Using graph-analytical methods modeling of system objects to determine integrated assessment of their state
In article is determined of object state in researching "system - environment" based on system analytic-graph modeling for representation real relationships and relations between any systems in nature. Justified non-standard solution according to forecasting states and changes results in &...
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Kozulia, T.V. Kozulia, M.M. 2023-12-03T14:17:42Z 2023-12-03T14:17:42Z 2019 Using graph-analytical methods modeling of system objects to determine integrated assessment of their state / T.V. Kozulia, M.M. Kozulia // Problems of atomic science and technology. — 2019. — № 3. — С. 116-123. — Бібліогр.: 12 назв. — англ. 1562-6016 PACS: 519.713: 631.411.6 https://nasplib.isofts.kiev.ua/handle/123456789/195152 In article is determined of object state in researching "system - environment" based on system analytic-graph modeling for representation real relationships and relations between any systems in nature. Justified non-standard solution according to forecasting states and changes results in "system - environment" based on constructed cognitive models and entropy analysis for action direction sustainability and implemented situations assessment. Practical usage of systematic methodological support for complex objects comprehensive research based on graph models sequential analysis. To analyze physical processes displacements between simple ideal system components, which are sources of potential and kinetic energy, changes in its capacity through matter or energy accumulation, is used structural graph-physical processes topological model. Визначено стан об'єкта при дослідженні "система - середовище", заснованого на системном граф-аналітичному моделюванні для представлення реальних зв'язків та відносин між будь-якими системами в природі. Обгрунтоване нестандартне рішення за прогнозними станами та змінами призводить до стану "системи - середовища", що базується на побудованих когнітивних моделях та аналізі ентропії для оцінки стійкості напрямку діяльності та реалізації ситуації. Практичне використання систематичної методологічної підтримки комплексних об'єктів комплексного дослідження базується на послідовному аналізі моделей графів. Для аналізу фізичних процесів зміщення між простими компонентами ідеальної системи, які є джерелами потенційної та кінетичної енергії, зміни його потужності через накопичення речовини або енергії, використовується структурний граф-топологічна модель фізичних процесів. Определено состояние объекта при исследовании "система - среда", основанного на системном граф-аналитическом моделировании для представления реальных связей и отношений между любыми системами в природе. Обоснованное нестандартное решение по прогнозным состояниям и изменениям приводит к состоянию "система - среда", основанному на построенных когнитивных моделях и анализе энтропии для оценки устойчивости направления деятельности и реализации ситуации. Практическое использование систематической методологической поддержки комплексных объектов комплексного исследования базируется на последовательном анализе моделей графов. Для анализа физических процессов смещения между простыми компонентами идеальной системы, которые являются источниками потенциальной и кинетической энергии, изменения его мощности через накопление вещества или энергии, используется структурная граф-топологичная модель физических процессов. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Computing and modelling systems Using graph-analytical methods modeling of system objects to determine integrated assessment of their state Використання граф-аналітичних методів моделювання системних об'єктів для визначення інтегральної оцінки їхнього стану Использование граф-аналитических методов моделирования системных объектов для определения интегрированной оценки их состояния Article published earlier |
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Using graph-analytical methods modeling of system objects to determine integrated assessment of their state |
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Using graph-analytical methods modeling of system objects to determine integrated assessment of their state Kozulia, T.V. Kozulia, M.M. Computing and modelling systems |
| title_short |
Using graph-analytical methods modeling of system objects to determine integrated assessment of their state |
| title_full |
Using graph-analytical methods modeling of system objects to determine integrated assessment of their state |
| title_fullStr |
Using graph-analytical methods modeling of system objects to determine integrated assessment of their state |
| title_full_unstemmed |
Using graph-analytical methods modeling of system objects to determine integrated assessment of their state |
| title_sort |
using graph-analytical methods modeling of system objects to determine integrated assessment of their state |
| author |
Kozulia, T.V. Kozulia, M.M. |
| author_facet |
Kozulia, T.V. Kozulia, M.M. |
| topic |
Computing and modelling systems |
| topic_facet |
Computing and modelling systems |
| publishDate |
2019 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Використання граф-аналітичних методів моделювання системних об'єктів для визначення інтегральної оцінки їхнього стану Использование граф-аналитических методов моделирования системных объектов для определения интегрированной оценки их состояния |
| description |
In article is determined of object state in researching "system - environment" based on system analytic-graph modeling for representation real relationships and relations between any systems in nature. Justified non-standard solution according to forecasting states and changes results in "system - environment" based on constructed cognitive models and entropy analysis for action direction sustainability and implemented situations assessment. Practical usage of systematic methodological support for complex objects comprehensive research based on graph models sequential analysis. To analyze physical processes displacements between simple ideal system components, which are sources of potential and kinetic energy, changes in its capacity through matter or energy accumulation, is used structural graph-physical processes topological model.
Визначено стан об'єкта при дослідженні "система - середовище", заснованого на системном граф-аналітичному моделюванні для представлення реальних зв'язків та відносин між будь-якими системами в природі. Обгрунтоване нестандартне рішення за прогнозними станами та змінами призводить до стану "системи - середовища", що базується на побудованих когнітивних моделях та аналізі ентропії для оцінки стійкості напрямку діяльності та реалізації ситуації. Практичне використання систематичної методологічної підтримки комплексних об'єктів комплексного дослідження базується на послідовному аналізі моделей графів. Для аналізу фізичних процесів зміщення між простими компонентами ідеальної системи, які є джерелами потенційної та кінетичної енергії, зміни його потужності через накопичення речовини або енергії, використовується структурний граф-топологічна модель фізичних процесів.
Определено состояние объекта при исследовании "система - среда", основанного на системном граф-аналитическом моделировании для представления реальных связей и отношений между любыми системами в природе. Обоснованное нестандартное решение по прогнозным состояниям и изменениям приводит к состоянию "система - среда", основанному на построенных когнитивных моделях и анализе энтропии для оценки устойчивости направления деятельности и реализации ситуации. Практическое использование систематической методологической поддержки комплексных объектов комплексного исследования базируется на последовательном анализе моделей графов. Для анализа физических процессов смещения между простыми компонентами идеальной системы, которые являются источниками потенциальной и кинетической энергии, изменения его мощности через накопление вещества или энергии, используется структурная граф-топологичная модель физических процессов.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/195152 |
| citation_txt |
Using graph-analytical methods modeling of system objects to determine integrated assessment of their state / T.V. Kozulia, M.M. Kozulia // Problems of atomic science and technology. — 2019. — № 3. — С. 116-123. — Бібліогр.: 12 назв. — англ. |
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| fulltext |
USING GRAPH-ANALYTICAL METHODS MODELING OF
SYSTEM OBJECTS TO DETERMINE INTEGRATED
ASSESSMENT OF THEIR STATE
T.V.Kozulia, M.M.Kozulia∗
National Technical University ”Kharkiv Polytechnic Institute”, 61002, Kharkiv, Ukraine
(Received March 18, 2018)
In article is determined of object state in researching ”system – environment” based on system analytic-graph model-
ing for representation real relationships and relations between any systems in nature. Justified non-standard solution
according to forecasting states and changes results in ”system – environment” based on constructed cognitive models
and entropy analysis for action direction sustainability and implemented situations assessment. Practical usage of
systematic methodological support for complex objects comprehensive research based on graph models sequential
analysis. To analyze physical processes displacements between simple ideal system components, which are sources of
potential and kinetic energy, changes in its capacity through matter or energy accumulation, is used structural graph
– physical processes topological model.
PACS: 519.713: 631.411.6
1. INTRODUCTION
Modern system theory presupposes the existence of
systemic entities in the form of socio-economic, socio-
ecological, ecological and economic objects of natural
and man-made content, which relate to complex sys-
tems, and, in accordance with sustainable develop-
ment provisions, they are united in socio-ecological
and economic research objects [1, 2]. A special com-
ponent for such systems is an information component
that takes into account the qualitative characteristics
of both individual elements and their relationships.
The unstable systems state leads to crises that are
conventionally equated with qualitative transforma-
tions in them. Thus, the study of modern complex
systems is becoming relevant in the processing of in-
formation data in accordance with the standard sys-
tem approach and the latest methods of information
theory [3].
Decision-making is an analogue of information ex-
change and is the basis of activity, including manage-
ment. The decision is determined by the achievement
of the goal in choosing the best (more acceptable, op-
timal) alternative from possible variety of options for
the purpose.
Under the research object study or development
in accordance with the general definition of J. Clare
[1] is understood part of the world, which for a given
period of time is a unit that reflects the natural
(ecological), economic and social aspects of life. The
object interacts with environment, which is central to
the investigated integrity [3] (as opposed to existing
approaches in solving complex system problems, be-
cause it is the basis of the functionality of the object).
2. THE STUDY GOAL AND TASKS
Investigated object assessment, organizational struc-
ture and multifunctionality by components ex-
pense, multidimensionality and knowledge diversity
in proper systems determining, initial conditions for
their creation, require a system analysis, enhanced
to manage situation or support / change the system
by a new element / property. A special feature of
such an analytical center should be complexity, in-
formation efficiency of state and processes identifica-
tion in components and object in general, taking into
account environment and interaction with it, which
creates uncertainty at inaccuracies, fuzziness, incom-
pleteness information providing complexity increase
and corresponding knowledge lack of it nature for
different systems – technical, economic, social, bio-
logical, ecological. Thus, the task of creating not just
an information system as in the analysis object, but
also the information shell toolkit, which allows to give
an assessment and integrate into a single information
space knowledge about system and process solved in
such tasks:
1) determination of object state in researching
”system – environment” based on system analytic-
graph modeling for representation real relationships
and relations between any systems in nature;
2) justification of non-standard solution according
to forecasting states and changes results in ”system –
environment” based on constructed cognitive models
∗Corresponding author E-mail address: mariya.kozulya7@gmail.com
116 ISSN 1562-6016. PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2019, N3(121).
Series: Nuclear Physics Investigations (71), p.116-123.
and entropy analysis for action direction sustainabil-
ity and implemented situations assessment;
3) practical use of systematic methodological
support for complex objects comprehensive resaech
based on graph models sequential analysis.
3. SCIENTIFIC RESULTS
Information visualization about the system as a re-
search object is widely used in various activity fields:
biological sciences, artificial intelligence, financial in-
formation analysis, etc. At solving complex problems
of studying state and functional correspondences at
interaction ”system – environment” at resaerch level
”state – process – state” proposed to refer to topo-
logical models – observational graphical display of el-
ements efficiency and system in whole to determine
system state indicators, taking into account its struc-
ture, elements interaction, functionality and external
influence both from the side of environment and con-
trol action.
Topological models contain structural (structural-
logical) schemes, parametric graphs, logic-functional
graphs (transitions intensity and state changes), sig-
nal graphs, tree failures.
Organizing optimizing communications task solv-
ing in complex systems from the determining stand-
point it state and possible adjustments assessment
in order to achieve maximum systems functionality
and interaction with environment, have to deal with
information flows and a significant amount by calcu-
lation and logical procedures. In this case, it is ap-
propriate to use analyzed objects topological models
in form of information flow multigraphs, parametric
information and signal graphs, using optimal strategy
algorithms.
Topological model appling allow using the in-
formation on GIS and establish investigated system
state and its relations with surrounding systems of
different nature: natural, namely ecosystems, so-
cial and economic, formed natural-technogenic re-
search object for ”state – process – state” analy-
sis. This approach involves the consistent solution
of deterministic tasks, statistical nature of informa-
tion support and dynamic, associated with influence
on system, processes in it and the regulatory action
on it to achieve stationary sustainable development.
Combination of topological and cognitive models is
suggested, where information base is taken for fac-
tors study as self-regulating mechanisms definition
for ”system – environment”, decisions on this system
object quality management.
To analyze physical processes displacements be-
tween simple ideal system components, which are
sources of potential and kinetic energy, changes in
its capacity through matter or energy accumulation,
is used structural graph – physical processes topolog-
ical model.
It is proposed to use simpler and mathematically
rigorous concept for programming with graphs loaded
only on horizontal arcs by symbols, expressions, and
functions from elementary mathematics. Such graph
is polyglot, has the ISO 8631/1989 standard and only
one is effectively used throughout software develop-
ment and operation process life cycle.
Error-free design processes of algorithms, pro-
grams, data, network graphs, proof of their correct-
ness, self-documentation and decision making docu-
menting motivation are greatly simplified, improved
and accelerated [4, 5].
Uncertainties overcoming due to unpredictable
situations in systems, stochastic – in the natural and
some knowledge lack about natural-technogenic for-
mations occur according to logical analysis procedure
in topological graphs system, which ensures decision-
making reliability and backed by knowledge oriented
base. This base consists of a corresponding infor-
mation set on state, processes and optimization re-
search systems and optimization decomposition prin-
ciples, construction special mathematical modeling
programs of complex systems. The availability of
such source data and provided research objects mod-
els is the base for solving majority technical problems
providing strategy building for solving research prob-
lems based on what becomes possible due to topolog-
ical models in form of information stream multimo-
graphs and information graphs.
The general task model for achieving the goal in
this case has form:
φ (my) =
s∑
i=1
∫
cif (y,my, σy) dy,
where φ (my) – estimated function – efficiency func-
tion of nominal optimum from mathematical ex-
pectation of random variable Y (indicator, factor);
f (y,my, σy) – distribution density Y : my, σy – math-
ematical expectation and mean square deviation re-
spectively; ci – utility i-th interval ⌈yiH , yiB⌉ of val-
ues Y ;
YiB∫
YiH
f(y,my, σy) – probability of falling y in
i-th values interval.
For ecological and economic tasks of environ-
mental quality management denomination is a value
that corresponds to objective homeostasis function
while preserving natural environment quality Y :
my = mynom. Thus, the denomination search – set-
ting for these conditions such relationships and pro-
cesses of systems coexistence within an object that
provides the minimum energy tension and corre-
sponding maximum entropy that does not lead to
its changes m0
y, that is, maximum systems ordering,
effective functionality maximum: max
my
φ(my) = φ0.
Target changes achievement in the best way by max-
imizing rule of generalized efficiency function of nom-
inal optimum takes the form:
φ0 max
my
φ
(
Mh, t
)
=
∫∫
S
...
∫
C(y)f
(
y,Mh, t
)
dcdydt,
taking into account the constraints on the generalized
efficiency function as moments control condition Mh
117
distribution: f(y,Mh): Mh = φ
(
X, t
)
, h = 1, 2, 3, 4
and constraints on managing factors X ∈ Xadd and
resultant one Y ∈ Yadd.
In complex systems analysis, identification it state
in quality management terms, it is advisable to switch
to cognitive models, which allows to determine possi-
ble variants of its behavior by pulsed modeling on
cognitive maps, obtain the necessary implementa-
tions number of pulsed processes [6, 7].
Cognitive modeling technology allows to deter-
mine possible and rational situation managing ways
in order to transition from initial to goal states ac-
cording to revealed factors of significant impact on
events development in system with internal changes
in it and external interaction with environment [8].
Thus, cognitive model determines system state and
its occurrence in certain situation in general – ”sys-
tem – (system – environment) – process – situational
system state”, based on logic, knowledge and experi-
ence.
In practice dynamic systems dominate, where dif-
ferent processes take place both in nature, society and
in technical devices, and it is therefore advisable to
refer to such system definition provided by Optin [9]:
system is a process that goes. It is therefore neces-
sary to substantiate the basis for the synthesis and
analysis of various specific complex systems. Such
system must include the object as material physi-
cal education, processes that occur when it interacts
with environment, in it with self-regulation, support
and homeostatic relations restoration with the envi-
ronment, stochastic transformations with new system
structure self-organization. Structural research con-
tinuity, for such complex systems, is ensured by re-
search system model image usage in form of topolog-
ical graph.
Topological models – graph, simplicial complex,
CW-complexes, provide system analysis integrity un-
der conditions of polydisciplinary approach usage
when considering problem tasks in assessment and
objects study based on psychology knowledge and
system representations about social systems, animate
and inanimate nature, man-made environments or-
ganization that provide symbiotic relations between
man and technical systems.
Taking into account introduced symbols accord-
ing to researched object components: X1, X2, X3, X4
– economic, social and ecological systems state and
environment according to influence independent vari-
able as assessment start X0 – input value represented
as a three-contour oriented graph, which is gener-
alized model of dynamic system and processes in it
(Fig.1).
Fig.1. System object structure schema in form of topologic model – oriented graph G = G
(
X,A
)
: Xi,j –
coordinate set of analized system, where i – system number, where information received; j – system number,
wich have influence, give an information; A – set of all connections between systems aji
Intoduced graph represents a system object,
which is defined by three closed loops structure, two
of which have inverse negative bonds and one com-
mon with positive inverse bond, external inverse in-
formation bond – a40. Each system in such interac-
tion with environment characterized by certain infor-
mativeness level, which depends on information com-
munications state aji, i.e. xi =
N∑
i=0
ajixi, i = 0, N ,
where N – systems number involved in analysis
with environment consideration – ”system – environ-
ment”. According to structure object, presented as
topological graph in Fig.1, following informativeness
is determined for systems:
x1 = a01x0 − a21x2 + a41x4;
x2 = a12x1;
x3 = a23x2 − a43x4;
x4 = a34x3.
(1)
Under the provided equations system from structured
scheme, graph variables are determined by Cramer
method: xi =
∆i
∆ , where ∆ – main system determi-
nant; ∆i – separate determinant. For k independent
variables used expression xi =
∑
k
∆ikxk
∆ .
For taking into account all information about
state ”system – environment” – the system proper-
ties through interactions variables and parameters,
involve matrix methods: A · X̌ = B · Y̌ , where A,B
– matrices of numerical system coefficients; X,Y –
coordinates vector; or X = CY,C = A−1B.
According to requirements of the World Bank and
the International Finance Corporation, the environ-
mental assessment of man-made systemic entities co-
existence and natural is determined by information
on environmental impact assessment (EIA) results,
ecological audit, ecological risk assessment, environ-
mental protection plan. When establishing this gen-
118
eral dynamic equilibrium indicator in the corporate
natural-technogenic research object representation by
state and processes analysis in it along with cognitive
maps structural matrices are used with corresponding
purposes.
System structural components transfer functions
view of direct relation Wdr and feedback Wfdb be-
tween elements determine input influence transfor-
mation xinput in initial characteristic of this process
and dynamic changes given by operator polynomials
relation:
xoutput (s)
xinput (s)
= Ws =
Q (s)
R (s)
, (2)
where Q (s) – personal operator of dynamic element
(component, system) that characterizes its proper-
ties; R (s) – communication operator between dy-
namic elements; s – complex variable in the Laplace
transform operator, which under zero initial condi-
tions is analogous to differentiation operator p = d
dt .
Thus, information transmission through any
structural element of considered system (object) is
characterized by a transfer function
Φs =
Wdr (s)
1−Wdr (s) ·Wfdb (s)
. (3)
For transformation processes analysis, transfer
function is revised accordingly, which according to
introduced entropy approach changes characteristics
in complex object ”state – process – state” constitute
information, proceeding from the following: arbitrary
processes function is characterized by ”deep” excel-
lent values, that is S → −∞ , but for reverse process
Srv.p ≈ Wrv.con (s) → 0.
In transition to change factors analysis and their
relationship according to elements interaction within
system it is expedient to use information transfer
characteristic from one concept to another using Mai-
son formula, which is dynamics assessment and at the
same time reliability (as ability to transmit external
influence / information and remain structured enti-
ties) systems:
Kjl =
∑
s
PsDs
D
, (4)
where Kjl – transfer rate from some source j to l-th
vertex graph; D – general graph determinant, simi-
lar to main determinant equations system describing
system elements; Ps – information transfer (or direct
process probability as arbitrary in interaction entropy
terms) s-th through path from source j to l-th vertex
graph; Ds – an algebraic complement to certain s-th
through path.
In turn, D,Ds, and Ps are determined by such
rules.
Values D,Ds reflect transmission by graph con-
tours, taking into account all contours, contiguous
and discontiguous contours, namely for D.
D = 1−
∑
r
L(1)
r +
∑
r
L(2)
r
∑
r
L(3)
r + . . . , (5)
where
∑
r
L
(1)
r – transfers sum along all r graph con-
tours;
∑
r
L
(2)
r – products sum of all passon combi-
nations for two discontiguous contours;
∑
r
L
(3)
r – the
same for three discontiguous contours, etc.
Algebraic supplementDs is determined by the for-
mula (4) and by the same rules only taking into ac-
count discontiguous contours (which have no common
vertices) with s-th through path.
Transmission Ps is one of all transfer product vari-
ants between intermediate vertices from j-th sources
to l-th (finite) vertex:
Ps =
i−l∏
j
aji, (6)
where aji – transfer from j-th to i-th structural ele-
ment in the contour, graph.
Similarly, transmissions along contours L are de-
termined.
As an example of topological models calcula-
tions, consider graph on Fig.1. The graph has only
one cross-sectional path from initial vertex to finale
and three contours, all of which are faced with this
through path. Two contours L1, L2 not facing with
each other. Determining elements the total transmis-
sion coefficient are:
L1 = −a12 · a21;L1 = −a34 · a43;
L1 = a12 · a23 · a34 · a41;
D = 1− (L1 + L2 + L3) + (L1 · L2) =
= 1− (−a12 · a21 − a34 · a43 + a12 · a23 · a34 · a41)+
+ (a12 · a21 · a34 · a43) ;
P04 = a01 · a12 · a23 · a34;D04 = 1 .
Output data is entered into graph transfer for-
mula (5) for determining coefficient value:
K04 =
P04D04
D
=
=
a01 · a12 · a23 · a34 · 1
1− (−a12 · a21 − a34 · a43 + a12 · a23 · a34 · a41)+
+(a12 · a21 · a34 · a43)
=
=
a01 · a12 · a23 · a34 · 1
1 + a12 · a21 + a34 · a43 − a12 · a23 · a34 · a41+
+a12 · a21 · a34 · a43
.
The general links orientation between system el-
ements, structuring it in integrity with the realiza-
tion of certain properties, should reflect whole pro-
cess progress in converting inputs into outputs. The
importance for maintaining a stable process is impor-
tant for system stability. This is possible if composite
elements are combined into closed contour with neg-
ative feedback. In general dynamic system physics
reflects different connections and contours set that
make up input, output, and itself process set – sys-
tem core. The system’s input and output are defined
as multi-dimensional vectors X input, Xouput Commu-
nications in system core, as elementary cores outputs,
119
in totality made up system vector state X
′′
state which
corresponds to generally accepted systems mathe-
matical description.
For complex state and processes representation in
analytical system proposed to provide system struc-
ture in structural entropy matrix form, which reflects
elements state correspondence and processes direc-
tion in elements relatively other elements state.
In contrast to O. Long, dynamic system state is
interpreted in following way: a stable / constant (per-
sistant) system has formed elements, that is struc-
tured, hence its entropy equals to ”0”, otherwise
matrix diagonal will be inconsistency value by state
function or the situation uncertainty according to in-
formation entropy (local can reach its maximum of
0.38) [10, 11]; processes in system with support of its
stable structure – ”1”, its negative consequences – ”-
1”, with system maintenance in equilibrium, natural
quality – ”0” (”Sij”) (Fig.2).
Fig.2. ”Structure system matrix” and ”action variaty matrix” given in view ”structure entropy matrix of
dinamic system”
Main diagonal elements are the own operators
of system dynamic parts (operating elements, in O.
Lange terminology) Q (s). On both sides of diagonal
and on right side of matrix, operators are mapped
R (s) (see (2)), which are used for structural complex
system formations studies.
System objects of natural and man-made content
are defined as target-oriented complexes, which in-
clude aims namely – the base of research, analysis
and evaluation, object state, input and output in-
formation resources, the object environment directly
(Fig.3).
Fig.3. Structure matrix ”system – environment” according to given aims taking into account components
and relations in system kernel
In proposed complex systems research direc-
tion by information-entropy (entropy-information)
approach with synergetic analysis elements (syner-
getics), the indicated division into groups [12] is as-
sociated with analyzed object division into 3 systems
”(system-environment) – processes-external environ-
ment – system state” or socio-ecological-economic
system, which is information input (socio-economic
aspects), research system core (socio-economic ele-
ments) and environment (socio-ecologycal aspects –
natural (ecological) systems state and men health).
According to this structural matrix form [12] is
changes – input from the left as information flow
components properties has an impact on the research
120
structure core elements, the right output factors that
have an impact on the external environment. Con-
struction and analysis by such matrix complex sys-
tem (object of research) state according to the infor-
mation entropy is envisaged, which includes dynamic
system entropy that is evaluation according to en-
tropy function (state – process – state) and synergy
with regard to the order establishment by the self –
organizing mechanism of arbitrary processes.
It is proposed to modify and complete complex
system research object analysis. According to ob-
served data by received structural matrix, it is expe-
dient to construct a model in graph form which have
cognitive map content, that is the base of the factor
analysis in relation to the systems dynamics and de-
termination self-organization direction regarding the
structurization of a stable systemic formation by in-
fluence factors – x1, x2, x3, x4 (first factors group) re-
sponsible x̄input = x̄6, x̄7, x̄8, x̄9 provided internal sys-
tem structure functionality provision (x1, x2 – system
development contributing, x3, x4 – negative impact)
and system elements state, namely x5, x6, x7, x8, x9
(second group) are relevant x̄syst = x̄1, x̄2, x̄3, x̄4, x̄5 ,
and action factors on external environment by sys-
tem side x̄output (third factors group) positive char-
acter x10 (system performance) and negative impact
in form of waste x11 (Fig.4).
Fig.4. Schema of system object graph model – oriented graph G = G (X,A): X – set of analized systems:
X1, X2, X3, X4 – environment recourses; climate; socio-economic environment; transport; X5, X6, X7, X8, X9
– state of atmosphere; hydrosphere; soil; flora, fauna; X10 – man state; X11 – external ecological environ-
ment; A – connections between systems aji where i – information entrance system, j – information exit
system
According to internal link data between param-
eters / properties X{xi} object components (exter-
nal influence systems – investigated object system –
target identification systems (initial influences recep-
tion systems)) determine system object mathematical
model:
aiixj =
l∑
i=1,j ̸=l
aji · xj (i = 1, 2, ..., n) . (7)
Depending on harmful effects intensity on given
121
approaches to modeling, ”environment – system – en-
vironment” can roughly calculate the decline in hu-
man health, population and, consequently, its social
impact reduction. The negative influence of external
environment on reproductive function is expressed in
its functionality decrease or defective offspring ap-
pearance due to gametes mutation, fetal developmen-
tal disorders, neuroendocrine transformation in body
due to stress (Fig.5).
Fig.5. Systems object graphical model schema – topological-cognitive model of object ”organism = (envi-
ronment – systems) – functionality – object state”:→ – material and energy connections between system
elements; – → – data transmission about general influence of factor physical activity on system
Thus, state and processes analysis and evalua-
tion in system object developed for study due to at-
tracted methodological support system for consistent
problem tasks solution, evaluation task solution in
uncertainty conditions allows to obtaine results on
a strict object base according to proposed combina-
tion of complex and system approaches into a single
whole.
4. CONCLUSIONS
1) To determine object systems transition dynam-
ics to co-operative coherence to achieve synergistic
realization set target point of positive states and sta-
ble functionality is proposed to use graph models of
natural and man-made objects for ”state (system –
environment) – process – system state” research.
2) Highly structured system ”object – environ-
ment” state assessment (see Figures 4, 5) and risk-
free solution adoption for stabilizing component sys-
tems, obtaining new systems properties, development
for target system used subject area conceptual mod-
els in structural matrix form of complex systems
(”object – environment”) with knowledge-oriented
databases development, which are based on research
methods, knowledge, information systems, namely
structural matrix ”organization – process (function-
ality)”, ”information structure – functionality”, ”or-
ganization – knowledge-oriented information struc-
ture”.
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ÈÑÏÎËÜÇÎÂÀÍÈÅ ÃÐÀÔ-ÀÍÀËÈÒÈ×ÅÑÊÈÕ ÌÅÒÎÄΠÌÎÄÅËÈÐÎÂÀÍÈß
ÑÈÑÒÅÌÍÛÕ ÎÁÚÅÊÒÎÂ ÄËß ÎÏÐÅÄÅËÅÍÈß ÈÍÒÅÃÐÈÐÎÂÀÍÍÎÉ ÎÖÅÍÊÈ
ÈÕ ÑÎÑÒÎßÍÈß
Ò.Â.Êîçóëÿ, Ì.Ì.Êîçóëÿ
Îïðåäåëåíî ñîñòîÿíèå îáúåêòà ïðè èññëåäîâàíèè ′′ñèñòåìà � ñðåäà′′, îñíîâàííîå íà ñèñòåìíîì ãðàô-
àíàëèòè÷åñêîì ìîäåëèðîâàíèè äëÿ ïðåäñòàâëåíèÿ ðåàëüíûõ ñâÿçåé è îòíîøåíèé ìåæäó ëþáûìè ñè-
ñòåìàìè â ïðèðîäå. Îáîñíîâàííîå íåñòàíäàðòíîå ðåøåíèå ïî ïðîãíîçíûì ñîñòîÿíèÿì è èçìåíåíèÿì
ïðèâîäèò ê ñîñòîÿíèþ ′′ñèñòåìû � ñðåäû′′, îñíîâàííîìó íà ïîñòðîåííûõ êîãíèòèâíûõ ìîäåëÿõ è àíà-
ëèçå ýíòðîïèè äëÿ îöåíêè óñòîé÷èâîñòè íàïðàâëåíèÿ äåÿòåëüíîñòè è ðåàëèçàöèè ñèòóàöèè. Ïðàêòè÷å-
ñêîå èñïîëüçîâàíèå ñèñòåìàòè÷åñêîé ìåòîäîëîãè÷åñêîé ïîääåðæêè êîìïëåêñíûõ îáúåêòîâ êîìïëåêñ-
íîãî èññëåäîâàíèÿ áàçèðóåòñÿ íà ïîñëåäîâàòåëüíîì àíàëèçå ìîäåëåé ãðàôîâ. Äëÿ àíàëèçà ôèçè÷åñêèõ
ïðîöåññîâ ñìåùåíèÿ ìåæäó ïðîñòûìè êîìïîíåíòàìè èäåàëüíîé ñèñòåìû, êîòîðûå ÿâëÿþòñÿ èñòî÷íè-
êàìè ïîòåíöèàëüíîé è êèíåòè÷åñêîé ýíåðãèè, èçìåíåíèÿ åãî ìîùíîñòè ÷åðåç íàêîïëåíèå âåùåñòâà èëè
ýíåðãèè, èñïîëüçóåòñÿ ñòðóêòóðíàÿ ãðàô-òîïîëîãè÷íàÿ ìîäåëü ôèçè÷åñêèõ ïðîöåññîâ.
ÂÈÊÎÐÈÑÒÀÍÍß ÃÐÀÔ-ÀÍÀËIÒÈ×ÍÈÕ ÌÅÒÎÄI ÌÎÄÅËÞÂÀÍÍß
ÑÈÑÒÅÌÍÈÕ ÎÁ'�ÊÒI ÄËß ÂÈÇÍÀ×ÅÍÍß IÍÒÅÃÐÀËÜÍÎ� ÎÖIÍÊÈ �ÕÍÜÎÃÎ
ÑÒÀÍÓ
Ò.Â.Êîçóëÿ, Ì.Ì.Êîçóëÿ
Âèçíà÷åíî ñòàí îá'¹êòà ïðè äîñëiäæåííi ′′ñèñòåìà � ñåðåäîâèùå′′, çàñíîâàíèé íà ñèñòåìíîìó ãðàô-
àíàëiòè÷íîìó ìîäåëþâàííi äëÿ ïðåäñòàâëåííÿ ðåàëüíèõ çâ'ÿçêiâ òà âiäíîñèí ìiæ áóäü-ÿêèìè ñèñòåìà-
ìè â ïðèðîäi. Îáãðóíòîâàíå íåñòàíäàðòíå ðiøåííÿ çà ïðîãíîçíèìè ñòàíàìè òà çìiíàìè ïðèçâîäèòü äî
ñòàíó ′′ñèñòåìè � ñåðåäîâèùà′′, ùî áàçó¹òüñÿ íà ïîáóäîâàíèõ êîãíiòèâíèõ ìîäåëÿõ òà àíàëiçi åíòðîïi¨
äëÿ îöiíêè ñòiéêîñòi íàïðÿìêó äiÿëüíîñòi òà ðåàëiçàöi¨ ñèòóàöi¨. Ïðàêòè÷íå âèêîðèñòàííÿ ñèñòåìàòè÷-
íî¨ ìåòîäîëîãi÷íî¨ ïiäòðèìêè êîìïëåêñíèõ îá'¹êòiâ êîìïëåêñíîãî äîñëiäæåííÿ áàçó¹òüñÿ íà ïîñëiäîâ-
íîìó àíàëiçi ìîäåëåé ãðàôiâ. Äëÿ àíàëiçó ôiçè÷íèõ ïðîöåñiâ çìiùåííÿ ìiæ ïðîñòèìè êîìïîíåíòàìè
iäåàëüíî¨ ñèñòåìè, ÿêi ¹ äæåðåëàìè ïîòåíöiéíî¨ òà êiíåòè÷íî¨ åíåðãi¨, çìiíè éîãî ïîòóæíîñòi ÷åðåç
íàêîïè÷åííÿ ðå÷îâèíè àáî åíåðãi¨, âèêîðèñòîâó¹òüñÿ ñòðóêòóðíà ãðàô-òîïîëîãi÷íà ìîäåëü ôiçè÷íèõ
ïðîöåñiâ.
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