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Fatigue limit state design check based on S-N curve and Palmgren-Miner rule approach is required by design standards for floating wind turbines since floating wind turbines are subjected cyclically varying environmental loads. Fatigue damage over a given period could be considered as a summation of short-term fatigue damage of each stationary environmental condition multiplying by the number of occurrence of the environmental condition during the given period. In reality, environmental condition varies continuously. While fatigue damage due to transient load processes that are induced by startup and shutdown operations cannot be captured by this conventional approach. Large data bases of real-time measurements show shutdown and startup operations may appear in any operational conditions and the number of the operations could be considerable. Analysis for startup and shutdown operations induced fatigue damage is required by standards for offshore wind turbines. However, relevant publications addressing this issue are very limited in particular for floating wind turbines. In contrast to bottom fixed wind turbines, floating wind turbines have rigid-body motions in 6 d.o.f.s, while the floating wind turbine hulls are moored by mooring lines rather than directly mounted on sea bed or land. This paper focuses on shedding light on the importance of startup and shutdown induced transient load processes on fatigue damage in the tower of two MW-level horizontal axis semi-submersible wind turbines by comparing short-term fatigue damage in several environmental conditions with and without transient load processes induced by startup and shutdown of the wind turbines. In some situations, 4,600 seconds short-term fatigue damage may be dominated by the transient load process induced fatigue damage which may make the fatigue damage be increased by up to 300%, while in many cases, the fatigue damage may be increased by 10% to 100%. The importance of the transient load processes on long-term fatigue damage is related to occurrence frequency of startup and shutdown events and needs more analysis in future.

A coupled numerical model has been developed and validated to study the fluid–structural interaction responses of a three-bladed tidal turbine in aligned waves and current. The unsteady blade element momentum (BEM) theory was combined with modal analysis for hydro-elastic calculation. Both the loading and deflection of the blade were studied. The dynamic loading on the blade due to structural deformation was much smaller than the wave-induced loading under linear wave conditions for the given condition. The linear response amplitude operators (RAOs) of the loads and the blade tip deflections were obtained and used to predict the linear responses. Although both sum- and difference-frequency responses can be identified from time domain simulations, the wave-induced load and the deflection of the blade are dominated by the first-order contributions. The maximum deflection of the blade tip could reach 1.3 m (203% of the means) in the flapwise direction and 0.35 m (210% of the mean) in the edgewise direction with a wave peak period of 11.3 s and a significant wave height of 5.5 m.

Common industrial practice for designing floating wind turbines is to set an operational limit for the tower-top axial acceleration, normally in the range of 0.2–0.3 g, which is typically understood to be related to the safety of turbine components. This paper investigates the rationality of the tower-top acceleration limit by evaluating the correlation between acceleration and drivetrain responses. A 5-MW reference drivetrain is selected and modeled on a spar-type floating wind turbine in 320 m water depth. A range of environmental conditions are selected based on the long-term distribution of wind speed, significant wave height, and peak period from hindcast data for the Northern North Sea. For each condition, global analysis using an aero-hydro-servo-elastic tool is carried out for six one-hour realizations. The global analysis results provide useful information on their own—regarding the correlation between environmental condition and tower top acceleration, and the correlation between tower top acceleration and other responses of interest—which are used as input in a decoupled analysis approach. The load effects and motions from the global analysis are applied on a detailed drivetrain model in a multibody system (MBS) analysis tool. The local responses on bearings are then obtained from MBS analysis and postprocessed for the correlation study. Although the maximum acceleration provides a good indication of the wave-induced loads, it is not seen to be a good predictor for significant fatigue damage on the main bearings in this case.

This paper presents a time-domain hydroelastic analysis method for bridges supported by floating pontoons in inhomogeneous wave conditions. The inhomogeneous wave effect is accounted for by adopting different wave spectra over different regions along the structure, then the time history of inhomogeneous first-order wave excitation forces on the floating pontoons can be obtained. The frequency-domain hydrodynamic coefficients are transformed into the time-domain hydroelastic model using Cummins' equations. The linear hydroelastic responses of a curved floating bridge with end supports, subjected to irregular waves with spatially varying significant wave heights and peak periods, are investigated. Moreover, sensitive analyses are performed to study the effects of the inhomogeneity on the hydroelastic responses. The primary results indicate that the inhomogeneity of the waves has a significant effect on the dynamic responses of the floating bridge.

Designing reliable and cost-effective floating bridges for wide and deep fjords is very challenging. The floating bridge is subjected to various environmental loads, such as wind, wave, and current loads. All these loads and associated load effects should be properly evaluated for ultimate limit state design check. In this study, the wind-, wave-, and current-induced load effects are comprehensively investigated for an end-anchored curved floating bridge, which was an early concept for crossing the Bjørnafjorden. The considered floating bridge is about 4600 m long and consists of a cable-stayed high bridge part and a pontoon-supported low bridge part. It also has a large number of eigen-modes, which might be excited by the environmental loads. Modeling of wind loads on the bridge girder is first studied, indicating that apart from aerodynamic drag force, aerodynamic lift and moment on the bridge girder should also be considered due to their significant contribution to axial force. Turbulent wind spectrum and spatial coherence play an important role and should also be properly determined. The sway motion, axial force, and strong axis bending moment of the bridge girder are mainly induced by wind loads, while the heave motion, weak axis bending moment, and torsional moment are mainly induced by wave loads. Turbulent wind can cause significant larger low-frequency eigen-mode resonant responses than the second-order difference frequency wave loads. Current loads mainly contribute damping and reduce the variations of sway motion, axial force, and strong axis bending moment.

In this paper, a methodology suitable for assessing the allowable sea states for installation of a transition piece (TP) onto a monopile (MP) foundation with focus on the docking operation is proposed. The TP installation procedure together with numerical analyses is used to identify critical and restricting events and their corresponding limiting parameters. For critical installation phases, existing numerical solutions based on frequency and time domain (TD) analyses of stationary processes are combined to quickly assess characteristic values of dynamic responses of limiting parameters for any given sea state. These results are compared against (nonlinear and nonstationary) time domain simulations of the actual docking operations. It is found that a critical event is the structural damage of the TP's bracket supports due to the potential large impact forces or velocities, and a restricting installation event (not critical) is the unsuccessful mating operation due to large horizontal motions of the TP bottom. By comparing characteristic values of dynamic responses with their allowable limits, the allowable sea states are established. Contact–impact problems are addressed in terms of assumed allowable impact velocities of the colliding objects. A possible automatic motion compensation system and human actions are not modeled. This methodology can also be used in connection with other mating operations such as float-over and topside installation.

Offshore wind turbines (OWTs) might be subjected to seismic loads with different peak accelerations during operation in the actively seismic regions. The earthquakes might be a potential risk for the OWTs due to its stochastic nature. Earthquake with wind and wave loads could act on OWT at the same time; thus, the structural responses of such OWTs should be analyzed taking into consideration the reasonable load combinations. Based on the hydro-elastic similarity, an integrated model of the combined National Renewable Energy Laboratory (NREL) 5 MW wind turbine and a practical pentapod substructure is designed for testing. The governing equations of motion of the integrated OWT are established. The dynamic tests and numerical analysis of the OWT model are performed under different combinations of seismic, wind, and sea load conditions. The El Centro and American Petroleum Institute (API)-based synthesized seismic waves with different peak ground accelerations (PGAs) are considered in this study. The numerical results are in good agreement with the experimental ones. The coupling effect of the OWT structure under the combined load conditions is demonstrated from the experimental and numerical results. The results indicate that the interaction of earthquake, wind, wave, and current should be taken into account in order to obtain proper structural response, especially with small PGA.

Installation of offshore wind turbines (OWTs) requires careful planning to reduce costs and minimize associated risks. The purpose of this paper is to present a method for assessing the allowable sea states for the initial hammering process (shallow penetrations in the seabed) of a monopile (MP) using a heavy lift floating vessel (HLV) for use in the planning of the operation. This method combines the commonly used installation procedure and the time-domain simulations of the sequential installation activities. The purpose of the time-domain simulation is to quantitatively study the system dynamic responses to identify critical events that may jeopardize the installation and the corresponding limiting response parameters. Based on the allowable limits and the characteristic values of the limiting response parameters, a methodology to find the allowable sea states is proposed. Case studies are presented to show the application of the methodology. The numerical model of the dynamic HLV–MP system includes the coupling between HLV and MP via a gripper device, and soil–MP interaction at different MP penetration depths. It is found that the limiting parameters are the gripper force and the inclination of the MP. The systematic approach proposed herein is general and applies to other marine operations.

The one-dimensional fast Fourier transform (FFT) has been applied extensively to simulate Gaussian random wave elevations and water particle kinematics. The actual sea elevations/kinematics exhibit non-Gaussian characteristics that can be represented mathematically by a second-order random wave theory. The elevations/kinematics formulations contain frequency sum and difference terms that usually lead to expensive time-domain dynamic analyses of offshore structural responses. This study aims at a direct and efficient two-dimensional FFT algorithm for simulating the frequency sum terms. For the frequency-difference terms, inverse FFT and forward FFT are implemented, respectively, across the two dimensions of the wave interaction matrix. Given specified wave conditions, the statistics of simulated elevations/kinematics compare well with not only the empirical fits but also the analytical solutions based on a modified eigenvalue/eigenvector approach, while the computational effort of simulation is very economical. In addition, the stochastic analyses in both time domain and frequency domain show that, attributable to the second-order nonlinear wave effects, the near-surface Morison force and induced linear oscillator response are more non-Gaussian than those subjected to Gaussian random waves.

Hooking events, defined as trawling gear becoming firmly “stuck” under a pipeline, rarely occur during bottom-trawling operations. However, hooking events can have detrimental consequences. There is no existing method for quantifying the hooking probability of bottom-trawling operations. In this study, an approach is proposed to quantify the trawl board hooking probability using simulation tools and statistical data. Numerical simulation use the SIMLA code to establish simplified hooking criteria. The criteria link the pipeline data to the fishing activities data, enabling the quantification of hooking probability. First, the numerical simulations of both pull-over and hooking events were compared with small-scale model test results. Reasonable agreement was reached. Based on the simulation results, simplified criteria for trawl board hooking were proposed. Finally, data from the EUROPIPE II pipeline section in the Norwegian sector were used as a case study. Data regarding free span as well as fishing activities in that region were used to obtain the statistical input. The Monte Carlo simulation technique was then used to estimate the hooking probability. Parametric studies were first performed to investigate the effects of important parameters. Then, based on the findings from the parametric studies, the hooking probability with the most reasonable parameters was estimated.

Hydrodynamic effects in ship collisions are usually considered by increased inertia force in the form of the equivalent added mass. It is necessary to reasonably estimate the equivalent added mass to calculate energy absorbed by ships in collisions. In this paper, motion equations in the horizontal plane for the struck rigid ship are first established considering hydrodynamic effects in the form of added mass, linear and quadratic damping. The equivalent added mass are obtained in three ways and analyzed. It is shown that the equivalent added mass for the sway motion depends on not only the duration of collision impact, impact force, but also the collision position, while the equivalent added mass for the yaw motion could be assumed to be independent of the collision position. In addition, a simple formula is proposed to relate the equivalent added mass for part of the vessel to that of the whole vessel, provided that the underwater area of the transverse section is known. As a consequence, it is possible to estimate rigid hull girder responses based on the simplified methodology, which could be used in design and probabilistic collision analyses. In the end, the hull girder responses are estimated considering both a flexible and rigid vessel. Comparisons are made between rigid and flexible hull girder responses.Copyright © 2010 by ASME

This paper investigates the effect of a passive and reactive control mechanism on the accumulated fatigue damage of a wave energy converter (WEC). Interest is focused on four structural details of the Wavestar arm, which is used as a case study here. The fatigue model is set up as an independent and generic toolbox, which can be applied to any other global response model of a WEC device combined with a control system. The stress responses due to the stochastic wave loads are computed by a finite element method (FEM) model using the frequency-domain approach. The fatigue damage is calculated based on the spectral-based fatigue analysis in which the fatigue is described by the given spectral moments of the stress response. The question will be discussed, which control case is more favorable regarding the tradeoff between fatigue damage reduction and increased power production.

This study addresses numerical modeling and time-domain simulations of the lowering operation for installation of an offshore wind turbine monopile (MP) with a diameter of 5.7 m and examines the nonstationary dynamic responses of the lifting system in irregular waves. Due to the time-varying properties of the system and the resulting nonstationary dynamic responses, numerical simulation of the entire lowering process is challenging to model. For slender structures, strip theory is usually applied to calculate the excitation forces based on Morison's formula with changing draft. However, this method neglects the potential damping of the structure and may overestimate the responses even in relatively long waves. Correct damping is particularly important for the resonance motions of the lifting system. On the other hand, although the traditional panel method takes care of the diffraction and radiation, it is based on steady-state condition and is not valid in the nonstationary situation, as in this case in which the monopile is lowered continuously. Therefore, this paper has two objectives. The first objective is to examine the importance of the diffraction and radiation of the monopile in the current lifting model. The second objective is to develop a new approach to address this behavior more accurately. Based on the strip theory and Morison's formula, the proposed method accounts for the radiation damping of the structure during the lowering process in the time-domain. Comparative studies between different methods are presented, and the differences in response using two types of installation vessel in the numerical model are also investigated.

The design of wind turbines requires information about joint data for wind and wave conditions. Moreover, combining offshore wind and wave energy facilities is a potential way to reduce the cost of offshore wind farms. To design combined offshore renewable energy concepts, it is important to choose sites where both wind and wave energy resources are substantial. This paper deals with joint environmental data for five European offshore sites which serve as basis for the analysis and comparison of combined renewable energy concepts developed in the EU FP7 project—MARINA Platform. The five sites cover both shallow and deep water, with three sites facing the Atlantic Ocean and two sites in the North Sea. The long-term joint distributions of wind and wave parameters are presented for these sites. Simultaneous hourly mean wind and wave hindcast data from 2001 to 2010 are used as a database. The joint distributions are modeled by fitting analytical distributions to the hindcast data. The long-term joint distributions can be used to estimate the wind and wave power output from each combined concept and to estimate the fatigue lifetime of the structure. The marginal distributions of wind and wave parameters are also provided. Based on the joint distributions, contour surfaces are established for combined wind and wave parameters for which the probability of exceedance corresponds to a return period of 50 years. The design points on the 50-year contour surfaces are suggested for extreme response analysis of combined concepts.

The shutdown of wind turbines may induce excessive loads on the structures and is an important factor to consider in their design. For pitch-regulated turbines, shutdown calls for blade pitching, and one- or two-blade shutdown may occur during pitch actuator failure. Through coupled analysis, this study investigated the dynamic responses of land-based and spar-type floating wind turbines (FWTs) during shutdown. We simulated the shutdown procedures by pitching one, two, or three blades, and by varying the pitch rate. The nonpitching blades have a fixed pitch angle during the process. Three generator torque conditions were considered: (1) grid loss, (2) mechanical braking, and (3) grid connection. The extreme response values and short-term and annual fatigue damages to the structural components were compared against these values under normal operation and parked conditions. Three-blade shutdown is recommended for both turbines. One- or two-blade shutdown with grid loss may result in a significant rotor overspeed and imbalanced loads acting on the rotor plane. Therefore, unfavorable structural responses are observed. Grid connection or mechanical braking alleviates the situation. The land-based turbine is more sensitive to the pitch rate when considering the tower bottom bending moment, but the blade moments and mooring line loads of the spar-type turbine are affected more.

Based on Gaussian load processes, a new formula suitable for evaluating the combined fatigue damage due to high- and low-frequency loads is derived. Then, by using of the Winterstein’s transformation, the developed formula is extended for the combination of non-Gaussian loads. The numerical simulation shows that the predicted damage by the derived formula is very simple to use and close to the rain-flow prediction.

Background. New challenges in LNG shipping, such as ship size growth, trading routes with more severe weather conditions, need for operating with unrestricted filling level and new propulsion systems attract very much attention in marine and offshore oriented community. One of the main concerns is the prediction of loads caused by violent fluid motion in cargo tanks. In the paper we address the problem of determining characteristic extreme values of sloshing pressures for structural design. This involves estimating ship motion in a long-term period, fluid motion in the tank, excited pressures, and relevant structural responses. Method of Approach. Ship motion analysis is based on linear strip theory. In order to investigate the dependence of the sloshing response on sea conditions, an approach based on statistical characteristics of the tank motion is utilized as well as a multimodal approach for fluid motion in a tank. However, an appropriate theoretical/numerical approach, which can be used for a realistic prediction of the most extreme pressure has not yet been developed. Thus, experiments are utilized for the most severe sea states for a chosen tank filling level. Results. Our main contribution in the paper includes the statistical analysis of experimental short term pressure distribution. The choice and fit of probability distribution models is addressed, with due account of different physical mechanisms causing impacts. The models are evaluated. The most critical tank areas for sloshing loads are briefly discussed. Appropriate dynamic response of the tank structure needs to be investigated by accounting for temporal and spatial distribution of sloshing loads. These two factors are also addressed in the paper. The variability of results obtained by processing data from multiple test runs is discussed. Conclusions. The three-parameter Weibull and generalized Pareto statistical models are fitted to the data and evaluated. They prove to accurately describe sloshing excited pressures. However, the highest data points are underestimated by the both distributions. Generalized Pareto model results in more conservative estimates. The threshold level of peaks used in a fit of generalized Pareto distribution was investigated. Based on this, it is set to a level of a 0.85–0.87 quantile of peak values. The big influence of spatial and temporal distribution on the estimates is reported. Uncertainty in measured pressures originating from inherent fluid motion variability exceeds the uncertainty resulting form ship motions' variability. Moreover, generalized Pareto model results in higher variability.

To reduce the occurrence of tanker drive-off, and to reduce the probability of recovery failure should drive-off happen, are two basic principles to reduce FPSO and DP shuttle tanker collision in tandem offloading. In this paper we focus on measures to reduce recovery failure. Previous analyses revealed that recovery failure probability is high due to a lack of time for the DP operator to initiate the recovery action in a tanker drive-off scenario. To increase the time window and to reduce the operator reaction time are therefore two main principles of recovery failure reduction. A substantial increase of the separation distance between FPSO and the tanker, and a possible reduction of the main propeller(s) forward thrust that can be used by the tanker DP system are two measures to increase the time window. The effective reduction of operator reaction time can be achieved by a number of measures, i.e., selection, training, procedure, crew resource management, and automation support, which are designed to improve early detection as well as effectively reduce the DP operator’s time in diagnosis and situation awareness.

Tandem offloading safety between FPSO and shuttle tanker is under concern. A few collisions between the two vessels have happened in the North Sea in recent years. In these incidents, excessive relative motions (termed as surging and yawing in this paper) between FPSO and tanker are identified as “failure prone situations” which have contributed to the initiation of most collision incidents. To quantitatively assess the probability of surging and yawing events, and more importantly, to effectively reduce their occurrence in tandem offloading operation, we present a simulation-based approach in this paper, which is carried out by a state-of-the-art time-domain simulation code SIMO. The SIMO simulation models are setup and calibrated for a typical North Sea purpose-built FPSO and a DP shuttle tanker. This 2-vessel system motion in tandem offloading is simulated. The simulated relative distance and relative heading between FPSO and tanker are analyzed by fitting their extreme values into statistical models. This gives out probabilities of surging and yawing events. Sensitivity studies are performed to analyze contributions from various technical and operational factors. Measures to minimize the occurrence of surging and yawing from design and operational point of view are proposed.Copyright © 2002 by ASME

The current paper deals with a study of a semisubmersible wind turbine (WT), where short-term tower base bending moments and tower fatigue damage were estimated by a frequency domain (FD) method. Both a rigid structure assumption and a generalized degree-of-freedom (DOF) model for including the first flexible mode of the turbine tower were investigated. First, response to wind and wave loads was considered separately, then superposition was used to find the response to combined wind and wave loading. The bending moments and fatigue damage obtained by these methods were compared to results from a fully coupled, nonlinear time domain (TD) analysis. In this study a three column, catenary moored semisubmersible with the NREL 5 MW turbine mounted on one of the columns was modeled. The model was inspired by the WindFloat concept. The TD simulation tool used was Simo-Riflex-AeroDyn from Marintek and CeSOS. The FD method gave a good representation of the tower base bending moment histories for wave-only analyses, for the moderate sea states considered in these analyses. With the assumption that the structure is completely rigid, bending moments were underestimated, but including excitation of the elastic tower and blades, improved the results. The wind-induced low-frequency bending moments were not captured very well, which presumably comes from a combination of nonlinear effects being lost in the linearization of the thrust force and that the aerodynamic damping model was derived for a fixed turbine. Nevertheless, standard deviations of the bending moments were still reasonable. The FD model captured the combined wind and wave analyses quite well when a generalized coordinates model for wind excitation of the first bending mode of the turbine was included. The FD fatigue damage predictions were underestimated by 0–60%, corresponding to discrepancies in standard deviations of stress in the order of 0–20%.

The dynamic responses of a spar, tension leg platform (TLP), and two semisubmersible floating wind turbines (FWTs) in selected misaligned wind and wave conditions are investigated using numerical simulation with an aero-hydro-servo-elastic computational tool. For a range of representative operational conditions, the platform motions and short-term fatigue damage in the tower base and tower top are examined. Although some misalignment conditions result in increased motions both parallel and perpendicular to the wave direction, aligned wind and waves cause the largest short-term tower base fatigue damage for the studied platforms and conditions. Several factors which lead to larger fatigue damage for certain platforms in particular conditions are identified, such as tower resonance due to the 3p blade passing frequency in low wind speeds; surge and pitch motions, particularly in the wave frequency range; and the variations in first-order hydrodynamic loads due to wave direction. A semisubmersible platform with large displacement suffers the least damage at the base of the tower.

Offshore structures are considered as fail safe and inspections are carried out during their service lifetime to assess their actual condition. In this paper, the effect of inspection updating on fatigue reliability of offshore structures is investigated. In particular, the effect of inspection on the reliability of both inspected and uninspected joints is assessed dependent upon the correlation of properties of different joints. The effect of repeated inspections and inspection sample size on fatigue reliability is also investigated. The influence of inspection of certain joints on the reliability of a series system is studied and the effect of system-based updating policy on fatigue reliability is investigated. It is found that the system reliability is significantly affected by the inspection updating policy. [S0892-7219(00)00403-9]

Structural reliability methods are applied to establish a measure of safety for pipelines during laying, and especially to calibrate semi-probabilistic ultimate limit state criteria based on measures of uncertainty, method of reliability, and a given target level. Ultimate collapse of thick tubes under combined external pressure, tension, and bending loads are studied applying the finite element method. Nonlinear effects of large deformations, effects of initial ovality, residual stresses, strain-hardening, yield anisotropy, and loading paths were accounted for in the analysis. A set of interaction equations is proposed. Load effects in the pipelines during installation by the S-lay method are studied. The effects of uncertainties in yield stress, mass, stiffness of the stinger, response amplitude operator and peak period for the wave spectrum were accounted for in the analysis. The major factors affecting strain concentration due to concrete coating are taken into account. A combination of design point calculation and importance sampling procedure is used to calculate the probability of failure. The study includes calibration of partial safety factors for the design format selected. The most important random variable is the model uncertainty for bending capacity, while the uncertainty of the load effect has minor importance for the probability of failure. The system effect is taken into account considering the correlation along the pipeline. The probability of failure is referred both to the total laying period as well as a 3-h period demonstrating that the target level needs to be defined in view of the reference time period. [S0892-7219(00)01501-6]

Recent efforts on wave loads and their structural effects, ultimate and fatigue resistance, and structural reliability issues relating to requalification of jackets are reviewed. The emphasis is on experiences with North Sea structures. [S0892-7219(00)01201-2]

The tension leg platform (TLP) concept is considered to be economically competitive with other offshore production concepts in deepwater locations. The critical part of this concept regarding structural failure is the tether system, in which fatigue is an important failure mode. The present paper presents a computational efficient and general probabilistic procedure for estimating the fatigue reliability of the TLP tether system. Two crack growth rate models of single crack sites are applied. Among uncertainties accounted are those in the long-term stochastic load process, the fatigue strength, and the initial crack sizes.

The ultimate limit state (ULS) is one of the design criteria used in the oil and gas industry in mooring system design for floating platforms. The 100 year level response in the mooring line should be applied for the ULS design check, which is ideally estimated by taking into account the dynamic mooring line tension in all sea states available at the operational site. This approach is known as a full long-term response analysis using the all-sea-state approach. However, this approach is time consuming, and therefore, the contour line method is proposed for estimation of the 100 year response by primarily studying the short-term response for the most unfavorable sea states along the 100 year environmental contour line. Experience in the oil and gas industry confirmed that this method could yield good predictions if the responses at higher percentiles than the median are used. In this paper, the mooring system of a two-body wave energy converter (WEC) is considered. Because this system involves the interaction between two bodies, the estimation of the ULS level response using the all-sea-state approach may be even more time consuming. Therefore, application of the contour line method for this case will certainly be beneficial. However, its feasibility for application to a WEC case must be documented first. In the present paper, the ULS level response in the mooring tension predicted by the contour line method is compared to that estimated by taking into account all sea states. This prediction is achieved by performing coupled time domain mooring analyses using Simo/Riflex for six cases with different mooring configurations and connections between two bodies. An axisymmetric Wavebob-type WEC is chosen for investigation, and the Yeu site in France is assumed as the operational site. Hydrodynamic loads including second-order forces are determined using Wamit. Finally, the applicability of the contour line method for prediction of the ULS level mooring tension for a two-body WEC is assessed and shown to yield accurate results with the proper choice of percentile level for the extreme response.

Floating wind turbines can be the most practical and economical way to extract the vast offshore wind energy resources at deep and intermediate water depths. The Norwegian Ministry of Petroleum and Energy is strongly committed to developing offshore wind technology that utilises available renewable energy sources. As the wind is steadier and stronger over the sea than over land, the wind industry recently moved to offshore areas. Analysis of the structural dynamic response of offshore wind turbines subjected to stochastic wave and wind loads is an important aspect of the assessment of their potential for power production and of their structural integrity. Of the concepts that have been proposed for floating wind turbines, spar-types such as the catenary moored spar (CMS) and tension leg spar (TLS) wind turbines seem to be well-suited to the harsh environmental conditions that exist in the North Sea. Hywind and Sway are two examples of such Norwegian concepts; they are based on the CMS and TLS, respectively. Floating wind turbines are sophisticated structures that are subjected to simultaneous wind and wave actions. The coupled nonlinear structural dynamics and motion response equations of these turbines introduce geometrical nonlinearities through the relative motions and velocities. Moreover, the hydrodynamic and aerodynamic loading of this type of structure is nonlinear. A floating wind turbine is a multibody aero-hydro-servo-elastic structural system; for such structures, the coupled nonlinear equations of motion considering nonlinear excitation and damping forces, including all wave- and wind-induced features, should be solved in the time domain. In this thesis, the motion and structural responses for operational and extreme environmental conditions were considered to investigate the performance and the structural integrity of spar-type floating wind turbines. The power production and the effects of aerodynamic and hydrodynamic damping, including wind-induced hydrodynamic and wave-induced aerodynamic damping, were investigated. Negative damping adversely affects the power performance and structural integrity. In this thesis, the controller gains were tuned to remove servo-induced instabilities. The rotor configuration effect on the responses and power production was investigated by comparing the upwind and downwind turbines. To develop robust design tools for offshore wind power, the competencies of the offshore technology and wind technology must be combined. Both the offshore and wind energy industries have begun to extend their existing numerical codes to account for the combined aerodynamic and hydrodynamic effects on the structure. As a result verifications of extended codes by doing experiments and code-to-code comparisons are needed. One of the aspects of the present research was to fill this gap by performing hydrodynamic and hydro-elastic comparison between commercial codes. For both CMS and TLS concepts, the comparisons were carried out prior to using the tools to study the behaviour of the CMS and TLS under wave- and wind-induced loads. Offshore structures encounter a variety of operational and harsh environmental conditions. Limit states such as ultimate, fatigue, accidental collapse and serviceability limit states (ULS, FLS, ALS and SLS) are defined as the design criteria for offshore structures. In performing realistic ultimate limit state analysis, the extreme responses of a floating wind turbine over its life should be estimated. This estimation requires detailed analysis of the extreme response. In the present thesis, extreme value analysis for spar-type wind turbines subjected to simultaneous wave and wind actions was preformed. The structural responses and the effect of modelled forces such as turbulence on these responses were investigated. The joint distribution of the environmental characteristics of the wave and wind was applied through the contour surface method. Stochastic wave and wind analysis showed that, while rigid body modelling was sufficient for obtaining accurate motions, consideration of the elastic behaviour of the tower/support structure was necessary to predict structural responses. The blades structural responses were found to be significantly affected by the turbulent wind. However, the mean and standard deviation of global motion and structural responses were not affected by the turbulence. Thus, to reduce the simulation time in fatigue analysis, a constant wind speed model can be applied. The CMS and TLS wind turbines are inertia-dominated structures, and the hydrodynamic viscous drag did not affect their wave-induced responses, while an increase in viscous drag could effectively reduce the resonant responses of such turbines. Under operational conditions, aerodynamic damping was found to be active in reducing both wave frequency and resonant responses. The results showed that, for a floating wind turbine, extreme response could occur in survival conditions, while for a fixed wind turbine, the extreme response occurs in operational cases related to the rated wind speed. To estimate the extreme value responses, extrapolation methods were used to reduce the sample size in Monte Carlo simulations. The accuracy of methods to estimate the extreme responses as a function of sample size and methods applied was investigated. The normalized responses for both CMS and TLS offshore wind turbines were presented to draw more generalized conclusions.

Current prognoses are that, unless counteracted by very strong political measures, the world will meet both energy shortage and climate crisis within a horizon of a few decades, both of which are strongly related to our dependence on fossil fuels. Renewable energy sources may be harvested sustainably, and developing technology for their exploitation therefore forms an obvious part of strategies to reduce emissions and secure energy supply. Wave energy is a resource with relatively high power density, readily available along the coasts, and thus coinciding with the areas where industry and people tend to be accumulated. In some regions this resource is large enough to form a significant part of the energy mix. The technology for harnessing the power of ocean waves is today still on the research and development stage. The challenge is to make a design where the costs of investment, operation and maintenance (in terms of money, resources and energy) can be justified by the availability and potential earnings. This thesis focuses on two aspects of systems for wave energy conversion: How to model such systems, which is important for understanding and design, and how to control their motion, which is crucial for the primary power conversion – the inevitable step that forms the basis for revenues and energy output from such a device. The dissertation is based on articles published in scientific conferences and journals, as well as an account for background of the undertaken research and the methods used. The bond graph modelling language has been chosen as a promising aid for the modelling of the power converter dynamics. It enables a systematic and transparent approach to the path from drawing board to mathematical equations. Examples show how energy conversion systems may be modelled and simulated within this framework. These include heave-motion models for a semi-submerged sphere, a platform/buoy two-body system and a smallscale oscillating water column (OWC), as well as wave-to-wire models of two made-up systems. The OWC model was also studied by laboratory experiments. A range of control strategies has been studied and compared by numerical simulation, and in one case also by laboratory experiments. These strategies include phase control by latching and by clutching, approximations to complex-conjugate control, and model predictive control (MPC). Constraint handling and real-time parameter tuning are discussed, too. The constrained optimal power absorption is investigated, and for the example of a semi-submerged heaving sphere in irregular waves it is found that MPC in combination with a Kalman filter predictor is able to provide an absorbed power in excess of 90% as compared to the non-causal (and hence not completely realisable) constrained optimum. Other causal controller implementations gives an absorbed power ranging from 10 to 90% of that achieved with MPC. The best performing control strategies, however, involve a large flow of reactive power through the machinery, which in normal irregular-wave operation may give peak-to-average power ratio as high as 25 and above. This represents a challenge to the design of machinery and controller. An interesting observation from the numerical simulations is the possibility of increased absorbed power in irregular waves as compared to regular waves having about the same wavelength characteristics and the same wave power level. An explanation is suggested for this phenomenon.

Current prognoses are that, unless counteracted by very strong political measures, the world will meet both energy shortage and climate crisis within a horizon of a few decades, both of which are strongly related to our dependence on fossil fuels. Renewable energy sources may be harvested sustainably, and developing technology for their exploitation therefore forms an obvious part of strategies to reduce emissions and secure energy supply. Wave energy is a resource with relatively high power density, readily available along the coasts, and thus coinciding with the areas where industry and people tend to be accumulated. In some regions this resource is large enough to form a significant part of the energy mix. The technology for harnessing the power of ocean waves is today still on the research and development stage. The challenge is to make a design where the costs of investment, operation and maintenance (in terms of money, resources and energy) can be justified by the availability and potential earnings. This thesis focuses on two aspects of systems for wave energy conversion: How to model such systems, which is important for understanding and design, and how to control their motion, which is crucial for the primary power conversion – the inevitable step that forms the basis for revenues and energy output from such a device. The dissertation is based on articles published in scientific conferences and journals, as well as an account for background of the undertaken research and the methods used. The bond graph modelling language has been chosen as a promising aid for the modelling of the power converter dynamics. It enables a systematic and transparent approach to the path from drawing board to mathematical equations. Examples show how energy conversion systems may be modelled and simulated within this framework. These include heave-motion models for a semi-submerged sphere, a platform/buoy two-body system and a smallscale oscillating water column (OWC), as well as wave-to-wire models of two made-up systems. The OWC model was also studied by laboratory experiments. A range of control strategies has been studied and compared by numerical simulation, and in one case also by laboratory experiments. These strategies include phase control by latching and by clutching, approximations to complex-conjugate control, and model predictive control (MPC). Constraint handling and real-time parameter tuning are discussed, too. The constrained optimal power absorption is investigated, and for the example of a semi-submerged heaving sphere in irregular waves it is found that MPC in combination with a Kalman filter predictor is able to provide an absorbed power in excess of 90% as compared to the non-causal (and hence not completely realisable) constrained optimum. Other causal controller implementations gives an absorbed power ranging from 10 to 90% of that achieved with MPC. The best performing control strategies, however, involve a large flow of reactive power through the machinery, which in normal irregular-wave operation may give peak-to-average power ratio as high as 25 and above. This represents a challenge to the design of machinery and controller. An interesting observation from the numerical simulations is the possibility of increased absorbed power in irregular waves as compared to regular waves having about the same wavelength characteristics and the same wave power level. An explanation is suggested for this phenomenon.

Level-crossing analysis of long-crested, Gaussian waves in space and time are studied in the context of wave loads on a fixed, horizontal deck-box above mean waterline. Vertical wave loads on decks due to insufficient airgap are a major concern for many in-service platforms. Reliable estimation of magnitude and duration of these loads is important in assessing structural and global response of an offshore platform. In the case of an irregular wave-impact on a flat deck of dimensions comparable to mean wavelength of the incident waves, both temporal and spatial variability of wave-kinematics need to be considered during the deck-wetting process. In the present study, we have used a multidimensional Gaussian formulation of incident wave-kinematics to derive a joint probability density function of deck-wetting (or exceedance) duration and its spatial extent. We have also derived a probability density function for initial slam force on deck. A numerical scheme for simulating wave-impact events on a two-dimensional deck is discussed, results from which are compared against corresponding analytical estimates. Vertical force on deck was estimated using the momentum method, which includes a von Kármán slamming model applied over the wetted-length determined from an undisturbed wave profile.

Hydroelasticity theory, considering the second-order fluid forces induced by the coupling of first-order wave potentials, is introduced briefly in this paper. Based on the numerical results of second-order principal coordinates induced by the difference-frequency and sum-frequency fluid forces in multidirectional irregular waves, the bending moments, as well as the vertical displacements of a floating plate used as a numerical example are obtained in an efficient manner. As the phase angle components of the multidirectional waves are random variables, the principal coordinates, the vertical displacements, and the bending moments are all random variables. Extreme values of bending moments are predicted on the basis of the theory of stationary stochastic processes. The predicted linear and nonlinear results of bending moments show that the influences of nonlinear fluid forces are different not only for the different wave phase angles, but also for the different incident wave angles. In the example very large floating structure (VLFS) considered in this paper, the influence of nonlinear fluid force on the predicted extreme bending moment may be as large as 22% of the linear wave exciting forces. For an elastic body with large rigidity, the influence of nonlinear fluid force on the responses may be larger than the first-order exciting forces and should be considered in the hydroelastic analysis.

This article deals with time-domain hydroelastic analysis of a marine structure. The convolution terms associated with fluid memory effects are replaced by an alternative state-space representation, the parameters of which are obtained by using realization theory. The mathematical model established is validated by comparison to experimental results of a very flexible barge. Two types of time-domain simulations are performed: dynamic response of the initially inert structure to incident regular waves and transient response of the structure after it is released from a displaced condition in still water. The accuracy and the efficiency of the simulations based on the state-space model representations are compared to those that integrate the convolutions.

This paper is concerned with evaluating the effect of heavy weather avoidance on the long-term wave-induced loads on ships. Two hydrodynamic codes, VERES based on a 2D strip theory and WASIM based on a 3D Rankine panel method, are employed to calculate the wave-induced loads and motions on various vessels. Two models for heavy weather avoidance are envisaged. The first one is based on the assumption that operational criteria relevant to vertical acceleration, green water, and bottom slamming are fulfilled. The second one is based on the assumption that the sea state forecasts are available to the shipmaster and that rerouting is made. Based on the first model, the effect of the heavy weather avoidance on the long-term wave-induced hull girder loads is evaluated. In particular, the effect of hydrodynamic analysis methods and wave scatter diagram are also assessed. The calculated values are compared with those given in ship rules. The results show that several factors should be critically assessed in evaluating the accuracy of the ship rule values.

An idealized structural unit model is constructed to represent the pre and post-ultimate strength behavior of a damaged tubular member with various boundary conditions subjected to various end loads. Local denting and overall permanent lateral deflection are considered as a damage. The calculated results using this model are compared with a large number of previous and new experimental results. A parametric study regarding the influence of damages on the ultimate strength of tubular members is also performed.