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New Trends in Mathematical Modeling, Analysis and Optimization for Engineering...
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New Trends in Mathematical Modeling, Analysis and Optimization for Engineering and Mechanics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 15049

Special Issue Editors

Dr. Pedro Navas

E-Mail Website
Guest Editor
Department of Continuum Mechanics and Structures, ETS Ingenieros de Caminos, Universidad Politécnica de Madrid, 28040 Madrid, Spain
Interests: computational mechanics; solid dynamics; mathematical modeling and computing; meshfree methods; geotechnical engineering
Special Issues, Collections and Topics in MDPI journals
Dr. Bo Li

E-Mail Website
Guest Editor
College of Engineering, Peking University, Beijing 100871, China
Interests: computational mechanics; advanced numerical methods; multiscale material modeling

Special Issue Information

Dear Colleagues,

Computational modeling has become essential in the engineering field in recent years for necessary analyses for real-life problems. Moreover, optimization techniques have arisen to improve results for several kinds of problems. Finally, in recent years, new techniques such as meshfree methodologies as well as novel finite element methods have emerged to complete a powerful range of tools capable of accurately reproducing the engineering mechanical problems of the 21st century.

This Special Issue focuses on new trends in engineering modeling, including but not limited to:

  1. Optimization techniques in computational mechanics;
  2. Meshfree techniques applied to engineering;
  3. Novel constitutive modeling for engineering materials;
  4. Computational analysis for mechanics and engineering;
  5. Bio-inspired optimization algorithms for computational modeling;
  6. Multiscale material modeling;
  7. Multiphase formulations applied to engineering;
  8. General new trends in computational mechanics.

Dr. Pedro Navas
Dr. Bo Li
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • computational modeling
  • numerical analysis
  • numerical optimization
  • computational mechanics
  • meshfree techniques
  • new finite element techniques
  • optimization and control
  • engineering problems

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Published Papers (8 papers)

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Research

20 pages, 4604 KiB  
Article
Analysis of Meshfree Galerkin Methods Based on Moving Least Squares and Local Maximum-Entropy Approximation Schemes
by Hongtao Yang, Hao Wang and Bo Li
Mathematics 2024, 12(3), 494; https://doi.org/10.3390/math12030494 - 4 Feb 2024
Viewed by 1721
Abstract
Over the last two decades, meshfree Galerkin methods have become increasingly popular in solid and fluid mechanics applications. A variety of these methods have been developed, each incorporating unique meshfree approximation schemes to enhance their performance. In this study, we examine the application [...] Read more.
Over the last two decades, meshfree Galerkin methods have become increasingly popular in solid and fluid mechanics applications. A variety of these methods have been developed, each incorporating unique meshfree approximation schemes to enhance their performance. In this study, we examine the application of the Moving Least Squares and Local Maximum-Entropy (LME) approximations within the framework of Optimal Transportation Meshfree for solving Galerkin boundary-value problems. We focus on how the choice of basis order and the non-negativity, as well as the weak Kronecker-delta properties of shape functions, influence the performance of numerical solutions. Through comparative numerical experiments, we evaluate the efficiency, accuracy, and capabilities of these two approximation schemes. The decision to use one method over the other often hinges on factors like computational efficiency and resource management, underscoring the importance of carefully considering the specific attributes of the data and the intrinsic nature of the problem being addressed. Full article
(This article belongs to the Special Issue New Trends in Mathematical Modeling, Analysis and Optimization for Engineering and Mechanics)
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21 pages, 789 KiB  
Article
An Accurate Metaheuristic Mountain Gazelle Optimizer for Parameter Estimation of Single- and Double-Diode Photovoltaic Cell Models
by Rabeh Abbassi, Salem Saidi, Shabana Urooj, Bilal Naji Alhasnawi, Mohamad A. Alawad and Manoharan Premkumar
Mathematics 2023, 11(22), 4565; https://doi.org/10.3390/math11224565 - 7 Nov 2023
Cited by 18 | Viewed by 2331
Abstract
Accurate parameter estimation is crucial and challenging for the design and modeling of PV cells/modules. However, the high degree of non-linearity of the typical I–V characteristic further complicates this task. Consequently, significant research interest has been generated in recent years. Currently, this trend [...] Read more.
Accurate parameter estimation is crucial and challenging for the design and modeling of PV cells/modules. However, the high degree of non-linearity of the typical I–V characteristic further complicates this task. Consequently, significant research interest has been generated in recent years. Currently, this trend has been marked by a noteworthy acceleration, mainly due to the rise of swarm intelligence and the rapid progress of computer technology. This paper proposes a developed Mountain Gazelle Optimizer (MGO) to generate the best values of the unknown parameters of PV generation units. The MGO mimics the social life and hierarchy of mountain gazelles in the wild. The MGO was compared with well-recognized recent algorithms, which were the Grey Wolf Optimizer (GWO), the Squirrel Search Algorithm (SSA), the Differential Evolution (DE) algorithm, the Bat–Artificial Bee Colony Optimizer (BABCO), the Bat Algorithm (BA), Multiswarm Spiral Leader Particle Swarm Optimization (M-SLPSO), the Guaranteed Convergence Particle Swarm Optimization algorithm (GCPSO), Triple-Phase Teaching–Learning-Based Optimization (TPTLBO), the Criss-Cross-based Nelder–Mead simplex Gradient-Based Optimizer (CCNMGBO), the quasi-Opposition-Based Learning Whale Optimization Algorithm (OBLWOA), and the Fractional Chaotic Ensemble Particle Swarm Optimizer (FC-EPSO). The experimental findings and statistical studies proved that the MGO outperformed the competing techniques in identifying the parameters of the Single-Diode Model (SDM) and the Double-Diode Model (DDM) PV models of Photowatt-PWP201 (polycrystalline) and STM6-40/36 (monocrystalline). The RMSEs of the MGO on the SDM and the DDM of Photowatt-PWP201 and STM6-40/36 were 2.042717 ×10−3, 1.387641 ×10−3, 1.719946 ×10−3, and 1.686104 ×10−3, respectively. Overall, the identified results highlighted that the MGO-based approach featured a fast processing time and steady convergence while retaining a high level of accuracy in the achieved solution. Full article
(This article belongs to the Special Issue New Trends in Mathematical Modeling, Analysis and Optimization for Engineering and Mechanics)
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24 pages, 1296 KiB  
Article
Global Asymptotic Stability and Synchronization of Fractional-Order Reaction–Diffusion Fuzzy BAM Neural Networks with Distributed Delays via Hybrid Feedback Controllers
by M. Syed Ali, Gani Stamov, Ivanka Stamova, Tarek F. Ibrahim, Arafa A. Dawood and Fathea M. Osman Birkea
Mathematics 2023, 11(20), 4248; https://doi.org/10.3390/math11204248 - 11 Oct 2023
Cited by 4 | Viewed by 986
Abstract
In this paper, the global asymptotic stability and global Mittag–Leffler stability of a class of fractional-order fuzzy bidirectional associative memory (BAM) neural networks with distributed delays is investigated. Necessary conditions are obtained by means of the Lyapunov functional method and inequality techniques. The [...] Read more.
In this paper, the global asymptotic stability and global Mittag–Leffler stability of a class of fractional-order fuzzy bidirectional associative memory (BAM) neural networks with distributed delays is investigated. Necessary conditions are obtained by means of the Lyapunov functional method and inequality techniques. The hybrid feedback controllers are then developed to ensure the global asymptotic synchronization of these neural networks, resulting in two additional synchronization criteria. The derived conditions are applied to check the fractional-order fuzzy BAM neural network’s Mittag–Leffler stability and synchronization. Three examples are given to demonstrate the effectiveness of the achieved results. Full article
(This article belongs to the Special Issue New Trends in Mathematical Modeling, Analysis and Optimization for Engineering and Mechanics)
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32 pages, 3805 KiB  
Article
An Improved Mathematical Theory for Designing Membrane Deflection-Based Rain Gauges
by Jun-Yi Sun, Ning Li and Xiao-Ting He
Mathematics 2023, 11(16), 3438; https://doi.org/10.3390/math11163438 - 8 Aug 2023
Cited by 1 | Viewed by 1226
Abstract
This paper is devoted to developing a more refined mathematical theory for designing the previously proposed membrane deflection-based rain gauges. The differential-integral equations governing the large deflection behavior of the membrane are improved by modifying the geometric equations, and more accurate power-series solutions [...] Read more.
This paper is devoted to developing a more refined mathematical theory for designing the previously proposed membrane deflection-based rain gauges. The differential-integral equations governing the large deflection behavior of the membrane are improved by modifying the geometric equations, and more accurate power-series solutions of the large deflection problem are provided, resulting in a new and more refined mathematical theory for designing such rain gauges. Examples are presented to illustrate how to analyze the convergence of the power-series solutions and how to numerically calibrate membrane deflection-based linear rain gauges. In addition, some important issues are demonstrated, analyzed, and discussed, such as the superiority of the new mathematical theory over the old one, the reason why the classical geometric equations cause errors, and the influence of changing design parameters on the input–output relationships of rain gauges. Full article
(This article belongs to the Special Issue New Trends in Mathematical Modeling, Analysis and Optimization for Engineering and Mechanics)
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14 pages, 2138 KiB  
Article
Fixed-Time Adaptive Chaotic Control for Permanent Magnet Synchronous Motor Subject to Unknown Parameters and Perturbations
by Qijia Yao, Hadi Jahanshahi, Stelios Bekiros, Jinping Liu and Abdullah A. Al-Barakati
Mathematics 2023, 11(14), 3182; https://doi.org/10.3390/math11143182 - 20 Jul 2023
Cited by 1 | Viewed by 791
Abstract
It is well known that the permanent magnet synchronous motor (PMSM) exhibits chaotic characteristics when its parameters fall within a certain range, which can lead to system instability. This article proposes an adaptive control strategy for achieving the fixed-time chaotic stabilization of PMSM, [...] Read more.
It is well known that the permanent magnet synchronous motor (PMSM) exhibits chaotic characteristics when its parameters fall within a certain range, which can lead to system instability. This article proposes an adaptive control strategy for achieving the fixed-time chaotic stabilization of PMSM, even in the presence of unknown parameters and perturbations. The developed controller is synthesized by combining a parametric adaptive mechanism with a fixed-time control technique. The stability analysis demonstrates that the system states under the developed controller can converge to small neighborhoods around the equilibrium point within a fixed time. Thanks to the adoption of the parametric adaptive mechanism, the developed controller is not only insensitive to unknown parameters but also robust against perturbations. Finally, simulated studies are conducted to verify and emphasize the effectiveness of the developed control strategy. Full article
(This article belongs to the Special Issue New Trends in Mathematical Modeling, Analysis and Optimization for Engineering and Mechanics)
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21 pages, 13364 KiB  
Article
Reinforcement-Learning-Based Level Controller for Separator Drum Unit in Refinery System
by Anwer Abdulkareem Ali, Mofeed Turky Rashid, Bilal Naji Alhasnawi, Vladimír Bureš and Peter Mikulecký
Mathematics 2023, 11(7), 1746; https://doi.org/10.3390/math11071746 - 6 Apr 2023
Cited by 5 | Viewed by 2356
Abstract
The Basrah Refinery, Iraq, similarly to other refineries, is subject to several industrial constraints. Therefore, the main challenge is to optimize the parameters of the level controller of the process unit tanks. In this paper, a PI controller is designed for these important [...] Read more.
The Basrah Refinery, Iraq, similarly to other refineries, is subject to several industrial constraints. Therefore, the main challenge is to optimize the parameters of the level controller of the process unit tanks. In this paper, a PI controller is designed for these important processes in the Basrah Refinery, which is a separator drum (D5204). Furthermore, the improvement of the PI controller is achieved under several constraints, such as the inlet liquid flow rate to tank (m2) and valve opening in yi%, by using two different techniques: the first one is conducted using a closed-Loop PID auto-tuner that is based on a frequency system estimator, and the other one is via the reinforcement learning approach (RL). RL is employed through two approaches: the first is calculating the optimal PI parameters as an offline tuner, and the second is using RL as an online tuner to optimize the PI parameters. In this case, the RL system works as a PI-like controller of RD5204. The mathematical model of the RD5204 system is derived and simulated using MATLAB. Several experiments are designed to validate the proposed controller. Further, the performance of the proposed system is evaluated under several industrial constraints, such as disturbances and noise, in which the results indict that RL as a tuner for the parameters of the PI controller is superior to other methods. Furthermore, using RL as a PI-like controller increases the controller’s robustness against uncertainty and perturbations. Full article
(This article belongs to the Special Issue New Trends in Mathematical Modeling, Analysis and Optimization for Engineering and Mechanics)
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21 pages, 608 KiB  
Article
Accurate Key Parameters Estimation of PEMFCs’ Models Based on Dandelion Optimization Algorithm
by Rabeh Abbassi, Salem Saidi, Abdelkader Abbassi, Houssem Jerbi, Mourad Kchaou and Bilal Naji Alhasnawi
Mathematics 2023, 11(6), 1298; https://doi.org/10.3390/math11061298 - 8 Mar 2023
Cited by 28 | Viewed by 2337
Abstract
With the increasing demand for electrical energy and the challenges related to its production, along with the need to be environmentally friendly to achieve sustainability for future generations, proton exchange membrane fuel cells (PEMFCs) are emerging as a clean energy source that can [...] Read more.
With the increasing demand for electrical energy and the challenges related to its production, along with the need to be environmentally friendly to achieve sustainability for future generations, proton exchange membrane fuel cells (PEMFCs) are emerging as a clean energy source that can effectively replace conventional energy sources, in various fields of application and especially in the field of transportation exploiting electric vehicles (EVs). To improve the development and control of the PEMFCs, the precise determination of its mathematical model remains an essential task. Indeed, the accuracy of such a model depends on the ability to overcome the constraints associated with the nonlinearity and the numerous involved unknown parameters. The present paper proposes a new Dandelion Optimizer (DO) to accurately identify, for the first time, the parameters of the PEMFC model. The DO addresses the weaknesses of the majority of metaheuristic algorithms related to the self-adaptation of parameters, the stagnation of convergence to local minima, and the ability to refer to the whole population. The high ability of the proposed method is investigated using both steady-state and dynamic situations. The DO-based parameters estimation approach has been assessed through a specific comparative study with the most recently published techniques including GWO, GBO, HHO, IAEO, VSDE, and ABCDESC is performed using two typical PEMFC modules, namely 250 W PEMFC and NedStack PS6. The results obtained proved that the proposed approach obtained promising achievements and better performances comparatively with well-recognized and competitive methods. Full article
(This article belongs to the Special Issue New Trends in Mathematical Modeling, Analysis and Optimization for Engineering and Mechanics)
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14 pages, 2764 KiB  
Article
On the Solution of Dynamic Stability Problem of Functionally Graded Viscoelastic Plates with Different Initial Conditions in Viscoelastic Media
by Abdullah Sofiyev
Mathematics 2023, 11(4), 823; https://doi.org/10.3390/math11040823 - 6 Feb 2023
Cited by 6 | Viewed by 1581
Abstract
The widespread use of structural elements consisting of functionally graded (FG) materials in advanced technologies has led to extensive research. Due to the difficulties encountered during modeling and problem solving, the number of studies on the dynamic behavior of structural elements made of [...] Read more.
The widespread use of structural elements consisting of functionally graded (FG) materials in advanced technologies has led to extensive research. Due to the difficulties encountered during modeling and problem solving, the number of studies on the dynamic behavior of structural elements made of FG viscoelastic materials is quite limited compared to the number examining FG elastic materials. This study is one of the first attempts to solve the dynamical problem by the mathematical modeling of functionally graded viscoelastic plates (FG-VE-Ps) and viscoelastic media together with different initial conditions. FG-VE-Ps on viscoelastic foundations (VE-Fs) are assumed to be under compressive edge load in the longitudinal direction. The governing equations for FG-VE-Ps on VE-Fs are derived using Boltzmann and Volterra concepts. The problem is reduced to the solution of integro-differential equation system using the Galerkin method. Then, by performing Laplace transforms, new analytical expressions for the time-dependent deflection function and critical time at different initial conditions are found. The loss of stability of FG-VE-Ps on VE-Fs is modeled to cover three time-varying ranges: the first is the range in which the deflection function decreases; the second is the transition interval; the third is the increase range of deflection function, which leads to the loss of stability. The time corresponding to the sharp increase of the deflection function is defined as the critical time, and is determined both theoretically and numerically. The results are compared with the results obtained by various methods to confirm their accuracy. Finally, the effects of VE-Fs, VE material properties, and FG profiles on the critical time behavior of plates are studied numerically. Full article
(This article belongs to the Special Issue New Trends in Mathematical Modeling, Analysis and Optimization for Engineering and Mechanics)
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