Інформаційні технології візуалізації технологічних процесів для дослідження режимів функціонування складних технологічних систем
The development of a mathematical model of a technical system based on the means of discrete-continuous networks and taking into account the interaction with a multimedia platform is presented. The efficiency of the process for visualizing the functioning of the complex technical system is increased...
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2021
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System research and information technologies| _version_ | 1867334417843748864 |
|---|---|
| author | Denisenko, Andrei Gurskiy, Alexander |
| author_facet | Denisenko, Andrei Gurskiy, Alexander |
| author_institution_txt_mv | [
{
"author": "Andrei Denisenko",
"institution": "Odessa National Polytechnic University, Odessa"
},
{
"author": "Alexander Gurskiy",
"institution": "Odessa National Academy of Food Technologies, Odessa"
}
] |
| author_sort | Denisenko, Andrei |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2021-09-16T11:48:22Z |
| description | The development of a mathematical model of a technical system based on the means of discrete-continuous networks and taking into account the interaction with a multimedia platform is presented. The efficiency of the process for visualizing the functioning of the complex technical system is increased by implementing the interaction of the modeling environment with the Unity platform in the feedback mode. The experiments linked to the integration of the DC-Net simulation software environment with the Unity cross-platform development environment are implemented. An example of developing the model of a technical system in the DC-Net environment and an example of developing a process for visualizing the functioning of a corresponding technical system based on the Unity platform are presented. The fundamental suitability of using the integration of various information technologies linked with various software environments has been confirmed. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2021.2.06 |
| first_indexed | 2025-07-17T10:27:27Z |
| format | Article |
| fulltext |
A.V. Denisenko, A.A. Gurskiy, 2021
74 ISSN 1681–6048 System Research & Information Technologies, 2021, № 2
TIДC
ПРОБЛЕМНО І ФУНКЦІОНАЛЬНО
ОРІЄНТОВАНІ КОМП’ЮТЕРНІ СИСТЕМИ
ТА МЕРЕЖІ
UDC 004.043
DOI: 10.20535/SRIT.2308-8893.2021.2.06
INFORMATION TECHNOLOGY OF VISUALIZATION FOR
TECHNOLOGICAL PROCESSES FOR RESEARCH MODES OF
FUNCTIONING OF COMPLEX TECHNOLOGICAL SYSTEMS
A.V. DENISENKO, A.A. GURSKIY
Abstract. The development of a mathematical model of a technical system based on
the means of discrete-continuous networks and taking into account the interaction
with a multimedia platform is presented. The efficiency of the process for visualiz-
ing the functioning of the complex technical system is increased by implementing
the interaction of the modeling environment with the Unity platform in the feedback
mode. The experiments linked to the integration of the DC-Net simulation software
environment with the Unity cross-platform development environment are imple-
mented. An example of developing the model of a technical system in the DC-Net
environment and an example of developing a process for visualizing the functioning
of a corresponding technical system based on the Unity platform are presented. The
fundamental suitability of using the integration of various information technologies
linked with various software environments has been confirmed.
Keywords: hybrid systems, discrete-continuous networks, Unity, multimedia plat-
form, Petri net.
INTRODUCTION
Information technology of visualization is going through the active stage of its
development. This technology in technical and research applications enables the
researcher to observe and correct the processes of functioning of a modulated ob-
ject or system. At the same time, this possibility is based on mathematical and
software support hidden from the researcher.
In the educational field, the technology of visualizing the process of mathe-
matical modeling is especially valuable for the successful mastering of educa-
tional material in technical disciplines. Also, visualization technology is important
for the acquisition of skills in practical work with complex technological systems
(СTS) in which mechanical, thermal, chemical, electrical, hydraulic and other
processes interact simultaneously [1–3].
Due to the increasing need for the use of interactive and distance learning
such research is rather relevant.
Visualization of the technological process is essential when modeling a
complex technical system. This complexity is caused by scientific and technical
Information technology of visualization for technological processes for research modes
Системні дослідження та інформаційні технології, 2021, № 2 75
progress, leading to the emergence of new, more and more complex technological
processes and complexes for which a qualitative analysis and appropriate control
methods are required. Naturally, methods and means of visualization must be im-
proved and developed in accordance with growing requirements.
The visualization technology of modeling processes for complex technical
systems is available in almost all known software modeling. However, not all
software tools are specialized in hybrid systems modeling [4, 5]. The theory of
discrete-continuous networks was proposed for modeling and research of such
hybrid systems in 1990–1993 [3]. The corresponding program DC-Net was de-
veloped in the Windows environment based on this theory. This program allows
for visualized editing of systems models represented by means of discrete-
continuous networks.
In addition to the development of the theory of discrete-continuous networks
and the DC-Net environment, the MATLAB / SIMULINK / SIKOSS software
complex stands out. This complex also provides for the use of special methods for
the synthesis of complex systems, but the MATLAB / SIMULINK / SIKOSS
complex has its drawbacks [3].
Despite the lack of specialized tools of discrete-continuous networks the
MATLAB / SIMULINK have great capabilities in the field of modeling complex
technical systems. But in the field of technology for visualization of technological
processes, the undisputed competitor is the tool package LabVIEW [6, 7]. How-
ever, the LabVIEW environment has its own process visualization format and its
own methods for developing virtual instruments and models of control systems.
The undeniably high visualization capabilities of various processes and
mathematical models is the Unity environment [8]. This environment is a cross-
platform development environment for computer games.
It is obvious that the greatest efficiency can be obtained by combining the
capabilities of various specialized software tools [9–11]. For example, a combina-
tion of the DC-Net program, which is specialized in modeling complex technical
systems, and the Unity environment, which provides the ability to efficiently visu-
alize the modeling processes. Accordingly, the work linked with the development
of some visualization information technology based on a combination of various
methods and tools of software is relevant.
The purpose of the scientific work is to increase the efficiency of the visu-
alization process of the functioning for complex technological complexes by im-
plementing the interaction of the modeling environment with the Unity platform
in the feedback mode.
PROBLEM STATEMENT
In order to achieve this purpose we need to develop a mathematical model of a
complex technical system based on the means of discrete-continuous networks,
taking into account the use of feedback functions from a multimedia platform.
Such multimedia platform provides visualization of the functioning of the com-
plex technical system.
The development of such a model involves the formation of a structure and
an algorithm for the operation of the complex of modeling, taking into account
the feedback functions from the Unity platform to the mathematical model repre-
sented by DC-Net tools.
A.V. Denisenko, A.A. Gurskiy
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 76
Ultimately, it is important to implement the developed schema using a real
example. It is important to establish the fundamental suitability of the complex of
modeling and it is also important to determine and confirm its advantages over the
analogs developed by the authors earlier.
MATERIALS AND METHODS
A multimedia platform for visualizing the functioning of the CTS is linked with a
virtual machine. This virtual machine is an integral part of the multimedia plat-
form and at the same time it can represent a certain model of a complex system.
For example, a description of the dynamic process of the functioning of the
CTS in ActionScript 3.0 allows further visualization of the corresponding proc-
esses, however, there is a high laboriousness of creating such a visualization sys-
tem. It is obvious that the creation of a CTS model by means of the DC-Net envi-
ronment is a less laborious process. But in this case, to integrate the multimedia
platform and the DC-Net software environment, it is necessary to present some
kind of information technology. The block diagram of the visualization system of
the corresponding information technology is shown in Fig. 1. As an example, a
not so complex system is considered in Fig. 1. The functioning of such a system
can be represented by a corresponding Petri net and some animation fragment.
This fragment represents the corresponding apparatus for the production of insu-
lated copper wire.
In this direction, it is important to implement the movement of visualization
objects im , defined in the Unity shell, which represents the corresponding multi-
uc(t) Wd DC-NET yc(t) xc(t) xd(td)
Fig. 1. Representation of CTS by means of discrete-continuous networks with feedback
from a multimedia platform
Information technology of visualization for technological processes for research modes
Системні дослідження та інформаційні технології, 2021, № 2 77
media platform. At the same time, the movement of visualization objects im , in
the field of coordinates
ii FF xy , depends on the variables )(tyc , )(txc , )(txd
according to the expressions presented in Fig. 1. The relationship between the
visualization process and the operation of technological equipment is presented in
Fig. 1. The functioning of the formed Petri net according to the variables )(tyc ,
)(txc , )(txd obtained from the DC-Net environment in Unity is also presented.
Thus, DC-Net simulates the necessary dynamic system and the multimedia
platform dynamically displays the necessary information and visualizes the
process of this system functioning.
In this example, the object of animation is a technological machine consist-
ing of equipment of continuous and discrete nature. The machine produces insu-
lated copper wire from bare wire and plastic. The constituent elements of the ma-
chine are discrete and continuous. Discrete elements are starting and stopping the
machine. Continuous elements are the movement of a copper wire and changes in
the level of liquid plastic in a container.
The functioning of the machine model is also represented by a Petri net, con-
sisting of P1, P2, P3, P4 positions and T1 transition.
Marking of position P1 means the presence of liquid plastic in the tank,
marking position P2 means the presence of a copper wire, marking position P3
means the presence of an insulated wire. If machine A fails or at least one mark is
missing, then the production of the insulated wire is stopped. In this case, the tran-
sition T1 does not work and the engine cannot start.
The main load on the development of the CTS simulation model is assumed
by the DC-Net graphic editor. In this case, the CTS model which is represented
by means of discrete-continuous networks together with a decision-making device
looks like shown in Fig. 2.
The continuous-event part of the system, represented by a discrete-
continuous network, is described by the following equations of state and the out-
put ))(),(()()( tutxtutx cc
ik
dc , ))(()()( txtuty c
ik
dc with a variable right-
hand side for the formation of a continuous state )(txc , where )( k
d tu
))(( л
d
л tyf is the vector function of controlling the operating modes, )(tuс is
the continuous control vector.
The discrete-continuous part is represented by the following equations of
state and output of the discrete subnet of the discrete-continuous network:
))(),(()( 1 к
d
лк
d
Vк
d
V tutxtx , )()( к
d
Vк
d
л txty , where )( к
d
л tu is the input ac-
tion for the logical part, )( к
d
V tx is the discrete vector of state ( is transition ma-
trix). The generated state vector T))(),(()( txtxtx dc is needed in the future to
control the visualization process.
Thus, in the DC-Net software environment, a state vector
)](),([ kdcIn txtxF is formed, which is enters in the transfer format of the vector
of continuous )(tX c and )( kd tX discrete variables from DC-net to the Unity
program, where )( kdl tu is the vector of discrete-event states from the continuous-
event part to the discrete-event part of the model in DC-Net.
A.V. Denisenko, A.A. Gurskiy
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 78
In the same way, the reverse transmission vector from Unity to DC-net is
formed )](),([out kdc twtuF , where Fi
c ytu )( ,
T
21 ...)( d
n
dd
kd wwwtw
is vector of discrete-event states from Flash to discrete-event part model in DC-
Net, where in
,,0
;,1
lFlFi
lFlFd
i vxvy
vxvy
w
i
ii
ii FF xy , is coordinates of the i -th object in the Unity — visualization window.
Accordingly, in the Unity-visualization window, the movement of objects
im or jm corresponds to the coordinates
ii FF xy , according to the following
expressions:
Fig. 2. Representation of CTS by means of discrete-continuous networks
Information technology of visualization for technological processes for research modes
Системні дослідження та інформаційні технології, 2021, № 2 79
,),(
;),(
:
tNfx
tNfy
m
i
i
F
F
i kN ,...,2,1 ,
if 1)( d
d tx then
.))((
;))((
:
txfx
txfy
m
c
F
c
F
j
i
i
Closing the parts of the discrete-event part and continuous-event part is real-
ized by means of the vector )( kddo txu .
The elements of this vector discretely change the coefficients of the equa-
tions representing the continuous-event part of the model, which is implemented
by means of DC-Net.
Thus, DC-Net simulates the necessary dynamic system, and Unity platform
dynamically visualizes the process of this system functioning.
For the correct interaction of two environments with different hierarchies
and principles of operation, the format of data transfer between systems had to be
standardized. The block diagram of the data exchange algorithm between DC-Net
and Unity is shown in Fig. 3. This algorithm determines the required values of
variables for animation of the process depending on the time interval of data ex-
change t .
ttk
ttfixedt
Fig. 3. Blok-diagram of the data exchange algorithm between Unity and DC-Net
A.V. Denisenko, A.A. Gurskiy
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 80
A method for organizing the vector of transfer of continuous and discrete
variables from DC-Net to Unity was also proposed to develop communication
between systems. These systems are combined into a single information technology
in which the DC-Net modeling system generates a parametric data transfer file.
EXPERIMENTS
In the software integrated environment DC-Net – Unity all necessary experiments
were carried out. To carry out an experiment, it is initially necessary to realize a
model of the investigated object in the software environment.
The continuous-event part of the mathematical model of the apparatus for
the production of an insulated wire is represented by the following equation in
matrix-differential form:
)())((|)|( 00 tutuBttX ckdkL ,
where
T
kmkLkL ttX
dt
d
ttX
dt
d
ttX )()()(
T
,
T
kmkLkL ttX
dt
d
ttX
dt
d
ttX )()()(
T
,
040302010 BBBBB ,
5000
05
01B ,
5000
00
02B ,
00
05
03B ,
00
00
04B
are constant matrices of the corresponding dimension )( mn ,
43210 ))(( kd tu is vector of modes control;
;00)()()(at0
,00)()()(at1
21
21
1 pptu
pptu
kod
kod
;01)()()(at0
,01)()()(at1
21
21
2 pptu
pptu
kod
kod
;10)()()(at0
,10)()()(at1
21
21
3 pptu
pptu
kod
kod
;11)()()(at0
,11)()()(at1
21
21
4 pptu
pptu
kod
kod
T
21 )()()( tututuc is input vector.
The discrete event part of the model is described by the following equation:
)()(||)()( 1 kdtkdkdkd tutWVWtxtx ,
where T|0...0)()(|)( mdcLdckdl XfXftu is vector of discrete-event
states from the continuous-event part to the discrete-event part of the DC-Net model;
W is an n × m matrix, the incidence matrix of Petri net;
Information technology of visualization for technological processes for research modes
Системні дослідження та інформаційні технології, 2021, № 2 81
T
21 ...)( d
n
dd
kd wwwtw is vector of discrete-event states from Unity
to discrete-event part of the model in DC-Net.
The discrete-continuous network editor window of the DC-Net program is
shown in Fig. 4. This editor realized a diagram of a model of an insulated wire
production apparatus.
The )(tX L , )(tX m , )(1 tu , )(2 tu variables and 13t , 23t , 33t structure-
controlled transitions of a discrete-continuous network are denoted in Figure 4.
The structure-controlled transitions provide a change in the coefficients of the
matrix iB0 , 4,,1i .
RESULTS
As a result of the work performed, a demonstration animation of the process in
functioning of the apparatus for the production of insulated wires was realized.
Also, visualization of the Petri net functioning was presented in parallel on the
same animation screen. This Petri net shows the work of the corresponding appa-
ratus. Thus, it is possible to obtain graphical information about changes in the pa-
rameters of a modeled object and its world linked with visualization (steam ex-
traction, color change, etc.) [12].
Ultimately, the requirements for the developed visualization system for the
modeling process were met.
DISCUSSION
The research results confirmed the assumptions that the introduction of feedback
from the visualization system to the model significantly expands the capabilities
Fig. 4. A fragment of the model diagram implemented by means of the DC-Net
environment
A.V. Denisenko, A.A. Gurskiy
ISSN 1681–6048 System Research & Information Technologies, 2021, № 2 82
of the developed information technology of visualization. It is obvious that such
information technology is necessary for distance learning and it is also possible to
find new applications of such technology.
Considering the above mathematical apparatus, one should focus on the d
iW
vector of discrete-event states of the model. Such vector is linked with specific
operations of creating feedback for DC-Net. This makes it possible to implement
the construction of new models. At the same time, additional structured transitions
are introduced into DC-Net for the further formation of a hierarchical system together
with the Unity platform. Feedback from this platform is shown in Fig. 1.
CONCLUSIONS
The scientific novelty of the results. The problem linked to with the develop-
ment of the mathematical model of a technical system based on the means of dis-
crete-continuous networks, taking into account the use of feedback functions from
the Unity platform was solved in the present work.
Thus the method of organizing the structure and formate of transferring the
vector of variables of the CTS model from the simulation software to the multi-
media platform and vice versa has got the further development.
The practical significance of the results. The developed methods for the
synthesis of CTS models based on an integrated multimedia platform and means
of discrete-continuous networks make it possible to implement a practical prob-
lem. This practical problem is linked with the implementation of virtual simula-
tors of distance learning systems.
The prospects for further research. Further development of the scientific
direction must be directly related to the formation of mathematical models for the
automated formation of algorithms or Petri nets within the framework of modern
intelligent technologies.
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Received 15.10.2020
INFORMATION ON THE ARTICLE
Andrei V. Denisenko, ORCID: 0000-0002-8610-0082, Odessa National Polytechnic
University, Odessa, Ukraine, e-mail: denisenko_1965@gmail.com
Alexander A. Gurskiy, ORCID: 0000-0001-5158-2125, Odessa National Academy of
Food Technologies, Odessa, Ukraine, e-mail: gurskiya2017@gmail.com
ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ ВІЗУАЛІЗАЦІЇ ТЕХНОЛОГІЧНИХ ПРОЦЕ-
СІВ ДЛЯ ДОСЛІДЖЕННЯ РЕЖИМІВ ФУНКЦІОНУВАННЯ СКЛАДНИХ
ТЕХНОЛОГІЧНИХ СИСТЕМ / А.В. Денисенко, О.О. Гурский
Анотація. Подано розвиток математичної моделі технологічної системи на ос-
нові засобів дискретно-неперервних мереж і з урахуванням взаємодії з муль-
тимедійною платформою. Забезпечено підвищення ефективності процесу візу-
алізації функціонування складної технологічної системи за рахунок реалізації
взаємодії середовища моделювання з платформою Unity в режимі зворотного
зв’язку. Реалізовано експерименти, що пов’язані з інтеграцією програмного
середовища моделювання DC-Net з інструментом для розроблення багатови-
мірних додатків Unity. Наведено приклад розроблення моделі технічної систе-
ми в середовищі DC-Net і приклад розроблення процесу візуалізації функціо-
нування відповідної технічної системи на основі платформи Unity.
Підтверджено принципову придатність використання інтеграції різних інфор-
маційних технологійб пов’язаних з різними програмними середовищами.
Ключові слова: складні технологічні системи, дискретно-неперервні мережі,
Unity, мультимедійна платформа, мережі Петрі.
ИНФОРМАЦИОННЫЕ ТЕХНОЛОГИИ ВИЗУАЛИЗАЦИИ ТЕХНОЛОГИЧЕ-
СКИХ ПРОЦЕССОВ ДЛЯ ИССЛЕДОВАНИЯ РЕЖИМОВ ФУНКЦИОНИ-
РОВАНИЯ СЛОЖНЫХ ТЕХНОЛОГИЧЕСКИХ СИСТЕМ / А.В. Денисенко,
А.А. Гурский
Аннотация. Представлено развитие математической модели технологической
системы на основе средств дискретно-непрерывных сетей и с учетом взаимо-
действия с мультимедийной платформой. Обеспечено повышение эффектив-
ности процесса визуализации функционирования сложной технологической
системы за счет реализации взаимодействия среды моделирования с платфор-
мой Unity в режиме обратной связи. Реализованы эксперименты, связанные с
интеграцией программной среды моделирования DC-Net с инструментом для
разработки многомерных приложений Unity. Приведен пример разработки
модели технической системы в среде DC-Net и пример разработки процесса
визуализации функционирования соответствующей технической системы на
основе платформы Unity. Подтверждена принципиальная пригодность приме-
нения интеграции различных информационных технологий, связанных с раз-
личными программными средами.
Ключевые слова: сложные технологические системы, дискретно-непрерывные
сети, Unity, мультимедийная платформа, сети Петри.
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| id | journaliasakpiua-article-239879 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:27:27Z |
| publishDate | 2021 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/33/4cdd7793bc9190348cce646338237a33.pdf |
| spelling | journaliasakpiua-article-2398792021-09-16T11:48:22Z Information technology of visualization for technological processes for research modes of functioning of complex technological systems Информационные технологии визуализации технологических процессов для исследования режимов функционирования сложных технологических систем Інформаційні технології візуалізації технологічних процесів для дослідження режимів функціонування складних технологічних систем Denisenko, Andrei Gurskiy, Alexander сложные технологические системы дискретно-непрерывные сети Unity мультимедийная платформа сети Петри складні технологічні системи дискретно-неперервні мережі Unity мультимедійна платформа мережі Петрі hybrid systems discrete-continuous networks Unity multimedia platform Petri net The development of a mathematical model of a technical system based on the means of discrete-continuous networks and taking into account the interaction with a multimedia platform is presented. The efficiency of the process for visualizing the functioning of the complex technical system is increased by implementing the interaction of the modeling environment with the Unity platform in the feedback mode. The experiments linked to the integration of the DC-Net simulation software environment with the Unity cross-platform development environment are implemented. An example of developing the model of a technical system in the DC-Net environment and an example of developing a process for visualizing the functioning of a corresponding technical system based on the Unity platform are presented. The fundamental suitability of using the integration of various information technologies linked with various software environments has been confirmed. Представлено развитие математической модели технологической системы на основе средств дискретно-непрерывных сетей и с учетом взаимодействия с мультимедийной платформой. Обеспечено повышение эффективности процесса визуализации функционирования сложной технологической системы за счет реализации взаимодействия среды моделирования с платформой Unity в режиме обратной связи. Реализованы эксперименты, связанные с интеграцией программной среды моделирования DC-Net с инструментом для разработки многомерных приложений Unity. Приведен пример разработки модели технической системы в среде DC-Net и пример разработки процесса визуализации функционирования соответствующей технической системы на основе платформы Unity. Подтверждена принципиальная пригодность применения интеграции различных информационных технологий, связанных с различными программными средами. Подано розвиток математичної моделі технологічної системи на основі засобів дискретно-неперервних мереж і з урахуванням взаємодії з мультимедійною платформою. Забезпечено підвищення ефективності процесу візуалізації функціонування складної технологічної системи за рахунок реалізації взаємодії середовища моделювання з платформою Unity в режимі зворотного зв’язку. Реалізовано експерименти, що пов’язані з інтеграцією програмного середовища моделювання DC-Net з інструментом для розроблення багатовимірних додатків Unity. Наведено приклад розроблення моделі технічної системи в середовищі DC-Net і приклад розроблення процесу візуалізації функціонування відповідної технічної системи на основі платформи Unity. Підтверджено принципову придатність використання інтеграції різних інформаційних технологійб пов’язаних з різними програмними середовищами. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2021-09-14 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/239879 10.20535/SRIT.2308-8893.2021.2.06 System research and information technologies; No. 2 (2021); 74-83 Системные исследования и информационные технологии; № 2 (2021); 74-83 Системні дослідження та інформаційні технології; № 2 (2021); 74-83 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/239879/238276 |
| spellingShingle | складні технологічні системи дискретно-неперервні мережі Unity мультимедійна платформа мережі Петрі Denisenko, Andrei Gurskiy, Alexander Інформаційні технології візуалізації технологічних процесів для дослідження режимів функціонування складних технологічних систем |
| title | Інформаційні технології візуалізації технологічних процесів для дослідження режимів функціонування складних технологічних систем |
| title_alt | Information technology of visualization for technological processes for research modes of functioning of complex technological systems Информационные технологии визуализации технологических процессов для исследования режимов функционирования сложных технологических систем |
| title_full | Інформаційні технології візуалізації технологічних процесів для дослідження режимів функціонування складних технологічних систем |
| title_fullStr | Інформаційні технології візуалізації технологічних процесів для дослідження режимів функціонування складних технологічних систем |
| title_full_unstemmed | Інформаційні технології візуалізації технологічних процесів для дослідження режимів функціонування складних технологічних систем |
| title_short | Інформаційні технології візуалізації технологічних процесів для дослідження режимів функціонування складних технологічних систем |
| title_sort | інформаційні технології візуалізації технологічних процесів для дослідження режимів функціонування складних технологічних систем |
| topic | складні технологічні системи дискретно-неперервні мережі Unity мультимедійна платформа мережі Петрі |
| topic_facet | сложные технологические системы дискретно-непрерывные сети Unity мультимедийная платформа сети Петри складні технологічні системи дискретно-неперервні мережі Unity мультимедійна платформа мережі Петрі hybrid systems discrete-continuous networks Unity multimedia platform Petri net |
| url | https://journal.iasa.kpi.ua/article/view/239879 |
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