Eng Cn Translate this page:
Please select your language to translate the article


You can just close the window to don't translate
Library
Your profile

Back to contents

Software systems and computational methods
Reference:

About Modeling Digital Twins of a Social Group

Kovalev Sergei

ORCID: 0000-0002-1132-6888

PhD in Technical Science

Associate Professor, Department of Computer Engineering, I.N. Ulianov Chuvash State University

428015, Russia, Republic of Chuvashia, Cheboksary, Moskovsky Prospekt, 15, office B-309

srgkov@gmail.com
Smirnova Tatiana

ORCID: 0000-0001-6687-9415

PhD in Physics and Mathematics

Associate Professor, Department of Mathematical and Hardware support of information Systems, I.N. Ulianov Chuvash State University

428015, Russia, Republic of Chuvashia, Cheboksary, Moskovsky Prospekt, 15, office B-304

smirnova-tanechka@yandex.ru
Filippov Vladimir

ORCID: 0000-0002-7240-4405

PhD in Physics and Mathematics

Associate Professor, Department of Mathematical and Hardware support of information Systems, I.N. Ulianov Chuvash State University

428015, Russia, Republic of Chuvashia, Cheboksary, Moskovsky Prospekt, 15, office B-304

filippov_v_p@mail.ru
Andreeva Antonina

ORCID: 0000-0003-0843-2230

PhD in Technical Science

Associate Professor, Department of Computer Engineering, I.N. Ulianov Chuvash State University

428015, Russia, Republic of Chuvashia, Cheboksary, Moskovsky Prospekt, 15, office B-309

antonina-andreeva21@yandex.ru

DOI:

10.7256/2454-0714.2022.4.39264

EDN:

MPUQIE

Received:

27-11-2022


Published:

30-12-2022


Abstract: The object of the study is mathematical modeling methods. The subject of the study is the application of mathematical methods in modeling digital twins of a social group. The aim of the work is to model the digital counterparts of a social group. A digital double is a digital copy of a physical object or process, with the right approach, it helps to improve the main and auxiliary business processes. This concept is part of the fourth industrial revolution and is designed to help detect problems faster, find out what will happen to the original in different conditions and, as a result, produce better products. In this article, some applied aspects are considered, the main provisions of the mathematical theory of digital twins of social groups are presented. To solve the problem of creating a digital double of a social group (students) as one of the tools, the authors proposed to use the technologies of population algorithms. The novelty of the research consists in the application of the swarm part algorithm for modeling digital twins of a social group. The particle swarm method was chosen as a research tool. As the social group under study finds the optimal position in space, so the element of the digital twin of the particle swarm model based on them can search in space, in particular, the extremes of functions. Which, for example, is applicable to finding the minimum of the loss function in machine learning. A graphical simulation in the Java Script language was performed using the three library.js. Data processing was performed using the C# Job System, which provides parallelization of computing processes and is integrated into the Entity Component System. A program was implemented that simulates the activity of a student group as one of the constituent elements of a digital twin of a social group. Swarm algorithms are promising in the field of practical application. On their basis, it is possible not only to solve the problems of digital twins, but also to manage groups of robots, robotic systems and complexes.


Keywords:

digital twin, social group, mathematical model, swarm algorithms, boids model, JavaScript language, population algorithms, library Job System, search algorithm, model parallelization

This article is automatically translated. You can find original text of the article here.

IntroductionA digital twin is a software analogue of a real object [1] that simulates internal processes [2], technical characteristics and behavior under the influence of interference and the environment [3].

This concept is part of the fourth industrial revolution [4] and is designed to help detect problems faster, find out what will happen to the original in different conditions and, as a result, produce better products [5]. The topic of the digital double is becoming popular in various subject areas, for example, it is considered in intelligent battery management systems [6], finds application in information modeling of parts based on ontology [7].

Currently, research is being actively conducted on mathematical modeling of the behavior of social groups (students, etc.) and their decision-making depending on emotional upbringing and logical experience.

Mathematical models are created according to scientific theories, including the general theory of human psychology.

This allows you to create digital doubles similar to real social groups of people, rather than fictional abstract creatures.

Numerical values are used as input "psychological" parameters of models that allow "calculating" the behavior of social groups. To describe the psychological behavior of social groups of people, the input parameters of mathematical models of a digital double are numerical characteristics inherent in a person (student).

Population algorithmsIn this article we will focus on the applied aspects and present some results of the mathematical theory of digital doubles of social groups (students).

To solve the problem of creating a digital double of a social group (students) as one of the tools, it is advisable to use technologies of population algorithms (evolutionary algorithms; algorithms using the concept of swarm algorithms; algorithms based on other mechanisms of living and inanimate nature) [8].

Swarm algorithms are a class of algorithms that appeared on the basis of observations of colonies of living creatures: flocks of birds, schools of fish, swarms of bees, colonies of ants [9].

The methodology of swarm algorithms is based on decentralized systems consisting of monotonous elements (agents) indirectly interacting with each other [10] and with the environment to achieve a predetermined goal [11]. It is this definition that underlies the swarm algorithm [12].

Swarm algorithms (part swarm algorithm, ant algorithm, etc.) arose as a result of modeling the behavior of birds in a flock [13] (part swarm algorithm [14]) and studying the principles of ant behavior in nature (ant colony algorithm or ant algorithm [15]). In [16], the proposed modification of the particle swarm algorithm is also justified using the theoretical concept of swarm intelligence, and not based on mathematical models of the algorithm. After the spread of swarm algorithms, various mathematical models were applied to them, including Markov chains. The use of Markov chains makes it possible to prove the convergence of the algorithms under consideration to the global optimum only theoretically, with the running time of the algorithm tending to infinity, but this does not explain the high efficiency of swarm algorithms shown in numerous experiments and for solving practical problems with time constraints.

The changes taking place in a group of students is an example of the collective behavior of a social group. They can move in a coordinated manner, split up and then reassemble into a group.

It was noticed that groups of people (students) often solve optimization problems, usually multi-criteria.

In the course of the work, it was decided to focus on the particle swarm method (the swarm part algorithm) and check how effective and convenient this method is to implement, and how it can be improved if such a need arises.

The classic rules of object behavior were formed by Craig Reynolds back in 1986 from his bird watching. With their help, he created a computer model of the flock, called boids. Here are the basic rules.

1. Each bird tries not to approach its relatives by less than some minimum allowable distance. This rule is designed to avoid collisions among birds.

2. Each bird tries to choose its own velocity vector so that it is closest to the average velocity vector of all birds in its local neighborhood. This rule coordinates the direction and speed of the birds.

3. Each bird tends to be located in the geometric center of mass of its local neighborhood. This rule forces each bird to stay inside its flock.

Application of swarm algorithms technology in modeling digital twins of a social group

stay_ptiz

Fig. 1. Graphical simulation of a group in Java Script using the library three.js

Figure 1 shows a graphical simulation of the group in the Java Script language using the three library.js, which is used to create and display animated 3D computer graphics in the development of web applications [17].

As the social group under study (a group of students) finds the optimal position in space, so the element of the digital twin of the particle swarm model based on them can search in space, in particular, the extremes of functions. Which, for example, is applicable to finding the minimum of the loss function in machine learning.

Students in the group move in two-dimensional space. Each person has a velocity vector, an acceleration vector, and a position vector. We will also introduce the concept of a local neighborhood of a person (the object of research), within which the student controls his position relative to the rest of the members of the social group.

The key value in the particle swarm method is an algorithm for updating the speed of movement of an individual. For example, by the formula

v[i] = v[i] + a(p[i] - x[i]) + b(g - x[i]),

where:

v[i] human speed;

p[i] is the simplest individual memory equal to the coordinates of the best point of the particle trajectory for the entire time of its existence;

g is the collective memory representing the coordinates of the best point reached by the whole swarm;

x[i] coordinates of the particle;

a and b are some coefficients, usually from the range [0; 1]; if parameter a is chosen randomly, then b = 1 a.

Here is the search algorithm.

1. A group of M people is created.

2. The vector p[i] and the vector g are calculated.

3. Students' speeds are randomly initialized.

4. The program runs until the stop criterion is met (the target is found with an accuracy that satisfies us).

5. For all students: choose random coefficients a and b in the range from 0 to 1.

6. v[i] = v[i] + a(p[i] - x[i]) + b(g - x[i]).

7. x[i] = x[i] + t*v[i].

8. If f(x[i]) > f(p[i]), then p[i] = x[i].

9. If f(x[i]) > f(g), then g = x[i].

10. We return the vector g (the assumed coordinates of the target).

In such an algorithm, the speeds increase uncontrollably, so you can enter the resistance of the medium for simulation.

v[i] = G*v[i] + a(p[i] - x[i]) + b(g - x[i]),

where R < 1 is the resistance coefficient of the medium. Or you can simply set the maximum speed of a person, above which she will not be able to accelerate.

The acceleration vector is formed from the results of three main functions:

alignment alignment;

cohesion cohesion;

separation separation.

These functions correspond to the three classical rules of behavior of the boids model. The results of the functions (vectors) add up and form the acceleration vector of a person.

During the development of the digital twin model element of a social group (students), the Entity Component System design pattern described by the Entity-Component-System structure was applied. Entities are containers for components. Components store all kinds of properties of events or objects (students). Systems determine the way they are processed and store methods for their execution.

Fig. 2. Entity Component System Design Pattern

Data processing was performed using the C# Job System, which provides parallelization of computing processes and is integrated into the Entity Component System. Computational tasks are formed for each student, which are distributed across computing processors, which gives a significant increase in productivity.

Fig. 3. Parallelization of the social group model (students) using JobSystem

In the course of the work, a program simulating a social group (students) was implemented as one of the constituent elements of the digital twin of a social group.

Swarm algorithms do not require the creation of new populations at each step by selecting and crossing agents of the previous population, but use collective decentralized movements of agents of one population, without selection procedures, destruction of old ones and generation of new ones [18].

Swarm algorithms are promising in the field of practical application. On their basis, it is possible not only to solve the problems of digital twins, but also to control groups of robots [19], robotic systems and complexes [20].

References
1. Zuikova A. What are digital doubles and where they are used [Electronic resource]. URL: https://trends.rbc.ru/trends/industry/6107e5339a79478125166eeb (Date of reference: 20.11.2022).
2. Liu, J., Liu J., Zhuang, C., Liu, Z., Miao, T. (2021). Construction method of shop-floor digital twin based on MBSE. Journal of Manufacturing Systems, 202160 R, 93-118. Retrieved from. doi:10.1016/j.jmsy.2021.05.004
3. Prokhorov A., Lysachev M. Digital double. Analysis, trends, world experience. Moscow : Alliansprint LLC, 2020. 309 p.
4. Jiewu, L., Dewen, W., Weiming Sh., Xinyu L., Qiang L., Xin C. (2021). Digital twins-based smart manufacturing system design in Industry 4.0: A review. Journal of Manufacturing Systems, 60 R, 119-137. doi:10.1016/j.jmsy.2021.05.011
5. Jun, Y., Zhifeng, L., Caixia, Zh., Tao, Zh., Congbin, Y. (2021). Research on flexible job shop scheduling under finite transportation conditions for digital twin workshop // Robotics and Computer-Integrated Manufacturing, 72, article no. 102198. doi:10.1016/j.rcim.2021.102198
6. Wang W., Wang J., Tian J., Lu J., Xiong R. (2021). Application of Digital Twin in Smart Battery Management Systems. Chinese Journal of Mechanical Engineering (English Edition), 34, article no. 57. doi:10.1186/s10033-021-00577-0
7. Dai, S., Zhao, G., Yu, Y., Zheng, P., Bao, Q., Wang, W. (2021). Ontology-based information mo deling method for digital twin creation of asfabricated machining parts // Robotics and Computer-Integrated Manufacturing, 72, article no. 102173. doi:10.1016/j.rcim.2021.102173
8. Gadasin D. V. Using the particle swarm method for load balancing in Internet of Things networks / D. V. Gadasin, N. A. Smalkov, I. A. Kuzin // Synchronization systems, signal generation and processing. 2022. Vol. 13. No. 2. pp. 17-23. EDN LIUWNT.
9. On the acquisition of research experience by future IT specialists in the conditions of a student circle / S. V. Kovalev, T. N. Kopysheva, T. V. Mitrofanova, T. N. Smirnova // Modern high-tech technologies. 2021. No. 7. Pp. 117122. DOI 10.17513/snt.38762. EDN YCJEAI.
10. Oskin A. F. Algorithm and numerical optimization program implementing the particle swarm method / A. F. Oskin, D. A. Oskin // Bulletin of the Polotsk State University. Series C. Fundamental Sciences. 2022. No. 4. pp. 26-31. DOI 10.52928/2070-1624-2022-38-4-26-31. EDN FNFWWC.
11. Larionov V. S. The effectiveness of particle swarm-based methods in optimizing ICLPSO training of neural networks / V. S. Larionov, L. H. Safiullina // Modern science: actual problems of theory and practice. Series: Natural and Technical Sciences. 2022. No. 4-2. pp. 81-87. DOI 10.37882/2223-2966.2022.04-2.22. EDN WMDMDX.
12. Larionov V. S. The efficiency of parallelization of the particle swarm-based method in optimizing neural network learning / V. S. Larionov, O. G. Maleev // Modern Science: actual problems of theory and practice. Series: Natural and Technical Sciences. 2022. No. 7. pp. 71-77. DOI 10.37882/2223-2966.2022.07.18. EDN EIZWEP.
13. Beni, G. & Wang, J. (June, 1989). Swarm Intelligence in Cellular Robotic Systems In Proc. of NATO Advanced Workshop on Robots and Biological Systems, 102, 703-712. Tuscany. Italy. doi:10.1007/978-3-642-58069-7_38
14. Kennedy, J. & Eberhart, R. (27 November 01 December, 1995). Particle Swarm Optimization. Proc. of IEEE International Conference on Neural Network, 19421948. Piscataway, NJ. doi:10.1109/ICNN.1995.488968
15. Dorigo, M., Birattari, M., Stutzle, T. (2006). Ant Colony Optimization. Artificial Ants as a Computational Intelligence Technique. IRIDIA. Technical Report Series. Technical Report No. TR/IRIDIA/2006-023. Brussels. Belgium. 14 pp. doi:10.1109/MCI.2006.329691
16. Pedersen, M., Chippereld, A. (2010). Simplifying Particle Swarm Optimization. Applied Soft Computing, 10, Issue 2, 618628. doi:10.1016/j.asoc.2009.08.029
17. Three.js Documentation: official website. URL: https://threejs.org/docs/ (Date of reference: 20.09.2022).
18. Beni, G. From Swarm Intelligence to Swarm Robotics (2005). Swarm Robotics. Lecture Notes in Computer Science, 3342, 19. doi.10.1007/978-3-540-30552-1_1
19. Sahin, E. (2005). Swarm robotics: From sources of inspiration to domains of application. Swarm Robotics. Lecture Notes in Computer Science, 3342, 1020.
20. Arkhipov M. V. Industrial robots: control of manipulative robots. M. : Yurayt, 2022. 170 p.

Peer Review

Peer reviewers' evaluations remain confidential and are not disclosed to the public. Only external reviews, authorized for publication by the article's author(s), are made public. Typically, these final reviews are conducted after the manuscript's revision. Adhering to our double-blind review policy, the reviewer's identity is kept confidential.
The list of publisher reviewers can be found here.

The article submitted for review examines the applied aspects of modeling digital twins of a social group. The research methodology is based on the study and generalization of literary sources on the topic of the work, the use of population algorithms technology (evolutionary algorithms; algorithms using the concept of swarm algorithms; algorithms based on other mechanisms of living and inanimate nature). The author of the article associates the relevance of the work with the fact that currently research is actively conducted on the mathematical modeling of the behavior of social groups (students, etc.) and their decision-making depending on emotional education and logical experience. The scientific novelty of the reviewed study, according to the reviewer, lies in the development of one of the constituent elements of the digital twin of a social group a program that simulates a social group based on the use of swarm algorithms. The following sections are structurally highlighted in the article: Introduction, Population algorithms, Application of swarm algorithms technology in modeling digital twins of a social group, as well as a Bibliography. The author outlines the methodology of swarm algorithms, focuses on the particle swarm method and checks how effective and convenient this method is to implement, how it can be improved if necessary. The article is illustrated with three figures, which reflect a graphical simulation of the group in the Java Script language using the three library.js, the Entity Component System design pattern and parallelization of the social group (student) model using JobSystem. The bibliographic list includes 20 sources publications of foreign and domestic scientists on the topic of the article. The text contains targeted references to literary sources confirming the existence of an appeal to opponents. A number of comments on the article should be made. Firstly, its text does not reflect the purpose and objectives of the study, respectively, it is not clear why it is specifically necessary to model the behavior of a social group, which specific aspects of behavior should be reflected in a model reflecting the movement of a social group of students in two-dimensional space. Secondly, the author does not specify which characteristics and input parameters were used in the development of mathematical models of the digital twin, and what information can be obtained as a result of their application. Thirdly, for some reason there was no place in the structural composition of the article for a conclusion or conclusion, where the results of the study would be reflected, the correspondence of the research results to the set goals was stated. The reviewed material corresponds to the direction of the journal "Software Systems and Computational Methods", has been prepared on an urgent topic, contains informative material on the development of mathematical models of digital twins of social groups, however, according to the reviewer, needs to be finalized in accordance with the comments made.