International Journal of Scientific & Engineering Research, Volume 5, Issue 7, July-2014 913
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Fabric Drape Prediction Using Artificial
Neural Networks and Finite Element Method
Hassen Hedfi1, Adel Ghith2 and Hédi BelHadjSalah1
1University of Monastir, National Engineering School of Monastir, Mechanical Engineering Laboratory, Tunisia
2University of Monastir, National Engineering School of Monastir, Thermal and Energetic Systems Studies Laboratory, Tunisia
Abstract— In this paper the mechanical behavior of woven materials is investigated in order to study and predict their dynamic draping. This model can simulate fabric deformation, taking into account its physical and mechanical properties. Once the model is tested and validated, an artificial neural network designed to train fabric drape is coupled with the finite element model to predict the drape behavior of various fabrics. The designed artificial neural network predicts physical and mechanical properties of the fabric from its technical parameters (design parameters). The predicted properties are used as inputs for finite element model that simulates and calculates parameters related to the fabric drape. The process is repeated until the difference between the actual drape and the simulated one becomes smaller than a limit value.
Index Terms— Artificial Neural Network, fabric drape, Finite Element Method, prediction and optimization
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FOR the past three decades, textile fabrics have not only the traditional role of clothing or home furnishings, but they become more and more genuine support for artistic creation and technological innovation [1]. Therefore, to satisfy the consumers has become a task increasingly dif- ficult to achieve. As a result, the adoption of new meth- odology for the design and manufacture of clothing has become a key requirement [2]. As for example, Tokumaru et al. [3] proposed a system named “Virtual Stylist”, which aims to help users find out their favorite clothes, which might fit them well. The system is composed of 3 parts as follows, (i) searching clothes in consideration of their color scheme harmonies and image sensations, (ii) adopting rules for evaluating color scheme image sensa- tions to a specific user’s feeling of color images, (iii) virtu- al fitting system. Guerlain and Durand [4] analysed sev- eral methods developed, evaluated and used as part of a
3D electronic tailor especially adapted to the clothing in-
dustry. Hu, et al. [5] proposed an immune-inspired interactive co-evolutionary CAD system. They gave the functionality model, modular architecture and data flow of the system. They also proposed the flow of co-design in the system. As a case demonstration, the authors studied a design sample of a leisure shirt. The experimental
studies show that this approach has promising
performance and appealing effects.
Moreover, given the constant development of comput- er‘s tools and e-commerce, it became advantageous to develop virtual platforms for interactive design of clothes, real-time visualization and virtual Try-On [6].
Lau et al. [9] used fuzzy expert system with gradient
descent optimization for prediction of fabric specimens in fashion product development. Unlike traditional methods which used fabric mechanical properties to predict fabric specimens, this fuzzy method accepts fabric hand descriptors which are more closely related to the sensory judgments made by individuals during fabric selection. The prediction accuracy is over eighty percent. Hadjianfar and Semnani [10] studied the textile fabrics’ luster. In their method, different fabric samples are classi- fied in six different classes based on the luster determined by judgment of ten different inspectors. The luster index, obtained by the use of image processing, is then classified in six fuzzy classes based on fuzzy logic theory. Results prove that fuzzy classification is confirmed by viewers’ judgments. More details on the use of intelligent methods in the textiles field may be found in [11], [12], [13].
In this context, several research papers are interested in
modeling and simulation of textile fabrics in order to pre- dict and assess their drape.
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Fabric drape is among the most important properties re- lated to the aesthetics of clothing and home furnishings. This exhibits comfort and satisfaction sensations among consumers and increases the marketing of textile goods. Textile fabric drape means the manner in which a fabric is deformed under the effect of its own weight when at- tached by one of its parts. The drape is generally charac- terized by the formation of folds with curves having vari- ous shapes and different geometric dimensions.
Stylios et al. [14] investigated the fabric drapabality. In
this study, the drape attributes of fabrics (drape coeffi- cient, number, depth and evenness of folds) were meas- ured. The relationship between these measurements and the subjective evaluation of the fabric drape were mod- eled for each end-use on a neural network using back propagation, which can correctly predict the grades of
90% of the samples. The relationship between the drape
attributes and fabric bending, shear and weight was also modeled using neural networks. It was found that using the natural logarithm of the material property divided first by the weight of the fabric produced the most predic- tive model.
Lam et al. [15] used Artificial Neural Networks (ANN) to predict the Drape Coefficient (DC) and Circularity (CIR) of many different kinds of fabrics. Two ANN models were used: the Multilayer Perceptron using Backpropaga- tion (BP) and the Radial Basis Function (RBF). The BP method was found to be more efficient than the RBF one but the RBF method was the fastest when it came to train- ing. Comparisons of the two models as well as compari- sons of the same models using different parameters are presented. The authors found that prediction for CIR was less accurate than for DC for both neural network archi- tectures.
Behera and Mishra [16] proposed an engineered approach to fabric development in which a radial basis function network is trained with worsted fabric constructional parameters to predict functional and aesthetic properties of fabrics. An objective method of fabric appearance eval- uation with the help of digital image processing is intro- duced. The prediction of fabric properties by the network with changing basic fibre characteristics and fabric con- structional parameters is found to have good correlation with the experimental values of fabric functional and aes- thetic properties.
Jedda et al. [17] investigated the relationship between the
fabric drape coefficient measured using drape meter and
mechanical properties obtained by experimental device: the Fabric Assurance by Simple Testing system (FAST). Different types of woven fabrics were tested. Three re- gression models are proposed using the multiple linear regressions. The regression results were analyzed and compared with those obtained from a neural model used to predict fabric drape. More accuracy is obtained with neural network model.
Pattanayak et al. [18] used an instrument based on a digi-
tal image processing technique to measure drape parame- ters and the Kawabata evaluation system (KES-F) to as- sess the low stress mechanical properties. They, then, predicted the drape parameters using multiple regres- sions method and feed-forward back-propagation neural network technique. Simple equations are derived using regressions method to predict the five shape parameters of drape profile (drape coefficient, drape distance ratio, fold depth index, amplitude and number of nodes) from the low stress mechanical properties. The authors claimed that bending, shear and aerial density affect the drape parameters most whereas the tensile and compression have little effect on the drape parameters.
In this paper, we propose to use the technical and physi- cal parameters to predict mechanical properties of textile fabric by means of Artifical Neural Network. Then, these properties are used as inputs for Fnite Element Model. The parameters of draped fabrics are then obtained by numerical simulation. The artificial neural network is tuned by comparison between the actual and simulated drape. In this way, we will not need to determine the me- chanical properties of textile fabrics experimentally.
In the next section, we briefly develop the finite element modeling of textile fabrics. Then we present the neural networks used for learning the fabric drape and the ANN-FEM coupling. Results and discussions will be the subject of the last paragraph.
A fabric is obtained by intercrossing two sets of yarn: the warp and weft yarn, according to a weave pattern. Sever- al parameters would be set to obtain a fabric with me- chanical, physical and aesthetic properties appropriate to the end-use of these fabrics.
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The characterization of textile fabrics includes:
It is the manner in which the warp and weft yarns are intercrossed to form a strong textile surface: the woven fabric. Several types of weave patterns are used for weav- ing. The most common weave patterns, also known as basic, are plain (Fig. 1), twill (Fig. 2) and satin (Fig. 3).
and for weft density: picks/cm, picks/10cm, or picks/inch. Fabric density indicates the tightness of the fabric for given yarn count.
The warp count is a number indicating the mass per unit length, or the length per unit mass of warp yarn. It indi- cates the fineness of warp yarn. The unit used can be the Nm - Metric system, in this case warp count is the No of
1000 meters length per kg of warp yarn.
The weft count is a number indicating the mass per unit length, or the length per unit mass of weft yarn. It indi- cates the fineness of weft yarn. The unit used can be the Nm - Metric system, in this case weft count is the No of
1000 meters length per kg of weft yarn.
a. Mass density ρ (g m-2): The measurement is per-
formed as follows: we cut a square part of the fabric of known area and we weigh the sample using a preci- sion balance. The test is repeated 5 times and an aver- age value is calculated.
b. Thickness of the fabric is denoted δ (mm)
a. The Young's moduli (MPa) in the warp (Ewp ), weft
(Wwt ) and bias (Wbias ) directions
b. The Poisson's ratios in the warp (υwp ) and weft
(υwt ) directions
4
H = −
1 − υ
wt −
−1
1 − υwp 
(1)
E E E
bias wp wt
d. The flexural moduli (µNm) in the directions:
warp (Rfwp ) and weft (Rfwt )
b. Drape coefficient DC:
( ) rm
2 − r 2
DC %
= × 100
r 2 − r 2
(2)
c. Drape Distance Ratio
Fabric density includes warp density (WpD) and weft
2
DDR (%) = ru − r
× 100
(3)
density (WtD). Each is a measure of number of yarns per
unit of length of the fabric in due direction. The units for warp density are: ends/cm, ends/10cm, or ends/inch;
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r 2 − r 2
d. Fold Depth Index
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FD( (%) = rmax − rmin × 100
(4)
n = ∂r × ∂r
∂r × ∂r
(14)
ru − rs
∂a ∂a
∂a ∂a
e. Amplitude to Radius
1 2 1 2
f ext : The external forces such as gravitational
AR = rmax − rmin
(5)
2
Where ru : The radius of undraped fabric, rs
the radius of
force f g = ρ g , g gravitational acceleration.
Equation 8 is solved using the finite element method. De- tails of the resolution algorithm and numerical results are
the fabric supporting-disc, rm the average of 16 measured
rays between disc centre and projected profile:
reported in [19].
1 16
rm = ∑ri
16 i =1
(6)
( ) ( )
rmax = max ri
, rmin = min ri
(7)
The equation of motion of the surface of the textile fabric can be formulated as follows: [19]
2
ρ ∂ r + µ ∂r + f int = f ext
(8)
∂t 2 ∂t
Where,
ρ : The surface density (kg m-2)
µ : The damping density (Kg m-2 s-1)
r : The vector of instantaneous position of a point P be-
longing on the fabric surface. We have =
, a ,t ) ,
r r a1 2
(a , a ) ∈ Ω2 denote the parametric variables, defined on parametric domain Ω2 ⊂ R2 , and t indicate the time.
f int : The internal elastic forces resulting of the defor-
mation occurred in the fabric during motion or when in- teracting with other solid object or with fluid flow.
Fig. 4. Fabric drape characterization (a) drape-meter, (b) circu- lar fabric sample draped over the support disc of drape-meter, (c) a schematic representation of the drape measurement, and (d) projected drape profile in which are presented the drape geometric drape attribute: Node, length, width, and depth
2 ∂
∂ 2
∂2
∂2
int r r
f = − ∑
∂a Sαβ ⋅
+
∂a
∂a ∂a
Cαβ ⋅
∂a ∂a
(9)
α , β =1 α
s t
α α , β =1
0
α β
b t
α β
0
Where, Sαβ = wαβ ( gαβ − gαβ ) and Cαβ = wαβ (bαβ − bαβ ) . These
coefficients describe material properties: ws αβ , for stretch and shear behaviour, and wbαβ , for bending.
Artificial Neural Networks (ANN) is used to predict me- chanical of textile fabrics from technical and physical pa- rameters. The learning database consists of a wide variety
ws = E
, ws
= H , ws
= H , ws
= E (10)
11 wp
12 21 22 wt
of textile fabrics. These fabrics are characterized in terms
wb = Rf
, wb
= wb
= 0, wb
= Rf (11)
of technical parameters (or parameters of construction),
11 wp
12 21 22 wt
mechanical, physical properties and in terms of drape
To describe fabric deformations, two tensors of surface
are used: euclidian tensor G and curvature tensor B.
properties (or drape attributes).
G = (
gαβ )
, gαβ
= ∂r ⋅ ∂r ;
(12)
All ANN inputs and outputs are normalized before train-
1≤α , β ≤ 2
∂a ∂a
ing step using following formula:
α β
2 t − t
B = b
1≤α , β ≤ 2
, bαβ
= ∂ r ⋅ n
∂aα ∂aβ
(13)
tn = i i
i
(15)
Where n denote the unit surface normal:
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Where, t n the normalized values of parameter i, t the
i i
measured values of parameter i, t its average, and σ its
The ANN model is coupled with the model using the fi-
nite element method (FEM-Model) developed for the
standard deviation. After normalization, each parameter
has an average of 0 and a standard deviation equal to 1. Experimental database is a divided randomly into three subsets:
1. Training subset containing 70% of samples used for
gradient computing and for ANN weights and biases updating.
2. Validation subset containing 15% of samples
3. Test subset containing 15% of samples, used for ANN
generalization
simulation of fabric drapemeter (Fig. 4). This would in- crease the efficiency of ANN-model and eliminate if not reduce the use of experimental characterization of me- chanical properties of textile fabrics.
Fig. 5. Architecture of Artificial Neural Networks (ANN) is used to predict mechanical of textile fabrics from technical and physical parameters.
The parameters of the neural network to be optimized are:
Fig. 6. Coupling ANN-Model for mechanical parameters prediction with Finite Element Model developed for simulat- ing drapemeter.
the number of neurons Nn
the number of hidden layer HL
the number of iterations Ni
The neural network architecture is shown in Figure. 5. This network is a feed-forward ANN trained with error back-propagation algorithm. The ANN weights and bias- es updating is carried out using the Levenberg- Marquardt optimization algorithm. The ANN optimality criteria are:
1. The correlation coefficient (R) between the predicted and measured values for each output.
2. The mean squares error (mse):
To validate the model, we simulated the tensile tests on several types of fabrics of different weaves (plain, twill and satin) but identical composition (100% cotton).
The tensile test is carried out according to the frensh standard NFG07-119, also known as the simplified meth- od. The displacement of the clamps is at constant speed (100 mm. mn-1).
In our study, the Young's modulus is the slope of the lin-
ear part of the stress-strain curve (for elongation values of
N 2
mse = ∑(ti − pi )
N i =1
Where: N is the number of samples,
(16)
ti the target value,
10% to 40%).
The Young's modulus is a measure of the stiffness of the material to stretch/compression deformation.
The results show a great similarity between the experi-
and
pi the predicted value.
mental tests and the simulated ones. Indeed, this similari-
The optimization of the neurons and hidden layers num-
bers is done in an incremental way using two algorithms developed in [20].
ty is even more important that the stress-strain curve is linear (strain less than 0.3).
For this reason, the Young's moduli obtained by the simu-
lations are very similar to those found experimentally.
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The results of this investigation are included in Figures 7 (twill fabric), 8 (satin fabric) and 9 (plain fabric).
TABLE 1
COMPARAISON BETW EEN EXPERIMENTAL AND SIMULATED RESULTS FOR YOUNG’S MODULI DETERMINATION
The values of experimental and numerical Young's modu-
lus are reported in Table 1.
Once the finite element model is validated, it is used to simulate the drape test and for the prediction of fabric drape attributes.
Fig. 7. Experimental and simulated traction test carried out on a twill fabric. This test is used for determing Young's moduli in warp, weft and bias directions
Experimental (MPa) Simulated (MPa)
E wp E wt Ebias E wp E wt Ebias
Twill 13.07 1.04 1.9 13.78 1.13 2.7
Satin 239.9 81.89 214 264.8 50 235
Plain 10 19.8 11.72 11.24 20.2 11.76
Fig. 9. Experimental and simulated traction test carried out on a plain fabric. This test is used for determing Young's moduli in warp, weft and bias directions
Fig. 8. Experimental and simulated traction test carried out on a satin fabric. This test is used for determing Young's moduli in warp, weft and bias directions
The ANN model is used to predict the mechanical prop- erties of textile fabrics based on their technical parameters and physical properties. We obtained the following re- sults:
and Rfwt )and the bias Young’s moduli (Ebias )
2. A lower capacity for predicting the Young's modulus (Ewp and Ewt ) and Poisson's ratios (υwp and υwt ) in warp and weft directions.
Figures 10 and 11 show an example of results obtained for
flexural moduli (Rfwp ) and warp Young moduli (Ewp )
Table 2 shows an example of results obtained on a plain fabric. The coefficient Error represents the error between the actual values of mechanical properties and those pre- dicted by the neural network without ANN-FEM cou- pling. R denotes the correlation coefficient between the val- ues predicted by theANN on the test set.
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tion of mechanical parameters of fabric from technical and physical parameters and improves the predictability of the parameters related to the stretch behaviour: Ewp , Ewt , υwp , and υwt by simulating the drapemeter test.
The algorithm is executed until the error between meas-
ured drape attributes and those found by the simulation
becomes less than a limit value ε = 10−2 .
Error ( DA) = Predicted DA-Actual DA ×100
Actual DA
Where, DA=DC, NN, DDR, ARR or FDI
(17)
The results obtained show the efficiency of coupling be- tween the ANN model and FEM-medel. Indeed, this cou- pling can increase the size of the training database by adding, new mechanical parameters obtained from the simulation based on the FEM model.
Figure 12 shows the evolution of the error on the predic- tion based on iterations of the ANN-FEM model. The number of iterations needed to improve the predictability varies from one parameter to another.
Fig. 10. Regressions between warp flexural moduli (Rfwp) and technical and physical properties using optimized ANN (Noro- ne-number=35, Hidden-layer=2, and Iterations-Number=30)
Fig. 12. Improving mechanical properties prediction from technical and physical parameters using ANN-FEM coupled model
Fig. 11. Regressions between warp Young moduli (Ewp) and technical and physical properties using optimized ANN (Noro- ne-number=35, Hidden-layer=2, and Iterations-Number=30)
ANN-FEM coupling is performed using the algorithm shown in Figure 6. This algorithm allows the identifica-
TABLE 2
MECHANICAL PROPERTIES PREDECTIBILITY USING ANN- MODEL
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Table 3 shows an example of results obtained on a plain fabric. The coefficient Error represents the error between the actual values of mechanical properties and those pre- dicted by the neural network using ANN-FEM coupling. R denotes the correlation coefficient between the values predicted by the ANN on the test set.
TABLE 3
IMPROVING MECHANICAL PROPERTIES PREDECTIBILITY US- ING ANN-FEM COUPLED MODEL
Figure 13 and 14 show the results of applying our method to improve the predictability of the parameters Ewp and Rfwp by coupling ANN-FEM models.
Fig. 14. Regressions between warp Young moduli (Ewp) and technical and physical properties using coupled ANN-FEM Model (Norone-number=35, Hidden-layer=2, and Iterations- Number=30)
Fig. 13. Regressions between warp Young moduli (Rfwp) and technical and physical properties using coupled ANN-FEM Model (Norone-number=35, Hidden-layer=2, and Iterations- Number=30)
In this paper, the objective is to predict with great effi- ciency the mechanical properties of textile fabrics from their technical parameters (warp and weft yarn counts and warp and weft yarn densities), and from two easily measurable physical properties (thickness and mass den- sity). The prediction was based on the use of artificial neural networks.
The problem encountered when using the ANN model is the low predictability of properties related to the tensile- compression behavior of fabric mainlyYoung's modulus and Poisson's ratios in warp and weft directions.
The idea is toimprove the predictability of these parame- ters by increasing the training database of neural network by adding data obtained from the simulated tests.
Indeed, a finite element model simulating the dynamic behavior of textile fabrics is developed and validated. This model is then used to simulate the drape meter.
The originality of this work is:
ize textile fabrics
This approach can be improved by adding fuzzy logic rules to decide about the acceptance and the incorpora- tion of the identified parameters in the training database.
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