Визначення узагальненого критерію оптимальності вибору засобів укриття цивільного населення від атак балістичними (крилатими) ракетами та ударними безпілотними літальними апаратами в урбанізованих районах
The object of the study is the planning of the selection of civilian shelter from attacks by ballistic (cruise) missiles and kamikaze drones in urbanized areas. A generalized model for assessing the choice of civilian shelter facilities has been developed by applying linear forms of factor linkage i...
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| author | Yakovenko, Vadim Furmanova, Nataliia Flys, Ihor Malyi, Oleksandr Farafonov, Oleksii Moroz, Harri |
| author_facet | Yakovenko, Vadim Furmanova, Nataliia Flys, Ihor Malyi, Oleksandr Farafonov, Oleksii Moroz, Harri |
| author_institution_txt_mv | [
{
"author": "Vadim Yakovenko",
"institution": "Odesa Military Academy, Odesa"
},
{
"author": "Nataliia Furmanova",
"institution": "Zaporizhzhia Polytechnic National University, Zaporizhzhia"
},
{
"author": "Ihor Flys",
"institution": "Hetman Petro Sahaidachnyi National Army Academy, Lviv"
},
{
"author": "Oleksandr Malyi",
"institution": "Zaporizhzhia Polytechnic National University, Zaporizhzhia"
},
{
"author": "Oleksii Farafonov",
"institution": "Zaporizhzhia Polytechnic National University, Zaporizhzhia"
},
{
"author": "Harri Moroz",
"institution": "Zaporizhzhia Polytechnic National University, Zaporizhzhia"
}
] |
| author_sort | Yakovenko, Vadim |
| baseUrl_str | http://journal.iasa.kpi.ua/oai |
| collection | OJS |
| datestamp_date | 2024-11-16T18:06:34Z |
| description | The object of the study is the planning of the selection of civilian shelter from attacks by ballistic (cruise) missiles and kamikaze drones in urbanized areas. A generalized model for assessing the choice of civilian shelter facilities has been developed by applying linear forms of factor linkage in combination with a generalized optimality criterion in the form of a linear combination of local criteria. The multivariate regression analysis method was chosen to study the correlation between the generalized criterion and the observed feature. A generalized criterion for the optimal choice of civilian shelter facilities from attacks by ballistic (cruise) missiles and kamikaze drones in urbanized areas is calculated in the form of regression coefficients. The criterion can facilitate a simplified determination of the generalized indicator of a linear model for planning the protection of civilians in cities outside the area of hostilities. The initial data is a set of physical (technical) states of shelters with a list of values and features sufficient to assess their resistance to high dynamic loads. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2024.3.02 |
| first_indexed | 2025-07-17T10:28:35Z |
| format | Article |
| fulltext |
Publisher IASA at the Igor Sikorsky Kyiv Polytechnic Institute, 2024
Системні дослідження та інформаційні технології, 2024, № 3 25
TIДC
МЕТОДИ ОПТИМІЗАЦІЇ, ОПТИМАЛЬНЕ
УПРАВЛІННЯ І ТЕОРІЯ ІГОР
UDC 519.81
DOI: 10.20535/SRIT.2308-8893.2024.3.02
DETERMINATION OF THE GENERALIZED OPTIMALITY
CRITERIA FOR SELECTING CIVILIAN SHELTER FACILITIES
FROM ATTACKS BY BALLISTIC (CRUISE) MISSILES AND
KAMIKAZE DRONES IN URBANIZED AREAS
V. YAKOVENKO, N. FURMANOVA, I. FLYS, O. MALYI,
O. FARAFONOV, H. MOROZ
Abstract. The object of the study is the planning of the selection of civilian shelter
from attacks by ballistic (cruise) missiles and kamikaze drones in urbanized areas.
A generalized model for assessing the choice of civilian shelter facilities has been
developed by applying linear forms of factor linkage in combination with a general-
ized optimality criterion in the form of a linear combination of local criteria. The
multivariate regression analysis method was chosen to study the correlation between
the generalized criterion and the observed feature. A generalized criterion for the op-
timal choice of civilian shelter facilities from attacks by ballistic (cruise) missiles
and kamikaze drones in urbanized areas is calculated in the form of regression coef-
ficients. The criterion can facilitate a simplified determination of the generalized in-
dicator of a linear model for planning the protection of civilians in cities outside the area
of hostilities. The initial data is a set of physical (technical) states of shelters with a list
of values and features sufficient to assess their resistance to high dynamic loads.
Keywords: optimality criterion, civilian shelter facilities, weighting factor, missile
attacks.
INTRODUCTION
The long-term evolution of the modern world hegemony of the rule of interna-
tional norms and humanity has failed completely. It was completely levelled after
the Russian Federation (RF) unleashed its so-called “aggression” against the sov-
ereign state of Ukraine [1]. After all, a war in the centre of Europe on such a scale
since the end of the Second World War is the trigger for the first shot of a new
global war. Consequently, the dictators felt the complete amorphousness of global
institutions, as well as the meaninglessness of any commitments and international
treaties [2–4]. Thus, the beginning of Russia’s aggression against Ukraine was
carried out using several indirect levers of pressure: political, financial and eco-
nomic, media, human and military [5, 6]. Subsequently, hybridity grew into the
so-called “special military operation” (SMO), a striking feature of which is a
categorical violation of all international legal norms [7] and crimes against civil-
ians. This raises the logical question of the safety of children, women, and the
V. Yakovenko, N. Furmanova, I. Flys, O. Malyi, O. Farafonov, H. Moroz
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 26
elderly living in peaceful towns and villages, but suffering from regular air attacks
by enemy forces using cruise (ballistic) missiles and attack kamikaze drones.
The world has a vast experience of successfully solving various complex
problems, but humanity is losing the war to brazen terrorism. The protection of
civilians in urbanized areas that are not involved in hostilities remains a serious
problem. Protecting ordinary citizens from missile and kamikaze drones attacks,
developing infrastructure that will protect them not only from death but also from
injury - these are questions that needed to be answered yesterday. It is necessary
to immediately create a fund for protective structures throughout the country
without exception.
Ukraine can learn from the experience of other countries. Israel, for exam-
ple, has many mobile shelters [8], especially in cities with short daylight hours in
the south in the form of bus stops or just separate blocks. The main types of Is-
raeli shelters are:
protected rooms (mamads), which in peacetime are used by Israelis as or-
dinary living quarters;
a folding bomb shelter that can fit in a room and unfold in a few minutes
in an apartment or house;
strengthening socially important facilities, including bus stops and schools;
temporary bell-shaped fortifications for a limited number of people that
can be placed in open space or near roads;
sewerage pipes as storage facilities, which are laid near houses in several-
metre-long lines.
In addition, Israel has a concept of protected space in the form of places that
were not designed as shelters, but can be used in the absence of better alterna-
tives. In general, such places mean any premises that are separated from the street
by more than two walls and do not have windows according to the rule of two
walls. This can significantly reduce the number of casualties even in the context
of mass attacks [9] and when using fragmentation and high-explosive shells that
have a high degree of damage to objects [10–12]. Thus, there is real experience in
protecting civilians from missile and UAV attacks. However, any country keeps
its experience in planning the choice of defences secret. The impression that it is
easy to choose certain protective structures is superficial, as, as a rule, separate
unrelated local tasks are solved. There is no comprehensive approach to achieving
the overall goal, so developing approaches to decision-making on the choice of
civilian shelter facilities from missile and kamikaze drones attacks is an urgent task.
LITERATURE ANALYSIS AND PROBLEM STATEMENT
Global weapons manufacturers are increasingly paying attention to limiting the
unexpected lethality of their weapons by “scalping” the enemy [13]. However,
this does not apply to the military and political leadership of the Russian Federa-
tion. In the current realities of the so-called undeclared wars, civilians are an inte-
gral part of these confrontations, and the use of UAVs for inflicting damage is
constantly increasing.
Article [14] discusses the current threats of kamikaze dronesand methodolo-
gies for assessing these threats, and proposes modelling the UAV threat through
an attack protection tree. Study [15] analyses in depth the use of UAVs in modern
confrontations and cyberattacks, and considers countermeasures based on the
Determination of the generalized optimality criteria for selecting civilian shelter facilities …
Системні дослідження та інформаційні технології, 2024, № 3 27
technical limitations and shortcomings of the aircraft. However, these works do
not address the issue of assessing the protection of shelter facilities.
Civilian sheltering facilities play an important role in protecting people from
enemy aggression and should therefore be considered an effective security
measure. The article [16] discusses some strategic considerations of passive
protection in the design and planning of urban shelters, in particular for countries
with a critical strategic and sensitive location and exposed to threats from
expansionist states. A comprehensive analysis of shelters, taking into account
their actual state, is proposed in [17]. In 2022, the State Fire Service of Poland
conducted an inventory of shelters for the population and posted an app with
information on their location and class. However, the authors note that the created
database is incomplete and often the data provided is not true. Therefore, it is
proposed to create an interdepartmental group of professionals to develop criteria
for assessing the suitability and protection of shelters from various types of
impacts (military operations, man-made accidents, environmental disasters, etc.).
Israel’s use of civilian shelter facilities is a part of a defence system, another
component of which is the Iron Dome, a missile defence system deployed around
Israel’s major urbanized areas. It was created to provide citizens with greater
protection from enemy missile attacks. The study [18] examined how civilians’
experience with the Iron Dome system affects their perceptions of its reliability,
their trust in it, their attitudes towards enemy missile alerts, and their decision to
stay in the ADS. Although the study takes into account various indicators of
reliability, the focus is on the perception of the proposals from the automated
decision-making system by the population.
A similar issue is raised by [19], which analyses the results of the erroneous
perception of the probability of being hit by ballistic missiles, as demonstrated by
the operator of an automated air defence system. This study confirms the need to
develop a comprehensive approach to threat assessment and recommendations for
actions without or with minimised operator involvement.
A major study [20] was commissioned by the United States Air Force Eu-
rope (USAFE). It addresses a number of issues related to protection against cruise
and ballistic missiles and UAVs, including the analysis of shelters and recom-
mendations for their modernisation. However, the work is analytical in nature and
does not raise the issue of collecting general information and selecting the optimal
civilian shelter facilities.
The importance of research on the development of decision support systems
is confirmed by [21], which describes an experiment on the implementation of
such a system within a defence operation. However, the modelling is based on the
results of a reconnaissance model of UAVs, which is the subject of a significant
part of the paper.
Thus, there are many works that solve individual problems of using civilian
shelter facilities from missile and kamikaze drones attacks, but there is no
comprehensive approach to achieving the overall goal. Therefore, there is a need
to develop a methodological approach to analysing the initial data with the
selection of an optimality criterion. It should approximate the determination of the
generalisation of the indicator of the linear planning model for selecting facilities
of sheltering the civilian population from attacks by ballistic (cruise) missiles and
kamikaze drones in urbanized areas.
PURPOSE AND OBJECTIVES OF THE STUDY
The purpose of the study is to develop a mathematical approach that will improve
the efficiency and accuracy of decision-making on the choice of civilian shelter
V. Yakovenko, N. Furmanova, I. Flys, O. Malyi, O. Farafonov, H. Moroz
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 28
facilities from attacks by ballistic (cruise) missiles and kamikaze drones in urban-
ized areas. This will provide an opportunity to improve the safety of civilians in
cities and towns outside the combat zone.
The following tasks were set to achieve this goal:
to develop a generalised model for assessing the selection of civilian shel-
ter facilities against attacks by ballistic (cruise) missiles and kamikaze drones s in
urbanized areas;
determine the vectors of weighting coefficients of the proposed model;
to justify the choice of a method for studying the correlation between a
generalised criterion and an observable feature.
MATERIALS AND METHODS OF RESEARCH
The object of the study is to plan the choice of civilian shelter facilities from at-
tacks by ballistic (cruise) missiles and kamikaze drones in urbanized areas. The
essence of the proposed approach is to adapt the existing mathematical apparatus
to the real conditions of operational decision-making by applying a generalised
optimality criterion. The weighting criteria make it possible to determine how
relevant individual means are in a particular situation, which will increase the ef-
ficiency of planning the selection of the civilian shelter facilities.
The following research methods were chosen:
generalization — to formulate an indicator of a linear model for planning
the protection of civilians from attacks by ballistic (cruise) missiles and kamikaze
drones in urbanized areas;
classification — to identify and substantiate the main factors affecting the
feasibility of using and the effectiveness of the protective properties of the protec-
tive equipment in a given situation;
analysis — to determine the criteria that can be used when deciding on the
choice of civilian shelter facilities from attacks by ballistic (cruise) missiles and
kamikaze drones in urbanized areas;
regression analysis — to study the correlation between the generalised cri-
terion and the observed feature;
synthesis — to develop a model for assessing the effectiveness of civilian
shelter facilities.
The mathematical modelling was carried out using ASNA software
(Ukraine), which provides a formalised representation of the structure and behav-
iour of a system engineering object.
RESULTS OF RESEARCH ON THE MATHEMATICAL APPARATUS FOR
ASSESSING THE EFFECTIVENESS OF CIVILIAN SHELTER FROM MISSILE
AND UAV ATTACKS
Development of a generalised model for assessing the choice of shelter from
missile and UAV attacks
Decisions on the choice of civilian shelter should be made taking into account all
the above criteria and in accordance with national and international standards.
The standards for this type of structure should also be taken into account.
Determination of the generalized optimality criteria for selecting civilian shelter facilities …
Системні дослідження та інформаційні технології, 2024, № 3 29
The optimal criteria for the selection of a civilian protective structure may
vary depending on the specific conditions and missile attacks. However, in gen-
eral, there are several criteria that can be used when deciding on the selection of
civilian protective equipment:
effectiveness of civilian shelter facilities: it is important that the type of
structures and method of their application are designed to protect people without
injury or maim from the fragmentation and blast effects of ballistic (cruise) mis-
siles and enemy UAVs;
minimizing collateral damage during relocation to a shelter: it is important
to take into account possible collateral damage based on the density of civilian
areas and the availability of convenient routes to access protective shelters;
minimizing collateral damage in the event of a direct hit by both aircraft
and their bulky fragments after being shot down by air defence forces. It is impor-
tant to take into account possible cases of hitting these structures and provide
them with medical supplies to provide first aid to the victims. It is also advisable
to place signalling devices to notify the State Emergency Service and medical
teams of damage to the civilian shelter facilities;
consideration of the specifics of the environment in urbanised areas. Con-
sideration should be given to the weather, time of day, terrain, built-up and illu-
mination of the area, the presence of parked cars on the way to the civilian shelter
facilities, the average length of the journey and other conditions that may impede
rapid movement;
cost-effectiveness: the cost of sheltering civilians, the ability of industry to
meet the needs of the population in a short time, and the cost of their maintenance
and upkeep should be taken into account.
In general, the choice of civilian shelter in urbanized areas should be based on
tools that can describe the degree of realisation of their potential capabilities (Fig. 1).
The analysis of Fig. 1 indicates a factor that affects the optimisation of deci-
sions. This may be the so-called wide range of protective structures from various
manufacturers. However, its main role is to implement simple concepts — pre-
serving not only civilian lives, but also health in the full sense of the word. After
all, the existing standards are more general [22] and do not fully reveal the es-
sence of protecting citizens from missile threats [23] or the threat of using kami-
kaze drones . Therefore, in order to determine the criterion for the optimal selec-
tion of an air defence system against attacks by ballistic (cruise) missiles and
kamikaze drones in urbanized areas, it is necessary to understand the relationship
between the nature of the attacks and the capabilities of the civilian shelter facili-
ties. For the practical implementation of the above, it is possible to use linear
forms of factor relationship in combination with a generalised optimality criterion
in the form of a linear combination of local criteria [24–26]:
,)(...)(...)()( 11 xfaxfaxfaxF KKii (1)
where ia are the weighting coefficients for local optimality criteria; i is the index
of the local criterion ),...,2,1( K .
V. Yakovenko, N. Furmanova, I. Flys, O. Malyi, O. Farafonov, H. Moroz
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 30
Determination of the weighting vectors of the proposed model
To determine the vector а of weighting coefficients, it is possible to apply an
approach with the selection of a certain local criterion as an indicator (basic opti-
mality criterion) )(xfi . Then, the dependence of the remaining criteria )1( K
on the given one can be represented as [27; 28]:
.)(...)()(...)()( 111111 xfaxfaxfaxfaxf KKiiiii
(2)
6. Implementation of
the adopted
decisions
1. Initial data on the procedure for the possible use
of civilian shelter facilities:
characteristics of the area's urbanisation and infrastructure;
the available list of shelter facilities and their protective properties;
an enemy aircraft:
ballistic missile;
cruise missile;
strike UAV;
the quantitative state of the civilian population and the age indicator.
3. Formation of acceptable options for selecting the type
and number of shelter facilities in urban areas:
evaluating and comparing them;
selecting the most appropriate one.
4. Modelling the conditions for the use of selected civilian
shelter facilities (results and consequences)
5. Decision-making on the choice of
civilian shelter facilities. Comparison
of the quality of acceptable options
No Yes
2. Selection of criteria for assessing shelter facilities
No Yes
Fig. 1. Flowchart of the model for assessing the effectiveness of the use of civilian
shelter facilities
Determination of the generalized optimality criteria for selecting civilian shelter facilities …
Системні дослідження та інформаційні технології, 2024, № 3 31
Based on the method of multivariate regression analysis and using depend-
ence (2), 0а will look like this [29–31]:
.)(...)()(...)()( 0
1
0
11
0
11
0
1 xfaxfaxfaxfaxf KKiiiii
Then the optimisation criterion in the linear model will be applied in the fol-
lowing interpretation:
.)(...)()(...)()()( 0
1
0
11
0
11
0
1 xfaxfaxfaxfaxfxF KKiiiii
Some local criteria kk 1 (time to move to shelters) should be minimised as
much as possible, and the rest (number of civilian shelter facilities, their degree of
protection) should be maximised:
max,)()()(
1
0
1
0
1
1
xfaxfaxF
K
ki
ii
k
i
ii
either:
.min)()()(
1
0
1
0
1
1
xfaxfaxF
K
ki
ii
k
i
ii
This approach is associated with the rapidity and unpredictability of attacks,
as well as possible sudden changes in the situation.
Selecting a method for studying the correlation between a generalised crite-
rion and an observable feature
To study the effectiveness of the relationship between the generalised criterion
)(xF and the observational feature ),1( Kifi as the weighting factor ia
),1( Ki of the function of the form (2), it is possible to apply the method of
multivariate regression analysis:
,)(...)(...)(),( 110 xfaxfaxfaaaxF mmjj
where m is the number of parameters under study, units.
In this case, the level of regression is described by the values of maaa ,,, 10
and the final variance. Replacing the values of maaa ,,, 10 with their estimates,
and )(xf j with jf , the regression equation will take the form:
.......)( 110 mmjj fbfbfbbxF
The initial data for calculating the coefficients mbb ,,0 are a sample from a
multidimensional population in the form of the matrix f and the vector F [32–34]:
,
21
222212
112111
mnjnnn
mj
mj
ffff
ffff
ffff
f
.2
1
nF
F
F
F
For the convenience of selecting the civilian shelter facilities through jf ,
it is advisable to define the j-th vector as the column f of the matrix
V. Yakovenko, N. Furmanova, I. Flys, O. Malyi, O. Farafonov, H. Moroz
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 32
},...,{ 21 jnjjj ffff , and through if to calculate the i-th vector as a row of the
corresponding matrix },...,,{ 21 miiii ffff :
n
i
n
i
n
i
n
i
imimimimmiimi
n
i
n
i
n
i
n
i
iimiimiii
n
i
n
i
n
i
imimi
Ffffbffbfb
Ffffbffbfb
Ffbfbnb
1 1 1 1
110
1 1 1 1
1111110
1 1 1
110
....
...........................................................................
;...
;...
(3)
Despite the fact that this system can be calculated by any method of linear
algebra, in conditions of limited time indicators, the inverse matrix method
can be used when selecting civilian shelter facilities, expressing through jb
),,2,1( mj [35–37].
Substituting the equation of the form (3) into the other expressions of the
system, we define the coefficient matrix by C with the unknown parameters
mbbb ,,, 21 and the substitution of 0b . The inverse matrix can be defined by
1C , respectively, the element located at the intersection of the i-th row and the j-
th column by 1
ijс :
).(
1
1 FfnFfcb jiji
n
i
ijj
,,...,2,1 mj .......110 mmjj fbfbfbFb
The estimate of the final variance 2
qps is the expression:
,
1
)]([
1
2
2
mn
fFF
s
n
i
ii
КН
where iF is the measured value of the performance attribute; )( ifF is the value
of the outcome variable calculated according to the regression equation.
To statistically substantiate the conclusion
jb
j
s
b
t each of the coefficients
),...,2,1,0( mj is different from zero (significance of the regression coefficient
estimates) and is calculated by the expression [38, 39]:
.,,...,2,1
,
,
1
1
1,
1
0
kjni
с
s
s
cff
n
s
s
jj
КН
b
n
kj
ijkj
КН
b
j
(4)
In accordance with the given significance level χ and the number of degrees
of freedom 1 mnk , the critical value of kt is as follows:
Determination of the generalized optimality criteria for selecting civilian shelter facilities …
Системні дослідження та інформаційні технології, 2024, № 3 33
ktt , the null hypothesis that the regression coefficient is equal to zero is
rejected and considered significant;
ktt , the estimate of the regression coefficient will be insignificant.
Due to the regression analysis, the expression for the generalised optimality
criterion will be as follows:
,)(...)()( 110 xfbxfbbxF mm
where mm — regression coefficients may be insignificant.
The multivariate regression analysis method was chosen due to its following
advantages:
allows for easy interpretation of the impact of individual independent vari-
ables on the dependent variable; regression coefficients help to understand how
much the dependent variable changes when the unit of the independent variable
changes, while holding other variables constant;
linear regression is a relatively simple and well-studied model, which
makes it a reasonable choice for the first analysis of data;
If the relationship between the variables is basically linear, then linear re-
gression can provide fairly accurate results;
it can help to identify statistically significant relationships between vari-
ables and highlight important factors;
it is possible to analyze the influence of one factor while others are fixed,
which helps to understand how variables interact with each other.
To conduct the analysis, it is proposed to determine the values of the weight-
ing coefficients for various attributes (Table).
Characteristics and common features of the object influencing on results
Type Characteristics and common features
local centre
centre of the periphery
commercial district
residential area
industrial area
Characteristics
of urbanized
areas
neighbourhood
rectangular
radiated
beam
beam-ring
contour shaped
wrong
combined planning
Planning of
urban streets
and their
importance
linear
small buildings (area is less than 180 m2)
medium-sized buildings (area from 180 m2 to 2000 m2)
large buildings (area from 2000 m2 to 4000 m2)
Characteristics
of buildings
by size
massive buildings (area exceeds 4000 m2)
low-rise (up to 3 floors inclusive, with a building height of up to 9 m)
multi-storey (up to 9 floors inclusive, with a building height of 9 m to 26.5 m)
Increased-storey (up to 16 floors inclusive, with a height of 26.5 m to 47 m)
Characteristics
of buildings
by height
high-rise (more than 16 floors, with a height of more than 47 m)
V. Yakovenko, N. Furmanova, I. Flys, O. Malyi, O. Farafonov, H. Moroz
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 34
Continued Table
Type Characteristics and common features
Wood
Brick buildings
Brick
Buildings with box walls
Reinforced concrete
Frame houses with heavy walls
Construction
materials
Steel or metal
Frame houses with lightweight walls
Storage
Special purpose buildings
Anti-radiation (anti-chemical) shelter
Dual-purpose buildings
Prefabricated modular civil defence structures
Rapidly built modular storage facilities
External enclosing structures of modular type prefabricated
radiation protection shelters
Type of facili-
ties that can be
used as a civil-
ian shelter
The simplest shelters
light flash Initial effect
of the explosion sound effect
Brisant effect
blast effect
thermal effect
fragmentation effect
Impact
of the explosion
(impact
on surrounding
infrastructure)
Secondary fragmentation
effect of the destroyed object
(breaking up the fragmentation
mass of the aircraft)
Impact of explosive particles on
the environment
Impact of particles of the object’s
fragmentation shell
on the environment
An enemy
aircraft
Ballistic missile
(rocket)
Cruise missile
Strike UAV
Explosion residual
effects (dispersion
and impact
of explosive particles
and
detonation products)
The impact of particles
of the destroyed object
on the environment
Quantitative
state of the civil-
ian population
Total quantity and ratio of urban and rural residents
Age structure of
the population Total quantity and ratio of people of different age groups
A farmstead (a house for 1 family, with accompanying buildings,
in rural areas) — up to 25 people
Village (small community registered in rural areas) —
from 100 to 1000 people
Urban-type settlements — from 1,000 to 10,000 people
Small towns — up to 50 thousand people
Average city — from 50 thousand to 250 thousand people
Large city — from 250,000 to 500,000 people
Large city — from 500,000 to 1 million people
Description and
population of
the settlement
Millionaire city — more than 1 million people
The concepts in Table have the following meaning.
Dual-purpose structures are ground or underground structures or their sepa-
rate parts that are designed or adapted for use for their main functional purpose,
Determination of the generalized optimality criteria for selecting civilian shelter facilities …
Системні дослідження та інформаційні технології, 2024, № 3 35
including for the protection of the population, and in which conditions for the
temporary stay of people are created.
Quick-build civil protection structures of modular type should ensure protec-
tion of the population to be sheltered from the estimated impact of destruction
means in accordance with ДБН В.2.2-5 within the normative time established in
accordance with ДБН В.1.2-4.
Quick-build modular storage facilities must provide protection against:
exposure to excessive pressure at the front of an airborne shock wave of
at least 100 kPa;
local and general effects of conventional munitions (small arms, frag-
ments of hand grenades, artillery ammunition and aerial bombs).
External enclosing structures of prefabricated modular radiation protection
shelters should provide protection of the public against:
local and general effects of conventional munitions (small arms, frag-
ments of hand grenades, artillery ammunition and aerial bombs);
exposure to external ionising radiation and excessive pressure of the air-
borne shock wave front, depending on the location.
The simplest shelters are fortifications or basements, or other underground
structures where people can temporarily stay in order to reduce the combined
damage from hazards and from the effects of munitions during a special period.
To understand the destructive effect of aircraft even after they are shot down
in the air, we will model this process. After an aircraft is detonated in the air, the
explosion products, expanding to a value equal to 10–12 charge radii before at-
mospheric pressure is restored, will displace the air adjacent to them, compressing
it and setting it in motion. However, the expansion process will not end there. By
inertia, it will increase to a value close to 20 charge radii. At this point, the layer
of compressed air is detached from the explosion products and, due to the energy
it receives, continues to move independently at supersonic speed, representing the
so-called air shock wave. The latter captures significant masses of air as it moves.
Thus, the enlarged air moves behind the shock wave front, leaving behind a re-
gion of rarefaction where the pressure drops below atmospheric pressure.
As the energy of the shock wave moves away from the centre of the explo-
sion, it is dispersed spherically in the environment, heating the air. Thus, the pres-
sure amplitude (jump) gradually decreases with increasing distance from the cen-
tre of the explosion, and the velocity at the wave front decreases, becoming the
speed of sound. As a result, the shock wave gradually fades away. However, the
depth of the wave, namely the time of its overpressure action, increases with dis-
tance from the centre of the explosion [40].
The shock wave from an aircraft crash reaches the ground and is reflected
from it and moves towards the centre of the explosion as a reflected shock wave.
As it moves in the air, which is thinned and heated by the previous shock (inci-
dent) wave, its speed is greater than the speed of the incident shock wave, and at a
distance approximately equal to the height of the explosion, the reflected shock
wave catches up with the incident shock wave and, merging with it, forms the so-
called main shock wave, which carries.
Thus, when an aircraft is shot down, the reflected wave will usually move
along with the main wave with the pressure at its front close to the main wave.
Therefore, there is a common assumption that the shock wave from a ground ex-
plosion of an aircraft and the shock wave from its impact within the irregular re-
flection zone are zones of increased pressure hypothetically created by a double
V. Yakovenko, N. Furmanova, I. Flys, O. Malyi, O. Farafonov, H. Moroz
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 36
mass charge. This will be true when calculating the dynamic loads of the rigid
surfaces of the civilian shelter facilities. However, when calculating non-rigid
surfaces, it is advisable to take into account the correction factor with the charge
mass.
Coefficients are assigned to the input values, and the ASNA software deter-
mines the weight of each value through mathematical modelling. This can take
into account mutual exclusions or complementarities in the Kolmogorov–
Chapman system of equations on which the selected software is based.
Using the systems engineering approach, it is possible to obtain calculations
for systems that do not yet exist, when reference values are not yet available. The
methodology allows values to be obtained if specific values are provided, such as
concrete thickness, reinforcement diameter, etc.
Based on the values given in Table, we calculated and obtained graphs
(Figs. 2–5), which allow us to conclude that the results obtained are adequate to
the values obtained by other scientists [41].
The analysis of Fig. 2 shows that
the distance (D) of the location of the
control centre from the dwellings
should not exceed 200 m. Depending
on the time of day (day, night),
weather conditions (slippery road in
winter, heavy rain in summer), pres-
ence of children under 6 years old
in the family, elderly people over
60 years old, people with different
health conditions, the time for moving
increases. Therefore, the location of a
civilian shelter facilities against air-
craft strikes at a distance of more than
200 m reduces the likelihood of pro-
tecting people from damage of vary-
ing degrees.
P
D, m
Fig. 2. Diagram of the location of the civilian
shelter facilities from the residence of citizens
Fig. 3. Graph of the probability of damage versus wall thickness of typical civilian
shelter facilities (1) and non-typical civilian shelter facilities (2)
P
1
2
D, m
Determination of the generalized optimality criteria for selecting civilian shelter facilities …
Системні дослідження та інформаційні технології, 2024, № 3 37
The authors of this paper argue that structures of different types in the form
of civilian shelter facilities can be combined as typical and non-typical. The anal-
ysis of Fig. 3 shows that the degree of protection of typical and atypical objects
with wall thicknesses from 20 mm to 60 mm steel equivalent, depending on its
ability to withstand shock waves and fragments of different fractions, has virtu-
ally the same properties of 54 mm thickness.
Analysis of Fig. 4 shows the following. Regardless of the type of shelter,
during the open impact of a warhead (within 50 kg) of a Shahed UAV (Russian
analogue is the “Герань-2”), the probability of sustaining damage at the level of
0.5 in the form of acubarotrauma of varying degrees or other injuries is within 34
m. In other words, the protection against direct impact of a Shahed-type kamikaze
drones on Mamad-type premises without additional obstacles in the form of
building walls or other structures (objects) is close to that of specially equipped
premises. The placement of the civilian shelter facilities directly in the room
allows to reduce the time for movement, i.e. staying in the unprotected area.
An analysis of Fig. 5 shows that, regardless of the type of settlement, when
the population is 87.000 or more, and despite the uniformity of the warning, the
number of collective-type civilian shelter facilities is significantly reduced. The
authors deliberately did not take into account cities with a population of more
Fig. 4. Diagram of comparative characteristics of protective properties of civilian shelter
facilities in the form of special rooms (2) and rooms of the “mamad” type (1)
D, m
P
1
2
Fig. 5. Graph of the dependence of the protective properties of the civilian shelter facili-
ties on the number of civilians in need of protection
P
1
2
V. Yakovenko, N. Furmanova, I. Flys, O. Malyi, O. Farafonov, H. Moroz
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 38
than one million people, because in these cities the communication infrastructure
and the sense of danger are more developed than in much smaller towns and vil-
lages, where people’s confidence in their own safety is based mainly on the prin-
ciple of self-complacency. Those settlements with a population of less than
87.000 should be considered according to a different principle or be merged into
certain structures. This is because it is difficult to assess the feasibility of building
civilian shelter facilities for a population of up to 10.000 inhabitants without tak-
ing into account economic indicators. Private households allow for the construc-
tion of various types of structures where it would be possible to hide from enemy
aircraft.
DISCUSSION OF THE RESULTS OF THE STUDY OF THE CRITERION
FOR THE OPTIMAL CHOICE OF CIVILIAN SHELTER FACILITIES
This paper calculates a generalised criterion for the optimality of the selection of
civilian shelter facilities in the form of regression coefficients (4). It is based on
the developed model for assessing the effectiveness of the use of civilian protec-
tive equipment, the flowchart of which is shown at Fig. 1. The optimality criterion
is capable of determining a generalised indicator of a linear model for selecting
civilian shelter facilities during attacks by ballistic (cruise) missiles and kamikaze
drones in urbanized areas.
The essence of the proposed approach is to adapt the existing mathematical
apparatus to the real conditions of operational decision-making through the use of
a generalised optimality criterion. The weighting criteria make it possible to de-
termine how relevant individual facilities are in a particular situation, which will
increase the efficiency of planning the selection of civilian shelter facilities during
attacks by ballistic (cruise) missiles and kamikaze drones s in urbanized areas.
In order to select sheltering civilians from attacks, it is necessary to have a
set of physical (technical) states of civilian shelter facilities with a set of values
and signs sufficient to assess their reliability. This necessitates the creation and
implementation of a new system of concepts based on a more detailed accounting
of the results of civilian protection. In turn, this to some extent limits the applica-
bility of the research results and requires preliminary data preparation for their use.
A similar study [42], which analysed the use of tunnels as civilian shelter fa-
cilities, is based on the use of hierarchy analysis. This requires users to perform a
large number of pairwise comparisons and importance assessments. For large and
complex problems, this can be a time-consuming and confusing process. Paper
[43] uses a stepwise weighting factor analysis to develop a model for rapidly as-
sessing the vulnerability of office buildings to explosion. However, this multi-
criteria decision-making method may not be sufficiently transparent about how it
arrives at the final rankings and decisions. This can be a concern in situations
where stakeholders need to understand the reasoning behind decisions. The re-
search presented in this paper does not have these shortcomings. Its peculiarity is
the focus on applying the choice of the civilian shelter facilities in urbanized ar-
eas, which leads to the inclusion of a significant number of indirect indicators in
the calculation.
The advantages of the proposed approach are as follows:
versatility: the generalised optimality criterion can be applied to different
types of civilian shelter facilities in the context of attacks by ballistic (cruise) mis-
siles and kamikaze drones s in urbanized areas;
Determination of the generalized optimality criteria for selecting civilian shelter facilities …
Системні дослідження та інформаційні технології, 2024, № 3 39
time and resource savings: compared to traditional assessment methods,
the time and resources required to assess the suitability of civilian shelter facilities
against ballistic (cruise) missile and kamikaze drones attacks can be reduced;
decision-making support: application of the generalised optimality
criterion can help to make a rational decision on the informed choice of civilian
shelter facilities with objective data and conclusions obtained also on the basis of
mathematical models on the course of possible consequences.
The limitation of this study is that the proposed solutions address only a few
types of possible causes of damage (ballistic missile, cruise missile or kamikaze
drones and do not include fragmentation and high-explosive projectiles.
Some possible disadvantages may include:
subjectivity of the choice of criteria: the choice of criteria used in the
model can be subjective and dependent on the researcher, which can lead to
incorrect or biased results;
increased requirements for input data: the development and application of
the model may require a significant amount of data that may be difficult to obtain
or process.
Increasing the protection of the population can be achieved by creating a
fund of protective structures and, on its basis, informing the population about the
optimal choice of civilian shelter facilities.
A fund of civilian shelters can be created by:
implementation of the provisions of the sections (schemes) of engineering
and technical measures for civil protection of urban planning and design
documentation of construction projects in terms of construction (adaptation) of
protective and dual-purpose structures;
integrated development of the underground space of cities and other
settlements to accommodate social, industrial and economic facilities;
creation and registration of existing dual-purpose structures and simple
shelters, other operated facilities, including underground and above-ground
buildings, mine and other workings and underground cavities;
construction of quick-build protective structures and arrangement of the
simplest shelters during the special period;
proactive acquisition (manufacture) and maintenance in peacetime of
special designs of quick-build shelters, including block-modular type, ready for
installation and use.
Public awareness will be based on the data on the protective structures fund.
It can take various forms: posting information on a website or physical objects,
development of an application for mobile phones that will take into account a per-
son’s location and distance to nearby civilian shelter facilities, etc. This is planned
to be put into practice in the course of further research and experiments.
Along with the results obtained, the authors of this paper consider it expedi-
ent to use the experience of Israel, which consists in partial abandonment of the
so-called “public” shelters in the future and transition to “individual” shelters in
the homes of Ukrainian citizens. First, the flight time of ballistic missiles is meas-
ured in minutes. Secondly, there is a problem of ignoring air raid warnings among
the public. Thirdly, the maintenance of collective civilian shelter facilities is a
rather cumbersome task even for Israel.
Thus, blindly and thoughtlessly copying the experience of other countries is
a futile exercise. After all, from the mentality of the population, traditions and
V. Yakovenko, N. Furmanova, I. Flys, O. Malyi, O. Farafonov, H. Moroz
ISSN 1681–6048 System Research & Information Technologies, 2024, № 3 40
geographical location to the enemy, all of which impose significant limitations on
someone else’s experience. Therefore, it is important to evaluate and take into
account the results of others, but the main thing is to create our own authentic
model of protecting civilians from missile and Kamikaze drones . Moreover, such
work should be carried out on an ongoing basis and not just for years, but for dec-
ades.
CONCLUSIONS
1. A generalised model for assessing the use of civilian shelter facilities se-
lecting has been developed by applying linear forms of factor linkage in combina-
tion with a generalised optimality criterion in the form of a linear combination of
local criteria.
2. The vectors of weighting coefficients of the proposed model were deter-
mined, taking into account their peculiarities in the context of attacks by ballistic
(cruise) missiles and kamikaze drones in urbanized areas.
3. The method of multivariate regression analysis was chosen as a method of
studying the correlation between the generalised criterion and the observed fea-
ture. Its advantages are the interpretability of the impact of individual independent
variables on the dependent variable, ease of use, good handling of linear depend-
encies and the ability to detect changes, as well as relatively simple modelling of
the influence of variables on each other.
Conflict of interest. The authors declare that there are no conflicts of inter-
est in this research, including financial, special nature, authorship or any other
nature that could affect the research and the results presented in this article.
Finance. The investigation was carried out without financial support.
Data availability. Data will be given for the connected power supply.
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Received 01.09.2023
INFORMATION ON THE ARTICLE
Vadim V. Yakovenko, ORCID: 0000-0001-8591-6998, Odesa Military Academy,
Ukraine, e-mail: yakob@ukr.net
Nataliia I. Furmanova, ORCID: 0000-0002-8670-2948, Zaporizhzhia Polytechnic Na-
tional University, Ukraine, e-mail: nfurmanova@gmail.com
Ihor M. Flys, ORCID: 0000-0001-6334-0027, Hetman Petro Sahaidachnyi National
Army Academy, Ukraine, e-mail: 9imf61@gmail.com
Oleksandr Yu. Malyi, ORCID: 0000-0002-8457-8154, Zaporizhzhia Polytechnic Na-
tional University, Ukraine, e-mail: docsasha2@gmail.com
Oleksii Yu. Farafonov, ORCID: 0000-0001-5963-5033, Zaporizhzhia Polytechnic Na-
tional University, Ukraine, e-mail: farafon@zntu.edu.ua
Harri V. Moroz, ORCID: 0000-0003-4636-4961, Zaporizhzhia Polytechnic National
University, Ukraine, e-mail: garrymrz206@gmail.com
ВИЗНАЧЕННЯ УЗАГАЛЬНЕНОГО КРИТЕРІЮ ОПТИМАЛЬНОСТІ
ВИБОРУ ЗАСОБІВ УКРИТТЯ ЦИВІЛЬНОГО НАСЕЛЕННЯ ВІД АТАК
БАЛІСТИЧНИМИ (КРИЛАТИМИ) РАКЕТАМИ ТА УДАРНИМИ
БЕЗПІЛОТНИМИ ЛІТАЛЬНИМИ АПАРАТАМИ В УРБАНІЗОВАНИХ
РАЙОНАХ / В.В. Яковенко, Н.І. Фурманова, І.М. Флис, О.Ю. Малий, О.Ю. Фара-
фонов, Г.В. Мороз
Анатоція. Об’єктом дослідження є планування вибору засобів укриття цивіль-
ного населення від атак балістичними (крилатими) ракетами та ударними без-
пілотними літальними апаратами (БпЛА) в урбанізованих районах. Розроблено
узагальнену модель оцінювання вибору засобів укриття цивільного населення
шляхом застосування лінійних форм зв’язку факторів у поєднанні з узагальне-
ним критерієм оптимальності у вигляді лінійної комбінації локальних критеріїв.
Як метод дослідження кореляції між узагальненим критерієм та спостережною
ознакою обрано метод багатовимірного регресійного аналізу. Розраховано
узагальнений критерій оптимальності вибору засобів укриття цивільного
населення від атак балістичними (крилатими) ракетами та ударними БпЛА в
урбанізованих районах у вигляді коефіцієнтів формування регресії. Критерій
здатен сприяти спрощеному визначенню узагальненого показника лінійної мо-
делі планування захисту мирних громадян у містах поза межами бойових дій.
Вихідними даними є набір фізичних (технічних) станів укриттів з переліком
величин і ознак, достатніх для оцінювання їх стійкості до високих динамічних
навантажень.
Ключові слова: критерій оптимальності, засоби укриття цивільного населен-
ня, ваговий коефіцієнт, ракетні атаки.
|
| id | journaliasakpiua-article-315141 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:28:35Z |
| publishDate | 2024 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/8b/a24fb0271e8d0f8394be2b9b3f5b268b.pdf |
| spelling | journaliasakpiua-article-3151412024-11-16T18:06:34Z Determination of the generalized optimality criteria for selecting civilian shelter facilities from attacks by ballistic (cruise) missiles and kamikaze drones in urbanized areas Визначення узагальненого критерію оптимальності вибору засобів укриття цивільного населення від атак балістичними (крилатими) ракетами та ударними безпілотними літальними апаратами в урбанізованих районах Yakovenko, Vadim Furmanova, Nataliia Flys, Ihor Malyi, Oleksandr Farafonov, Oleksii Moroz, Harri критерій оптимальності засоби укриття цивільного населення ваговий коефіцієнт ракетні атаки optimality criterion civilian shelter facilities weighting factor missile attacks The object of the study is the planning of the selection of civilian shelter from attacks by ballistic (cruise) missiles and kamikaze drones in urbanized areas. A generalized model for assessing the choice of civilian shelter facilities has been developed by applying linear forms of factor linkage in combination with a generalized optimality criterion in the form of a linear combination of local criteria. The multivariate regression analysis method was chosen to study the correlation between the generalized criterion and the observed feature. A generalized criterion for the optimal choice of civilian shelter facilities from attacks by ballistic (cruise) missiles and kamikaze drones in urbanized areas is calculated in the form of regression coefficients. The criterion can facilitate a simplified determination of the generalized indicator of a linear model for planning the protection of civilians in cities outside the area of hostilities. The initial data is a set of physical (technical) states of shelters with a list of values and features sufficient to assess their resistance to high dynamic loads. Об’єктом дослідження є планування вибору засобів укриття цивільного населення від атак балістичними (крилатими) ракетами та ударними безпілотними літальними апаратами (БпЛА) в урбанізованих районах. Розроблено узагальнену модель оцінювання вибору засобів укриття цивільного населення шляхом застосування лінійних форм зв’язку факторів у поєднанні з узагальненим критерієм оптимальності у вигляді лінійної комбінації локальних критеріїв. Як метод дослідження кореляції між узагальненим критерієм та спостережною ознакою обрано метод багатовимірного регресійного аналізу. Розраховано узагальнений критерій оптимальності вибору засобів укриття цивільного населення від атак балістичними (крилатими) ракетами та ударними БпЛА в урбанізованих районах у вигляді коефіцієнтів формування регресії. Критерій здатен сприяти спрощеному визначенню узагальненого показника лінійної моделі планування захисту мирних громадян у містах поза межами бойових дій. Вихідними даними є набір фізичних (технічних) станів укриттів з переліком величин і ознак, достатніх для оцінювання їх стійкості до високих динамічних навантажень. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2024-09-28 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/315141 10.20535/SRIT.2308-8893.2024.3.02 System research and information technologies; No. 3 (2024); 25-43 Системные исследования и информационные технологии; № 3 (2024); 25-43 Системні дослідження та інформаційні технології; № 3 (2024); 25-43 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/315141/306030 |
| spellingShingle | критерій оптимальності засоби укриття цивільного населення ваговий коефіцієнт ракетні атаки Yakovenko, Vadim Furmanova, Nataliia Flys, Ihor Malyi, Oleksandr Farafonov, Oleksii Moroz, Harri Визначення узагальненого критерію оптимальності вибору засобів укриття цивільного населення від атак балістичними (крилатими) ракетами та ударними безпілотними літальними апаратами в урбанізованих районах |
| title | Визначення узагальненого критерію оптимальності вибору засобів укриття цивільного населення від атак балістичними (крилатими) ракетами та ударними безпілотними літальними апаратами в урбанізованих районах |
| title_alt | Determination of the generalized optimality criteria for selecting civilian shelter facilities from attacks by ballistic (cruise) missiles and kamikaze drones in urbanized areas |
| title_full | Визначення узагальненого критерію оптимальності вибору засобів укриття цивільного населення від атак балістичними (крилатими) ракетами та ударними безпілотними літальними апаратами в урбанізованих районах |
| title_fullStr | Визначення узагальненого критерію оптимальності вибору засобів укриття цивільного населення від атак балістичними (крилатими) ракетами та ударними безпілотними літальними апаратами в урбанізованих районах |
| title_full_unstemmed | Визначення узагальненого критерію оптимальності вибору засобів укриття цивільного населення від атак балістичними (крилатими) ракетами та ударними безпілотними літальними апаратами в урбанізованих районах |
| title_short | Визначення узагальненого критерію оптимальності вибору засобів укриття цивільного населення від атак балістичними (крилатими) ракетами та ударними безпілотними літальними апаратами в урбанізованих районах |
| title_sort | визначення узагальненого критерію оптимальності вибору засобів укриття цивільного населення від атак балістичними (крилатими) ракетами та ударними безпілотними літальними апаратами в урбанізованих районах |
| topic | критерій оптимальності засоби укриття цивільного населення ваговий коефіцієнт ракетні атаки |
| topic_facet | критерій оптимальності засоби укриття цивільного населення ваговий коефіцієнт ракетні атаки optimality criterion civilian shelter facilities weighting factor missile attacks |
| url | https://journal.iasa.kpi.ua/article/view/315141 |
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