An effective hybrid particle swarm—artificial neural network optimization for predicting green bio-fiber mechanical characteristics and optimizing biomaterial performance

When it comes to the production of novel green bio-products, integration and harmony between distinct green composite ingredients are becoming increasingly desirable traits [1–3]. Composites that have been reinforced with natural fibers are considered as examples of developed composite materials [4–6]. Since natural fibers are more biodegradable than synthetic fibers, the use of natural fibers in an expanding number of different applications, such as automobiles, medical items, pharmaceuticals, power generation, and various other sophisticated technologies, is now being researched as a direct result of the present worldwide emphasis on environmental as well as cost-effective issues [7–9].

As researchers have become more mindful of the environment, more attention has been paid to the suppliers of cellulosic fibers—such as kenaf, cotton, jute, and hemp—since these fibers are used in an extensive range of products and composites [10–13]. In particular, the use of these fibers as reinforcements in polymer composites has garnered this interest [14–19]. Table 1 presents the results of numerous experimental investigations into the mechanical characteristics of the natural fibers.

In fact, numerous aspects influence the tensile mechanical characteristics of natural fibers. For instance, parameters such as cellulose content, fiber diameter, microfibrillar angle, moisture content, and other relevant factors. The incorporation of fibers into a polymer matrix significantly enhances the tensile characteristics of composites due to their superior strength and stiffness. Hence, the impact of the fiber composition on the tensile characteristics of fiber reinforced composites has significant attention and importance among several researchers. Some present studies investigate the impact of hemp fiber content, for example, on the tensile characteristics of the composite materials produced. The tensile strength, when fibers are aligned in the parallel direction, exhibited a peak value of strength as the fiber loading increased [27].

One more illustration: The findings of some experiments showed that an increase in fiber loading led to a rise in the tensile strength of both kenaf and jute fiber reinforced composites. It has been discovered that the values of the tensile strength of natural fiber reinforced composites rose with increasing fiber loading. Because of this, the use of natural fiber in composite materials seems to have a great deal of potential [28, 29].

These composites, on the other hand, showed several technical challenges, such as the low adherence between the reinforcement and the matrix material. These challenges are quite concerning owing to the direct influence that they have on the fiber-matrix interface of the composite and, as a result, the mechanical characteristics of the composite [23, 30, 31]. Therefore, in order to improve the mechanical features of biomaterials, it is of the utmost significance to make an accurate prediction of the mechanical properties of these natural fibers to properly utilize the biomaterials for green bio-products. This is because mechanical qualities can only be discovered by experimentation, and they might differ from one fiber to another. Because of the difficulty of such a prediction, it is necessary to make use of suitable methods, such as the combination of an artificial neural network (ANN) [32] and a particle swarm optimization (PSO) [33, 34]. As with biological neural networks, an ANN consists of a collection of interconnected nodes called artificial neurons [35, 36]. The neuron's output is calculated by applying a non-linear activation function to the sum of its inputs, and each input signal is represented as a real number [37, 38]. As a matter of fact, the ANN is widely used in different fields such as structural engineering, concrete expansion prediction, robotics applications, and composite materials [39–41]. On the other hand, PSO is a top optimization approach, as its application method and algorithm are simple and user-friendly. In addition to that, the global convergence it has; its robustness and accuracy [42–44]. The estimation of the mechanical characteristics of natural fiber–reinforced composite constituents is not getting a lot of scientific attention yet. Because of this, the objective of this study is to develop a method for accurate prediction of the mechanical characteristics of natural fibers by utilizing a combination of an ANN and PSO rather than carrying out any experimental work [45, 46].

This will allow the researchers to improve the choices of natural fibers for biomaterials on the basis of cellulose content, the microfibrillar degree angle, and the diameter of natural fibers, decreasing the duration of the process required to characterize materials experimentally. Equally important, predicting the mechanical characteristics of these natural fibers would dramatically enhance the performance of the natural fiber-based composites, which can result in reducing the amount of energy used during the production of such biomaterials, as well as enhance their overall characteristics to produce more desirable properties with more reliable time–span performance. This, in order, can be seen as a significant attribute that will boost energy efficiency in the transformation of energy into financial revenue, given the measure's potential effects on economies and ecosystems. By way of illustration, the idea behind this work may be used for several areas, including facilities, tools, and company processes, to cut down on energy use. Moreover, the suggested technique would enhance technical assessment of green fibers and establish their application for the future feasible environmentally friendly manufacturing concept as a substitute material that promotes green product fulfillment.

An ANN is a mathematical framework that has been facilitated and motivated by the natural structure and operation of the brain. Transfer function, network layout, and learning rules are the essential elements that must be considered to create a particular ANN model. A multilayered perceptron feed-forward neural network is the most common form of ANN. In this ANN variant, the input layer, the hidden layer(s), and the output layer are all made up of neurons with weighted linkages [37]. Given that the input layer takes information from outside influences, the output layer, having passed the information via the network's hidden levels, returns one or more values. Neurons are the fundamental building blocks of ANNs and are used in the output determination process. In addition, the neuron has the benefit of gathering the inputs from several other neurons, multiplying those inputs by the weights that have been provided to it, and then applying an activation function to the final product before heading on to the next variable. Even though this mathematical procedure may seem straightforward at first glance, an ANN that is capable of doing incredibly difficult tasks may be created by layering enormous neurons in a variety of different configurations. Throughout the process of the training, each signal that was generated by neurons was sent along to the next layer using a log-sigmoid transfer function, which is the function that is most often used to link the hidden and output layers. The mathematical connection that underlies this function is represented by equation (1), which reads as follows:

$$\begin{equation}{\text{logsig}}\left( {\text{n}} \right){\text{ }} = \frac{1}{{1 + {e^{ - n}}}}.\end{equation} \tag{ 1 }$$

In practical applications, the Log-sigmoid neural network is a well-known multi-layer neural network that is trained to positive infinity with the help of the back-propagation technique. This function produces outputs that range from 0 to 1 when the net input of the neurons varies from negative to positive infinity. In general, a qualitative approach in which models (networks) are generated by randomly assigning weights to the connections between neurons is used in ANNs. After that, the real output is contrasted with the outputs of the network in order to draw a conclusion on the output error. The error that was acquired is then sent back across the network, which adjusts the weights for each individual node. However, this process takes time and might produce high errors due to weights–adjusting criteria as random weights are given at the beginning of the process. Optimizing the weight and bias of ANNs employing PSO, which is a worldwide search technique, is made possible as it is considered to boost the performance of ANNs.

PSO is widely regarded as one of the most effective methods for optimizing. This is due to the fact that both its application technique and its algorithm are straightforward and user-friendly. In addition to these capabilities, PSO can achieve global convergence, tremendous robustness, and accurate results. It was created in 1995, and its fundamental tenet is derived from the dynamics of social birds [47]. In the general technique of PSO, particles represent the entire number of any individual that take part in the algorithm according to the language used for PSO. These particles come together to create a population that is more formally referred to as a swarm. PSO gets started off with a collection of random particles, which are referred to as solutions, and these particles are given locations and velocities at random. In this context, locating the best locations and velocities of these particles in a space is the goal is to optimize a solution by either increasing or decreasing a given function throughout repeated procedures. Every particle continues to keep a record of its personal best (best position), sometimes abbreviated as p_best, which is the best outcome it has achieved for itself in an effort to locate a viable solution. On the other side, the global best, often known as g_best, is the most desirable value for any particle (i.e. the best value globally) [48].

According to its current position, its current velocity, the space between the present location and the best position, and how far away it is from its theoretical optimal location, each particle adjusts its position. After then, the p_best and g_best velocities are given an arbitrary weighting in order to offer an updated velocity measurement for this particle. This updated velocity measurement will have an influence on the next position of the particle in the iteration that comes after it [49]. Equations that provide for the possibility of changing the speed at which each particle travels during the whole search are:

$$\begin{equation}{s_n} = w.{s_o} + {j_1}\,{c_1}\,X\,\left( {{P_{{\text{best}}}} - P} \right) + {j_2}\,{c_2}\,X\left( {{g_{{\text{best}}}} - P} \right)\end{equation} \tag{ 2 }$$

$$\begin{equation}{P_n} = P + \,{s_n}.\end{equation} \tag{ 3 }$$

P_n and P exhibit the new and present positions, respectively, just as S_n and S_o indicate the new and current velocities, respectively. The inertia weight is denoted by w and the uniformly distributed random numbers are (j₁, j₂). C₁ and C₂ are predetermined coefficients; P_best is the particle's own personal best position, and g_best is the particle's position in the overall best global position among all the particles.

In order to determine the suitable number of particles (swarm size), a variety of different sensitivity assessments were carried out. For these analyses, a predetermined value of 1.9 was used for both the C₁ and C₂ coefficients, and an iteration number of 800 was established for each model across a variety of particle counts, ensuring that every particle is drawn towards the center (i.e. average) of the p_best and g_best values. In addition to that, If W is equal to one, then the particle's movement is fully controlled by the movement it had before, and it is therefore possible for the particle to continue moving in the same manner. On the other hand, if 0 < W < 1 then such an impact is minimized, which implies that a particle will instead move to other areas in the search domain. Thus, the inertia weight is adjusted such that it is set at 0.50.

Following that, the PSO-based ANN goes through training by using the preliminary weights and biases, also known as the starting location of particles. More specifically, PSO searches for a global minimum in the search space, while ANN makes use of the optimized parameters in order to locate the best results. After then, errors are computed based on the difference between anticipated and actual values. Changing the positions of the particles results in a decrease in the computed errors made at each computation. This method is carried out again and again until it satisfies the termination requirements. For PSO-based ANN models, the ideal number of particles is determined by monitoring the mean square error (MSE) over time and selecting the iteration that produces the optimal number of particles. After a noticeable improvement in network performance for particle counts between 10 and 600, the best results were achieved with swarm sizes of 600, as the MSE is nearly 0.04. The correlation between swarm size and MSE is seen in figure 1.

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It is vital to establish the ideal network design after determining the PSO parameters to get greater performance out of the hybrid PSO-based ANN network, obtaining the desired results. It was previously said that the only thing a PSO can do to an ANN model is altering its weights and biases in order to reduce the amount of learning error. In point of fact, PSO is incapable of configuring the most effective network design. The architecture of the network is made up of the number of hidden layers that are present as well as the number of nodes that are present in each hidden layer. PSO can only modify the weights and biases to reduce the learning error, whereas the network design (the number of hidden layer(s) and the number of nodes in each hidden layer) needs to be set using a method that involves trial and error.

The stimuli model in this work is built using the MATLAB environment to predict the tensile stress and the young modulus. A hidden layer with six neurons is noticed to have a protentional performance. The flowchart depicting the PSO algorithm and the network topology—according to this work—is shown in figure 2.

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The created model has three inputs, specifically the calluses content, fiber diameter, and the microfibrillar angle. On the other hand, the model has a singular output, either the Young's modulus (E) or the tensile strength (σ_t). In accordance with these principles, each signal produced by the neurons is transmitted to the subsequent layer via the Log-sigmoid transfer function, which is deemed suitable for linking the hidden and output layers.

The hybrid particle swarm—ANN optimization—was established to form the prediction models. The work being done here to develop the prediction models is on the based-on data that was gathered via experimentation and is shown in table 1. Here, tensile strength and modulus of elasticity were measured using a hybrid PSO based neural network (PSO-ANN) via MATLAB environment. In line with experimental results from previous studies, as can be seen in the contour plot of peak function values in figure 3, the values that were predicted for tensile strength and modulus of elasticity were rather close to those that were actually measured. In point of fact, the contour plot of peak function values depicted in this figure is representative of both the experimental and projected outcomes.

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This effort has resulted in the creation of a system that has three inputs and two outputs. Figures 4–6 analyze many possible permutations of inputs, with the tensile strength serving as the model's output. It is plain to observe that the outcomes that were anticipated are obviously quite close to the ones that were really achieved experimentally, validating the predicted models created in this work. In addition, visualizing how the predicted data (black dots) are laid out on the experimental surface offers more evidence of the usefulness of this model.

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In spite of this, while the notion of doing research on the tensile strength mechanical property is not impossible, conducting research on the modulus of elasticity appears plausible. All the same, figures 7–9 demonstrate the relationships and validations of the predicted modulus of elasticity and the experimental results in accordance with the input used, which was clearly explained previously.

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In an equivalent way, these figures indicate how close the predicted results are in comparison to the experimental ones, providing another proof of the accuracy that the created model has in this research. However, the above figures suggest that, although there was a slight difference between the predicted and observed values for mechanical features, it is important to investigate all potential sources of error and not dismiss any possibility. Upon examining tables 2 and 3, it can be observed that the PSO-ANN models have shown numerical indications, providing that the tensile strength and modulus of elasticity values are very close to the experimental results. Further, the relative error (RE) is relatively minor, as illustrated in figures 10 and 11.

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RE is computed according to the following formula:

$$\begin{equation}Relative\,Error\,\% = \frac{{\left| {{h_{\text{p}}} - {h_{\exp}}} \right|\,}}{{{h_{\exp}}}}X\,100\,\% .\end{equation} \tag{ 4 }$$

The theoretical value for a mechanical property, represented by ${h_{\text{p}}}\,$, is compared with its experimental value, ${h_{{\text{exp}}}}$.

The prediction for the correlation coefficient R² can be found in figure 12, and it is shown for each linear degree model. With successively high values of R² in both tensile strength and modulus of elasticity, the indicated model moved further to accurately predict the mechanical characteristics. Clearly, the R² values are computed as:

$$\begin{equation}{R^2} = \,\frac{{\mathop \sum \nolimits_{i = 1}^J {{\left({h_{{\text{p}},j}} - {h_{\exp,j}}\right)}^2}}}{{\mathop \sum \nolimits_{i = 1}^J {{\left({h_{{\text{p}},j}}\right)}^2}}} \end{equation} \tag{ 5 }$$

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Moreover, tables 4 and 5 demonstrate the expected values that were derived from simultaneously analyzing all three input parameters in order to adjust the fiber prediction. Random values of these inputs are taken to show strong evidence of the accuracy the model has, where a positive correlation was found between the inputs and outputs. All things considered, and as can be seen from the tables, the proposed PSO-ANN model that has been described here appears to be extremely suited for predicting the type of natural using the contemporaneous hybrid prediction model, as compared with the experimental results arises in table 1.

In reality, the purpose of this research was to determine how useful it would be to include PSO in a neural network framework. However, in order to get to the point of this work, it is crucial to compare the ANN methodology alone without the hybrid PSO-ANN technique, to extra validate the efficiency of this work. To be more specific, the PSO is ignored in the reimplementation of this work. The RE evaluation (figure 13) clearly demonstrates the superiority of the PSO-ANN over the ANN as the most noticeable result of the analysis.

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Due to the global focus on environmental and cost-effective issues, natural fiber—reinforced composites are being used in a wide range of applications. Thus, researchers have paid greater attention to them as they become more environmentally conscious. However, predicting the mechanical characteristics of these composites may be difficult due to issues during manufacturing, such as inadequate reinforcement-matrix adhesion. In view of that, to improve the mechanical features of biomaterials for green bio-products without resorting to time-consuming experimentation, this study introduces a novel, robust hybrid PSO—ANN methodology. The hybrid PSO-ANN is considered a top optimization method since its application method and algorithm are straightforward, robust, and user-friendly. As a matter of fact, there is a high degree of complexity involved in the process of predicting the capabilities of bio-fibers, due to the fact that the mechanical properties of green bio-fibers may vary from one fiber to another as a result of various parameters that interact. Consequently, this study makes use of appropriate methodologies that have a non-linear activation function, making it possible for the researchers to enhance the selection of natural fibers for biomaterials on the basis of the cellulose content, the microfibrillar degree angle, and the diameter of natural fibers. As a result, the duration of time needed to experimentally describe materials may be reduced. The created model is validated by comparing the results of tensile strength and Young's modulus for different types of natural fibers. The model that was projected is capable of reliably measuring mechanical performance with a significant degree of consistency. Precisely, swarm sizes of 600 showed a MSE of nearly 0.04 in both tensile strength and Young's modulus, facilitating the ANN task in determining the initial weights and biases of the network. The reliability of the PSO-ANN model was investigated using yet another descriptive demonstration, which consisted of testing the correlation coefficient. Results produced R-square values that were close to one, which provided evidence that the work was accurate. To further validate the efficiency of this study, reimplementation of the analysis ignores PSO (i.e. performing ANN only). Results showed again that the hybrid PSO-ANN outperformed the ANN in the RE evaluation.

Given the potential impact on economies and ecosystems in predicting the mechanical properties of these natural composites, which may increase energy efficiency in energy-to-financial income conversion, the findings of this study also have the effect of making the researchers' duties of selecting the most suitable natural fiber composites easier. Furthermore, this work's concept can reduce energy usage in facilities, tools, and corporate operations, improving the technical assessment of green fibers and establishing their use as a replacement material for green product fulfillment in future environmentally friendly production.

On behalf of all authors, the corresponding author states that there is no conflict of interest.