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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Methods for Assessing the Risk of Approaching Ships as an Integral Part of the Vessel Traffic Control System</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Victor Strelbitskyi</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Nataliia Punchenko</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Oleksandra Tsyra</string-name>
          <email>aleksandra.tsyra@gmail.com</email>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Odesa State Environmental University Odesa</institution>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Odessa National Maritime University</institution>
          ,
          <addr-line>Odesa</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>State University Of Intellectual Technologies And Communications Odesa</institution>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <abstract>
        <p>The article presents a brief overview of methods for ensuring the navigation safety of vessel traffic, which are divided into three categories: methods of early detection of the collision possibility of ships, methods of maneuvering to avoid a collision and planning trajectory methods of the ship. A detailed theoretical review of methods for assessing the risk of a dangerous approach of ships, associated with ensuring the navigation safety of ship traffic, is carried out in detail. The representation of ship domains is disclosed to assess the risk of a dangerous approach of ships. The work provides links to sources that clarify the presented material.</p>
      </abstract>
      <kwd-group>
        <kwd>1 Navigation safety</kwd>
        <kwd>navigational control methods</kwd>
        <kwd>risk assessment</kwd>
        <kwd>ship convergence</kwd>
        <kwd>"ship domain"</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>The science of ensuring safe navigation in the
civil and military spheres is in the process of
improvement. A global issue in this scientific area
is prevention of groundings and collisions of
ships. This science examines the aspect of the
problem of navigation safety from all sides.
Navigation figure 1, since antiquity, as a result,
has created problems of navigation safety.
Ensuring navigational safety is a task that is a
complex multi-level complex.</p>
      <p>
        To solve this problem, the forces are united:
manufacturers of maritime navigation aids,
international organizations, administrations of
states participating in world shipping. The
cooperation of these entities forms a system for
ensuring safe navigation. Despite such
cooperation, a high percentage of ship accidents
at sea is an objective reality that cannot be denied
and is primarily due to the peculiarities of external
and internal factors accompanying navigation,
which will always be present regardless of the
human factor. The level of state and reliability of
navigation in modern conditions, the real
accuracy of navigation and the quality of
navigation problems is about twice worse than
expected. It follows that the complete elimination
of the accident rate of ships has no chance. But it
is quite possible to influence the number of
accidents with the help of various measures and
try to achieve its relative maximum reduction for
a period that is limited. Such a drop in the accident
rate can be achieved up to a certain level, after
which the accident rate will inevitably grow again
or temporarily stabilize [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. This conclusion
follows from the realities of the present time,
which can be characterized:
1. An increase in the volume of water
transport
2. The increasing traffic intensity in areas of
busy shipping leads to a constant increase in
the workload on boat masters
      </p>
      <p>
        Experimental studies show that the largest
number of accidents in water transport occur in
the areas of responsibility of ports and on the
approaches to them. In this regard, the problem of
safe movement at sea becomes most acute in
limited waters and cramped navigation conditions
[
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. Aspects of the tasks for ensuring the navigation safety</title>
      <p>
        One of the seven ancient man-made wonders
of the world - the Pharos lighthouse, and the
miraculous miracle - the Pillars of Hercules were
navigational landmarks on the approaches to
Alexandria and Gibraltar and helped mariners
prevent their ships from aground. And this is one
of the proofs that at that time the knowledge,
experience and intuition of the navigator was not
enough to guarantee the safety of navigation. In
modern conditions when the main cause of
maritime accidents is breakdown, damage, or
equipment failure. The worst regions in terms of
maritime accidents, according to the AGCS
report, are the waters of southern China,
Indonesia, and the Philippines. Every fourth
incident occurs in those areas. Even though Asia
remains the most unfavorable region due to the
busiest routes and the old fleet. Next come the
Eastern Mediterranean and the Black Sea and the
British Isles. From the analysis of catastrophes,
the existing problems of the safety of navigation
becomes acute in limited waters and cramped
navigation conditions. As a result, special
methods of preventing collisions of ships,
introduced into complex technical navigation
systems, are in great demand [
        <xref ref-type="bibr" rid="ref4 ref5">4,5</xref>
        ]. The legal
framework at this stage, despite the emergence of
unmanned navigation, regulates that the
management of a ship is the exclusive right of its
captain. In his actions, the boat master is only
guided by the information provided by various
navigation aids, but the final decision on the
movement of the vessel is made only by the boat
master. And because of this, it has led to the fact
that in navigation, extraordinary approaches to
traffic management have developed and are used.
Because of this, the methods of ensuring the
navigation safety of vessel traffic can be divided
into three categories: methods of early detection
of the collision possibility (collision risk
assessment), methods of maneuvering to avoid a
collision (collision avoidance), and planning
trajectory methods of the safe movement of the
vessel. Brief comparative characteristic these
methods:
      </p>
      <p>
        Method 1. On-board radio and computer
systems, which are called on-board collision
avoidance systems, have been recognized as
highly effective means of preventing collisions in
shipping. The English name for these complexes
is Collision Avoidance System. The on-board
collision avoidance system is a proven system
based on the use of surveillance radar signals and
other navigational aids. It operates independently
of ground equipment and provides information on
situations that other vessels can create in various
navigational conditions. The collision avoidance
system provides information to the officer of the
watch on the situation in the navigation area
through the provision of visual and voice
information, ensures the timely detection of
threatening vessels, classifies vessels according to
their degree of danger, and issues
recommendations for the appropriate maneuver.
The collision avoidance system monitors vessels
in the surrounding water area within a radius of up
to 24 miles from own vessel [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. Such observation
makes it possible to determine the trajectory of the
relative movement of each oncoming object, to
assess the risk of collision of own ship with other
objects. With the help of communication
facilities, coordination of planned maneuvers can
be carried out with other vessels.
      </p>
      <p>Method 2. The problem of divergence of
vessels in the water area is a priority in the
management of the vessel. Without disregarding
the increasing intensity of traffic on all
international water communications, it is possible
to ensure a satisfactory level of traffic safety in
recent years using innovative means of radio
navigation. For this reason, the problem of
divergence of ships should be considered only in
accordance with the section "Use of automatic
radar plotting means".</p>
      <p>
        The main document among the normative ones
that determine the reliability of the divergence of
ships is the "International rules for preventing
collisions of ships at sea" (IRPCSS-72) [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ].
      </p>
      <p>These Rules oblige each vessel to carry the
appropriate lights and signs, to sound the
appropriate sound signals, to use all available
means in accordance with the prevailing
circumstances and conditions to enable each of
them to:</p>
      <p>1. To detect in advance the presence of other
vessels;</p>
      <p>2. To determine the degree of danger in order
to identify the existence of a collision hazard;
3. Take into account the mutual obligations
when maneuvering the gap;</p>
      <p>4. Ensure safe divergence in all visibility
conditions.</p>
      <p>Method 3. The lack of a quantitative
description of the concept of "limited visibility" in
the IRPCSS-72 causes a contradiction between
R. 19 ("Swimming with limited visibility") and
R. 15 ("Situation of intersecting courses in sight
of each other") in cases where the visibility range
is of the same order of magnitude with D. Having
detected in such conditions with the help of the
radar an approaching vessel from the right side, a
prudent navigator will make way for him, without
waiting for this vessel to come within the distance
of visual visibility and he will have to act in
conditions: the short period of time and minimal
space.</p>
      <p>In addition, the International Maritime
Organization at the United Nations (IMO) in 1978
adopted the Convention on the Training,
Certification and Watchkeeping of Seafarers. This
Convention defines the minimum requirements
for the knowledge and practical skills of boat
masters in relation to ship divergence and the use
of radar information. IMO has also formulated
requirements for programs for radar surveillance,
laying and use of automatic radar laying facilities.
All this is aimed at increasing the reliability of the
divergence of ships.</p>
      <p>
        Method 3. Get answers to the questions:
determination of the current coordinates of the
vessel in the coordinate system - bearing and
distance relative to a given point; determination of
the actual trajectory of the vessel's movement, the
actual elements of movement, is possible with the
help of navigation methods for monitoring the
position and movement of the vessel. Evaluation
of the trend of the vessel's movement to predict
the current coordinates in time, control of the
lateral deviation of the vessel from and calculation
of the course correction. The listed monitoring
tasks are referred to as “Real-time tasks”. The
more difficult the navigation conditions are, the
shorter the “real time clock” should be. The
advantage of each navigation method is
determined by the main features of the
characteristics: the accuracy of determining the
current coordinates of the vessel, the duration of
navigation determination and the discreteness of
the definitions [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ]. Methods of control over the
position and movement of the vessel are divided
into two groups: "navigational" and "pilotage".
With “navigator” control methods based on
navigation measurements, the point at which the
vessel was located, and depending on the position
of this point relative to the line of the given path,
solve the remaining navigation problems. The
navigational methods include the reckoning of the
ship's coordinates, its refinement along one line of
position, navigational observations, as well as
methods formed by their combinations, including
"corrected dead reckoning"
2.1.
      </p>
    </sec>
    <sec id="sec-3">
      <title>Security Domains</title>
      <p>The area around a ship of a certain radius,
shape, and size, not considering geometry, actual
dimensions, the current course, into which the
oncoming ship should not enter is called the ship's
domain. The ship's heading is determined by
evaluating the speed vector from radar
observations during several turns of the antenna.
This definition indicates that the information is
not received in real time, but nevertheless this area
is called the "navigation safety zone". In methods
for assessing the risk of dangerous approach by
the foundation, there is a point of the shortest
approach of ships (closest point of approach). For
navigational safety, the shortest distance is greater
than the critical value. The following values are
provided: "time of movement to the point of the
shortest approach of ships" (time of closest point
of approach), "distance to the point of the shortest
approach of ships" (distance to closest point of
approach).</p>
      <p>Research groups that study the issue of ship
collision avoidance use a variety of domains:
circular, elliptical, and other complex shapes. The
domain boundary is interpreted as a function of
the ship's heading angle. At this point in time, to
use the security domain, each domain is analyzed
separately. Based on this, we can conclude that the
domain cannot fully solve all the problems of
discrepancy due to strictly defined domain
boundaries.</p>
      <p>The Goodwin domain model is divided into 3
sectors. The dimensions of the free zone from
other objects are different. Depends on the
situation in a certain period. The radius of the
sectors corresponds to the critical values of the
closest approach of ships for each scenario
Figure 2.</p>
      <p>Deepening the idea of Goodwin is carried out
by the Davis domain, presented in the form of an
ellipse with an offset center, divided into sectors.
For the navigator, this is an indicator for deciding
to perform an evasive maneuver when other
objects intrude into the active domain Figure 3.</p>
      <p>Caldwell's ship domain is a different
configuration depending on the ship's
approaching scenario. With oncoming traffic in
the domain, the stern part is completely absent.
When overtaking, the domain has an ellipsoidal
shape.</p>
      <p>
        Tszyu's ship domain is based on neural
networks trained by the backpropagation method,
which makes it possible to partially consider the
influence of the external environment without
resorting to complex classical deterministic
mathematical models of its description [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ].
      </p>
      <p>
        The ship domain proposed by
S. V. Smolentsev, A. E. Filyakov considers the
navigation features of the navigation area and the
hydrometeorological situation. Eliminates the
occurrence of false alarms when a vessel enters
the safety domain that is moving in the opposite
direction in its lane [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. The position of the
security domain boundary is parameterized and
depends on the value of one parameter, which is
convenient for performing calculations. In
addition, the border of the proposed safety zone is
smooth, which excludes jumps in solutions for
different course angles of entry of targets into this
zone [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ].
      </p>
      <p>There are groups of our and foreign researchers
who are working towards assessing the risk of
collision and improving ship domains. An
unconventional method for clarifying the situation
of approaching ships at sea based on information
from an automatic identification system was
proposed by Bukaty Vitaly Mikhailovich,
Morozova Svetlana Yurievna. Titov A.V., Zaikova
S.N., Volynskiy I.A., Khmelnitskaya A.A. in their
work the current state and problems of using inland
waterways (on the example of the Volga-Caspian
Sea shipping canal) and Nitsevich A.A., Melnikov
N.V., Khristich D.Yu., Lebedev V.P. in work
Collision of ships use the method of M.A.
Konoplev, who presents the risk assessment in the
form of a fuzzy system.</p>
    </sec>
    <sec id="sec-4">
      <title>3. Conclusions</title>
      <p>One of the main problems of navigation,
namely the navigation safety, remains unresolved,
although the work is carried out by all groups
according to the law of a conical spiral.</p>
      <p>The article presents a brief overview of
methods for ensuring the navigation safety of
vessel traffic, which are divided into three
categories: methods of early detection of the
possibility of collision of ships, methods of
maneuvering to avoid a collision and methods of
planning the trajectory of the safe movement of
the ship. A detailed theoretical review of methods
for assessing the risk of a dangerous approach of
ships, associated with ensuring the navigation
safety of ship traffic, is carried out in detail. To
assess the risk of a dangerous approach of ships,
the presentation of ship domains of complex
figures is given - a dangerous approach of ships.</p>
      <p>The work provides links to sources that clarify
the presented material.</p>
    </sec>
    <sec id="sec-5">
      <title>4. Acknowledgements</title>
      <p>We wish to thank V. Kychak, prof., I.
Trotsyshyn, prof., O. Punchenko, prof., G.
Bortnyk, prof. for their insightful comments on
earlier drafts.</p>
      <p>We would also like to thank Vinnitsa National
Technical University for the application of
theoretical and practical research in the R&amp;D
"Development of the theory and methodology of
digital radio signal processing in real time"
(Ministry of Education and Science of Ukraine,
Vinnitsa National Technical University);</p>
      <p>R&amp;D "Development of methods for designing
a fiber-optic transmission system" (Ltd
"Budivelnik-3", Vinnitsa National Technical
University).</p>
    </sec>
    <sec id="sec-6">
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