Author Information

Laboratory of Biomaterials and Transport Phenomena (LBMPT), Faculty of Technology, University Yahia Fares of Medea, Medea 26000, Algeria

*

Authors to whom correspondence should be addressed.

Received: 19 September 2024 Accepted: 22 October 2024 Published: 23 October 2024

© 2024 The authors. This is an open access article under the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0/).

ABSTRACT:
The
analysis of rheological properties of suspensions requires the use of models
such as Einstein’s formulation for viscosity in dilute conditions, but its
effectiveness diminishes in the context of concentrated suspensions. This study
investigates the rheology of suspensions containing solid particles in aqueous
media thickened with starch nanoparticles (SNP). The goal is to model the
viscosity of these mixtures across a range of shear rates and varying amounts
of SNP and SG hollow spheres (SGHP). Artificial neural networks (ANN) combined
with swarm intelligence algorithms were used for viscosity modeling, utilizing
1104 data points. Key features include SNP proportion, SGHP content,
log-transformed shear rate (LogSR), and log-transformed viscosity
(LogViscosity) as an output. Three swarm algorithms**—**AntLion
Optimizer (ALO), Particle Swarm Optimizer (PSO), and Dragonfly Algorithm (DA)**—**were evaluated for optimizing ANN hyperparameters. The ALO
algorithm proved most effective, demonstrating strong convergence, exploration,
and exploitation. Comparative analysis of ANN models revealed the superior
performance of ANN-ALO, with an R^{2} of 0.9861, mean absolute error (MAE) of 0.1013, root mean
absolute error (RMSE) of 0.1356, and mean absolute percentage error (MAPE) of
3.198%. While all models showed high predictive accuracy, the ANN-PSO model had
more limitations. These findings enhance understanding of starch suspension
rheology, offering potential applications in materials science.

Keywords:
Starch suspensions; Rheology modeling; Starch nanoparticles; Artificial
Neural Networks; Swarm intelligence algorithms

Colloid science has gained significance due to the commercial success of nanotechnologies, which generate, process, and employ nanomaterials. Suspensions are materials composed of liquid continuum and solid, submicrometre particles found in various products like ink, paints, and lotions. Their distinction from true solutions depends on physical phenomena like scattering, membrane penetration, and rheological studies [1]. Colloidal suspensions can be dispersed, coagulated or flocculated, depending on the particle-particle interaction energy and particle concentration. In weakly flocculated dispersions, particles form a volume-spanning network, which can be deformed to increase the total potential energy and produce an interparticle force. A colloidal gel is a special state of strongly flocculated systems where a continuous network of particles forms by aggregation, resulting in a high viscosity [2].
Starch is a natural, renewable, and biodegradable polymer found in plant roots, stalks, seeds, and staple crops like rice, corn, wheat, tapioca, and potato. Starch’s composition consists of two glucosidic macromolecules: amylose and amylopectin. Some mutant types have high amylose content and low amylose content [3]. Starch suspensions play a significant role in stabilizing emulsions and enhancing the texture and mouthfeel of food products, resulting in a smooth and creamy consistency. These suspensions exhibit distinctive properties, including high viscosity, which can be modulated by altering the concentration of starch, and the capacity to form gels upon cooling. This versatility renders them valuable in a variety of culinary applications. Furthermore, starch suspensions can enhance the mechanical properties of composite materials, thereby contributing to their strength and durability while being environmentally sustainable. The microstructural properties of starch suspensions are defined by the presence of granules that exhibit variability in size and shape, typically ranging from 1 to 100 μm. Upon hydration, these granules undergo swelling and may experience gelatinization, resulting in the disruption of their crystalline structure and the formation of a viscous gel-like matrix. The interactions among starch molecules, including hydrogen bonding and the presence of amylose and amylopectin, significantly influence the suspension’s rheological behavior, stability, and texture. These properties are critical for the functionality of starch in both food and industrial applications [4].
The rheological property of starch is crucial as it is often used as a thickener in various applications. Viscosity measures a fluid’s resistance to flow when a shear rate or strain is applied. Starch suspensions, which form from starch granules, determine the thickening power of starch for stability and various applications, including pharmaceutical formulations [5]. The analysis of rheological properties required using models specifically designed to distinguish discrete proportions or fractions of particle loadings. Among these models, Einstein’s formulation for viscosity in dilute suspensions of spheres, as articulated in Equation (1) [6], has served as a foundational construct. Nevertheless, the efficacy of this model diminishes significantly in the context of concentrated suspensions [7]. The limitation of Einstein’s model in addressing concentrated suspensions underscores the need for more versatile and comprehensive models capable of understanding the dynamics within suspension systems. The identification and application of more sophisticated models are indispensable for understanding rheological phenomena across a spectrum of particle loadings and types.
where: *η* and *η*_{0} are the viscosities related to the volume fraction of particles and solvent, respectively.
Metaheuristic algorithms play a vital role in addressing complex optimization problems that may be inadequately solved by traditional methods, especially in high-dimensional or non-linear contexts. These algorithms utilize mechanisms such as population-based search, randomization, and local search to effectively navigate the solution space, thereby increasing the likelihood of identifying optimal or near-optimal solutions. Their applicability extends across diverse domains, including clustering, scheduling, and optimizing machine learning models, rendering them versatile instruments for confronting real-world challenges [8]. Machine learning models are optimized by applying metaheuristic algorithms, which automate the search for optimal hyperparameters, architectural designs, and feature representations. These algorithms emulate natural phenomena to navigate the solution space, utilizing intensification and diversification strategies to circumvent local minima and identify high-quality solutions. By assigning fitness values to potential solutions and generating new candidates via reproduction operators, metaheuristics effectively address complex optimization challenges within the field of machine learning [9].
The present study builds upon the recent research conducted by G. Ghanaatpishehsanaei and R. Pal, which focused on exploring the rheology of suspensions containing solid particles in aqueous matrix liquids thickened with starch nanoparticles (SNP) [10]. Their research aimed to comprehend the impact of SNP addition on the rheological behavior of these suspensions. Their findings revealed Newtonian and non-Newtonian shear-thinning behaviors in different concentration ranges of solid particles. In continuation of this work, this study aims to model the shear viscosity of these mixtures across a diverse range of shear rates and varying amounts of SNP and SGHP (solid particles—SG hollow spheres). To achieve this, Artificial Neural Networks (ANN) hybridized with three Swarm algorithms: AntLion Optimizer (ALO), Particle Swarm Optimizer (PSO), and Dragonfly Algorithm (DA) were employed. The objective is to compare the optimizing efficacy of these algorithms in determining the optimal hyperparameters of the ANN, thereby contributing to a deeper understanding of the rheological characteristics of the suspensions and enhancing the ability to predict and control their rheological behavior.

```latex\eta(\phi)=\eta_0(1+5/_2\phi)```

```latex\eta_r=\left[1-\left\{1+\left(\frac{1-\phi_m}{\phi_m}\right)\sqrt{1-\left(\frac{\phi_m-\phi}{\phi_m}\right)^2}\right\}\phi\right]^{-2.5}```

```latexy_{j,k}=F_k(\sum\nolimits_{i=1}^{N_{k-1}}w_{ijk}y_{i(k-1)}+\beta_{jk})```

- Initialization: In this phase, a population of antlions and ants is randomly generated. Antlions represent the potential solutions to the optimization problem, while ants move around the antlion traps, representing the search for the optimal solution.
- Optimization: During this phase, the antlions update their positions based on the positions of the ants. If an ant finds a better position (higher fitness value), the antlion in that location will move towards the ant, mimicking the hunting behavior of antlions in nature. This process helps the algorithm explore the search space and exploit promising regions.
- Update: The best antlion obtained so far is saved as an elite solution, ensuring that the best solution found is preserved throughout the optimization process. This elitism feature helps the algorithm maintain the best solutions and avoid getting stuck in local optima.

- Initialization: The algorithm starts by initializing a population of particles randomly in the search space.
- Velocity and Position Update: Each particle adjusts its velocity and position based on two main components:
- Cognitive Component: The particle’s memory of its best position (personal best).
- Social Component: The particle’s neighborhood’s best position (global best).
- Fitness Evaluation: The fitness of each particle is evaluated based on the objective function to be optimized.
- Update Personal Best and Global Best: Each particle updates its personal best position and shares information with its neighbors to update the global best position.
- Iteration: The process of velocity and position update, fitness evaluation, and best position update is iterated for a certain number of generations or until a stopping criterion is met.
- Optimal Solution: The algorithm aims to converge to an optimal solution by iteratively adjusting the positions of the particles in the search space based on their own experience and the experience of their neighbors.

- Initialization: Initialize the population of dragonflies and set the algorithm parameters.
- Fitness Evaluation: Evaluate the fitness of each dragonfly in the population based on the objective function(s) of the optimization problem.
- Update Position: Update the position of each dragonfly based on its current position, the positions of neighboring dragonflies, and the best position found so far.
- Update Archive: Maintain an archive of the best solutions found (Pareto optimal set) during optimization.
- Selection of Food Sources: Choose food sources (solutions) for dragonflies from the least populated region of the obtained Pareto optimal front to improve the distribution of the solutions.
- Selection of Enemies: Select enemies (non-promising crowded areas) for the dragonflies from the most populated region of the Pareto optimal front to discourage exploration in those areas.
- Archive Management: Implement a mechanism to manage the archive, ensuring it is updated regularly and does not become full.
- Convergence and Coverage: Aim for convergence by determining accurate approximations of Pareto optimal solutions and ensure coverage by distributing the obtained solutions uniformly across all objectives.

```latex\mathrm{R}^2=1-\frac{\sum_{i=1}^N(\eta_i-\hat{\eta}_i)^2}{\sum_{i=1}^N(\eta_i-\bar{\eta}_i)^2}```

```latex\mathrm{MAE}=\frac{\sum_{i=1}^N|\eta_i-\hat{\eta}_i|}N```

```latex\mathrm{RMSE}=\sqrt{\sum\nolimits_{i=1}^N\frac{(\eta_i-\widehat{\eta}_i)^2}N}```

```latex\mathrm{MAPE}=\left(\frac1N\sum\nolimits_{i=1}^N\left|\frac{\eta_i-\widehat{\eta}_i}{\eta_i}\right|\right)\times100```

In conclusion, this study explored the complex domain of modeling the viscosity of starch suspensions by utilizing a combination of artificial neural networks (ANN) and swarm intelligence algorithms. The comprehensive examination of a dataset comprising 1104 data points enabled a nuanced understanding of the rheological behavior of these suspensions. Key features such as starch nanoparticles (SNP) proportions, solid particles of hollow spheres (SGHP) content, and log-transformed shear rate (LogSR) were identified as crucial determinants in predicting viscosity.
The investigation involved exploring three swarm algorithms—AntLion Optimizer (ALO), Particle Swarm Optimizer (PSO), and Dragonfly Algorithm (DA)—for hyperparameter optimization in developing ANN models. Through trajectory analysis, exploration versus exploitation graphs, and relative fitness value (RMSE) comparisons, the ALO algorithm emerged as the most efficient in balancing exploration and exploitation, showcasing faster convergence and covering the entire search space.
Regression analysis and a comparative performance evaluation of ANN variants—ANN-ALO, ANN-PSO, and ANN-DA—underscored the superior predictive capabilities of ANN-ALO. The model consistently outperformed its counterparts in terms of R^{2} score, MAE, RMSE, and MAPE, reflecting its robustness and accuracy in predicting transformed viscosity (Log viscosity). While all models demonstrated a high degree of alignment between predicted and actual viscosities, the ANN-PSO model exhibited limitations, especially in predicting extremely high viscosities under extreme shear conditions.
The findings contribute to the understanding of starch suspension rheology but also highlight the efficacy of the integrated approach employing ANN and ALO in predicting viscosity. The identified correlations between input features and viscosity, and the strengths and limitations of the swarm algorithms, offer valuable insights for future studies in this domain. In essence, the combination of artificial intelligence and swarm intelligence offers a promising approach to understanding the complexities of colloidal suspensions, thereby contributing to the wider field of materials science and industrial applications.

The authors would like to acknowledge the Laboratory of Biomaterials and Transport Phenomena and SAIDAL of Medea.

Conceptualization, M.K.A. and F.O.; Methodology, M.K.A. and F.O. and A.M.; Software, M.K.A.; Validation, M.K.A. and M.H.; Formal Analysis, M.K.A.; Investigation, M.K.A. and F.O. and A.M. and M.H.; Writing—Original Draft Preparation, M.K.A.; Writing—Review & Editing, M.K.A.

Not applicable.

Not applicable.

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

1.

Babick* *F.* Suspensions of Colloidal Particles and Aggregates*,* *20th* *ed.;* *Springer:** **Berlin,* *Germany,* *2016

2.

Genovese DB, Lozano JE, Rao MA. The Rheology of Colloidal and Noncolloidal Food Dispersions. * J. Food Sci. *** 2007**,* 72,* R11–R20. [Google Scholar]

3.

Le Corre D, Bras J, Dufresne A. Starch Nanoparticles: A Review. * Biomacromolecules *** 2010**,* 11,* 1139–1153. [Google Scholar]

4.

Fazeli* *M.* *Development* *of* *hydrophobic* *thermoplastic* *starch* *composites.* *Unpublished* *work,* *2018.

5.

Ai Y, Jane JL. Gelatinization and rheological properties of starch. * Starch—Stärke *** 2015**,* 67,* 213–224. [Google Scholar]

6.

Einstein* *A.* Investigations on the Theory of Brownian Movement*;* *Dover:* *New* *York, NY,* *USA,* *1975;* *p. 591.

7.

Mendoza CI, Santamaría-Holek I. The rheology of hard sphere suspensions at arbitrary volume fractions: An improved differential viscosity model.* J. Chem. Phys. *** 2009**,* 130,* 44904. [Google Scholar]

8.

Nanda SJ, Panda G. A survey on nature inspired metaheuristic algorithms for partitional clustering.* Swarm Evol. Comput. *** 2014**,* 16,* 1–18. [Google Scholar]

9.

Akay B, Karaboga D, Akay R. A comprehensive survey on optimizing deep learning models by metaheuristics.* Artif. Intell. Rev. *** 2022**,* 55,* 829–894. [Google Scholar]

10.

Ghanaatpishehsanaei G, Pal R. Rheology of Suspensions of Solid Particles in Liquids Thickened by Starch Nanoparticles. * Colloids Interfaces *** 2023**,* 7,* 52. [Google Scholar]

11.

Pal R. A new model for the viscosity of asphaltene solutions. * Can. J. Chem. Eng. *** 2015**,* 93,* 747–755. [Google Scholar]

12.

Zou* *J,* *Han* *Y,* *So* *SS.* *Overview* *of* *Artificial* *Neural* *Networks.* *In* Artificial Neural Networks: Methods and Applications*,* *1st* *ed.;* *Livingstone* *DJ,* *Ed.;* *Humana* *Press:* *Totowa,* *NJ,* *USA,* *2009;* *pp.* *1**–**30.

13.

Heidari E, Sobati MA, Movahedirad S. Accurate prediction of nanofluid viscosity using a multilayer perceptron artificial neural network (MLP-ANN). * Chemom. Intell. Lab. Syst. *** 2016**,* 155,* 73–85. [Google Scholar]

14.

15.

Eberhart* *R,* *Kennedy* *J.* *A* *new* *optimizer* *using* *particle* *swarm* *theory.* *In* *Proceedings of the MHS’95 Sixth International Symposium on Micro Machine and Human Science,* *Nagoya,* *Japan,* *4**–**6 October 1995;* *pp.* *39**–**43.

16.

Wang D, Tan D, Liu L. Particle swarm optimization algorithm: An overview.* Soft Comput.*** 2018**,* 22,* 387–408. [Google Scholar]

17.

Mirjalili S. Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. * Neural Comput. Appl. *** 2016**,* 27,* 1053–1073. [Google Scholar]

18.

Arbia* *W,* *Kouider* *AM,* *Adour* *L,* *Amrane* *A.* *Maximizing* *chitin* *and* *chitosan* *recovery* *yields* *from* *fusarium* *verticillioides* *using* *a* *many-factors-at-a-time* *approach.* Int. J. Biol. Macromol. ***2024**,* *136708. doi:10.1016/j.ijbiomac.2024.136708.

19.

Shahsavar A, Khanmohammadi S, Karimipour A, Goodarzi M. A* *novel* *comprehensive* *experimental* *study* *concerned* *synthesizes* *and* *prepare* *liquid* *paraffin-Fe_{3}O_{4}* *mixture* *to* *develop* *models* *for* *both* *thermal* *conductivity* *&* *viscosity:* *A* *new* *approach* *of* *GMDH* *type* *of* *neural* *network.* ** Int. J. Heat Mass Transf.*** 2019**,* 131,* 432–441. [Google Scholar]

20.

Hai T, Basem A, Alizadeh A, Sharma K, Jasim DJ, Rajab H, et al. Optimizing Gaussian process regression (GPR) hyperparameters with three metaheuristic algorithms for viscosity prediction of suspensions containing microencapsulated PCMs. * Sci. Rep. *** 2024**,* 14,* 20271. [Google Scholar]

21.

Sharma KV, Talpa Sai PHVS, Sharma P, Kanti PK, Bhramara P, Akilu S. * *Prognostic* *modeling* *of* *polydisperse* *SiO_{2}/Aqueous* *glycerol* *nanofluids’* *thermophysical* *profile* *using* *an* *explainable* *artificial* *intelligence* *(XAI)* *approach.* ** Eng. Appl. Artif. Intell. *** 2023**,* 126,* 106967. [Google Scholar]

22.

Hemmat Esfe M, Tatar A, Ahangar MRH, Rostamian H. A comparison of performance of several artificial intelligence methods for predicting the dynamic viscosity of TiO2/SAE 50 nano-lubricant.* Phys. E Low-Dimens. Syst. Nanostruct. *** 2018**,* 96,* 85–93. [Google Scholar]

23.

Ramzi M, Kashaninejad M, Salehi F, Sadeghi Mahoonak AR, Ali Razavi SM. Modeling of rheological behavior of honey using genetic algorithm–artificial neural network and adaptive neuro-fuzzy inference system.* Food Biosci. *** 2015**,* 9,* 60–67. [Google Scholar]

Kouider Amar M, Omari F, Madani A, Hentabli M. Modeling Viscosity in Starch-Polymer Suspensions: A Comparative Analysis of Swarm Algorithm-Aided ANN Optimization. *Sustainable Polymer & Energy* **2024**, *2*, 10009. https://doi.org/10.70322/spe.2024.10009

Kouider Amar M, Omari F, Madani A, Hentabli M. Modeling Viscosity in Starch-Polymer Suspensions: A Comparative Analysis of Swarm Algorithm-Aided ANN Optimization. *Sustainable Polymer & Energy*. 2024; 2(4):10009. https://doi.org/10.70322/spe.2024.10009

TOP