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Predicting the tensile properties of cotton/spandexcore-spun yarns using artificial neural network andlinear regression modelsAlsaid Ahmed Almetwallya, Hatim M.F. Idreesb & Ali Ali Hebeishc

a Textile Engineering Department, Textile Research Division, National Research Center,Cairo, Egyptb Faculty of Applied Arts, Damietta University, Damietta, Egyptc Textile Research Division, National Research Center, Cairo, EgyptPublished online: 14 Feb 2014.

To cite this article: Alsaid Ahmed Almetwally, Hatim M.F. Idrees & Ali Ali Hebeish (2014) Predicting the tensile propertiesof cotton/spandex core-spun yarns using artificial neural network and linear regression models, The Journal of The TextileInstitute, 105:11, 1221-1229, DOI: 10.1080/00405000.2014.882043

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Predicting the tensile properties of cotton/spandex core-spun yarns using artificial neuralnetwork and linear regression models

Alsaid Ahmed Almetwallya*, Hatim M.F. Idreesb and Ali Ali Hebeishc

aTextile Engineering Department, Textile Research Division, National Research Center, Cairo, Egypt; bFaculty of Applied Arts,Damietta University, Damietta, Egypt; cTextile Research Division, National Research Center, Cairo, Egypt

(Received 24 October 2013; accepted 7 January 2014)

Recently, core-spun yarns showed many improved characteristics. The tensile properties of such yarns are accepted asone of the most important parameters for assessment of yarn quality. The tensile properties decide the performance ofpost-spinning operations; warping, weaving, and knitting, and the properties of the final textile product; hence, itsaccurate prediction carries much importance in industrial applications. In this study, artificial neural network (ANN) andmultiple regression methods for modeling the tensile properties of cotton/spandex core-spun yarns are investigated. Yarnbreaking strength, breaking elongation, and work of rupture of the core-spun yarns are studied. The two models wereassessed by verifying root mean square error, mean bias error, and coefficient of determination (R2-value). The results ofthis study revealed that ANN has better performance in predicting comparing with multiple linear regression.

Keywords: neural networks; back-propagation; core-spun yarn; spandex; regression methods; tensile properties

Introduction

Core-spun yarns

Core-spun yarns are structures consisting of twocomponent fibers, one of which forms the core of theyarn, and the other forms sheath or covering. Mostly, thecore is a continuous monofilament or multi-filament yarn,while staple fibers are used for the sheath of the yarn(Sawhney & Ruppenicker, 1997). Core-spun yarns havebeen produced successfully by many spinning systemssuch as ring, rotor, friction, and air jet. These yarns havebeen used to improve the strength, esthetic, durability, andfunctional properties of fabrics (Sawhney & Ruppenicker,1997). The application of core-spun yarns in the textileindustry is very versatile. In these yarns, the sheath partcauses surface physical and esthetic properties, while thecore part affects the mechanical properties of yarn andimproves yarn strength and permits the use of lower twistlevels (Menghe Miao, How, & Ho, 1996; Sawhney &Ruppenicker, 1997).

Core-spun yarn shows some improved characteristicsover 100% cotton yarn or 100% filament yarns.Core-spun yarn was preferred to blend staple-spun yarnin terms of strength and comfort (Graham &Ruppenicker, 1983; Harper, Ruppenicker, & Donaldson,1986). Phenomenal improvements in durability andesthetic properties were observed in core-spun yarn(Radhakrishnaiah & Sawhney, 1996; Sawhney, Robert,& Ruppenicker, 1989) compared to cotton-spun yarn.

Core-spun yarns, which use spandex as the core andare covered with natural fibers or other staple fibers,have important properties; they have the same feel as theshield fibers and possess good moisture absorptiondependent on the fibers which cover the outer layer. Wecan also modify their elasticity to fit different endproducts (Su, Maa, & Yang, 2004). Therefore, core-spunyarns containing spandex have found a wide range ofapplication areas in the textile industry.

Core-spun yarns containing spandex have been thesubject of some researches (Babaarslan, 2001; Su et al.,2004; Weber, 1993). Su et al. investigated the effects ofdraw ratio and feed-in angle of the spandex on thecore-spun yarns’ structure, and performance at themodified ring spinning frame. They concluded that ahigher feed-in angle provides a better cover effect, and adraw ratio of 3.5 yields better dynamic elastic recovery(Su et al., 2004). Babaarslan showed that spandexpositioning has a direct effect on the properties, structureand performance of core-spun yarns produced on amodified ring spinning frame (Babaarslan, 2001).

Overview of artificial neural networks

An artificial neural network (ANN) is an informationprocessing system that has certain performancecharacteristics in common with biological neural networks.This technique is useful when there are a large number ofeffective factors on the specific process (Fausett, 1994;Rajamanickam, Hansen, & Jayaraman, 1997).

*Corresponding author. Email: saaa_2510@yahoo.com

© 2014 The Textile Institute

The Journal of The Textile Institute, 2014Vol. 105, No. 11, 1221–1229, http://dx.doi.org/10.1080/00405000.2014.882043

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A neural network consists of a large number ofsimple processing elements called neurons, units, cells,and nodes. Each neuron receives connections fromother neurons and/or itself, each with an associatedweight. The interconnectivity defines the topology ofthe ANN. The weights represent information being usedby the neural network model to solve a problem. Oneof the central issues in neural network design is toutilize systematic procedures (a training algorithm) tomodify the weights directly from the training datawithout any assumptions about the data’s statisticaldistribution (Fausett, 1994; Principe, Euliano, &Lefebvre, 1999).

There are different kinds of topologies and trainingalgorithms but the multi-layered feed-forward neuralnetwork with back-propagation learning algorithms ismore popular and commonly used (Ogulata, Sahin, &Ogulata, 2006). In this structure, the neurons are locatedin layers and these layers are connected each other withlinks to carry the signals between them. There is aweight for each connection link which acts as amultiplication factor to the transmitted signal. Anactivation function such as linear or sigmoid is appliedto each neuron’s input to determine the output signal.Usually, a feed-forward neural network consists ofseveral layers of nodes, one input layer, one outputlayer, and some hidden layers in between.

The training of a neural network by back-propagationinvolves three stages: the feed-forward of the inputtraining pattern, the calculation and back-propagation ofthe associated error, and the adjustment of the weights(Principe et al., 1999). The calculation of error vector toadjust the weights is done according to the calculatedmean square error (MSE) form the difference betweenactual and predicted outputs according to the followingrelationship.

MSE ¼ 1

N

XNi¼1

ðyi � xiÞ2; (1)

where N = the number of observations, yi = the neuralnetwork predicted values, and xi = the actual targetvalues.

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

DWjiðnÞ ¼ �g @ðMSEÞ=@WjiðnÞ� �

; (2)

where Wji(n) is the weight connecting the neurons j and iat the nth iteration; ΔWji(n) is the correction applied to

Wji(n) at the nth iteration; and η is a constant known aslearning rate (Beltran, Wang, & Wang, 2004;A. Majumdar, P. K. Majumdar, & B. Sarkar, 2005a).

Prediction of yarn properties

Generally, modeling and prediction of yarn propertiesbased on fiber properties and process parameters havebeen considered by many researchers. Over the years,one of the first approaches has been the use ofmechanistic models. In this category, some studiessuch as the work of Bogdan (1956, 1967) to predictcotton yarn strength and spinning quality, Hearle,El-Behery, and Thakur (1961) in relation to structuralmechanics of fibers, yarns, and fabrics, the predictionof yarn strength by Frydrych (1992), and worksperformed by Linhart (1975), Lucas (1983), Kimand El-sheikh (1984) and Yong Ku Kim and El-sheikh(1984) can be mentioned. However, statisticalregression models for this purpose have been usedby some researchers, namely El-Mogahzy (1988),Ethridge, Towery, and Hembree (1982) and Hunter(1988).

The limitation of mechanistic and statisticalregression models was described in previous works(Fan & Hunter, 1998; Ramesh, Rajamanickam, &Jayaraman, 1995). ANNs, genetic algorithm, and fuzzyset theory are presented as attractive alternatives forpredictive modeling. ANN algorithms have been usedby many researchers for modeling the different textileprocesses, especially for predicting different kinds ofyarn and fabric properties based on process parametersand fiber and yarn parameters (Beltran et al., 2004; Fan& Hunter, 1998; Jeffrey, Hsiao, & Wa, 2004; Rameshet al., 1995; Shiau, Tsai, & Lin, 2000; Ucar &Ertugrul, 2002). Beltran, Wang, and Wang (2006)predicted the pilling tendency of wool knits (Beltranet al., 2006). The performance of ANN model wascompared with statistical regression and fuzzyregression to develop the predictive models forpolyester dyeing (Nasiri, Shanbeh, & Tavanai, 2005).The ANN model has also been used to predictbreaking elongation of open–end spun yarn (Majumdaret al., 2005a). Bursting strength of cotton plain knittedfabrics was predicted using ANN and neuro-fuzzyapproaches by Ucar and Ertugrul (2002). They used atotal of 62 data pairs. Three pairs were reserved fortesting and 59 pairs for training.

The objective of the present study is to use themulti-layered feed-forward back-propagation neuralnetwork for the prediction of tensile properties of cotton/spandex core-spun yarns. We also compared theprediction outcomes from this model with those obtainedfrom multivariate linear regression.

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Experimental

Materials and methods

In this study, 40 cotton/spandex core-spun yarn sampleseach of count 30/1 Ne were spun on Zinser 513 spinningmachine. These yarn samples are composed of spandexfilament with four different linear densities, i.e. 22, 33,44, and 78 dtex as a core, and 100% Egyptian cottonfibers as a sheath. Each spandex filament was subjectedto five different levels of drawing ratios, i.e. 2.4, 2.8,3.3, 4, and 4.4, respectively. Each yarn sample wasproduced with two twist multipliers, namely 4 and 4.2.The characteristics of cotton fibers used as a sheath arelisted in Table 1, and the features of the spandexfilaments are tabulated in Table 2.

Tensile properties of cotton/spandex core-spun yarnswere characterized by measuring the breaking strength(cN), breaking elongation (%), and work of rupture(N cm) respectively. These tensile properties of the yarnsamples were investigated on a Tensorapid tensiletester with constant rate of elongation (according toASTM-2256-97) at a cross-head speed 300 mm/min anda pre-tensional force 9.85 gf. For each yarn sample, 50readings were taken and then the averages werecalculated.

Neural network design

Architecture

First, the size of the network must be determined by thenumber of hidden layers and the number of neurons inthese layers. A network with three layers is sufficient formost practical applications. The number of input neuronsnormally corresponds to the number of input variables ofthe process to be modeled. In selecting the outputneurons, note that it is generally inadvisable to train anetwork for several tasks simultaneously. To determine

the number of hidden nodes, several rules have beenproposed. These include using “2n + 1” (Hecht-Nielsen,1990; Lippmann, 1987), “2n” (Wong, 1991), “n” (Tang& Fishwick, 1993), “n/2” (Kang, 1991) where n is thenumber of input nodes. However, none of these heuristicchoices works well for the problem under study, sopurely empirical approach is necessary here. Therefore,we have selected a network with three layers: an inputlayer with three neurons, hidden layer with 12 neurons,and an output layer with one neuron corresponding toone dependent variable subject to the analysis at a time.

Learning strategy and transfer functions

Before learning, the whole experimental data weresegregated into training, validation, and testing patterns:60% of the patterns were randomly selected for training,20% were for testing the neural network, and theremaining 20% of patterns were for validating themodel’s performance. Training is an important feature ofneural networks. The objective of the training process isto minimize the squared error between the networkoutput and the desired output. This is done by adjustingthe connection weights across the network. Thevalidation set is a part of the data used to tune networktopology or network parameters other than weights. Forexample, it is used to define the number of units todetect the moment when the neural network performancestarted hidden to deteriorate. To choose the best network(i.e. by changing the number of units in the hiddenlayer), the validation set is used. Whereas, the test set isa part of the input data-set used to test how well theneural network will perform on new data. The test set isused after the network is ready (trained), to test whaterrors will occur during future network application. Thisset is not used during training and thus can beconsidered as consisting of new data entered by the userfor the neural network application.

The learning method is back-propagation withLevenberg–Marquardt algorithm. Three of the mostcommonly used transfer functions are linear, sigmoid,and tanh:

Linear : f ðxÞ ¼ x; (3)

Table 1. Characteristics of cotton fibers used as a sheath.

Effective length, mm 32.5Uniformity, % 86.6Breaking strength, g/tex 45.1Breaking elongation, % 6.4Micronaire, μg/inch 4.52Maturity, % 89

Table 2. Main features of spandex filaments.

Linear density of spandex filaments (dtex)

22 33 44 78

Luster Clear Clear Clear ClearTenacity, g/d 1.55 ± 0.15 1.50 ± 0.15 1.40 ± 0.15 1.25 ± 0.15Elongation, % 650 ± 50 650 ± 50 640 ± 50 700 ± 70

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Sigmoid : f ðxÞ ¼ 1

ð1þ e�xÞ; (4)

Tanh: f ðxÞ ¼ ðex � e�xÞðex þ e�xÞ: (5)

A fixed linear transfer function is set for the inputlevel of the multi-layered feed-forward back-propagationneural network, as this layer only functions as a buffer.For The hidden and output layers, the sigmoid and lineartransfer functions are chosen, respectively.

The topology architecture of feed-forwardthree-layered back-propagation neural network isillustrated in Figure 1. MATLAB 9.1 package was usedfor training and testing the network model for tensileproperties prediction. The training parameters used inthis investigation are listed in Table 3.

Performance of the neural network

To evaluate the model, the neural network predictedvalues of the model are calculated and compared withactual output values. The various error measurementscan be determined from this. We have used the rootmean square error (RMSE), the mean bias error (MBE),

and coefficient of determination as error measurementsin our study: RMSE provides information on the short-term performance which is a measure of the variation ofpredicated values around the measured data. The lowerthe RMSE, the more accurate is the estimation. MBE isan indication of the average deviation of the predictedvalues from the corresponding measured data and canprovide information on long-term performance of themodels; the lower the MBE, the better is the long-termmodel prediction. A positive MBE value indicates theamount of overestimation in the predicated cotton/spandex core-spun yarn properties and vice versa.Coefficient of determination, R2, is defined as the ratioof the sum of squares of the regression (SSregression) andthe total sum of squares (SStotal). R2 measures thereduction in the total variation of the dependent variable(cotton/spandex tensile properties) due to the multipleindependent variables (spandex linear density, spandexfilament drawing ratio, and twist multiplier). R2 takes onvalues between 0 and 1. When the R2 value approaches1, the model fits the data results very well and itbecomes reliable to be used in predicting.

Finally, these parameters attest to the accuracy of themodels used for predicting the tensile properties ofcotton/spandex core-spun yarn. Generally, theexpressions for the aforementioned error measurementsare:

Root mean squared error: RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

N

XNi¼1

ðyi � xiÞ2vuut ;

(6)

Mean bias error: MBE ¼ 1

N

XNi¼1

ðyi � xiÞ�����

�����; (7)

Coefficient of determination: R2 ¼ SSregressionSStotal

¼PN

i¼ðyi � �yÞ2PNi¼1ðxi � �xÞ2 ;

(8)

where N = the number of observations, yi = the neuralnetwork predicted values of yarn tensile properties,xi = the actual values of yarn properties, �x = the meanof N observations of actual values of yarn properties,and �y = the mean of N observations of predicted valuesof yarn properties.

Statistical regression

Statistical regression is a model for analyzing andmodeling of dependent variables as a function of one ormore independent variables. The simplest form ofregression is multiple linear regression. The statisticalregression, especially multiple linear regression, has been

Table 3. Training parameters used.

Parameter Value

Number of input nodes 3Number of hidden nodes

(Feed forward)12

Number of output nodes 1Learning rule Levenberg–MarquardtNumber of epochs 1000Error goal 0.001Marquardt adjustment (MU) 0.01Minimum performance gradient 0.00001Learning rate (lr) 0.4

Linear density

Drawing ratio

Twist multiplier

Inputlayer

Hiddenlayer

Outputlayer

Tensile property

Figure 1. ANN architecture used.

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one of the most popular methods during the second halfof the twentieth century of making predictive models ina wide range of textile relateds (A. Majumdar,K. Majumdar, & B. Sarkar, 2005b; P. K. Majumdar &A. Majumdar, 2004; Wasserman, 1993), and is known asa conventional method (Wesserman, 1993).

In this study, multiple linear regression was used fordeveloping three predictive models of yarn breakingstrength, yarn breaking elongation, and work of ruptureof cotton/spandex core-spun yarns. In this concern, thesame sets of data used for evaluating ANN model wereused in a multiple linear regression algorithm.Independent variables were linear density of core part(spandex linear density, dtex), drawing ratio of thespandex filament (%), and twist multiplier.

The following linear regression models correlate thetensile properties of cotton/spandex core-spun yarns withthe independent variables, i.e. spandex linear density(dtex), spandex drawing ratio (%), and twist multiplier.

Breaking strength ðcNÞ ¼ 34:1� 1:4� linear density

þ 33:2� drawing ratio

þ 71� twist multiplier; ð9Þ

Breaking elongation ð%Þ ¼ �7:2þ 0:02� linear density

þ 1:1� drawing ratio

þ 2:4� twist multiplier; ð10Þ

Work of rupture ðNcmÞ ¼ �30:1� 0:02� linear density

þ 2:3� drawing ratio

þ 7:5� twist multiplier: ð11ÞAs seen from the regression models above, spandex

linear density affected the breaking strength and work ofrupture negatively and affected breaking elongation

positively. However, spandex drawing ratio and twistmultiplier have a positive influence on all tensileproperties.

Results and discussion

In this study, we have adopted a three-layer neuralnetwork consisting of a three-input layer, a 12-neuronhidden layer, and a one-neuron output layer at a time,focusing on tensile properties of cotton/spandex core-spun yarn, i.e. breaking strength (cN), breakingelongation (%), and work of rupture (N cm). The neuralnetwork learning model is in accordance with theexperiment data of three inputs and three targets, parts ofwhich are listed in Table 4. The general view of theneural network used in this study is shown in Figure 1.

The RMSE, the MBE, and coefficient ofdetermination (R2) were used to judge the performanceof ANN and regression models.

Breaking strength

The actual and predicted breaking strength values ofcotton/spandex core-spun yarn using ANN andregression models and its performance are presented inTables 5 and 6 and in Figure 2, respectively. The resultsshowed that the ANN model gives the best performancewith the least RMSE, MBE, and highest R2 values. TheRMSE of training data was 4.87 and 27.45 for ANN andregression models, respectively, whereas the MBE valueswere 1.35 and 1.81 for ANN and regression models,respectively. The R2 values of ANN and regressionmodels were 0.99 and 0.71, respectively. This meansthat ANN model fits the experimental data very well andit is better than multi-regression one for predictingbreaking strength of cotton/spandex core-spun yarns. Thevalue of the determination coefficient (R2 = 0.99)

Table 4. Some learning data of the back-propagation neural network.

SampleNo.

Inputs Targets

Drawing ratio(%)

Linear density(dtex)

Twistmultiplier

Breaking strength(cN)

Breaking elongation(%) Work of rupture (N cm)

1 2.8 22 4 393.12 6.113 62 2.4 33 4 342.16 6.315 4.513 3.3 33 4 353.99 6.432 5.7224 4 33 4 418.6 6.9 6.9005 4.4 33 4 391.3 8.2 11.56 3.3 44 4 347.62 6.804 7.2287 4 44 4 408.59 6.800 7.0098 4.4 78 4 316.68 8.3 59 2.4 22 4.2 400.4 5.48 5.24610 2.8 22 4.2 406.77 6.28 711 3.3 33 4.2 368.55 6.78 7.80012 4 33 4.2 434.07 7.380 9.36913 2.8 44 4.2 373.1 7.280 6.90014 3.3 44 4.2 361.27 6.98 7.8

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indicates that only 1% of the total variations are notexplained by the ANN model. Therefore, it can be saidthat the neural network model with one hidden layer canfit the nonlinear relationships very well.

From Table 5, it is also noticed that the minimumand maximum absolute errors for regression model are4.425 and 8.619%, while the minimum and maximumprediction error of the data predicted using ANN modelare 0.073 and 6.282%. This confirms that ANN modelhas a better predictive performance than regressionanalysis to predict the breaking strength of cotton/spandex core-spun yarns.

Figure 2 compares the predicted outputs of the ANNmodel and multi-linear regression model with theexperimentally actual breaking strength of cotton/spandex core-spun yarns. It is noticed that ANN modelreproduced the trend in the measured values better thanregression model; and the ANN model has morecapability of making quantitatively accurate breakingstrength predictions. The correlation coefficient betweenactual and predicted yarn breaking strength using ANNand regression models were 0.996 and 0.842,respectively.

Breaking elongation

Actual and predicted values of breaking elongation ofcotton/spandex core-spun yarn and its predicted errorsare listed in Table 7. A Comparison between theperformances of the ANN and multi-regression modelson the data-sets is provided in Table 8. It is shown thatANN model achieved an average RMSE and MBE ofzero. Comparing this to the regression model with an

Table 5. Breaking strength predicted by multi-linear regression and neural network.

Actual value (%)

Multi-linear regression Artificial neural network

Predicted value (%) Absolute error (%) Predicted value (%) Absolute error (%)

279.37 303.4241 8.610123 296.921 6.282361310.31 337.0558 8.619058 309.2493 0.341823347.62 366.9645 5.564841 347.8977 0.079884368.55 396.3419 7.540876 371.1197 0.697241397.67 334.2361 15.95139 397.6173 0.013255423.15 404.4228 4.425665 420.9831 0.512089445.9 417.7155 6.320812 448.2668 0.5308455 433.8824 4.641231 455.3348 0.073583

Table 6. Comparison of prediction performance of ANN andregression models for breaking strength.

Statistical parameters Regression ANN

Coefficient of determination, R2 0.708872 0.9939Mean bias error, MBE 1.809913 1.3459Root mean square error, RMSE 27.4456 4.871123

290310330350370390410430450470

310 330 350 370 390 410 430 450 470

Actual values

Pre

dict

ed v

alue

s

ANN Regression

Figure 2. Actual vs. predicted values using ANN andregression models for breaking strength.

Table 7. Breaking elongation predicted by multi-linear regression and neural network.

Actual value (%)

Multi-linear regression Artificial neural network

Predicted value (%) Absolute error (%) Predicted value (%) Absolute error (%)

5.48 5.825141 6.298193 5.48 0.0006.1 6.310793 3.455623 6.1 0.0006.78 6.987741 3.064027 6.78 0.0006.98 7.184688 2.932493 6.98 0.0007.28 7.935751 9.007569 7.28 0.0007.68 7.793435 1.477018 7.68 0.0008.3 8.493676 2.333446 8.3 0.0008.68 8.167983 5.898813 8.68 0.000

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average RMSE and MBE of 0.372 and 0.074,respectively, suggested that the ANN model highlyoutperformed the regression model.

It was also found that ANN model is capable ofachieving a very good fit to the measured breakingelongation values, as evidenced by the high R2 value of1. While, the R2 value associated with multi-regressionmodel was lower to some extent (R2 = 0.84), whichmeans that regression model failed to explain 16% of thetotal variation in breaking elongation values of cotton/spandex core-spun yarns. The poor performance ofmultiple linear regression in predicting the breakingelongation indicates that the relationship betweenindependent parameters and breaking elongation ofcore-spun yarns is nonlinear, because the multiple linearregression is based on the first-order equations.

As seen from Table 7, the predicted errors associatedwith ANN models were all equal to zero, while thataccompany regression one range between 1.477 and 9,which confirms the superior ability of ANN model topredict the breaking elongation values of cotton/spandexcore-spun yarns.

The actual and predicted breaking elongation valuesby ANN and regression models are depicted in Figure 3.It is observed that the predicted values are in goodagreement with the actual values for ANN model andthe predicted errors are almost nonexistent. Whereas, thepredicted values in regression model are randomlyscattered around the regression line. Therefore, ANNmodel can perform good prediction with least error,which can be confirmed with the high correlationcoefficient for ANN model (R = 1) and lower one forregression model (R = 0.92).

Work of rupture

Actual and predicted values of core-spun yarn work ofrupture using ANN and regression models are listed inTable 9. It is apparent that the absolute error of work ofrupture predicted by regression model is more than thatpredicted using ANN model. The absolute error of workrupture predicted by regression model ranges between2.98 and 20.1%, whereas the error predicted by ANNmodel is between 0.39 and 5.8%. This gave a highdegree of confidence in the accuracy of ANN model.

The R2, RMSE, and MBE values of work of rupturefor cotton/spandex core-spun yarn predicted by ANNand regression models are introduced in Table 10. It isnoticed that the values which belong to ANN model ismuch better than that belonging to regression one. Theaverage R2, MBE, and RMSE for the values predictedvia ANN model are 0.989, 0.314, and 0.463,respectively. While such values predicted usingregression model are 0.762, 0.832, and 1.118 for R2,MBE, and RMSE, respectively. The coefficient ofdetermination values show that ANN model explainedabout 98.9% of the variations in the work of rupture of

Table 8. Comparison of prediction performance of ANN andregression models for breaking elongation.

Statistical parameters Regression ANN

Coefficient of determination, R2 0.844482 1Mean bias error, MBE 0.074075 0.000Root mean square error, RMSE 0.372214 0.000

5

6

7

8

9

5 6 7 8 9

Actual values

Pre

dict

ed v

alue

s

ANN Regression

Figure 3. Actual vs. predicted values using ANN andregression models for breaking elongation.

Table 9. Work of rupture predicted by multi-linear regression and neural network.

Actual value (%)

Multi-linear regression Artificial neural network

Predicted value (N cm) Absolute error (%) Predicted value (N cm) Absolute error (%)

4.9 4.52902 7.57102 5.181534 5.7455825.5 6.36942 15.80764 5.819239 5.8043456.1 5.46113 10.47328 6.597327 8.1529086.9 6.69428 2.981449 6.95034 0.7295717.8 8.11627 4.054744 8.008919 2.6784519.4 10.00433 6.429043 10.02512 6.65016211.5 9.18958 20.09061 11.54513 0.39240612 10.67958 11.0035 12.64372 5.364373

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cotton/spandex core-spun yarns, whilst this variation isexplained nearly about 76.2% by the regression model.All This confirms that ANN model is more superior toregression one in work of rupture prediction. Thesuperior prediction capability of the ANN modelstemmed from the ability of this model to directly takeinto account any nonlinear relationships between theinput variables and yarn work of rupture.

The measured and predicted values of work ofrupture of cotton/spandex core-spun yarns for ANN andregression models are shown in Figure 4. As can beseen, the predicted values by ANN model are very closeto the actual values and tracked it very well. While, thepredicted values by regression model are randomlyscattered around the regression line. The correlationcoefficient between predicted and actual values is 0.995and 0.873 for ANN and regression models, respectively.

Conclusion

Knowledge of the relationship between performance andcharacteristic parameters of yarns assists the producers toarrange the technological processes. This will allow aproducer to make an informed decision that accounts forthe required quality of the yarn at the best price. So,modeling and predicting yarn properties by puttingforward the relationship between the fiber and the yarnproperties are two of the most remarkable subjects fortextile researchers.

In the recent years, neural networks have became themost efficient predicting tool in textile industry becauseof its requirement of less formal statistical training,ability to describe highly complex and nonlinearproblems, ability to detect all possible interactionsbetween predictor variables, and its allowing of theinclusion of a large number of variables.

In this study, tensile properties of cotton/spandexcore-spun yarns were predicted using ANN and regressionmodels. The independent variables in the predictedmodels were spandex filament drawing ratio, spandexfilament linear density, and twist multiplier of thecore-spun yarns. Dependent variables, tensile propertiesof yarn samples, were characterized by breaking strength,breaking elongation, and work of rupture. The findings ofthis study can be sum up as follows:

� For breaking strength of cotton/spandex core-spunyarns, the R2, RMSE, and MBE for the datapredicted using ANN model are 0.99, 4.87, and1.345, respectively. While such values for theexperimental data predicted by regression modelwere 0.71, 27.4, and 1.81, respectively. This meansthat ANN model has more capability of makingquantitatively accurate breaking strength predictions.

� In the case of breaking elongation, the predictedvalues by the ANN model tracked the actual valuesvery well, which are shown by the higher R2 andlower RMSE and MBE values compared to regressionmodel. It is noticed that the average values of R2,RMSE, and MBE of experimental data predicted byANN model are one, zero, and zero, respectively.Whereas, such values belonging to regression modelare 0.84, 0.372, and 0.074, respectively.

� In the case of work of rupture, it was found that ANNmodel has more predictive power than regressionmodel in terms of high R2 and lower RMSE and BBEvalues compared to regression one. The R2, RMSE,and MBE values of the experimental data predicted byANN model are 0.989, 0.463, and 0.314, respectively.While, for regression model the values of suchparameters are 0.762, 1.12, and 0.832, respectively.

Finally, we can conclude that ANN modeloutperformed the regression one in the prediction process,therefore this model can be used efficiently to predict thetensile properties of cotton/spandex core-spun yarns.

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Table 10. Comparison of prediction performance of ANN andregression models for work of rupture.

Statistical parameters Regression ANN

Coefficient of determination, R2 0.761917 0.989588Mean bias error, MBE 0.83193 0.314489Root mean square error, RMSE 1.118002 0.46376

5678910111213

5 6 7 8 9 10 11 12 13

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dict

ed v

alue

s

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Figure 4. Actual values vs. predicted values using ANN andregression models for work of rupture.

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