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1 INTRODUCTION

Parametric rolling divides the maritime world into

those that regard it as a rare phenomenon and therefore

poses little or no danger to spng, and those that regard

parametric rolling as a ubiquitous serious hazard to

shipping.

The challenge is to attribute specific marine

accidents to parametric rolling. As a result, numerous

investigation reports end up stating that heavy rolling

caused the marine accident, but not parametric rolling.

Nevertheless, few accidents are attributed to

parametric rolling. As in 2008 when the CMV

CHICAGO EXPRESS [2] experienced severe rolling of

up to 44 degrees during a typhoon and one seaman

died and another was hospitalized with serious

injuries. Despite the presence of parametric roll

detection documentation on board, the M/S

FINNBIRCH [3] sank between Öland and Gotland in

2006, experiencing roll angles of 30-35 degrees. But

even weather forecasts cannot prevent this

phenomenon, as experienced by the SVENDBORG

MAERSK [4] on February 17, 2014, when she

encountered heavy weather on her way from

Rotterdam behind the English Channel and

experienced rolling angles of up to 41 degrees. 517

containers went overboard and 250 were damaged.

Parametric rolling may affect almost the entire

range of ships, not only on the open sea, but also on the

coast and even in the North and Baltic Seas. The hull

forms most at potential risk tend to be those with flared

fore and aft extremities or a flat transom stern paired

with wall-sided ship sides near the waterline amidship

[5] such as container ships and pure car/truck carriers

[6].

In the process of maritime automation, an early

warning system for parametric rolling becomes

indispensable. To this purpose, the present thesis first

explains the phenomenon of parametric rolling in

Chapter 2, followed by the state of the art in Chapter 3.

Chapter 4 contains a separate approach to risk

prediction of the probability of parametric rolling of

ships based on ship motions and sea state parameters.

Classification of Parametric Rolling for Seagoing Ships

and Percentage Distribution for Multiple Sea State

Parameters

S. Chhoeung & A. Hahn

Carl von Ossietzky University Oldenburg, Oldenburg, Germany

ABSTRACT: In this paper, parametric rolling is divided into 5 heavy grades, establishing a classification for

parametric rolling. This is achieved by a multi-parameter application in the simulations. For this purpose,

parametric rolling, established criteria and the state of the art are considered and the results are summarized.

Based on this, parametric rolling is successfully simulated using discrete simulation in MARIN [1]. Five heavy

grades are introduced so different classes of parametric rolling can be distinguished. Furthermore, dependencies

and probabilities for the occurrence of parametric roles in relation to the see are determined numerically. This

will later be used in an assistance system on board ships to compute the prediction of parametric roll using an AI.

http://www.transnav.eu

the International Journal

on Marine Navigation

and Safety of Sea Transportation

Volume 16

Number 4

December 2022

DOI: 10.12716/1001.16.04.19

770

The evaluation follows in Chapter 5, with a discussion

in Chapter 6.

2 THE PHENOMEN OF PARAMETRIC ROLLING

In this chapter first the phenomenon of parametric

rolling in longitudinal directed waves is described and

then the sea and ship parameters supporting

parametric rolling.

2.1 Parametric Rolling

Parametric rolling bases on the change of ship stability

over a short period of time in wave trough (solid line)

and wave crest (dashed line) in longitudinal directed

waves as shown in figure 1. This concerns larger

vessels with flared fore and aft decks for instance pure

car/truck carriers and container vessels [6].

Figure 1. Wave trough and crest.

Figure 1 shows the ship in a wave trough (solid

line). Here, the area of the water surface increases

because the bow and stern immerse deeper into the

water. Consequently, the water surface coefficient cw

increases compared to the calm position, which also

increases the longitudinal stability. In the wave crest

(dashed line), the behavior is the reverse. The

waterplane area decreases due to the fact that the

midship lies deeper in the water, but the bow and stern

come out of the water. This reduces the longitudinal

stability. As a result, the metacentric height GM

increases and decreases with longitudinal directed

waves and oblique waves.

In the design phase of a vessel the metacentric

height GM has been calculated according to the intact

stability rules (example: DNV GL, Rules and

Guidelines I-1-1-Section 28-B.2 Design Criteria [7] for

each ship by the restoring moment and the

corresponding lever arm. On the other hand, if the

wavelength is about equal to the ship's length and the

ship's rolling period is about twice the frequency of the

encounter, there will be a righting moment that is not

sufficiently damped by the water and thus causes the

ship to rapidly oscillate. This oscillation within a short

time is called parametric rolling or parametric rolling

resonance.

2.2 Parameters

This chapter describes the requirements that support

parametric rolling.

Primary characteristics are:

1. If the rolling period TR of the ship is twice the

encounter Te period [8].

TT

(1)

where

1,8 2,1



[9]

2. The wavelength



is about the ship length between

the perpendiculars Lpp [8].





(2)

with

0,7 1,3





[9]

3. Longitudinal or quartering sea with the encounter

angle



[8].

For forward sea:

315 45



  

(3a)

For aft sea:

135 225



  

(3b)

Secondary characteristics are:

4. The variation of the location of the metacentric

height GM in figure 2 plays an important role for

the stability of the ship, as described in chapter 2.2.

The relation of the variation of GM and the

parameter (1) can be simplified without damping as

follows [10].

( )

0,25 1 2 4f x x for x= − +  

(4a)

( )

0,25 1 4 6f x x for x= +  

(4b)

Figure 2. Variation of the metacentric height GM, with the

initial metacentric height GM0

5. After the guide for the assessment of parametric roll

resonance in the design of container carriers [8]

following inequality must be satisfied that the

vessel may be susceptible to parametric rolling,

with



0 the roll natural frequency of vessel,



a the

roll natural frequency to magnitude of changing

GM,



e the frequency of encounter for head and

following seas with:

/ 0,0524* * ,

w s w m

  

+−

the roll natural frequency to mean value of GM,



the frequency of wave and



the roll damping.

0,25–0,5 –0,125 0,03125

384

0,25 0,5

q q q

  +  −

  + 

(5)

where:

771

( )

7,854

0,03

q and p

and

  







−



7,85





where

( )

0,5

m max min

GM GM GM=+

7,85





where

( )

0,5

a max min

GM GM GM=−

0,0524

0,0524 .

e w s w

v for head seas and

v for following seas

  

= +  

= −  

6. And when the inequality (5) is met, following must

be checked [8]:

1 2 3

* * * 1

q k k k







−

(6)

where

1 0,1875

1,002 0,16 0,759

352 1024

16 16

k p q

q q p

=−

= + +

−

From different existing works these 6 parameters

and their limits (1-6) have been identified for this

paper, which will find their meaning in chapter 4. First

follows chapter 3 with the existing works and their

application of the specified parameters.

3 RELATED WORK

Due to the controversial nature of the topic, various

methods and approaches have already been developed

to avoid or mitigate parametric rolling. In this chapter,

the various methods are divided into three categories.

First, there are the methods that provide a preventive

guide (3.1) and thus can be applied before starting to

sail. Next are the monitoring methods (3.2), which

focus on warnings during an ongoing voyage. And

finally, the methods that serve to predict (3.3) the

parametric rolling.

3.1 Guiding methods

The IMO developed a guidance document in

MSC.1/Cir. 1228 to avoid dangerous situations such as

parametric rolling. Based on the parameter (1), (3a) and

(3b) the following polar plot was generated [11]. This

plot (figure 3) shows a dangerous zone where the risk

of parametric roll is high if the above three parameters

are met in a certain combination. Using this ship-

specific diagram, the navigator is capable of avoiding

exactly these combinations by changing the speed or

the course.

Figure 3. Dangerous zones of synchronous and parametric

rolling motions, v is the vessel speed in knots, Tw, the wave

period in seconds, α is the encounter angle, whereby 180° are

following seas.

The OCTOPUS Software [12] is a ship motion

analysis software for sea-keeping analysis of ships and

offshore floating structures. It can therefore also be

used to represent parametric and synchronous rolling

in polar diagrams. In addition to parameters (1), (2)

and (3a/b), a critical wave height and low roll damping

are supplemented in this case, resulting in a polar

diagram for rolling motion. This illustrates different

areas for surfing, parametric and synchronous rolling

in relation to the ship's speed and the angle of

encounter with the waves. This plot (figure 4) serves as

an orientation for the navigator, under which loading

conditions the ship could get into dangerous situations.

So, the navigator can also avoid these areas by

adjusting the speed or course.

Figure 4. Polar diagram generated by Octopus Software for

the sea state Hs=4,99m (significant wave height), Tz=6,80s

(zero crossing period) and Tp=8,49s (modal period). The

radius shows the ship speed, the colors show the dangerous

zones, the headings from 0° to 360° are outlines around, MPE

= most probalbe extreme in degree.

S. Ribeiro and C.G. Soares [5] present a prediction

method based on time domain non-linear strip theory

model with six degrees of freedom. Whereby the roll

damping is determined directly from experimental

772

data and by applying Frank’s Close fit method, the

hydrodynamic effects are based on a potential flow

stripe theory. The validation is carried out by

comparing the numerical predictions with the

experimental results for a container ship based on the

parameter (3) and (4). In the polar plot (figure 5) the

risk zones of the parametric rolling are highlighted.

Speeds from 0 to 16kn were recorded and simulated in

heading sea. Also, in this case, the polar plots serve as

an operational guidance for the navigator to avoid

parametric rolling by avoiding the red areas.

Figure 5. Polar diagram of predicted roll motion, for

headings from 0-45 degrees and 135-180 degrees. The warm

colors show the areas which exceed 20 degrees of rolling

angle. Under the limits, the colors are cold. Vessel speed is

from 0-16 knots, the wave height is given with 6 meters and

the ratio between ship lengths and wavelength is 1.4. The

simulations took each 1200 seconds.

3.2 Monitoring Methods

PAROLL [13] is a real-time detection system for

merchant vessels and is patented as condition-

monitoring system. It is based on low-cost motion

sensors, whereby an algorithm extrapolate

information’s about the frequency, the roll and pitch

motion. First the algorithm examines parameter (1),

whether the rolling period is approximately twice the

period of the wave encounter by using the pitch

oscillation as equivalent. Secondly, the algorithm

analyses whether the rolling and pitching movements

are phase synchronous. Also the parameter 2, 3a and

3b in addition to the wave height has to be fulfilled. So

that an alarm is emitted. In the full-scale validation,

predictions were made in approximative 70% of cases.

This refers to rolling movements above 10°. PAROLL

is able to issue a warning 40 roll cycles in advance,

giving the crew 1.5 to 12 minutes to act. The systems

work without any ship parameters so that it is easy to

install on any ship.

3.3 Prediction Methods

MARIN [14] presents a prediction based on linear

calculations of ship movements, which estimate the

hydrostatic stability variations as the cause of

parametric roll (parameter 4). With a reduction in roll

damping according to Dunwoody, the safe operating

limits of the vessel are obtained (see Figure 6).

Figure 6. Comparison of test results, line is the calculated

result, the markers are experimental, Hs is the significant

wave height and TP the wave peak period, for a container

vessel of 250 meters lengths.

WaveSignal SigmaS6 basing on WaMoS II from

OeanWavesS GmbH [15] is a real-time system to warn

of waves in a specific time window. The forecast covers

the following 180 seconds and identifies abnormal

waves by using x-band radar and predictive analytics.

A non-adaptive algorithm was used at the beginning,

which assimilated all raw radar data over the entire

sampling range at rates of more than 2.1 Msps. This

simplified the testing phase, so adaptive algorithmic

methods were added at a later stage. First, the sea

surface is measured over a spatio-temporal range,

hereinafter referred to as the observation range. This is

followed by the application of pre-processing methods

and the calculation of the magnitude and phase of

wave vector coefficients. Finally, the phase shift of the

wave vector coefficients is used for propagation,

therefore for the prediction of the sea surface profile at

space-time offsets.

This results in the prediction (see Figure 7) of a

wave field derived from statistical sea state parameters

as well as 3-dimensional sea surface height maps from

nautical X-band radars. The method is based on the

spectral analysis of radar data using a 3-dimensional

(fast) Fourier transform.

Figure 7. Prediction of T+180s of the wave field, the colors

indicate the wave elevation in meters, with a wave direction

towards north-east over 3 kilometers.

3.4 Recapitulation of Existing Works

The previous methods are based on the isolated

parameter as they are described in Chapter 2, so the

methods do not combine all the evaluated parameter

(1-5) and uses them for prediction or probability

calculation. The difficulty in predicting parametric

rolling lies in the conditions that vary every passing

second, the same as the sea. The parametric rolling

773

should be predicted in a time frame in which the ship's

command can react, but no false alarms should occur.

In addition, the previous methods do not reflect the

severity of the parametric rolling (classification) or the

probability. The own approach is to increase the

accuracy of the detection by using multiple parameters

so that no early warnings are generated.

4 CLASSIFICATION OF PARAMETRIC ROLLING

USING MULTI PARAMETER IN THE

SIMULATION

To begin the question of understanding what

parametric rolling means numerically must be

clarified. For this purpose, accident reports and

simulation are used as the basis of identification.

Numerical limits are set which describe parametric

rolling. Once it has been established what parametric

rolling is numerically, parametric rolling can be

simulated. For this process the multiple parameters

from chapter 2.2 are used for. Their dependencies are

represented in an event tree. The five severity classes

of parametric rolling will result from the simulations.

They are then described in detail. An algorithm, which

perpetuates the numerical conditions for parametric

rolling from IV.A, recognizes and counts the events

which occur, allowing the probability of occurrence

under certain conditions for parametric rolling to be

calculated.

4.1 Identification of Parametric Rolling

To define numerical values, we return to the definition

of parametric rolling from the relevant literature.

Parametric rolling is defined as a significant increase in

rolling motion that becomes dangerous for the crew,

the cargo and the ship [8]. Neither the time nor the roll

angle is specified.

In effort to localize parametric roll from the

simulations, it is necessary to have limit values at

which a roll movement is considered as parametric roll.

For this context, values found in accident reports as

well as in the previous studies are compared (see tab.1).

Table 1. Roll angel, time range and encounter angle for

parametric rolling from related works and accident reports

________________________________________________

No. Vessel Reference roll time encounter

type angel range angle

[deg] [s] [deg]

________________________________________________

1 RoPax [16] 25 50 35

2 Research [16] 35 20 315

3 Panmax [17] >15 / /

4 Container [12] 20 25 /

5 Container [2] 44 / 100-130

6 Container [13] 18 100 /

7 Container [9] 20 / 335-25

8 Container [18] 20 100 120-240

9 Container [19] 30 30 155-180

10 Container [3] 30-35 3 moves 2

11 Container [4] 38-41 / /

12 Container [20] 30-40 / 155-205

13 Container [21] 25-30 5 moves 180

14 Container [22] 30 100 335-25

15 Container [23] 18 10 /

16 Container [24] 20 2 moves /

17 Container [25] 15-20 / 30

18 Container [5] 20 / 335-25

155-205

________________________________________________

From table 1, the definition of parametric rolling can

now be defined in more detail:

1. Ship type/model

As can be seen from table I, these are container

ships, most of which suffer from parametric rolling

or are used for investigations. To ensure the

comparability with other methods and due to the

vulnerability of specific ship designs with flared

fore and aft extremities or a flat transom stern

paired with wall-sided ship sides near the waterline

amidship [5] to parametric rolling, a container ship

is used for the simulations. The acquired ship model

for the MARIN software [1], has a length overall of

400m, between perpendiculars 382m, a beam of

56m, a draught of 15.5m and a dry mass of 214,000t.

2. Roll angel

In the table 1 the existing works present roll angles

of 20 degrees and above. Nevertheless, when

considering the accident reports, higher roll angles

of 25 degrees and even closer to 30 degrees are

found. Less than one third of the accidents are

caused by roll angles around 20 degrees. Therefore,

for further considerations and the identification of

the parametric rolling, roll angles over 25 degrees

are examined.

3. Time range t

Conversely, the time ranges for the theoretical work

are set very high with up to 100 seconds and the

time ranges of the accident reports are very short

from only two rolling movements to approx. 30 to

100 seconds. It follows that, for safety reasons, short

time ranges must be recorded in which the ships

build up to high rolling angles. In this work, time

windows of less than 60 seconds are thus

considered.

4. Encounter angle

According to the accident and investigation reports

in table 1, these are longitudinal or quartering sea

which induces parametric rolling.

For this paper the following threshold values can be

derived from these observations and characteristics

and subsequently used for simulation of parametric

rolling.

RESULT: Concrete definition of parametric rolling.

It can be concluded from this that parametric rolling is

identified in the simulations for a containership, for

forward sea with an encounter angle of β = 0°, when

the roll angle increases from a small roll angle (<5°) to

more than 25° within a period of 60 seconds and no

damping takes place within the roll-up (see description

of parametric rolling in chapter 2.2).

4.2 Generating of parametric Rolling

For the simulation of the parametric rolling, the

software of MARIN is used. Also, a container ship

model with a length of 400 m, a width of 56 m and a

draught of 15.5 m is used [1].

To be able to identify parametric rolling, the ship

model must be simulated under different parameters.

For this purpose, all wave periods, lengths, heights,

and ship speeds could be compared step by step. Due

to the presence of these multiple parameters in

multiple combinations, this would lead to an immense

number of simulations. To simplify this, the

parameters are narrowed down by including the

774

requirements mentioned in chapter 2.3. By specifically

limiting the parameters and simulating them in

combinations, a parameterization is therefore carried

out by means of a discrete simulation.

1. Encounter period Te

In the first step the wave period Te1 is set to 1.8

times.

2. Wavelength λ

The wavelength λ is calculated the minimum, mean

and maximum of the range as in chapter 2.2 for 0.7,

1 and 1.3 times.

3. Angle of encounter β

The encounter angle is first set to β = 0°.

4. The variation of GM is not considered in the first

step.

5. Ship's speed vs

Corresponding from the formula (5) the ship’s

speed is applied vs single, double, triple and

quadruple.

6. Wave height ζ

The wave heights are needed for the simulation. For

an initial parameterization, the wave heights are

used in a step size of 1m from 1-20m, as no

information is available on the areas in which

parametric rolling occurs more strongly.

This leads to an event tree for the discrete

simulation:

Figure 8. Event tree for Te1=TR/1,8

The figure 8 shows that the wave period Tw2 is

divided into 4 different possible ship's speed

si T s

v v i=

with i = 1…4. From here, only the

encounter angles β=0° are initially parameterized,

further into three calculated wavelengths



each for

0,7



=

1 1,3.and

   

=  = 

Here the

parameterization continues with twenty different

wave heights ζ(1-20). The simulation is carried out using

the MARIN software based on this event tree in order

to next identify the dependencies of the multiple

parameters (parametrization).

4.3 Discrete Simulation

For parameterization, the individual simulations are

performed according to the specifications of the event

tree. For this purpose, the simulations are performed

over a duration of 7200 seconds and with an increment

of 1s.

All simulations have been summarized in tabular

form. Table 2 is an exemplary listing of some

simulations that showed parametric rolling.

Table 2. Examples for simulations with parametric rolling

________________________________________________

Sim Vs Tw λ ζ β start roll roll

No [kn] [rad/s] [m] [m] [°] time angle move-

[s] max[°] ment

________________________________________________

21 7,464 17,87 496,6 11,92 0 6770 25,94 x

139 3,732 17,87 382 11,92 0 477 43,05 x

140 3,732 17,87 382 13,11 0 3013 30,89 4

144 3,732 17,87 382 17,88 0 840 29 3

145 3,732 17,87 382 19,07 0 678 43,03 3

145 3,732 17,87 382 19,07 0 896 27,43 3

145 3,732 17,87 382 19,07 0 1951 39,81 3

149 3,732 17,87 382 23,84 0 1335 31,26 2

175 3,732 17,87 267,4 11,92 0 477 43,05 x

________________________________________________

The evaluation of the individual simulations

showed large differences between the types of

parametric rolling. Strong and less strong, as well as

faster and slower reactions of the ship were shown.

Another feature was the frequency of occurrence

within a simulation, which was reduced to a single or

multiple events. These differences provide evidence

for the characteristics of serial parametric rolling and

the classification into 4 severity classes.

4.4 Classification of Parametric Rolling

Most Different degrees of severity of parametric rolling

can now be derived from the previous simulations of

parametric rolling. Here, the accident reports coincide

with the simulations generated.

4.4.1 Serial parametric rolling

Describes the repeated occurrence of parametric

rolling within the same simulation. The ship

experiences several continuous parametric rolling (see

figure 9 and table 2) within 7200 seconds. In the

simulation 145 the parametric rolling appeared 3 times.

Figure 9. Serial parametric rolling with vs= 7,25kn, β = 0°,

Tw=17,87s, λ= 382m, H=19,07m

4.4.2 Class1: Very extreme parametric rolling

After two rolling movements of the vessel (see

figure 10 and table 2). The simulation 149 shows that

the vessel moves two times and is rolling up to 31,26°.

775

Figure 10. Very extreme parametric rolling with vs= 7,25kn,

β = 0°, Tw=17,87s, λ= 382m, H=23,84m

4.4.3 Class2: Extreme parametric rolling

After three rolling movements of the vessel (see

figure 11 and table 2). The simulation 144 shows the

exceeding of 25° roll angle after the third movement

with even 29°.

Figure 11. Extreme parametric rolling with vs= 7,25kn, β = 0°,

Tw=17,87s, λ= 382m, H=17,88m

4.4.4 Class3: Strong parametric rolling

After fore rolling movements of the vessel (see

figure 12 and table 2). In the simulation 140 the ship

was rolling fore times to exceed 25° and reached even

an angle of rolling of 30,89°.

Figure 12. Strong parametric rolling with vs= 7,25kn, β = 0°,

Tw=17,87s, λ= 382m, H=17,88m

4.4.5 Class4: Simple parametric rolling

After more than fore rolling movements of the

vessel parametric rolling is identified (see figure 13).

See as example in the table 2 the simulation 175, where

several moves of the vessel results in 43,05° of rolling.

Figure 13. Simple parametric rolling with vs= 7,25kn, β= 0°,

Tw=17,87s, λ= 267,4m, H=11,92m

For the encounter period Te1=TR/1,8, parametric

rolling was detected in the discrete simulation in

35.71%. Within the simulations, serial parametric

rolling occurred in 67.5% at a ship speed of 7.25kn. The

highest roll angles of up to 44.82° occurred at the ship

speed of 7.25kn. Class1 was achieved 15% of the time,

Class2 47.5%, Class3 also 15% and Class4 22.5%.

The simulations indicate the dependencies of the

multiple parameters on each other so that the

parametrization and conditional probability follows.

4.5 Parametrization and conditional probability

These dependencies for the multiple parameters of the

discrete simulation are shown in figure 14 and are used

to calculate the conditional probability of parametric

rolling for Te2=TR/1,8. The highest probability for

parametric rolling is for wave heights over 11m (ζ10-20)

independently from the wavelength λ and the vessel

speed v.

Figure 14. Conditional probability of parametric rolling

776

5 EVALUATION

In the evaluation, the accuracy of the multiple

parameter application is compared to the related

works (see table 3).

Table 3. Comparability with related works

________________________________________________

Parameter Identification

of p.R.

________________________________________________

IMO [11] 1,3a,3b 100,00%

OCTOPUS [12] 1,2,3a,3b, 100,00%

wave height

Silva and Soares [5] 3,4 x

PAROLL 1,2, wave height 100,00%

(R. Galeazzi, 2014)

MARIN [14] 4 x

WaveSignal [15] Radar x

Multiple Parameter 1,2,3a,3b,5, 48,00%

wave height

________________________________________________

Table 3 shows that IMO [11], OCTOPUS [12] and

PAROLL [13] would have deflected 100% across all

simulations. Silva and Soares [5], as well as MARIN

[14] and WaveSignal [15], cannot yet be portrayed

because they use the variation of GM and a radar

image. The own approach of multiple parameters

reacted 35.71% of the time or identified parametric

rolling in 35.71% of the simulations. By using multiple

parameters in combination, it seems that a higher

accuracy was achieved compared to the IMO [11],

OCTOPUS [12] and PAROLL[13]. Whereas with the

three methods listed, each simulation would have been

identified as a parametric roll and thus an alarm would

have been raised, by using the multiple parameters in

combination, a smaller amount of simulation was

identified. The limitations that parametric roll must

occur from a roll angle of 25°, within 60 seconds, as well

as that no damping may occur in the meantime, seem

to have increased the accuracy. There is still no

comparability with the work of Silva and Soares [5],

MARIN [14] and WaveSignal [15], as the metacentric

height was not yet considered in this work.

Additionally, as a novelty, the severity of

parametric rolling is distinguished in four classes and

serial parametric rolling was identified.

6 CONCLUSION/DISCUSSION

During multi-parameter discrete simulation for one

wave period, a classification with 4 classes and 1

characteristic were introduced to describe parametric

rolling in more detail like the serial parametric rolling,

which was already outlined in several accident reports.

This opens a more detailed view of the phenomenon.

Similarly, the severity of parametric rolling was not

differentiated in the past, although differences in the

accident reports can be seen here as well. This

subdivision into very extreme (class1), extreme

(class2), strong (class3) and simple (class4) parametric

rolling leads to a much more detailed view than before.

It is now possible to distinguish whether a ship enters

parametric rolling within 2, 3, 4 or more rolling

motions and can thus bring about different

countermeasures.

This work therefore allows considering parametric

rolling not as a unique phenomenon, but in its diversity

of occurrence with the risk of repetition (serial

parametric rolling).

As further research, the simplification from chapter

4 would have to be removed and the simulations

carried out. This will allow an even more accurate view

of this phenomenon. Furthermore, other ship models

in MARIN [1], such as a cruise ship or a RoRo (roll-

on/roll-off) ship, would also be conceivable for further

signings. The vulnerability of the different hulls would

be a main point of investigation. Additionally, a further

simulation software would have to be used for an

evaluation and reliability of the results. Similarly,

parameter 4 (variation of GM) needs to be investigated

to establish comparability with MARIN [14] and Silva

and Soares [5]. Comparability with WaveSignal [15]

would only be possible by running both applications

simultaneously over a simulation and labelling the

deflections.

The next step would be to implement an artificial

intelligence, which will serve real-time prediction in

the current sea state for assistance systems.

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