169
1 INTRODUCTION
Maritime transport is the primary mode of cargo
transportation in international trade. In 2012,
approximately80%ofglobaltradeintermsofvolume
and over 70% in terms of value was transported by
sea and distributed among ports and economies
worldwide[14].Tomeetthishugedemand,
shipsare
constantlyevolvingandbecominglarger.
Theincreaseinthevolumeofgoodstransportation
has driventhe sizeof cargo ships.According to ITF
(International Transport Forum) [8], the average
capacityofnewlyconstructedcontainerships ranged
from approximately 3,400 Twenty‐foot Equivalent
Units (TEUs) between 2001 and 2008, to
5,800 TEUs
between2009and2013,reachingapproximately8,000
TEUsin2015.
As the size of vessels have increased, ports have
sought wider and deeper nautical spaces. The
consequence of this is the displacement of ports,
generally towards the sea, where protection from
environmentalactionsis less, orinsome
cases,non‐
existent.
The construction ofport terminals in unsheltered
areas leave vessels vulnerable to environmental
actions, especially vessels docked at the pier. To
ensurethesafetyofvesselsdockedatportterminals,
itisessentialtostudytheforcesonmooringlinesand
the displacements of the vessel relative to
the pier
duringcargohandlingoperations.
Experimental tests using physical models emerge
asoneof themostimportanttoolsinengineeringto
represent the port nautical environment and its
interaction with environmental conditions, allowing
Displacement Measurement System for Small-Scale
Vessels Berthed in Physical Models of Port Terminals
R.deOliveiraBezerra
1
,J.C.deMeloBernardino
2
&R.Esferra
1
1
HydraulicTechnologicalCenterFoundation,SaoPaulo,Brazil
2
UniversityofSaoPaulo,SaoPaulo,Brazil
ABSTRACT: This paper presents the development of a displacement measurement system for small‐scale
physicalmodelsofmooredships,aimedatprovidingdatatoevaluatedisplacementamplitudesanddetermine
whether they surpass predetermined operational limits. The system, which combines cameras and inertial
sensors,
capturessixdegreesoffreedom,allowingmeasurementsofsurge,sway,heave,yaw,roll,andpitch.
The developed system was initially tested isolating each degree of freedom for analysis, and subsequently
appliedtoascalemodelofaportterminalberth,withabulkcarriervesseldocked,subjecttowaveaction.Scale
modelsofportterminalshavebeenextensivelyvalidatedovernumerousyearsofresearchanddevelopment.
Toevaluatethesystemʹsresponse,displacementmeasurementsobtainedthroughthedevelopedsystemwere
comparedwithacommercialsystemwidelyrecognizedformeasuringrigidbodymovements,theQualisys®
system. Thiscomparison showsboth systems obtainedsimilar results, indicatingthat the developed system
meetsitsintendedpurpose.Overall,thesystemprovidesareliabletoolforstudyingthecomplexbehaviorof
mooredvesselsandevaluatingoperationalandsafetyconditionsinportterminals.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 18
Number 1
March 2024
DOI:10.12716/1001.18.01.1
7
170
for the simulation of scenarios of vessels moored at
berths and monitoring their movements when
subjectedtoenvironmentalactions orthepassage of
other vessels. According to Bernardino et al. [2]
physical models are generally small‐scale
representations of any physical system and its
applications in Engineering are widely
discussed in
theinternationalliterature,inreferencessuchas[11],
[10],[5]and[17].Inthecaseofportstudies,hydraulic
physicalmodels,alsoshortlycalledscalemodels,can
beusedtorepresenttheentireinterestarea,including
topography,bathymetry,docking structures, vessels,
andtheenvironmentalconditions,suchaswaterlevel
variations,waves,winds,andsoon[11].
Whenthedisplacementsin relationtothepierof
moored vessels exceeded certain limits, there are
implications for both safety and efficiency of port
operations. The excessive movement of moored
vesselscanstoptheloadingprocessesand,inextreme
cases, damage the mooring
lines, winches, bollards,
and fenders. The PIANC (Permanent International
Association of Navigational Congresses) [12] has a
series of recommendations for vessel displacements.
Therecommendedlimitsforeach displacementvary
accordingtothetypeofvesselandthetypeofloading
equipment.
In scale models, measurement systems for vessel
displacementsmustbe
abletoaccuratelymeasurethe
six degrees of freedom, which is generally not a
simple task due to the small scales of these models.
Traditionally, vessel displacement measurements in
scale models are performed using potentiometric
systems coupled to the vessel or by utilizing
accelerometersandgyroscopes[6].BriggsandMelito
[4] present an example of a displacement
measurement system using accelerometers and
gyroscopes.
According to ITTC (The International Towing
Tank Conference) [7], the traditional approach to
monitoringvesseldisplacements in scalemodels has
been replaced by a measurement system that uses
videoimagecaptureandanalysis.Kieviet[9]presents
asystem
thatanalyzesasequenceofvideoimagesofa
known three‐dimensional object positioned on the
vesselʹsdeck.Benetazzo[1]presentsasimilarsystem
that utilizes a quad grid marker target on the deck,
ratherthanathree‐dimensionalobject.
Currently,thistypeofdisplacementmeasurement
hasbecomewidely
usedinhydrauliclaboratoriesdue
toitsnon‐intrusivemeasurementtechnique,avoiding
instrument contact with the water and equipment
interferencewiththevessel.
This paper presents the development of a six‐
degree‐of‐freedomdisplacementmeasurementsystem
forscale modelsof vessels berthed at port terminals
subjected to wave action. The
developed system
combinesmeasurementsbyimagepatternrecognition
algorithmwithmeasurementsbyinertialsensors.The
systemwastestedonascalemodelofaportterminal
at the Hydraulics Laboratory of the School of
Engineering of the University of Sao Paulo (CTH‐
USP).
2 MATERIALANDMETHODS
2.1 Thedisplacement
measurementsystem
Thedisplacementmeasurementsystemforsmall‐scale
ship models in experimental simulators was
developed by the CTH‐USP team. The system
measuresthedisplacementofvesselsinrelationtothe
pier, providing data that allows the evaluation of
safetyduringcargohandlingoperations.Thesystem
canbeappliedto
anyscalemodelofberthedvessels
withenoughspacetopositionthesystemstructure.
The system contains a set of inertial sensors
coupledunderamarkertargetandacamerafixedto
the pier. The sensors and the marker target are
positioned on the vesselʹs deck, and the geometric
centerofthistargetisthesameasthegeometriccenter
ofthevesselʹsdeck.
Figure1showstheinertialsensorsandthemarker
target, assembled in image A (in the same way as
whentheyareinstalledonthesmall‐scalevessel)and
disassembledinimageB.
Figure1. The inertial sensors and the marker target
assembled(A)anddisassembled(B).Source:Bezerra[3].
TheelementinFigure1(A)hastotaldimensionsof
230x100x25mm,whichcanbeadapteddepending
ontheneedsof the test.However, it isimportantto
pointoutthatareductioninthesedimensionscannot
be exaggerated, since the accuracy of the system
wouldbe
impaired.
Another element of the measurement systemis a
camerafixedtothepier,positionedoverthemarker
target. This camera transmits images of the marker
target to a computer that processes the images and
obtains the displacements. Figure 2 provides an
overviewofthesystem.
Themeasurementuncertaintyof
thedisplacement
capturesystemthroughimagesdependsonthepixel‐
to‐millimeterratio,whichitisdefinesbythenumber
ofdivisionsthealgorithmwilluseforeachmillimeter.
Thismeasurementuncertaintydepends primarilyon
the number of pixels in the image generated by the
camera and the distance between the
marker target
andthecamera.
171
Figure2. Schematic drawing showing the displacement
measurementsystemwhichconsistsoftwoparts:onefixed
tothepierandtheotheronthevessel.Source:Bezerra[3].
For the case study of this paper, the camera was
fixedat150mmabovethemarkertargetplacedonthe
vessel. This provides a ratio for the system of 0.163
mm/pixels, providing a measurement uncertainty of
approximately 0.082 mm to the surge and sway
displacements captured using images. The yaw
displacements,alsocapturedusingimages,presenta
measurementuncertaintyof0.05°.
The heave displacements, unlike other
displacements measured by image, are obtained
throughtheimagescalingfactoroftheimagepattern
recognition algorithm, thus its measurement
uncertaintyis 0.168mm with the cameraat150mm
from the marker target.
Figure 3 shows the
displacementmeasurementsysteminascalemodel.
Figure3.Displacementmeasurementsystemassembledina
scalemodel.Source:Bezerra[3].
Tocomplementthecamerasystem,amulti‐sensor
type IMU (Inertial Measurement Unit) model GY‐80
wasusedtomeasureotherdisplacements(pitchand
roll). This IMU hasa gyroscope,an accelerometer, a
magnetometer, and a pressure and temperature
sensor.
For this work,the measurementof rolland pitch
movements was
performed using the combined
resultsoftheaccelerometerandgyroscopepresentin
the IMU. This combination betweenthe two sensors
reducesorientationerrors(drift)andvibrationerrors,
providingamoreaccuratemeasurementofrotational
displacements.Figure4presentstheresultsobtained
from the combination of sensor outputs under the
influence
of a sinusoidal motion. The use of a
sinusoidal motion is a common approach in
engineeringtotestthedynamicresponseofasystem.
Figure4. A sinusoidal motion with a frequency of 0.2 Hz
andamplitudeof15°isappliedtothedevelopedsystem.
Therotationaldisplacementsmeasuredbyinertial
sensors (roll and pitch) exhibit a measurement
uncertaintyof0.5°foramplitudesgreaterthan2°.
2.2 Scalemodel
Aftertestingthedisplacementmeasurementsystemin
the instrumentation laboratory, its performance was
evaluated in a scale model of a port terminal. This
model represents a specialized
iron ore terminal
located in a bay in southeastern Brazil. This bay is
semi‐protected from wave action and the port
terminalisconnectedtothemainlandbyaconveyor
beltusedtotransportironoretomooredships.
Thescalemodelwasbuiltinareducedgeometric
scale of
1:170, without distortion, according to
Froudeʹssimilaritycriteria.Thismodelcanrepresent
tidal currents and their effects on ships, as well as
representing regular and irregular waves. The
generation of irregular waves is based on the
JONSWAP(JointNorthSeaWaveProject)parametric
spectrum model, used in most engineering projects
relatedtocoastalregionsforcalculatingwavespectra.
Figure 5 shows the scale model used to evaluate
thedevelopedsystem.
Figure5. Three‐dimensional scale model with wave
generatorsystemlocatedattheCTH‐USP.Geometricscale:
1:170.Source:Bezerra[3].
Thedisplacementmeasurementsystemwastested
intwodifferentwavescenarios:regularandirregular.
Table1presentsthetypeofwavegenerated,aswell
172
as the significant wave height (Hs) and the peak
period (Tp), presenting both prototype values and
values measured in the geometric scale of 1:170
model.
Table1.Scenariostestedinthescalemodel.
________________________________________________
WaveTypePrototypeModel(1:170)
Hs(m) Tp(s) Hs(mm) Tp(s)
________________________________________________
Scenerio1Regular 2.514 14.71 1.08
Scenerio2Irregular 1.512 8.82 0.92
________________________________________________
Thesescenarioswereselectedbecausetheyarethe
mostrepresentativeoftheincidentwavesinthestudy
area.
2.3 Qualisys®System
The Qualisys® system has been widely used in
various fields, includingthe measurement ofmotion
in scale models. The system works by capturing
motiondatathrougha seriesofhigh
‐resolutiondigital
cameras and reflective markers. The cameras are
placed strategically around the object being tracked,
andthe markers areplaced on specific point sof the
object.
AccordingtoQualisys®[13],thebenefitsofusing
optical motion capture for marine applications are
thatthesystemdoesnotrequirewiringfor
thevessel
during the experiment, the position of the vessel is
captured by cameras mounted on the side of the
basin,avoidinganychangeinshipmovementdueto
connectedwires.
The measurement uncertainty of the Qualisys®
system can depend on several factors, including the
specific hardware and software configuration used,
thecalibrationprocess,andtheenvironmentinwhich
thesystemisused.However,Qualisys®reportsthat
theirsystemhasameasurementaccuracyoflessthan
0.1mmand0.1degrees[13].
Therefore,asitisawell‐establisheddisplacement
measurement system, the Qualisys® system can be
usedasanevaluation
parameterfortheresultsofthe
developedsysteminthiswork.
3 RESULTSANDDISCUSSION
In this chapter, a comparison of results between the
displacement measurement developed system with
the Qualisys® system, previously described, is
presented. The results were divided into the two
simulatedwavescenarios,asdescribedinTable1.
Firstly, the comparison of the measured values
wascarriedoutusingstatisticalparametersextracted
fromtheseriesofmeasurementsofeachdisplacement
(section 3.1 for regular waves and section 3.2 for
irregularwaves).Thestatisticalparametersusedwere
the arithmetic mean (Mean), the root mean square
(RMS),thestandarddeviation
andtheamplitude.
Then,theresultswere comparedusingtwointer‐
comparison methods that assesses the agreement or
similarity between measurements obtained by two
different systems or instruments (Section 3.3). The
inter‐comparison methods used were Relative Mean
Absolute Error (RMAE) [15] and the coefficient R²
[16]. These methods are widely
used for comparing
sensorresults.
To facilitate the analysis of the results, all
differencesgreaterthan10%werehighlightedinred.
3.1 Mooredvesselunderregularwaveaction
Themooredvesselwassubjectedtoascenariounder
theactionofregularwaves,wheretheregular wave
generatedinthescale
model(1:170)hasanamplitude
of14.71millimetersandapeakperiodof1.08seconds.
These values, when scaled up to the prototype,
represent regular waves with an amplitude of 2.5
metersandapeakperiodof14seconds.
Forvisualizationoftheresultsundertheactionof
regular waves, Figure
6 shows a comparison of the
results obtained by the developed measurement
system and the Qualisys® measurement system for
the translational displacements (surge, sway, and
heave)inascenarioofregularwaves.Figure7,onthe
other hand, shows thecomparison forthe rotational
displacements (roll, pitch, and yaw) in
the same
scenario.
Figure6. Translation displacements measured by the
developed system and Qualisys® system for the moored
vesselundertheactionofregularwaves.
Figure7. Rotational displacements measured by the
developedsystemandtheQualisys®systemforthemoored
vesselundertheactionofregularwaves.
Table 2 presents the statistical parameters of
translational surge displacement measured for each
system, as well as the percentage error between the
analyses.Table3andTable4presentthesameresults
for translational sway and heave displacements,
respectively.
173
Table2.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemfortranslationalsurgedisplacement
undertheactionofregularwaves.
________________________________________________
Surge(mm)System Qualisys® Difference%
________________________________________________
Mean0.859 0.856 ‐0.32%
RMS1.500 1.631 8.01%
StandardDeviation 1.231 1.389 11.38%
Amplitude9.338 10.612 12.00%
________________________________________________
Table3.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemfortranslationalswaydisplacement
undertheactionofregularwaves.
________________________________________________
Sway(mm)System Qualisys® Difference%
________________________________________________
Mean12.753 13.026 2.10%
RMS13.133 13.455 2.39%
StandardDeviation 3.141 3.370 6.81%
Amplitude22.039 23.493 6.19%
________________________________________________
Table4.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemfortranslationalheavedisplacement
undertheactionofregularwaves.
________________________________________________
Heave(mm)System Qualisys® Difference%
________________________________________________
Mean‐1.482‐1.5967.14%
RMS2.078 2.265 8.25%
StandardDeviation 1.457 1.608 9.35%
Amplitude6.628 6.644 0.24%
________________________________________________
Tables5,6and7presentthestatisticalparameters
of roll, pitch, and yaw rotational displacements,
respectively.
Table5.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemforrollrotationaldisplacementunderthe
actionofregularwaves.
________________________________________________
Roll(°)System Qualisys® Difference%
________________________________________________
Mean0.244 0.209 ‐16.74%
RMS0.825 0.845 2.33%
StandardDeviation 0.788 0.819 3.69%
Amplitude3.460 3.307 ‐4.64%
________________________________________________
Table6.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemforpitchrotationaldisplacementunder
theactionofregularwaves.
________________________________________________
Pitch(°)System Qualisys® Difference%
________________________________________________
Mean0.073 ‐0.066210.84%
RMS0.481 0.471 ‐2.12%
StandardDeviation 0.476 0.472 ‐0.94%
Amplitude2.457 1.490 ‐64.89%
________________________________________________
Table7.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemforyawrotationaldisplacementunder
theactionofregularwaves.
________________________________________________
Yaw(°)System Qualisys® Difference%
________________________________________________
Mean‐0.274‐0.272‐0.54%
RMS1.021 0.996 ‐2.53%
StandardDeviation 0.984 0.958 ‐2.69%
Amplitude3.910 3.636 ‐7.52%
________________________________________________
For the regular waves scenario, the translational
displacements (surge, sway and heave) and yaw
(rotationaldisplacementmeasuredbycamera)present
amaximumpercentagedifferenceof12%betweenthe
statistical parameters of both measurement systems,
demonstratinggoodagreementintheresults.
Ontheotherhand,somecomparisonsofrotational
displacementsmeasuredby
inertialsensors(rolland
pitch) present much larger differences than
translationaldisplacements.However,itisimportant
to point out that, for the simulation carried out
(Scenario1),thesedisplacementspresentedrelatively
small values, within a range that the developed
system is unable to measure adequately, which
explainsthehigherdifferences
obtainedinrelationto
theQualisys®system.
3.2 Mooredvesselunderirregularwaveaction
Themooredvesselissubjectedtoascenariounderthe
actionof irregularwaves usingthe JONSWAPwave
spectrumwith asignificantwave heightof 8.82mm
and a peak period of 0.92 seconds in scale model
values. These values, when scaled to the prototype,
represent irregular waves with a significant wave
heightof1.5metersandapeakperiodof12seconds.
Forvisualizationoftheresultsundertheactionof
irregularwaves,Figure8showsacomparisonofthe
results obtained by the developed measurement
system and the Qualisys® measurement system for
the translational displacements (surge, sway, and
heave)inascenarioofregularwaves.Figure9,onthe
other hand, shows thecomparison forthe rotational
displacements (roll, pitch, and yaw) in the same
scenario.
Figure8. Translation displacements measured by the
developed system and Qualisys® system for the moored
vesselundertheactionofirregularwaves.
Figure9. Rotational displacements measured by the
developedsystemandtheQualisys®systemforthemoored
vesselundertheactionofregularwaves.
Table 8 presents the statistical parameters of
translational surge displacement measured for each
measurementsystemused,aswellasthepercentage
error between the analyses. Tables 9 and 10 present
174
the same results for translational sway and heave
displacements,respectively.
Table8.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemfortranslationalsurgedisplacement
undertheactionofirregularwaves.
________________________________________________
Surge(mm)System Qualisys® Difference%
________________________________________________
Mean0.942 0.946 0.39%
RMS1.153 1.192 3.27%
StandardDeviation 0.664 0.725 8.40%
Amplitude3.841 4.196 8.47%
________________________________________________
Table9.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemfortranslationalswaydisplacement
undertheactionofirregularwaves.
________________________________________________
Sway(mm)System Qualisys® Difference%
________________________________________________
Mean1.742 1.751 0.54%
RMS2.131 2.178 2.17%
StandardDeviation 1.228 1.296 5.22%
Amplitude6.810 7.492 9.10%
________________________________________________
Table10.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemfortranslationalheavedisplacement
undertheactionofirregularwaves.
________________________________________________
Heave(mm)System Qualisys® Difference%
________________________________________________
Mean‐0.685‐0.6890.55%
RMS0.842 0.862 2.25%
StandardDeviation 0.491 0.518 5.32%
Amplitude2.883 2.945 2.09%
________________________________________________
Tables 11, 12 and 13 present the statistical
parameters of roll, pitch, and yaw rotational
displacements,respectively.
Table11.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemforrollrotationaldisplacementunderthe
actionofirregularwaves.
________________________________________________
Roll(°)System Qualisys® Difference%
________________________________________________
Mean0.065 0.083 21.46%
RMS0.324 0.229 ‐41.45%
StandardDeviation 0.317 0.213 ‐48.59%
Amplitude2.192 1.003 ‐118.56%
________________________________________________
Table12.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemforpitchrotationaldisplacementunder
theactionofirregularwaves.
________________________________________________
Pitch(°)System Qualisys® Difference%
________________________________________________
Mean0.012 ‐0.004413.15%
RMS0.210 0.100 ‐109.68%
StandardDeviation 0.210 0.100 ‐109.50%
Amplitude1.385 0.360 ‐284.18%
________________________________________________
Table13.Comparisonofthestatisticalparametersofthe
measurementsbetweenthedevelopedsystemand
Qualisys®systemforyawrotationaldisplacementunder
theactionofirregularwaves.
________________________________________________
Yaw(°)System Qualisys® Difference%
________________________________________________
Mean0.027 0.027 2.86%
RMS0.129 0.136 4.72%
StandardDeviation 0.126 0.133 4.80%
Amplitude0.801 0.753 ‐6.27%
________________________________________________
As inthe scenarioof the simulation with regular
waves, the percentage differences between the
statisticalparameters forthedisplacementsin surge,
sway,heaveandyawpresentrelativelysmallvalues
(lessthan10%),demonstratinggoodagreement.But,
once again, for the rolland pitch displacements, the
percentagedifferencespresentedmuchlarger
values.
In the same way as explained in section 3.1, these
differencesoccurredduetotherelativelysmallvalues
obtained for these displacements in the test carried
out (Scenario 2), lying within a range that the
developedsystemisnotabletomeasureproperly.
3.3 Comparisonbetweentheresultsof
thetwosystems
Thecomparisonbetweentheresultsofthedeveloped
systemand theresults of theQualisys® systemwas
carried out using the Relative Mean Absolute Error
(RMAE)andthecoefficientR².Table14summarizes
theresultsofthesetwointer‐comparisonmethodsfor
both regular and irregular waves, considering
all
measureddisplacements.
Table14.Comparisonoftheresultsofthetranslationaland
rotationaldisplacementsofthemooredvesselunderthe
actionofregularandirregularwaves.
________________________________________________
Displacement RMAE R
2
________________________________________________
Regular Surge(mm) 0.16 0.980
Waves Sway(mm)0.03 0.987
Heave(mm) 0.26 0.860
Roll(°) 0.42 0.790
Pitch(°) 0.76 0.451
Yaw(°) 0.11 0.987
Irregular Surge(mm) 0.13 0.956
Waves Sway(mm)0.18 0.913
Heave(mm) 0.28 0.751
Roll(°) 0.96 0.437
Pitch(°) 1.82
0.043
Yaw(°) 0.36 0.824
________________________________________________
Analyzing Table 14, it is possible to observe that
thepitchdisplacement presents theworst values for
the mathematical methods both in regular and
irregular wave scenarios. The roll displacement also
shows poor results, with RMAE values close to or
above1. Forthe other displacements, the developed
systemshowsresults
closetothemeasurementsmade
bytheQualisys®system.
4 CONCLUSIONS
This work presents the development of a
measurementsystemforthedisplacementofmoored
vessels in physical scale models, which combines
image analysis measurements with inertial sensor
measurements.
For the displacements in surge and sway, the
developedsystemshows
aresultclosertoQualisys®
data, with RMAE values less than 0.18, a result
classifiedasʺExcellentʺaccordingtotheclassification
of Walstra et al. [15]. The heave displacements
presentedRMAE<0.28andyawpresentedRMAE<
0.36, both results classified asʺGoodʺ, according to
[15].Thequalityof
theresultsobtainedforthesefour
displacementscanalsobeverifiedbycomparingthe
175
statisticalparametersofthemeasurements(items3.1
and3.2),which resulted inpercentage differencesof
lessthan12%.
The PIANC [12] recommendations for maximum
displacements of moored vessel include three main
displacements: surge, sway, and yaw. Therefore,
whenevaluatingtherecommendationsofPIANCina
scalemodel,thedeveloped
systempresentedexcellent
resultsforsurgeandswayandgoodresultsforyaw
comparedtotheQualisys®system.
Theworstresultswerefoundfortherollandpitch
displacements, with RMAE values close to 1 and
percentage differences of statistical parameters with
highvalues,reachingvaluesgreaterthan400%.These
differences
foundforrollandpitchdisplacementsare
justified because the Qualisys® system is capable of
measuring displacements with small angular
amplitudes, while the developed system is not
capable of measuring angles smaller than 2 degrees.
This fact can also be observed by comparing the
differencesobtainedinpitchdisplacementfor
regular
wave conditions (RMAE < 0.76) and irregular wave
conditions (RMAE < 1.82). Irregular waves have
smaller displacement amplitudes and, consequently,
greater comparative difference in relation to regular
waves.
Itis importanttopoint out thatalthough PIANC
[12] does not define operational limits for pitch and
roll displacements, the operational
practice of most
ports tends to consider that small values for these
displacements (such as lesser than 2 degree) do not
affect cargo handling and do not put at risk the
operational safety of theterminal. Therefore, even if
thedevelopedsystemisnotabletoproperlymeasure
small angles,
this does not prevent the use of the
systemforpracticalEngineeringpurposes.
Intheend,asasuggestionforfutureresearchthe
developedsystemcouldbenefitfromutilizinghigher
precision sensors to improve the accuracy of
measurementsforrollandpitchdisplacements.
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