In the prediction of tensile properties of cotton-covered spandex yarn, the ANN model shows considerable lower mean square error (MSE) than the multiple regression analysis in both testing and training data, reveal M H Elshakankery, Mona M Salem and M M Mourad.

In 1958, Dupont had introduced elastic fibres with different trade names such as Spandex, LycraR, GlospanR, DorlastanR, LinelR, etc. These fibres, are made of long chain polymer containing at least 85% segment polyurethane^[1]. Spandex fibres are synthetic fibres that are built up of linear macromolecules. Spandex fibres have superior stretch and elastic recovery ability, that is why clothes containing spandex fibres fit well and are comfortable. At least 85% of their composition by weight is segmented polyurethane. Spandex can be stretched by a factor of 4 to 8.

Spandex is used exclusively in conjunction with other textile fibres, to give moderate stretch since high extensibility is not desired with most textiles and to protect the spandex from mechanical damage^[1,2]. Elastic yarns could be produced as core or composite yarns. It could be known as multi-component yarns in which one component, ie, the core material stays nearly at the center of the yarn while the others cover it. Multi-component yarns, could be divided in to two groups: soft yarn with elastic core part and hard yarns with non-elastic core yarn^[3].

The application of core-spun yarns in the textiles industries is limited to some extent. These yarns are used to improve the physical and mechanical properties of fabrics such as breaking strength, abrasion resistance …etc^[4]. Composite or core yarns containing spandex are frequently required by textile fabric producers for manufacturing elastic textile products and accessories. Important market segments for elastic yarns are hosiery, swimwear, sportswear, underwear, lace, as well as fashionable clothing^[5].

There are several methods for producing elastic yarns, that are, core-spun on a modified ring frame, hollow spindle technique, air entangling, friction spinning, and siro spinning^[6,7]. Researches about core-spun yarns containing spandex have are limited research. Babaarslan described a mechanism for producing polyester/viscose core-spun yarn containing spandex using a modified ring spinning frame[3]. Min, et al showed the properties of wool/spandex core spun yarn produced on modified woollen spinning frame^[8].

Su et al investigated the effects of draw ratio and feed-in angle of the spandex on the core-spun yarns' structure and performance at the modified ring spinning frame. They concluded that a higher feed-in angle provides a better cover effect, and a draw ratio of 3.5 yields better dynamic elastic recovery^[9]. Babaarslan showed that spandex positioning has a direct effect on the properties, structure and performance of core-spun yarns produced on a modified ring spinning frame^[3]. Weber and Sawhney described a mechanism for producing core-spun yarns on ring spinning frame^[6,10]. Zhang reported a method of making cover spun yarns on an open-end rotor spinning frame^[11].

In general, modeling and predicting of yarn strength based on fibre properties and process parameters have been considered by many researchers. There are essentially five modeling tools for predicting yarn strength, namely the mathematical model, the statistical model, the empirical model, the computer simulation model and the neural network model. Frydrych reported that the mathematical models have their basis in applied physics and derived from first principles to provide a better understanding of the complex interrelationships of different parameters that determine yarn properties^[12].

Hearle et al have reported fundamental theories for short fibre yarns^[13]. Subramanian, Zurek et al, Rajamanickam et al and Morris et al have made significant contributions in this filed. They are derived from the fundamental laws of science can be used to explain the effects of various parameters on yarn breaking load. These models are based on certain idealised assumptions^{[14,15,16,17]}. Pan in a series of papers has shown how the entire stress-strain curve of yarn can be predicted from fibre properties^[18] . Bogdan and Subramanian et al have been established an empirical relationship between fibre properties and yarn strength^[19,20].

Very little work has been done in the area of tensile properties of cotton-covered spandex. In this study, the capability of artificial neural networks and multiple regression methods for modeling the tensile at break of cotton-covered spandex yarns based on process parameters are investigated.

Artificial Neural Networks

A neural network is a parallel processing architecture consisting of a large number of interconnected processors, called neurons, organised in layers. A neuron node is the basic processing unit that has an activation function. Neuron modes are arranged in a layered structure. The Neuron modes in consecutive layers are fully connected by connection weights. The first layer is called the input layer and the second and third are called hidden and output layers, respectively. A connection weight has a weighting value for the node connection weights are important because their value contain knowledge and determine the behaviour of the network.

A neural network is usually trained so that a particular input leads to a specific output. The process of training is adjusting these weight values and descending down the error surface. Among the various kinds of algorithms for training neural network, back propagation is the most widely used one. This algorithm was detailed by Patterson^[21] and Schalkoff^[22]. After a set of inputs has been fed through the network, the difference between true or desired output and computed output represent an error. Sum of squared errors is direct measure of performance of the network in mapping inputs to desired outputs.

Experimental

To study the effect of fibre properties and process parameters such as HVI fibre properties, count of spandex (see Table 2 core part properties), spandex pretension while feeding to front roller of ring spinning machine, count of sheath part and twist factor of yarn. The linear density of spandex is investigated by using two counts at one level of pretension 0.5 gram/tex. Also, the effect of linear density of sheath part is investigated through using three counts 20, 30 and 40 Ne. Each yarn is spun at three different of twist factors 3.2, 3.6, and 4.

Table 1: HVI cotton fibres properties

Table 2: Core part properties

To evaluate the interaction among the parameters, full factorial design is used (A total of 54 samples were spun). All of samples were spun on the same spinning position and condition to minimize the variation among the samples. For measuring the yarn tensile properties, a Tensorapied Tensile Tester was used (according to ASTM 2256 - 97). Thirty measurements were made on each sample.

Multiple regression analysis

Using particular input and output variable, a stepwise multiple regression analysis was used to predict the core yarn tensile properties. The analysis was carried out using MINITAB statistical software. The stepwise regression technique insert or remove variables from a regression model according to the statistical inclusion criterion (5% level of significance) until a fitting regression equation is reached.

ANN design

Neural network design is a complex process because there are important decisions are required to establish a suitable and stable network. In developing the neural network model, various network structures were tried with one hidden layer. It has been shown that multi-layer feed-forward with hidden layers is able to model any complex liner function provided there is a sufficient hidden neurons number available^[23].

Therefore, one of the primary aspects of the neural network training process is the selection of the best possible number of hidden neurons. A network with too few hidden neurons would be incapable of variance between complex patterns, leading to only a linear estimate of the actual trend. While, if networks have too many hidden neurons, they will follow the noise in the data, leading to poor generalisation for untrained data. To establish the optimal number of neurons required in the hidden layer, an experimental process was conducted by steadily varying the number of neurons. The hyperbolic tangent sigmoid transfer function was assigned as the activation function in the hidden layer and the linear function was used in the output layer.

For predicting the tensile properties of cotton covered spandex core yarn, neural network models were designed had eleven input units (HVI fibre properties and yarn specification) and two output units, as neurons. The number of hidden layers is usually adjusted by trail and error. Studies by various researchers have shown that the second hidden layer can improve the performance of the network if there is a complex relationship between input and output. In either set or cases, the data sets were normalised between limits of -1 and +1 with the average value set to zero. The normalised variable X_inorm is represented as follows:

Where X_i is an input or output variable, X_i,avg is the average value of the variable over the data set, X_i,max is the maximum value of the variable, X_i,min is the minimum value of the variable and R_i,max is the maximum range between the average value and either the minimum or the maximum value. Training is equivalent to find proper weight for all connections of nodes between layers such that a desired output is generated for a corresponding input. The major training algorithms are as follows:

1. Initialise all the value of connection weight W_ij between node j in the output layer and node i in the input layer.

2. Present an input for each node i in the input layer and specify the desired output for each node j in the output layer.

3. Calculate actual output of all nodes j using the present value of the W_ij. The output of node j denoted by X_i, is function of its total input:

4. Find an error term for each output node and hidden node, and then update weights W_ij.

5. Return to step (2) to present another new input for each node until all the training sets have been learned and the weights have stabilised. During the process, the learning data were used to train the network to get minimum mean square error (MSE) between measured and network outputs. These were used to measure the performance of the model

Results and discussion

For multiple regression models, a high correlation was found between fibre properties and yarn strength (0.944). After regression analysis, it was found that the fibre tenacity, fibre elongation, core yarn count, yarn count and twist factor had a significant influence on yarn tenacity. Table 3 shows the regression coefficient of variables, the t-values and significance level of each variable. A stepwise method was used for multiple regression analysis; therefore significance values obtained which based on fitting a model had been invalid. After stepwise multiple regression analysis had used to predict the core yarn tensile strength, it was found that the model's coefficient of multiple determination R² = 0.894, adjusted R² = 0.862 and standard error of estimate = 0.774. That mean the predictive power of the model is very high.

According to multiple regression analysis, the breaking elongation is high influenced by the fibre tenacity, fibre elongation, core yarn count, yarn count and twist factor. The breaking elongation increased with increase fibre elongation, twist factor and decreased with fibre fineness and finer both yarn count and spandex. Table 4 shows the regression coefficient of variables, the t-values and significance level of each variable.

A stepwise method was used for multiple regression analysis. After stepwise multiple regression analysis had used to predict the core yarn breaking elongation, it was found that the worse model's coefficient of multiple determination R² = 0.724, adjusted R² = 0.702 and standard error of estimate = 2.08. That mean the predictive power of the model is very low. The prediction power of breaking elongation regression model was not very high because the relationship between independent variables and yarn elongation was not very linear.

For the ANN models, the effect of number of hidden neurons from three to eight was studied six hidden neurons (two layers) gave the best prediction results for yarn breaking strength with an MSE of 0.0433, whereas with four inputs, with ten hidden neurons gave the best prediction results for yarn breaking elongation with an MSE of 0.05416.

To compare and evaluate the predictive power of multiple regression model and ANN model, correlation coefficient R value and minimum mean square error (MSE) are used between measured and network outputs. Table 5 shows the overall R value and MSE for the ANN training. Table 6 shows the feat of multiple regressions on training data cycles. The obtained results of average correlation coefficient R value and MSE of testing data indicated that the performance of neural networks model was better than multiple regression.

The difference between the MSE value of two models for predicting breaking strength and breaking elongation of training data were 0.7677 and 0.9686 respectively. In relation to breaking strength, the maximum MSE in the neural network model for predicting testing data set as it was 0.0513. It was 1.0571 for the multiple regression models on training data cycles. On the other data set, the maximum MSE for predicting the breaking elongation was 0.0762 in the neural network model and it was 1.2558 for the multiple regression models.

Both of these data were related to the sixth data of training cycles and data sets. That mean, the ANN models were obtained to be more accurate than multiple regressions and it is important to determine the lowest MSE in the predicting testing data occurring in the neural network model. The difference between correlation coefficient was shown in table 7.

Conclusion

In this study, the authors used two methodologies (ANN with variable training rate and multiple regressions) to predict the tensile properties of cotton-covered spandex core spun yarn based on three different Egyptian cotton fibres, HVI cotton fibres properties, spandex linear density, linear density of sheath part and twist factors. The ANN models were obtained to be more accurate than multiple regressions. Prediction of tensile properties by ANN model showed considerable lower mean square error (MSE) than multiple regression analysis in both testing and training data.

References

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Note: For detailed version of this article please refer the print version of The Indian Textile Journal October 2011 issue.

M H Elshakankery

National Textile Dept, National Research Center,

Cairo

Mona M Salem

National Textile Dept, National Research Center,

Cairo

M M Mourad

Faculty of Education, Helwan University,

Cairo, Egypt.