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An optimal artificial neural network system fordesigning knit stretch fabricsHamza Alibi a , Faten Fayala a , Naoufel Bhouri a , Abdelmajid Jemni a & Xianyi Zeng ba LESTE, ENIM, University of Monastir, Monastir, Tunisiab GEMTEX, ENSAIT, Roubaix, FranceVersion of record first published: 15 Jan 2013.

To cite this article: Hamza Alibi , Faten Fayala , Naoufel Bhouri , Abdelmajid Jemni & Xianyi Zeng (2013): Anoptimal artificial neural network system for designing knit stretch fabrics, Journal of The Textile Institute,DOI:10.1080/00405000.2012.756134

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An optimal artificial neural network system for designing knit stretch fabrics

Hamza Alibia*, Faten Fayalaa, Naoufel Bhouria, Abdelmajid Jemnia and Xianyi Zengb

aLESTE, ENIM, University of Monastir, Monastir, Tunisia; bGEMTEX, ENSAIT, Roubaix, France

(Received 26 June 2012; final version received 3 December 2012)

In this paper, a computer-aided system for designing knit stretch materials is presented. It allows designers to opti-mize the structure of knit stretch materials according to the functional properties. This system aims at modelingthe relation between functional properties (outputs) and structural parameters (inputs) of knitted fabrics. Thirteenfeatures characterizing knit structures and operating parameters were taken as input parameters of the artificial neu-ral networks (ANNs). These parameters were preselected according to their possible influence on the outputswhich were the elongation, growth, and elastic recovery. In order to reduce the complexity of the models, an origi-nal fuzzy logic-based method was proposed to select the most relevant parameters which were taken as input vari-ables of the ANNs. The selection procedure of structural parameters allows designers to focus on the mostrelevant parameters in order to conduct production experiments related to the new product. Then, two types ofmodel are set up by utilizing multilayer feed forward neural networks, which take into account the generality andthe specificity of the product families, respectively. The presented models have been validated with the use ofexperimental data concerning several families of knitted fabrics.

Keywords: comfort-stretch; knit fabrics; elongation; elastic recovery; artificial neural network; fuzzy logic

Introduction

Elastic fabrics are an important way to achieve stretchcomfort (freedom of movement) for body fitted withsports and outdoor wear. Elastic cloths used in athlet-ics and sports may enhance the athlete’s performancein swimming, cycling, and so on. This type of fabricenables freedom of body movement by reducing thefabric resistance to body stretch. A simple body move-ment may enlarge the body skin by about 50% andthe fabric must easily go with the stretch and recoveron relaxation. Strenuous movements involved in activesports may require even better garment stretch. Drasticdifferences between skin and fabric movements resultin limitations of movement to the wearer. Elastic fiber,yarn, and fabric provide the requisite elasticity tocloths (Voyce, Dafniotis, & Towlson, 2005).

Fabrics containing elastane stretch fiber have awide application value, especially because of theirincreased extensibility, elasticity, high degree of recov-ery, good dimensional stability, and simple care(Ceken, 1996; Mukhopadhyay, Sharma, & Mohanty,2003; Tasmac, 2000).

The clothing industry uses two types of basic pat-tern blocks, one for woven fabrics and the other forknitted fabrics. For woven fabrics, an extra amount(ease) is added which allows for a degree of body

movement. The actual amount of recommended easeadded varies between authors but is usually within therange of 4–6 cm per half pattern. In the case of knittedfabrics pattern blocks, the ease can be largely ignoredas the inherent stretch properties of the fabrics allowfor body movement.

Many researches interest for dealing with the prob-lems of designing for today’s stretch fabrics. Theytried to establish a flexible and economical system fordesigning well-fitting body contouring apparel withknitted elastomeric. The methods used consisted ofpattern construction and how to produce a reducedpattern and this has been applied to a garment pro-duced from knitted stretch fabric of known extensionand recovery properties (I-Chin, Cassidy, Cassidy, &Shen, 2002; Ziegert & Keil, 1988). Several criteria ofthe product design are given as follows: (1) satisfyingthe target values of the functional properties of knitstretch fabrics; (2) optimizing the final structure offabrics; and (3) minimizing the quantity and the costof raw materials.

In the literature, some studies aimed to conceivenew plating devices or to design new plated fabrics(Baozhu & Weiyuan, 2007; Bruer, Powell, & Smith,2005; Doyle, 1953; Munden, 1959; Pusch, Wünsch, &Offermann, 2000). Cuden, Srdjak, and Pelko (2000)

*Corresponding author. Email: alibi_hamza@yahoo.fr

The Journal of The Textile Institute, 2013http://dx.doi.org/10.1080/00405000.2012.756134

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focused on the measurement of plated fabric propertiessuch as elasticity and shrinkage before and afterlaundering, but did not investigate the effect ofelastane ratio on these characteristics. Some researches(Gorjanc & Bukosek, 2008; Özdil, 2008) concernedonly weaved fabrics made with lycra core-spun weftyarns.

Other works (Ben Abdessalem, Ben Abdelkader,Mokhtar, & Elmarzougui, 2009; Ceken, 1996;Chemani & Halfaoui, 2006; Marmarali, 2003;Marmarali & Özdil, 2006; Miller, Atkins, & Rummel,2006; Pfangen, 2003; Singh, 1974; Tasmac, 2000)have studied the effect of some single factors oncomfort stretch properties. These properties areinfluenced by the finishing treatment, the amount ofelastane, yarn count, yarn twist, yarn composition,fabric’s structure, and the operating parameters (gauge,loop length, etc.).

They have not considered the combinationaleffects of several factors. Without considering thecomplex interactions of the various factors at the dif-ferent processing stages, the weight of each factor andtheir synergistic effect on extension and recoveryproperties cannot be fully understood. When studyingthe effect of each structural parameter on the func-tional properties selected from the final product speci-fications, it is quite difficult to produce a large numberof samples. In practice, the amount of learning sam-ples is strongly constrained by the production orexperiment costs.

Accordingly, it is necessary to set up a model tosolve it. It is the aim of our study. We try to developa design support system for product designers usingfuzzy logic and neural networks.

By the support developed, we predict elongation,growth, and recovery test results of knits stretch fabricfor course and wale direction. In order to reducethe model complexity, an original fuzzy logic-based

sensitivity variation criterion was developed to selectthe most relevant input variables and small-scaled arti-ficial neural network (ANN) models have been set upwith specific architectures adapted to the productdiversity before the modeling procedure.

Based on these models, designers, industrial, andresearchers can optimize the comfort stretch of knitproduct according to the specifications, also permit toreduce machines adjustment duration.

Experimental procedure

Sample production

Twenty different knit fabrics were used to select themost relevant input parameters. Table 1 shows themaximum, minimum, average, and standard deviationof knit fabric features used under study. The numericvalues 0 and 1 were used to encode the correspondingknit feature and yarn composition (given in brackets).

The greige fabrics were partially finished beforeevaluating their properties. The finishing conditionswere chosen according to industrial tests adapted toelastane ratio of 5%.

Fabric testing

First, we note that the fabrics samples were condi-tioned in the testing laboratory under standard atmo-spheric conditions of 20 ± 2°C and 65 ± 2% relativehumidity after a minimum period of 24 h conditioningin an NF ISO17025 certified laboratory. In this study,the tests carried out were concerning the determinationof these parameters according to the French nationalorganization for standardization (French Associationof Normalization [AFNOR]).

The evaluations of elastic properties (outputs) areexecuted according the AFNOR standard (NF EN14704-1, 2005) with a cyclic loading standard testby using a constant speed gradient dynamometer

Table 1. The maximum, minimum, average, and standard deviation of knit fabric features used to select the most relevantinput parameters.

Inputs parameters Mean value Standard deviation Maximum value Minimum value

Knitted structures – – 1 (rib1&1) 0 (jersey)Yarn composition – – 1 (100% viscose) 0 (100% coton)Yarn count (Nm) 50,000 10,000 60 40Loop length (cm) 0.327 0.0822 0.74 0.25Yarn twist (aNm) 110,000 10,000 120 90Gauge 23,770 4213 28 24Machine diameter (inch) 31,000 2000 32 30Lycra proportion (%) 3500 1122 5 2Lycra yarn count (dtex) 8070 14,665 44 22Lycra consumption (cm) 0.207 0.0322 0.36 0.101Lycra tension (cN) 4000 0.800 7 2Weight per unit area (g/m2) 200,000 31,000 250 140Thickness (m) 0.00086 0.00029 0.00105 0.00065

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LRX 2.5K (Lloyd, UK) (500mmmin�1). The fabricsample (50� 300 mm) is grabbed with two rollclamps. Specimen loading starts by graduallyincreasing the load to 15N and then decreasing theload until load zero.

Loading was performed till the inelastic zone(15N) in order to examine fabric recovery. Samplesare tested in wale and course directions and cyclicloading curves are reported in Figure 1 (it wasrepeated five times).

Three performance criteria of the fabric wereinvestigated in this study, elongation, residual exten-sion, and elastic recovery. Elongation can be explainedas the changing of the form of material temporarilywith the effects of out forces (pull etc.). This deforma-tion recovers when the effect of out forces disappear.Residual extension is the permanent deformationamount of material with the effect of the force appliedto it over a definite time. Recovery can be explainedas the ratio between the original dimension and thepermanent deformation.

Cyclic loading test is a dynamic test that simulatesdeformation applied on fabric during wearing. Afterelongation, knitted fabric does not recover initialdimension. It can be explained by the hysteresis

phenomenon of spun yarns (Figure 1), yarn composi-tion and structure, knitted fabric structure and proper-ties, etc.

Some related pictures of tested fabrics before cyc-lic loading test (a) and after cyclic loading test (b) inwale and course direction are illustrated in Figure 2.

Modeling with ANNs

In this section, we use ANNs for modeling the rela-tionship between the structural parameters and theelastics properties of knitting fabrics. Different tech-nologies are used to manufacture knitting fabrics. Inthis case, the structure of materials varies with appliedtechnology and the corresponding knitting fabrics arethen classified into a number of families eachcorresponding to one type of structure. Consequently,all the operating parameters and characteristics of yarnand fabric are divided into two groups. One groupcontains public parameters available for all the fami-lies of knits and the other group contains specialparameters existing for each specific family. Therefore,two ANN models are developed. The general model(Figure 3(a)) takes into account the public parametersas inputs. This model can be used by all the families

Figure 1. Fabric cyclic loading diagram.

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Figure 2. Appearance of some tested knitted fabrics.

Figure 3. General model including only public structural parameters: (a) special model including public and special structuralparameters (b).

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of knits. For each family, a special model was estab-lished (Figure 3(b)). It takes into account both thepublic and the special parameters as inputs.

In order to solve the problems related to the lackof available learning data or samples, small-scaledANN models are built (Huang & Moraga, 2004;Raudys & Jain, 1991; Vroman, Koehl, Zeng, & Chen,2008; Yuan & Fine, 1998).

The Levenberg–Maquardt learning procedure,based on a backpropagation algorithm, is used for cal-culating the unknown parameters of the general modelfrom the public learning data-sets. In the specialmodel, the weights connecting the public inputs tothe hidden neurons (HN) are kept invariable. Merely,the weights connecting the special input neurons to theHN are calculated during the learning phase using theerror backpropagation algorithm.

Variable selection and data preprocessing forneural network models

The fuzzy logic based sensitivity variation criteriondeveloped by Deng, Vroman, Zeng, and Koehl (2007)was used to select the most relevant structural vari-able. The important benefit of this technique is that itcan deal with a small number of learning data-set. Itsprinciple consists to calculate Euclidean distances orsensitivity variation of each input variable related tothe output variable.

The sensitivity variation for all inputs is definedaccording to the two following principles:

(1) If a small variation of an input variable Dx cor-responds to a large variation of the output vari-able Dy; then this input variable has a greatsensitivity value S.

(2) If a large variation of an input variable Dx cor-responds to a small variation of the output vari-able Dy; then this input variable has a smallsensitivity value S:

Based on these principles, a fuzzy model is builttaking into account the input data variation Dx and theoutput data variation Dy as two input variables andthe sensitivity S as output variable (Deng et al.,2007).

To simplify the selection procedure, we developedan original method using fuzzy C-means (FCM) (Bez-dek, 1981), based on this fuzzy sensitivity variationcriterion, to classify sensitivity variation values intoclasses depending on the application. Inputsconstituting the smallest class are eliminated; the rest(list CE) is used for the selection algorithm in the nextsection.

Inputs: process input variables X ¼ fx1; . . . ;xk ; . . . ; xmg, and one related specific output yl.

Output: relevant process parameters Xr and relatedsensitivity variation value DScorr(xp; xk) denotes cor-relation between xp and xk

(1) Calculate the sensitivity variation of inputs inX related to yl denoted DSl ¼ fDS1;l; :::;DSk;l; :::;DSsize(X );lg,

(2) Classify DSl into FCM classes; eliminate inputsthat constitute the smallest class,

(3) For each pair of relevant inputs (xk ; xp), calcu-late the linear correlation coefficient,

(4) If DSk;l 2 CE; and maxk–pjcorr (xk ; xp)j\a(correlation threshold). Then xk is consideredrelevant to y1:

(5) If DSk;l and DSp;l 2 CE; jcorr (xk ; xp)j � a andDSk;l > DSp;l. Then xk is considered relevant toy1; xp is correlate to xk and should beeliminated.

(6) Xr ¼ CEnfxpg:

The α value is defined by the experts. Over α issmall, less variables in the final list are correlated.

When this procedure is completed, we couldobtain a significant and independent list of the mostrelevant parameters related to specific output yl.

Model design and network training

Having choosing appropriate input variables, the fol-lowing steps build the models according to selectedparameters. The data in neural networks are catego-rized into two sets: training or learning sets and testor overfitting test sets. The learning set is usedto determine the adjusted weights and biases of anetwork.

The test set is used for calibration, which preventsovertraining networks. The overfitting test set shouldconsist of a representative data-set. It should beapproximately 10–40% of the size of the training setof data. The sigmoid function is used (Larose, 2005;Oussar, Monari, & Dreyfus, 2004).

The overall function represented by the networktype is:

y ¼ f (x) ¼XHidj¼1

SigmXni¼1

xijwij � Vj

!vj � h; (1)

where x is a n-dimensional input vector, w is theweight vector connecting the input units with the sin-gle output neuron, and h is the output neuron’s biasvalue; Hid is the number of HN, v is the weightvector connecting the hidden layer with the output

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neuron, and V is the HN’ bias values. Sigm(x) is thecommon sigmoid transfer function:

Sigm (x) ¼ 1

½1� exp (� x)�: (2)

The input to individual ANN nodes must benumeric and fall in the closed interval [0,1]. Becauseof this conversion method, the normalization tech-nique was used in the proposed ANN according to thefollowing formula:

x0 ¼ xi �min (x)

max (x)�min (x); (3)

where xi is a feature instance and x represents the setof a feature type.

Output values resulted from ANN were also in therange [0,1] and converted to its equivalent valuesbased on reverse method of normalization technique.

Selecting the optimal model architecture

The fitted model is expected not merely to predictaccurately the observed data-set but also to generatesatisfactory predictions for unseen (test) data-setdrawn from the same population as the observed(training) data. Such a model is able to generalize(extrapolate) well within the data-set range.

The estimation of the best fit parameters based onthe naïve minimization of a merit function based onthe fidelity to the learning data-set alone can steer to afitted model with very poor predictive aptitude. Givena sufficient number of parameters (degrees of free-dom), the model can be fitted to pass through eachobserved data points perfectly. This strict interpolationis undesirable and must be avoided in practice sincethe observed data are unavoidably corrupted withmeasurement noise. This overfitting phenomenon canbe avoided using the leave-one-out cross-validationcriterion for estimation of optimal regularizationparameters of the regularization networks (Rogier &Geatz, 2003). Obviously, traditional a multilayerperception networks are not equipped with any noisefiltering capacity and the above procedure cannot beapplied to such networks.

Model selection was performed basically by esti-mating the generalization aptitude of the modelstrained as described, using the “leave-one-out score”Ep:

Ep ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXnk¼1

R(�k)k

h i2s; (4)

where R(�k)k is the prediction error on the example k

when the latter has been removed from the learningdata-set and the model has been trained with theremaining examples. Since the computation of theleave-one-out score is computer-intensive, approxima-

tions of the leave-one-out errors R(�k)k were computed

by the “virtual leave-one-out” method, described in(Oussar et al., 2004).

In this application, the model is based on « p »samples of knits fabrics. Training uses the leave-one-out technique. After training, the optimal model archi-tecture was chosen by using a selection methodology(Alibi, Fayala, Jemni, & Zeng, 2012; Geman, Bienen-stock, & Doursat, 1992; Golub & Van Loan, 1996;Monari & Dreyfus, 2000, 2002; Rogier & Geatz,2003; Vapnik, 2000).

Model evaluation and interpretation

Performance measure

In order to evaluate the performance of the obtainednetwork models, three statistical performance criteria,including root-mean-square error (RMSE), coefficientof correlation (R), and mean absolute relative error(MARE), were used in this study. These parameterswere calculated for training (tr) and testing (T) phases:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPnk¼1 yk

p � yk� �2n

vuut; (5)

R2 ¼Pn

k¼1 yk � �ykp

� �2Pn

k¼1 ykp � �yk

p

� �2; (6)

MARE ¼ 1

N

XNi¼1

yk � ykp

ykp

����������; (7)

where yk and ykp, respectively, the prediction of theoutput by the model and measured value of the pro-cess output for observation k:

Model interpretation

In spite of their many advantages such as universalfunction approximation, robustness, capability to takeinto account the nonlinear relationship of structuraland functional parameters, and ability to learn fromexamples, one of the main limitations of ANN modelsis their “black-box” system approach which is unableto explain the weights of each inputs and their syner-gistic effect on outputs (Table 2).

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Numerous methods have been proposed to conquerthis shortcoming (Jayadeva, Guha, & Chattopadhyay,2003). In this paper, the connection weight approachproposed by Olden and Jackson (2002) was used tocalculate the importance of ANN input variables, asOlden, Joy, and Death (2004) found that this approachprovided the best overall technique for accuratelyranking ANN input relevancy in comparison to othercommonly used techniques.

This approach consists to calculate the product ofthe raw input-hidden and hidden-output weightsbetween each input and output neuron. Next, it sumsthe products across all HN, which is defined as Si Therelative contributions of ANN inputs in calculatingthe output are dependent on the scale and direction ofthe connecting weights. Input variable with biggerconnection weights (higher Si) is more relevant in theprediction process compared to the inputs with smallerconnection weights (lower Si). Negative and positiveconnection weights, respectively, decrease andincrease the value of the predicted response.

Results and discussion

Fuzzy sensitivity variation for selecting relevantprocess parameters

The fuzzy-based method presented in this paper wasused for selecting the relevant input variables andremoving irrelevant ones. We have chosen to presentthe selecting procedure, the results and discussionsrelated to the elastic recovery in wale direction as anapplication example.

According to our application, DSk;l values are clas-sified into three classes (small, medium and large)using FCM algorithm. Table 3(a) represents the firststep to classify the sensitivity variation of structuralparameters related to elastic recovery in wale directionand then removing small class’s inputs. Table 3(b)shows the next step for identifying independent list ofmost relevant inputs.

According to these tables, the relevant parametersselected from this criterion could be ranked in a signif-icant order of relevancy: lycra yarn count (x9) > thick-ness (x13) > yarn composition (x2) > knitted structures(x1) >weight per unit area (x12) > lycra proportion (x8)> loop length (x4) > gauge (x6) > yarn count (x3).Therefore, by using the fuzzy sensitivity variation cri-terion, the number of structural parameters wasreduced from 13 to 9. Therefore, it can be concludedthat the fuzzy sensitivity variation criterion could effi-ciently filter data complexity related to elastic recoveryand provide merely an enhanced ranking result accord-ing to the process variables relevancy. This permitted agood comprehension on the structural variable sincethe adjustable variables are more concise and easier tobe interpreted physically. The selected parameters wereused to build the ANN models.

Optimum neural networks architecture

The focus of this research was constrained to pure cot-ton, pure viscose, viscose/lycra, and cotton/lycra pla-ted knitted constructions. We produced a series of 340knitted fabrics commonly used in the clothing industry

Table 2. Input and output parameters.

Factors Variable names

Processing parameters (input) Knitted structures (x1), yarn composition (x2), yarn count (x3), loop length (x4), yarn twist(x5), gauge (x6), machine diameter (x7), lycra proportion (x8), lycra yarn count (x9), lycraconsumption (x10), lycra tension (x11), weight per unit area (x12), and thickness (x13)

Properties (output) Elastic recovery in wale direction (y1)

Table 3. Selection of relevant (a) and independent (b) input variables related to elastic recovery in wale direction, using thefuzzy logic-based sensitivity variation criterion.

(a) InputsSignificance ranked byascending order DS

Most relevant inputs(list CE)

Irrelevantinputs

All inputs, x1 to x13 x9, x13, x2, x1, x12, x8, x4, x6,x3, x5, x10, x11, x7

x9, x13, x2, x1, x12, x8,x4, x6, x3, x5, x10

x11, x7

(b) Remaining inputs (list CE) Correlate input (α = 0,8) Significant and independent list of themost relevant inputs

x9, x13, x2, x1, x12, x8,x4, x6, x3, x5, x10

x5, x10 x9, x13, x2, x1, x12, x8, x4, x6, x3

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by using different industrial circular knitting machines(single jersey, double jersey, interlock; tubular andlarge diameter; diameter = 16–34 inch, gauge = 18–28).Ground yarn was a 100% combed cotton (1) and100% viscose yarn (2) (Nm=28–80) and plating yarnwas a lycra monofilament (22, 33, and 44 dtex) platedat half feeder. The fabric samples were comprised ofnine different knitted structures, single jersey (1),single lacoste (2), double lacoste (3), polo pique(4), visible molleton (5) invisible molleton (6), 1/1 rib(7), 2/2 rib (8), and interlock (9).

The 340 measurements were randomly divided intoa training database of 244 values for training andmodel selection, and a test database of 96 values forthe final assessment of the generalization performanceof the model. Table 4 presents the statistical values ofselected input and output parameters of training andtest set fabrics.

The network architecture used a three-layeredfeed-forward network with sigmoid hidden-unitactivity and a single linear output unit.

There are six knitting fabrics families different inthe formation (simple or complex structure) and theknitting technologies (simple and double needlemachine or interlock machine).

A general model is built using a neural network forall the knitting samples. It characterizes the relation-ship between the selected structural parameters and thecorresponding functional property. For the functionalproperties, using the fuzzy logic-based sensitivityvariation criterion, we take the eight most relevantstructural parameters as public input variables.

A special model is built for the family of knittingmaterials produced using a specific knitting technol-ogy (Exp: interlock machine). Its architecture andparameters are built based on the corresponding gen-eral model. For example, the interlock loop length isadded to the set of the input variables of the generalmodel to build the special model corresponding tointerlock knitting family. Figure 4 shows the specialmodel built for predicting the functional propertieswith eight public parameters (knitted structures, cottonyarns counts, gauge, lycra proportion, lycra yarncount, lycra consumption, weight per unit area, andthickness) as input variables. The special structuralparameter is then added to the set of these eight inputvariables. The architecture and parameters of specificmodel are built based on the corresponding generalmodel. Only the weights connecting the specific inputneurons to HN are added. Therefore, this model

Table 4. Statistical values of input (a) and outputs (b) parameters of training and test set fabrics.

Mean value Standard deviation Maximum value Minimum value

Train Test Train Test Train Test Train Test

(a) Inputs parametersKnitted structures – – 2.775 2.75 9 9 1 1Yarn composition – – 0.303 0.24 2 2 1 1Yarn count 49.138 50.28 10.163 10.64 80 80 20 20Gauge 23.770 24.17 4.213 3.99 28 28 16 14Lycra proportion (%) 1.123 0.93 2.122 1.98 10 8 0 0Lycra yarn count (dtex) 8.070 6.19 14.665 12.88 44 44 0 0Weight per unitarea (g/m2)

220.679 209.09 64.351 61.56 548 422 120 119

Thickness (m) 0.00078 0.00076 0.00021 0.00022 0.00153 0.0016 0.00044 0.00044Interlock loop length (cm) 1.43 1.03 0.287 0.256 2.42 2.72 1.08 0.95Jersey loop length (cm) 0.327 0.267 0.0822 0.0745 0.74 0.68 0.25 0.251&1 rib loop length (cm) 0.6125 0.565 0.0699 0.0621 0.83 0.92 0.37 0.322&2 rib loop length (cm) 0.675 0.486 0.0876 0.0569 0.87 0.79 0.62 0.58

(b) Outputs parametersOutput 1: elongation in waledirection (%)

30.85 25.61 24.97 16.78 139.24 106.44 12.68 10.13

Output 2: elastic recovery inwale direction (%)

77.34 75.92 8.07 7.95 96.16 91.54 55.55 52.83

Output 3: residual extensionin wale direction (%)

5.77 5.51 2.43 2.45 17.25 14.75 1.5 2

Output 4: elongation incourse direction (%)

91.96 82.44 57.51 34.53 563.99 167.00 13.26 28.12

Output 5: elastic recovery incourse direction (%)

67.65 65.84 14.20 14.19 91.5 91.79 30.49 28.60

Output 6: residual extensionin course direction (%)

30.65 30.56 24.14 21.74 159.5 109.5 2 3.25

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benefits from both the specificity of each stretch knit-ted fabrics class and the generality of all these classes.Consequently, we need to build these two types ofmodels to solve the problems related to the lack ofavailable learning samples.

The goal of ANN design is to find a model forwhich the estimate of the root-mean-square generaliza-tion error is on the order of the standard deviation ofthe noise present in the training data (Geman et al.,1992). To that effect, models of increasing complexity(i.e. increasing number of HN) were trained, and thevirtual leave-one-out score Ep of each model wascomputed. The root-mean-square error on the trainingset (RMSEtr) was also computed; those quantities arereported in Table 5. As expected, Ep decreases whenthe number of HN increases and starts increasingwhen the number of parameters is big enough foroverfitting to arise. On the other hand, RMSEtr on thetraining data-set decreases when the number of HNincreases (Table 5). Moreover, the learning taskenhanced when the number of HN exceeds the eight,

but the generalization ability degraded. In fact, thegeneralization error decreases and the overfittingphenomenon starts.

These results can be explained by the fact thatANN architecture with small number of HN is unableto extract the nonlinearity between the inputs and out-puts. Whereas, a model with too many HN can per-fectly adjust the training examples and the modeldedicated a large part of its degrees of freedom tolearn these examples. Therefore, it fit the noise thatexists in the data, hence generalizes poorly. As aresult, the predictions will be deprived of significancebecause its performance will depend for the largestpart on the particular training data-set. Accordingly,the selected model should guarantee the optimumtrade-off between learning aptitude and generalizationability.

For our case, the generalization error Ep does notincrease significantly when the number of HN exceedsthe eight, in the investigated range. In order to mini-mize the number of parameters, eight HN were

Figure 4. Special model for the interlock knitting family.

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selected. The final optimized architectures of neuralnetwork are shown in Figure 4, corresponding to 81parameters.

To test the generalization performance of the opti-mal trained network, validating processes was appliedusing the test database (Table 4). The main qualityindicator of a neural network is its generalization abil-ity, its ability to predict accurately the output ofunseen data. The experimental vs. predicted values oftest data-set are shown in Figure 5, as it can beobserved, the predictability of ANN fits very well.

RMSET and R2T for the feed-forward neural net-

work were computed. Computations were performedfor all outputs (Table 6).

Neural networks provide quite satisfactory predic-tions for all functional properties from a global pointof view: R2

T is larger than 0.9 while RMSET is lowerthan 3.5.

Mean absolute relative errors MARET were usedto evaluate the performance of the proposed ANN inprediction technique. These levels of error (mean 6%)are satisfactory and smaller than errors that normallyarise due to experimental variation and instrumenta-tion accuracy.

Prediction assessment of the product functionalproperties

Table 7 gives the details of the experimental resultson the functional properties and the correspondingpredicted results obtained from the general modelsand the special models. Figure 6 compares the pre-dicted values of these functional properties obtainedfrom the general and the special models and the realphysical measures, respectively.

The results demonstrated good agreement betweenthe experimental and predicted values from specialmodels (R2

tr > 0.9).From these outcomes, it should be noted that the

special models give lower prediction errors (aver-aged error: 6%) than the general models (averagederror: 12%). This observation can be explained asfollows:

• The general model uses samples from numerousfamilies which differ from each other in manyaspects while the special model merely usessamples from the same family. The general

Table 5. Optimization of the number of HN for the neural networks: wale direction (a) and course direction (b).

Output 1: elongation in waledirection

Output 2: elastic recovery inwale direction

Output 3: residual extension inwale direction

RMSEtr q Ep RMSEtr q Ep RMSEtr q Ep

(a) Number of HN

1 32.85 11 26.883 5.017 11 7.231 1.794 11 1.9372 25.215 21 29.652 4.656 21 5.217 1.534 21 1.7563 6.48 31 11.246 4.235 31 5.094 1.366 31 1.7064 5.891 41 16.519 3.873 41 5.034 1.168 41 1.7015 6.237 51 11.075 3.466 51 5.704 1.037 51 1.6026 4.969 61 11.616 3.502 61 6.19 0.895 61 1.5097 4.056 71 10.503 2.84 71 5.674 0.888 71 1.7268 2.966 81 10.801 2.689 81 5.796 0.714 81 1.3079 2.525 91 10.906 2.329 91 5.897 0.68 91 1.95510 1.461 101 12.071 2.277 101 6.631 0.556 101 1.703

(b) Number of HNOutput 4: elongation in course

directionOutput 5: elastic recovery in

course directionOutput 6: residual extension in

course direction

RMSEtr q Ep RMSEtr q Ep RMSEtr q Ep

1 35.266 11 50.124 7.23 11 7.55 46.121 11 26.2992 27.674 21 41.478 6.274 21 7.138 9.963 21 13.3183 23.018 31 40.99 5.729 31 6.959 9.183 31 12.8284 18.281 41 35.23 5.343 41 7.443 7.33 41 14.4575 15.778 51 31.781 4.541 51 7.757 7.907 51 12.6256 14.126 61 24.639 4.465 61 7.242 7.284 61 14.0287 12.926 71 27.52 4.153 71 18.064 6.249 71 15.068 4.405 81 9.79 3.725 81 7.752 5.445 81 11.5269 6.342 91 22.076 3.576 91 38.57 5.205 91 13.61110 5.861 101 31.082 3.22 101 17.637 4.967 101 18.464

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model cannot benefit from the specificity of eachstretch knitted fabrics family.

• The special model is set up based on the corre-sponding structure of the general model. Merely,

the weights connecting the specific input to HNare added. Thus, it takes into account both thespecificity of each stretch knitted fabrics familyand the generality of all families.

Figure 5. Experimental vs. predicted values for studied properties: data-set validation.

Table 6. Results of testing and validating neural network models for all comfort-stretch properties.

Outputs RMSET MARET (%) R2T

Output 1: elongation in wale direction 2.2 6 0.983Output 2: elastic recovery in wale direction 3 7 0.87Output 3: residual extension in wale direction 0.5 3 0.956Output 4: elongation in course direction 3.16 7 0.936Output 5: elastic recovery in course direction 3.5 4 0.937Output 6: residual extension in course direction 3.8 9 0.95

Table 7. Experimental results on the comfort-stretch properties for all product families.

Outputs

General model Special model

Avg. error (%) SD (%) R2tr Avg. error (%) SD (%) R2

tr

Output 1: elongation in wale direction (%) 8 13 0.912 4 5 0.995Output 2: elastic recovery in wale direction (%) 3 3 0.81 2 3 0.91Output 3: residual extension in wale direction (%) 14 13 0.842 9 10 0.915Output 4: elongation in course direction (%) 17 18 0.924 7 5 0.971Output 5: elastic recovery in course direction (%) 6 6 0.865 4 4 0.93Output 6: residual extension in course direction (%) 23 24 0.867 6 7 0.944

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Figure 6. Comparison between general and special models, related to comfort stretch properties in course and wale direction:residual extension (a,b), elastic recovery (c,d), and elongation (e,f).

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Typical plots of the experimental vs. predicted val-ues of selected stretch knitted fabrics are shown inFigures 7–9 and the results are discussed as following:for some materials (i.e. cotton and viscose), the pre-dicted values of elastic recovery in course directionclosely matched to experimental values (Figure 7(b)),showing the ANN model capability, whatever the typeof raw materials and the available amount of data.Though, whatever the knitted structure’s the ANNmodel fits very well, solving the lack of availabledata-set of some knitted structures due to productionconstraints (Figure 7(a)). As well, the model accu-rately predicted the desired elastic recovery in coursedirection at high and lower values. Moreover, themodel was able to predict elastic recovery in coursedirection whatever the gauge (Figure 8(b)). The devel-oped ANN model is expected to be used for severalcircular knitting machines.

Results show also the robustness with good accu-racy of the special models for extreme value of yarncount (Figure 8(a)), lycra proportion (Figure 9(a)), andlycra yarn count (Figure 9(b)). It should be noted thatthis modeling procedure has proved its ability to pro-cess the existing constraints in others techniques, suchas the nonlinearity in statistic techniques and initialand boundary conditions in numerical simulations(Hasan, Sulaiman, & Othman, 2011; Layeghi, Karimi,& Seyf, 2010).

The developed ANN models are expected to helpengineer to decide about designing new stretch knittedfabrics before the actual manufacturing by taking intoaccount, mainly, the operating parameters, large typesof knitted structures, and elastane properties. As well,using operating parameters as inputs of ANN modelto predict comfort, stretch properties of fabrics werenot investigated before.

Figure 7. Experimental and neural network predict values of elastic recovery in course direction for: knitted structures (a)and yarn composition (b).

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Prediction interpretation

Table 8 gives the connection weights between theinput and hidden layers and the connection weightsbetween the hidden and output layers of the selectedANN model. These weights could be utilized for inter-pretation of the physical effect of inputs on outputs.To compare, the ranking of inputs as per relativeimportance obtained from the fuzzy sensitivity varia-tion criterion and the connection weights technique,we use the same output (elastic recovery in waledirection).

The relative importance of the input variables asdetermined following the connection weight technique(Olden et al., 2004) is presented in Table 9. Resultsshowed that lycra yarn count was the most importantparameter for elastic recovery in wale direction (Sivalue 14.9095) followed by thickness (Si value

12.591). Moreover, it could be noticed that the rank-ing of inputs as per relative importance for elasticrecovery in wale direction was the same resultobtained from the fuzzy sensitivity variation criterion.

This finding confirmed that the selected parametershad an influence on the elastic recovery. However, itcould be shown that weight per unit area and knittedstructures had a negative influence on the predictionof the output. This result indicated that elastic recov-ery values decreased with increase in weight per unitarea and knitted structures values. Conversely, lycrayarn count, lycra proportion, thickness, loop length,yarn composition, gauge and yarn count had a positiveinfluence on the prediction of the output.

The increasing of ground yarn count resulted inimproved elastic recovery. In fact, we can introducemore elastane fiber on stitch formed by a thinner

Figure 8. Experimental and neural network predict values of elastic recovery in course direction for: yarn count (a) andgauge (b).

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Figure 9. Experimental and neural network predict values of elastic recovery in course direction for: lycra proportion (a) andlycra yarn count (b).

Table 8. Values of weights between the input (a), output (b) layer and the hidden layer of the ANN.

HN1 HN2 HN3 HN4 HN5 HN6 HN7 HN8

(a) InputKnitted structures �4.34 �1.84 1.07 �4.49 4.42 �1.14 0.7 �4.85Yarn composition �0.97 �0.72 �0.47 1.27 �0.51 �1.03 �1.73 �0.35Yarn count 0.76 �2.85 �0.86 �1.5 1.91 �1.89 0.06 1.13Gauge �4.02 4.04 1.2 6.27 �6.18 1.47 0.05 2.36Lycra proportion (%) 0.76 2.98 0.26 2.22 4.37 �3.92 �0.55 0.03Lycra yarn count (dtex) 1.13 0.98 �0.5 �3.17 �1.18 �3.36 �0.49 �7.7Weight per unit area (g/m2) 4.75 10.04 �1.27 �11.03 �6.09 �2.95 �1.62 4.48Thickness (m) 6.2 5.91 �2.14 �2.55 �3.3 �2.15 �0.1 �7.3Loop length (cm) 1.05 0.86 �0.3 �3.93 �0.88 �2.21 �0.37 �1.2

(b) OutputElastic recovery in wale direction (%) 1.8 �1.27 2.92 1.08 �1.46 �2.21 �2.67 �1.11

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ground yarn. In the same way, the increasing rate ofelastane causes freedom of stitch and they will not bemore locked because the elastane yarn is less tight.This results in a decrease of stitches density thusreducing weight per unit area.

The elastic recovery values increased with increasein lycra yarn count and lycra proportion values; this isdue to the increase of potential energy inside fabricthat allows the improved recovery levels of fabricdimensions. This finding also indicated that viscoseknit fabrics achieved better recovery than cotton fab-rics. This result can be explained by the fact that vis-cose fiber has greater elasticity than cotton. The largerpartial recovery of the cotton knitted fabric is due tohysteresis phenomenon of cotton spun yarns havingmore plastic deformation behavior related to the slip-page and viscoelasticity of cotton fiber. The residualdeformation obtained after cyclic loading test can beexplained by plastic deformation due to fiber residualextension and/or fiber slippage because elastane yarnis purely elastic. Fiber residual extension depends onthe fiber viscoelasticity, while fiber slippage phenome-non depends on torsion and bending of the yarn.

In addition, it indicated that by considering fabricmade of the same fiber type, the elastic recovery ofsimple structure fabrics was better than more complexfabrics. An open knit fabric offers higher stretch thana close knit structure; the stitches will not be morelocked.

These results were consistent with previous works(Ben Abdessalem et al., 2009; Mukhopadhyay et al.,2003; Singh, 1974).

As a result, the outcomes obtained from ANNmodels could be used to validate physical knowledgeon the relationship between structural parameters andcomfort stretch properties. Hence, a conclusion can bedraw that the developed ANN models could explainthe physical effect of inputs on the outputs.

Conclusions

In this study, a support system was built up for opti-mizing the design of knit stretch fabrics, in agreementwith the specifications. The relationship between thestructural parameters and fabrics features of knitstretch products is established using ANN. In order toreduce the complexity of the ANN models and solvethe lack of available data-set, also deal with the riskof losing some relevant variable, an original selectionprocedure was proposed using FCM algorithm toselect the most relevant structural parameters. Theselection procedure of structural parameters allowsfabric designers to focus on the most relevant parame-ters in order to conduct actual manufacturing of thenew knit stretch product. According to this approach,it was found that lycra yarn count, thickness, yarncomposition, knitted structures, weight per unit area,lycra proportion, loop length, gauge, and yarn countwere important parameters. This shows that the effectson comfort stretch properties depend not only on knit-ting parameters but also on fabric features.

In the modeling procedure, two types of modelsare set up. A general model is firstly developed for allfamilies of knit stretch products. It is built from thedata-set of public inputs. A special model is then builtfor each family of knit stretch products by adding spe-cial structural parameters to the data-set of publicinputs.

The leave-one-out approach has been used to testthe efficiency of the general and special model. Thedeveloped ANN models were different in trainingalgorithms. The neural network optimization methodhad enhanced the model accuracy. Results show lowprediction errors of special models compared to gen-eral models. The simulation of these models allowsdesigners to optimize structure of materials more sys-tematically, substituting the traditional hit-and-trialapproach and hence reduce testing time and cost.

Table 9. Relative importance of different inputs as per connection weight approach for prediction of elastic recovery in waledirection by the ANN.

Output

OutputElastic recovery in wale direction (%)

Si value as per connection weight approach Ranking of inputs as per relative importance

Knitted structures �6,4712 4Yarn composition 7,1961 3Yarn count 0.8301 9Gauge 0.9298 8Lycra proportion (%) 4,4584 6Lycra yarn count (dtex) 14,9095 1Weight per unit area (g/m2) �5,0581 5Thickness (m) 12,591 2Loop length (cm) 4,1662 7

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The relative importance of the input parameterswas established via the connection weight approach.The outcomes were found to agree with those calcu-lated via the fuzzy logic-based sensitivity criterion.Therefore, it is believed that ANN models couldefficiently be applied to the knitting industry tounderstand, evaluate, and predict comfort stretchtaking into account knitting parameters and fabricfeatures as inputs.

ReferencesAlibi, H., Fayala, F., Jemni, A., & Zeng, X. (2012). A neu-

ral network system for prediction of thermal resistanceof knit fabrics. Special Topic in Porous Media, 3, 35–53.

Baozhu, K. & Weiyuan, Z. (2007). The optimal design ofthree-layer plated fabrics. Fibres & Textiles in EasternEurope, 15, 59–61.

Ben Abdessalem, S., Ben Abdelkader, Y., Mokhtar, S., &Elmarzougui, S. (2009). Influence of elastane consump-tion on plated plain knitted fabric characteristics. Jour-nal of Engineered Fibers and Fabrics, 4, 30–35.

Bezdek, C. (1981). Pattern recognition with fuzzy objectivefunction algorithms. New York: Plenum Press.

Bruer, S. M., Powell, M., & Smith, G. (2005). Three dimen-sionally knit spacer fabrics: A review of productiontechniques. Journal of Textile and Apparel, Technologyand Management, 4, 1–31.

Ceken, F. (1996). Some investigations of the dimensionalproperties of knitted fabrics containing different materi-als (Unpublished doctoral thesis). Ege University, Izmir,Turkey.

Chemani, B. & Halfaoui, R. (2006). Influence of twist,diameter and account of the weft yarn on fabric elastic-ity: Application to pancake band. Paper presented at the2nd International Conference on Applied Research inTextile. Monastir, Tunisia.

Cuden, A. P., Srdjak, M., & Pelko, H. (2000). Optimizationof the cotton/Lycra plain knitted fabric parameters. Inter-national Journal of Polymeric Materials, 47, 633–648.

Deng, X., Vroman, P., Zeng, X., & Koehl, L. (2007). Afuzzy criterion for selecting relevant process parametersfor the development of nonwoven products. Journal ofInformation and Computing Science, 2, 93–102.

Doyle, P. J. (1953). Fundamental aspects of the design ofknitted fabrics. Journal of The Textile Institute, 44,561–578.

Geman, S., Bienenstock, E., & Doursat, R. (1992). Neuralnetworks and the bias/variance dilemma. Neural Com-puting, 4, 1–58.

Golub, G. H. & Van Loan, C. G. (1996). Matrix computa-tions (3rd ed.) (p. 694). Baltimore, MD: Johns HopkinsUniversity Press.

Gorjanc, S. & Bukosek, V. (2008). The behaviour of fabricwith elastane yarn during stretching. Fibres and Textilesin Eastern Europe, 16, 63–68.

Hasan, M. K., Sulaiman, J., Karim, S. A. A., & Othman, M.(2011). Development of some numerical methods apply-ing complexity reduction approach for solving scientificproblem. Journal of Applied Science, 11, 1255–1260.

Huang, C. & Moraga, C. (2004). A diffusion-neural-net-work for learning from small samples. InternationalJournal of Approximate Reasoning, 35, 137–161.

I-Chin, D. T., Cassidy, C., Cassidy, T., & Shen, J. (2002).The influence of woven stretch fabric propertieson garment design and pattern construction. Transactionsof the Institute of Measurement and Control, 24, 3–14.

Jayadeva Guha, A. & Chattopadhyay, A. (2003). A studyon the capability of a neural network ranking fibreparameters having an influence on yarn properties. Jour-nal of The Textile Institute, 94, 186–193.

Larose, D. T. (2005). Discovering knowledge in data(pp. 105–120). New York: John Wiley & Sons.

Layeghi, M., Karimi, M., & Seyf, H. R. (2010). A numeri-cal analysis of thermal conductivity, thermal dispersionand structural effects in the injection part of the resintransfer molding process. Journal of Porous Media, 13,375–385.

Marmarali, A. (2003). Dimensional and physical propertiesof cotton/spandex single jersey fabrics. Textile ResearchJournal, 73, 11–14.

Marmarali, A. & Özdil, N. (2006). Stretching properties ofcotton/elastane single jersey fabrics. Paper presented atthe 2nd International Conference on Applied Researchto Textiles, Monastir, Tunisia, MAT 30, PDT 47.

Miller, R. A., Atkins, J. D., & Rummel, D. R. (2006).Cotton jersey fabric construction having improvedstretch characteristics. US Patent 7040124.

Monari, G. & Dreyfus, G. (2000). With drawing an exam-ples from the training set/an analytic estimation of itseffect on a non-linear parameterized model. Neuro Com-puting Letters, 35, 195–201.

Monari, G. & Dreyfus, G. (2002). Local overfitting controlvia leverages. Neural Computing, 14, 1481–1506.

Mukhopadhyay, A., Sharma, I. C., & Mohanty, A. (2003).Impact of lycra filament on extension and recovery char-acteristics of cotton knitted fabric. Indian Journal ofFibre & Textile Research, 28, 423–430.

Munden, D. L. (1959). The geometry and dimensional prop-erties of plain-knit fabrics. Journal of The Textile Insti-tute, 50, 448–471.

NF EN 14704–1. (2005). Determination of the elasticity offabrics - Part 1: Strip tests. Paris: French Association ofNormalization (AFNOR).

Olden, J. D. & Jackson, D. A. (2002). Illuminating the“black box”: A randomization approach for understand-ing variable contributions in artificial neural networks.Ecological Modelling, 154, 135–150.

Olden, J. D., Joy, M. K., & Death, R. G. (2004). An accu-rate comparison of methods for quantifying variableimportance in artificial neural network using simulateddata. Ecological Modelling, 178, 389–397.

Oussar, Y., Monari, G., & Dreyfus, G. (2004). Repley tothe comments on “Local overfitting control via lever-ages”. Neural Computation, 16, 419–444.

Özdil, N. (2008). Stretch and bagging properties of denimfabrics containing different rates of elastane. Fibres andTextiles in Eastern Europe, 16, 63–67.

Pfangen, T. (2003). Finishing of woven and knitted fabricswith elastane fibers. Asian Textile Business, 585, 46–51.

Pusch, T., Wünsch, I., & Offermann, P. (2000). Dynamicsof yarn tension on knitting machines. AUTEX ResearchJournal, 1, 55–63.

The Journal of The Textile Institute 17

Dow

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ina

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e U

nive

rsity

] at

06:

36 1

4 M

arch

201

3

Raudys, S. J. & Jain, A. K. (1991). Small sample sizeeffects in statistical pattern recognition: Recommenda-tions for practitioners. IEEE Transaction on PatternAnalysis and Machine Intelligence, 13, 252–263.

Rogier, J. R. & Geatz, M. W. (2003). Data mining: A tutorial-based primer (pp. 104–113). New York: Addison-Wesley.

Singh, S. A. P. (1974). The effect of fabric structure on theproperties of two-way stretch fabrics made from elasticcore-spun yarns of cotton and wool blend. TextileResearch Journal, 44, 506–512.

Tasmac, M. (2000). Effects of spandex yarn on single jerseyfabrics. Tekstil Konfeksiyon, 6, 422–426.

Vapnik, V. (2000). The nature of statistical learning theory(p. 314). New York: Springer.

Voyce, J., Dafniotis, P., & Towlson, S. (2005). Textiles insport (1st ed.). Cambridge: Woodhead Publishing.

Vroman, P., Koehl, L., Zeng, X., & Chen, T. (2008).Designing structural parameters of nonwovens usingfuzzy logic and neural networks. International Journalof Computational Intelligence Systems, 4, 329–339.

Yuan, J. L. & Fine, T. L. (1998). Neural-network design forsmall training sets of high dimension. IEEE Transactionon Neural Networks, 9, 266–280.

Ziegert, B. & Keil, G. (1988). Stretch fabric interactionwith action wearables: Defining a body contouring pat-tern system. Clothing and Textiles Research Journal, 6,54–64.

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