Yarn Strength Prediction: A Practical Model Based on Artificial Neural Networks

Yarn strength is one of the most significant parameters to be controlled during yarn spinning process. This parameter strongly depends on both the rovings' characteristics and the spinning process. On the basis of their expertise textile technicians are able to provide a raw and qualitative prediction of the yarn strength by knowing a series of fiber parameters like length, strength, and fineness. Nevertheless, they often need to perform many tests before producing a yarn with a desired strength. This paper describes a Feed Forward Back Propagation Artificial Neural Network-based model able to help the technicians in predicting the yarn strength without the need of physically spinning the yarn. The model performs a reliable prediction of the yarn strength on the basis of a series of roving parameters, commonly measured by the technicians before the yarn spinning process starts. The model has been trained with 98 training data and validated with 50 new tests. The mean error in prediction of yarn strength, using the validation set, is less than 4%. The results have been compared with the one obtained by means of a classical method: the multiple regression. Nowadays, the developed model is running in the laboratory of New Mill S.p.A., an important textile company that operates in Prato (Italy).


Introduction
During yarn spinning, textile experts commonly controls a series of parameters like the fiber strength, the fiber length, the twist yarn, the yarn count, and the fineness.Strength parameters of yarns are especially important for rotor-spun yarns.More in detail a very important parameter that technicians want to control is the yarn strength.This is defined as the breaking force of a spinning yarn, and it is commonly measured in cN.On the basis of their skill, the expert operators are capable of giving a qualitative, raw prediction of the yarn strength; unfortunately the empirical estimation of the actual value of the yarn strength is not straightforward.The assessment of such parameter is essential for obtaining high quality of the yarn.Accordingly, in the last two decades, the modeling of yarn properties has become one of the most important and decisive tasks in the textile research field.A considerable number of predictive models have been implemented to evaluate some yarn properties like strength, elongation, evenness, and hairiness.The relationship between fiber properties and yarn properties has been the focal point of several works [1][2][3].The studies in literature have shown that the relationship between yarn strength and fiber properties is nonlinear.Accordingly mathematical models based on the fundamental mechanics of woven fabrics often fail to reach satisfactory results.Some studies have been performed so far for modeling the yarn strength using linear regression [4][5][6].The main limitation of these studies is related to the need of defining a predefined linear model.In order to model a nonlinear relationship between input and output it is possible to devise an Artificial Intelligence-based approach.For this reason the problem of yarn properties prediction has been faced by some researchers by employing some knowledge-based approaches like artificial neural networks (ANNs) [7,8] and neuro-fuzzy models [9].Ramesh et al. [10], Zhu and Ethridge [11], Guha et al. [12], and Majumdar et al. [13] have successfully used the artificial neural network (ANN) and neuralfuzzy methods to predict various properties of spun yarns.The fabric strength was modeled by Zeydan using neural networks and Taguchi methodologies [14].Support vector machines (SVMs), based on statistical learning theory, have been developed by Yang and Xiang [15] for predicting yarn properties.The investigation indicates that in the small data sets and real-life production, SVM models are capable of maintaining the stability of predictive accuracy.A comparison between physical and artificial neural network methods has been presented recently.The results show that the ANN model yields a very accurate prediction with relatively few data points [16].Moreover, it is proved that the parameters of the raw material that significantly influence the basic quality parameters of the yarns are length, strength, and fineness of fibers [17][18][19].The effect of yarn count and of twist yarn in the final yarn strength is also well established [20].
The objective of the present work is to propose an approach for predicting the yarn strength based on Feed Forward Back-propagation Artificial Neural Network (FFBP ANNs).In authors' opinion this work, strongly based on scientific literature, has its advantage in the fact that the FFBP ANN model has been trained by means of fiber parameters that are typically measured by the technicians for controlling the yarn spinning.In other words, the technicians are not supposed to carry out none of adjunctive experimental test than they commonly assess.The reliability and goodness of results, in comparison with linear regression models, prove that the present work may be considered a practical method for assessing the yarn strength.
The developed system does not require technicians to produce a yarn and to measure its strength.The experts have only to test the rovings in order to assess some fiber properties.This operation is normally done before producing the yarn.Accordingly, by means of the devised model, the experience of the technicians is merged together with a simple approach in order to give an accurate prediction of the yarn strength.

Material and Methods
With the aim of developing a model of the yarn spinning, three tasks have been carried out:

Database Creation.
The first step for the development of the ANN-based system able to predict the yarn strength on the basis of some fibers parameters was to perform a series of experimental tests.The main intent of such an experimental approach was to create a database of fiber parameters to use as input of an ANN-based algorithm.A total of 6 different families of rovings (obtained mixing together different kinds of fibers) were collected from an important spinning mill operating in Prato (Italy).For each of them, several different values for fiber strength, fiber length, twist yarn, and yarn count have been tested (see Table 1).The result is a set of 98 different tests.The fiber length has been evaluated by means of a Classifiber Model KCF/LS.The output of the Classifiber measurement (see Figure 1) is given by the mean value of length (ML), the humidity values (UHM and UI%), and the standard deviation in % (CV%).The fineness was measured with an OFDA100, an image analysis system recognized with a Test Method from the (International Wool Textile Organization) IWTO.The OFDA instrument is used to certify mean fiber diameter.The output of the measurement is a statistical distribution of the fineness.The mean value is assumed as the fineness parameter (see Figure 2(a)).The fiber strength was measured with a precision fiber dynamometer.In Table 2 the value of the parameters of some of the 98 tests is listed.
As may be noticed, each roving is composed by different kinds, in different percentages, of fibers.Each fiber is characterized by a different value of length and fineness.For instance the roving named "velox 2" belongs to the family "Velox" composed by 25% viscose, 25% nylon, 10% cashmere, and 40% wool.These fibers are characterized by different length and fineness.In order to use these data for modeling the yarn spinning, it is possible to evaluate a single parameter for both length and fineness.
This can be easily carried out by defining, for each roving: (i) weighted average length (W L ), computed as the average weighted length of the fibers from a roving composed by a number i of different materials and defined by the following equation: (ii) fiber weighted average fineness (W F ), computed as the average weighted fineness of the fibers from a roving composed by a number i of different materials and defined by the following equation: (iii) fiber weighted average strength (W S ), computed as the average weighted strength of the fibers from a roving composed by a number i of different materials and defined by the following equation: In the example of the roving named "velox 2", the values for W L , W F , and W S might be evaluated as follows: Advances in Mechanical Engineering 3 By means of ( 1), (2), and (3), for each of the 98 different tests a set of 5 input parameters may be defined.In Table 3 a subset of this input set is listed.It is important to remark that the parameters α i , L i , F i , and R i might be used for training the ANN as well, thus probably leading to accurate results.However, when the number of components composing a roving increases, the number of inputs increases as well thus resulting in a more complex ANN architecture.Moreover, as already mentioned, the aim of the present work is to propose a practical approach to be used by the technicians and practitioners using parameters (like W L , W F , and W S ) that they typically assess during the spinning process.
From each of the 98 selected rovings, the textile technicians produced a yarn by using a ring frame machine (Marzoli ring spinning frame RST-1, see Figure 2(b)).The process parameters adopted for producing the yarn were maintained constants with the exception of the twist yarn.This is due to the fact that, as already stated, the twist yarn influences the yarn strength; therefore such a parameter has been used as an input for the devised model.Once produced, the yarn strength of the 98 different yarns has been measured by means of a dynamometer.Some of the values of yarn strength (YS) are listed in the last column of Table 3.

Definition of Training Parameters.
The result of the experimental process consists in a dataset of 98 × 5 fiber parameters and of 98 values for yarn strength.For instance, in Table 4 the whole dataset related to cashmere family is showed.
The dataset may be used as a training set for the FFBP ANN model.In detail, the training set P is composed by a matrix 5 × 98 composed by 98 vectors of 5 elements: As previously mentioned the FFBP ANN is required to find a nonlinear correlation between this training set and a target set T, defined as a vector (size 1 × 98) whose elements are the yarn strength values of the 98 yarns:  3, has the following characteristics: (i) three layers: input, hidden, and output layer; (ii) hidden layer made of logistic neurons followed by an output layer of linear neurons; (iii) 5 input, h hidden, and 1 output units.
The number of hidden neurons of feed-forward neural networks, generally decided on the basis of experience [21], is an important factor for the training, in order to avoid over fitting in the function approximation.From one point of view the number of hidden units may be stated a priori by means of empirical equations provided by the literature [22].
On the other hand it is possible to select the best network by estimation, for a given problem, of the network architecture and parameters within a set of candidate configurations [23].In the present work the value h was evaluated varying from 2 to 14 with a step of 2 units, monitoring the performance of response using the training data.As known, during the training, the weights and the biases of the network are iteratively adjusted to minimize the network error function.The network error used in this work is the mean square error (MSE) correspondent to the training set elements.This error is monitored during the training process and will normally decrease during the initial phase of the training.However, when the network becomes excessively specialized in reproducing the training data, the early stopping error will typically begin to rise.When the early stopping error increases for a specified number of iterations, the training is stopped, and the weights and biases at the minimum early stopping error are returned.The selected network is characterized by h = 10 units.The training was carried out using a training rule based on the Levemberg-Marquardt descent backpropagation algorithm with an adaptive learning rate [24].Training set (input and target) has been scaled in the range [0-1] with a min-max algorithm.Training was automatically performed until the early stopping error increases for a specified number of iterations.This goal was obtained in 22 epochs (see Figure 4).

Results
Once trained, the network is able to correlate the training set elements to the target ones.In other words the ANN is able to receive any vector of 5 elements composed by the fiber parameters of any roving in input and to give, as output, the prediction of the yarn strength of the yarn produced with that roving.Hence, The predicted value of the yarn strength (YS predicted ) must be compared with the real value (YS real ) in order to assess the reliability of the prediction.The comparison may be evaluated, in percentage, by defining a coefficient η, called "prediction error", given by Smaller is the value of η and better is the prediction.In order to validate and test the approach a new series of experimental test (called "validation set") has been carried out.This new experimental phase consisted in collecting the parameters of 50 new rovings (see last column of Table 1).These parameters are used as a test set for the devised ANN.
More in detail the ANN has to give a response closer to the real value of the really produced yarn strength.In Table 5 some of the 50 × 5 parameters are showed.In order to clarify the approach described above, an example is provided below.Let suppose we want to predict the yarn strength of the "gamma 19" roving whose parameters are listed in Table 5.The input set for the ANN is given by the following vector: The ANN response to this input vector is given by output The real value of yarn strength measured with a dynamometer (after producing the yarn) is given by YS real = 356.6. ( Finally the prediction error is given by In Table 5 the results of 11 of the whole set of 50 new inputs are provided.Referring to Table 5 the mean error in prediction of yarn strength is 3.07% with a standard deviation equal to 0.0127.The maximum value in error prediction is equal to 5.17%.These results may be compared with the one obtained by means of a multiple regressionbased model.The regression equation (evaluated using, as input, the values of Y c , Tw, W L , W F , and W S normalized in the range [0-1]) is given by This linear regression model, as depicted in the last column of Table 5, leads to an average estimation error equal to 5.55%.In Table 6 the results of simulation performed with the FFBP ANN model on the whole set of 50 rovings are listed.Referring to this validation set the mean error in prediction by using the FFBP ANN is 3.5%.The standard deviation is equal to 0.015.In some cases, like for instance for the roving named "joy 18", the maximum error may be relevant (in this case it is equal to 7.5%).This higher error may be reduced using more data for training the ANN.Future works will be addressed for the building of a more consistent database.

Conclusions
With the devised model the textile technicians may test any kind of rovings composed by different percentages of fibers.As stated above the experts are capable of knowing the yarn strength without physically processing it by using the provided model.The model gives an output in less than 1 sec and uses parameters that are commonly measured by the technicians before starting the spinning process.As a result they can quickly test a large number of rovings until they reach the best desirable strength property.After this phase of testing they may effectively spin the yarn.Furthermore, also an unskilled user is able to correctly choose the best roving for a desired yarn after a few trials.This is translated into a lossless time process.The devised model is running in the New Mill S.p.A. Laboratory and will be subjected to further implementations.

Nomenclature
L i : Length of the ith fiber composing a roving F i : Fineness of the ith fiber composing a roving R i : Resistance of the ith fiber composing a roving α i : Percentage of the ith fiber composing a roving Y ci : Yarn count of the ith roving Tw i : Twist yarn of the ith roving W Li : Weighted average length of the fibers from ith roving W Fi : Weighted average fineness of the fibers from the ith roving W Ri : Weighted average strength of the fibers from the ith roving YS i : Strength of the ith yarn.
(i) database creation, (ii) definition of training parameters, (iii) artificial Neural Network construction and training.

Figure 2 :Figure 3 :
Figure 2: (a) Example of output obtained by means of the OFDA instrument: statistical distribution of the fineness.The mean value is assumed as the fineness parameter.(b) Ring frame machine used in the work.

Figure 4 :
Figure 4: Training performance (MSE versus Epochs).The best training has been reached for 22 epochs.
weighted average length, the weighted average fineness, and the weighted average strength of a roving.This is possible if the ANN is properly training by means of the training and target sets.Both structure and training of the ANN have been developed by using the Artificial Neural Network Toolbox working into Matlab environment.The constructed FFBP ANN, showed in Figure

Table 1 :
Figure 1: Example of output of the Classifiber Model KCF/LS measurement: the mean value of length (ML), the humidity values (UHM and UI%), and the standard deviation in % (CV%) of a lot of rovings are showed.Number of different tests performed for each roving in order to train the ANN system.

Table 2 :
percentage, yarn count, twist, length, fineness, and fiber strength of some rovings within the 98 tested ones.

Table 3 :
Values of yarn count, twist, W L , W F , W R , and yarn strength for 12 of the 98 different tests.

Table 4 :
values of yarn count, twist, W L , W F , W R , and yarn strength (YS) related to "cashmere" family.

Table 5 :
Some of the 50 × 5 parameters used for testing the ANN.The mean value in prediction error and the standard deviation for both the ANN and the multiple regression models are

Table 6 :
Results of simulation for the 50 new rovings.The mean value in prediction error and the standard deviation are also showed.