP model than ANN model.

The better performance of GEP algorithm can be
explained based on the method of optimization of its
parameter, which was based on the genetic algorithm.
Although applying the genetic algorithm to optimize
the ANN model parameters is a useful method to
improve the predictive performance of ANN model,
this increases the complexity of modeling process
compared with GEP algorithm. Finally, presenting a

Obtaining a specific mathematical equation
describing the relation between dependent and
independent parameters was a time consuming
process, especially when there was not a clear
relationship between input and output parameters, but
this case was easily obtainable by the GEP algorithm.
The GEP algorithm results in an equation that can be
easily programmed even into a pocket calculator to
use in future predictions. All of the obtained results
accompanied with this benefit demonstrate the
advantages of the GEP model when compared to the
ANN model.

In this study, Gene Expression Programming (GEP)
algorithm as a new intelligent methodology was
applied to obtain a predictive model of breaking
strength of cotton rotor spun yarns based on three
main draw-frame machine parameters. An Artificial
Neural Network (ANN) model was also developed as
a criterion to evaluate the predictive power of the
GEP algorithm. An ANN model with two hidden
layers and four processing elements in each was
obtained as the best model. The obtained results from
extensive computational tests indicated the better
prediction performance of the GEP model compared
to the ANN model. The difference between the MSE
and R
-value of two proposed models in predicting
test data was 33.01% and 4.96%. GEP was found as a
powerful programming algorithm in predicting the
breaking strength of rotor spun yarns. Based on the
results of this research, we plan to apply this
algorithm to other textile manufacturing processes in
the future.

Journal of Engineered Fibers and Fabrics 9
Volume 7, Issue 2 – 2012

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Abdolrasool Moghassem, Ph.D.
Islamic Azad University,
Gaemshahr Branch
Departement of Textile Engineering
Nezami Street, Ghaemshahr, Mazandaran, 163

Alireza Fallahpour
Department of Management
Firoozkooh Branch
Islamic Azad University

Mohsen Shanbeh
Department of Textile Engineering
Isfahan University of Technology