UDK 677.017:519.233.4 ISSN 1580-2949 Original scientific article/Izvirni znanstveni članek MTAEC9, 49(3)325(2015) PREDICTING THE PHYSICAL PROPERTIES OF DRAWN NYLON-6 FIBERS USING AN ARTIFICIAL-NEURAL-NETWORK MODEL NAPOVEDOVANJE FIZIKALNIH LASTNOSTI VLEČENIH VLAKEN IZ NAJLONA 6 Z UPORABO MODELA UMETNE NEVRONSKE MREŽE Ruhollah Semnani Rahbar1, Morteza Vadood2 1Department of Textile and Leather, Faculty of Chemistry and Petrochemical Engineering, Standard Research Institute (SRI), Karaj, P. O. Box 31745-139, Iran 2Department of Textile Engineering, Amirkabir University of Technology, Tehran, Iran semnani@standard.ac.ir Prejem rokopisa - received: 2013-08-13; sprejem za objavo - accepted for publication: 2014-07-11 doi:10.17222/mit.2013.128 Low-oriented nylon-6 fibers were drawn in a multistage drawing process, during which the number of drawing steps and the temperature of each step were changed. The physical properties of these fibers were measured and compared with the values predicted by a multiple-linear-regression model. Moreover, six input variables and four output variables were used in an artificial neural network (ANN) to establish the logical relationships between the inputs and outputs. Attempts were also made to determine the effective parameters for each physical property and explain the observed trends. The results showed that the models based on the ANN performed well and provided stable responses in predicting combined interactions between independent variables. Keywords: drawing process, artificial neural network, modeling, physical properties Malo orientirana vlakna najlon 6 so bila vlečena z večstopenjskim postopkom, pri čemer se je pri vsakem vleku spreminjala stopnja vlečenja in temperatura. Izmerjene vrednosti teh vlaken so bile primerjane z vrednostmi, napovedanimi z modelom multivariantne linearne regresije. Poleg tega je bilo v umetni nevronski mreži (ANN) uporabljenih šest vhodnih spremenljivk in štiri izhodne, da bi ugotovili logične odvisnosti med vhodnimi in izhodnimi spremenljivkami. Poskušalo se je ugotoviti učinkovite parametere za vsako fizikalno lastnost in razložiti opažene tendence. Rezultati so pokazali, da so modeli na osnovi ANN dobri in ponujajo stabilne odgovore pri predvidevanju kombiniranih interakcij neodvisnih spremenljivk. Ključne besede: postopek vlečenja, umetna nevronska mreža, modeliranje, fizikalne lastnosti 1 INTRODUCTION technological problems2-4,6-9. However, they have certain limitations as they require a specialized knowledge of Synthetic-fiber drawing is a critical process to obtain both the statistical methods and techniques of experi- fibers with desired properties for final applications. mental design. Moreover, the prediction ability of the There are various parameters in this process that should regression analysis may be limited in the case of an be controlled to yield a fiber with acceptable technical analysis of multidimensional technical problems10,11. specifications. These variables include the draw ratio, the In recent years, artificial neural network (ANN) has drawing temperature, the number of drawing steps, the been used as an alternative modeling method in many drawing speed and the distribution of draw ratio in the different engineering fields to predict the properties of multistage drawing1. Because of the complex relation- materials. ANN can be considered as a black box con- ships between the fiber properties and the drawing-pro- sisting of a series of complex equations for estimating cess variables, there is a need for a sound experimental the outputs on the basis of a given series of input values. design and a careful analysis of the experimental results. The advantage of ANNs is the ability of representing In this way, the relationships between a measured complex relationships directly from the data being characteristic of a drawn fiber and the influencing factors modeled, while their representation (modeling) is always can be identified and optimized. The understanding of nonlinear12-14. these relationships reduces the processing cost and Many researches were done in the textile industry to provides for reproducibility in a day-to-day production. predict the properties of yarns, woven and nonwoven Moreover, the risk of excessive downtime for trials is fabrics and many other characteristics of textile mate- reduced2-5. rials10,13-25. Among these, just few studies are devoted to Due to their simplicity, regression-based models and melt spinning and drawing of synthetic fibers. It seems statistical analyses were extensively used to solve textile that there is a lack of information concerning the appli- cation of ANN for predicting fiber properties during multistage drawing. Therefore, in this paper, an ANN model was used to predict some physical properties of drawn nylon-6 fibers upon multistage drawing. 2 EXPERIMENTAL WORK 2.1 Materials and methods A low-oriented nylon-6 multifilament yarn, 340 dtex, 24 filaments, was kindly supplied by Alyaf Co. (Iran). Nylon 6 (polyamide 6) is made up of linear macromole-cules whose structural units are linked with an amide linkage (-NH-CO-group). This synthetic fiber is used for a variety of different applications ranging from garments to industrial usages. Fiber samples were prepared by melt spinning and the take-up speed of 800 m/min. The undrawn multifilament yarn had a polymerization degree of 148. The drawing process was performed on an industrial Zinser draw-twisting machine (Germany), type 520-2. The details of the drawing process were explained in the previous work26. The fixed drawing conditions are listed in Table 1. Table 1: Fixed operating conditions of the drawing experiments Tabela 1: Pogoji obratovanja pri preizkusih vle~enja Temperature of the feeding roller (°C) Temperature of the third godet roller (°C) Drawing speed (m/min) Intermingling jet pressure (bar) Spindle speed (r/min) Room temperature Room temperature 400 2 4000 Six process parameters of drawing trials included the first-stage draw ratio (FSDR), the second-stage draw ratio (SSDR), the third-stage draw ratio (TSDR), the first-godet temperature (FGT), the block-heater temperature (BHT), and the second-godet temperature (SGT). In the trials, one-, two- and three-stage drawn fibers and also the fiber heat-treated without drawing were produced to have a broad range of fibers with different structures. A total of 61 different fibers were prepared and the drawing trials are reported in Table 2. Table 2: Experimental array for the drawing process Tabela 2: Pogoji eksperimenta pri postopku vle~enja Run w « fo CÖ t« t« w a -13 c^ « Q MOQ OQ o o w O ^ ird-ati ir ^ ^ (j ^r te oe lp ^ a 1 1.1 4.126 1.3 100 170 170 2 2.098 1.611 1.626 100 170 170 3 2.8 1.621 1.3 100 170 170 4 1.755 1.5 1.3 100 170 170 5 1.755 2.586 1.3 100 170 170 6 1.615 1.884 1.939 100 170 170 7 1.1 2.488 1.3 100 170 170 8 1.1 2.551 2.102 100 170 170 9 1.1 1.5 1.3 100 170 170 10 1.315 2.074 1.564 100 170 170 11 1.755 1.97 1.3 100 170 170 12 1.348 1.611 2.53 100 170 170 13 1.8 1.5 2.185 100 170 170 14 1.1 1.5 2.102 100 170 170 15 1.1 1.5 3.4 100 170 170 16 1.637 1.5 1.792 150 170 170 17 1.1 1.739 2.3 150 170 170 18 1.1 1.5 1.729 150 150 150 19 1.1 1.615 2.3 30 30 30 20 1.1 3.077 1.3 150 150 150 21 1.1 2.313 1.729 30 170 170 22 1.253 1.975 1.676 60 80 80 23 1.1 3.077 1.3 90 170 170 24 2.1 1.612 1.3 150 170 170 25 1.1 1.5 1.3 30 30 30 26 1.1 1.5 1.3 30 170 170 27 1.1 2.148 1.3 150 150 150 28 1.1 1.5 1.3 90 90 90 29 2.1 1.5 1.397 30 30 30 30 1.1 3.077 1.3 30 170 170 31 1.637 1.5 1.792 30 170 170 32 1.275 1.5 2.3 30 100 100 33 1.52 1.5 1.3 30 170 170 34 1.732 1.591 1.506 90 110 110 35 1.52 2.227 1.3 30 30 30 36 1.1 1.5 1.3 150 170 170 37 2.1 1.612 1.3 30 170 170 38 1.1 1.5 2.3 30 170 170 39 1.1 3.077 1.3 30 30 30 40 1.637 1.5 1.792 30 30 30 41 1.275 1.5 2.3 90 90 90 42 1.1 1.5 1 100 170 170 43 1.1 4.2 1 100 170 170 44 1.1 4.2 1.3 100 170 170 45 2.8 1 1 30 30 30 46 2.8 1 1 100 30 30 47 1.1 4.126 1.3 100 30 170 48 1.1 4.126 1.3 100 60 170 49 1.1 4.126 1.3 100 100 170 50 1.1 4.126 1.3 100 150 170 51 1.008 4.6 1 100 170 170 52 1.1 4.215 1 100 170 170 53 1.1 3.242 1.3 100 170 170 54 2.8 1.648 1.3 100 170 170 55 2.8 1.506 1.3 100 170 170 56 1.187 1.5 2.5 30 30 30 57 2.1 1.564 1.3 30 30 30 58 1.579 1.5 1.879 30 30 30 59 1.1 1 1 30 30 30 60 1.1 1 1 100 30 30 61 1 1 1 100 30 30 The yarn linear density (expressed in dtex) was determined in accordance with ASTM D 1577-96. The mean value is the average of five measurements. Stress-strain curves were obtained with an EMT-3050 tensile testing machine (Elima Co., Iran). The initial lengths of the fibers and cross-head speeds were 300 mm and 500 mm/min, respectively. From the stress-strain plots, the initial modulus, the tenacity and the specific work of rupture were evaluated. The reported values for all the mechanical properties were averaged over at least ten independent measurements. Yarn-shrinkage measurements were made according to DIN 53840 at 130 °C for 10 min. The initial and final lengths were measured at room temperature and the total shrinkage was defined as the fraction of the initial sample length remaining after the exposure to the elevated temperature. The reported values are the average of eight tests. 2.2 Artificial neural network Neural networks are mainly composed of the processing elements called neurons with interconnections. The exclusive structure of an ANN makes it very appropriate for modeling a complex system with nonlinear relations between the parameters. Generally, an ANN can be made of many layers, namely the input, output and several hidden layers. The neurons in each layer are connected with the associated weights to the other neurons in the next layer. The input layer receives the input parameters and, through the hidden layers based on Equation (1), the output can be calculated in the output layer19. Figure 1 indicates the topology of an ANN with one hidden layer: = f rn / n Xwikf Xwiixi + b1 j=1 +b2. (1) Here Wj, Wj., bij and b2k are the weight between the i'h input neuron and the jth hidden neuron, the weight bet- ween the jth hidden neuron and the .th output neuron, the bias for the jth hidden neuron and the bias for the .th output neuron, respectively. The f(x) is the activation function2728. All the data is divided into three groups known as the training, validation and testing sets. The first group is used to train the ANN. When the network begins to overfit the data, the training is stopped for a specified number of iterations (maximum number of fails) and the weights and biases are returned with the minimum error on the validation set. The testing group is used to control the error after the training process21. In this study, to apply ANNs, the Matlab R2008 software was used. The ANNs were trained on the basis of the error back-propagation algorithm using the "Trainlm" function to avoid an over-fitting error. The activation functions for all the hidden and output layers were considered as the hyperbolic tangent and linear function, respectively (this type of ANN is called the perceptron). 3 RESULTS AND DISCUSSION 3.1 Linear regression model In this research, multiple linear regression (MLR) was employed to evaluate the performance of different models. In order to determine the variables that can directly affect the physical properties, as well as decreasing the number of variables, a traditional linearregression model at the 90 % confidence level was accomplished. This procedure was only used for three variables including the FSDR, SSDR and TSDR because they were varied at multiple levels. The FSDR, SSDR and TSDR were changed at the 18th, 21st and 17th levels, respectively. Moreover, theses parameters were individually considered with respect to the responses of the linear-regression model. Table 3 shows the Pearson correlation coefficient (PCC) and the corresponding P-value between the measured parameters (FSDR, SSDR and TSDR) and the physical properties. Table 3: PCC and P-value between the measured parameters and physical properties Tabela 3: PCC in P-vrednost med izmerjenimi parametri in fizikalnimi lastnostmi Shrinkage Specific work of rupture Tenacity Initial modulus PCC P- value PCC P- value PCC P- value PCC P- value FSDR 0.23 0.08 -0.25 0.05 0.23 0.08 0.25 0.06 SSDR -0.19 0.14 -0.49 0.00 0.59 0.00 0.31 0.01 TSDR 0.38 0.00 -0.32 0.01 0.14 0.29 0.36 0.00 Figure 1: ANN with one hidden layer Slika 1: ANN z eno skrito plastjo The PCC varies between -1 and 1; the more absolute value of the PCC indicates the existence of a strong relation between two parameters. P-values are used for testing the hypothesis of no correlation. Each P-value is the probability of getting a correlation as large as the observed value by random chance when the true correlation is zero. If a P-value is less than 0.1, the corresponding correlation is significant. But the data for the FGT, BHT and SGT were different and they were varied only at the 5'h, 9'h and 7'h levels, respectively. Hence, a one-way ANOVA was used to evaluate their effects on the physical properties and the results are listed in Table 4. The confidence level was 90 %. As mentioned before, the parameters with the P-value below 0.1 have a significant effect on the physical parameters. The greater the F-value, the greater are the influence and the relevance of the source factor. Table 4: ANOVA results identifying the statistical significance of FGT, BHT, and SGT for the physical properties Tabela 4: Rezultati ANOVA prikazujejo statisti~no pomembnost FGT, BHT in SGT na fizikalne lastnosti Shrinkage Specific work of rupture Tenacity Initial modulus SSE 103.202 62.662 4003.172 386497.497 E-H DF 4.000 4.000 4.000 4.000 MSE 25.801 15.665 1000.793 96624.374 F 3.480 0.703 5.435 2.339 P 0.013 0.593 0.001 0.066 SSE 185.671 240.453 3159.013 710707.421 CQ DF 8.000 8.000 8.000 8.000 MSE 23.209 30.057 394.877 88838.428 F 3.627 1.461 1.841 2.323 P 0.002 0.194 0.090 0.033 SSE 176.808 235.435 3412.317 694829.932 E-h Co DF 6.000 6.000 6.000 6.000 MSE 29.468 39.239 568.720 115804.989 F 4.659 1.971 2.817 3.119 P 0.001 0.086 0.019 0.011 SSE: sum of squares, DF: degree of freedom, MSE: mean squared error, F: F-statistic (the ratio of the mean squares), P: P-value According to Tables 3 and 4, the effective factors for each physical property were determined and shown in Table 5. Table 5: Parameters affecting the physical properties Tabela 5: Parametri, ki u~inkujejo na fizikalne lastnosti Shrinkage Specific work of rupture Tenacity Initial modulus FSDR + + + + SSDR - + + + TSDR + + - + FGT + - + + BHT + - + + SGT + + + + + : effective, - : non-effective After determining the effective parameters, multiple-linear-regression (MLR) analyses based on Table 5 were performed. The results (Figure 2) indicated that the developed MLR models provided different predictions for the physical properties. According to Figure 2, MLR can predict the specific work of rupture and the shrinkage with the highest and Figure 2: Results of the MLR prediction for various physical properties (R2 = PCC) Slika 2: Rezultati MLR-napovedovanja razli~nih fizikalnih lastnosti (R2 = PCC) the lowest accuracies, respectively. Table 6 shows the coefficients of MLR for predicting physical properties. Actually, each coefficient in MLR is a partial derivative of the model response with respect to the variable of that coefficient. So, the contribution of each variable in predicting the model response can be assessed by checking the coefficient values. Referring to Table 6, the TSDR and the SGT have the highest and the lowest effects on the shrinkage, respectively. A similar trend was observed for the specific work of rupture. Moreover, for the tenacity and the initial modulus, the FSDR and the TSDR play the main roles, respectively. Also, the BHT and the FGT have the lowest effects on the tenacity and the initial modulus, respectively. Although increasing the order of the regression equation gives better results, it makes the regression equation more complicated. For example, using a quadratic regression including linear, interaction and square terms to predict the initial modulus increases the number of coefficients up to 28. Therefore, using an ANN model in this situation can be very beneficial. The ANN contains various parameters such as the number of hidden layers and the number of neurons in each hidden layer that directly affect the output of the ANN. Hence, to determine the best set of the ANN parameters, the trial-and-error method was applied. The numbers of hidden layers and neurons in each hidden layer were considered to be between 1 to 5 and 1 to 6, respectively. In this study the stopping criteria for the ANN training were the following three options: the training tolerance level (0), the maximum number of fails (6 iterations) or the total number of iterations for training (1000 iterations). The experimental data were used to train the network; 37, 12 and 12 data sets were randomly chosen for the training, validation and testing groups, respectively. To evaluate the accuracy of the developed ANN, the absolute value of the PCC between the ANN outputs and the actual values for the testing set was calculated. A higher PCC indicates a higher accuracy of the ANN. To remove the effects of the initial weights and biases on the ANN output, each ANN structure was created five times with the weights and biases chosen randomly and the ANN with the highest absolute value of the PCC was considered for that structure. Table 6: Coefficients of MLR models for predicting the physical properties Tabela 6: Koeficienti MLR-modela za napovedovanje fizikalnih lastnosti Shrinkage Specific work of rupture Tenacity Initial modulus Constant 1.777 36.461 -14.612 -697.759 FSDR 1.688 -6.795 15.768 251.684 SSDR - -4.518 10.865 115.788 TSDR 2.899 -6.892 - 270.758 FGT 0.008 - -0.014 0.347 BHT -0.023 - -0.010 -1.231 SGT 0.003 -0.002 0.065 2.084 models in terms of the PCC, as given in Table 7. The individual values of the predictions of the models, along with the experimental values, are shown in Figure 3. By comparing Table 7 and Figure 2, it can be found that the prediction potential of the ANN models is superior to that of the MLR. This means that removing some input variables could not enhance the quality of the MLR predictions as compared to the ANN models. Table 7: Best ANN structure for predicting various mechanical properties Tabela 7: Najbolj{a struktura ANN za napovedovanje razli~nih mehanskih lastnosti Physical property Maximum PCC Hidden layer Shrinkage 0.9182 [1-1-2] Specific work of rupture 0.9907 [3] Tenacity 0.981 [3-4-2] Initial modulus 0.9917 [2-1-3] Unlike the regression method, an ANN can predict physical properties simultaneously with four neurons in the output layer, but such results showed an insufficient accuracy. In this way the prediction ability of an ANN for each output neuron only involves the weights between the last hidden layer and the output layer; so, considering separate ANNs for each physical property (one neuron in the output layer) would give a higher accuracy in the prediction. As the ANN calculations using computers can be performed quickly, to consider all the terms of the effects, such as linear terms or interactions, all the input parameters were considered for the ANN models. As expected, it was found that the structure of the neural network for each physical property was different and exhibited a high prediction performance of the Figure 3: Predictions of ANN models for the testing group Slika 3: Napovedi ANN-modelov za preizku{eno skupino In Table 7, [1-1-2] in the hidden-layer column means that the ANN contains three hidden layers with 1, 1 and 2 neurons in the first, second and third hidden layers, respectively. As can be seen in Figure 2, the PCC value for the specific work of rupture modeled with MLR is 0.96, indicating that the relation between this parameter and its effective variables is not complicated. Also, according to Table 7, a simple ANN can model the specific work of rupture with the PCC value of almost 1 which indicates a perfect prediction. As observed from Table 7, there is an increase in the PCC values for the shrinkage, tenacity and initial modulus compared to the values of the MLR predictions as shown in Figure 2. This means that the relations between the parameters are no longer linear and the MLR prediction is not reliable any more, whereas the ANN using multilayers could predict these responses very well. 3.2 Sensitivity analysis of the ANN model Because of the complex and nonlinear form of the ANN analysis, a sensitivity analysis was conducted to study the influence of the input variables on the output. As a matter of fact, the aim of this analysis was to evaluate the effects of the changes in each input on the ANN output. In this process, the value of one input variable from the initial condition is slightly changed (10-50 %) and then the output value is predicted, while all the other variables are set to the selected constant values. This process is repeated for all the input variables. The robustness of the model is determined by examining how well the predictions compare with the available structural knowledge. Figure 4 shows the effects of the changes in the input variables from -50 % to +50 % in the scale of 0.1 for the physical properties. It is evident from Figure 4a that the shrinkage initially increases with the TSDR and then reaches a constant value as the TSDR moves toward higher values. The changes in the other input variables have no significant Figure 4: Effects of the changing input variables on the mechanical properties: a) shrinkage, b) specific work of rupture, c) tenacity, d) initial modulus. Since the variation of TSDR is higher than the ones of the other parameters, it is shown on the right vertical axis in Figure 4a. Slika 4: Vpliv spremenjenih vhodnih spremenljivk na mehanske lastnosti: a) krčenje, b) specifično delo pri pretrgu, c) trdnost, d) začetni modul. Ker je spreminjanje TSDR večje od drugih parametrov, je to prikazano na desni vertikalni osi na sliki 4a. effect on the shrinkage. The internal stress achieved with the third-stage draw ratio increases the fiber shrinkage. This is related to the absence of heat in the third stage of drawing. A further crystallization after a critical TSDR, along with an increase in the orientation of the amorphous region, led to a negligible change in the shrinkage value. According to Figure 4b, the effects of the FSDR, SSDR and TSDR on the specific work of rupture are the same and the effect of the SGT is also very similar to them. By increasing these parameters, a decrease in the specific work of rupture can be achieved. But the BHT has an opposite effect on this parameter and an increase in the BHT gives rise to an increase in the specific work of rupture. After a critical BHT, a reorientation begins which is accompanied by a decrease in the orientation and confirmed by a significant increase in the specific work of rupture. Moreover, the FGT has no appreciable effect on the specific work of rupture. Based on Figure 4c and considering the tenacity variation, the variables can be divided into effective/ non-effective categories; the FGT, BHT and SGT are categorized as the non-effective group, while the FSDR, SSDR, and TSDR are considered as the effective group. By increasing the values of the effective group, the tenacity increases, and with even higher values the tenacity almost reaches the plateau. As shown in Figure 4d, the initial modulus increases due to the increased FSDR, SSDR, TSDR and SGT, while the FGT and BHT have no visible effect on the initial modulus. It seems that the temperature of the block heater mainly affects the crys- talline structure of the fibers that restricts the chain orientation in the third stage of drawing. This explains why the initial modulus did not change significantly as the BHT increased. 3.3 Important index analysis of the ANN model To study the contributions of different input variables to the ANN output model, various methods were introduced, like the weights method29,30. A modified weights method was introduced by Gevrey et al.31 and their results are very close to the weights method. In this study, the modified weights method was implemented to determine the percentage contribution of each input variable to the physical properties. Referring to the modified weight method and Figure 1, the relative importance (RT) is calculated through Equations (2) and (3): n y Q, =-n-, j =1,2, ..., m i =1 W , RT = m m n 'LILq.. j =1 i =1 -v100 (2) (3) It must be noted that only the first hidden layer is considered in the modified weights method. The RI values for all the input variables were obtained and shown in Figure 5. Figure 5: RI for all the input variables versus the physical properties Slika 5: RI vseh vhodnih spremenljivk proti fizikalnim lastnostim Figure 5 indicates that the main effect of the TSDR is more pronounced on the shrinkage than the other factors and that among the temperature variables, the BHT plays the main role. In the case of the tenacity, although all the draw ratios and temperatures influence this mechanical property, the tenacity of drawn fibers is primarily governed by the draw ratios. The initial modulus and the specific work of rupture correlate with all the variables except for the FGT. Among them, the second-stage drawing variables have significant effects on the initial modulus. 4 CONCLUSION The results of this investigation suggest that an ANN can be used quite effectively for a prediction of the physical properties of drawn fibers. The ANN approach was better at fitting the measured response in comparison to the regression model. According to the obtained results, it can be seen that, though only a limited number of samples were available for the training and testing, the overall prediction capabilities of the models were good and would be very useful for optimizing the hot multistage drawing process with regard to the time, quality and price. 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