=Paper=
{{Paper
|id=Vol-3668/paper16
|storemode=property
|title=Automatic Prevention of the Vessel’s Parametric Rolling on the Wave
|pdfUrl=https://ceur-ws.org/Vol-3668/paper16.pdf
|volume=Vol-3668
|authors=Vitaliy Kobets,Serhii Zinchenko,Oleh Tovstokoryi,Pavlo Nosov,Ihor Popovych,Igor Gritsuk,Victor Perederyi
|dblpUrl=https://dblp.org/rec/conf/colins/KobetsZTNPGP24
}}
==Automatic Prevention of the Vessel’s Parametric Rolling on the Wave==
https://ceur-ws.org/Vol-3668/paper16.pdf
Automatic Prevention of the Vessel’s Parametric Rolling
on the Wave
Vitaliy Kobets2, Serhii Zinchenko1, Oleh Tovstokoryi1, Pavlo Nosov1, Ihor Popovych2,
Igor Gritsuk1 and Victor Perederyi3
1 Kherson state maritime academy, 20, Ushakova ave., Kherson, 73000, Ukraine
2 Kherson state university, 27, Universytetska str., Kherson, 73003, Ukraine
3 Admiral Makarov national university of shipbuilding, 9, Heroes of Ukraine ave., Mykolaiv, 54007, Ukraine
Abstract
Parametric resonance is one of the most dangerous phenomena that occurs during a storm. In the event
of a parametric resonance, an undamaged and properly loaded vessel can capsize within seconds. The
essence of parametric resonance is to change the parameters of the vessel as an oscillating system. In
this case, the coefficients of the differential equations of the vessel model become functions of time.
Parametric oscillations are observed at a certain ratio between the frequency of the external influence
and the frequency of the system's own oscillations. Parametric resonance in the roll channel is especially
dangerous, which leads to a sharp increase in the amplitude of the vessel's rolling, water entering the
deck and inside the vessel's hull, loss of stability and possible capsizing. The existing methods of
storming are not effective enough, which is due to the use of visual methods for estimating the
parameters of turbulence and manual graphic constructions, significant time delays between obtaining
data for calculation and determining safe parameters of motion, the lack of constant measurement of
turbulence parameters and refinement of safe motion parameters, the difficulty of selecting the
dominant factor from the system dangerous factors, intuitive assessment of the level of danger. The
authors have developed a method of automatic avoidance of parametric resonance, which differs from
existing methods in that it automates the processes of measurement and information processing,
reduces delays in decision-making, reduces the influence of the human factor on control processes,
reduces crew fatigue, reduces the risks of losing the vessel and cargo, and in general increases the
navigation safety. The developed method can be used for both manual and automatic control. In the
manual control mode, the shipmaster has the opportunity to use automatically measured information
and the results of its processing - visualization of parametric resonance areas and the position of the
phase point for making management decisions. In the automatic control mode, the system itself
calculates and implements safe movement parameters, and the shipmaster only observes its operation.
The obtained results are reproducible and can be used to develop the functionality of automated
systems and/or automatic parametric resonance avoidance modules.
Keywords
Intelligent systems, human factor, navigation safety, automated systems, parametric rolling 1
1. Introduction
Analysis of global and domestic accident statistics shows that the main cause of ship death is the
loss of seaworthiness of the vessel in storm conditions [1]. Stormy sailing conditions are one of
the most difficult sailing conditions on the route. The pitching, the need for constant
concentration of attention greatly exhausts the crew and leads to wrong decisions. The situation
worsens also due to the fact that during a storm, such dangerous phenomena as harmonic and
parametric resonances occur much more often, deforming forces and moments increase, which
can reach the maximum allowable values and lead to the destruction of the hull, the lateral
COLINS-2024: 8th International Conference on Computational Linguistics and Intelligent Systems, April 12–13, 2024,
Lviv, Ukraine
vkobets@kse.org.ua (V. Kobets); srz56@ukr.net (S. Zinchenko); otovstokory@gmail.com (O. Tovstokoryi);
pason@ukr.net (P. Nosov); Ihorpopovych999@gmail.com (I. Popovych); gritsuk_iv@ukr.net (I. Gritsuk);
viperkms1@gmail.com (V. Perederyi)
0000-0002-4386-4103 (V. Kobets); 0000-0001-5012-5029 (S. Zinchenko); 0000-0003-3048-0028 (O.
Tovstokoryi); 0000-0002-5067-9766 (P. Nosov); 0000-0002-1663-111X (I. Popovych); 0000-0001-7065-6820 (I.
Gritsuk); 0000-0002-9241-3034 (V. Perederyi)
© 2024 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
stability of the ship in following seas decreases, etc. Works [2-4] are devoted to the study of the
strength of vessel hulls, materials for the manufacture of hulls. Guidelines and Recommendations
for safe sailing in difficult weather conditions are given in IMO documents [5,6].
Parametric resonance is one of the most dangerous phenomena that occurs when a vessel
rocks in a storm. If parametric resonance occurs, an intact and properly loaded vessel can capsize
within seconds. The essence of parametric resonance is the change, under the influence of
external forces during movement, of the parameters of the vessel as an oscillating system. In this
case, the coefficients of differential equations, depending on the parameters of the system,
become functions of time. Such oscillations are called parametric. They can be fading or
increasing over time. Parametric oscillations are observed at a certain ratio between the
frequency of external influence and the frequency of natural oscillations of the system. For this
reason, the dangerous relationships that arise between the frequency of forced and natural
vibrations of a vessel are called parametric resonance. Parametric resonance due to roll can lead
to a sharp increase in the amplitude of the vessel's rolling, to sea water entering the deck as the
roll angles increase during the rolling, to water getting inside the vessel's hull, to loss of stability
and, as a consequence, to a possible capsizing of the vessel. The existing methods of storming are
not very effective, as they have low accuracy, due to the use of visual methods of estimating the
parameters of turbulence and manual graphic constructions, significant time delays between
obtaining data for calculation and determining safe parameters of movement, lack of constant
measurement of parameters of turbulence and refinement of safe parameters of movement, the
difficulty of identifying the dominant factor from the system of dangerous factors, intuitive
assessment of the level of danger.
The authors of the article believe that the most effective direction in the development of ship
traffic control systems is the use of automatic control modules in automated systems, which will
significantly reduce the influence of the human factor on the processes of ship traffic control and
increase the safety of shipping.
2. Related works
The question of safe sailing in a storm has been previously considered by many authors. The
books [7,8] should be included among the fundamental works of this direction.
In the work [9] the author cites dangerous phenomena that can occur during storm sailing, in
particular: surf-riding and broaching, which occur when the vessel is on the steep front edge of a
high wave in following seas. In this case, the vessel can be accelerated by going down the wave,
but there is a danger of capsizing with a sudden change of course; reduction of intact stability
when riding a wave crest amidships, occurs when the vessel moves on the crest of a wave. The
danger of the situation is a significant decrease in stability, especially when the wavelength is (0.6
- 2.3) the length of the vessel; synchronous rolling motion, also known as synchronous resonance,
occurs when the period of the vessel's own oscillations coincides with the period of oncoming
waves; parametric roll motions, also known as parametric resonance, leads to a sharp increase in
roll amplitude due to a periodic change in stability at the crests and troughs of waves. The author
describes the possible situations of occurrence of parametric resonance: the period of natural
oscillations of the vessel coincides with the period of waves, the stability of the vessel decreases
to a minimum once per oscillation period, the situation is characterized by asymmetric
oscillations, when the roll amplitudes in different directions differ from each other, the transition
of this type of parametric resonance is possible in synchronous; when the period of the vessel's
own oscillations is twice as long as the wave period, the stability of the vessel decreases to a
minimum of two times during the oscillation period, the situation is characterized by symmetrical
oscillations; when there is a consistent and periodic submersion and surfacing of the stern and
bow part of the vessel, which can lead to serious rolling movements, even if the vessel is stable.
The work also includes mathematical formulas that describe the conditions for the occurrence of
dangerous phenomena.
In the article [10] listed the main precautions to be taken when sailing in storms, namely:
switch to manual steering to avoid sudden waves hitting the rudder; check all oil levels,
connections and other important steering control elements; create conditions for obtaining the
maximum torque on the rudder shaft; ensure a sufficient man power including senior officers
to be present in the bridge; ensure a sufficient number of engineers in the engine room;
monitoring all the parameters of the main propulsion plant and auxiliary power plant
machineries; after getting rough weather warning, all the spares in the engine room are to be
stowed and lashed properly; in bad weather, propeller will come in and out of water and will
fluctuate the main engine load. Hence rpm is to be reduced or main engine control setting is
to be put on rough weather mode; always make sure for correct sump level of all the
machineries as during rough sea ship will roll, resulting in false level alarm which can even
trip the running machine and lead to dangerous situation in bad weather; level of all
the important tanks is to be maintained so that pump inlet should not loose suction at any time;
stand by generator is to be kept on load until the bad weather situation stops; water tight
doors in the machinery spaces to be closed; sky light and other opening to be closed; all trays
are to be avoided from spilling in event of rough weather; all deck items (mooring cables, lashing
equipment, drums, etc.) should be properly secured; all openings on the cargo deck and other
spaces must be closed; keep all openings leading to the dwelling closed; everyone must know
their duties according to their rank; turn off the elevators to avoid injury; wear personal
protective equipment, hold on to handrails to avoid tripping and falling; be alert and work in a
team.
In the article [11] considered issues of increasing speed and reducing energy consumption
during cargo and ballast transits of a tanker. Based on the results of experiments and
observations carried out on the tanker itself, a method of increasing speed and reducing fuel
consumption in stormy conditions is proposed. It is shown that an increase in speed and fuel
economy can be achieved with the same wind and wave angles. This rule must be taken into
account both at the stage of planning the transition and in conditions of stormy sailing. The
obtained results can be extended to other types of vessels.
In the candidate's thesis [12] the author established a relationship between: steady motion of
the vessel, its seaworthiness characteristics and wave parameters, presented in the form of a non-
linear mathematical model; the shape of the submerged part of the cross-section of the hull and
its local draft, presented in the form of a two-layer artificial neural network; parameters of the
vessel's movement, the work spent on the transition and the additional work spent on
compensating the disturbing forces and reducing the risk associated with them in the form of
integral dependence; volatility parameters and the level of risk, using methods of heuristic
analysis and fuzzy logic. Improved: the method of calculating the seaworthiness of the vessel due
to more accurate determination of the zones of dangerous side rocking, slamming, flooding and
loss of speed in irregular waves; a two-level system for evaluating the effectiveness of route
planning and ship management in stormy conditions using methods of fuzzy logic and risk
assessment.
In the doctoral thesis [13], in the part of storm sailing, the author considered the forces and
moments acting on the vessel's hull, mathematical modeling of the vessel's rocking (chapter 3)
and simulation of stability in real time on waves (chapter 4). A conclusion was made regarding
the expediency of using different models depending on the navigational task, namely: a linear
model of vessel rocking in 6 degrees of freedom, which is advisable to use for calculating
amplitude-frequency characteristics in the linear range, for estimating rocking amplitudes,
optimizing the vessel's route, when designing channels and fairways, when planning vessel
operations at shallow depths; a non-linear model of vessel sway in 6 degrees of freedom, which
is used for modeling dynamics in studies of stability, parametric resonance, broaching, etc.
In the article [14] investigated issues of parametric roll on regular excitation. Parametric roll
is a dangerous phenomenon that can lead to a sharp increase in the amplitude of oscillations at
the frequency of the external influence, which coincides with the frequency of the vessel's own
oscillations. The problem was investigated experimentally on a typical Norwegian fishing vessel
with a blunt hull and a small ratio of length to width, as well as using numerical simulations. Tests
were performed without and with longitudinal velocity, with corresponding Froude numbers
Fn 0.09 and Fn 0.18 . Nonlinearities in Froude-Krylov loads and recoverable loads were
taken into account by integrating the pressure on the instantaneous wetted surface of the hull. It
was found that near the instability boundary of the Mathieu 1-DOF diagram, the physical and
numerical predictions were different in terms of the appearance of parametric roll. The limits of
instability in the experiment also differed from the limits of instability of the 1-DOF Mathieu
diagram. The instability region for the 6-DOF experiments and simulations spans a wider range
of frequency ratios, and the metacentric height change amplitude threshold was found to be lower
than that predicted by the 1 DOF Mathieu diagram. The results also showed that the region of
instability, in the presence of speed, shifts towards smaller ratios of frequencies of natural and
forced oscillations.
According to the authors of the article [15], container shipping accounts for 52% of the world's
total maritime trade, and safe container shipping practices are paramount in maritime trade.
Between 2008 and 2016, about 568 containers were lost annually in accidents and about 1,582
containers in disasters. This led to disruptions in major supply chains. The most common and
most dangerous phenomenon that causes the loss of containers is the parametric rocking on the
oncoming and traveling wave, which arises as a result of the dynamic instability of the vessel. The
container ship APL China suffered the most damage due to parametric rocking (406 containers
were lost and 1000 were damaged, the amount of damage was 100 million dollars). This incident
led to the revision of the IMO Code on the Stability of an Intact Vessel and the Master's Guide for
Avoiding Dangerous Situations in Adverse Weather Conditions. The causes of parametric roll are
periodic (with a period twice the period of the oncoming wave) changes in the metacentric height
during the movement of the ship across the waves. Parametric roll is also facilitated by special
hull shapes (use of extended sides in the front of the hull, etc.). The authors of the article, in the
MATLAB environment, investigated the influence of various parameters (wave height,
wavelength, and ship speed) on the parametric resonance of a specific container ship. The
enveloping stability curve for counter and accompanying excitation is determined. Damping
effects are taken into account when evaluating the range of metacentric height change.
In the article [16] considered the issues of choosing the optimal route of a sea vessel, building
universal storm charts that would allow avoiding the dangers of stormy navigation and ensure
proper seaworthiness in difficult weather conditions. In the Excel program, a universal storm
diagram was built, the zones of synchronous and parametric resonances, broaching were
calculated, and the ship's speed was estimated on waves. The safest and most efficient route of
the ship in stormy sailing conditions is chosen. A comparison of the behavior of the ship model,
calculated according to the considered scheme, and the behavior of the real ship was made. It has
been found that the danger zones shown on the chart agree well with the danger zones obtained
by observation on the vessel. The simplicity and availability of the method of choosing the optimal
combinations of course and speed while sailing in stormy weather conditions has been proven.
In the article [17] stated that the conditions for the occurrence of chaotic roll are most likely
in the zone of the main parametric resonance, when its period is successively doubled, and
subharmonic oscillations turn into chaotic ones. This circumstance necessitates a detailed study
of the modes of parametric roll: issues of its occurrence, development and establishment, as well
as methods of calculating its amplitudes. In the paper, the research of parametric roll was carried
out on the basis of Luhovsky's formula. Additional nonlinear moments obtained using the small
parameter method are taken into account. The results of parametric roll calculation for five
different vessels moving at different course angles both with and without taking into account
nonlinear moments are presented. The obtained results showed a significant influence of
nonlinear moments on the maximum amplitudes of parametric roll, especially in the case of beam
waves.
In the work [18] investigated parametric vibration and combined resonance of a turbine blade
under the action of parametric and forced excitation. The blade is modeled as a rotating beam
taking into account centrifugal, gyroscopic and bending-torque forces and moments. The region
of instability of a linear system with parametric excitation is analyzed using the Floquet theory,
the influence of blade parameters on the region of instability is discussed. Parametric oscillation
in the torsion channel caused by parametric excitation in the bending channel was found. The
results showed that the size and position of the resonance region depend on the aspect ratio of
the blade and its installation angle. A multi-scale method is used to study the combined resonance
caused by forced excitation and a gyroscopic element. The influence of blade parameters and
excitation characteristics on the regions of combined resonance was studied. It was established
that the change in the excitation frequency caused the phenomenon of heteroclinic bifurcation,
as a result of which the harmonic components accompanying the bifurcation changed. The multi-
period characteristic, in which the excitation frequency and subharmonic components
predominated, shifted to the single-period characteristic, in which the subharmonic components
predominated. The conducted research gives a theoretical explanation of the non-synchronous
resonance of blades and subharmonic signals in the vibration of blades, allows to determine the
design parameters of blades, especially for wind turbines.
The human factor plays a significant negative role in ship management, especially in stormy
conditions. In order to reduce the influence of the human factor on control processes, work [19]
considered the issues of automated identification of the shipmaster's condition and the formation
of warning messages. At the same time, according to the authors of this article, the most effective
way to reduce the influence of the human factor on management processes is the use of automatic
modules in automated systems. Articles [20,21] consider the issue of using such modules to
optimize control processes in bottlenecks, and article [22] considers the issue of automatic
control of redundant structures of executive devices.
From the given overview of literary sources, it is possible to see a range of issues that have
been solved by the authors recently. However, the authors of this article did not find methods of
automatic avoidance of parametric resonance. Therefore, conducting such research is an urgent
scientific and technical task.
3. Methods and materials
The IMO documents and the works of a number of authors describe the causes of parametric
resonance - the coincidence of the change period in the vessel's metacentric height with the
period of forced oscillations in the roll channel. The differential equation of the angular motion of
the vessel in the roll channel can be written in the form
I x 44 x M x ( x ) M x ( ) M x (t ) , (1)
where I x is the axial inertia moment in roll channel, 44 is the inertia moment of the attached
mass of water, M x (x ) is the damping moment, M x ( ) - is the restoring moment, M x (t ) is the
moment of external influences of wind, current and turbulence, x is the angular rate in the roll
channel, - is the roll angle.
The linearized equation (1) will have the form
I x 44 x M x ( x ) x M x ( ) M x sin t , (2)
x
M x ( x ) M x ( )
where is the coefficient of the damping moment in the roll channel, is the
x
coefficient of restoring moment, M x is the amplitude of external influence, is the frequency
of external influence.
Taking into account that x , x , equation (2) will be rewritten in the form
1 M x ( x ) 1 M x ( ) M sin( t .
x (3)
I x 44 x I x 44 I x 44
After entering the markings
M x ( x ) M x ( )
m
1 1 Mx
x 2 D ,
x
mx 0 ,
2
m ,
I x 44 x I x 44 I x 44 x
the differential equation (3) will take the form
2 D 02 m x sin t . (4)
The differential equation (4) is an oscillatory chain, where D is the damping decrement and
0 is the frequency of the natural oscillations. The occurrence of parametric resonance is related
to the harmonic change of the parameter
M x ( )
mx 02
1
(5)
I x 44
due to the presence of a harmonic component in the restoring moment coefficient
M x ( )
M x M x sin t , (6)
where M x is the average value of the restoring moment coefficient, M x is the amplitude of
the harmonic component of the restoring moment coefficient, is the frequency of the harmonic
component of the restoring moment coefficient. Taking (5) into account, equation (6) can be
written in the form
mx mx mx sin t
, (7)
2 2 m sin t
0 0 x
Equation (4) can be rewritten in the form
2 D 02 mx sin t mx sin t (8)
The component mx sin t is the cause of parametric resonance. Figure 1 shows the result of
modeling the differential equation (8) for mx 0 .
Figure 1: Change of roll angle over time with parametric resonance
As can be seen from Fig. 1, even in the absence of external influences ( mx 0 ), a harmonic change
in the component mx sin t of the restoring moment can lead to swaying of the roll angle
(parametric resonance). The possibility of swinging depends on the value of the damping
coefficient and the amplitude of the harmonic component of the restoring moment.
The condition for the occurrence of parametric resonance is the coincidence of the period of
forced oscillations TE with the period of natural oscillations TC of the vessel in the roll channel,
TC
or the coincidence of the period of forced oscillations TE with half the period of natural
2
oscillations of the vessel
TE TC
TC (9)
TE 2
The period of forced oscillations can be written in the form
TE , (10)
С V cos q
where is the wavelength, С 1,25 is the speed of wave propagation, V is the vessel’s
speed, q is the course angle of the wave.
Taking formula (10) into account, system (9) can be rewritten in the form
V cos q 2 1,25
TC
(11)
V cos q 1,25
T
C
Equations of system (11) determine the regions of parametric resonance of the first and
second type in the "Vsinq-Vcosq" coordinate system. In fig. 2 shows the areas of parametric
resonance for the period of the vessel's natural oscillations TC 12 .5 s and the wavelength
90 m .
Figure 2: Areas of parametric resonance
As can be seen from the given diagram, the regions of parametric resonance are elongated
along the Vsin(q) axis. The most dangerous option is to remove the phase point A from the area
of parametric resonance by a combined maneuver (velocity vector Vn3), when the phase point
moves along the resonance zone. When maneuvering the course (velocity vector Vn2), the phase
point A will move along the circle depicted by the dashed line. In this case, the time the phase
point stays in the resonance zone is significantly reduced. The optimal speed maneuver (velocity
vector Vn1) is when the phase point moves along the Vcos(q) axis and is removed from the
resonance zone by the shortest path.
In fig. 3 shows a fragment of the module for creating controls in the MATLAB environment.
Figure 3: A fragment of the control formation module
In rows 26-28, the set motion parameters necessary for the module are transferred from the
general data array: the set values of speed, course, and lateral displacement. In line 29, the
imaginary period of the wave is calculated. In rows 30-32, the period of the vessel's own
oscillations is compared with the calculated imaginary period of the wave and its double
imaginary period. If one of the imaginary periods coincides with the period of natural oscillations,
the set speed of movement is reduced by 20%. In rows 34-35, projections of the vessel's speed
on the axis of the base coordinate system are calculated. In rows 37-42, the gain coefficients of
the PID controller are specified. In rows 44-47, the angular and lateral deviations from the
specified movement parameters and the integrals of these deviations are calculated. In rows 49-
51, the deviations of the stern are calculated to work out the angular and lateral deviations of the
vessel from the given values. In row 52, the angle of deviation of the telegraph is determined to
ensure the movement of the vessel at a given speed.
4. Experiment
The workability and effectiveness of the method of automatic prevention of parametric
resonance are verified by mathematical modeling in the MATLAB environment.
In fig. 4, 5 show the results of the experiments in the form of graphs of the change in time of
the ship's movement parameters for the starting point A, Fig. 2. The first and second graphs show
the change in time of longitudinal speed V x [ m / s ] and longitudinal displacement X g [m] . The
third and fourth graphs show the change in time of lateral speed V y [ m / s ] and lateral
displacement Yg [m] . The fifth and sixth graphs show the change in time of the roll angular rate
x [dg / s] and the roll angle [dg ] . The seventh and eighth graphs show the change in time of
the trim angular rate y [dg / s ] and the trim angle [dg ] . The ninth and tenth graphs show the
change in time of yaw angular rate z [dg / s] and yaw angle [dg ] . The eleventh and twelfth
graphs show the change in time of vertical speed Vz [m / s] and draft T [m] .
The first experiment. The initial parameters of the movement of the vessel and the wave
correspond to the p. A of the parametric resonance area, fig. 2: ship course is K (0) 0 dg , ship
speed is V (0) 2.5m / s , wave course is KW 180 dg , wave speed is C 11.9m / s . The control
system maintains the vessel's initial course and speed. The simulation results are shown in Fig. 4.
Figure 4: Results of the first experiment
As can be seen from the results of the experiment, the period of forced oscillations is ~ (6-7)
s., which can be seen from the period of the vertical speed oscillations Vz , draft T , trim angular
rate y and trim angle . The period of oscillation in the roll of the channel is 12.5 s , which
coincides with the period of free oscillations of the vessel in the roll channel and is twice the
period of forced oscillations. In combination with a significant amplitude of oscillations 50dg ,
this indicates the presence of parametric resonance of the 2-nd type.
The second experiment. As in the first experiment, the initial parameters of the vessel's
movement and the wave correspond to the p. A of the parametric resonance area, fig. 2: ship
course is K (0) 0 dg , ship speed is V (0) 2,5m / s , wave course is KW 180 dg , wave speed
is C 11,9m / s . The control system constantly monitors the conditions for the occurrence of
parametric resonance. The simulation results are shown in Fig. 5.
Figure 5: Results of the second experiment
As can be seen from the given results, starting from the time t 0 s control system starts to
reduce the speed of movement. This is explained by the fact that the initial position of phase point
A is in the area of parametric resonance, and to avoid its development, the control system
* *
automatically calculated the safe speed and course, which are V 2,1 m / s, K 0 dg and
began to reduce the speed to the calculated safe value. At the same time, the control system
maintains a safe course with accuracy K 2 dg .
The results also show that during the decrease in speed, an increase in the amplitude of
oscillations in the roll channel is observed, which reached a value of
max
40 dg by t 60 s .
After t 60 s , the increase in the amplitude of oscillations stops, and starting from t 100 s , the
amplitude of oscillations in the roll channel sharply decreases to the value of forced oscillations,
which indicates an exit from the parametric resonance area.
Analysis of the given results shows that the control system allows to automatically calculate
the safe parameters of the vessel's movement and support them when deriving the phase point
from the parametric resonance area.
5. Discussion
A method of automatic avoidance of parametric resonance has been developed, which consists
in: constant, with the on-board computer, measuring the speed and course of the vessel, the
length and course of the wave, the roll angle; using the measured parameters to calculate the
imaginary period of the wave; construction and visualization of parametric resonance area;
construction and visualization of the position of the phase point in the coordinate system of
parametric resonance areas; estimation of the phase point position relative to the areas of
parametric resonance; calculating the safe speed and course of the vessel when the phase point
approaches the area of parametric resonance; changes in current speed and course by safe means
of the automatic control system.
The developed method differs from existing manual control methods in that it automates
manual control processes, reduces delays in decisions, reduces the influence of the human factor
on control processes, reduces crew fatigue, reduces the risks of vessel and cargo loss, and
generally improves shipping safety.
The developed method can be used for both manual and automatic control. In the manual
control mode, the shipmaster has the opportunity to use automatically measured information and
the results of its processing - visualization of parametric resonance areas and the position of the
phase point for making management decisions. In the automatic control mode, the system itself
calculates and implements safe movement parameters, and the shipmaster only observes its
operation.
The obtained results are reproducible and can be used to develop functions of automated
systems and automatic parametric resonance avoidance modules.
6. Conclusion
A method of automatic avoidance of parametric resonance has been developed, which allows
automating vessel control processes when parametric resonance occurs, reduces the influence of
the human factor on control processes, reduces decision-making time, reduces risks of vessel and
cargo loss, and generally improves shipping safety.
The obtained results are explained by the use of an on-board computer, constant, with the
clock of the on-board computer, measurement of the vessel’s movement parameters and waves,
calculation of parameters inaccessible to direct measurement, construction and visualization of
parametric resonance areas and the position of the phase point in the coordinate system of the
parametric resonance areas, assessment of the position of the phase point relative to the areas
parametric resonance, calculation and implementation of safe vessel movement parameters.
The theoretical significance of the obtained results lies in the development of a method of
automatic parametric resonance avoidance.
The practical significance of the obtained result lies in the possibility of applying the method
for the development of modules for the automatic avoidance of parametric resonance, which will
allow to automate control processes, reduce the influence of the human factor on control
processes, reduce delays in making management decisions, reduce the risks of vessel and cargo
loss, and generally increase the shipping safety.
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