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Recent Advances of Mathematics in Industrial Engineering
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Recent Advances of Mathematics in Industrial Engineering

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

Deadline for manuscript submissions: closed (30 April 2024) | Viewed by 13026

Special Issue Editors

Dr. Idelfonso B. R. Nogueira

E-Mail Website
Guest Editor
Department of Chemical Engineering, Norwegian University of Science and Technology, 7034 Trondheim, Norway
Interests: artificial intelligence; scientific machine learning; process system engineering; systems control & optimization; cyber-physical systems; digital twins
Special Issues, Collections and Topics in MDPI journals
Dr. Jozef Husar

E-Mail Website
Guest Editor
Department of Industrial Engineering and Informatics, Faculty of Manufacturing Technologies with a Seat in Prešov, Technical University of Košice, Prešov, Slovakia
Interests: IIoT; PLC; simulation; AR/MR; Industry 4.0/5.0; cyber security
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In the era of Industry 4.0, real-time data collection and analysis based on mathematical theory is extremely important. Creating active information systems which are characterized by the ability to learn and adapt to rapidly changing conditions supporting real decision-making processes would not be possible without the use of calculus, fuzzy logic solutions, statistics, quantitative methods, neural networks, big data analysis, and much more. It is necessary for the development of the industrial engineering area to exchange knowledge and experience in this area, which is the main purpose of this Special Issue.

Editors are invited to submit original and high-quality papers on the application of mathematics to industrial engineering education.

Dr. Idelfonso B. R. Nogueira
Dr. Jozef Husar
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

  • applied mathematics
  • quantitative methods
  • statistics theory
  • mathematical modeling
  • fuzzy logic
  • neural networks
  • fractional differential equations
  • big data mining and analysis
  • modularity measure
  • grey system theory
  • rough sets theory
  • digital technologies in mathematics
  • knowledge and learning technologies
  • optimization-based decision-support models
  • web-based decision-support systems
  • soft modeling in industrial engineering
  • applications of methods and decision-support systems in industrial engineering

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Published Papers (6 papers)

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Research

17 pages, 878 KiB  
Article
Efficient Parallel Processing of R-Tree on GPUs
by Jian Nong, Xi He, Jia Chen and Yanyan Liang
Mathematics 2024, 12(13), 2115; https://doi.org/10.3390/math12132115 - 5 Jul 2024
Viewed by 948
Abstract
R-tree is an important multi-dimensional data structure widely employed in many applications for storing and querying spatial data. As GPUs emerge as powerful computing hardware platforms, a GPU-based parallel R-tree becomes the key to efficiently port R-tree-related applications to GPUs. However, traditional tree-based [...] Read more.
R-tree is an important multi-dimensional data structure widely employed in many applications for storing and querying spatial data. As GPUs emerge as powerful computing hardware platforms, a GPU-based parallel R-tree becomes the key to efficiently port R-tree-related applications to GPUs. However, traditional tree-based data structures can hardly be directly ported to GPUs, and it is also a great challenge to develop highly efficient parallel tree-based data structures on GPUs. The difficulty mostly lies in the design of tree-based data structures and related operations in the context of many-core architecture that can facilitate parallel processing. We summarize our contributions as follows: (i) design a GPU-friendly data structure to store spatial data; (ii) present two parallel R-tree construction algorithms and one parallel R-tree query algorithm that can take the hardware characteristics of GPUs into consideration; and (iii) port the vector map overlay system from CPU to GPU to demonstrate the feasibility of parallel R-tree. Experimental results show that our parallel R-tree on GPU is efficient and practical. Compared with the traditional CPU-based sequential vector map overlay system, our vector map overlay system based on parallel R-tree can achieve nearly 10-fold speedup. Full article
(This article belongs to the Special Issue Recent Advances of Mathematics in Industrial Engineering)
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28 pages, 2329 KiB  
Article
Application of Structural Equation Modelling to Cybersecurity Risk Analysis in the Era of Industry 4.0
by Miroslav Gombár, Alena Vagaská, Antonín Korauš and Pavlína Račková
Mathematics 2024, 12(2), 343; https://doi.org/10.3390/math12020343 - 20 Jan 2024
Cited by 3 | Viewed by 1741
Abstract
In the current digital transformation to Industry 4.0, the demands on the ability of countries to react responsibly and effectively to threats in the field of cyber security (CS) are increasing. Cyber safety is one of the pillars and concepts of Industry 4.0, [...] Read more.
In the current digital transformation to Industry 4.0, the demands on the ability of countries to react responsibly and effectively to threats in the field of cyber security (CS) are increasing. Cyber safety is one of the pillars and concepts of Industry 4.0, as digitization brings convergence and integration of information technologies (IT) and operational technologies (OT), IT/OT systems, and data. Collecting and connecting a large amount of data in smart factories and cities poses risks, in a broader context for the entire state. The authors focus attention on the issue of CS, where, despite all digitization, the human factor plays a key role—an actor of risk as well as strengthening the sustainability and resilience of CS. It is obvious that in accordance with how the individuals (decision-makers) perceive the risk, thus they subsequently evaluate the situation and countermeasures. Perceiving cyber threats/risks in their complexity as a part of hybrid threats (HT) helps decision-makers prevent and manage them. Due to the growing trend of HT, the need for research focused on the perception of threats by individuals and companies is increasing. Moreover, the literature review points out a lack of methodology and evaluation strategy. This study presents the results of the research aimed at the mathematical modelling of risk perception of threats to the state and industry through the disruption of CS. The authors provide the developed factor model of cyber security (FMCS), i.e., the model of CS threat risk perception. When creating the FMCS, the researchers applied SEM (structural equation modelling) and confirmatory factor analysis to the data obtained by the implementation of the research tool (a questionnaire designed by the authors). The pillars and sub-pillars of CS defined within the questionnaire enable quantification in the perception of the level of risk of CS as well as differentiation and comparison between the analyzed groups of respondents (students of considered universities in SK and CZ). The convergent and discriminant validity of the research instrument is verified, and its reliability is confirmed (Cronbach’s alpha = 0.95047). The influence of the individual pillars is demonstrated as significant at the significance level of α = 5%. For the entire research set N = 964, the highest share of risk perception of CS threats is achieved by the DISRIT pillar (disruption or reduction of the resistance of IT infrastructure). Full article
(This article belongs to the Special Issue Recent Advances of Mathematics in Industrial Engineering)
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26 pages, 5072 KiB  
Article
Rescheduling Out-of-Gauge Trains with Speed Restrictions and Temporal Blockades on the Opposite-Direction Track
by Zhengwen Liao
Mathematics 2023, 11(12), 2659; https://doi.org/10.3390/math11122659 - 11 Jun 2023
Cited by 1 | Viewed by 1219
Abstract
Out-of-gauge trains are trains with loading freight that exceeds the loading limitation border. Considering collision avoidance, the out-of-gauge trains have speed restriction of their own, and the trains running on the parallel track. Therefore, it is necessary to execute a train rescheduling procedure [...] Read more.
Out-of-gauge trains are trains with loading freight that exceeds the loading limitation border. Considering collision avoidance, the out-of-gauge trains have speed restriction of their own, and the trains running on the parallel track. Therefore, it is necessary to execute a train rescheduling procedure to rearrange the train paths of the out-of-gauge trains and the affected trains based on the fundamental timetable. For rescheduling the timetable, considering the blockades and the speed restrictions caused by the out-of-gauge trains, this paper proposed a time-space-state network representation for describing the out-of-gauge train rescheduling problem. A novel concept, speed allowance, is introduced to describe the train speed restriction due to the out-of-gauge trains. An integer programming model based on the time-space network is proposed to minimize the total train delay when running the out-of-gauge trains. The model can be solved by the rolling-time horizon approach for reducing computational time. A numerical example is conducted based on the conventional railway in China, demonstrating the solution performance of the model and the practical use of the methodology. Gurobi solver cannot obtain an optimal solution within 1 h when the planning-time horizon is greater than 120 min. With the rolling-time horizon approach, the rescheduled timetable can be obtained within 124 s for the 300 min planning-time horizon using 180 min rolling-time window. Full article
(This article belongs to the Special Issue Recent Advances of Mathematics in Industrial Engineering)
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13 pages, 2371 KiB  
Communication
Logarithm-Based Methods for Interpolating Quaternion Time Series
by Joshua Parker, Dionne Ibarra and David Ober
Mathematics 2023, 11(5), 1131; https://doi.org/10.3390/math11051131 - 24 Feb 2023
Cited by 1 | Viewed by 2348
Abstract
In this paper, we discuss a modified quaternion interpolation method based on interpolations performed on the logarithmic form. This builds on prior work that demonstrated this approach maintains C2 continuity for prescriptive rotation. However, we develop and extend this method to descriptive [...] Read more.
In this paper, we discuss a modified quaternion interpolation method based on interpolations performed on the logarithmic form. This builds on prior work that demonstrated this approach maintains C2 continuity for prescriptive rotation. However, we develop and extend this method to descriptive interpolation, i.e., interpolating an arbitrary quaternion time series. To accomplish this, we provide a robust method of taking the logarithm of a quaternion time series such that the variables θ and n^ have a consistent and continuous axis-angle representation. We then demonstrate how logarithmic quaternion interpolation out-performs Renormalized Quaternion Bezier interpolation by orders of magnitude. Full article
(This article belongs to the Special Issue Recent Advances of Mathematics in Industrial Engineering)
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33 pages, 14147 KiB  
Article
Evaluation of Machine Learning-Based Parsimonious Models for Static Modeling of Fluidic Muscles in Compliant Mechanisms
by Monika Trojanová, Alexander Hošovský and Tomáš Čakurda
Mathematics 2023, 11(1), 149; https://doi.org/10.3390/math11010149 - 28 Dec 2022
Cited by 6 | Viewed by 2170
Abstract
This paper uses computational intelligence and machine learning methods to describe experimental modeling performed to approximate the static characteristics of one type of fluidic muscle from the manufacturer FESTO for three different muscle sizes. For the experiments, measured data from the manufacturer and [...] Read more.
This paper uses computational intelligence and machine learning methods to describe experimental modeling performed to approximate the static characteristics of one type of fluidic muscle from the manufacturer FESTO for three different muscle sizes. For the experiments, measured data from the manufacturer and data from a real system (i.e., test device) were used. The measurements, which took place on the experimental equipment, were carried out in two stages (i.e., when the muscle was pressed and when the muscle was relaxed). The resulting measured characteristics were obtained by averaging two values at a given moment. MATLAB® software was used for simulations, in which four models were created: MLP, SVM, ANFIS, and a custom model (i.e., polynomial model). Given that most articles mainly interpret their results graphically when approximating characteristics, in this article, the outputs of the models are also compared with the measured data based on the SSE, NRMSE, SBC, and AIC performance indicators, enabling a more relevant and comprehensive overview of the performance of the individual models. The outputs of the best models described in this article reach an accuracy of 89.90% to 98.74% (all from the MLP group), depending on the muscle size, compared to real measured outputs. Full article
(This article belongs to the Special Issue Recent Advances of Mathematics in Industrial Engineering)
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16 pages, 1346 KiB  
Article
Using Regression Analysis for Automated Material Selection in Smart Manufacturing
by Ivan Pavlenko, Ján Piteľ, Vitalii Ivanov, Kristina Berladir, Jana Mižáková, Vitalii Kolos and Justyna Trojanowska
Mathematics 2022, 10(11), 1888; https://doi.org/10.3390/math10111888 - 31 May 2022
Cited by 35 | Viewed by 3099
Abstract
In intelligent manufacturing, the phase content and physical and mechanical properties of construction materials can vary due to different suppliers of blanks manufacturers. Therefore, evaluating the composition and properties for implementing a decision-making approach in material selection using up-to-date software is a topical [...] Read more.
In intelligent manufacturing, the phase content and physical and mechanical properties of construction materials can vary due to different suppliers of blanks manufacturers. Therefore, evaluating the composition and properties for implementing a decision-making approach in material selection using up-to-date software is a topical problem in smart manufacturing. Therefore, the article aims to develop a comprehensive automated material selection approach. The proposed method is based on the comprehensive use of normalization and probability approaches and the linear regression procedure formulated in a matrix form. As a result of the study, analytical dependencies for automated material selection were developed. Based on the hypotheses about the impact of the phase composition on physical and mechanical properties, the proposed approach was proven qualitatively and quantitively for carbon steels from AISI 1010 to AISI 1060. The achieved results allowed evaluating the phase composition and physical properties for an arbitrary material from a particular group by its mechanical properties. Overall, an automated material selection approach based on decision-making criteria is helpful for mechanical engineering, smart manufacturing, and industrial engineering purposes. Full article
(This article belongs to the Special Issue Recent Advances of Mathematics in Industrial Engineering)
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