WELCOME FROM THE CONFERENCE CHAIRS file ://E:\data\chair-welcome.htrnl 8-6-2009 OMAE2009: Welcome from the Conference Chairs Page 1 of2 ft Cengiz Ertekin H. Ronald Riggs Conference Co-Chair Conference Co-Chair OMAE 2009 OMAE 2009 Aloha! On behalf of the OMAE 2009 Organizing Committee, it is a pleasure to welcome you to Honolulu, Hawaii for OMAE 2009, the 28th International Conference on Ocean, Offshore and Arctic Engineering. This is the first conference with the new name, which reflects the expanded focus of the OOAE Division and the conference. OMAE 2009 is dedicated to the memory of Prof. Subrata Chakrabarti, an internationally known offshore engineer, who passed away suddenly in January. Subrata was the Offshore Technology Symposium coordinator, and he was also the Technical Program Chair for OMAE 2009. He was involved in the development of the OMAE series of conferences from the beginning, and his absence will be sorely felt. OMAE 2009 has set a new record for the number of submitted papers (725), despite an extremely challenging economic environment. The conference showcases the exciting and challenging developments occurring in the industry. Program highlights include a special symposium honoring the important accomplishments of Professor Chiang C. Mei in the fields of wave mechanics and hydrodynamics and a joint forum of 'Offshore Technology', 'Structures, Safety and Reliability' and 'Ocean Engineering' Symposia on Shallow Water Waves and Hydrodynamics. We believe the OMAE 2009 program will be one of the best ever. Coupled with our normal Symposia, we will also have special symposia on: Ocean Renewable Energy Offshore Measurement and Data Interpretation Offshore Geotechnics Petroleum Technology We want to acknowledge and thank our distinguished keynote speakers: Robert Ryan, Vice President - Global Exploration for Chevron; Hawaii Rep. Cynthia Thielen, an environmental attorney who has a special passion for ocean renewable energy; and John Murray, Director of Technology Development with FIoaTEC, LLC. A conference such as this cannot happen without a group of dedicated individuals giving their time and talents to the conference. In addition to the regular symposia coordinators, the coordinators of the special symposia deserve many thanks for their efforts to organize new areas for OMAE. We also want to express our appreciation to Dan Valentine, who stepped into the Technical Program Chair position
Transcript
WELCOME FROM THE CONFERENCE CHAIRS
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OMAE2009: Welcome from the Conference Chairs Page 1 of2
ft Cengiz Ertekin H. Ronald RiggsConference Co-Chair Conference Co-Chair
OMAE 2009 OMAE 2009
Aloha!
On behalf of the OMAE 2009 Organizing Committee, it is a pleasure to welcome you to Honolulu,Hawaii for OMAE 2009, the 28th International Conference on Ocean, Offshore and ArcticEngineering. This is the first conference with the new name, which reflects the expanded focus of theOOAE Division and the conference.
OMAE 2009 is dedicated to the memory of Prof. Subrata Chakrabarti, an internationally known offshoreengineer, who passed away suddenly in January. Subrata was the Offshore Technology Symposiumcoordinator, and he was also the Technical Program Chair for OMAE 2009. He was involved in thedevelopment of the OMAE series of conferences from the beginning, and his absence will be sorely felt.
OMAE 2009 has set a new record for the number of submitted papers (725), despite an extremelychallenging economic environment. The conference showcases the exciting and challengingdevelopments occurring in the industry. Program highlights include a special symposium honoring theimportant accomplishments of Professor Chiang C. Mei in the fields of wave mechanics andhydrodynamics and a joint forum of 'Offshore Technology', 'Structures, Safety and Reliability' and'Ocean Engineering' Symposia on Shallow Water Waves and Hydrodynamics. We believe the OMAE2009 program will be one of the best ever. Coupled with our normal Symposia, we will also havespecial symposia on:
Ocean Renewable EnergyOffshore Measurement and Data InterpretationOffshore GeotechnicsPetroleum Technology
We want to acknowledge and thank our distinguished keynote speakers: Robert Ryan, Vice President -Global Exploration for Chevron; Hawaii Rep. Cynthia Thielen, an environmental attorney who has aspecial passion for ocean renewable energy; and John Murray, Director of Technology Developmentwith FIoaTEC, LLC.
A conference such as this cannot happen without a group of dedicated individuals giving their time andtalents to the conference. In addition to the regular symposia coordinators, the coordinators of thespecial symposia deserve many thanks for their efforts to organize new areas for OMAE. We also wantto express our appreciation to Dan Valentine, who stepped into the Technical Program Chair position
on very short notice, following Subrata's passing. We also want to thank Ian Holliday and CarolinaLopez of Sea to Sky Meeting Management, who have done a great job with the organization. Thanksalso go to Angeline Mendez from ASME for the tremendous job she has done handling the on-linepaper submission and review process.
Honolulu is one of the top destinations in the world. We hope that you and your family will be able tospend some time pie or post conference enjoying the island of Oahu. Whether you're learning to surf inlegendary Waikiki, hiking through the rich rainforests of Waimea Valley, or watching the brilliant pastelsof dusk fade off of Sunset Beach, you'll find variety at every turn on Oahu.
Mahalo nui ba,
R. Cengiz Ertekin and H. Ronald Riggs, University of HawaiiOMAE 2009 Conference Co-Chairmen
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OMAE2009: Welcome from the Conference Chairs Page 2 of 2
MESSAGE FROM THE TECHNICAL PROGRAM CHAIR
Welcome to the 28th International Conference on Ocean, Offshore and Arctic-Engineering (OMAE 2009). This is the 28th conference in the OMAE seriesguided by and influenced significantly by our friend and colleague, Subrata K.Chakrabarti. It was a shock for me to learn that he had passed away so suddenly;all involved with this conference express sincere condolence to his family, friendsand colleagues (the sentiments echoed by all of us are eloquently expressed inthe dedication included in this program). It is a great honor for me to have beenasked to continue his work on this conference. I and our community will miss hisleadership and friendship greatly. Although this series of conferences wasformally organized by ASME and the OOAE Division of the InternationalPetroleum Technology Institute (IPTI), it was Subrata's skill and dedication to this
Daniel T. Valentine division of ASME that made this series of conferences the success that it hasTechnical Program Chair
OMAE 2009 been and is today.
The papers published in this CD were presented at 0MAE2009 in thirteensymposia. They are:
SYMP-1: Offshore TechnologySYMP-2: Structures, Safety and ReliabilitySYMP-3: Materials TechnologySYMP-4: Pipeline and Riser TechnologySYMP-5: Ocean Space UtilizationSYMP-6: Ocean EngineeringSYMP-7: Polar and Arctic Sciences and TechnologySYMP-8: CFD and VIVSYMP-9: CC. Mei Symposium on Wave Mechanics and HydrodynamicsSYMP-lO: Ocean Renewable EnergySYMP-1 1: Offshore Measurement and Data InterpretationSYMP-12: Offshore GeotechnicsSYMP-13: Petroleum Technology
The first eight symposia are the traditional symposia organized by the eighttechnical committees of the OOAE Division. The other symposia are specialtysymposia organized and encouraged by members of the technical committees tofocus on topics of current interest. The 9th symposium was organized torecognize the contributions of Professor C. C. Mei. Symposia 10, 11, 12 and 13offer papers in the areas of renewable energy, measurements and datainterpretation, geotechnical and petroleum technologies as they relate to ocean,offshore and polar operations of industry, government and academia.
The first symposium, Symposium 1: Offshore Technology was always SubrataChakrabarti's project. It was typically the largest of the symposia at OMAE. Hisexemplary work on this symposium provided the experience and guidance forothers to continue to develop the other symposia. Symposium 1 in conjunctionwith the OMAE series of conferences is Subrata's legacy. The ExecutiveCommittee has a most difficult yet honorable task of finding a successor to carryon this important annual symposium in offshore engineering. We are all grateful
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OMAE2009: Message from the Tecimical Program Chair Page 1 of2
OMAE2009: Message from the Technical Program Chair Page 2 of 2
for the inspiration and encouragement provided to all of us by Subrata.
Please enjoy the papers and presentations of OMAE2009.
Daniel T. Valentine, Clarkson University, Potsdam, New YorkOMAE2009 Technical Program Chair
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OMAE2009: International Advisory Committee Page 1 of 1
INTERNATIONAL ADVISORY COMMITTEE
R.V. Ahilan, Noble Denton, UKR. Basu, ABS Americas, USAR. (Bob) F. Beck, University of Michigan, USAPierre Besse, Bureau Veritas, FranceRichard J. Brown, Consultant, Houston, USAGang Chen, Shanghai Jiao Tong University, China
Jen-hwa Chen, Chevron Energy Technology Company, USAYoo Sang Choo, National University of Singapore, SingaporeWeicheng C. Cui, CSSRC, Wuxi, ChinaJan lnge Dalane, Statoil, NorwayR.G. Dean, University of Florida, USAMario Dogliani, Registro Italiano Navale, ItalyR. Eatock-Taylor, Oxford University, UKGeorge Z. Forristall, Shell Global Solutions, USAPeter K. Gorf, BP, UKBoo Cheong (B.C.) Khoo, National University of Singapore, SingaporeYoshiaki Kodama, National Maritime Research Institute, JapanChun Fai (Collin) Leung, National University of Singapore, SingaporeSehyuk Lee, Samsung Heavy Industries, JapanEike Lehmann, TU Hamburg-Harburg, GermanyHenrik 0. Madsen, Det Norske Veritas, NorwayAdi Maimun Technology University of Malaysia, MalaysiaT. Miyazaki, Japan Marine Sci. & Tech Centre, JapanT. Moan, Norwegian University of Science and Technology, NorwayG. Moe, Norwegian University of Science and Technology, NorwayA.D. Papanikolaou, National Technical University of Athens, GreeceHans Georg Payer, Germanischer Lloyd, GermanyPreben T. Pedersen, Technical University of Demark, DenmarkGeorge Rodenbusch, Shell IntI, USAJoachim Schwarz, JS Consulting, GermanyDennis Seidlitz, ConocoPhillips, USAKirsi Tikka, ABS Americas, USAChien Ming (CM) Wang, National University of Singapore, SingaporeJaap-Harm Westhuis, Gusto/SBM Offshore, NetherlandsRonald W. Yeung, University of California at Berkeley, USA
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OMAE2009: Copyright Information Page 1 of 1
Proceedings of theASME 2009 28th International Conference on Ocean, Offshore and ArcticEngineering (OMAE2009)May 31 - June 5, 2009. Honolulu, Hawaii, USA
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Proceedings of the ASME 2009 28th International Conference on Ocean, Offshore and Arctic Engineering0MAE2009
May 31 - June 5, 2009, Honolulu, Hawaii, USA
OMAE2009-79366
REAL TIME ESTIMATION OF SHIP MOTIONS IN SHORT CRESTED SEAS
ABSTRACTThe presented research is part of the developnient of an
onboard wave and motion estimation system that aims topredict wave elevation and vessel motions some 60 - 120 Sahead, using wave elevation measurements by means of X-band radar.In order to validate the prediction model, scale experimentshave been carried out in short crested waves for 3 different seastates with varying directional spreading, during which waveelevation and vessel motions were measured.To compare predicted and measured wave elevation, threewave probes were used at different distances from a large set ofwave probes that was used as input to the model . At one of theprediction locations, also tests were performed to measurevessel motions.This setup allowed validation of a method that was used forinitializing the linear wave prediction and ship motionprediction model.Various observations and conclusions are presented concerningoptimal combinations of prediction model parameters, probeset-up and sea state.
INTRODUCTIONWithin an international joint industry project called OWME(Onboard Wave and Motion Estimation) a system is beingdeveloped which aims to predict ship motions some 60 secondsahead. The main purpose of such a system is to increase safetyand operability during offshore operations that are critical withregard to vessel motions, e.g. top-site installation (float-over orlifting), helicopter landing on floating vessel and LNGoffloading connection. Use is being made of newest wavesensing techniques by means of X-band radar: The OceanWaves' WAMOS II radar image processing sofhvare is capableof providing real-time time traces of wave elevation at a largenumber of locations.This paper describes the validation of a model used to computea deterministic prediction of wave elevation and ship motion byusing remote wave elevation measurements in short crested
waves. Linear theory is used resulting in a very simple andstraightforward propagation model. The challenging part iswithin the initialization of this model which is the main focusof the present study.To assess the accuracy of the prediction, extended model testshave been carried out at the Maritime Research InstituteNetherlands (MARIN). During these experiments the 2dimensional wave field was measured by using a large array ofwave probes. The measured wave field is used to predict waveelevation and ship motion at various distant locations. Thepredictions are validated by means of measurements of bothwave elevation and vessel motions at the prediction location.
EXPERIMENTS
Wave measurementsAs mentioned the present study aims to predict wave elevationand vessel motion in a deterministic way using measured timetraces of wave elevation at various locations. To validate themodel that will be described in the next paragraph, modelexperiments at a scale of 1:70 were carried out at MARIN, theNetherlands.For a selection of 3 short crested wave conditions, waveelevation was recorded by means of a wave probe arrayexisting of 10 x 10 wire-type wave gauges.
Figure 1, 10 x 10 wave gauge array
P. Naaijen R.R.T. van Dijk R.H.M. Huijsmans A.A. El-MouhandizDeift University of MARIN DeIft University of MARIN
Technology Wageningen, Technology Wag en i ng enDeift, The Netherlands The Netherlands DeIft, The Netherlands The Netherlands
Tests were repeated with the wave gauge array positioned atdifferent locations in the basin, thus obtaining a relatively largenumber of wave measurements that could be used to optimizeand validate the prediction model. Figure 2 shows all wavegauge array positions for which tests were performed. Positions1, 2 and 3 are the locations for which predictions will be madeand compared with the measurements. The probes at theremaining locations are used as input for the model. The mainwave direction is in positive X direction as indicated in thefigure.
ENcfl
>(0
Figure 2, wave gauge array positionsAs the different tests were not performed simultaneously,checks were carried out in order to confirm that different wavetests are reproducible. Figure 3 shows a sample of two wavemeasurements from different tests, measured at the samelocation. As can be seen good reproducibility is obtained.
2900 950 1000 1050 1100
time [s]
Figure 3, comparison of measured waveelevation during different tests at identicallocations
Concerning the wave conditions the choice was made only tovary the amount of directional spreading. (The effect of wavesteepness was examined in earlier work. (Naaijen et al. [9])).Tests were performed for a Jonswap spectrum with a peakperiod T of 9.0 s, significant wave height H of 2.5 m andpeakedness factory of 3.3.To include directional wave spreading the following spreadingfunction was used:
D(p) = Do cos2s( - /10)
with
D0 =. 2s
Jcos (i-1i1)d1,
p0-9O
and
S (cv, u) = S (co) D(,u)
Three different values for the spreading parameter s were used,being 4, 10, and 50 corresponding to very short crested windwaves, average wind waves and an average swell respectively.(Measurements at position #5, #6, #10 and #11 as indicated inFigure 2 were only performed for the tests with s10.)For practical reasons concerning the wave maker, thedirectionality was cut off leaving the sector of-IS deg - 15 degfor s=50, -30 deg - 30 deg for s=l0 and -45 deg - 45 deg fors=4.
Ship motion measurementsApart from wave elevation measurements, motions of a modelof an offshore support vessel, without forward speed, located atposition #2 (see Figure 2) were recorded. The model, beingkept in position by a soft mooring system such that the relativewave direction was 165 degrees, is depicted in Figure 4.
(1)
Figure 4, 1:70 model of offshore supportvessel
The main particulars of the vessel are:
94.2 [ml - Length between perpendicularsL 101.5 [ml - Length on waterline
Figure 6, directional wave spectrum for s=1Oand discrete components used inrepresentationAs an estimate for the wave component amplitudes thespectral values S(w,j) were converted to amplitudes:
Focusing on the prediction of vertical motions, mainly heaveand pitch motions were considered, of which the RAO's weredetermined using a linear 3D diffraction program. Additionaltests were carried out in irregular (white noise) long crestedwaves for relative wave directions varying from bow to bowquartering. Calculated RAO's appeared to be in goodagreement with the RAO's determined from the mentionedexperiments.
From Fourier analysiS, frequency components of the measuredtime traces at J locations can be obtained, corresponding to thefollowing representation
(3)
where:j = index of location for which time trace is provided
n = index of frequency component
N=number of samples of considered time trace
= amplitude and phase angle for frequency component n
of measured time trace at location j following from FFT
From a predefined number M of directional components to beused in equation (2), the discrete wave directions p, werechosen as was suggested by Zhang [11: the average directionalwave spectrum was determined from the measurements bymeans of the MLM method. For each frequency the energycontent was examined and the direction of the most energeticcomponent was identified. Ignoring on both sides of this mostenergetic direction a predefined small amount of wave energy,a range of wave directions is obtained that is divided into Msegments whose center values are used for (The values ofi,,, determined this way will be frequency dependent which iswhy a double index nm is used.) Figure 6 shows an example ofdiscrete w - p,,, combinations (marked with dots) determinedas described above for M=l0, together with the underlyingtwo dimensional spectrum for the wave condition with slO.
0 5 1.5
(radIs]
Figure 5, 1D wave spectrum and RAO's forrelative wave direction of 165 deg.Figure 5 shows the calculated heave and pitch RAO's togetherwith the one-dimensional wave spectrum.
PROPAGATION MODELThe theoretical model used to describe the wave field is a linearsuperposition of cosine waves with different frequenciestraveling in different directions:
(,l_kx .cos(/i,,, )-ky1 sin(p,,, )+e,)
} (2)
where:= real part
= amplitude of frequency component in
propagation direction u,,,,
co = frequency of component n
k, = wave number of component n
x1,y = co-ordinates of locationj
= propagation direction of directional
component m for frequency n
enm = initial phase angle of component nun
M = number of directional components
per frequency
04 06 06 07 08 09o (rad/si
2
1.8
1.6
1.4
CE1.2
0.8.c
0.6
0.4
0.2
Where:dp = the band width of each of the M segments mentioned above
This way the only unknowns left in equation (2) are the initialphase angles
By assuming that the above 2D representation of a wave timetrace at location j (equation (2)) should equal the measuredtrace represented by (equation (3)), the unknown initial phaseangles in (2) can be solved. This is done by considering afrequency domain representation of both measurement and 2Drepresentation.
One method to solve the unknown phase angles is proposed byZhang [1]:For each frequency, an error can be defined as follows:
= e'' - e'"' .cos(p,,,, )-ky1 sin(p,, )+efl,)(5)
n=1
The unknown initial phase angles can be solved by minimizinga target function Rn defined by the sum over all J locations ofthe absolute squared error:
R,, = {A})2+ m}) (6)
Another way to solve the phase angles is by defining a matrixvector equation, Ax=b as given in equation (7), and solvingthis.Ax=b=,- cos(p, )-k,, su1(u,i)) e"'' cos(p,M )-ky1 sin(p,,,,))
(Xj cos(p i )-k,y, srn(p,)) cos(p,%, )-Iç,y, sin(p,1))nM
'rnI e'"
1 j6,j\ I I(7)
Applying a Singular Value Decomposition (SVD) on A as doneby Janssen et. al. [4] appeared to give the best results. Allresults and conclusions mentioned in next paragraphs are basedon the latter method.Having solved the phase angles from equation (2), the waveelevation can be calculated at any time and any location bysubstituting the desired values for t, x and y in the equation.However, in order to ensure physical significance of the
prediction, 1, x and Yj have to be chosen within certain limits.This will be explained in more detail in the next paragraph.Using the RAO's for the ship motions (obtained from linear 3Ddiffraction calculations) a ship motion prediction can be madein a straight forward way:
PREDICTABILITYHaving described the propagation model in the previouschapter, sonie attention is paid to the question how thedifference between real surface waves and our representation ofthem effects the predictability of those surface waves.Let's reconsider equation (2). If no restrictions are put to thedomain in space (xj, yj) and time (t) for which we consider thisrepresentation to be valid, we practically assume it to be able todescribe the entire ocean for an unlimited period of time.Obviously, this isn't a realistic assumption. The validity of therepresentation as given in equation (2) will be limited in spaceand time.To discuss these limitations, the one-dimensional case isrevisited here briefly. The space-time diagram for a longcrested wave traveling in positive X-direction showing thepredictable zone is depicted in Figure 7.
In this diagram, introduced by Morris et al [7] and used as wellby Edgar et al [8] and Naaijen et al [9], the triangles indicatethe zone in space and time where the wave elevation can bepredicted or reconstructed using a recorded time trace of thewave elevation which is represented by the horizontal line atthe base of the triangle.The second horizontal line represents the prediction based onthis recorded time trace, AX away from the measurementlocation, shifted At seconds ahead. Only its part within thepredictable zone (gray triangle) is supposed to be useful.In the mentioned publications the slopes of the left and rightboundaries of the predictable zone were considered to equal thephase velocity of the shortest and longest wave componentspresent in the recorded time trace. 1-lowever, as explained byWu [10], it is not the phase velocity but the group velocity ofthe shortest and longest wave components that governs the sizeof the predictable zone. This also explains that it was observedduring the experiments by Naaijen et al [9] that predictions ofthe wave elevation could be extended further into the futurethan expected based on the predictable zone bounded by thehighest and lowest phase velocities: when applying a longenough duration D of the recorded wave elevation, only thefastest wave components will limit the prediction and as theirgroup velocity is lower than their phase velocity, the steepnessof the right-hand boundary is decreased, meaning that theprediction can be extended further into the future.
The concept of the predictable zone can be extended for thethree-dimensional case. Considering the three-dimensionalwave field to be a superposition of wave components travelingin different directions, a similar predictable zone diagram canbe constructed for one specific traveling direction. See Figure8.
For any point in space and time, the wave elevation due to allcomponents traveling in the considered direction is asuperposition of all frequency components traveling in thatdirection. Depending on which point in space and time isconsidered, not all these components might originate from themeasurement. The highest and lowest group velocities of thosecomponents just originating from the measurement for a givenprediction point in space and time (xv. y,,, 1,,) can be defined asrespectively:
cg1 = ((xe _i)cos(i)+(y _-p)sin(tf))/(t,, _D)
Cg2 = ((xe _i)cos(ji)+(y _)sin(ft))/t
Where a tilde denotes the measurement location.Denoting o and 2 as the corresponding wave frequencies andwj0, and COJ,igl, as the frequencies of the shortest and longestwave components that occur in the wave field, an error estimatefor the predicted wave elevation can be defined as the relative
(9)
amount of wave energy represented by those components at (xv,y,,, r,,) that do not originate from the measurement:
Err(x,y,t) =
Figure 8, predictable zone for one directionalcomponent of a short crested sea
I 2,r"(P)
f f S(w,p)dwdpo c(i)2g '°h&,h
$ Js(w,p)ddpOa )
(10)
As described in the previous chapter nmltiple probe records areused to find the representation of the wave field given byequation (2). However, keeping in mind the limitedrepresenting capabilities in space and time of thisrepresentation, it can only represent a decomposition of oneprobe record.Imagine that for one specific direction the frequencycomponents in the three-dimensional wave representationrepresent a decomposition of a measurement of length D at
location (i,j).
Figure 8 shows that a measurement at location (x,, , can
only be represented by this decomposition between th and te..(The vertical axis in Figure 8 corresponds with the spatialcoordinate x , parallel to the traveling direction of theconsidered wave components.)The short wave components present in the part before h do not
originate from the location For any point in time of
the wave elevation time trace at (x,y), the error Err as
defined in equation (10) can be determined. A representative
mean error value for the whole time trace at (x,y) can
then be defined as follows:t
Err,,,ean (x,y)=- JErr(x,y,t)dt (11)
So when attempts are made to find a three-dimensional wavefield representation (equation(2)) that yields for a certain period
of time D at location (i,5) , only those parts of thesimultaneously measured time traces at surrounding probe
locations (denoted by (xv, y1,) ) should be used that are
within the predictable zone. The presented methods to find thethree-dimensional wave field representation are ignoring thisfact since they are frequency domain methods for which it isnot possible to take it into account in a straightforward way.(Wu [101 describes a time domain method for solving the three-dimensional representation for which it is possible to accountfor limitations in the usable part of the time traces to be used.)
In the area where the wave probes were located, Err,nea fromequation (11) is shown for the three wave conditions forwhich experiments were carried out in Figure 10. Locations ofthe frames containing the probes whose simultaneousmeasurements were used for decomposing the wave field areindicated by the squares. (The dots indicate the used probepositions that appeared to give the optimal results for theconsidered wave condition and prediction location #2.) As canbe seen the probe positions are chosen such that Err,ne,, doesnot exceed 0.1 for any of the conditions.
s=i0.t=*E0
09
08
07
06
05
04
03
02
01
0
Figure 9, predictable zone for s=10 andforecast-time of 60 s
04
035
03
025
02
0 15
01
005
04
035
03
025
02
o is
01
006
04
030
O 3
026
82
0 10
0.1
005
Figure 10, Errmean for s50, 10 and 4 andavailable probe-frame positions
When calculating the values for Err according to equation (10)for a prediction of the wave elevation at a given set of locations(Xp,yp) for a given moment in time t, , the optimal relativepositions of measurement and prediction can be determined.For a forecast-time of 60 s and wave spreading s=l0, the valueof Err is presented in a similar way as was done by Blondel[11] in Figure 9.
As shown by Figure 9, prediction location #2, the locationwhere also the ship model was located, was chosen such that itwould be optimal for a 60 seconds prediction for the wavecondition with s=I0.
RES U LTSSeveral aspects have an effect on the accuracy of the waveprediction:The setup of the probes whose measurements are used to solvethe system of equation (7) should be such that their in-between distances are optimal to identify phase differences forthe whole frequency range that contains wave energy. Asshown by Voogt et al. [l2J, for one regular wave componentthis optimal probe distance amounts to ¼ of the wave length.Therefore it was aimed to use a probe setup that provided forall relevant frequencies in-between distances (projected in thedirection of each of the wave directions used in therepresentation) of '/4 of the wave length.The probe setup that appeared to give the best results for aprediction at location #2 in waves with direction spreading ofs=l0 is shown in Figure 9. For each of the 10 discrete wavedirections that were used at the peak frequency in the two-dimensional representation, intermediate distances between theused probes, projected in each of the 10 wave directions, weredetermined. Figure II shows the 2D spectrum based onwavelength I peak wavelength ratio. The dots indicate all theavailable intermediate probe distances divided by ¼ peakwavelength. This way of presenting should result in a high-density of dots in the most energetic part of the spectrum for afavorable probe set-up according to the statement above.
tO 16
Figure 11, relative probe distances for optimalsetup s=1O, prediction position #2Another important variable that effects the accuracy to a greatextend is the number of directional components that is used inthe representation of the wave field. With a large number ofdirectional components, the directional spreading is bettercovered. However, for a given probe set-up, choosing a toolarge number of directional components dramatically decreases
the condition of system matrix A in equation (7) resulting inpoor predictions. For cases where the number of directionalcomponents was too large, it was found that adding more proberecords to the equation (7) not necessarily improves theprediction. The extra probe records have to add 'information' tothe system. Adding probes positioned in frame numbers 4 and12 (Figure 2) for example did not improve the prediction forany of the cases. When the requirement to the probe set-up asstated above is fulfilled, the only way to improve the conditionof the matrix is to decrease the number of wave directions. Theset-ups shown in Figure 10, using 9 probes per frame asindicated by the dots, were found to give the best results forprediction at location #2. By extending the number of inputmeasurements by using all available probes i.e. 100 per frame,no improvements were obtained.Apart from the combination of probe set-up and number ofdirectional components, that determines the condition of thematrix in (7), the combination of probe set-up and theprediction location was found to have a significant impact. Itwas observed that the use of extending the probe set-up in y-direction is limited related to the amount of wave spreading andthe prediction location. See Figure 9. The angle u between thedashed lines starting from prediction location #2 equals thesector angle that bounds the directionality of the wavecondition: as mentioned, for practical reasons the directionalitywas cut off at 30 and -30 degrees for this condition (s=10)resulting in u = 60 deg. It was observed that usingmeasurement probes outside this angle did not improve theaccuracy. This observation was found to be consistent for allcombinations of prediction location and directional spreadingas far as the available measurements allowed to verify it. (Forthe most short crested condition with s=4, measurements atpositions #5, #6, #10 and #11 that would enable confirmationof this observation were not available.)To assess the accuracy of the predictions an error value iscalculated that is defined as:
(t) - :(t))2
(12)
Where:
E(t) = normalized prediction error
= n'' realization of predicted wave elevation
ç°(t) n realization of measured wave elevation
N = total number of realizations
= RMS of measured wave elevation
Figure 12 shows the normalized error of the wave predictionaveraged over N =100 realizations at location 3, 2 and 1 for thecase with s=l0. The vertical dashed lines indicate the
boundaries of the predictable zone in time. As expected theerror increases outside the predictable zone. The solid verticalline indicates the boundary between hind cast and forecast.Error values averaged over the predictable part of the predictedtraces are given in Annex A, Table 1. All values are based on anaverage over 100 realizations.
t Is]
Figure 12, prediction error for locations 3,2and 1 for s=1O
Since for the applications of the onboard wave and motionestimation system we are interested in the prediction of quietperiods rather than in an exact deterministic prediction, also theenvelope of the deteniiinistic prediction has been determined:the predicted deterministic signal has been post processed bytaking the absolute value of its Hubert transform. Its error,which is defined similarly to the error of the wave elevation /ship motion itself is in general significantly smaller.For location #2, Figure 13 shows time traces of predicted andmeasured wave elevation and heave and pitch motion for thecase with s10. The maximum prediction time has beendetermined from the measured mean two-dimensionalspectrum, allowing a value of Err as defined in equation (10)of 0.1 and amounts to 78 s. The vertical solid line againindicates the boundary between hind cast and forecast. Therightmost vertical dashed red line indicates the end of thepredictable zone in time.In Annex B, samples of time traces are shown for all waveconditions at all prediction locations. For each predictionlocation the most favorable probe set-up is plotted at the righthand side of each of the correspoiiding time traces: The blackdots indicate the used probes, the grey cross with the circleindicates the concerning prediction probe. The color indicatesthe Err value as defined in equation (10) for the allowedmaximum forecast time that was aimed for (which is 30 s forprobe 3, 60 s for probe 2 and 120 s for probe 1). As can be seenthe chosen prediction locations match the intended forecasttime well in that sense that for all conditions they arepositioned in the predictable zone (where Err is app. 0.)
Figure 13, sample time traces of predictionand measurement of wave elevation, heaveand pitch motion, location # 2, s=1O
As can be seen from both the mean error values in Table I andfrom the samples of the time traces in Figure 15, predictions fors-4 are rather poor especially for locations I and 2. This iscaused by the fact that probe measurements at locations furtherfrom the X-axes, that would be required for an optimal set-upwere not available for this condition.
ACKNOWLEDGMENTSThis paper is published by courtesy of all participants andpartners of the OWME-JIP for which they are gratefullyacknowledged.Special thanks to MARIN for facilitating the experiments.
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