Introduction

In the last several years, nanofibers have become a particularly interesting type of nanomaterial and have drawn a lot of interest from researchers. They differ from traditional materials due to their unique properties, which include a notable high surface area to volume ratio, remarkable mechanical strength, and significant porosity. Due to these special qualities, nanofibers are seen as very promising materials with a wide range of uses in several fields such as adsorption, sensing, and catalysis1,2,3,4,5. Alongside the development of nanotechnology, there have been significant advances in the electrospinning process. The development of improved nanostructured materials for nearly every possible application has been greatly aided by electrospinning. Scholars from several regions have made significant contributions to the advancement of electrospinning principles by revealing the potential of this process. Over the last two decades, the number of articles and patents submitted has grown dramatically and continuously, demonstrating significant progress in understanding its principles and applications. By applying high voltage (usually between 5 and 30 kV), this technique makes it easier to produce fine fibers by causing a polymer solution to transfer from a capillary tip to a collector. Electric forces involved in this method break the polymer’s surface tension, causing instabilities that could separate into fibers with a reduced diameter and cause elongation. The subject of nanofiber technology has advanced tremendously due to this technique’s versatility in producing nanoscale fibers from a wide variety of polymeric materials6,7,8,9,10,11,12. While it is evident that electrospinning is an attractive method for creating a wide range of unique micro and nanoscale fibers, there are still certain issues that need to be resolved. A small amount of study has been devoted to modeling, but no widely recognized simulation model has been created that can reliably forecast the needle-based or needleless electrospinning characteristics.

Scientists have been using electrospinning to produce and characterize PVA nanofibers and its blends for several years in order to investigate the effects of the parameters such as the applied voltage and concentration, etc., on the diameter and uniformity of the fabricated fibers. For the purpose of obtaining fibers of the highest quality with the required homogeneity of their shape, the influence of these parameters is still investigated for the most suitable values13,14,15,16,17,18,19,20. Polyvinyl alcohol nanofibers showed a high potential for applications in different areas because they are biocompatible and soluble in water21. Apart from that they are more promising in biomedical application areas like drug delivery systems, wound healing as well as in tissue engineering22. Due to high mechanical strength and flexibility of PVA nanofibers they are useful in reinforcing materials in the modern composites for enhancing the mechanical and functional properties23,24. Furthermore, PVA nanofibers are effective in filtration because of their porous structures, which provide a surety of removing impurities. Besides, PVA nanofibers are versatile to be employed in the sensor applications because the large surface area enhances sensitivity. It is believed that subsequent researches will focus on the development of new composites and additives for PVA nanofibers and their application in different technological fields and for the solution of new tasks25.

Response surface methodology (RSM) and artificial neural network (ANN) are two modeling tools that help identify the complex patterns of factors that impact a process. These modeling strategies reduce the expense and duration of conducting tests while aiding in the knowledge of a process. RSM is a statistical technique that investigates the quantitative relationship between process output and independent factors. RSM can provide a mathematical equation that explains the link between the factors and the response in detail. Artificial neural networks replicate a biological neural system using computer technology and are computational tools for pattern detection26,27. Several studies have been conducted to investigate electrospinning processes utilizing (RSM) and (ANN)28,29,30. ANNs may generate an output for new inputs by learning complicated interactions among inputs through training on a known set of data. This technique has emerged as a novel method for simulating the relationship between the diameter of nanofibers and electrospinning parameters. Neural networks have been used in research which are based on the prediction of electrospun based nanofibers diameter31,32,33,34. For instance, Ming Ma and colleagues proposed an accurate polyacrylonitrile (PAN) nanofiber diameter prediction model employing an ANN trained on diameter and process parameter data obtained from electrospinning35. Moreover, Mohaddessin Sharifi and his coworkers incorporated poly(ℇ-caprolactone) (PCL)/poly (lactic acid) (PLA) with Nigella sativa (NS) extract at different concentration to fabricate novel blend scaffolds using electrospinning. RSM and ANN were employed in the modeling and optimization of PLA/PCL/NS extract nanofibers productions to treat skin wounds. Based on the results, the mean goodness values of the used ANN model were higher than those of the RSM36.

To assess ANNs capability to be used as a forecasting tool in order to estimate the diameter of the fibers produced through electrospinning, a comprehensive study was conducted by Sarkar et al.37. The results of their study showed that the method they used – the neural network approach – is a stable and effective one in terms of accurately predicting nanofiber diameter. In addition, for the first time, Valentinus Galih Vidia Putra and his collaborators used ANNs and adaptive neuro-fuzzy inference systems (ANFIS) in their study to accurately estimate the electrospun PVA/TiO2 fiber diameter38. A diameter estimate for electrospun PVA/CS blend nanofibers was given by Karimi et al.39. In this study they considered four process control variables which include the applied voltage, CS/PVA concentration, temperature, and distance between the collector and the tip of the needle were used to evaluate the feasibility of ANN models for predicting nanofiber diameter. Moreover, the intricate procedure of estimating nanofiber diameter is examined by Kalantary et al.40,41. The authors do acknowledge the intricate relationships that exist between the various influencing parameters and the resulting complexity. In the lack of a comprehensive method, they further emphasize how challenging it is to forecast nanofiber diameter. When it comes to electrospun nanofiber diameter prediction, their study highlights the ANN modeling approach shows a great degree of accuracy in comparison to the results produced by multiple regression analysis. Although several polymers spun fibers have been studied using neural networks, but no effort has been made to model the parameters involved in the electrospinning process for producing standalone PVA nanofiber, which is extensively used in a variety of applications. In this article, we utilized the neural network approach for predicting the diameter of PVA fibers which is not being studied till now to the best of our knowledge. Specifically, we examine five parameters: concentration, flow rate, high voltage, the speed of the revolving collector, and the distance between the needle tip and the collector, to control and forecast the average fiber diameter of PVA. Furthermore, we discuss the proposed ANN model accuracy with the already established model based on RSM and regression reported by Mohamed Elkasaby and et al.30.

Materials and methods

This work attempts to predict the PVA (molecular weight 130,000 g/mol, Sigma-Aldrich) nanofiber diameters fabricated during electrospinning process using an already existing30 experimental dataset of twenty-seven samples. The cabin temperature and relative humidity for the experiment were 23oC and 45%, respectively. Table 1 provides a detailed presentation of the average fiber diameters (FD) (around 100 measurements were made at random for each sample30) and electrospinning parameters for each of the 27 samples. The dataset is composed of one solution parameter namely concentration (B) and four process parameters namely applied voltage (A), revolution per minute (C) of collector, distance (D) between syringe nozzle and collector, and flow rate (E).

Table 1 Data (Inputs and the output average FD resulted)30 used in this study (Copyright © 2017 John wiley & sons Inc.).
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In order to develop a model, which addresses the nonlinear interaction between the above mentioned parameters and the resulted average fiber diameters, using multi-layer perceptron (MLP) algorithm is the main objective this section. Muti-layer perceptron is a type of feedforward artificial neural network (ANN). An ANN is primarily made up of artificial neurons, or nodes, arranged in layers: an input layer, one or more hidden layers, and an output layer. A conventional simplest model for ANN is shown in Fig. 1.

Fig. 1
figure 1

Basic ANN structure. Each colored circle represents a neuron or node.

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In our case, the input layer had five neurons, each corresponding to a process parameter and the output layer had one neuron corresponding to the predicted fiber diameter. The hidden layers composed of a set of neurons linked with all the neurons in the prior layer. Each connection had a weight and each neuron had a bias term associated with it. The input to each neuron is obtained by taking a weighted sum of the inputs from the previous layer, while the output of each neuron in the layer is achieved with the help of activation function, usually, a sigmoid function shown in Eq. (1) utilizes this sum. This enables the model to capture non-linearity that exists in the data set used to build the model.

$$\:f\left(x\right)=\frac{1}{1+{e}^{-x}}$$
(1)

Where \(\:x\) is the weighted sum of the inputs and biases. Furthermore, equation used to calculate the output \(\:{a}_{j}\:\)of a neuron can be written as:

$$\:{a}_{j}=f\left(\sum\:_{i=1}^{n}{w}_{ij}{x}_{i}+\:{b}_{j}\right)$$
(2)

Here, \(\:{x}_{i}\) is the input from neuron \(\:i\), \(\:{a}_{j}\) is the output of neuron \(\:j\), f indicates the activation function, \(\:{w}_{ij}\) are the weights of the connection between neuron \(\:{x}_{i}\) and \(\:{a}_{j}\), and \(\:{b}_{j}\) is the bias term for neuron \(\:j\). In similar way, the predicted output, which corresponds to the fiber diameter (\(\:{FD}_{i})\), was calculated using the same formula applied to the output neuron. To do this the weighted sum of the outputs from the final hidden layer was passed through the activation function of the output neuron to produce the final prediction.

The training of the MLP model was done through the backpropagation technique which is a feedback method for minimizing the difference between the desired and estimated fiber diameter (FD). The error was estimated using Mean Squared Error (MSE) loss function shown in Eq. (3).

$$\:MSE=\frac{1}{n}\sum\:_{i=1}^{n}{({FD}_{i}-{\widehat{FD}}_{i})}^{2}$$
(3)

With backpropagation, the model was able to set the weights and the biases in the network, by propagating the error backwards from the output layer to the input layer and then changing the weights with the gradient descent. The weights \(\:{w}_{ij}\)​ are updated according to the following rule:

$$\:{w}_{ij}={w}_{ij}-\rho\:\frac{\partial\:MSE}{\partial\:{W}_{ij}}$$
(4)

where \(\:\rho\:\) and \(\:\frac{\partial\:MSE}{\partial\:{W}_{ij}}\) represents the learning rate and the gradient of the error with respect to the weight respectively. The learning rate is an important factor in deciding how significantly weights would be changed during evaluation process. In addition to that a momentum term is further incorporated in calculations (see Eq. 5), which aids in speeding up the training process by eliminating fluctuations. Moreover, the model was trained for a number of epochs and each epoch simply means that the model has gone through the training data set once.

$$\:{\varDelta\:w}_{ij}={\alpha\:\varDelta\:w}_{ij}\left(t-1\right)+\rho\:\frac{\partial\:MSE}{\partial\:{W}_{ij}}$$
(5)

Where \(\:\alpha\:\) and \(\:{\varDelta\:w}_{ij}\left(t-1\right)\:\)represents the momentum parameter and the weight update from the previous iteration respectively.

Execution in WEKA

All the computations in this work have been done using WEKA (Waikato Environment for Knowledge Analysis) software, version 3.9.6. The experimental data mentioned in Table 1 is utilized to train the artificial neural network model. Initially, all the 27-observation dataset was imported as CSV data file into WEKA, and the target attribute was chosen to be the output variable i.e., fiber diameter. To enable efficient modeling and assessment using WEKA, the samples are firmly separated into two groups: a training group, and a testing group. Moreover, to ensure a comprehensive analysis of the model’s predictive capability, the entire dataset was resampled and divided into six different combination of train-test splits. Table 2 summarizes the splitting percentage of the training and the testing data of each of the combination used in this work. The division was performed on random basis and both the training and the test sets were a random sample generating from the whole dataset. This procedural approach enabled the understanding of the stability of the model in terms of data distribution.

Table 2 Different percentage of data considered in each sample for training and developing the model.
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After that the required algorithm i.e., MLP was chosen from the “functions” category in the classifier section, and all the parameters of the model were set. As for the six train-test splits, each of them were used, and the model was trained based on the training sets. A trained model was then used to predict the fiber diameters of the test datasets with the ultimate aim of assessing the accuracy of the model. The MLP was tested with different number of hidden layer, number of neurons in each hidden layer, learning rate, momentum, and number of training epoch. From the variety of experiments, it was determined that the best setting for the ANN was two hidden layers with total of 9 neurons (5 in first hidden layer and 4 in the second hidden layer), learning rate of 0.1, momentum value of 0.3, and 1200 epochs. This configuration gave the best prediction when using to calculate the diameter of fiber. We have achieved this network architecture by considering and examining different topologies in ANNs that composed of single and double hidden layers with different numbers of nodes for each layer.

Results and discussion

In this work the electrospinning parameters including the concentration of polymer, distance between the nozzle and collector, flow rate, RPM and the voltage applied, were examined to establish a predictive model for the diameter of PVA fibers. With the help of WEKA, the relationship between these attributes and nanofiber diameter is neatly captured by employing neural network methods. The measures that were employed in order to evaluate the model includes; correlation coefficient (R) and root mean squared error (RMSE)35,42,43. The higher the R value, the greater the ability of the model to identify the interconnection of input parameters and the resulted output, fiber diameter in this case. On the other hand, the RMSE quantifies the overall deviation of the predictions from the actual values, which help us for understanding the model’s accuracy. Weka calculates the value of R as well as the RMSE as a part of the evaluation and therefore allows us to assess the model’s performance from different perspectives. We used both R and RMSE to make sure that the model fits the data well and also that the model can make accurate predictions of fiber diameter on a new or unseen data. Table 3 listed the values of R and RSME obtained from the developed model for all the six different combinations of data used after the training and testing evaluation of the model. The model structure consisted of five neurons in the input layer for applied voltage, concentration, RPM, distance, and flow rate, one neuron for fiber diameter (output layer), and 9 neurons in the two hidden layers having topology 5 − 4 serving as the fitness function.

Table 3 Values of R, MAE, & RSME calculated from five samples used which are separated according to different percentage for training and testing data.
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The best ANN model is opted in a way that it not only gives high value of R and low value of RMSE on the training set as well as on the test set, but we also compare each individual values computed from the succeeded model with the experimental data30 used for all the six samples. So, the best values of R and RMSE is considered for sample 5 (see Table 3, values are highlighted in bold) while pay special care and attention in comparing each of the predicted values of the nanofiber diameter. From Table 4; Fig. 2, one can easily draw a comparison between the experimental30 and estimated (predicted using the model) fiber diameter. The table also shows the difference between the two which presents the error in the value of fiber diameter calculated with the help of Eq. (6).

$$\:Absolute\:Error=\:\left|{FD}_{actual}-{FD}_{predict}\right|$$
(6)
Table 4 Listed the results of actual30 and predicted values using ANN and respective absolute error.
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Fig. 2
figure 2

Plot of experimental results against ANN-based model findings.

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To compare our computed results obtained from the proposed ANN model we used predictive models based on RSM for PVA electrospinning that had been successfully built and reported30. These mathematical models were attempted to provide a direct connection between process responses to aid in the electrospinning process’s optimization. Two different mathematical models were reported that illustrate the overall impacts of different process parameters. Based on the results of an initial analysis of variance (ANOVA) test, the first model was developed. By offering insights into the main variables affecting electrospinning, this model advances our fundamental knowledge of the important variables involved. The developed second model, expands on the ANOVA-based model by exploring the complex interactions between different process parameters. This model provides a broader perspective than the separate analysis of individual parameters since it considers the synergistic effects and interactions between many factors. They used Eq. (7)30 for average model accuracy (AMA) to validate the developed mathematical model. The computations for the first model showed an average model accuracy of 84.34%, whereas for the second model resulted in an average model accuracy of 80%. The model developed using ANN in this study reveals an average model accuracy of 94% and is also calculated by using Eq. (7) which represents a respectable degree of precision and is better than the models developed using RSM. The scatter diagram comparing the expected and actual values is also displayed in Fig. 3. It demonstrates how well the model’s prediction matches the results of the experiment.

$$\:AMA=\frac{{\sum\:}_{i=1}^{n}1-\frac{Abs({FD}_{actual}-{FD}_{predict})}{{FD}_{actual}}}{n}$$
(7)
Fig. 3
figure 3

The ANN model scatter graph showing anticipated versus experimental30 values.

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Figure 3 is further providing an evidence that the established ANN model demonstrated a good degree of fit with a fit coefficient of 0.993, 0.8857, and 0.973 on the training set, testing set, and the entire data set respectively. Since the output value and target value fit curves are quite well, suggesting that the developed ANN model has good prediction power.

Conclusion

In general, the type, composition, and electrospinning process parameter determine the qualities of the nanofibers. Neural network techniques are utilized in this study to estimate the diameter of polyvinyl alcohol nanofiber from electrospinning parameters, namely, applied voltage, nozzle-collector distance, polymer concentrations, RPM, and flow rate. The neural network predicts the diameter with an average model accuracy of 94%. The acquired data show that neural network performance surpasses that of regression method.