Study of improved quantum particle swarm optimization for modeling of wasted surgical mask

Abstract

Keywords: Artificial Neural Network (ANN); Improved Particle Swarm Optimization; Parametric Optimization; Plastic Board

Introduction

The daily applications of plastic polymers have a number of good effects in society, but the microplastic (MP) particles linked with the plastic era have health and environmental issues [1]. Multiples of the research on plastic polymers have been carried out, some of which are highlighted in this section. In late 2019, the outbreak of the COVID-19 pandemic resulted in a surge in the use of using single-use personal protective equipment (PPE), in particular surgical masks [2,3]. Consequently, there is increasing concern about the manner in which these masks are to be disposed of since they are disposed of in improper ways, a factor that will lead to environmental degradation. Surgical masks are usually crafted in the form of non-woven polypropylene, and their property may come in handy during waste sorting and management. [4,5]. Numerous works were devoted to measuring the effectiveness of various ways of using surgical masks in an environmentally friendly way. Such practices involved burning, landfill dumping, as well as sterilization before disposal in an effort to reduce the possible risks [6]. Other scholars investigated the possibility of recycling surgical masks to extract useful resources from them, e.g., polypropylene. The building materials and textiles, among other items, were made using the materials of masks. The research into the ways of reclaiming and reusing those materials may help to save resources and lower the volume of waste [7,8]. Researchers investigated the biodegradability of surgical mask materials in light of the trend toward more sustainable waste management practices. Some studies have assessed the potential for incorporating surgical mask components into composting processes, considering their biodegradable properties under specific conditions. Few studies investigated the potential of developing biodegradable surgical masks using sustainable materials. These masks could help alleviate the environmental impact associated with traditional single-use masks [9,10]. Other new avenues that have been researched are novel technologies of transforming used surgical masks into energy or other useful products via things such as pyrolysis or gasification. The polypropylene has a high percentage of energy content which in turn could be utilized by controlled incineration which may serve as an extra energy source to the waste-to-energy facility [11,12]. Although surgical masks are traditionally used in health care facilities to prevent infections, uses in waste management are also discussed in the context of sustainability as a whole. Whiteboards, writing boards, chalkboards or marker boards are typical learning tools that are used in brainstorming, presentations and creativity. The choice of the right writing board material is important so that it needs to be long-lasting and functional. Writing boards WBs are available in different materials so that each has different characteristics. Melamine boards: This type is composed of a paper surface infused with resin on a fiberboard and consists of a core; the boards are cheap yet tend to be stained and ghosted; the

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durability of the boards is decent and good enough to use in mild and moderate activities [13,14]. Porcelain steel boards or ceramic steel boards are created by gluing porcelain enamel on a metal surface, making it highly strong, hard, and removable. And, they do not get scratched or soiled, and can be used in heavy-duty and strenuous environments like schools [15,16]. Toughened safety glass in the form of tempered glass boards has a smooth appearance, excellent erasability, and great durability, albeit being likely to break when hit [17]. Acrylic boards are lightweight and a low-cost alternative that has proper erasability and average durability, but can be easily scratched and stained. The mechanical properties of these materials play a significant role in their performance. Hardness influences scratch resistance, with porcelain and glass being highly resistant, while melamine and acrylic are more vulnerable. Durability is best in porcelain and glass due to their robust nature, with melamine and acrylic being less so. Erasability is better in porcelain and glass; however, melamine and acrylic boards can stain and ghost. Impact resistance varies, with glass being the weakest and porcelain and melamine being the strongest [13-16]. An NP-complete problem is the modeling of plastic boards employing waste surgical masks as the key concern for minimizing plastic waste as part of solid waste power consumption [18]. The transmission of thermal energy is also associated with the other dimension of the research on nanofluids. Ahmed et al. [19] examined the dynamics and behaviour of gyrotactic microorganisms in magnetohydrodynamic (MHD) Eyring-Powell nanofluid flow with a focus on the influences of thermal radiation and Darcy-Forchheimer relation. The study will add to the knowledge of bioconvection in the behavior of fluids in different applications. Faizan Ahmed et al. [20] indicated the importance of the flow of bioconvection in tangent hyperbolic nanofluids, especially on the minimisation of entropy. The study is critical in the use of this in biomedical engineering and thermal management systems. Faizan Ahmed et al. [21] highlight the importance of the bioconvection flow in the tangent hyperbolic nanofluids, especially in the entropy minimization. The study is critical in the use of this in biomedical engineering and thermal management systems. Ali et al. [22] investigate the role of bioconvective studies in tangent hyperbolic nanoliquids and highlight the possibilities of improving energy systems with the mentioned property. The study is critical in explaining how nanofluids may enhance the thermal management of different processes. In bioconvection on a stretching sheet, Puneeth et al. study the thermal properties of Ree–Eyring nanofluid [23]. The study is notable because it is based on prior literature on non-Newtonian fluids and bioconvection, offering information on the heat transfer. Ali and Zaib [24] analyse the erratic flow of Eyring-Powell nanofluid near a stagnation point following a stretched sheet that has gone through convective heating. This study plays an important role in determining how the non-dynamism of nanofluids is in thermal use [24]. Ali

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and Summayya [25] investigate numerical simulation of the Cattaneo -Christov theory of double-diffusion in MHD Eyring-Powell nanofluid with the emphasis on the effects of thermal radiation at a stagnation point. This research is significant in understanding fluid dynamics under complex thermal and magnetic influences. Back propagation neural network (BP) is a form of artificial neural network that can, however, without any knowledge of the relationship between the input and the output data, simulate any non-linear or linear functional link [18, 26]. Nonetheless, BP has many drawbacks, such as long time calculation, slow convergence, and the risk of local minima. As a result, a range of hybrid optimization approaches based on global optimization algorithms were developed to increase the generalization ability of artificial neural networks [27,28]. However, because PSO is limited in its search power, it may become imprisoned in the local optima of the objective function when used to pick ANN parameters [ 29-31]. In 2004, a new variant of particle swarm optimization under the name quantum-behaved particle swarm optimization method was proposed [32]. Furthermore, simulation results of a variety of complicated benchmark functions revealed that QPSO outperforms the standard PSO in terms of global searching capabilities [33,34]. As a result, QPSOs are commonly utilized to tackle difficult optimization issues such as hydrothermal scheduling and economic dispatch [35,36]. However, there have been a few reports regarding employing QPSO for artificial neural network parameter calibration. To enhance the capacity for generalization and computational effectiveness of artificial neural networks, this study develops a hybrid approach for daily reservoir runoff forecasting. The QPSO algorithm is selected as the neural network’s training algorithm to improve the accuracy of hydrologic forecasts. The use of Gaussian and differential sequences in GQPSO and DQPSO improves premature convergence to local optima observed in QPSO performance. However, the objective of this paper is to find out the optimum, efficient, and accurate estimate of manufacturing plastic board parameters such that two different benchmark functions, namely Elongation at fracture (EF) and Percentage of total elongation at maximum force (MF) are minimized. For this purpose, we have used an artificial neural network (ANN) based linear equation that was optimized by using Particle swarm optimization and its different improved versions of PSO. Briefly, the contributions of this research are as follows: • Implement the linear model using an artificial neural network with input-output parameters of the plastic board using a waste surgical mask. • To optimize material composition using ANN via comprehensive fractional design based on process modeling. • Using PSO and its three upgraded PSO approaches, the impacts of the input variables (polypropylene (PP), Maleic anhydrite Grafted polypropylene (MA), Titanium dioxide (TiO2), and Tensile Strength (TS))

on two responses (Elongation at fracture (EF) and Percentage of total elongation at maximum force (MF)) were explored and optimized. The remainder of the paper is organized as follows: Section 2 discusses the materials and techniques of the current study, followed by Section 3, which describes Neural network modeling and characteristics of various advanced PSO for continuous optimization. Section 4 discusses nonlinear model optimization strategies. Section 5 presents the results of the optimization and compares the methods of solving case studies of engineering troubles. Lastly, Section 6 will provide a conclusion to the paper.

Materials And Method

Initially, discarded surgical masks undergo a cleaning process and are subsequently shredded into small fibrous components. The masks, PP, and TiO2 are then blended using various mixing ratios utilizing a Sigma blade mixer from Brabender, Germany. This blending operation lasts 5 minutes at a temperature of 180°C, with MA-g-PP acting as the compatibilizer. Subsequently, the composite material undergoes compression molding at a temperature of 160°C and is maintained for 5 minutes to achieve the intended thickness. Finally, tensile testing samples are taken from the molded sheet having a 30mm gauge length, 4.31mm width, and a thickness of 1.85mm (approx.). Tensile tests are carried out with a tensile testing instrumentfollowing ASTM D638and three specimens for each different composition. Throughout all scenarios, the strain rate is kept constant at 50mm/min. Figure 1 depicts the experimental approach of the current study, whereas Figures 2 and 3 depict the results of the process. Table 1 shows the input parameters and their ranges.

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Mathematical Modelling

Table 1. Range of input parameters Process Parameters (Variables)

Neural Network Model for Elongation at Fracture (EF) and Percentage of Total Elongation at Maximum Force (MF) From the experimental work, it has been observed that there is a certain linear relationship between process input variables, Polypropylene (PP), Maleic anhydride Grafted Polypropylene (MA), Titanium dioxide (TI), and Tensile Strength (TS), with output variables Elongation at Fracture

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(EF) and Percentage of Total Elongation at Maximum Force (MF). Now, the fitness function (FF) of improved versions of PSO for this work is the obtained regression equation of Elongation at Fracture (EF), and Maximum Force (MF), which is a function of Polypropylene (PP), Maleic anhydride Grafted Polypropylene (MA), Titanium dioxide (TiO2), and Tensile Strength (TS). A simple Neuron with no buried layers represents a linear function. As a consequence, it is possible to write it as FF= EF = f1 (PP, MA, TI, TS)

The objective is to determine the best condition (optimal values of PP, MA, TiO2, and TS) to minimize the value of EF and MF. During the mathematical formulation of the ANN model using input and output variables, Polypropylene (PP), metal removal rate (MA), Titanium oxide (TiO2), and TS are kept in input nodes, whereas Elongation at fracture (EF) and Percentage of total elongation at maximum force (MF) are output layer nodes of the ANN model. Therefore, the dimension of the search for an improved version of PSO is 5. The weights w1,w2, w3, w4 re-applied to the three inputs, while the bias term β is assigned to the output node. The absence of an activation function is not a classification issue in this circumstance. As a consequence, using a neural network model, Elongation at fracture (EF) and Percentage of total elongation at maximum force may be stated as follows

the particle’s journey. In Newtonian mechanics, the particle proceeds following a predetermined course, but this is not the case in quantum mechanics. The word trajectory has no significance in the quantum realm since xi and vi, of a particle, following the uncertainty, exhibits quantum behavior, the PSO algorithm is bound to behave differently [26]. Instead of position and velocity, the state of a particle is expressed by wave function ψ(x, t) (Schrödinger equation) [27] in the quantum form of a PSO termed QPSO. The probability of the particle occurring in location xi from the probability density function ‖ψ(x,t)‖2 [28]. When applying the Monte Carlo technique, the particles move in accordance with the iterative equation [28-30]. Its position xi(t + 1) may now be computed using the following equation: (6) where b is a contraction-expansion coefficient, u is a design parameter, and k [38] are values created using uniform probability distribution functions in the range [0, 1]. Mean Best (Mbest) The population’s global point is defined as the mean of Pbest locations of all particles (7) The best particle index by “g” among all the particles and a local attractor of PSO convergence has the following coordinates: (8)

(3) (4) Now we have to determine the most optimal values for the weights and bias parameters in equations 3 and 4. We employed particle swarm optimization and its improved version to optimize the ANN model implemented for two response variables, EF and MF, respectively. The proposed NN model was created using training datasets gathered through experiments. Proposed algorithms are used to find the coefficient of w1,w2, w3, w and β So that squared error should be minimum [37-39]. (5) Where t and c are the targets and estimated outputs from the training data, and E is the objective function. Quantum Particle Swarm Optimization (QPSO) Evolutionary Strategy in Process Modelling In classical mechanics, a particle is represented by its location vector xi and velocity vector vi, which defines

Quantum-Behaved Particle Swarm Optimization Using Gaussian Mutation (GQPSO) Uniform probability distribution is a method that most commonly produces random numbers. However, another new technique can be used to update the PSO velocity by the use of Gaussian, Cauchy, and exponential probability distributions [35]. In GQPSO, we offer a mutation operator in QPSO using a Gaussian probability distribution. For the stochastic coefficients of GQPSO, generating Gaussian distribution sequences with zero mean and unit variance abs [N(0,1)] may provide a good compromise to move away from the current point and escape from local minima (Table 2). These novel QPSO techniques in conjunction with the mutation operator are as follows: Approach 1: Update the positional vector with the following equation: (9) where G = abs (N(0,1)).

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Approach 2: Update the parameters c1 and c2 by the following equation: (10) Where, g =abs [N(0,1)]. Approach 3: This approach uses Eqn. (9) and (10)

Optimization Of Mathematical Model

Table 3 represents the basic parameters of PSO and quantum-inspired PSO. In this section, three linear NN model response variable equations (Eqn. 11- Eqn. 18) optimized by PSO, QPSO, DQPSO, and GQPSO& finally obtained the co-efficient (shown in Table 3) & their response variable equations respectively. To execute this algorithm, we used MATLAB 2013A with processor specification 11th Gen Intel(R) Core (TM) i5-1155G7 @ 2.50GHz 2.50 GHz.

As the algorithms are heuristics so there is a chance that in every iteration it produces a different fitness value, for this reason, we run each algorithm 10 times with several iterations taken 1000, 2000, 3000,4000 & 5000 respectively, and all values are taken as average from the outcomes. Model Validation on Testing Dataset Table 5 & Table 6 represent the average computational time for all the algorithms during cross-validation & RMSE. Where, accuracy in % = (100-RMSE) in %. Response variable equation obtained after the optimization of NN model representing by the following equations: (EF)DQPSO-ANN = -0.3792*PP – 0.3391*M + 7.0282*TI – 0.0381*TS + 15

(EF)GQPSO-ANN = -0.42166*PP – 0.4109*M + 15*TI – 0.02200*TS + 12.832

Table 2. Flow chart of the proposed ANN-GQPSO-based method Preparation

Set the GQPSO to maximize iterations and population size Divide the total data into training and validation sets Define the transfer function of neurons Both the training and validation datasets are normalized Encode each particle by the initial connection weights vector and the thresholds vector of the ANN

Start the evolution from the 1st generation Randomize a fixed population of different individual networks (weights of all connections & initial threshold)

Construct a network with the corresponding particles one by one. Input the training & testing data into each constructed network Compute the values of the objective function for all networks Update the best-known position of each and the whole population Calculate the mean best position of the whole population Calculate the contraction-expansion coefficient Reproduce the subpopulation by updating the particle swarm position

Maximum iteration reached if yes go to Step 3 Otherwise, increase the maximum iteration by 1 & go to the next Step The optimal model is obtained The forecast value is obtained Stop

Global Learning Coefficient, c2 =2.0; No. of Populations: npop=100

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Table 4. Coefficient of NN model of response variable Name of the algorithms

Coefficients of the NN model after Elongation at Fabrication (EF) Optimizations w1

Gqpso

NN model coefficients after optimization of Percentage of total elongation at maximum force (MF) w1

Gqpso

Table 5. Time required to compute both objective functions maximum force elongation facture and percentage of total elongation Name of algorithm

Gqpso

Table 6. Model accuracy of testing dataset Name of algorithm

Gqpso

(MF)PSO-ANN = -0.0069*PP – 0.0109*M (15) + 0.4213*TI + 0.0411*TS + 0.3216 (MF)QPSO-ANN = -1.1755*PP – 1.5437*MA (16) + 0.2425*TI – 1.1315*TS + 3.1451 (MF)DQPSO-ANN = -0.3865*PP – 0.3163 *M + 5.7625*TI – 0.1528*TS + 15 (MF)GQPSO-ANN = 0.3705*PP + 0.3077*MA – 5.1539*TI + 0.2437*TS – 15

Figure 4 and Figure 5 shows the deviation characteristics of PSO-ANN, QPSO-ANN, DQPSO-ANN & GQPSOANN algorithms for both the response variables Elongation at fracture (EF) and Percentage of total elongation at maximum force (MF). Figure 6 represents the objective function of all the algorithms during model validation.

Result And Discussion

All the techniques are simulated using MATLAB 2015a in a computer with 16 GB RAM, Processor11th Gen Intel(R) Core (TM) i5-1155G7 @ 2.50GHz, 2496 Mhz, 4 Core(s), 8 Logical Processor(s) and Windows11 Operating System.

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Figure 4. A comparative study based on Elongation at fracture (EF).

Figure 5. Comparative study based on and percentage of total elongation at maximum force (MF).

Cross-validation of Model This part compares four computational models, PSOANN, QPSO-ANN, DQPSO-ANN, and GQPSO-ANN to determine the best-fitting model based on 16 experimental datasets. To do this, each set of input variables is entered into Eqn. 11-14 to determine the response variables of Elongation at fracture (EF) and Percentage of total elongation at maximum force (MF). The cross-validation comparison research for EF and MF is given in Figures 1 and

2. Table 6 depiction clearly shows that the GQPSO-ANN

model outperformed other upgraded PSO-ANN models. Another significant aspect of determining the optimum optimization model is computational time. Model Prediction Based on Improved PSO-ANN Model validation is done in this portion for 10% of the experimental dataset (2 experimental data). Table 5 compares model validation between PSO-ANN and three

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Gqpso

upgraded PSO-ANN procedures (QPSO-ANN, DQPSOANN, and GQPSO-ANN). According to the results, the average RMSE for GQPSO-ANN in response variables EF& MF is much lower. Optimal Condition for ANN Based Model According to the preceding section, GQPSO-based ANN beat the other three optimization models in cross-validation and model prediction. In this phase, the best conditions for proper modeling of manufactured plastic boards are determined by searching for optimal values of polypropylene (PP), Maleic anhydrite grafted polypropylene (MA), Titanium dioxide (TiO2), and tensile strength (TS), such that elongation at fracture (EF) and percentage of total elongation at maximum force (MF) ismaximized. A new fitness function (OF) is defined as a combination of EF and MF by their numerical values. OF = (EF)GQPSO-ANN + (MF)GQPSO-ANN OF = (-0.0069*PP – 0.0109*MA + 0.4213*TI (19) + 0.0411*TS + 0.3216) + (0.3705*PP + 0.3077*MA – 5.1539*TI + 0.2437*TS – 15)

Maximum polypropylene (PP) concentration is 29.678%, minimum Maleic anhydrite Grafted polypropylene (MA) concentration is 11.082%, maximum Titanium dioxide (TiO2) concentration is 0.4412%, and maximum Tensile Strength (TS) is 26.712. GQPSO is the best evolutionary algorithm to minimize the combined objective function (OF) of the developed neural models for EF and MF. OF will have the highest value when PP, TiO2, and TS have the highest values and MA has the lowest value. This determined optimal value has been confirmed by experimental data, indicating that the output of this procedure is extremely excellent. The GQPSO-NN model takes 23.931 seconds to achieve the optimal condition.

Conclusion

The parametric analysis of plastic boards employing waste surgical maskswas performed in our current study. The efficient and accurate estimate of manufacturing plastic board characteristics depends on two potential functions, Elongation at fracture (EF) and Percentage of total elongation at maximum force (MF). To achieve the optimal

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estimate of plastic board characteristics we performed three improved particle swarm optimization techniques. The outcomes of the present research are drawnout below: 1. Elongation at fracture (EF) and Percentage of total elongation at maximum force (MF) increased by increasing the concentration of independent variables such as material compositions of material composition of polypropylene (PP), Titanium dioxide (TiO2), and Tensile Strength (TS), while keeping Maleic anhydrite Grafted Polypropylenes (MA) as minimum value. 2. Overall dataset split into 9:1 ratio for perform cross-validation and model validation. During cross-validation, it has been observed that proposed all ANN-based improved PSO techniques obtained better accuracy but ANN-based GQPSO achieved the maximum accuracy in both the response variables Elongation at fracture (EF) and Maximum force (MF) about 95.533% and 96.0292% respectively. 3. For multi-response optimization, the optimal parametric conditions for polypropylene (PP), Maleic anhydrite Grafted polypropylene (MA), Titanium dioxide (TiO2), and Tensile Strength (TS) during waste surgical mask design are 29.678%, 11.082%, 0.4412%, and 26.712, respectively.

4. The

Gaussian Quantum behaved Particle Swam Optimization (GQPSO)-based artificial neural network (ANN) optimization technique is more suitable than artificial neural network (ANN) optimized Particle Swam Optimization (PSO), Quantum behaved Particle Swam Optimization (QPSO), and Differential Quantum behaved Particle Swam Optimization (DQPSO) using computation time, better cross-validation, and best-fitted model for testing dataset.

5. The model’s accuracy may be increased further by

increasing the number of experimental datasets and employing various mathematical models (Response Surface Methodology & Analysis of variance) optimized heuristic optimization approaches.

Authorship Contributions

There are no ethical issues with the publication of this manuscript.

Statement On The Use Of Artificial Intelligence

Artificial intelligence was not used in the preparation of the article.

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