Wave Scatter Diagram Research Articles

Comparison of two statistical wave models for fatigue and fracture analysis of ship structures

Ocean crossing ship structures are continuously suffering from wave loads when sailing at sea. The wave loads cause large variation of structural stresses, leading to fatigue accumulation in ship structures. For the fatigue life prediction of ship structures, it is important to obtain both the long-term distribution and the time history of wave-induced loads. An essential step is to get reliable wave statistics and accurate description of the stochastic nature of sea state along a ship's sailing routes during her service time. Generally, the wave statistics are provided by the classification societies as a joint probability of significant wave height and mean wave period, also known as wave scatter diagram. In addition, different statistical wave models have been developed to describe wave environments along arbitrary shipping routes based on different data sources, e.g., hindcast data, satellite measurements, buoys, etc. In this paper, two statistical wave models based on hindcast data and satellite wave measurements are briefly introduced and compared with the wave measurements carried out by onboard radar. Both of the wave models are then used to generate the wave environments along given shipping routes. The effectiveness of the wave models is demonstrated by comparing the stochastic nature and the statistical characteristics of simulated sea state histories with those of the source oceanographic data. Finally, an application of the wave model to the fatigue assessment is presented.

Wave energy assessment based on trivariate distribution of significant wave height, mean period and direction

Based on the Vine copula theory, a trivariate statistical model of significant wave height, characterized wave period and mean wave direction was constructed. To maintain the properties of the different types of variables, a special copula function was derived from the model developed by Johnson and Wehrly based on the maximum entropy principle. It was then combined with the Archimedean copulas to construct the proposed model. An effective algorithm for generating corresponding joint pseudo-random numbers was also developed. Statistical analysis of hindcast data for the significant wave height, mean wave period, and direction, which were collected from an observation point in the North Atlantic every three hours from 1997 to 2001, was performed. The marginal distributions of the significant wave height and mean wave period were fitted by a modified maximum entropy distribution, and the mean wave direction was fitted by a mixture of von Mises distributions. It was shown that the proposed model is a good fit for the data. The seasonal wave energy resources in the target area were assessed using the model estimates. Histograms of the directional wave energy, wave energy roses, and scatter and energy diagrams were presented.

Numerical and Experimental Study on Trimaran Cross-Deck Structure’s Fatigue Characteristics Based on the Spectral Fatigue Method

Spectral fatigue analysis is performed on the trimaran cross-deck structural detail. A global finite element (FE) model with local fine meshes at hot spot locations is built for the calculation of structural response. Three-dimensional linear potential flow theory and global FE analysis are used for wave load and stress transfer function calculations. Then, the hot spots’ fatigue damage is calculated, considering various factors influencing spectral analysis, which includes cycle counting correction factors, wave scatter diagram, and the distribution coefficient of wave headings. A full-scale model fatigue test is used to investigate the fatigue behavior of the cross-deck structural detail. Using the fatigue test data, the S - N curve characteristic of the cross-deck structural detail is produced. Finally, the trimaran cross-deck structural detail’s fatigue characteristics are summarized and the effects of the factors influencing spectral fatigue analysis are reported.

Fluctuating wind and wave simulations and its application in structural analysis of a semi-submersible offshore platform

A semi-submersible offshore platform always operates under complex weather conditions, especially wind and waves. It is vital to analyze the structural dynamic responses of the platform in short-term sea states under the combined wind and wave loads, which touches upon three following work. Firstly, a derived relationship between wind and waves reveals a correlation of wind velocity and significant wave height. Then, an Improved Mixture Simulation (IMS) method is proposed to simulate the time series of wind/waves accurately and efficiently. Thus, a wind-wave scatter diagram is expanded from the traditional wave scatter diagram. Finally, the time series of wind/wave pressures on the platform in the short-term sea states are converted by Workbench-AQWA. The numerical results demonstrate that the proposed numerical methods are validated to be applicable for wind and wave simulations in structural analyses. The structural dynamic responses of the platform members increase with the wind and wave strength. In the up-wind and wave state, the stresses on the deck, the connections between deck and columns, and the connection between columns and pontoons are relatively larger under the vertical bending moment. These numerical methods and results are wished to provide some references for structural design and health monitoring of several offshore platforms.

Bivariate Extreme Value Statistics of Offshore Jacket Support Stresses in Bohai Bay

This paper presents a generic Monte Carlo-based approach for bivariate extreme response prediction for fixed offshore structures, particularly jacket type. The bivariate analysis of extremes is often poorly understood and generally not adequately considered in most practical measurements/situations; that is why it is important to utilize the recently developed bivariate average conditional exceedance rate (ACER) method. According to the current literature study, there is not yet a direct application of the bivariate ACER method to coupled offshore jacket stresses. This study aims at being first to apply bivariate ACER method to jacket critical stresses, aiming at contributing to safety and reliability studies for a wide class of fixed offshore structures. An operating jacket located in the Bohai bay was taken as an example to demonstrate the proposed methodology. Satellite measured global wave statistics was used to obtain realistic wave scatter diagram in the jacket location area. Second-order wave load effects were taken into account, while simulating jacket structural response. An accurate finite element ANSYS model was used to model jacket response dynamics, subject to nonlinear hydrodynamic wave and sea current loads. Offshore structure design values are often based on univariate statistical analysis, while actually multivariate statistics is more appropriate for modeling the whole structure. This paper studies extreme stresses that are simultaneously measured/simulated at two different jacket locations. Due to less than full correlation between stresses in different critical jacket locations, application of the multivariate (or at least bivariate) extreme value theory is of practical engineering interest.

Long-term offshore Bohai bay Jacket strength assessment based on satellite wave data

ABSTRACTThis paper presents generic Monte Carlo-based approach, based on satellite wave data, for extreme response prediction of offshore structures, particularly Jacket type. An operating Jacket in Bohai bay was taken as an example to demonstrate proposed methodology. Satellite-based global wave statistics was used to obtain wave scatter diagram in the area of interest. Effects of second-order waves and sea current were taken into account. The detailed finite element Analysis System (ANSYS) model was employed to study non-linear Jacket dynamics, subject to hydrodynamic wave loads. Stresses in the most critical structural members were extracted and extreme value study was carried out. Proper extrapolation technique was applied to predict stresses with 10–50 year return periods, which is of practical interest for the design and operation of offshore structures.

Fatigue sensitivity analysis of steel catenary riser near touchdown point

By transforming the platform response obtained from coupled hydrodynamic analysis to the top motions of steel catenary riser (SCR), the nonlinear dynamic analysis of the SCR is carried out in Abaqus/Aqua. In this analysis, the SCR-seabed interaction is well taken into account by introducing the seabed trench model and hysteretic seabed model. The fatigue damage of the SCR near touchdown point (TDP) is calculated using rain-flow counting methodology, and the sensitivity of the fatigue damage to the seabed and wave parameters are investigated. The results indicate that as seabed stiffness increases, the fatigue life and its sensitivity to seabed stiffness decrease. Seabed trenching may benefit the fatigue life of the SCR and the trench position should be elaborated for realistic fatigue damage prediction. Due to the induced platform response, significant wave height and spectral peak period have significant effects on the fatigue damage, thus the short-term sea state bins should be carefully selected from the wave scatter diagram.

Wave Statistics for the Middle Adriatic Sea

The paper presents the methodology and results of the sea state statistics development for the middle Adriatic Sea. The study is based on the World Waves Atlas containing data of sea states in the Adriatic Sea calibrated using different satellite missions and numerical wave model simulations during the period of past 23 years. Wave scatter diagram and wave rose at the location in the middle Adriatic Sea are derived from the data. The 3-parametric Weibull distribution and the log-normal distribution for significant wave height and peak spectral periods respectively, are fitted through the data in the World Waves Atlas. Based on available data, the relation between wind speed and wave height is established by regression analysis. Comparison of the relationship between the significant wave height and peak spectral period is performed between the data from the World Waves Atlas and the Tabain’s wave spectrum, frequently used for sea states in the Adriatic Sea. Finally, the most probable extreme sea states for different return periods are calculated and results are compared with another relevant study for the long-term prediction of sea states in the Adriatic Sea.

An innovative block partition and equivalence method of the wave scatter diagram for offshore structural fatigue assessment

The fatigue assessment plays an increasing role for the offshore structural safety. Many fatigue assessment methods have been developed for this purpose. Among those methods, the time domain method is regarded as the most accurate method but less adopted in practice due to time consuming. In order to improve the efficiency of the time domain method, an innovative block partition and equivalence method of the wave scatter diagram is developed for offshore structural fatigue assessment. After the wave scatter diagram is partitioned into several blocks, the newly developed method, involves determination of the equivalent wave height, wave period and occurrence probability of the representative sea states based on modified energy equivalent principle. The equivalent wave period of the representative sea state is calculated via the spectral moment formula in which the equivalent spectral moments of zero and second order are obtained based on the weighted averaging principle. Combining with the determined wave period, the equivalent significant wave height can be determined by reversing the wave spectrum integral formula, where the equivalent wave energy of a divided block of the wave scatter diagram is modified by introducing a factor to compensate the effect of low- and high-amplitude cycles fatigue damage. The equivalent occurrence probability is equal to the summation of the original sea states’ occurrence probability within the divided block. The developed method has the advantage of preserving the stochastic characteristics of the short term sea states within the divided block during determining the representative sea state. At the same time the newly developed method has no limitation on block partition and can be applied on different offshore structure. Two structural models, a fixed mono-pile platform and a floating semi-submersible platform, are demonstrated in the numerical examples. Results indicate that the newly developed method is robust, computationally affordable, and accurate within engineering expectations.

Fatigue assessment for the floating collar of a fish cage using the deterministic method in waves

Fish farms have moved into the open sea in recent years and the failure risk of fish cages has increased in the harsher environmental conditions. Fatigue failure is an important limit state for the floating system of the fish cage under the long-term action of waves. A fatigue analysis of the high-density polyethylene (HDPE) floating system in waves is presented in this study based on the deterministic method and finite element analysis combined with a hydrodynamic model. As the basis of the fatigue assessment, a stress analysis of the floating pipes is first performed based on the joint use of the finite element model and the hydrodynamic model. The fatigue lifetime is then calculated using the Palmgren–Miner cumulative damage theory together with the deterministic method in which the stochastic sea state is decomposed into a reasonably high number of individual wave scatter diagrams. The results show that the recommended replacement period of the HDPE floating pipes is 20 years and that the fatigue lifetime of the floating pipes is more sensitive to the wave period than to the wave height. In addition, the effects of mooring line arrangements, wave incident angle and typhoons are also investigated. Comparisons of the fatigue lifetimes of the floating pipes for different mooring line arrangements indicate that the fatigue lifetime increases dramatically with increasing number of mooring lines. For a symmetrically arranged four-point mooring fish cage, the most unfavourable wave loading angle is 45°. Typhoons lead to a significant decrease in the fatigue lifetime of the floating pipes despite the short durations of the typhoons.

Spectral Fatigue Analysis for Topside Structure of Offshore Floating Vessel

In this study, a spectral fatigue analysis was performed for the topside structure of an offshore floating vessel. The topside structure was idealized using beam elements in the SACS program. The fatigue analysis was carried out considering the wave and wind loads separately. For the wave-induced fatigue damage calculation, motion RAOs calculated from a direct wave load analysis and regular waves with different periods and unit wave heights were utilized. Then, the member end force transfer functions were generated covering all the loading conditions. Stress response transfer functions at each joint were produced using the specified SCFs and member end force transfer functions. fatigue damages were calculated using the obtained stress ranges, S-N curve, wave spectrum, heading probability of each loading condition, and their corresponding occurrences in the wave scatter diagrams. For the wind induced fatigue damage calculation, a dynamic wind spectral fatigue analysis was performed. First, a dynamic natural frequency analysis was performed to generate the structural dynamic characteristics, including the eigenvalues (natural frequencies), eigenvectors (mode shapes), and mass matrix. To adequately represent the dynamic characteristic of the structure, the number of modes was appropriately determined in the lateral direction. Second, a wind spectral fatigue analysis was performed using the mode shapes and mass data obtained from the previous results. In this analysis, the Weibull distribution of the wind speed occurrence, occurrence probability in each direction, damping coefficient, S-N curves, and SCF of each joint were defined and used. In particular, the wind fatigue damages were calculated under the assumption that the stress ranges followed a Rayleigh distribution. The total fatigue damages were calculated from the combination with wind and wave fatigue damages according to the DNV rule.

Wave power potential assessment of Aegean Sea with an integrated 15-year data

In this study, wave power atlas is generated for Aegean Sea for years from 1999 to 2013 using a third-generation spectral wave model MIKE 21 SW. Wind data was obtained from ECMWF(ERA-Interim) with 0.125° spatial resolution and 6 hourly temporal resolution which was then interpolated to 10 min interval data. Distribution plots and statistical parameters were used to evaluate the performance of the model. Calibration results with 9 observational buoy data show high accuracy of the model. Analyses of the proposed model are done for offshore in this study. Analysis in time domain is divided into 15-year, seasonal and monthly mean wave height and wave powers. For analysis in space domain, wave characteristics are calculated on 4 bands with different widths parallel to Turkish coast. Moreover, 10 separate points were selected in different locations of the domain to derive wave roses and scatter diagrams. Maximum wave power values occur in Winter in northern part of the Aegean Sea with more than 8 kW/m. Maximum mean wave power occurrence location changes from north to middle southern part of the study region between Crete and Kasos islands in the period of Winter to Spring season.

Fatigue damage assessment of fixed offshore wind turbine tripod support structures

The objective of this work is to carry out a fatigue damage assessment of a fixed offshore wind turbine support structure due to combined wave and wind – induced loading. Considering the operational mode of the wind turbine 3 loading conditions are identified and for each loading condition 4 critical regions located in different zones of the supporting structure are studied. The stress transfer function is obtained by carrying out dynamic finite element analysis in the frequency domain. A wave scatter diagram of the North Atlantic is used in order to account for the environmental effects. The stress transfer function is formulated such that a sufficient number of frequencies can be used in the Inverse Fast Fourier Transform with random phase angles in order to obtain the stress time histories. An up-to-date rainflow cycle counting method is adopted to count the total number of cycles related to stress range bins. The S–N approach is employed to estimate fatigue damage.

전산유체역학을 이용한 컨테이너 선수갑판 쇄파판에 작용하는 충격하중 계산

In this study, numerical studies using a Computational Fluid Dynamics(CFD) method were carried out to estimate the green water load acting on the breakwater plate of bow deck of container carrier, KCS. For the green load water load analysis, a full load condition was considered. The relative motions at bow deck were calculated from the seakeepig analysis. Statistical analysis were carried out to estimate the long term response of the relative motions with the North Atlantic wave scatter diagram. The equivalent design wave was determined from the RAO of the relative motions at bow and the long term responses. CFD geometry modeling with three different locations and simulations for the green water loads were carried out in the equivalent design waves. A commercial CFD program, STAR-CCM+ Ver. 8.04, was used and the green water pressures on the breakwater plate were calculated successfully. The CFD analysis for green water loads can be used as a useful design tool for the evaluation of the breakwater plate of the container vessel. Ke ywords : Green water(그린 워터), Bow deck(선수 갑판), Breakwater plate(쇄파판)

Dynamic response sensitivity of an offshore wind turbine for varying subsoil conditions

In this paper, a comprehensive study is performed on the dynamic response of an offshore wind turbine installed on a monopile. The aim is to evaluate to what extent a change of the soil properties affects the fatigue loads for parked conditions. Based on consistent lumped-parameter models calibrated to semi-analytical impedance functions of a monopile embedded in a linear viscoelastic soil layer, fully coupled aero-hydro-elastic simulations are conducted in the nonlinear multi-body code Hawc2. Correlation of wind speeds and waves is derived on basis of wind–wave scatter diagrams from the North Sea. Changes of the soil stiffness, the soil damping and the presence of sediment transportation at seabed are shown to be critical for the fatigue damage equivalent moment at mudline that may change with more than 30% for parked wind turbine conditions.

Operability assessment of high speed passenger ships based on human comfort criteria

The growing popularity of passenger cruise lines means continual challenges are faced concerning both a vessel׳s design and its operational ability. Vessel dimensions, service speeds and performance rates are rapidly increasing to keep pace with this expanding interest. It is essential that vessels demonstrate high performances, even in adverse sea and weather conditions, and ensure the comfort of passengers and the safety of cargo. A vessel׳s operability can be defined as the percentage of time in which the vessel is capable of performing her tasks securely. In order to calculate a vessel׳s operability index, many key parameters are required. These include the dynamic responses of the ship to regular waves, the wave climate of the sea around the ship׳s route, and the assigned missions of the vessel. This paper presents a procedure to calculate the operability index of a ship using seakeeping analyses. A discussion of the sensitivity of the results relative to three different employed seakeeping methods is then given. The effect of seasonality on a ship׳s estimated operability is also investigated using wave scatter diagrams. Finally, a high speed catamaran ferry is explored as a case study and its operability is assessed with regards to human comfort criteria.

Influence of seabed trench formation on fatigue performance of steel catenary risers in touchdown zone

The subsea survey results using remote operating vehicles (ROV) show that trenches with a depth of several riser diameters can be developed underneath the steel catenary risers (SCR). Therefore, an important question in respect of the riser–seabed interaction is, how the trench formation beneath the riser affects the riser fatigue performance in the touchdown zone. A common methodology reported in literature to study the impact of trench formation on riser fatigue life is the insertion of an artificial mathematical expression of the riser profile into the seabed. This study shows that such methodology can be inconsistent and leading to contradictory results. The current paper has employed ABAQUS finite element software and coded a non-linear soil hysteretic model to automatically simulate the variable seabed stiffness and the gradual trench development through the touchdown zone. In this method, the seabed model parameters are initially adjusted to extreme values allowing trench with desired depth to be developed over a moderate number of displacement cycles of the SCR. The design wave scatter diagram is then applied, simulating a generic Spar system, after switching the model parameters to values with normal range. The paper presents the impact of trenches of different depths on the fatigue performance of SCRs in the touchdown zone.

Mooring system influence on the efficiency of wave energy converters

The paper presents an analysis of the mooring system effects on the dynamics of an arbitrary floating wave energy converter (WEC) and on the efficiency of the device. The mooring system dynamics are calculated by a finite differences method, which accounts for the lines’ physical characteristics such as mass and stiffness, as well as for the hydrodynamic inertial and damping characteristics. A method is proposed and applied to consider the inertial, damping and stiffness effects of the mooring system on the WEC’s linear dynamics. An identification method is used to determine the linear mooring system coefficients from pre-calculated nonlinear time domain forces of the mooring system on the floater (the importance of nonlinear effects is assessed as well). Finally the mooring system dynamics is represented by additional inertial, damping and stiffness matrices which are added to the ones of the WEC. The influence of the mooring system on the WEC dynamics and efficiency is assessed in terms of wave induced motions and absorbed power. Results are presented for the transfer functions, statistics in selected stationary sea states and the expected annual absorbed energy. A wave scatter diagram representative of the Portuguese Pilot Zone is used for the annual predictions.

Effects of Avoidance of Heavy Weather on the Wave-Induced Load on Ships

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.

Use of Vertical Wave Bending Moments From Hydrodynamic Analysis In Design of Oil Tankers

SUMMARY The paper describes calculation of design vertical wave bending moments for unconventional oil product tankers of new generation that are characterized by low length-to-beam ratio. The linear strip theory is employed for the calculation of transfer functions, while standard IACS procedure is used for long-term prediction of extreme values. Since the calculated design vertical wave bending moments at midship largely overestimate the values from IACS UR S11, additional analyses are performed to explain these differences. For that purpose, the same analysis is performed for conventional oil tanker which fully complies with contemporary IACS rules. Large overestimations of rule vertical wave bending moments are obtained also for that ship. The inaccuracies of the linear strip theory may partially explain these overestimations, as discussed in the paper. The wave scatter diagram proposed by IACS is analysed and found to be too severe for strength analysis of ship structures. However, the severity of the IACS scatter diagram is compensated by some other unconservative assumptions in the standard long-term prediction procedure, which is also elaborated. After all these aspects are put together, the obvious conclusion is that the IACS rule vertical wave bending moment should be substantially increased to enable safe design of oil tankers navigating in the North Atlantic wave climate. Finally, some suggestions regarding incorporation of hydrodynamic analysis for the calculation of extreme wave loads in ship design are given.