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Prediction of an advanced spar’s horizontal motions, validated by fullscale observation data
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The Science of Making Torque from Wind (TORQUE 2020)
Journal of Physics: Conference Series
1618 (2020) 052035

IOP Publishingdoi:10.1088/1742-6596/1618/5/052035

Prediction of an advanced spar’s horizontal motions,validated by full scale observation data
Haruki Yoshimoto1 , Christopher Wright2 , Ryota Wada2 and Ken
Takagi2
1
2

Japan Marine United Corporation, Yokohama-City, Kanagawa, Japan.
The University of Tokyo, Tokyo, Japan.

E-mail: wrightc@edu.k.u-tokyo.ac.jp
Abstract. As the offshore wind industry moves into deeper waters, the number of different
floating wind platform concepts continues to expand. Accurately predicting the motion
characteristics of these novel platforms is crucial to the safe and economic conversion of windenergy into electricity. A challenge in the currently used numerical simulation methods involves
successfully predicting the slow drift motions and damping, especially in complex realistic
environmental conditions which include multi-directional spectral waves, current and windloading. Of most uncertainty to these predictions is determining the low frequency viscousdamping which dominates the resonant surge and sway motions. In this paper, full-scale motion
observations of the Fukushima FORWARD’s floating wind substation are used to determine theplatforms viscous drag forces. These drag coefficients are used in a combined potential flow andMorison’s equation model to capture the observed behaviour. This validated numerical modelis then used to describe the required fidelity of mooring line models, in order to aid platform
developers in the early stages of design.

1. Introduction
As the offshore wind energy industry moves into deeper waters, floating platforms for supporting
wind turbines are being proposed, developed and installed as the solution. There are numerous
designs for floating structures in all stages of design, from conceptualisation to full scale
deployment, with vastly different design characteristics, however these platform types can begenerally categorised by how the primary stability mechanism is achieved. Spar buoys achieve
stability through counter weight ballast, semi-submersibles through water plan area righting
moment and tension leg platforms through excess buoyancy providing pretension in the mooringlines. From these primary categories there can be numerous sub categories, for example spar
platforms can be mono-column, advanced spar, truss spar or pendulum spar amongst others.
Each type has a number of unique attributes and as the floating wind industry platform designers
have not converged to a single type, there is also much research into the benefits and challengesof each.
This research concentrates on the main horizontal motions of advanced spar type platforms(surge and sway, as yaw motion is negligible). Horizontal motions are excited by wind, wave
and current and dominate the design of mooring systems. Limits on horizontal motions arealso required to ensure the safe operations of power umbilical cables connecting floating windturbines (FWTs) to the wind farm grid system. For mooring system and power umbilical design,
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The Science of Making Torque from Wind (TORQUE 2020)
Journal of Physics: Conference Series
1618 (2020) 052035

IOP Publishingdoi:10.1088/1742-6596/1618/5/052035

accurately predicting the horizontal motions is crucial. As platforms horizontal (surge and sway)
natural frequencies are commonly much below the wave excitation frequencies, it is second
order wave, wind and current which provide the excitation forces. Low frequency damping
is a combination of wave drift damping, floater viscous damping, mooring and umbilical line
damping, current, wind and radiated wave damping. Large amplitude slow drift oscillations are
known to make the viscous flow separation more significant compared to the small oscillation
wave frequency oscillations [1]. The authors previous research [2] on an advanced spars platform’s
low frequency motion concluded that the viscous drag dominated the damping due to theplatform geometry, and showed a tendency to increase with increasing wave severity. Common
numerical modelling methods using potential flow theory neglect any viscous forces due to theassumptions that flow is inviscid and irrotational. Viscous forces are generally added to potential
flow theory models in order to increase the accuracy of predictions made by those models, onesuch method is using only the drag component of Morison’s equation [3]. Selection of thedrag coefficients to use in drag force formulas is critical to the accurate use of such methods.
Coefficients are generally selected from a combination of the following methods: the modeler’s
experience of similarly shaped offshore platforms, a literature review, scaled model experiments
in wave basin tests, computational fluid dynamics or from full scale deployments. Each method
has its own unique challenges, and consistency across methods varies. Drag coefficients areseen to vary between still water and across varying sea-states. Lemmer [4] showed throughexperimental testing and a reduced order numerical model of the tripple-spar floating windturbine that the required drag coefficient reduces from 2.0 in still water to 0.8 and 0.6 withincreasing wave severity. This inverse relationship between sea-state intensity and damping has
been shown in other research, described as accounting for missing additional nonlinear wave
excitation, which become more significant with increasing wave height [5]. Operational Modal
Analysis (OMA) has also been successfully used to analyse the damping rates of floating windturbines. Pegalajar [6] analysed experimental data of a semi-submersible FWT using OMA andfound that the damping generally increased with increasing wave severity. Errors in surge andsway grew with increasing sea-states, likely due to a simplification of the second order quadratictransfer functions (QTF’s) and neglecting a third order viscous mean drift force. The thirdorder viscous mean drift force arises from integrating the viscous force up to the instantaneous
free surface, or when the instantaneous floater position is used to apply the force [7].
Improvements to classic numerical modelling techniques have also been proposed and verified
in recent years. For example using frequency dependent hydrodynamic parameters in Morison’sequation type models [8]. Stansberg [9] found interaction effects between wave and current forceson wave drift motions and proposed an empirical correction factor to improve potential flow
models. When compared against tank testing of a semi-submersible platform this correction led
to good estimates of slow drift motions. The empirical correction factor has been generalised toinclude the effects of non-collinear waves and current [10] and has further tank testing validations[11] which indicate that the damping increases with increasing wave heights. Compared to thecalm water damping, the low frequency surge damping in waves increases between 60 and 80 %for moderate and severe sea states without current and around 50 % for the checked severe sea
state with current.
Validation of numerical modelling and design by full scale at sea observations is a vital
aspect in furthering the understanding of hydrodynamics. Such validations has been undertaken
historically on offshore oil and gas or purely experimental platforms, for example the Oryx
Neptune Production Spar [12] or the POSEIDON experimental semi-submersible platform [13].
With the increased deployment of prototype offshore FWTs, there has been a recent interest in
validating the modelling of these smaller more dynamic offshore platforms. For example the fullscale Hywind FWT was deployed off the coast of Norway in 2009 and showed that the motion
characteristics could be accurately predicted using NREL’s FAST software [14].

2The Science of Making Torque from Wind (TORQUE 2020)
Journal of Physics: Conference Series
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IOP Publishingdoi:10.1088/1742-6596/1618/5/052035

The floating substation of the Fukushima FORWARD floating wind farm has also beenstudied previously [2, 15, 16]. The 7MW Fukushima FORWARD V-shaped semi-submersible
FWT has also been used for design and numerical modelling validation purposes [17, 18].
2. Objectives
In this paper the required viscous damping for the Fukushima FORWARD’s floating substation
is analysed. Numerical model drag coefficients are tuned to observation data from the full scale
deployment across a range of sea-states. The required mooring model fidelity is also analysed. As
computational expense increased with increasing mooring line fidelity these results are important
for the use of early stage design tools.
3. Methodology
3.1. Numerical model
A numerical model is developed using combinations of the two software packages; ANSYS
Aqwa and Orcina OrcaFlex. A detailed description of the model set up can be seen in [2].
Frequency domain hydrodynamic parameters are calculated using ANSYS Aqwa, which arethen implemented into a time-domain numerical model developed in Orcina OrcaFlex. Viscousdamping is applied using drag only Morison’s equation elements as shown in Equation 1, where
Fd . is the drag force, ρ is the density of sea-water, Cd . is the drag coefficient, A is the normal
projected area and vr . is the relative velocity between water particle and vessel. Although
the platform is composed of octagonal hulls interconnected by cylindrical elements, in order
to simplify the implementation of Morison’s equation all elements are modelled as cylindricalelements of equal projected area in the normal direction. In order to account for the thirdorder mean viscous drift force the viscous force is integrated to the instantaneous water line bymeans of Wheeler stretching [19]. The instantaneous vessel position is used to apply all forces
including the drag force. The selection of the drag coefficients to implement is non trivial as
seen in the author’s previous publication on this platforms low frequency horizontal motions [2].
In order to best compare the varying simulation methods with the observed data, the dragcoefficients for each individual sea-state are fitted. Details of this method are given in Section
3.2. Due to the small differences in results using Newman’s formula for generating second-orderforces over the more accurate full QTF method for wave heights as dealt with in the authors
previous research [2], and the much quicker computational time, all simulations in this work
use Newman’s formula. For the mild to moderate sea-states used for this study the difference
between low frequency surge and sway results using full QTF’s and Newman’s formula is lessthan 5%.
1(1)
Fd = ρCd Avr |vr |2
Environmental force data includes a multi-directional wave spectra, discretized into 15 wave
directions, a mean current velocity and direction, and a wind velocity time-series, all recorded on
the observation platform. The original data groupings are used as in [2]. Two selection criteria
are used to select which environmental cases to use. Firstly cases with a significant wave height
above 2 m and a wind speed below 10 m/s, and secondly cases were selected with a significant
wave height above 3.5 m without any wind speed limit. Current velocity was in the range of
0.1 to 0.6 m/s. Wind and current drag forces are calculated using the method outlined in [20]with the addition of the relative wind/current velocity between the platform and wind/current.
Wind and current drag force coefficients were validated by prior experimental testing.
Modelling of mooring line is compared using the following methods, ranked in order of fidelity,with the highest first: 1) Finite-element model (FEM), 2) Analytic Catenary (AC) equations,3) Nonlinear Catenary Spring, 4) Linear Spring. For 3) the Nonlinear Catenary Spring, the3The Science of Making Torque from Wind (TORQUE 2020)
Journal of Physics: Conference Series
1618 (2020) 052035

IOP Publishingdoi:10.1088/1742-6596/1618/5/052035

horizontal force is the quasi-static restoring force as predicted by the FEM model. For 4) the
Linear Spring, the force was linearised with the assumption of an extremely small offset. No
vertical restoring forces are provided by either of the spring models. Only the FEM includes
viscous damping induced by the motions of the mooring line. Mooring line drag coefficients are
selected as 2.6 in the normal direction and 1.4 in the axial direction. A sensitivity study onmooring line drag damping showed the effects to be negligible in comparison with hull viscousdamping. Mooring line damping can effect line tensions and has been used to tune numericalline tensions to experimental results in the past [21]. In the case of this work no observed line
tensions are available so this was not considered further here. No additional damping to accountfor the loss of mooring line damping is added to the other methods. As both spring methods
do not provide any of the additional weight that the catenary chain provides, an additional
mass component equal to the submerged weight of the chains is added to the spar. For the“observed” line tensions, the motions of the platform are used to derive the line forces using theanalytical catenary equations. No direct measurements of line tensions were undertaken during
the observations, so this method is used to get the closest approximation. An attempt was madeto use the platform motions coupled to a FEM mooring model, but noisy accelerations in theobserved motion data, led to large inertial shock loads in the mooring system that were deemed
to be unrealistic.
3.2. Tuning of drag coefficients to observed results
In this work the largest uncertainty involves a combination of the short term variability inthe random wave seeds and the drag coefficients required to match the numerical models low
frequency horizontal translations to the observation recordings. This section gives a descriptionof how these are taken into consideration.
A single drag coefficient value is fitted to each of the observation data points. The squareroot of the variance of the low frequency surge and sway motions are used as the fit, as shown in
eqn. 2 and as calculated spectrally by eqn. 3, where σ is the variance of motion, m0 is the zeroth
moment of the low frequency surge or sway motions, σX , σY and σXY refer to the variance of thesurge, sway and combined surge sway respectively, the subscripts OBS and SIM refer to observed
and simulated results respectively. Low frequency motion is defined as that below 0.01 Hz. An
iterative slope based approach is used to determine the next simulations drag coefficient, until
a match to the observation data is found. Convergence here is denoted as a percentage error ofless than 2.5% as shown in eqn. 4.
2
σXY = (σX
+ σY2 )0.5(2)

σ = m00.5(3)

σXY,OBS − σXY,SIM≤ ±0.025
σXY,OBS(4)

3.2.1. Short term variability in low frequency motions As the observed wave recordings areof a spectral nature, no information exists about the exact wave time history. This presentsa challenge to establishing the exact drag coefficients that are required to match the viscousdamping in the numerical model with the observed data. An inherent short term variability exists
in the simulated wave field due to the random wave phases applied to each wave component, thisvariability leads to variations in the simulated motions, particularly the low frequency motions,which are greatly affected by the exact wave train. As this work deals with numerical modelling
validated by full scale observational data recorded at 20 minute, the standard simulation time4The Science of Making Torque from Wind (TORQUE 2020)
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IOP Publishingdoi:10.1088/1742-6596/1618/5/052035

duration of 3 hours cannot be used. Recorded sea-state conditions are not stable for such longa duration.
In order to account for this issue, a short term variability study is performed on each recorded
wave spectrum. The numerical model is set up according to the description in Section 3.1, withthe viscous damping drag coefficients set to zero. 32 cases are created for each environmental
condition, varying the wave seed of each of the 15 directional wave spectra individually. Random
wave seeds are created using the Matlab function “Rand”, which generates pseudorandom andpseudoindependent numbers. After simulations are completed, the standard deviation of low
frequency motion combined surge and sway motion for each case is analysed. The random wave
seed which gives the closest result to the mean of all seeds is used for the drag coefficient fitting.
An example of the procedure is shown in Figure 1.

Figure 1: Example of random wave phase seed study for low frequency motions. Note: platform
motions have no additional viscous damping here
The drag coefficient will also be fitted to the random wave seeds that give the maximum andminimum motions for one observation point in each group. The single observation point fromeach of the groups to have this further fitting will be selected randomly.
4. Results
The required drag coefficient are successfully tuned for 64 of the 97 observed data points andare plotted against significant wave height in Figure 2. A failure was found in 33 of the cases,
where even with a drag coefficient of zero, the simulated motion was smaller than that observed.
In these cases the random wave seed which gave the mean motion was deemed to produce toolarge motions. No further analysis of these data points was undertaken in this work. In the
figure error bars indicate the drag coefficients required to fit to random wave seed which gave
the maximum and minimum offsets. The fitted drag coefficients range from almost zero toabout 6.5, while no discernible trend correlated with wave height can be observed. The meanof all environmental cases fitted drag coefficient is 1.86. The required drag coefficient for the
maximum to minimum random wave seed range can be as small as 0.3 or as large as 3.
Comparisons were made to the drag coefficients resulting from each of the environmental
selection criteria, i.e. with or without the wind speed limit of 10 m/s in order to identify if

5The Science of Making Torque from Wind (TORQUE 2020)
Journal of Physics: Conference Series
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IOP Publishingdoi:10.1088/1742-6596/1618/5/052035

wind damping was to account for the variance in wave viscous damping. As Figure 2 shows,the variance in drag coefficients for wave heights below 3.5m are similar to those above 3.5m,
indicating that wind damping is not a significant cause in this case. A similar comparison to
current velocity also showed no correlation to drag coefficient value.
There is little published literature on the surge drag coefficients of advanced spar platforms,
however Hirai [22] calculated the required surge drag coefficients for an advanced spar using
OpenFOAM CFD. A parameter study on the spars hull diameter found the required dragincreased from 1.9 for a pure spar platform to 3.3 for an advanced spar with column to hull
ratio of 6. For comparison the column to hull ratio of the advanced spar used in this work is
6.68, but is composed of 2 fully submerged hulls and 1 semi-submerged hull, as opposed to asingle fully submerged hull as in Hirai’s work
In parallel to this work, the authors have experimentally studied the low frequency surge
drag damping of a generic advanced spar platform. Results from these experiments in stillwater and regular waves indicate a strong KC and wave height/period relationship [23]. The
drag coefficients are seen to be inversely proportional to KC number. In that paper the fitted
drag coefficients from Figure 2 are plotted against the observed KC number, showing a similar
inverse relationship.

7

Drag Coefficient [Cd]

6
5
4
3
2
1
0

2

3

4

5

6

7

Wave Height [HS]Figure 2: Results of drag coefficients fitted to observation data. Error bars indicate the fit to
the max and the min random wave seeds
Wave frequency surge and sway motions are extremely well predicted by all mooring modelling
methods used in this work and as discussed in the authors previous research and are not discussed
further in this work. Surge/sway natural periods are around 165 s, meaning only around 7
oscillations per are recorded per observation point. In order to further take into account thewave elevation short term variability as described in section 3.2.1, individual observation points
are grouped as in the authors previous research [2]. Shown in detail in this work are the groups
8, 12 and 14, details of which are given in table 1.
In Figure 3, cumulative exceedence probabilities are plotted for the three groups, comparing
the observed low frequency motions with those simulated by the various mooring models. Results
are normalised by the largest motion of the observed data. The standard deviations are shownin an insert bar plot, where error bars indicate the maximum and minimum standard deviationof each group, while the bar indicates the group mean. As the FEM model is tuned to the6The Science of Making Torque from Wind (TORQUE 2020)
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Table 1: Grouping dataGroup
numberMin significant
wave height
HS [m]Max significant
wave height
HS [m]

Min peakperiodTP [s]Max Peak
PeriodTP [s]

Count

8
12
14

4.0
5.5
5.5

4.5
6.0
6.0

13.00
11.05
13.35

14.20
12.20
14.50

9
10
4

observed values, an extremely close fit as seen here is expected. The tails of the distributions
are of most interest and significance to the design of such a platform and mooring system, andalthough drag coefficient values are tuned on the standard deviation of motions, the tails also
agree extremely well. For groups 8 and 14, the motion peak is nearly exactly predicted by the
FEM model, while for group 12 it shows a 10 % over the observed data.
The analytical catenary models show a slight increase over the FEM model. This difference
is attributed mostly due to the lack of viscous mooring line damping applied in this model. In
general the difference between the analytical catenary and FEM models grow with increased
motions. Both spring methods greatly over predict motions for groups 8 and 14, while showa reasonable prediction for group 12. The linear spring shows a surprising slight improvement
over the catenary spring for group 12.
In Figure 4, cumulative exceedance probabilities are given for the fair lead line tensions, again
values are normalised by the peak of the observed data. For groups 8 and 12, the shape of all
distributions are very similar, although the “observed” values over predict the FEM tensions
by about 7-8%. The analytical catenary values over predict the FEM values by about 1-3 %.
For group 14, both FEM and the analytical catenary methods give slight over predictions of theobserved data of about 3-4 % at the peak. Across all groups the FEM models better predict the
sharp increase of tensions at the low probability extreme values more similar to the observed
data.
Differences in the FEM model tensions and those from the “observed” analytical catenary
data are most likely due to a combination of the following; small changes in the predicted andsimulated mean offset, the lack of additional line damping and added mass in the analyticalcatenary model and lack of line shape effects in the analytical catenary model. It should also
be noted that the “observed” values here are from the analytical catenary
5. Conclusions
In this paper, a numerical model of the Fukushima FORWARD floating substation was comparedagainst the observed data recorded in real full scale sea conditions. The required viscous dragcoefficient was tuned so as to match the numerical models standard deviation of low frequency
surge and sway to the observed data. A large spread in drag coefficients is observed, from almost
zero to over six, which is mostly attributed to the short observed time series, where metocean
conditions are stable. The mean of all environmental cases fitted drag coefficient is 1.86. Witha natural surge frequency of about 165 seconds, these 20 minute observed recordings only give
approximately 7 low frequency oscillations. A study to account for the range in required dragcoefficients according to wave random phase short term variability also showed a large spreadin the required drag coefficients. No trend in the drag coefficients correlated to wave height
was observed. However an inverse KC drag coefficient relationship has been observed based on
the results from this fitting [23]. The large spread in fitted drag coefficients may also indicate
something missing from the numerical model.

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The Science of Making Torque from Wind (TORQUE 2020)
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40

Exceedance Probability (%)

060

9 Environmental Cases
Number of Data Points:
111 Observed
20 131 FEM
127 Analytical Catenary
131 Nonlinear Spring
129 Linear Spring

0

0

0.5

1

Standard
Deviation
XY [m]

1
0.5
Obs
FEM
Analytical Catenary
Catenary Spring
Linear Spring

Standard
Deviation
XY [m]

Exceedance Probability (%)

80

Low Frequency Motion, Group 12

100

80

2

40
10 Environmental Cases
Number of Data Points:
119 Observed
20 143 FEM
138 Analytical Catenary
145 Nonlinear Spring
145 Linear Spring

2.5

0

0.2

0.4

0.6

0.8

1

1.2

Low Frequency XY Motion
Normalised by peak of Observed Data [m/m]Low Frequency XY Motion
Normalised by peak of Observed Data [m/m](a) Group 8(b) Group 2
Low Frequency Motion, Group 14

80

60

40

2
1
0

Obs
FEM
Analytical Catenary
Catenary Spring
Linear Spring

Standard
Deviation
XY [m]

100

Exceedance Probability (%)

0

60

0

1.5

1

Obs
FEM
Analytical Catenary
Catenary Spring
Linear Spring

Low Frequency Motion, Group 8100

IOP Publishingdoi:10.1088/1742-6596/1618/5/052035

4 Environmental Cases
Number of Data Points:
48 Observed
20 45 FEM
44 Analytical Catenary
48 Nonlinear Spring
48 Linear Spring

0

0

0.5

1

1.5

2

2.5

Low Frequency XY Motion
Normalised by peak of Observed Data [m/m](c) Group 3

Figure 3: Cumulative exceedance probability and standard deviation of low frequency motions,groups 8, 12 and 14

Various station keeping numerical modelling methods were compared. The extreme tail of
the FEM models low frequency motions distribution compared favourably with the observed
data. The analytical catenary equation model showed a slight over prediction of the peak data.
Generally both spring methods greatly over predicted the peak, by about 2.2-2.5 times, although
for a single group, group 12, the spring methods showed consistent results with the observed
data, with only the extreme tail showing an over prediction.
As no recorded line tensions are available from the floating substation, the vessels motions
are used as input to the analytical catenary model, which result in a quasi-static approximationof the observed loads. Predictions by numerical models are always within 10% of the observed
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The Science of Making Torque from Wind (TORQUE 2020)
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Line Tension, Group 8100

IOP Publishingdoi:10.1088/1742-6596/1618/5/052035

Line Tension, Group 12

100"Observed"
FEM
Analytical Catenary

80

Exceedance Probability (%)

Exceedance Probability (%)"Observed"
FEM
Analytical Catenary

60

40

9 Environmental Cases

20 Number of Data Points:
160 "Observed"
161 FEM
157 Analytical Catenary

0
0.75

0.8

0.85

80

60

40

10 Environmental Cases

20 Number of Data Points:

179 "Observed"
181 FEM
175 Analytical Catenary

0.9

0.95

0
0.75

1

Line 2 Tension
Normalised by peak of "Observed" Tension [kN/kN]

0.8

0.85

0.9

0.95

1

Line 2 Tension
Normalised by peak of "Observed" Tension [kN/kN](a) Group 8(b) Group 2Line Tension, Group 14

100

Exceedance Probability (%)"Observed"
FEM
Analytical Catenary

80

60

40

4 Environmental Cases

20 Number of Data Points:
70 "Observed"
70 FEM
69 Analytical Catenary

0
0.75

0.8

0.85

0.9

0.95

1

1.05

Line 2 Tension
Normalised by peak of "Observed" Tension [kN/kN](c) Group 3

Figure 4: Cumulative exceedance probability and standard deviation of mooring line tensions,groups 8, 12 and 14

values, and in most cases a closer fit is achieved. This work further validates the numericalmodelling of the advanced spar floating substation. The use of a quasi-static mooring line
model such as the analytical catenary equations here give reasonable results.
Acknowledgements
This research is carried out as a part of the Fukushima floating offshore wind farm demonstration
project funded by the Ministry of Economy, Trade and Industry. The authors wish to express
their deepest gratitude to the concerned parties for their assistance during this study.

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References[1] Jiang Z, Cui J, Gao Y, Liu J and Zhao Y 2016 Ship Technology Research 63 26–37[2] Wright C, Yoshimoto H, Wada R and Takagi K 2019 Numerical modelling of a relatively small floating
body’s wave and low frequency motion response, compared with observational data Proc. ASME 2019
38th Int. Conf. on Ocean, Offshore and Arctic Engineering (American Society of Mechanical Engineers
Digital Collection)[3] Bhinder M A, Babarit A, Gentaz L and Ferrant P 2015 Int. J. of Marine Energy 10 70–96[4] Lemmer F, Yu W, Cheng P, Pegalajar-Jurado A, Borg M, Mikkelsen R F and Bredmose H 2018 The triplespar
campaign: Validation of a reduced-order simulation model for floating wind turbines Proc. ASME 2018
37th Int. Conf. on Ocean, Offshore and Arctic Engineering (American Society of Mechanical Engineers
Digital Collection)[5] Madsen F J, Pegalajar-Jurado A, Bredmose H, Faerron-Guzman R, Müller K and Lemmer F 2015 LIFE50+
Deliverable D4.6 Model validation against experiments and map of model accuracy across load cases[6] Pegalajar-Jurado A and Bredmose H 2019 Marine Structures 66 178–96[7] Faltinsen O 1993 Sea Loads on Ships and Offshore Structures vol 1 (Cambridge: Cambridge university press)[8] Ishihara T and Zhang S 2019 Renewable energy 131 1186–207[9] Stansberg C T, Kaasen K E, Abrahamsen B C, Nestegård A, Shao Y, Larsen K et al. 2015 Challenges inwave force modelling for mooring design in high seas Offshore Technology Conference (Offshore Technology
Conference)[10] Yang L, Falkenberg E, Nestegård A and Birknes-Berg J 2017 Viscous drift force and motion analysis ofsemi-submersible in storm sea states compared with model tests Proc. ASME 2017 36th Int. Conf. on
Ocean, Offshore and Arctic Engineering (American Society of Mechanical Engineers Digital Collection)[11] Fonseca N and Stansberg C T 2017 Wave drift forces and low frequency damping on the exwave fpso Proc.
ASME 2017 36th Int. Conf. on Ocean, Offshore and Arctic Engineering (American Society of MechanicalEngineers Digital Collection)[12] Prislin I, Halkyard J, DeBord F, Collins J I, Lewis J M et al. 1999 Full-scale measurements of the oryx neptune
production spar platform performance Offshore Technology Conference (Offshore Technology Conference)[13] Saito M, Kato S, Ohkawa Y et al. 1993 Free decaying test and simulation of slow drift motion of prototype
floating structure” poseidon” The Third International Offshore and Polar Engineering Conference(International Society of Offshore and Polar Engineers)[14] Driscoll F, Jonkman J, Robertson A, Sirnivas S, Skaare B and Nielsen F G 2016 Energy Procedia 94[15] Yoshimoto H, Yoshida H and Kamizawa K 2018 Validation of applicability of low frequency motion analysis
theory using observation data of floating offshore substation ASME 2018 37th International Conferenceon Ocean, Offshore and Arctic Engineering (American Society of Mechanical Engineers Digital Collection)[16] Yoshimoto H and Kamizawa K 2019 Validation of the motion analysis method of floating offshore windturbines using observation data acquired by full scale demonstration project International Conference on
Offshore Mechanics and Arctic Engineering (American Society of Mechanical Engineers)[17] Nakamura A, Hayashi Y and Ichinose H 2018 Verification of load calculation based on site measurementsof a 7mw offshore wind turbine on v-shaped semi-submersible floating structure Grand Renewable Energy
proceedings Japan council for Renewable Energy (Japan Council for Renewable Energy)[18] Komatsu M, Mori H, Tanaka H, Ohta M, Karikomi K and Ishii H 2018 Comparison between measured value
and simulated value of motion and mooring force in mitsubishi 7mw floating offshore wind turbine Grand
Renewable Energy proceedings Japan council for Renewable Energy (Japan Council for Renewable Energy)[19] Stansberg C T and Gudmestad O T 1996 Non-linear random wave kinematics models verified against
measurements in steep waves Tech. rep. American Society of Mechanical Engineers, New York, NY (UnitedStates)[20] OCIMF 1994 Prediction of wind and current loads on vlccs (Oil Companies International Marine Forum
London)[21] Berthelsen P A, Bachynski E E, Karimirad M and Thys M 2016 Real-time hybrid model tests of a bracelesssemi-submersible wind turbine: Part iii—calibration of a numerical model Proc. ASME 2016 35th Int.
Conf. on Ocean, Offshore and Arctic Engineering (American Society of Mechanical Engineers Digital
Collection)[22] Hirai T, Sou A and Nihei Y 2018 Wave load acting on advanced spar in regular waves Proc. ASME 2018
37th Int. Conf. on Ocean, Offshore and Arctic Engineering (American Society of Mechanical Engineers
Digital Collection)[23] Wright C, Yoshimoto H, Wada R and Takagi K 2020 Experimental identification of an advanced spar’s
low frequency drag damping in waves Proc. ASME 2020 39th Int. Conf. on Ocean, Offshore and Arctic
Engineering (American Society of Mechanical Engineers Digital Collection)

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