Irregular Wave Conditions Research Articles

Experimental and numerical study of coupling effects between vessel motion and pipeline tension in deepwater J-laying

During deepwater J-lay operations, the J-lay vessel and pipeline together form a coupled system. The dynamic responses of this system, including the vessel motion and pipeline tension caused by environmental loads, inevitably exhibit coupling effects. This paper describes the results of experimental and numerical studies conducted to investigate the effects of vessel–pipeline coupling on the global dynamic responses of J-lay vessels and pipelines under irregular wave conditions based on practical engineering. Large-scale full-depth experiments of the complete system are conducted in a 10-m-deep wave basin. The similarity of both the submerged unit weight and pipeline stiffness is considered in the design of the pipeline model. Numerical simulations are performed to further investigate the coupling effects on the dynamic characteristics of vessel motion and pipeline tension, and to analyze the coupling effects of J-lay operations in greater water depths. The results reveal that the coupling effects between the J-lay vessel and the pipeline are nonnegligible for both the vessel motion and pipeline tension responses in J-lay operations. The influence of these coupling effects is strongly related to the operation depth and pipeline properties. Overall, this study provides a reference for the design of J-lay systems and the development of J-lay simulation models.

Hydrodynamic analysis and validation of the floating DeepCwind semi-submersible under 3-h irregular wave with the HOS and CFD coupling method

Recent studies, such as the Offshore Code Comparison, Collaboration, Continued, with Correlation (OC5) led by NREL, have identified significant under-prediction of low-frequency pitch and surge responses in the DeepCwind semi-submersible platform when comparing model test results with predictions from engineering tools like OpenFAST, which rely on potential flow theory assumptions for hydrodynamics. To address this mismatch, a newer experimental campaign was conducted as part of the OC6 Phase 1A study. In this work, a coupling numerical approach was employed to replicate various scenarios of the floating DeepCwind semi-submersible, including decay, regular, and 3-h irregular waves, which were explored during the OC6 Phase 1A model testing. The numerical technique involved utilizing far-field nonlinear waves simulated using the High-Order Spectral (HOS) method and applying them to a near-field Computational Fluid Dynamics (CFD) domain. This allowed for the solution of wave-structure interactions using the overset mesh capabilities of StarCCM+. The critical hydrodynamic responses of the freely floating DeepCwind semi-submersible were modeled and validated against the model test results. The results obtained from the coupling approach were then presented and compared with simulations using OpenFAST and results from other researchers. The coupling strategy demonstrated improved agreement, especially for low-frequency responses in surge and pitch motion, under the 3-h irregular wave conditions, compared to OpenFAST simulations. While the validation investigation showed overall success in capturing low-frequency and wave-frequency surge and heave motion, there was an underestimation of low-frequency pitch motion in the TCOMS coupling tool. This underprediction can be attributed, at least in part, to the effect of wave overtopping on the rear columns, which resulted in deviations from the experimental pitch motion, particularly during extreme events.

SIMULATIONS OF EXTREME WAVE LOAD ON AN OSCILLATING WATER COLUMN WAVE ENERGY CONVERTER

Extreme load analysis is an essential step in the design of structural and mooring systems for wave energy converters (WEC). The current study aims to evaluate the structural loads on the MARMOK Oscillating Water Column (OWC) WEC under both regular and irregular wave conditions, as well as to evaluate the effectiveness of its station keeping (mooring) systems. The project employs the open source computational fluid dynamics simulation software OpenFOAM to model the fully moored floating system. The WEC device hydrodynamics are validated against laboratory data for free decay in heave and pitch motions. In addition, the station keeping model is validated against mooring tension static offset tests and benchmarked against experimental data in irregular waves. An elegant method of numerically recreating irregular wave inflow conditions from empirical measurements is shown which allows for consistent comparison between the model and experimental results. The calibrated numerical model is then employed to study the full-scale system’s responses. Preliminary results of structural loadings on the fixed and floating spar buoy (with one mooring configuration as sample) are presented in the paper.

Numerical performance assessment of a new wave energy conversion system

The greater wave energy content in deeper waters has initiated substantial research in offshore wave energy converters (WECs). However, the existing WECs are hindered by their high initial costs, primarily attributed to the demanding mechanical workloads they endure. This paper describes a novel wave energy conversion system developed at IST for deep waters (around 20-50 meters) based on a floater and a ballast, suspended by a set of cables. In the novel approach, the WEC is made up essentially by membranes, without a rigid structure, thus reducing the initial cost of investment comparing to other solutions.A simplified numerical model in the time-domain of the system based on linear theory is developed and a preliminary performance assessment under regular and irregular wave conditions (for conditions prevalent along the western coast of Portugal) is performed. Additionally, the effect of the ballast mass is considered. The results reveal the system's non-linear behavior during the floater's ascending phase and emphasize the significant influence of the ballast's mass on power production.

Overview of an experimental campaign for arrays of wave energy conversion systems

It is already well-known that the vast energy available in ocean waves can provide a massive contribution towards effective decarbonisation. Nonetheless, due to the irregular reciprocating motion of ocean waves, convergence towards a single type of technology becomes rather difficult, and tailored research, aiming at ultimately providing reliable WEC systems, is still required to achieve commercialisation.
 Once a given concept is established, numerical models become almost automatically required for a (very) large variety of tasks, including e.g. dynamical and performance assessment, control technology, geometry optimisation, and mooring design, among others. Depending on the requirements associated with a specific task, different types of models are used, with very different levels of complexity (both computational and analytical) and fidelity. For instance, a fully nonlinear estimation of the hydrodynamic response of a WEC would often require high-fidelity numerical modelling techniques, based on e.g. computational fluid-dynamics (CFD), while control applications prefer analytical expressions able to capture the main underlying dynamics in a simplified form.
 Regardless of the associated complexity, validation is always required for the reliable utilisation of a specific model for a given application, with experimental validation being the most valuable tool to secure this objective. In recent years, different initiatives were put in place, aiming at the identification of numerical model accuracy through a set of widely available case studies. For instance, the OES-Task 10 has been running a number of experiments followed by blind numerical model validations for several single-body wave energy converters. While the proposed methodologies proved to be efficient, the cases under study are all focused on single-body devices.
 Since the sector is slowly approaching a pre-commercial stage, it is important to prove the capabilities of numerical models also for farm configurations which are, ultimately, the way in which WEC systems will be effectively deployed. Motivated by this, we present, in this paper, an overview of an experimental campaign performed at Aalborg University during the period of September-October 2021, where 8 different array layouts of up to 5 devices have been tested, using a 1:20 prototype of the Wavestar WEC system as a baseline device (see PDF file for reference). Data has been collected systematically for regular and irregular wave conditions, including e.g. free-surface elevation at different points in the wave tank (with 19 wave probes in place), effective wave excitation forces acting on each device and layout, and associated motion variables. Furthermore, each different layout has been also tested under (reactive) controlled conditions, providing experimental data on PTO forces and associated motion (i.e. under controlled conditions). The results of this experimental campaign will be available as part of an Open-Access dataset, being an extremely valuable tool for reliable modelling within the WEC research/industrial community.
 This paper intends to provide a detailed account of the technical aspects concerning the full experimental campaign, including setup, test design, synergies between collected data, and examples of how these results can be used to validate a variety of models, from different input/output points, depending on the requirement of each specific application.

Experimental measurements of two elastic taut-slack mooring configurations for the multi-float M4 WEC

Moorings are a vital and often problematic component of any floating offshore renewable energy system, whether for wind or wave energy conversion, and here we consider the multi-float WEC system M4 in a 122 configuration. Previous experimental work has shown elastic cables to reduce extreme snap loads by a factor of about 6 when considering single cables between the bow float and a mooring buoy, and between the mooring buoy and the bed [1]. Here we compare results for two alternative configurations designed to reduce the mooring footprint as well as extreme snap loads. The first system, shown in Figure 1 (a), consists of a large surface buoy connected to the seabed with three equi-spaced elastic cables in pre-tension, with a single elastic cable to the bow float. The second system, shown in Figure 1 (b) has a smaller submerged buoy, again connected to the seabed with three equi-spaced elastic cables in pre-tension, however, this is connected to a smaller surface buoy which is subsequently connected to the bow float. Both systems are taut-slack. In this paper we present experimental measurements taken at the COAST laboratory at the University of Plymouth. Both configurations are tested in irregular (JONSWAP) wave conditions up to limiting steepness, with run times of 35 mins at 1:40 scale or about 3.5 hours full scale. Peak, mean and rms bed loads for both configurations are presented along with rms and peak relative angular pitch response with drive train disengaged (free hinge between mid and stern floats).
 References[1] P. Stansby et al., “Experimental study of mooring forces on the multi-float WEC M4 in large waves with buoy and elastic cables,” Ocean Eng., vol. 266, no. P4, p. 113049, 2022.

Laboratory Investigation of Hydrodynamic and Sand Dune Morphology Changes Under Wave Overwash

AbstractSince the field measurement of wave overwash is difficult to obtain during severe storms, a laboratory experiment is conducted to measure the time and space evolution of the overwash and beach profile over the sand dune continuously using high‐speed video image analysis for different wave conditions of irregular waves and solitary waves. Characteristics of the cross‐shore sediment transport and morphology change are discussed from the laboratory experiment data. The inflection point, which marks the shifting turn in dune crest movement during overwash, is determined by analyzing feature points in the variation of dune geometry. It is confirmed that the overwash water volume rate reaches a maximum value when the inflection point occurs. Additionally, the overwash water volume is found to be linearly related to the deposited sediment volume, and the dune erosion volume is proportional to wave energy flux during the overwash process. The presence of secondary dunes is found to significantly alleviate coast erosion during overwash and reduce shoreline retreat by more than 40%, regardless of the height of the secondary dune crest. Furthermore, the advances and limitations in overwash hydrodynamics are discussed. It is recommended that this continuous morphological change monitoring data be combined with a wave resolution model for detailed hydrodynamic simulations to further understand the overwash process.

Experimental Study on Submerged Horizontal Perforated Plates under Irregular Wave Conditions

This study presents novel analytical solutions for analyzing wave dissipation effect and bottom flow field characteristics of permeable submerged horizontal plates through physical model trials. The experimental results show that a solid submerged horizontal plate effectively attenuates wave cycles, with a greater periodic attenuation effect at smaller submerged depths. However, this attenuation effect becomes reduced or less pronounced after a certain threshold. Selecting an optimal opening ratio becomes key to achieving the desired cycle attenuation. When the inundation depth of the horizontal plate is large, the wave dissipation effect is weak. Reducing the opening rate can improve the wave dissipation effect, but only to a certain extent. Under irregular wave actions, the velocity field of the submerged horizontal plate is uniformly distributed. The relative submerged depth has minimal effect on the maximum flow velocity and root mean square flow velocity. Increasing the wave height and increasing the open holes on a plate can improve the flow velocity at the bottom of the plate. However, increasing the opening ratio also leads to insignificant changes in flow velocity. A correlation between the transmission coefficient of the open plate and the maximum flow velocity has also been determined. The findings of this paper serve as a research foundation for the implementation of submerged horizontal plate wave dissipation structures in engineering.

Effect of floater flexibility on global dynamic responses of a 15-MW semi-submersible floating wind turbine

Floater structural flexibility plays a significant role in accurate predictions of global dynamic responses of floating wind turbines (FWTs), especially for ultra-large wind turbines with increasing size and cost-effective floater design. The conventional analysis of FWTs often considers the floater as one rigid body, which cannot capture the correct resonant responses of the floater (especially the column that supports the tower). In this paper, a new approach where the floater is divided into multiple rigid bodies connected by flexible beams is developed for advanced modelling of flexible floaters in combination with coupled time-domain simulations. The hydrostatic and hydrodynmaic loads on each body from a one-body hydrodynamic analysis, together with gravitational loads and inertial loads, are implemented in the beam-based finite element model of the floater to carry out a time-domain analysis. The proposed approach is used to compare the responses of a 15-MW semi-submersible FWT considering a rigid and a flexible floater. The inclusion of floater flexibility reduces the tower natural frequency. It leads to larger bending moment amplitudes at the tower base close to the tower bending natural frequency, particularly in only-wind, irregular wave and wind-wave conditions, but smaller dynamic responses in regular wave conditions.

Artificial neural network framework for prediction of hydroelastic response of very large floating structure

The response of a very large floating structure (VLFS) must take into consideration the elastic deformation of the structure (commonly termed hydroelastic response) under wave action. Conventionally, the hydroelastic response could be computed by using the coupled finite element-boundary element (FE-BE) method, where the mat-like structure is modelled using plate theory and the water modelled using the potential theory. The FE-BE method requires the structure to be discretised into finer elements and the wetted surface boundary to be represented by smaller panels to accurately capture the hydroelastic response of the structure. Thus, the coupled FE-BE method could be computationally expensive when the structure gets larger or when subjected to waves of smaller wavelengths. To accelerate the computational time in predicting the hydroelastic response of the VLFS, a surrogate model trained using the feed-forward neural network is proposed. The hydroelastic responses under different wavelengths, structural stiffnesses and wave directions are first generated where these data are split into three groups for training, validation, and testing (prediction) purposes. The accuracy of the prediction in terms of correlation coefficient R is compared for the different train datasets, the number of neurons and hidden layers as well as the optimisation techniques. The finding shows that an accuracy of close to 99% to the ground truth could be achieved with only 80% of the train dataset. The hydroelastic response under irregular wave conditions predicted using the feed-forward neural network framework is also presented.

Design of an electrical energy storage system for hybrid diesel electric ship propulsion aimed at load levelling in irregular wave conditions

This paper focuses on the design stage of an electrical energy storage system which is intended to be used to level the power required by ships for propulsion when sailing in irregular seas. Particularly, a preliminary analysis has been carried out aimed at choosing, between two storage technologies namely battery and ultracapacitor, the more adequate storage system for the levelling action with respect to the period of the sea waves. A sizing procedure based upon a Hilbert transform decomposition of load demand is used. More specifically, a specified threshold frequency has been identified such that, power fluctuations related to irregular seas which are characterized by frequencies higher than the specified threshold, indicate the ultracapacitor as the more appropriate device for load levelling. For sizing the storage device, the load demand has been decomposed into two signals without overlapping frequencies. An optimal control strategy is proposed, by exploiting the decomposition of the load power, which allows simulating ultracapacitor real-time operation within the previously determined size constraints. Numerical results have been carried out referring to a Ro-Pax ferry powered by an electrical motor.

Numerical Study on Wave Dissipation Performance of OWC-Perforated Floating Breakwater under Irregular Waves

This paper utilizes ANSYS-AQWA hydrodynamic simulation analysis software (2022 R2) to investigate the wave dissipation performance of an Oscillating Water Column (OWC) perforated floating breakwater under irregular wave conditions. The study examines the effect of spacing, width of the OWC opening, water depth, incident wave angle, and significant wave height on the wave dissipation performance of the floating breakwater. The results indicate that the wave dissipation performance of the OWC-perforated floating breakwater surpasses that of similar structures. The transmission coefficient is significantly influenced by spacing and water depth when subjected to irregular waves. The width of the OWC opening also affects the wave dissipation to some extent, with wider openings demonstrating improved performance in the case of long-period waves. The incident wave angle of 0 degrees yields enhanced wave dissipation performance. Although the meaningful wave height has minimal impact on wave dissipation, it increases proportionally with the rise in meaningful wave height. This study offers valuable insights for the design and implementation of floating breakwaters and holds significant practical implications for the research on integrated devices combining floating breakwaters and wave power generation.

Real-time control of ship's roll motion with gyrostabilisers

The safety of ship manoeuvring operations is greatly affected by large roll motions under severe wave conditions. While existing studies have focused on optimizing hydrodynamic performance devices, these approaches may not be effective under realistic sea conditions where wave frequency and direction are irregular. Thus, predicting ship motion tendencies and implementing a reasonable control approach is crucial for improving ship safety. This study proposes a novel and practical control strategy that can effectively suppress roll motion of ships under realistic random wave conditions. The approach utilizes a real-time controller based on model predictive control (MPC) that is actuated by a dual gyrostabilizer. The ship's roll motion response in beam waves is calculated using one degree-of-freedom hydrodynamic modeling, and the wave memory effect is taken into consideration by employing system identification. A synthetic mathematical model of MPC and the dual gyrostabilizer method is introduced in state-space representation to compensate for wave excitation moment in real-time. The proposed method's efficacy is validated by comparing with a roll stabilization scenario of a particular ship in the literature, and control performance of a standard ship under regular and irregular wave conditions is separately discussed. Results indicate that the proposed method can significantly reduce roll motion amplitude and is feasible for nonlinear ship motion control problems. This study sheds light on the multi-degree-of-freedom motion control of ships under beam wave conditions.

Numerical simulation of a full spine of Edinburgh Duck modules in uni- and multi-directional irregular wave climates, with a view to design optimisation

Long, flexibly-jointed spines of Edinburgh Duck modules have the potential to enable the extraction of a large proportion of the wave energy from our seas and oceans. It is well-known that the ‘duck’ shape is able to efficiently absorb wave energy, and that jointed but controlled interconnections between ducks as part of a full spine can also benefit the performance. However, in order to progress further towards achieving optimal performance in real wave climates, a greater understanding of the significance of the spine configuration and scale, spine orientation, and directional, irregular wave conditions is required. By using an efficient hydrodynamic model of a ten-duck spine in conjunction with a constrained frequency-domain control strategy, this paper investigates the effects of the above factors on device performance (as a function of power extraction) in uni- and multi-directional versions of an irregular wave climate. A series of inferences are drawn from the simulations and discussed with regards to informing the direction of future duck spine designs.

Experimental comparison of a dual-spar floating wind farm with shared mooring against a single floating wind turbine under wave conditions

Shared mooring can potentially be a cost-reduction factor for future floating wind farms. To assess the effect of shared mooring on the response dynamics of floating wind turbines (FWTs), experiments have been conducted for two spar FWTs with a shared mooring configuration and for a single spar FWT with catenary mooring, both at a scale of 1:47. Various regular and irregular wave conditions were tested and only one wave heading was considered. From the test results, the response amplitude operators and response spectra of platform motions and statistics of mooring tensions are compared for the two configurations. In the extreme wave condition, the shared mooring configuration leads to a 40% increase in the platform surge motion compared with the single spar FWT. Still, the absolute offset is within allowable limits prescribed by power cables. The fairlead tensions of the anchor lines are not significantly increased in the shared mooring configurations, but the shared line shows extreme tension peak events that are seldom present in the anchor lines. This study demonstrates the technological promises and challenges of a shared mooring system from an experimental perspective. Results and videos are made available and can be used to validate numerical models.

Modelling and Control Tank Testing Validation for Attenuator Type Wave Energy Converter - Part II: Linear Noncausal Optimal Control and Deterministic Sea Wave Prediction Tank Testing

Tank testing results from applying Linear non-causal optimal control (LNOC) to the Mocean M100 wave energy converter (WEC) are presented in this paper. Based on the two state-space models derived from Part I, two LNOC algorithms designed to increase power capture of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1/20$</tex-math></inline-formula> scaled M100 WEC prototype are tested separately in real-time under various irregular wave conditions. The deterministic sea wave prediction (DSWP) algorithm is employed to provide the required wave elevation/excitation force predictions for the LNOC using real-time wave measurements. Experimental data shows that the DSWP can predict the incoming waves with sufficiently high accuracy in various sea states. Compared with a well-tuned passive damper, LNOC based on a hydrodynamic model increases the power capture by up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$128\%$</tex-math></inline-formula> while LNOC based on a system identification (SysID) model increases the power capture by up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$323\%$</tex-math></inline-formula> . The technologies are transferrable. The testing procedure and the results also provide informative guidance for the tank testing of other advanced optimal controllers and their implementations on other types of WECs.

Large-scale experimental study on scour around offshore monopile under combined wave and current condition

This work conducts large scale (1:13) experiments to study local scour around a monopile under combined irregular wave and current condition. The Keulegan–Carpenter (KC) numbers range from 1.1 to 6.73, and the relative current strength parameter Ucw numbers range from 0.17 to 0.77. The large-scale experiment indicates the 3D shape of scour holes is always an inverted cone under wave-current condition which has nothing to do with wave irregularity and Ucw. The changes of maximum scour location are associated with KC and Ucw numbers. The location of maximum scour depth is shifted from upstream to downstream of the monopile with large KC number under current-dominated condition. The characteristic scour timescale is closely related to KC, Ucw and Shields parameter θw when Ucw<0.3 and may be only related to θw when Ucw>0.7. The equilibrium scour depth is a function of vortex scale parameter referring to KC and Ucw numbers. A change in the definition of KC can improve the accuracy of existing formula under large-scale experimental condition, and scour volume formulae are further proposed from the relation with maximum scour depth. Finally, a scour volume formula of KC and Ucw numbers is suggested to estimate the protection material amount around monopile.

Performance of a hybrid TLP floating wind turbine combined with arrays of heaving point absorbers

In the present study, the hydrodynamic performance of circular and concentric arrangements of cone-cylinder-type heaving point absorbers around a Submerged Tension-Leg Platform (STLP) is analysed using the numerical model in the frequency domain based on the potential flow theory. The presence of the Wave Energy Converters (WECs) around the STLP floating wind turbine platform affects the hydrodynamic performance of the hybrid floating platform. So to illustrate the effects of WECs on the platform, the ratio of hydrodynamic coefficients for a single WEC system to that for a hybrid system is analysed. An array of heaving point absorbers is placed in circular and concentric patterns to understand the performance of heaving point absorbers in the absorption of wave energy. The cone-cylinder type heaving point absorber is selected for the present study as they yield more power as compared to other shaped point absorbers. The study compares the wave power absorption of each point absorber around the platform for irregular wave conditions of the North Sea. The effect of incoming waves is illustrated by analysing four different wave heading angles. To quantify the performance of the WECs in an array, the q-factor and coefficient of variation are studied for each array at different sea states. The study suggested the best possible arrangement pattern for wave power absorption and power uniformity among the floaters in the array. The study performed will be helpful in the design and analysis of the possible arrangement of point absorbers around the floating wind turbine platform for wave power absorption.

Design and model test of a soft-connected lattice-structured floating solar photovoltaic concept for harsh offshore conditions

Various types of floating solar photovoltaic (FPV) devices have been previously proposed, designed and constructed with applications primarily limited to onshore water bodies or near-shore regions with benign environmental conditions. This paper proposes a novel FPV concept which can survive harsh environmental conditions with extreme wave heights above 10 m. This concept uses standardised lightweight semi-submersible floats made of circular materials as individual modules. The floating modules are soft connected with ropes to form an FPV array. We first present the conceptual design of the floats and the connection systems, including hydrostatic, hydrodynamic, and structural assessments of the floats. To verify the motion response performance, we carried out 1:60 scaled model tests for a 2 by 3 array under regular and irregular wave conditions. From the time series and response spectra, the motion characteristics of the array and the mooring responses are analysed in detail. The proposed concept exhibits excellent performances in terms of modular motions with limited wave overtopping and no contact is observed between adjacent modules under the extreme wave conditions. The findings of this study can serve as a valuable reference to developing reliable and cost-effective FPV technologies for offshore conditions.

Predictive Control of a Heaving Compensation System Based on Machine Learning Prediction Algorithm

Floating structures have become a major part of offshore structure communities as offshore engineering moves from shallow waters to deeper ones. Floating installation ships or platforms are widely used in these engineering operations. Unexpected wave-induced motions affect floating structures, especially in harsh sea conditions. Horizontal motions on the sea surface can be offset by a dynamic positioning system, and heave motions can be controlled by a heave compensation system. Active heave compensation (AHC) systems are applied to control vertical heave motions and improve safety and efficiency. Predictive control based on machine learning prediction algorithms further improves the performance of active heave compensation control systems. This study proposes a predictive control strategy for an active heave compensation system with a machine learning prediction algorithm to minimise the heave motion of crane payload. A predictive active compensation model is presented to verify the proposed predictive control strategy, and proportion–integration–differentiation control with predictive control is adopted. The reliability of back propagation neural network (BPNN) and long short-term memory recurrent neural network (LSTM RNN) prediction algorithms is proven. The influence of the predictive error on compensation performance is analysed by comparing predictive feedforward cases with actual-data feedforward cases. Predictive feedforward control with regular and irregular wave conditions is discussed, and the possible strategies are examined. After implementing the proposed predictive control strategy based on a machine learning algorithm in an active heave compensation system, the heave motion of the payload is reduced considerably. This investigation is expected to contribute to the motion control strategy of floating structures.