Mathematical Modelling for Solving Engineering Problems

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

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 5626

Special Issue Editors

Department of Mechanical Engineering Technologies, Academy of Engineering, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow 117198, Russia
Interests: mechanical engineering; manufacturing process; machining process; machine tools; vibration; damping; fatigue
Laboratory of Automated Queuing Systems and Signal Processing, V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65, Profsoyuznaya Str., Moscow 1179997, Russia
Interests: control; computer science and communication; heterogeneous systems and networks; complex stochastic systems; mathematical and simulation models of heterogeneous networks; asymptotic analysis; artificial neural networks; speech analytics system; concept of artificial and human intelligence interaction; network design software; Intelligent robotic systems; hydroacoustic communication; underwater networks; uninhabited underwater vehicles; autonomous navigation; local positioning; visual odometry; mobile robots; control of moving objects
1. Department of Transport, Academy of Engineering, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow 117198, Russia
2. Director of Mechanical Characteristics Laboratory, Center for Laboratory Services, Sharif University of Technology, Tehran 11365, Iran
Interests: fatigue; structural fatigue; vehicle; shot-peening; random loading; applied mechanics; solid mechanics; structural integrity; fracture; residual stress; optimization; welding; surface treatment
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Special Issue Information

Dear Colleagues,

Mathematical modeling is often considered an art in formulating and solving equations rather than a science and is highly dependent on the experience and knowledge of the researchers involved. It requires both a good understanding of the nature of the process and familiarity with existing models and methods. In some practical cases, the studied phenomena are very complex, and any mathematical description is only an average approximation. Unavoidable simplifications and approximations made during the modeling process can greatly alter the predicted behavior of real-world phenomena. This is why applied mathematical modeling does not make sense without defining the purpose of modeling. Before developing a model, a specific existing problem must be explained, and the possible implications and benefits of the model must be explored. Modeling goals should be realistic, but not oversimplified. In general, the level of complexity of mathematical models varies considerably for different applied problems. In this regard, some mathematical equations for engineering problems and other phenomena in human daily life become classical equations and can be generalized for different conditions. However, for some complex issues, the derived equations are only specific to those conditions and cannot be used in similar cases. Therefore, it is necessary to carry out fundamental research by considering different conditions in an engineering problem or industrial challenge, and mathematical modeling of the system is done by fully covering the parameters affecting the system’s performance and the relationships between them. Although with the progress of science and technology various simulation software tools which can be used to analyze problems by considering initial and boundary conditions entered the market, we should not forget that behind the scenes of these tools there are mathematical relationships and models presented by scientists that can be generalized to different issues.

This Special Issue on “Mathematical Modelling for Solving Engineering Problems” focuses on advancing knowledge, specifically for the mathematical modeling of problems in different fields of engineering subjected to complex conditions, as well as their solution based on various solution techniques, including classic, data mining, machine learning, etc.

Dr. Siamak Ghorbani
Prof. Dr. Mais Farkhadov
Prof. Dr. Kazem Reza Kashyzadeh
Guest Editors

Manuscript Submission Information

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Keywords

  • engineering problems
  • industrial challenges
  • catastrophic failures in various fields of engineering
  • interdisciplinary issues
  • design
  • improvement
  • optimization
  • fundamental research
  • mathematical approximations
  • numerical solution algorithms
  • machine learning techniques

Published Papers (5 papers)

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Research

29 pages, 10606 KiB  
Article
Damage Detection in Structures by Using Imbalanced Classification Algorithms
Mathematics 2024, 12(3), 432; https://doi.org/10.3390/math12030432 - 29 Jan 2024
Viewed by 448
Abstract
Detecting damage constitutes the primary and pivotal stage in monitoring a structure’s health. Early identification of structural issues, coupled with a precise understanding of the structure’s condition, represents a cornerstone in the practices of structural health monitoring (SHM). While many existing methods prove [...] Read more.
Detecting damage constitutes the primary and pivotal stage in monitoring a structure’s health. Early identification of structural issues, coupled with a precise understanding of the structure’s condition, represents a cornerstone in the practices of structural health monitoring (SHM). While many existing methods prove effective when the number of data points in both healthy and damaged states is equal, this article employs algorithms tailored for detecting damage in situations where data are imbalanced. Imbalance, in this context, denotes a significant difference in the number of data points between the healthy and damaged states, essentially introducing an imbalance within the dataset. Four imbalanced classification algorithms are applied to two benchmark structures: the first, a numerical model of a four-story steel building, and the second, a bridge constructed in China. This research thoroughly assesses the performance of these four algorithms for each structure, both individually and collectively. Full article
(This article belongs to the Special Issue Mathematical Modelling for Solving Engineering Problems)
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24 pages, 510 KiB  
Article
Queueing-Inventory Systems with Catastrophes under Various Replenishment Policies
Mathematics 2023, 11(23), 4854; https://doi.org/10.3390/math11234854 - 02 Dec 2023
Cited by 1 | Viewed by 737
Abstract
We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival process and they can be queued in an [...] Read more.
We discuss two queueing-inventory systems with catastrophes in the warehouse. Catastrophes occur according to the Poisson process and instantly destroy all items in the inventory. The arrivals of the consumer customers follow a Markovian arrival process and they can be queued in an infinite buffer. The service time of a consumer customer follows a phase-type distribution. The system receives negative customers which have Poisson flows and as soon as a negative customer comes into the system, he causes a consumer customer to leave the system, if any. One of two inventory policies is used in the systems: either (s,S) or (s,Q). If the inventory level is zero when a consumer customer arrives, then this customer is either lost (lost sale) or joins the queue (backorder sale). The system is formulated by a four-dimensional continuous-time Markov chain. Ergodicity condition for both systems is established and steady-state distribution is obtained using the matrix-geometric method. By numerical studies, the influence of the distributions of the arrival process and the service time and the system parameters on performance measures are deeply analyzed. Finally, an optimization study is presented in which the criterion is the minimization of expected total costs and the controlled parameter is warehouse capacity. Full article
(This article belongs to the Special Issue Mathematical Modelling for Solving Engineering Problems)
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20 pages, 4412 KiB  
Article
A Review of Mathematical Models Used to Estimate Wheeled and Tracked Unmanned Ground Vehicle Kinematics and Dynamics
Mathematics 2023, 11(17), 3735; https://doi.org/10.3390/math11173735 - 30 Aug 2023
Viewed by 1025
Abstract
This paper presents mathematical models to estimate the kinematics and dynamics of wheeled and tracked robots. The models account for the physical–mechanical characteristics of the ground, the influence of the center of gravity displacement on the cornering moment of resistance, and the influence [...] Read more.
This paper presents mathematical models to estimate the kinematics and dynamics of wheeled and tracked robots. The models account for the physical–mechanical characteristics of the ground, the influence of the center of gravity displacement on the cornering moment of resistance, and the influence of the interaction of the crawler with the roadway. The results of the models are characterized by defining computational relationships for a robot’s equations of motion, longitudinal forces, transverse forces, and resistive turning moments generated via longitudinal forces and transverse forces. Full article
(This article belongs to the Special Issue Mathematical Modelling for Solving Engineering Problems)
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15 pages, 5320 KiB  
Article
Lithium-Ion Battery Modeling and State of Charge Prediction Based on Fractional-Order Calculus
Mathematics 2023, 11(15), 3401; https://doi.org/10.3390/math11153401 - 04 Aug 2023
Cited by 3 | Viewed by 986
Abstract
Predicting lithium-ion batteries’ state of charge (SOC) is essential to electric vehicle battery management systems. Traditional lithium-ion battery models mainly include equivalent circuit models (ECMs) and electrochemical models (EMs). ECMs are based on integer-order component modeling, which cannot characterize the internal electrochemical reaction [...] Read more.
Predicting lithium-ion batteries’ state of charge (SOC) is essential to electric vehicle battery management systems. Traditional lithium-ion battery models mainly include equivalent circuit models (ECMs) and electrochemical models (EMs). ECMs are based on integer-order component modeling, which cannot characterize the internal electrochemical reaction mechanism of the battery, resulting in lower SOC prediction accuracy. In contrast, due to their complex structure, EMs are limited in their application. This study takes lithium batteries as the research object and proposes a fractional-order impedance model (FOIM) that characterizes the dynamic properties of the internal behavior of lithium-ion batteries using fractional-order elements. Considering the highly nonlinear characteristics of lithium-ion batteries, this study introduces the theory of fractional-order calculus into the extended Kalman filter (EKF) algorithm, and proposes the fractional-order extended Kalman filter (FEKF) algorithm applied to the prediction of battery charge state. Comparative analysis of simulation and experimental results shows that the accuracy of the FOIM, compared to ECMs, is significantly improved. The FEKF algorithm has good robustness in estimating the SOC, and the SOC prediction accuracy achieved with the algorithm is also improved compared with that obtained using the EKF algorithm of the integer-order model. Full article
(This article belongs to the Special Issue Mathematical Modelling for Solving Engineering Problems)
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21 pages, 4651 KiB  
Article
Seismic Bearing Capacity Solution for Strip Footings in Unsaturated Soils with Modified Pseudo-Dynamic Approach
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Mathematics 2023, 11(12), 2692; https://doi.org/10.3390/math11122692 - 14 Jun 2023
Cited by 3 | Viewed by 1185
Abstract
In engineering mathematics, the unsaturated nature of soil has a significant impact on the seismic bearing capacity solution. However, it has generally been neglected in the published literature to date. Based on the kinematic approach of limit analysis, the present study proposes a [...] Read more.
In engineering mathematics, the unsaturated nature of soil has a significant impact on the seismic bearing capacity solution. However, it has generally been neglected in the published literature to date. Based on the kinematic approach of limit analysis, the present study proposes a method for calculating the bearing capacity of shallow strip footings located in unsaturated soils, taking four common types of soils as examples. The modified pseudo-dynamic (MPD) approach is used to calculate the seismic forces varying with time and space, and the layerwise summation method is used to derive the power generated by the seismic forces. In the calculation of internal energy dissipation, this paper introduces the effective stress based on the suction stress to derive the cohesion expression at different depths. The analytical formula of bearing capacity is obtained by the principle of virtual work, and its value is optimized by the Sequential Quadratic Programming (SQP) algorithm. In order to verify the validity of the proposed method, the present results are compared with the solutions published so far and a good agreement is obtained. Finally, a parametric study is performed to investigate the influence of different types of parameters on the bearing capacity. Full article
(This article belongs to the Special Issue Mathematical Modelling for Solving Engineering Problems)
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