fabric quality optimization by using desirability function ... · fabric quality optimization by...

Fabric Quality Optimization by Using Desirability Function and

Neural Networks

Hajer Souid

Textile Research Unit of ISET of Ksar-Hellal, B.P 68, Avenue Hadj Ali SOUA, 5070

Ksar Hellal, Tunisia

E-mail: [email protected]

Amel Babay




Mehdi Sahnoun




Abstract

The present paper presents a new method to

estimate objective reflection of Denim fabric

quality by using desirability function and neural

networks. The global fabric quality was defined

through one index belonging to the closed interval

[0, 1]. For this reason, we have created a first

algorithm that is modified when the definition of

fabric quality is changed. This prediction would

allow fabric producer to estimate customer’s

quality satisfaction level. The present approach

has conferred a good evaluation and prediction of

the all-encompassing denim fabric quality. In the

second stage of the study, we developed a model to

predict global fabric quality from fiber, yarn,

weaving parameters and finishing characteristics

by using neural networks. The neural network

model is accomplished by using a second

algorithm based on back-propagation concept.

The results have shown that the neuronal networks

could predict global fabric quality of the untrained

fabrics with better precision.

Keywords: Fabric; quality; desirability

function; optimization, yarn, neural networks

1. Introduction

Fabric quality has been in consideration for

many years. Seeking for it needs a satisfaction of

several properties at the same time [1]. It is now

an accepted principle that „satisfying the

customer‟ in all respects is in practice the

meaning of quality [2]. Many theoretical and

experimental investigations [3; 4; 5; 6; 7; 8] over

many decades have been focused on fabric

quality and performance but combining many

properties into one objective notion still reveal

hard to define. In this survey, our objective is to

quantify the overall quality of denim fabric by an

amalgam of eight fabric parameters which include

warp and weft breaking strength, warp and weft

tear strength, warp and weft elongations,

stiffness, and weight. Our implementation relies

on the formulation of desirability functions.

The present approach is an important useful

method. It represents a statistical tool that

translates product quality from a set of multiple

subjective concepts into one single objective

notion. The concept of desirability was first

introduced by Harrington in 1965 [9] and was

developed by Derringer and Suich [10]. The

method finds operating conditions that

simultaneously provide the "most desirable" value

of each fabric response.

This study places customer exigency as the

main goal to reach. In our work, in conjunction

with desirability approach, we have exploited the

tools furnished with neural networks to improve

fabric quality modeling. Neural networks

constitute learning systems for modeling and

optimization that have been increasingly applied

to textile problems during the last 30 years [11]. It

Hajer souid et al ,Int.J.Computer Technology & Applications,Vol 3 (1), 356-364

IJCTA | JAN-FEB 2012 Available [email protected]

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ISSN:2229-6093

mailto:[email protected]



is well known that, neural nets are useful tools for

functional prediction and system modeling where

the physical processes are not understood or are

highly complex. This is generally the case of

fabric quality definition and estimation. Hence,

by combining these tools, we have tried to

evaluate the overall quality of fabrics. A large

data base and a model to predict global fabric

quality from fiber, yarn, weaving parameters and

finishing characteristics were then developed.

2. Materials and methods

An experimental data base of 1180 denim

fabric samples has been elaborated in a Tunisian

integrated factory specialized in producing

finished denim fabric.

Table 1: Summary of statistics for fabric properties

Manufacturing process includes all stages

from yarn to finished fabric. The studied fabric is

100% cotton twill. The characteristics of studied

fabrics and their corresponding test methods are

shown in Table 1. Each sample of the database is

tested 20 times for each property. The difference

between the minimum and maximum value of

each response refers to the variety of fabrics

produced in the factory where we accomplished

the work. The experimental set-up related to yarn

characteristics and resulting fibre-to-yarn

database used for this optimization were

evaluated according to international standards

using Uster tensiorapid 3 and Uster tester 3.

The warp yarn is a ring spun yarn and the weft

yarn is whether an Open-End or a Ring spun yarn.

The data base includes the following yarns types

(Table 2).

Table 2: Fabric yarns types

Warp Weft

Yarn counts

(Nm)

12.5 RS* and 15 RS

10 OE**; 12.5 OE ; 15 OE ; 17 OE; 20 RS;

* RS: Ring Spun yarn; ** OE: Open-End Spun

yarn

The warp and weft properties are respectively

described in Table 3 and Table 4.

Table 3: Warp yarn properties

Yarn property Symbol Instrument Mean Standard deviation

Minimum value

Maximum value

Tenacity (cN/ Tex) RKM Uster tensiorapid 3 17,76 0,21 15,92 18,14

Tenacity evenness (%)

CVRKM Uster tensiorapid 3 6,85 3,17 4,54 7,96

Breaking elongation

(%) E% Uster tensiorapid 3 7,87 0,11 7,28 8,24

Breaking work

(Joule) TR Uster tensiorapid 3 2,83 0,85 1,27 6,58

Regularity (%) U% Uster tester 3 13,23 1,24 10,89 17,33

Number of Thick

places THIK Uster tester 3 350,85 7,24 123,65 463,53

Number of Thin places

THIN Uster tester 3 2,17 1,49 0,54 11,27

Fabric property Test method Mean value

Standard deviation

Minimum value

Maximum value

Warp Breaking strength (kg)

ASTM D5034-90 95,60 7,69 42 128

Weft Breaking

strength (kg) ASTM D5034-90 66,08 8,11 36 94

Warp elongation (%) ASTM D5034-90 44,23 5,28 24,50 63

Weft elongation (%) ASTM D5034-90 29,24 3,50 21 74

Stiffness (kg) ASTM D4032-94 1,38 0,80 0,10 5,80

Warp Tear strength

(10-3

Kg) ASTM D1424-96 7261 8,37 2000 9734

Weft Tear strength (10

-3Kg )

ASTM D1424-96 5775 7,92 3232 8934

Weight (10-3

Kg /m2) LS&C° Method21 416 10 260 480



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Number of Neps BOUT Uster tester 3 21,12 3,60 16,01 44,66

Hairiness PILO Uster tester 3 9,14 0,16 7,65 9,33

Twist (turns/m) TWIST Twistmeter 486 13,79 478 624

Table 4: Weft yarn properties

Yarn property Symbol Instrument Mean Standard

deviation

Minimum

value

Maximum

value

Tenacity (cN/ Tex) RKM Uster tensiorapid 3 15,26 1,91 13,17 19,46

Tenacity evenness

(%) CVRKM Uster tensiorapid 3 8,22 2,06 4,61 12,00

Breaking elongation

(%) E% Uster tensiorapid 3 7,96 0,59 7,26 9,40

Breaking work (Joule)

TR Uster tensiorapid 3 2,30 0,67 1,56 5,20

Regularity (%) U% Uster tester 3 12,16 1,48 9,84 15,37

Number of Thick places

THIK Uster tester 3 59 13,26 23,75 195,49

Number of Thin

places THIN Uster tester 3 3,52 3,66 0,17 15,67

Number of Neps BOUT Uster tester 3 12,85 8,31 0,75 57,67

Hairiness PILO Uster tester 3 7,30 0,73 6,69 9,10

Twist (turns/m) Twist Twistmeter 518 8,99 417 624

To optimize yarn and fabric qualities with

desirability approach, we have followed these

steps:

First, we defined an individual desirability

function for each yarn and fabric responses. We

used Derringer and Suich (1980) individual

desirability function (id ) using the provided

goals and boundaries for each response. The

goal of each response can be one of the three

following choices:

1/ Targeting a response: In this case, the

individual desirability function is assigned as

follow:

iLSTiYoriLITiYif

iiYif

iLSTiYiif

q

iLSTi

iLSTiY

iiYiLITif

p

iLITi

iLITiY

id

0

1

(1)

Where:

iY = predicted value of ith

response

i = target value for ith response

iLIT = lowest acceptable value for ith response

iLST = highest acceptable value for ith response

With p and q determining how important it is

to fit the target value. The exponents of

desirability function of ith response are two

requirement levels to make less or more

importance to the response when it is lower or

higher than the target. In fact, the customer can

be more rigorous when the response is lower

than the target. The shape of the desirability

function between the lower limit (respectively

upper limit) and the target is determined by the

choice of weight.

For 1 qp , the desirability function

increases linearly towards target i (Figure 1);

for p < 1, q < 1, the function is convex, and for

p > 1, q > 1, the function is concave.

Figure 1: Function of desirability to reach a

target value.

In this study, we took 1p and 1q which

means that we have the same requirement if it is

under or upper the target.

2/ Minimizing a response: For this case, the

corresponding individual desirability is as

defined in Equation 2.

p>1 q>1

p<1 q<1

1

0

id

iY iLIT

iLST

ietT arg

p=1 q=1



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iLSTiYif

iiYiLITif

p

iLITi

iLITiY

iLITiYif

id

1

0

iLSTiYif

iLSTiYiif

q

iLSTi

iLSTiY

iLITiYif

id

0

1

(2)

The illustration below shows the shape of

desirability function when the goal is to

minimize the response.

Figure 2: Desirability function to minimize.

A weight q equals to one places equal

emphasis on the target and bounds for a

response. The desirability decreases linearly

toward the upper limit. Whereas, a weight

greater than one places more emphasis on the

target. A response value must be very close to

the target to have a high desirability (Red

curve).

3/ Maximizing a response by using the

following individual desirability.

(3)

When we want to maximize a response, the

illustration of the desirability function is

represented in the following Figure 3:

Secondly, we maximized the overall desirability

wD which constitutes a measure of how the

solution has satisfied the combined goals for all

the responses with respect to the controllable

fabric factors and processing. Thus, for each

sample, we have different individual

desirabilities corresponding to each response

and one global desirability.

Figure 3: Desirability function to maximize.

The overall (composite or global)

desirability w

D is manifested in Equation 4. It

represents the weighted geometric mean of the

individual desirabilities ( id ) of all responses:

w nwnd

wd

wd

wD ...2

21

1 (4)

iww ; iw is the weight of ith

response.

With n denoting the number of responses. For

the warp and weft yarns, the number of

responses is nine for each. For the fabric, we

have eight responses.

In the composite desirability, the weight values

are accorded to put less or more emphasis on a

response. If some responses are more important

than others, we can consider this information

into the optimal solution by setting unequal

importance values. For instance, the customer

can require more importance to Stiffness then

Strength. Here, in this case, we give similar

importance to responses by choosing a weight

value equal to one.

Both, the individual and the composite

desirabilities have a range of zero to one. They

represent an univariate and unitless measure. A

desirability of zero represents a completely

undesirable property level that is expected to

make the product unacceptable. A desirability

value equals to one represents completely

desirable or ideal response value at which a

small increase or decrease will not further

improve the product.

iU iY

q>1

ietT arg

q<1 1

0

id

As response decreases,

The desirability increases

id =1 id =0 1,0id

q=1

p>1

id

1

0 iLIT iY i

p<1

p=1

As response increases,

The desirability increases

0id 1,0id 1id



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Table 5: Warp yarn responses optimization

Table 6: Weft yarn responses optimization

Responses Symbol Objectives Lower limit Target Upper limit

Tenacity (cN/ Tex) RKM Maximize 13,17 15,26 -

Tenacity evenness (%) CVRKM Minimize - 8,22 12,00

Breaking work (Joule) TR Maximize 1,56 2,30 -

Hairiness (cm of fibers/ cm of yarn) PILO Minimize - 7,30 9,10

Breaking elongation (%) E% Minimize - 7,96 9,40

Regularity (%) U% Maximize 9,84 13,16 -

Number of Thick places THIK Minimize - 59 195,49

Number of Thin places THIN Minimize - 3,52 15,67

Number of Neps BOUT Minimize - 12,85 57,67

3. Results and discussion

3.1. Optimizing warp and weft yarns

qualities with desirability approach

The Optimization of the global desirability

D was carried out by using Excel combined

with visual basic software. We set the weft and

warp yarns quality definition respectively in

Table 5 and Table 6.

The factors settings that maximize the yarn

and fabric quality can be obviously modified

according to customer demands. As mentioned

in Equation 2 and Equation 3, when we want to

minimize or maximize a response, we don‟t

need to mention in the algorithm initialization,

the lower limit and the upper limit respectively.

This is represented in Tables 5, 6 and 7 by „-„.

For all yarn samples of the data base, we have

calculated warp and weft individual

desirabilities, corresponding to the responses

objectives mentioned in Tables 5 and 6.

3.2. Optimizing fabric quality with

desirability approach In order to optimize fabric responses, first

we have to mention the objective of each fabric

response and the corresponding ranges.

Generally, the desired objectives of each

response of the fabric depend on customers

necessities.

Also, there is no norm that specifies the

general optimal objectives to reach for a fabric.

In this paper, we have defined fabric quality as

described in Table 7. The algorithm made can

be flexible for other customer objectives and

boundaries.

The steps followed during the program

developing to determine weft and warp yarns

and fabric qualities are described as follow:

- Initialization of warp, weft and fabric weights

( p , q , iw )

- Initialization of warp, weft and fabric

responses:

Targets

Upper limits

Lower limits

- Calculating warp, weft and fabric responses

individual desirabilities

- Calculating warp, weft and fabric global

quality

Responses Symbol Objective Lower limit Target Upper limit

Tenacity (cN/ Tex) RKM Maximize 15,92 17,76 -

Tenacity evenness (%) CVRKM Minimize - 6,85 7,96

Breaking work (Joule) TR Maximize 1,27 2,83 -

Hairiness (cm of fibers/ cm of yarn) PILO Minimize - 9,14 9,33

Breaking elongation (%) E% Minimize - 7,87 8,24

Regularity (%) U% Maximize 10,89 13,23 -

Number of Thick places THIK Minimize - 350,85 463,53

Number of Thin places THIN Minimize - 2,17 11,27

Number of Neps BOUT Minimize - 21,12 44,66



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Table 7: Response optimization of the fabric

Fabric properties Objectives Lower limit Target Upper limit

Warp Breaking strength (kg) Maximize 42 95,60 -

Weft Breaking strength (kg) Maximize 36 66,08 -

Warp elongation (%) Minimize - 44,23 63

Weft elongation (%) Minimize - 29,24 74

Stiffness (kg) Target 0,10 1,38 5,80

Warp Tear strength (10-3

kg) Maximize 2000 7261 -

Weft Tear strength (10-3

kg) Maximize 3232 5775 -

Weight (10-3

kg /m2) Minimize - 416 480

The fabric quality definition previously

mentioned in Table 7 implicated 1180 different

global desirabilities values. The best fabric

global quality has reached 0,95. The

corresponding individual desirability and

predicted value of each response of the fabric

are shown in Table 8.

Table 8: Fabric global desirability

Fabric Response Predicted

Responses

Individual

desirability

Warp Breaking

strength (kg) 89 0,88

Weft Breaking strength (kg)

58

0,73

Warp elongation (%) 44,40 0,99

Weft elongation (%) 29,80 0,99

Stiffness (kg) 1,30 0,94

Warp Tear strength

(10-3

kg) 7104 0,97

Weft tear strength

(10-3

kg) 5184 0,77

Weight ((10-3

kg)/m2) 395 1,00

The overall fabric quality is of 0.95.

According to Harrington standards [9], the

global desirability belongs to the interval [0.8,

1]. According to this scale, the result is

considered to be acceptable and excellent. It

represents an unusual quality or performance

well beyond anything commercially available

[9].

3.3. Prevision of Denim fabric global

quality with Neural Networks In order to predict fabric overall quality

through warp and weft qualities, we applied the

neural networks approach. This tool uses the

optional test data when training for a better

performance of the model [12]. We developed

for this goal a muti-layer perceptron neural

network of one hidden layer. The developed

algorithm is based on the back-propagation

system. The network should have one output

neuron since there is one target to reach. The

output parameter expresses fabric global quality

by D value which includes the physical

parameters described in Table 1.

For the database inputs, we used different

spinning production parameters, which are

related to yarn, ends and picks counts and

finishing (Table 9). All the input variables are

continuous except the finishing. The different

levels of this discreet variable are introduced in

the model as follows:

1= Mercerization

2= Mercerizing then the application of acrylic

resin

3= Pigments dyeing applied by using foaming

process including Gaston system

Table 9: Input and output parameters of the

neural network model

Inputs Symbol Output

Finishing Finishing

Fabric global

quality

D

Yarn properties

Warp

yarn global

quality

GD Warp

Weft yarn

global quality

GD Weft

Warp

yarn

count

Nm warp

Weft yarn count

Nm weft

Construction

parameter

Ends

count Cpte Ch f

Picks

count Cpte Tr f

As the input vector is composed of seven

parameters, the network is set up with an input

layer of seven nodes. The activation function of

the hidden layer is the tangent sigmoid transfer

function. The output is calculated according to

Equation 5:



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1)2exp(1

2)(

xxG (5)

The transfer function of the output layer is

the log sigmoid function. The neural network is

trained by adjusting the connections (weights)

between the nodes by using the Newton

function which has the advantage to provide

faster optimization. We calculated the sum of

the squared differences between the target and

actual output values on the output global

desirability which constitutes error. A value of

error close to zero indicates a better fit. Two

error values were then considered:

trainRMSE : The mean square root error

generated by the training data in Equation 6

[12].

21

1

2),((

N

Nwixgiy

trainRMSE (6)

N : Number which represents 80% of database.

iy : Yarn quality index calculated from the

training database corresponding to the input ix .

),( wixg : Yarn quality index calculated by the

neural network corresponding to the input ix for

a weight value w .

),( wixgiy : The individual error

testRMSE : The mean square root error

generated by the test data in Equation 7:

21

1

2),((

P

Pwixgiy

testRMSE (7)

P : Number of test data places = 236 = 20% of

input-output data pairs were used as the test set.

The second parameter conferring the

reliability of the model is the correlation

coefficient ( R value), obtained by calculating

the regression coefficient of the measured

values with estimated values. When the model

is reliable, this coefficient has to be close to one.

In the experiment, we have selected 80% of

the data base for training and the rest for testing.

The repartition of the ideal proportion between

the test/train examples is until now unknown,

but the proportion of 20/80 is generally

considered as the most convenient [12].

0,00

0,01

0,02

0,03

0,04

0,05

0,06

3 4 5 6 7 8 9

Number of neurons in the hidden layer

RM

SE

trai

n

0,00

0,05

0,10

0,15

0,20

3 4 5 6 7 8 9


RM

SE

test

Figure 4: Time series plot of trainRMSE (a),

testRMSE (b) versus the number of hidden

nodes.

0,00

0,20

0,40

0,60

0,80

1,00

3 4 5 6 7 8 9


R%

Figure 5: Time series plot of correlation

coefficient R against the number of hidden

nodes.

We have tried the back-propagation neural

net with one hidden layer and different hidden

nodes and epochs. We remarked that out of

seven neurons in the hidden layer, the difference

between training and test error(s) increases

which risks having an overfitting (Figure 5).

Besides, the correlation coefficient is the highest

for seven neurons in the hidden layer. Having a

correlation coefficient near to 1 with small and

comparable errors test and train, contributes to a

good performance of the network. Hence, the

appropriate number of hidden layer inducing the

best performance of the neural network is of

seven.

(a)

(b)



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Figure 6: Learning curve of the artificial

neural network model.

As shown in the learning curve in Figure 6,

the right number of epochs reached is 300. The

scattering diagram of the model, represented in

Figure 7, illustrates the network outputs (A)

plotted versus the targets (T) as open circles.

The perfect fit is indicated by the dashed line.

The perfect fit line corresponds to an output

equals to targets (A=T) which constitutes the

bisector. Therefore, for this line, the slope

would be 1, and intercept the axes in zero. The

scattering around the bisector gives an idea of

the quality of the modeling. The prediction is

perfect when all points are aligned on this line.

Here, the fit seems to be good since most places

are aligned on the bisector.

The linear fit calculated by the model has

contributed to the following Equation 8:

0375.005.1 TA (8)

The Equation 9 is represented in the Figure 8

by the solid line. It constitutes the best fit line

generated by the model. As shown, the best fit

line (solid line) is very close to the perfect fit

line (dashed line).

Figure 7: Relationship between actual and

predicted values of the fabric quality index.

4. Conclusion The purpose of this study was to develop a

composite quality index which will closely

depict the perception of the suitable denim

fabric quality as preferred by consumers. As

fabric quality is a multi-criteria phenomenon

that requires the satisfaction of several

properties at the same time, we used a new

adaptive method permitting the combination of

all properties (or quality criteria) in order to

reach optimal denim fabric global quality. The

definition of the overall denim quality can be set

according to production quality criterions

depending on customer requirements. Our

computation has also enabled to find the global

yarn properties and fabric properties that have

lead to reach the highest global desirability. The

global fabric definition can be set according to

each customer requirements by varying the

target, the weight and the tolerance interval of

each property. Other important fabric

parameters related to fabric handle and aspect

can also be included to give more reliable

significance to quality concept.

Our study has demonstrated that the

applications of desirability functions with neural

network can be good tools for assessing more

rigorous fabric quality. The present methods

have been studied for Denim fabric and for

some fabric properties, but it can be generalized

for non Denim fabric while including other

customer requirements simultaneously.

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[2] Roach A.R., “Meeting Customer Needs for

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micromechanical model of the tensile behavior of

woven fabric‟‟. Textile Research Journal, vol. 67,

445–459; 1997 [4] Fun J., Hunter L., “An artificial neural network

model for predicting the properties of worsted

fabrics”, Textile Research Journal, 68 (10): 763-771;

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[5] Taibi E. H., Hammouche A., Kifani A., “Model of

the tensile stress strain behaviour of fabrics”, Textile

Research Journal, 71 (7) 582-586; 2001

[6] Sun F., Seyam A.M., Gupta B. S., “A generalized model for predicting Load- extension properties of

woven fabrics”, Textile Research Journal, 67 (12):

866-874; 1997

[7] Borzone P., Carosio S., and Durante A. “Detecting fabric defects with a neural network using

two kind of optical patterns”, Textile Research

Journal, 72(6), 545-550; 2002



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[8] Fan J., Newton E., et Au R. “Predicting garment

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