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Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition
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Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition

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

Deadline for manuscript submissions: closed (31 July 2024) | Viewed by 22685

Special Issue Editor

Dr. Mario Versaci

E-Mail Website
Guest Editor
Dipartimento di Ingegneria Civile Energia Ambiente e Materiali (DICEAM), Mediterranea University, I-89122 Reggio Calabria, Italy
Interests: physical–mathematical models for magnetorheological fluids; thermodynamic theories for fluids; rheological models for biological fluids; nonlinear waves propagation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is clear that the cooperation among Universities and Industries determines the progress of social, cultural, technological and economic innovation.  The cooperation between these two worlds is an essential tool for the development of knowledge guaranteeing greater competitiveness. The conditions for a virtuous exchange of knowledge among Universities and Industries are set in motion by cooperating to find ways, languages and opportunities to achieve the necessary coordination: requests and offers from the Industries and offer of knowledge and skills from the Universities. Thus, the need in the University world in general, and in particular in the fields of Electrical and Industrial Engineering, matures to realize research projects shared with the Industry world. There is no doubt that mathematical modeling is the first important step in managing industrial problems. However, such models are often complex, requiring numerical techniques to obtain solutions, especially when the enormous amount of input data is affected by uncertainty.

This Special Issue of Mathematics aims to explore, from a broad perspective, the most recent developments in the field of mathematical modeling for problems of interest in electrical and industrial engineering. Topics of interest range from analytical, numerical and soft computing modeling techniques to solve industrial problems.

Prof. Dr. Mario Versaci
Guest Editor

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Keywords

  • artificial intelligence
  • complex systems
  • delayed systems
  • dynamical systems
  • machine learning
  • mathematical modeling
  • neural networks
  • numerical techniques
  • physics-based modeling
  • soft computing techniques
  • stability
  • uncertain systems
  • applications in industrial and electrical engineering

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Published Papers (12 papers)

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Research

20 pages, 1503 KiB  
Article
A Mathematical Programming Model for Minimizing Energy Consumption on a Selective Laser Melting Machine
by Chunlong Yu and Junjie Lin
Mathematics 2024, 12(16), 2507; https://doi.org/10.3390/math12162507 - 14 Aug 2024
Viewed by 692
Abstract
The scheduling problem in additive manufacturing is receiving increasing attention; however, few have considered the effect of scheduling decisions on machine energy consumption. This research focuses on the nesting and scheduling problem of a single selective laser melting (SLM) machine to reduce total [...] Read more.
The scheduling problem in additive manufacturing is receiving increasing attention; however, few have considered the effect of scheduling decisions on machine energy consumption. This research focuses on the nesting and scheduling problem of a single selective laser melting (SLM) machine to reduce total energy consumption. Based on an energy consumption model, a nesting and scheduling problem is formulated, and a mixed integer linear programming model is proposed. This model simultaneously determines part-to-batch assignments, part placement in the batch, and the choice of build orientation to reduce the total energy consumption of the SLM machine. The energy-saving potential of the model is validated through numerical experiments. Additionally, the effect of the number of alternative build orientations on energy consumption is explored. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
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19 pages, 348 KiB  
Article
On a Local and Nonlocal Second-Order Boundary Value Problem with In-Homogeneous Cauchy–Neumann Boundary Conditions—Applications in Engineering and Industry
by Tudor Barbu, Alain Miranville and Costică Moroşanu
Mathematics 2024, 12(13), 2050; https://doi.org/10.3390/math12132050 - 30 Jun 2024
Viewed by 985
Abstract
A qualitative study for a second-order boundary value problem with local or nonlocal diffusion and a cubic nonlinear reaction term, endowed with in-homogeneous Cauchy–Neumann (Robin) boundary conditions, is addressed in the present paper. Provided that the initial data meet appropriate regularity conditions, the [...] Read more.
A qualitative study for a second-order boundary value problem with local or nonlocal diffusion and a cubic nonlinear reaction term, endowed with in-homogeneous Cauchy–Neumann (Robin) boundary conditions, is addressed in the present paper. Provided that the initial data meet appropriate regularity conditions, the existence of solutions to the nonlocal problem is given at the beginning in a function space suitably chosen. Next, under certain assumptions on the known data, we prove the well posedness (the existence, a priori estimates, regularity, uniqueness) of the classical solution to the local problem. At the end, we present a particularization of the local and nonlocal problems, with applications for image processing (reconstruction, segmentation, etc.). Some conclusions are given, as well as new directions to extend the results and methods presented in this paper. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
30 pages, 2933 KiB  
Article
Methodology for Power Systems’ Emergency Control Based on Deep Learning and Synchronized Measurements
by Mihail Senyuk, Murodbek Safaraliev, Andrey Pazderin, Olga Pichugova, Inga Zicmane and Svetlana Beryozkina
Mathematics 2023, 11(22), 4667; https://doi.org/10.3390/math11224667 - 16 Nov 2023
Cited by 3 | Viewed by 1491
Abstract
Modern electrical power systems place special demands on the speed and accuracy of transient and steady-state process control. The introduction of renewable energy sources has significantly influenced the amount of inertia and uncertainty of transient processes occurring in energy systems. These changes have [...] Read more.
Modern electrical power systems place special demands on the speed and accuracy of transient and steady-state process control. The introduction of renewable energy sources has significantly influenced the amount of inertia and uncertainty of transient processes occurring in energy systems. These changes have led to the need to clarify the existing principles for the implementation of devices for protecting power systems from the loss of small-signal and transient stability. Traditional methods of developing these devices do not provide the required adaptability due to the need to specify a list of accidents to be considered. Therefore, there is a clear need to develop fundamentally new devices for the emergency control of power system modes based on adaptive algorithms. This work proposes to develop emergency control methods based on the use of deep machine learning algorithms and obtained data from synchronized vector measurement devices. This approach makes it possible to ensure adaptability and high performance when choosing control actions. Recurrent neural networks, long short-term memory networks, restricted Boltzmann machines, and self-organizing maps were selected as deep learning algorithms. Testing was performed by using IEEE14, IEEE24, and IEEE39 power system models. Two data samples were considered: with and without data from synchronized vector measurement devices. The highest accuracy of classification of the control actions’ value corresponds to the long short-term memory networks algorithm: the value of the accuracy factor was 94.31% without taking into account the data from the synchronized vector measurement devices and 94.45% when considering this data. The obtained results confirm the possibility of using deep learning algorithms to build an adaptive emergency control system for power systems. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
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25 pages, 1124 KiB  
Article
An Inhomogeneous Model for Laser Welding of Industrial Interest
by Carmelo Filippo Munafò, Annunziata Palumbo and Mario Versaci
Mathematics 2023, 11(15), 3357; https://doi.org/10.3390/math11153357 - 31 Jul 2023
Cited by 9 | Viewed by 1849
Abstract
An innovative non-homogeneous dynamic model is presented for the recovery of temperature during the industrial laser welding process of Al-Si 5% alloy plates. It considers that, metallurgically, during welding, the alloy melts with the presence of solid/liquid phases until total melt is [...] Read more.
An innovative non-homogeneous dynamic model is presented for the recovery of temperature during the industrial laser welding process of Al-Si 5% alloy plates. It considers that, metallurgically, during welding, the alloy melts with the presence of solid/liquid phases until total melt is achieved, and afterwards it resolidifies with the reverse process. Further, a polynomial substitute thermal capacity of the alloy is chosen based on experimental evidence so that the volumetric solid-state fraction is identifiable. Moreover, to the usual radiative/convective boundary conditions, the contribution due to the positioning of the plates on the workbench is considered (endowing the model with Cauchy–Stefan–Boltzmann boundary conditions). Having verified the well-posedness of the problem, a Galerkin-FEM approach is implemented to recover the temperature maps, obtained by modeling the laser heat sources with formulations depending on the laser sliding speed. The results achieved show good adherence to the experimental evidence, opening up interesting future scenarios for technology transfer. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
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20 pages, 2293 KiB  
Article
Analysis of a State Degradation Model and Preventive Maintenance Strategies for Wind Turbine Generators Based on Stochastic Differential Equations
by Hongsheng Su, Yifan Zhao and Xueqian Wang
Mathematics 2023, 11(12), 2608; https://doi.org/10.3390/math11122608 - 7 Jun 2023
Cited by 5 | Viewed by 1414
Abstract
Preventive maintenance is widely used in wind turbine equipment to ensure their safe and reliable operation, and this mainly includes time-based maintenance (TBM) and condition-based maintenance (CBM). Most wind farms only use TBM as the main maintenance strategy in engineering practice. Although this [...] Read more.
Preventive maintenance is widely used in wind turbine equipment to ensure their safe and reliable operation, and this mainly includes time-based maintenance (TBM) and condition-based maintenance (CBM). Most wind farms only use TBM as the main maintenance strategy in engineering practice. Although this can meet certain reliability requirements, it cannot fully utilize the characteristics of TBM and CBM. For this, a state model based on the stochastic differential equation (SDE) is established in this paper to describe the spatio-temporal evolution process of the degradation behavior of wind turbine generators, in which the components’ failure is represented by a proportional hazards model, the random fluctuation of the state is simulated by the Brownian motion, and the SDE model is solved by a function transformation method. Based on the model, the characteristics of TBM and CBM, and the asymptotic relationship between them, are discussed and analyzed, the necessity and feasibility of their combination are expounded, and a joint maintenance strategy is proposed and analyzed. The results show that the stochastic model can better reflect the real deterioration state of the generator. Moreover, TBM has a fixed maintenance interval, depending on global sample tracks and, only depending on the local sample track, CBM can follow the component state. Finally, the rationality and effectiveness of the proposed model and results are verified by a practical example. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
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42 pages, 3668 KiB  
Article
An Augmented Social Network Search Algorithm for Optimal Reactive Power Dispatch Problem
by Shahenda Sarhan, Abdullah Shaheen, Ragab El-Sehiemy and Mona Gafar
Mathematics 2023, 11(5), 1236; https://doi.org/10.3390/math11051236 - 3 Mar 2023
Cited by 16 | Viewed by 1565
Abstract
Optimal Reactive Power Dispatch (ORPD) is one of the main challenges in power system operations. ORPD is a non-linear optimization task that aims to reduce the active power losses in the transmission grid, minimize voltage variations, and improve the system voltage stability. This [...] Read more.
Optimal Reactive Power Dispatch (ORPD) is one of the main challenges in power system operations. ORPD is a non-linear optimization task that aims to reduce the active power losses in the transmission grid, minimize voltage variations, and improve the system voltage stability. This paper proposes an intelligent augmented social network search (ASNS) algorithm for meeting the previous aims compared with the social network search (SNS) algorithm. The social network users’ dialogue, imitation, creativity, and disputation moods drive the core of the SNS algorithm. The proposed ASNS enhances SNS performance by boosting the search capability surrounding the best possible solution, with the goal of improving its globally searched possibilities while attempting to avoid getting locked in a locally optimal one. The performance of ASNS is evaluated compared with SNS on three IEEE standard grids, IEEE 30-, 57-, and 118-bus test systems, for enhanced results. Diverse comparisons and statistical analyses are applied to validate the performance. Results indicated that ASNS supports the diversity of populations in addition to achieving superiority in reducing power losses up to 22% and improving voltage profiles up to 90.3% for the tested power grids. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
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30 pages, 4856 KiB  
Article
A Gradient-Based Optimizer with a Crossover Operator for Distribution Static VAR Compensator (D-SVC) Sizing and Placement in Electrical Systems
by Ghareeb Moustafa, Mostafa Elshahed, Ahmed R. Ginidi, Abdullah M. Shaheen and Hany S. E. Mansour
Mathematics 2023, 11(5), 1077; https://doi.org/10.3390/math11051077 - 21 Feb 2023
Cited by 18 | Viewed by 1561
Abstract
A gradient-based optimizer (GBO) is a recently inspired meta-heuristic technique centered on Newton’s gradient-based approach. In this paper, an advanced developed version of the GBO is merged with a crossover operator (GBOC) to enhance the diversity of the created solutions. The merged crossover [...] Read more.
A gradient-based optimizer (GBO) is a recently inspired meta-heuristic technique centered on Newton’s gradient-based approach. In this paper, an advanced developed version of the GBO is merged with a crossover operator (GBOC) to enhance the diversity of the created solutions. The merged crossover operator causes the solutions in the next generation to be more random. The proposed GBOC maintains the original Gradient Search Rule (GSR) and Local Escaping Operator (LEO). The GSR directs the search to potential areas and aids in its convergence to the optimal answer, while the LEO aids the searching process in avoiding local optima. The proposed GBOC technique is employed to optimally place and size the distribution static VAR compensator (D-SVC), one of the distribution flexible AC transmission devices (D-FACTS). It is developed to maximize the yearly energy savings via power losses concerning simultaneously different levels of the peak, average, and light loadings. Its relevance is tested on three distribution systems of IEEE 33, 69, and 118 nodes. Based on the proposed GBOC, the outputs of the D-SVCs are optimally varying with the loading level. Furthermore, their installed ratings are handled as an additional constraint relating to two compensation levels of 50% and 75% of the total reactive power load to reflect a financial installation limit. The simulation applications of the proposed GBOC declare great economic savings in yearly energy losses for the three distribution systems with increasing compensation levels and iterations compared to the initial case. In addition, the effectiveness of the proposed GBOC is demonstrated compared to several techniques, such as the original GBO, the salp swarm algorithm, the dwarf mongoose algorithm, differential evolution, and honey badger optimization. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
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25 pages, 14006 KiB  
Article
Design of Confidence-Integrated Denoising Auto-Encoder for Personalized Top-N Recommender Systems
by Zeshan Aslam Khan, Naveed Ishtiaq Chaudhary, Waqar Ali Abbasi, Sai Ho Ling and Muhammad Asif Zahoor Raja
Mathematics 2023, 11(3), 761; https://doi.org/10.3390/math11030761 - 2 Feb 2023
Cited by 4 | Viewed by 2028
Abstract
A recommender system not only “gains users’ confidence” but also helps them in other ways, such as reducing their time spent and effort. To gain users’ confidence, one of the main goals of recommender systems in an e-commerce industry is to estimate the [...] Read more.
A recommender system not only “gains users’ confidence” but also helps them in other ways, such as reducing their time spent and effort. To gain users’ confidence, one of the main goals of recommender systems in an e-commerce industry is to estimate the users’ interest by tracking the users’ transactional behavior to provide a fast and highly related set of top recommendations out of thousands of products. The standard ranking-based models, i.e., the denoising auto-encoder (DAE) and collaborative denoising auto-encoder (CDAE), exploit positive-only feedback without utilizing the ratings’ ranks for the full set of observed ratings. To confirm the rank of observed ratings (either low or high), a confidence value for each rating is required. Hence, an improved, confidence-integrated DAE is proposed to enhance the performance of the standard DAE for solving recommender systems problems. The correctness of the proposed method is authenticated using two standard MovieLens datasets such as ML-1M and ML-100K. The proposed study acts as a vital contribution for the design of an efficient, robust, and accurate algorithm by learning prominent latent features used for fast and accurate recommendations. The proposed model outperforms the state-of-the-art methods by achieving improved P@10, R@10, NDCG@10, and MAP scores. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
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18 pages, 4575 KiB  
Article
Physics-Based Observers for Measurement-While-Drilling System in Down-the-Hole Drills
by Gabriel Bout, Diego Brito, René Gómez, Gonzalo Carvajal and Guillermo Ramírez
Mathematics 2022, 10(24), 4814; https://doi.org/10.3390/math10244814 - 18 Dec 2022
Cited by 9 | Viewed by 3122
Abstract
Measurement While Drilling (MWD) is a technology for assessing rock mass conditions by collecting and analyzing data of mechanical drilling variables while the system operates. Nowadays, typical MWD systems rely on physical sensors directly installed on the drill rig. Sensors used in this [...] Read more.
Measurement While Drilling (MWD) is a technology for assessing rock mass conditions by collecting and analyzing data of mechanical drilling variables while the system operates. Nowadays, typical MWD systems rely on physical sensors directly installed on the drill rig. Sensors used in this context must be designed and conditioned for operating in harsh conditions, imposing trade-offs between the complexity, cost, and reliability of the measurement system. This paper presents a methodology for integrating physics-based observers into an MWD system as an alternative to complement or replace traditional physical sensors. The proposed observers leverage mathematical models of the drill’s electrical motor and its interaction with dynamic loads to estimate the bit speed and torque in a Down-the-Hole rig using current and voltage measurements taken from the motor power line. Experiments using data collected from four test samples with different rock strengths show a consistent correlation between the rate of penetration and specific energy derived from the observed drilling variables with the ones obtained from standardized tests of uniaxial compressive strength. The simplicity of the setup and results validate the feasibility of the proposed approach to be evaluated as an alternative to reduce the complexity and increase the reliability of MWD systems. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
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20 pages, 570 KiB  
Article
Solution Properties of a New Dynamic Model for MEMS with Parallel Plates in the Presence of Fringing Field
by Paolo Di Barba, Luisa Fattorusso and Mario Versaci
Mathematics 2022, 10(23), 4541; https://doi.org/10.3390/math10234541 - 1 Dec 2022
Cited by 1 | Viewed by 1171
Abstract
In this paper, starting from a well-known nonlinear hyperbolic integro-differential model of the fourth order describing the dynamic behavior of an electrostatic MEMS with a parallel plate, the authors propose an upgrade of it by formulating an additive term due to the effects [...] Read more.
In this paper, starting from a well-known nonlinear hyperbolic integro-differential model of the fourth order describing the dynamic behavior of an electrostatic MEMS with a parallel plate, the authors propose an upgrade of it by formulating an additive term due to the effects produced by the fringing field and satisfying the Pelesko–Driscoll theory, which, as is well known, has strong experimental confirmation. Exploiting the theory of hyperbolic equations in Hilbert spaces, and also utilizing Campanato’s Near Operator Theory (and subsequent applications), results of existence and regularity of the solution are proved and discussed particularly usefully in anticipation of the development of numerical approaches for recovering the profile of the deformable plate for a wide range of applications. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
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29 pages, 1725 KiB  
Article
Risk Factors Assessment of Musculoskeletal Disorders among Professional Vehicle Drivers in India Using an Ordinal Priority Approach
by Gajender Sharma, Shafi Ahmad, Z. Mallick, Zahid A. Khan, Ajith Tom James, Mohammad Asjad, Irfan Anjum Badruddin, Sarfaraz Kamangar, Syed Javed, Azam Ali Mohammed and N. Ameer Ahammad
Mathematics 2022, 10(23), 4492; https://doi.org/10.3390/math10234492 - 28 Nov 2022
Cited by 4 | Viewed by 2886
Abstract
Professional driving involves sitting in uncomfortable positions, navigating difficult terrain and roads, and occasionally conducting small repairs and other auxiliary transportation duties while at work for long periods. Drivers who engage in these activities may develop a variety of musculoskeletal disorders (MSDs). MSDs [...] Read more.
Professional driving involves sitting in uncomfortable positions, navigating difficult terrain and roads, and occasionally conducting small repairs and other auxiliary transportation duties while at work for long periods. Drivers who engage in these activities may develop a variety of musculoskeletal disorders (MSDs). MSDs in professional drivers are accompanied by several risk factors. In this study, the various risk factors for MSD have been identified through the literature reviews, discussions with professional drivers, and consultations with ergonomics specialists. This study employed the ordinal priority approach (OPA), a multi-criteria decision-making (MCDM) technique, to rank the identified risk variables for MSD in order of importance. The same OPA method has also been used to identify the group of professional drivers who use eight different types of vehicles and are more likely to develop MSDs. The analyses findings show that the five main risk factors for MSDs among drivers are prolonged sitting, restricted posture, working hours, alcohol consumption, and uncomfortable seating. Additionally, among all drivers regarded as professionals, truck drivers are found to be the most at risk. For the study’s conclusions to be validated, a sensitivity analysis was also carried out. The results of this study are anticipated to help formulate strategies for lowering these hazards through the ergonomic design of drivers’ cabins by automobile OEMs (Original Equipment Manufacturers) and vehicle scheduling by concerned transportation organizations to reduce driver tiredness. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
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18 pages, 371 KiB  
Article
Electrostatic-Elastic MEMS with Fringing Field: A Problem of Global Existence
by Paolo Di Barba, Luisa Fattorusso and Mario Versaci
Mathematics 2022, 10(1), 54; https://doi.org/10.3390/math10010054 - 24 Dec 2021
Cited by 2 | Viewed by 1993
Abstract
In this paper, we prove the existence and uniqueness of solutions for a nonlocal, fourth-order integro-differential equation that models electrostatic MEMS with parallel metallic plates by exploiting a well-known implicit function theorem on the topological space framework. As the diameter of the domain [...] Read more.
In this paper, we prove the existence and uniqueness of solutions for a nonlocal, fourth-order integro-differential equation that models electrostatic MEMS with parallel metallic plates by exploiting a well-known implicit function theorem on the topological space framework. As the diameter of the domain is fairly small (similar to the length of the device wafer, which is comparable to the distance between the plates), the fringing field phenomenon can arise. Therefore, based on the Pelesko–Driscoll theory, a term for the fringing field has been considered. The nonlocal model obtained admits solutions, making these devices attractive for industrial applications whose intended uses require reduced external voltages. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering, 2nd Edition)
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