# Predicting the Breaking Elongation of Ring Spun Cotton Yarns Using Mathematical, Statistical, and Artificial Neural Network Models

Predicting the Breaking Elongation of Ring Spun Cotton Yarns Using Mathematical, Statistical, and Artificial Neural Network Models

Majumdar, Prabal Kumar

ABSTRACT

This paper presents a comparative study of three modeling methodologies for predicting the breaking elongation of ring spun cotton yarns. Constituent cotton fiber properties and yarn count are used as inputs to these models. The predictive powers of the three different models-mathematical, statistical, and artificial neural network-are estimated and compared. The relative importance of various cotton fiber properties measured by a high volume instrument is also investigated using the artificial neural network model.

Among the measurable properties of spun yarns, breaking elongation probably receives the least attention from spinning technologists. However, the importance of yarn elongation can never be ignored, since it influences the performance of spun yarns during winding, warping, and weaving. Yarn elongation, like other yarn properties, is chiefly influenced by fiber properties, yarn twist, and yarn count [5, 8]. Because there is a strong correlation between yarn elongation and loom efficiency, it would be very helpful if a prediction model could forecast yarn elongation accurately. However, prediction models dealing with the breaking elongation of cotton yarns are quite few in number. Mathematical models proposed by Aggarwal [1, 2], Frydrych [6], and Zurec et al. [16] predicted the breaking elongation of yarn only with limited success. On the other hand, statistical models yielded reasonably good elongation predictions [4, 7].

In recent years, artificial neural network (ANN) models have been widely used to predict various yarn properties [3, 4, 10-12, 14, 15]. However, there is dearth of published work that encompasses the scope of predicting ring yarn elongation from cotton fiber properties with ANN models. In this work, we attempt to predict the breaking elongation of ring spun cotton yarns using mathematical, statistical, and ANN models. We also quantify the relative importance of various cotton fiber properties as contributors to yarn elongation with the ANN model.

Models

MATHEMATICAL MODEL

The limitation of this model is that it should not be used to predict breaking elongation beyond the range of inputs employed to develop the model.

ARTIFICIAL NEURAL NETWORK MODEL

An artificial neural network (ANN) is a powerful datamodeling tool that is able to capture and represent any kind of input-output relationships. In this kind of network, each neuron or “processing element” (PE) receives a signal from the neurons of the previous layer, and each of these signals is then multiplied by a separate weight known as a synaptic weight. The weighted inputs are then summed up and passed through a transfer function, which converts the output to a fixed range of values. The output of the transfer function is then transmitted to the neurons of the next laver.

Experimental

DATA COLLECTION

Cotton crop study data of 1997 and 1998 published by the International Textile Center, U.S.A., were used in our investigation [13]. Seven cotton fiber properties measured by HVI-fiber bundle tenacity, elongation, upper half mean length (UHML), uniformity index, micronaire, reflectance degree, and yellowness-were the input parameters along with yarn count (Ne). The yarn twist multiplier was an additional input parameter for the mathematical model only. The summary statistics for fiber properties and yarn count are shown in Table I. The only output of each prediction model was the breaking elongation of yarns. From the crop study results, we had 87 samples of input-output data for carded ring spun yarns. We used 72 and 15 samples, respectively, for training and testing all the prediction models.

NEURAL NETWORK PARAMETERS

Results and Discussion

COMPARING THE PREDICTION PERFORMANCE OF THE MODELS

After the completion of model development or training, all the three models were subjected to the unseen testing data set. Statistical parameters such as the correlation coefficient between the actual and predicted breaking elongation (R), mean squared error, and mean absolute error% were used to judge the predictive power of various models. The results are shown in Table II. It is evident from Table II that the predictive power of the ANN model is the best of the three models considered here. The correlation coefficient between actual and predicted elongation is very high (R = 0.938) for the ANN model. In addition, the mean absolute error is less than 5%. In contrast, the mathematical model has the least predictive power, as marked by a relatively low correlation coefficient (R = 0.731) and relatively high mean absolute error (10.05%). The predictive power of the statistical model lies between the ANN and mathematical models. The correlation coefficient and mean absolute error for the statistical model are 0.870 and 6.696%, respectively.

The mathematical model considered here does not include cotton fiber properties such as UHML, uniformity index, reflectance degree, and yellowness, thus resulting in poor prediction performance. The dominance of the ANN model over the statistical model could be ascribed to the fact that the former can handle nonlinear relationships more aptly than the latter. Table II shows that for the mathematical, statistical, and ANN models, there are six, four, and two test samples, respectively, that show more than 10% absolute error. In addition, the mathematical model exhibits a maximum error as high as 34.04% in contrast to 13.23% for the ANN model.

ANALYZING THE RELATIVE IMPORTANCE OF INPUT PARAMETERS

Since the ANN model yields the best prediction results, we opted to employ it to analyze the relative importance of various input parameters. We conducted an input saliency test by eliminating only one designated input from the optimized ANN model at a time. The increase in mean squared error value in the testing set compared to the optimized ANN model was considered as the indicator of importance of the eliminated input. The results are shown in Table III. Note that fiber elongation dominates, as expected, the other input parameters as contributors to yarn elongation. Our findings agree with the findings of Fiori et al. [5]. Uniformity index and yellowness are the next two cotton fiber properties in the hierarchy of contributors to yarn elongation. Higher length uniformity probably hinders fiber slippage and thereby ensures greater translation of fiber elongation into yarn elongation. Yarn count ranks next to yellowness, and micronaire and UHML seem to have a minimal influence on cotton ring spun yarn elongation.

Conclusions

We have predicted the breaking elongation of ring spun cotton yarns with mathematical, statistical, and ANN models. We have found that prediction performance is best for the ANN model followed by the statistical and mathematical models. The breaking elongation of ring spun cotton yarns is mostly influenced by fiber elongation. Fiber length uniformity, yellowness, and yarn count are the other dominant parameters. However, a more exhaustive study with enormous training data could provide better insight into the relative importance of input parameters. Similar studies could be conducted for the rotor spun yarns as well.

Literature Cited

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Manuscript received April 21, 2003; accepted September 5, 2003.

PRABAL KUMAR MAJUMDAR

College of Textile Technology, Serampore, West Bengal 712 201, India

ABHIJIT MAJUMDAR1

College of Textile Technology, Berhampore, West Bengal 742 101, India

1 To whom correspondence should be addressed: phone: 0091-03482-263530; fax: 0091-03482-252809; email: abhitextile@rediffmail.com

Copyright Textile Research Institute Jul 2004

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