Elastic knitted fabrics are gaining popularity for apparel use due to its improved comfort functional properties. This paper presents the modeling of thermal conductivity of knitted fabrics made from pure yarn cotton (cellulose) and viscose (regenerated cellulose) ï¬bers and plated knitted with elasthane (Lycra) fibers using an artificial neural network (ANN). Knitted fabric structure type, yarn count, yarn composition, gauge, elasthane fiber proportion (%), elasthane yarn linear density, fabric thickness, loop length and fabric areal density, were used as inputs to the ANN model. Two types of model are set up by utilizing multilayer feed forward neural networks, which take into account the generality and the specificity of the product families respectively. A virtual leave one out approach dealing with over fitting phenomenon and allowing the selection of the optimal neural network architecture was used. The developed model was able to predict the thermal conductivity of fabrics with very good accuracy. These findings can be used for selecting of optimum raw material and structural parameters of stretch knitted fabrics for a particular end-use.
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KEY WORDS: artificial neural network; virtual leave one out; modeling; stretch knitted fabrics; thermal conductivity.
Knitted fabrics are usually preferred for underwear, casual wear and sportswear because their stretchability and elasticity which makes them comfortable and provided more transpiration than other type of fabrics. Plated elasthane yarns, into knitted fabrics, have been used to enhance these properties.
Thermal conductivity is one of the major comfort properties of fabrics. Apart from thermal comfort to the wearer, thermal conductivity also influences the 'coolness' and 'warmness' to touch.
This property becomes important depending on the season in which the fabric is intended to be used. During the winter season, the fabric with 'warm' feeling will be preferred and vice versa.
Thermal properties of fabrics are influenced by fiber type, yarn properties, fabric structure (Li, 2001). The influence of yarn structure on the thermal properties of fabrics has been reported by researchers such as Ozdil, et al. (2007), Das and Ishtiaque, 2004, Du et al., 2007), Ozcelik, et al. (2007), Nida and Arzu, 2007).
Majumdar et al. (2010) compared the thermal properties of different knitted fabric structures made from cotton, regenerated bamboo and cotton-bamboo blended yarns. It was found that the thermal conductivity of knitted fabrics generally reduces as the proportion of bamboo fiber increases. For the same fiber blend proportion, the thermal conductivity was lower for fabrics made from finer yarns. The thermal conductivity values of interlock fabric were the maximum followed by the rib and plain fabrics.
Stankovic et al. (2008) compared the thermal properties of plain knitted fabrics made from different natural (hemp and cotton) and regenerated cellulosic (viscose) fibres.
They found that heat transfer through the fabrics is highly related to both capillary structure and surface characteristics of yarns (a continuous package of short ï¬bers), as well as air volume distribution within the fabrics.
However, it seems that the conduction by ï¬bers is a dominant heat transfer mode, since the viscose knit exhibited the highest thermal conductivity.
There have been some researches (Gorjanc et al., 2012; Cuden and Elesini, 2010; Tezel and Kavusturan, 2008) focuses on the influence of elastane (Spandex) incorporation on the thermal comfort of various fabrics.
The influence of different fibers of the socks mentioned on the thermal conductivity coefficient of plain knits and plated plane knits with textured polyamide (PA) or elastane (Lycra) wrapped with textured polyamide thread was investigated by Ciukas et al. (2010). It was determined that a higher thermal conductivity coefficient is characteristic for knits with textured polyamide (PA) thread: lower - for knits with Lycra thread and those from pure yarns. The thermal conductivity coefficient marginally increases when the linear density greatly increases; Lycra thread changes the thickness, area density, porosity and thermal conductivity coefficient of knitted samples. They also noted that no linear correlation was found between the thermal conductivity coefficient and area density or thickness when knits from pure yarns plated with Lycra or PA thread were used. This could be explained by the fact that Lycra or textured PA thread change the size and density of the loop.
Chidambaram et al. 2011 studied the thermal comfort properties of bamboo knitted fabrics in relation to loop length and yarn linear density. In general, the thermal conductivity tended to increase with the constituent yarn linear density but decreased with an increase in loop length.
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These studies were applied to estimate cause-effect relationships between fabric parameters and thermal comfort properties through these of statistical methods. But, these methods have unfortunately some limits. One of the most common dilemmas faced in statistical modeling is the non linear relationship of different fabric parameters with thermal comfort properties.
In addition, the majority of previous studies haven't considered the combinational effects of several factors. Without considering the complex interactions of the various factors at the different processing stages, the weight of each factor and their synergistic effect on thermal properties cannot be fully understood.
Hence, this phenomenon depends on many factors and parameters that handicap mathematical modeling. During the last decade, computer simulations by use of numerical methods derived from mathematical models in the form of differential equations have been widely used for predicting results of many phenomena in porous media and engineering fields (Admon et al., 2011; Du et al., 2007; Ganesh and Krishnambal, 2006; Hasan et al., 2011; Layeghi et al., 2010). Numerical techniques help to minimize machine setup times and toolings costs as well as optimize processing parameters to yield desired ï¬nal part speciï¬cations. However, have the following shortcomings: (1) modeling generally requires many simplifying assumptions, thereby leading to a limited accuracy of simulation results; (2) A constitutive equation must be used. Clearly, reliable constitutive equations for adequately describing the nonlinearity that exist between inputs and outputs; (3) Numerical simulations generally require too great a computational effort for online use. In addition, numerical simulations have no ability to handle effects of all inputs parameters at the same time. The artiï¬cial neural network technique has been applied widely to various areas. The advantages of employing neural networks over simulations based on numerical techniques include: (1) no or a minimal number of simplifying assumptions; (2) no need for constitutive equations and thus no need for difï¬cult-to-obtain rheological data; (3) online prediction for process monitoring and control; (4) faster response.
The process by which the ANN model is obtained is called the ANN training. It is an optimization process that involves minimizing a cost function until a specified fit between observed target output, and output predicted by the model, is achieved. There are many ways to formulate the training process and to go down the slopes of the cost function (Bishop, 1995; Cichocki and Unbehauen, 1993), but in order to get the desired result, two fundamental questions must be answered: 1) to what level should the available observed training data be fitted by the predicted output? and 2) of the many models resulting in that fit, how to select the one that will give the best prediction?
Nowadays, several researchers have successfully used "Virtual Leave One Out" approach to select the optimal ANN architecture to predict various fabric properties (Alibi et al., 2012; Babay et al., 2005; Bhattacharjee and Kothari, 2007; Monari and Dreyfus, 2002). All these researchers have obtained high prediction accuracy of the ANN models.
The textile industry lacks an objective approach for determining the level of clothing comfort which takes into account both operating parameters and intrinsic features of yarn and fabric proved a strong motivation to the present paper for using such method (ANN) to develop an optimal model. When studying the effect of each structural parameter on the functional properties selected from the final product specifications, it is quite difficult to produce a large number of samples. In practice, the amount of learning data or learning samples is strongly constrained by the production costs or experiment costs. So it is necessary to construct a model to solve it.
In this investigation, an attempt has been made to develop an ANN-based model to predict the thermal conductivity of knitted fabrics made from pure yarn cotton (cellulose) and viscose (regenerated cellulose) ï¬bers and plated knitted with elasthane (Lycra) fibres according to their material, fabric construction and clothing design. A small-scaled ANN models have been built from a limited with specific architectures adapted to the product diversity before the modeling procedure. Select the optimum model by using the "Leave One Out" approach. Using the developed model, it would be possible to find the optimum combination of raw materials and other parameters to achieve a targeted value of thermal conductivity.
MATERIAL AND METHOD
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The focus of this research was conducted on pure cotton, pure viscose, viscose/Lycra and cotton/LycraÂ® plated knitted constructions. We produced a series of 340 knitted fabrics commonly used in the clothing industry by using different industrial circular knitting machines (single jersey, double jersey, interlock; tubular and large-diameter; Diameter = 16, 34 inch, gauge = 18 to 28). Ground yarn was a 100% combed cotton (1) and 100% viscose yarn (2) (Nm=28 to 80) and plating yarn was a LycraÂ® monofilament (22, 33 and 44 dtex) plated at half feeder. The fabric samples were comprised of nine different knitted structures, single jersey (1), single lacoste (2), double lacoste (3), polo pique (4), 1/1 rib (5), 2/2 rib (6), interlock (7), visible molleton (8) and invisible molleton (9). The fabrics samples were conditioned in the testing laboratory under standard atmospheric conditions of 20 Â± 2Â°C and 65 Â± 2% relative humidity after a minimum period of 24 hours conditioning in an NF ISO17025 certified laboratory. In this study, the tests carried out were concerning the determination of these parameters according to the French national organization for standardization (AFNOR). Table 1 shows the maximum, minimum, average and standard deviation of knit fabric features used under study.
The functional parameter, thermal conductivity of these samples, is obtained using the apparatus of adiathermic property (Fayala et al., 2008) illustrated in Fig. 1. This property is calculated according to Eq. 1:
is the radius of heating resistance (m); is the sample thickness added to radius of heating resistance (m);
is the area through which the heat is conducted (m2);
is the heating flow through the sample (W/m2);
is the temperature of leather (external surface of the heating resistance) (K);
is the temperature of external surface of the sample (K).
Here the heating flow through the sample is
is the electric tension applied to resistance and
is the resistance of heating element.
Modeling with Artificial Neural Networks: In this section, we use ANNs for modeling the relationship between the structural parameters and the elastics properties of knitting fabrics. Different technologies are used to manufacture knitting fabrics. In this case, the structure of materials varies with applied technology and the corresponding knitting fabrics are then classified into a number of families each corresponding to one type of structure. Consequently, all the structural parameters are divided into two groups. One group includes public structural parameters available for all the families of products and the other group includes special structural parameters available for each specific family. Accordingly, two neural network models are built. The general model (Fig. 2a) takes all the public structural parameters as its input variables. This general model can be used by all the families of products. For each specific family, a special model is developed (Fig. 2b). It takes both the public and the special structural parameters of this family as its input variables.
In order to solve the problems related to the lack of available learning data or samples, small scaled ANN models are built (Huang and Moraga, 2004; Raudys and Jain, 1991; Vroman et al., 2008; Yuan and Fine, 1998).
In the general model, the Levenberg-Maquardt fast learning procedure, based on a second order error back propagation algorithm, is then used for determining the parameters of the neural network from the public learning data sets.
In the special model of each family, the weights and biases connecting the public inputs to the hidden layer neurons, as well as those connecting the hidden layer to the output layer, are kept as the same values as in the general model. Only the weights connecting the special input neurons to the hidden layer neurons are adjusted using the error back propagation algorithm.
Selecting the optimal model architecture: The fitted model is expected not only to recall the observed data with the required accuracy but also to produce acceptable predictions for unseen (test) data drawn from the same population as the observed (training) data. Such a model is said to generalize (interpolate) well within the data range.
Model selection was performed essentially by estimating the generalization ability of the models trained as described, using the "leave-one-out score":
where is the prediction error on the example when the latter has been withdrawn from the training set and the model has been trained with all other examples. The leave-one-out score is known to be an unbiased estimate of the generalization error of the model. Since the computation of the leave-one-out score is computer-intensive, approximations of the leave-one-out errors 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 architecture was chosen by using a selection methodology (Alibi et al., 2012; Golub and Van Loan, 1996; Monari and Dreyfus, 2002; Vapnik, 1999).
RESULTS AND DISCUSSION
The network architecture used a three layered feed-forward network with sigmoid hidden-unit activity and a single linear output unit.
There are six knitting fabrics families different in the formation (simple or complex structure) and the knitting technologies (simple and double needleÂ machine or interlock machine).
The 340 measurements were randomly divided into a training database of 244 values for training and model selection, and a test database of 96 values for the final assessment of the generalization performance of the model. Table 2 present the statistical values of inputs and output parameters of training and test set fabrics.
A general model is built using a neural network for all the kniting samples. It characterizes the relationship between the structural parameters and the corresponding functional property. A special model is built for the family of knitting materials produced using a specific knitting technology (Exp: interlock machine). Its architecture and parameters are built based on the corresponding general model. For example, the Interlock Loop Length is added to the set of the input variables of the general model to build the special model corresponding to interlock knitting family. Figure 3 shows the special model built for predicting the functional properties () with eight public parameters (Knitted Structure's, Cotton Yarns Counts, Gauge, Lycra Proportion, Lycra Yarn Count, Lycra consumption, Weight per Unit Area and Thickness) as input variables. The special structural parameter is then added to the set of these eight input variables.
Optimum neural networks architecture: Models of increasing complexity (i.e. increasing number of hidden neurons) were trained, and the virtual leave-one-out score of each model was computed. The root mean square error () and coefficient of correlation () on the training set were also computed; those quantities are reported in Table 3. As expected for the feed-forward model, the leave-one-out score decreases as the number of hidden neurons increases and starts increasing when the number of parameters is large enough for over-fitting to occur (number of hidden neurons > 2). This is in contrast to the behavior of the on the training set, which decreases as the number of hidden neurons increases. For our case (Table 2), the generalization error does not increase significantly when the number of hidden neurons exceeds the eight, in the investigated range. In order to minimize the number of parameters, eight hidden neurons (HN) were selected. The final optimized architectures of neural network are shown in Fig. 3, corresponding to 81 parameters. The experimental versus predicted values of training dataset is shown in Fig. 4.
To test the generalization performance of the optimal trained network, validating processes was applied using the test database (Table 2). The main quality indicator of a neural network is its generalization ability, its ability to predict accurately the output of unseen data. The experimental versus predicted values of test dataset is shown in Fig. 5, as it can be observed, the predictability of ANN fits very well.
The root mean square error () and coefficient of correlation () on the test set for the feed-forward neural network were computed (Table 4). Neural networks provide quite satisfactory predictions for functional properties () from a global point of view: is larger than 0.9 while is lower than 0.003 (W/m.k).
Mean absolute relative errors were used to evaluate the performance of the proposed ANN in prediction technique. These levels of error (4%) are satisfactory and smaller than errors that normally arise due to experimental variation and instrumentation accuracy.
Prediction assessment of the product functional properties: Table 5 gives the details of the experimental results on the functional properties () and the corresponding predicted results obtained from the general models and the special models. Figure 6 compares the predicted values of thermal conductivity obtained from the general and the special models and the real physical measures, respectively.
The results demonstrated good agreement between the experimental and predicted values from special models (>0.9).
From these experimental results, we can see that the special models give lower prediction errors (averaged error: 4%) than the general models (averaged error: 9%). This observation can be explained as follows:
The general model makes use of samples from several families which differ from each other in many aspects while the special model only uses samples from the same family. The specificity of each family cannot be taken into account in the general model.
The special model is built based on the same structure as the general model. Only the weights connecting the specific input to hidden neurons are introduced. So, it takes into account both the specificity of each product family and the generality of all families.
Typical plots of the experimental and ANN predicted values of selected product are shown in Fig. (7-12). Whatever the knitted structure's the predictability of ANN fits very well (Fig.7). At the same time, the model accurately predicted the expected thermal conductivity at high and lower values. While for some materials (i.e. cotton, viscose) the predicted values of thermal conductivity closely matched that of experimental values (Fig. 8). The ANN model was able to predict thermal conductivity values with acceptable accuracy both forÂ small and largeÂ valueÂ of gauge, Yarn Count, Lycra Proportion and Lycra Yarn Count (Fig. 9-12).
In this paper, a support system is proposed for modeling the thermal conductivity of knitted fabrics made from pure yarn cotton (cellulose) and viscose (regenerated cellulose) ï¬bers and plated knitted with elasthane (Lycra) fibers using special models of ANN and virtual leave one out approach dealing with over fitting phenomenon and allowing the selection of the optimal neural network architecture. The prediction accuracy was very good for the training as well as the testing dataset. The mean absolute relative error of prediction was lower than 5% and the correlation coefficient was higher than 0.95 for both the datasets. Before the actual manufacturing of fabrics, the fabric engineer can feed a plausible combination of input parameters into the developed ANN model and predict the expected thermal conductivity value of the stretch knitted fabrics. If the predicted value does not match with the target value of thermal conductivity, then the fabric engineer can modify the values of the input parameters, and reach closer to the target value. Thus, the desired thermal conductivity of the fabric can be attained more systematically, eliminating the traditional hit-and-trial approach.