Manoeuvring behaviour of ships in extreme astern seas

In an attempt to contribute to efforts for a robust and effective numerical tool addressing ship motion in astern seas, this paper presents the development of a coupled non-linear 6-DOF model with frequency dependent coefficients, incorporating memory effects and random waves. A new axes system that allows straightforward combination between seakeeping and manoeuvring, whilst accounting for extreme motions, is proposed. Validation of the numerical model with the results of benchmark tests commissioned by ITTC's Specialist Group on Stability demonstrated qualitative, yet not fully satisfactory agreement between numerical and experimental results in line with other predictive tools. The numerical results indicate that the inclusion of frequency coefficients definitely affects the accuracy of the predictions. In order to enhance further the numerical model and obtain useful information on motion coupling, extensive captive and free running model tests were carried out. Good agreement with the experimental results was achieved. These studies provide convincing evidence of the capability of the developed numerical model to predict the dangerous conditions that a ship could encounter in extreme astern seas. As a result, it could offer new insights towards establishing relationships linking ship behaviour to design, environmental and operational parameters.     

On the parametric rolling of ships using a numerical simulation method

This paper has shown a numerical motion simulation method which can be employed to study on parametric rolling of ships in a seaway. The method takes account of the main nonlinear terms in the rolling equation which stabilize parametric rolling, including the nonlinear shape of the righting arm curve, nonlinear damping and cross coupling among all 6 degrees of freedom. For the heave, pitch, sway and yaw motions, the method uses response amplitude operators determined by means of the strip method, whereas the roll and surge motions of the ship are simulated, using nonlinear motion equations coupled with the other 4 degrees of freedom. For computing righting arms in seaways, Grim's effective wave concept is used. Using these transfer functions of effective wave together with the heave and pitch transfer functions, the mean ship immersion, its trim and the effective regular wave height are computed for every time step during the simulation. The righting arm is interpolated from tables, computed before starting the simulation, depending on these three quantities and the heel angle. The nonlinear damping moment and the effect of bilge keels are also taken into account. The numerical simulation tool has shown to be able to model the basic mechanism of parametric rolling motions. Some main characteristics of parametric rolling of ships in a seaway can be good reproduced by means of the method. Comprehensive parametric analyses on parametric rolling amplitude in regular waves have been carried out, with that the complicated parametric rolling phenomena can be understood better.     

Time domain modelling of the transient asymmetric flooding of Ro-Ro ships

This work aims at contributing to improve knowledge on transient asymmetric flooding through theoretical and experimental research. First, a time domain theoretical model of ship motions and flooding is described. Results from experimental work are presented evidencing that transient asymmetric flooding may cause the capsizing of a Ro-Ro shaped barge. The theoretical model is used to predict the capsize of the Ro-Ro shaped barge. Reasonable agreement between experimental and theoretical results was found. Finally, a review of the European Gateway accident is given and the theoretical model is applied to the study of this type of accident. The conclusion is that this theoretical model, together with an accurate modelling of the flooding of machinery compartments, reproduces successfully the capsizing of the European Gateway due to transient asymmetric flooding. Therefore, the internal arrangement of Ro-Ro ships should be carefully studied at the design stage in order to avoid this phenomenon.     

A parametric study of wave loads on trimaran ships traveling in waves

In this paper, we present a spectral analysis based on wave loads to select suitable side-hull arrangements for a trimaran ship traveling in waves. Neglecting the steady flow effect, the three-dimensional source-distribution method, using a pulsating source potential incorporating the panel method, is adopted to solve the corresponding hydrodynamic coefficients. The significant values for wave loads, including shear forces, bending moments, and torsion moments at different locations on the main hull and connected deck with respect to different staggers and clearances, are derived by the spectral analysis. Several ship speeds and wave headings are also considered for comparison. This study offers more information for selecting the side-hull arrangement from the viewpoint of wave loads on trimaran ships, which may be regarded as helpful references for seakeeping design of these types of ships.     

Influence of non-linearities on the limits of stability of ships rolling in head seas

The present paper describes an investigation on parametric resonance in head seas in which a new third-order coupled mathematical model is considered. The restored modes of heave, roll and pitch are contemplated. The discussion is illustrated for the case of a transom stern fishing vessel at different speeds. It is pointed out that numerical simulations employing the new model are successfully compared to experimental results previously obtained for the vessel.Considering that analyticity is an important tool when handling complex stability issues, some theoretical dynamic characteristics of the equations are discussed. By means of the analysis of the coupled linear variational equation derived from an extended third-order model, the appearance of super-harmonics and increased rigidity proportional to wave amplitude squared due to third-order terms is demonstrated.In the present paper, an important tool is explored, that is the analysis of the limits of stability obtained from the new model. Limits of stability are a well-known and practical way of looking into the problem of parametric resonance. New limits of stability are derived and compared to the more conventional Strut diagram. Dynamic characteristics associated with the new limits of stability are discussed. The influence of different parameters is investigated, including vessel speed, damping and tuning. Consistent and revealing results are obtained through the analysis of the new limits of stability for different speeds and damping.     

On unstable ship motions resulting from strong non-linear coupling

In this paper, the modelling of strong parametric resonance in head seas is investigated. Non-linear equations of ship motions in waves describing the couplings between heave, roll and pitch are contemplated. A third-order mathematical model is introduced, aimed at describing strong parametric excitation associated with cyclic changes of the ship restoring characteristics. A derivative model is employed to describe the coupled restoring actions up to third order. Non-linear coupling coefficients are analytically derived in terms of hull form characteristics.The main theoretical aspects of the new model are discussed. Numerical simulations obtained from the derived third-order non-linear mathematical model are compared to experimental results, corresponding to excessive motions of the model of a transom stern fishing vessel in head seas. It is shown that this enhanced model gives very realistic results and a much better comparison with the experiments than a second-order model.     

A nonlinear model of parametric rolling stabilization by anti-roll tanks

The present paper describes a mathematical model in which the fluid motion inside a U-tank is nonlinearly coupled to the heave, roll and pitch motions of the ship. The main purpose of the investigation is centred on the control of roll motion in the case of parametric resonance in longitudinal waves. A transom stern small vessel, known to be quite prone to parametric amplification, is employed in the study. Four tank designs are employed in order to study the influence of tank mass, tank natural frequency and tank internal damping on the control of parametric rolling at different head seas conditions. Additionally, the influence of the vertical position of the tank is also investigated. The main results are presented in the form of limits of stability, with encounter frequency and wave amplitudes as parameters. Distinct dynamical characteristics are discussed and conclusions are drawn on the relevant parameters for the efficient control of the roll amplifications in head seas.     

Identification-based simplified model of large container ships using support vector machines and artificial bee colony algorithm

The 6 degrees of freedom (DOF) model with a high degree of complexity for capturing ship dynamics is generally able to track the nonlinear and coupling dynamics of ships. However, the 6 DOF model makes challenges in estimating model coefficients and designing the model-based control. Therefore, simplified ship dynamic models within allowed accuracy are essential. This paper simplified the 6 DOF nonlinear dynamic model of ships into two decoupled models including the speed model and the steering model through reasonable assumptions. Those models were tested through maneuvering simulations of a container ship with a 4 DOF dynamic model. Support vector machines (SVM) optimized by the artificial bee colony algorithm (ABC) was used to identify parameters of speed and steering models by analyzing the rudder angle, propeller shaft speed, surge and sway velocities, and yaw rate from simulated data extracted from a series of maneuvers made by the container ship. Comparisons with the first order linear and nonlinear Nomoto models show that the simplified nonlinear steering model can capture more complicated dynamics and performs better. Additionally, comparisons among three different parameter identification methods demonstrate similar identification results but the different performance involving the applicability and effectiveness. SVM optimized by ABC is relatively convenient and effective for parameter identification of ship simplified dynamic models.     

深水波中进动共振的数值模拟研究

进动(precession)共振是一种非线性共振相互作用,2016年才有学者对这一现象进行研究。采用非静压二维自由表面流模型模拟了深水条件下重力波的进动共振现象。通过边界造波的方法产生双色波,分析了触发进动共振的初始条件;探讨了进动共振在小振幅前提条件下发生的简化初始条件。数值模拟分析两组对称测点,对不同测点的波面、能量谱进行对比分析。数值结果表明:非静压二维自由表面流模型可以模拟进动共振现象,并且可以采用双色波作为条件来研究深水五波进动共振现象,进动共振需要一定的能量转化时间,进动共振发生的条件是三波组合的进动频率等于一个系统存在的非线性频率。     

Harbor resonance induced by subaerial landslide-generated impact waves

Past studies of harbor resonance have mainly been restricted to the quasi-steady oscillations induced by steady wave conditions. This paper investigates the response of a rectangular harbor to subaerial landslide-generated impact waves based on physical models, in order to compare the oscillations induced by steady and transient waves. In response to steady incident waves, oscillations within the harbor need to experience a long process to obtain their maximum value before the input energy and the losses are balanced. Landslide-generated impact waves usually include components with solitary wave characteristics and also components with dispersive wave characteristics. Each component travels with a different celerity. Usually, solitary wave components propagate faster, and arrive in the harbor first. Oscillations attain their maximum status as soon as these components arrive. The subsequently arriving components with dispersive characteristics do not enhance the resonance oscillations. So the waves with solitary characteristics are considered to play an important role in harbor resonance. Numerical experiments, using the FUNWAVE model, were conducted in order to further verify these conclusions.     

Practical control of underactuated ships

This paper presents a design of global smooth controllers that achieve the practical stabilization of arbitrary reference trajectories, including fixed points and nonadmissible trajectories for underactuated ships. These ships do not have an independent actuator in the sway axis. The control design is based on several nonlinear coordinate changes, the transverse function approach, the back-stepping technique, the Lyapunov direct method, and utilization of the ship dynamics. Simulation results illustrate the effectiveness of the proposed control design.     

深吃水半潜式平台参数共振研究

深吃水半潜式平台(deep draft semi-submersible,DDS)作为一种新型海洋结构物,既继承了传统半潜式平台的优点,又改善了传统半潜式平台垂荡运动性能差的不足。但随着吃水的增加,DDS纵摇运动参数共振也成为一个不容忽视的问题。当DDS纵摇运动固有周期和垂荡运动周期满足一定关系时,纵摇运动将发生参数共振,纵摇角度将会显著增大。研究推导了DDS纵摇运动方程,并简化为标准的马修方程,运用希尔无穷行列式法求解马修方程,得到了含阻尼的马修稳定性图谱,并结合具体算例讨论了不同参数对DDS纵摇运动参数共振问题的影响。研究表明:深吃水半潜式平台的参数共振,是设计人员在设计之初必须考虑的问题;通过合理选取平台的系统参数,可以有效避免纵摇运动参数共振现象的发生。     

Field observations of waves generated by passing ships: A note

This short contribution reports the results of a field study on the nearshore characteristics of waves generated by both conventional and high speed passenger ferries. The field observations took place in the late summer of 2005, at a beach close to the port of Mytilene (Island of Lesbos, Greece), and involved the visual observation of ship waves, using digital video recordings and image processing techniques. The results showed that passage of the fast ferry was associated with a longer, more complex and energetic nearshore event; this event not only did include higher nearshore waves (up to 0.74 m) and was organised in different wave packets, but it was also an order of magnitude longer (∼ 680 s) than the conventional ferry event. Regarding the effects on beach sediment dynamics, the fast ferry waves were estimated to be very efficient in mobilising the nearshore sediments in contrast to those of the conventional ferry. The fast ferry service appears to generate daily prolonged nearshore events, which contain waves with higher energy than those expected from the normal summer wind wave regime of the area; these events also include some high and very steep waves, which can be particularly erosive. Therefore, fast ferry wakes may have considerable impacts on the seasonal beach sediment dynamics/morphodynamics and the nearshore benthic ecology, as well as they may pose significant risks to bathers, affecting the recreational use of the beaches exposed to fast ferry traffic. Finally, the study has shown that satisfactory field observations of the nearshore characteristics of ship-generated (and wind) waves can be obtained using inshore deployments of calibrated poles, digital video cameras and appropriate image processing algorithms.     

Breaking Basel: The elements of the Basel Convention and its application to toxic ships

Developing nations seeking to apply the Basel Convention on the Control of Transboundary Movements in Hazardous Wastes to prevent toxic ships from entering their waters for shipbreaking are faced with legal uncertainty. This paper responds to that uncertainty by adopting a definition of the offence of illegal traffic in end-of-life ships, and further proposing evidentiary burdens and potential sources of proof for that offence. While a shipowner's intention to scrap a ship for its value in steel was previously difficult to prove, recent market analysis of the shipbreaking industry provides potential proof sufficient to halt the importation of a toxic ship.     

涡激致顶张力立管双频参量共振研究

研究了涡激力作用导致顶张力立管基于双频激励的参量共振机理。随着海洋油气开发走向深水,参量共振成为深海立管设计面临的挑战之一。立管系统一旦发生参量共振,将因应力过大或疲劳损伤而发生破坏,造成油气泄漏从而带来环境污染和重大经济损失。顶张力立管受涡激力作用产生横向运动,引起轴向张力波动,满足一定条件时,立管将发生参量共振。目前研究多以单频外激励探讨立管的马修不稳定性,而实际激励为多频叠加,因此双频外激励被提出并被应用于对立管参量稳定性的探讨。研究建立了顶张力立管非线性耦合的运动方程,并推导了多频激励马修方程,采用布勃诺夫-伽辽金法求解有阻尼马修方程,对比分析了单频和双频激励对顶张力立管参量稳定性的影响,探讨了双频激励马修方程设计深海顶张力立管参量稳定性的应用。研究表明:涡激致顶张力立管产生轴向应力波动,进而导致立管系统发生参量共振的现象值得设计人员关注;此外,实际工程设计中激励函数的选取,对被研究系统参量稳定性特性以及阻尼特性的预测具有决定性影响。     

Automatic collision avoidance of multiple ships based on deep Q-learning

As the number of ships for marine transportation increases with the globalisation of the world economy, waterways are becoming more congested than before. This situation will raise the risk of collision of the ships; hence, an automatic collision avoidance system needs to be developed. In this paper, a novel approach based on deep reinforcement learning (DRL) is proposed for automatic collision avoidance of multiple ships particularly in restricted waters. A training method and algorithms for collision avoidance of ships, incorporating ship manoeuvrability, human experience and navigation rules, are presented in detail. The proposed approach is investigated not only by numerical simulations but also by model experiments using three self-propelled ships. Through the systematic numerical and experimental validation, it is demonstrated the developed approach based on the DRL has great possibility for realising automatic collision avoidance of ships in highly complicated navigational situations.     

Prediction potential of the parametric rolling behaviour of a post-panamax containership

A systematic investigation on the prediction of parametric rolling exhibited by a post-panamax containership is described, on the basis of several techniques. Analytical formulae that appear in current industrial guidelines are evaluated in a step-by-step process against various numerical predictions. The method of continuation of nonlinear dynamics is introduced in order to expedite the identification of the instability boundary and the prediction of steady amplitudes of roll oscillation. A well-known panel code is shown to be capable of reproducing parametric roll growth.     

Kinematics of extreme waves in deep water

The velocity profiles under crest of a total of 62 different steep wave events in deep water are measured in laboratory using particle image velocimetry. The waves take place in the leading unsteady part of a wave train, focusing wave fields and random wave series. Complementary fully nonlinear theoretical/numerical wave computations are performed. The experimental velocities have been put on a nondimensional form in the following way: from the wave record (at a fixed point) the (local) trough-to-trough period, T_TT and the maximal elevation above mean water level, η_m of an individual steep wave event are identified. The local wavenumber, k and an estimate of the wave slope, ε are evaluated from ω²/(gk)=1+ε², where ω=2π/T_TT and g denotes the acceleration of gravity. A reference fluid velocity, is then defined. Deep water waves with a fluid velocity up to 75% of the estimated wave speed are measured. The corresponding kη_m is 0.62. A strong collapse of the nondimensional experimental velocity profiles is found. This is also true with the fully nonlinear computations of transient waves. There is excellent agreement between the present measurements and previously published Laser Doppler Anemometry data. A surprising result, obtained by comparison, is that the nondimensional experimental velocities fit with the exponential profile, i.e. e^ky, y the vertical coordinate, with y=0 in the mean water level.     

Estimation of infragravity waves at intermediate water depth

The accuracy of nearshore infragravity wave height model predictions has been investigated using a combination of the spectral short wave evolution model SWAN and a linear 1D SurfBeat model (IDSB). Data recorded by a wave rider located approximately 3.5 km from the coast at 18 m water depth have been used to construct the short wave frequency-directional spectra that are subsequently translated to approximately 8 m water depth with the third generation short wave model SWAN. Next the SWAN-computed frequency-directional spectra are used as input for IDSB to compute the infragravity response in the 0.01 Hz–0.05 Hz frequency range, generated by the transformation of the grouped short waves through the surf zone including bound long waves, leaky waves and edge waves at this depth. Comparison of the computed and measured infragravity waves in 8 m water depth shows an average skill of approximately 80%. Using data from a directional buoy located approximately 70 km offshore as input for the SWAN model results in an average infragravity prediction skill of 47%. This difference in skill is in a large part related to the under prediction of the short wave directional spreading by SWAN. Accounting for the spreading mismatch increases the skill to 70%. Directional analyses of the infragravity waves shows that outgoing infragravity wave heights at 8 m depth are generally over predicted during storm conditions suggesting that dissipation mechanisms in addition to bottom friction such as non-linear energy transfer and long wave breaking may be important. Provided that the infragravity wave reflection at the beach is close to unity and tidal water level modulations are modest, a relatively small computational effort allows for the generation of long-term infragravity data sets at intermediate water depths. These data can subsequently be analyzed to establish infragravity wave height design criteria for engineering facilities exposed to the open ocean, such as nearshore tanker offloading terminals at coastal locations.     

Seakeeping of two ships in close proximity

Underway replenishment is an essential component of long-term naval operations. During underway replenishment, two ships travel in close proximity at moderate forward speed. This paper examines the hydrodynamic interactions that can influence seakeeping during such operations. Presented numerical predictions include the influence of interaction effects on hydrodynamic forces for two ships in waves. A scarcity of validation material for numerical predictions prompted new towing tank experiments for two ships in waves. The experiments used semi-captive models, and the numerical code was modified to include restraining forces for specified modes. The numerical predictions and experiments show that the presence of a larger ship can significantly influence the motions of a smaller ship in close proximity.