Machine learning in optimization of nonwoven fabric bending rigidity in spunlace production line

Spunlace nonwoven fabrics have been extensively employed in different applications such as medical, hygienic, and industrial due to their drapeability, soft handle, low cost, and uniform appearance. To manufacture a spunlace nonwoven fabric with desirable properties, production parameters play an important role. Moreover, the relationship between the primary response and input parameter and the relationship between the secondary response and primary responses of spunlace nonwoven fabric were modeled via an artificial neural network (ANN). Furthermore, a multi-objective optimization via genetic algorithm (GA) to find a combination of production parameters to fabricate a sample with the highest bending rigidity and lowest basis weight was carried out. The results of optimization showed that the cost value of the best sample is 0.373. The optimized set of production factors were Young’s modulus of fiber of 0.4195 GPa, the line speed of 53.91 m/min, the average pressure of water jet 42.43 bar, and the feed rate of 219.67 kg/h, which resulted in bending rigidity of 1.43 mN \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{cm}}^{2}$$\end{document}cm2/cm and basis weight of 37.5 gsm. In terms of advancing the textile industry, it is hoped that this work provides insight into engineering the final properties of spunlace nonwoven fabric via the implementation of machine learning.


Artificial neural network
Nowadays, artificial neural network (ANN) as an advanced procedure of modeling is enormously applied in the engineering of materials and processes.Furthermore, the fitness of artificial neural networks is much higher than regression models if a complex relationship between variables exists.Using a feed-forward back-propagation learning algorithm, any function with any degree of complexity can be estimated.The precision of such networks is increased when a single output is considered [57][58][59][60][61][62][63] .In this work, four parallel feed-forward back-propagation networks for primary responses including basis weight ( W ), thickness ( T ), number of couples ( C ), and fiber orientation angle in the MD direction ( O ) with the similar topology of four, five, and one nodes in the input layer, hidden layer, and output layer, respectively, were developed.Moreover, another feed-forward back-propagation network with the same topology for secondary response (bending rigidity in the MD direction ( B )) was built.Table 1 summarizes the value of hyperparameters that were undertaken for different networks.
During the development of the network, the best combination of hyper parameters was selected based on the procedure used by Refs. 55,56,64,65.Moreover, the MATLAB toolbox was used to implement such networks. (1) Table 1.The parameter settings of different networks.

Genetic algorithm
There are various methods of optimization such as the golden section search (GSS) method, sequential quadratic programming (SQP) method, genetic algorithms (GAs), particle swarm optimization (PSO), ant colony optimization (ACO), and gray wolf optimizer (GWO), composite desirability function (CDF), and self-learning batch-to-batch optimization (SLBBO) method.All of the mentioned methods can be coupled with any function to perform optimization.In a condition where an ANN is applied, they are the only choices because differentiation cannot be employed [66][67][68][69] .Due to simplicity, GA was utilized to perform multi-objective optimization.The purpose of optimization was to achieve the maximum bending rigidity in the MD direction while keeping basis weight at a minimum.Thus, the cost function was constructed as Eq. ( 3).
where − → x and − → v are vectors of the candidate solutions with four primary responses and vectors of the candidate solution with four independent parameters, respectively.It is worth mentioning that terms belonging to the normalized bending rigidity in the MD direction have more weight (0.6) than normalized basis weight (0.4) due to the importance of the parameters in end-use.Besides, the optimization was conducted in a way to obtain a fabric with the highest bending rigidity and lowest cost.In fact, nonwoven fabrics are sold based on fiber types and the basis weight.So, the basis weight acts as a function that lowers the total cost of fabric.During the optimization step, the constant settings as brought in Table 2 were used for GA under MATLAB software.Figure 1 illustrates the whole algorithm developed in this work to seek out the combination of production parameters to obtain a nonwoven fabric with maximum bending rigidity and minimum basis weight.In this algorithm, after training networking for primary responses via experimental data and paralleling them together, a network is trained for secondary response using corresponding experimental data.In the next step, the cost function is formulated and coupled to the GA.When the cycle is complete, the GA creates a new individual and recalls the networks of primary responses.Then, the outputs are fed to network of secondary response.Finally, the cost function is evaluated and the stop criteria are checked by GA.Under the condition that stops criteria are satisfied, the best combination as the best individual is presented by GA.

Statistical results
The mean value of primary and secondary responses for 30 samples is outlined in Table 3.According to the physics of the problem, when a sample possesses a higher basis weight (W), higher thickness (T), a higher number of couples (C), and higher fiber ordination distribution along the bending axis (O), more bending rigidity (B) will be achieved.Overall, a similar effect as the physics of the problem can be found in the data.However, there is some violations in data due to using different types of fiber.
Speaking of modeling via either RSM or ANN, it is favorable to avoid the redundancy of input variables of models.In fact, when there is a linear correlation between the input parameter of a model either positive or negative, multicollinearity has occurred which can make a negative impact on the accuracy of the model 51 .As can be (3) seen in Fig. 2, low collinearity can be found between primary responses.Thus, elimination was not required for further steps.For elimination purposes, [− 0.9, 0.9] was considered a safe domain of correlation.

RSM-based models
Table 4 provides an overview of the RSM-derived models created for both primary and secondary outcomes.The primary responses are determined by control parameters, while the input parameters for secondary responses are based on the primary outcomes.Figure 3 compares the normalized value of predicted and experimental values for different responses.It can be seen that there are deviations between predicted and experimental values in all cases.This demonstrates that a relationship with a higher degree of nonlinearity lies among variables.Thus the developed RSM-based models are not reliable.
To compare the predictability of RSM-based models, the total goodness value which is the summation of the goodness value of training and testing steps multiplied by their corresponding data fraction that goodness value itself is the summation of the coefficient of determination and means the squared error is shown in Table 5.The ideal value of total goodness when the model is completely fit is 2. According to the information, the highest (1.9732) and lowest (1.8840) total goodness value was owned by basis weight and thickness, respectively.

ANN-based models
Figure 4 shows the topology of networks trained for four primary responses ( W , T , C , O ) and a secondary response ( B ).As can be observed, four parallel feed-forward back-propagation network was trained in which production factors ( Y , L , P , F ) were the input parameters.Moreover, the output of four primary responses was fed to a network of secondary responses to result in bending rigidity.Surprisingly, all networks got four, five, and one node in their input, hidden, and output layers, respectively.
To provide information to build such networks mentioned above, weight and bias values are summarized in Tables 6, 7, 8 and 9 for primary responses and Table 10 for the secondary response.
To assess the performance of the network trained for various responses, predicted and experimental values were plotted as shown in Fig. 5.It is evident that the network was trained with a high performance of predictability.This means that they are able to perfectly map from input parameters to output ones.However, a few points of settlements were detected which are negligible.
To verify the better performance of networks compared to RSM-based models, a quantitative analysis of total goodness value is carried out.Table 11 demonstrates that all networks owned a total goodness value close to the ideal one (2).In fact, the high total goodness value indicates that the weight and bias values are adjusted perfectly.
In order to specify the contribution of each input parameter in every network trained for prediction, Eq. ( 6) was used.
where V and W are weights acting between the input layer and hidden layer and between the hidden layer and output layers, respectively.Parameters n I and n H indicate the number of nodes in the input layer and hidden layer, respectively.Figure 6 depict the results of sensitivity analysis conducted based on Eq. ( 6) for primary and secondary responses.According to Fig. 6a, it is clear that pressure (46%) makes the highest impact in the case of number of couples, while the most effecting node in network developed for thickness is line speed (43%).Turning to orientation at MD direction (29%) and basis weight (38%), it can be found that feed rate has the highest www.nature.com/scientificreports/contribution in both cases.In the case of secondary response, the network is mostly effected by basis weight (43%) than other primary response as shown in Fig. 6b.

Optimization results
When optimization was performed via GA, the trend of reduction of cost value was observed as shown in Fig. 7.
As can be seen that diversity of the constructed GA was high enough to avoid early convergence.Moreover, as more generation was created, the distance between best and mean value declined.At the end of the optimization, 0.0731 was the lowest cost value that resulted from Eq. ( 3).The way that GA reduced the cost value is by creating new combinations of production factors as new individuals and then calculating the primary and sequentially, secondary responses.Finally, when the cost value of the individuals is computed, the lowest one as the best individual is reported.
To consider the similarity and differences between optimized and optimum samples, production factors, primary responses, and secondary responses of them are summarized in Table 12.As it can be found that Young's modulus of the optimized sample is lower than the optimum one while line speed and pressure were kept almost constant.Meanwhile, the feed rate of the optimized sample also went from 335 to 219.67 kg/h.Physically speaking, Young's modulus of 0.4195 GPa indicate the viscose fiber which is more flexible than polyester (0.6870 GPa).As Young's modulus of fiber lessens, its bending rigidity of it diminishes.So, at the constant line speed and pressure, more entanglement of fiber could be obtained.This will result in higher bending www.nature.com/scientificreports/rigidity of the final product due to considerable cooperation of fiber under bending moment.In addition, the reduction of feed rate directly affects the basis weight.Besides, when a lower feed rate is set, the fiber has more opportunity to be entangled under water jet pressure.In other words, a reduction in feed rate increases the bending rigidity of nonwoven fabric.However, a low amount of feed rate is possibly having a negative effect on the bending rigidity of nonwoven fabric.To wrap it up, there is a feed rate that leads to the highest bending rigidity in which the negative effect and positive effects are balanced.With regard to the primary response, it can be said that the basis weight due to the lower feed rate was significantly reduced from 48 to 37.5 gsm.Consequently, the thickness witnessed a reduction from 0.59 to 0.39 mm.Furthermore, the number of couples turned down from 1.04e+05 to 4.47e+04 because of the lower number of fiber acting within the fabric.In the case of fiber orientation disruption, a slight reduction was found (from 67.88 to 62.82%) which is the result of lowering the given time and applying force to fiber to orientate themselves along the machine direction according to the new combination of production factors.Ultimately, it can be seen that the bending rigidity of nonwoven fabric optimized by GA was close to the optimum sample while the basis weight was reduced.This brings about a cost value of the optimized sample lower than the optimum one.
In terms of perdition, it can be seen that prediction value regarding primary response was close to the experiment ones, whilst predicated cost value underwent an unacceptable difference.The driving force behind this could be the information data provided according to the design of the experiment.It is obvious that if a higher number of combinations were undertaken during the designing of the experiment, more information would be provided for the network.However, the high cost and time-consuming of taking more combinations limit the domain of work.

Conclusions
By way of conclusion, in this work, a systematic study on mechanical and physical properties of spunlace nonwoven fabric was carried out to acquire information to train experimental-based methods such as artificial neural network and response surface methodology.Next, an optimization problem to achieve the highest bending rigidity and lowest basis weight of the nonwoven fabric was defined using a genetic algorithm.The results are as follows: Response surface methodology not only is an effective procedure to collect data for modeling via experimental-based methods, but it also is capable of constructing a regression-based formula for prediction purposes.However, the performance of models developed by response surface methodology was not high enough.Thus, they have not been used in this work.www.nature.com/scientificreports/An artificial neural network as a modeling tool has the capability of creating experimental-based models with a high performance of predictability (R 2 = 1).Its performance is much better than the response surface methodology based on the total goodness value obtained for different variables.The genetic algorithm as an optimizer provides a combination of production factors (Young's modulus of fiber of 0.4195 GPa, the line speed of 53.91 m/min, the average pressure of water jet 42.43 bar, and the feed rate of 219.67 kg/h) which leads to a sample with higher bending rigidity (1.43 mN cm 2 /cm) and lower basis weight (37.5 gsm) compared to the samples fabricated accordant to the design of experiment.

Materials and experimental design
To produce nonwoven fabric with different types of fibers, three kinds of fiber including polypropylene (PP), viscose, and polyester (PET) were sourced from Nikoogroup company.The Characteristics of fibers are summarized in Table 13.
To design an experiment, four independent parameters according to Table 14 namely called Young's modulus with three levels (0.1820, 0.4195, 0.6872 GPa ), line speed with three levels (50, 56, 60 m/min ), the average pres- sure of water jet with three levels (38, 43, 48 bar ) and feed rate with four levels (205, 270, 335, 400 kg/h ) were selected as control variables.
Using Design-Expert 13 software to reduce the total number of samples, 30 combinations of independent parameters under the I-optimal type of central design of the experiment (CDOE) with a quadratic model based on randomized subtype without any blocks with 15 additional model points were determined as shown in Table 15.In addition, the training and testing datasets were shuffled by the randomized selection method with a split ratio of 27:3 for further steps.

Fabrication method
Samples were fabricated via two sequential carding where an ANDRITZ Perfojet machine with a water jet was installed under a temperature of 32 °C and humidity of 40%.According to Table 15, through feeding different types of fibers with various values of line speed, pressure, and feed rate, a variety of samples were produced.Figure 8 demonstrates the schematic illustration of the production line.

Characterization methods
Fiber diameter was measured via Scanning electron microscopy (SEM, XL30-SFEG Philips, Japan) and utilizing Digimizer software in 100 points.Having determined the weight with a dimension of 10 × 10 cm 2 and 15 repeti- tions for each sample, the basis weight was specified.Relying on ASTM D 5729-97 test method, the thickness of samples was measured 15 times using Shirley digital thickness tester.Number of fiber was defined according to volume of fiber ( V f ) occupied in a fibrous layer with a volume of V as below where A , d f , and l f refer to the effective area of the layer, the diameter of the fiber, and the mean length of the fiber, respectively.When a fibrous layer undergoes a bending moment, the fibers also witness bending moments.Meanwhile, fibers that are positioned on each other creating contact points, are building a multi-region couple of moments as shown in Fig. 9a.Considering the number of contact points and a number of couples, it can be seen that number of contact points is one unit less than the number of couples ( C).Thus, the formula derived by Komori and Makishima was used to estimate the number of fiber-to-fiber contact points and obtain the number of couples acting during the bending loading condition 71 .( 7)

Figure 3 .
Figure 3. Performance of different RSM-based models during training and testing steps.(a,b) Basis weight,(c,d) thickness (e,f) number of couples, (g,h) orientation at MD direction, and (i,j) bending rigidity at MD direction.

Figure 4 .
Figure 4. Topology of developed networks for primary and secondary responses.

Figure 5 .
Figure 5. Performance of different ANN-based models during training and testing steps.(a,b) Basis weight, (c,d) thickness, (e,f) the number of couples, (g,h) orientation in the MD direction, and (i,j) bending rigidity in the MD direction.

Figure 7 .
Figure 7. Performance of GA during optimization.

Figure 9 .
Figure 9. Fiber deformation under a multi-region couple of moments.

Table 2 .
Parameter settings of GA.

Table 3 .
Mean value of primary and secondary responses.

Table 4 .
RSM-based models for different responses.

Table 5 .
Quantitative comparison of RSM-based models.

Table 6 .
Weight and bias values of the ANN model of basis weight.

Table 7 .
Weight and bias values of the ANN model of thickness.

Table 8 .
Weight and bias values of the ANN model of number of couples.

Table 9 .
Weight and bias values of the ANN model of orientation at MD direction.

Table 10 .
Weight and bias values of the ANN model of bending rigidity at MD direction.

Table 11 .
Quantitative comparison of ANN-based models.

Table 12 .
Comparison between production factors, primary response and secondary response value of optimized and optimum samples.

Table 13 .
Characteristics of materials.

Table 14 .
Independent parameters and their boundaries.

Table 15 .
Combination of independent parameters.