Mathematical modelling of response amplitude operator for roll motion of a floating body: Analysis in frequency domain with numerical validation

This paper investigates mathematical modelling of response amplitude operator （RAO） or transfer function using the frequency-based analysis for uncoupled roll motion of a floating body under the influence of small amplitude regular waves. The hydrodynamic coefficients are computed using strip theory formulation by integrating over the length of the floating body. Considering sinusoidal wave with frequency （ω ） varying between 0.3 rad/s and 1.2 rad/s acts on beam to the floating body for zero forward speed, analytical expressions of RAO in frequency domain is obtained. Using the normalization procedure and frequency based analysis, group based classifications are obtained and accordingly governing equations are formulated for each case. After applying the fourth order Runge-Kutta method numerical solutions are obtained and relative importance of the hydrodynamic coefficients is analyzed. To illustrate the roll amplitude effects numerical experiments have been carried out for a Panamax container ship under the action of sinusoidal wave with a fixed wave height. The effect of viscous damping on RAO is evaluated and the model is validated using convergence, consistency and stability analysis. This modelling approach could be useful to model floating body dynamics for higher degrees of freedom and to validate the result.     

Dynamic interaction of parallel moving ships in close proximity

Nowadays,there are many studies conducted in the field of marine hydrodynamics which focus on two vessels traveling and floating in sufficiently close proximity to experience significant interactions.The hydrodynamic behavior of parallel moving ships in waves is an interesting and important topic of late.A numerical investigation has been carried out for the prediction of wave exciting forces and motion responses of parallel moving ships in regular waves.The numerical solution was based on 3D distribution technique and using the linear wave theory to determine the exciting forces and ship＇s motion.The speed effects have been considered in the Green function for more realistic results.The numerical computations of wave exciting forces and motion responses were carried out for a Mariner and Series 60 for the purpose of discovering different Froude numbers and different separation distances in head sea conditions.Based on the numerical computations,it was revealed that the sway,roll and yaw have a significant effect due to hydrodynamic interaction.     

浮体横摇运动传递函数数学建模的频域分析研究及相关数值验证(英文)

This paper investigates mathematical modelling of response amplitude operator(RAO) or transfer function using the frequency-based analysis for uncoupled roll motion of a floating body under the influence of small amplitude regular waves. The hydrodynamic coefficients are computed using strip theory formulation by integrating over the length of the floating body. Considering sinusoidal wave with frequency( ω) varying between 0.3 rad/s and 1.2 rad/s acts on beam to the floating body for zero forward speed, analytical expressions of RAO in frequency domain is obtained. Using the normalization procedure and frequency based analysis, group based classifications are obtained and accordingly governing equations are formulated for each case. After applying the fourth order Runge-Kutta method numerical solutions are obtained and relative importance of the hydrodynamic coefficients is analyzed. To illustrate the roll amplitude effects numerical experiments have been carried out for a Panamax container ship under the action of sinusoidal wave with a fixed wave height. The effect of viscous damping on RAO is evaluated and the model is validated using convergence, consistency and stability analysis. This modelling approach could be useful to model floating body dynamics for higher degrees of freedom and to validate the result.     

应用零航速减摇鳍的海洋机器人近水面时的横摇减摇控制(英文)

A zero-speed fin stabilizer system was developed for rolling control of a marine robot.As a robot steering device near the sea surface with low speed,it will have rolling motion due to disturbance from waves.Based on the working principle of a zero-speed fin stabilizer and a marine robot’s dynamic properties,a roll damping controller was designed with a master-slave structure.It was composed of a sliding mode controller and an output tracking controller that calculates the desired righting moment and drives the zero-speed fin stabilizer.The methods of input-output linearization and model reference were used to realize the tracking control.Simulations were presented to demonstrate the validity of the control law proposed.     

Prediction of Stabilization of Ship in Random Wave

In this paper we show thc method of energy in part with which we can get the model of random wave,and predict theroll motion of unstabilized ship and stabilized ship using the wave model.The control parameters of fin stabilizer are determinedaccording to the performance index. The simulation of the system is also made in this paper. The comparison of the simulationwith real ship indicates that the method can be used in the prediction of roll motion of a stabilized ship in random wave.     

嵌入拉格朗日元法估算某些水下装置吸收波浪能研究(英文)

A simple approach is described to estimate the wave power absorption potential of submerged devices known to cause wave focusing and flow enhancement.In particular,the presence of a flow-through power take-off(PTO)system,such as low-head turbines,can be accounted for.The wave radiation characteristics of an appropriately selected Lagrangian element(LE)in the fluid domain are first determined.In the limit of a vanishing mass,the LE reduces to a patch of distributed normal dipoles.The hydrodynamic coefficients of this virtual object are then input in a standard equation of motion where the effect of the PTO can be represented,for example,as a dashpot damping term.The process is illustrated for a class of devices recently proposed by Carter and Ertekin(2011),although in a simplified form.Favorable wave power absorption is shown for large ratios of the LE wave radiation coefficient over the LE added mass coefficient.Under optimal conditions,the relative flow reduction from the PTO theoretically lies between 0.50 and 1 2≈0.71,with lower values corresponding to better configurations.Wave power capture widths,the sensitivity of results to PTO damping and sample spectral calculations at a typical site in Hawaiian waters are proposed to further illustrate the versatility of the method.     

护卫舰横摇稳定舵的H∞/H2控制器的设计和比较（英文）

The roll motions of ships advancing in heavy seas have severe impacts on the safety of crews, vessels, and cargoes; thus, it must be damped. This study presents the design of a rudder roll damping autopilot by utilizing the dual extended Kalman filter(DEKF)–trained radial basis function neural networks(RBFNN) for the surface vessels. The autopilot system constitutes the roll reduction controller and the yaw motion controller implemented in parallel. After analyzing the advantages of the DEKFtrained RBFNN control method theoretically, the ship's nonlinear model with environmental disturbances was employed to verify the performance of the proposed stabilization system. Different sailing scenarios were conducted to investigate the motion responses of the ship in waves. The results demonstrate that the DEKF RBFNN–based control system is efficient and practical in reducing roll motions and following the path for the ship sailing in waves only through rudder actions.     

The method of imbedded Lagrangian element to estimate wave power absorption by some submerged devices

A simple approach is described to estimate the wave power absorption potential of submerged devices known to cause wave focusing and flow enhancement. In particular, the presence of a flow-through power take-off （PTO） system, such as low-head turbines, can be accounted for. The wave radiation characteristics of an appropriately selected Lagrangian element （LE） in the fluid domain are first determined. In the limit of a vanishing mass, the LE reduces to a patch of distributed normal dipoles. The hydrodynamic coefficients of this virtual object are then input in a standard equation of motion where the effect of the PTO can be represented, for example, as a dashpot damping term. The process is illustrated for a class of devices recently proposed by Carter and Ertekin （2011）, although in a simplified form. Favorable wave power absorption is shown for large ratios of the LE wave radiation coefficient over the LE added mass coefficient. Under optimal conditions, the relative flow reduction from the PTO theoretically lies between 0.50 and 1 2 ≈ 0.71, with lower values corresponding to better configurations. Wave power capture widths, the sensitivity of results to PTO damping and sample spectral calculations at a typical site in Hawaiian waters are proposed to further illustrate the versatility of the method.     

海洋观测平台在波浪中运动响应的数值模拟(英文)

Offshore observation platforms are required to have great ability to resist waves when they are operating at sea. Investigation on the motion characteristics of the platforms in the sea can provide significant reference values during the platform design procedure. In this paper, a series of numerical simulation on the interaction of a triple-hulled offshore observation platform with different incident waves is carried out. All of the simulations are implemented utilizing our own solver naoe-FOAM-SJTU, which is based and developed on the open source tools of OpenFOAM. Duration curves of motion characteristics and loads acting on the platform are obtained, and a comparison between the results of the amplitude in different incident waves is presented. The results show that the solver is competent in the simulation of motion response of platforms in waves.     

超大型浮体连接器载荷时域计算（英文）

Loads generated after an air crash, ship collision, and other accidents may destroy very large floating structures(VLFSs) and create additional connector loads. In this study, the combined effects of ship collision and wave loads are considered to establish motion differential equations for a multi-body VLFS. A time domain calculation method is proposed to calculate the connector load of the VLFS in waves. The Longuet–Higgins model is employed to simulate the stochastic wave load. Fluid force and hydrodynamic coefficient are obtained with DNV Sesam software. The motion differential equation is calculated by applying the time domain method when the frequency domain hydrodynamic coefficient is converted into the memory function of the motion differential equation of the time domain. As a result of the combined action of wave and impact loads, high-frequency oscillation is observed in the time history curve of the connector load. At wave directions of 0° and 75°, the regularities of the time history curves of the connector loads in different directions are similar and the connector loads of C1 and C2 in the X direction are the largest. The oscillation load is observed in the connector in the Y direction at a wave direction of 75° and not at 0°. This paper presents a time domain calculation method of connector load to provide a certain reference function for the future development of Chinese VLFS     

三体船横摇运动

介绍了关于三体船横摇运动的研究工作。采用能量法，由自由横摇衰减试验测量数据计算了三体船横摇阻尼系数，分析横摇过程中阻尼非线性作用的特点，讨论侧体横向布置位置、舭龙骨和航速对三体船横摇运动的影响，对线性、非线性方法用于预报三体船横摇运动进行比较分析。三体船模型横摇试验包括静水中的自由横摇衰减试验、规则波中的零速横摇试验。试验中通过系列变化侧体横向布置位置，并对侧体安装舭龙骨进行对比试验，研究侧体布置和舭龙骨对三体船横摇运动的影响。经与试验结果对比，本文对三体船横摇运动预报的结果令人满意。     

三体船横摇模型试验及其特性分析

三体船在波浪中的横摇特性和优点是三体新船型研发的技术支撑,采用模型试验和理论分析相结合的方法,对三体船横摇运动特性进行探讨。开展三体船静水横摇、正横浪零速波浪横摇模型试验,得出三体船线性、非线性阻尼假设下的横摇阻尼、频率响应和周期。通过横摇响应曲线的分析和对比,得出三体船不同侧体位置下波浪中横摇附加惯量、阻尼和运动响应、周期特性,以及侧体位置对以上各横摇特性影响的规律。研究表明：三体船横摇阻尼远大于常规单体船,而横摇运动幅值响应远小于常规单体船;侧体的横位置对三体船横摇具有显著影响,侧体纵向位置对横摇影响很小。综合考虑运动响应和横摇周期,在不规则波中三体船的横摇比常规单体船缓和得多。     

基于神经网络的围网渔船横摇运动研究

为了快速预报一艘65 m的围网渔船在任意载况规则波中横摇运动频率响应函数及不规则波中各海况下的横摇角有义值,应用神经网络的原理和算法,以该船7种实际航运载况的耐波性计算数据为训练样本,建立满足精度要求的围网渔船横摇运动神经网络预估模型。并分析吃水、重心高度、航速和浪向对横摇运动的影响。该模型可应用于风浪中船舶航行安全性评估。     

船舶非线性横摇运动方程的线性化研究

考虑阻尼力矩和恢复力矩的非线性,运用能量法对正横规则波中船舶非线性横摇运动方程进行等效线性化,导出等效线性系数表达式,并验证其工程实用性,为船舶横摇预报提供理论分析计算模型。     

URANS prediction of roll damping for a ship hull section at shallow draft

It is analytically difficult to calculate roll damping of ships due to the effects of viscosity. Therefore, computational fluid dynamics (CFD) has become a powerful tool in predicting roll damping recently. The unsteady flow around a forced rolling hull section with bilge keels can be calculated using a commercial URANS code which includes the viscous effects. In this study, two-dimensional (2D) roll damping calculations for a S60 midsection with bilge keels including free surface effects are performed for shallow draft case. The first objective of the study is to show whether the URANS code can be used to predict roll damping coefficient correctly. The second one is to show why Ikeda’s estimation method is insufficient at shallow draft case. Sinusoidal forced roll motion calculation method of roll damping moment with the help of a sliding interface and a fixed roll axis is successfully applied to predict roll damping coefficient. The calculations are carried out for different roll motion periods and amplitudes to validate the accuracy of the URANS code for different cases. Numerical results are compared with experiments, which were carried out at the towing tank facility of Osaka Prefecture University (OPU), and Ikeda’s estimation method. The results show that the URANS code is capable of predicting roll damping coefficients in a good agreement with experimental results and can be used further to develop a better model for prediction of roll damping.     

二代稳性衡准纯稳性丧失直接评估方法研究(二)

针对国际海事组织(IMO)正在制定的船舶第二代完整稳性衡准中的纯稳性丧失直接评估衡准,本文提出了纵荡-横荡-横摇-首摇4自由度运动耦合的标准数学模型,进行了纯稳性丧失直接评估.该方法首先基于MMG操纵性标准方法,构建纵荡-横荡-横摇-首摇4自由度运动方程,同时考虑了舵控制方程,其次在纵荡、横荡、横摇、首摇方程右边考虑时域波浪力/力矩,且横摇方程右边进一步考虑了粘性横摇阻尼力矩和波浪中复原力臂变化.最后采用ONR内倾船进行了尾斜浪中纯稳性丧失直接数值计算,为纯稳性丧失直接稳性评估衡准的应用奠定了基础.     

Calibration of response amplitude operators based on measurements of vessel motions and directional wave spectra

A vessel's response to waves is dependent on a large number of parameters, some of which are both frequency and direction dependent. To predict vessel response, these parameters are used to construct response amplitude operators (RAOs) that act as transfer functions between the directional wave spectra and the motion spectra of the vessel. In particular situations, however, vessel motions predicted using RAOs calculated with general-purpose radiation-diffraction codes and measured wave spectra are found to deviate from measured vessel responses. To address this problem, a methodology for calibrating RAOs based on measurements of the directional wave spectra and vessel motions is proposed. Use is made of a vector fitting method through which the frequency dependent hydrodynamic properties of the vessel can be approximated by a ratio of two polynomials, thus greatly reducing the number of parameters that need to be calibrated. The reduced set of parameters is subsequently related to previously identified causes of RAO inaccuracy in order to arrive at optimization algorithms for identifying more accurate RAOs from the measurements. It is shown that the RAOs can be improved with accuracy in situations where the discrepancies are caused by imprecise estimates for the vessel's radii of gyration, center of gravity, or viscous damping. When the discrepancies in the RAOs are related to the potential mass, damping and wave forces, however, the problem becomes highly non-convex and it is not possible to find a unique RAO that satisfies the data.     

粘性流中船舶横摇阻尼计算

船舶横摇阻尼的确定是准确预报船舶在波浪中运动的关键之一.本文以粘性流理论为基础,以连续性方程和N-S方程为控制方程.对Series 60船型的二维横剖面绕流进行了数值模拟,计算分析了不同工况下船体剖面的横摇阻尼系数,并与相关实验结果进行了比较.对比和研究表明,本文的方法能给出船舶横摇运动诱导的涡,船体的横摇阻尼等,可进一步拓展应用于船舶在波浪中运动的分析预报和优化设计等方面.     

Influence of initial heeling angle on ship roll motion response北大核心CSCD

[目的]系统地研究初始横倾角对随机横浪下船舶横摇运动响应的影响。[方法]以路径积分法为基础,通过数值求解控制横摇运动微分方程概率属性的Fokker-Planck方程,得到横摇运动响应的概率分布。[结果]结果显示,初始横倾角对船舶横摇运动响应谱的影响有限,但对横摇角概率分布以及横摇运动响应极值分布的影响十分明显,且会造成船舶安全性的显著恶化。[结论]路径积分法可作为研究随机海浪下船舶横摇运动特性的有效数值方法。     

随机横浪中船舶倾覆过程模拟与安全域计算

研讨了随机海浪中船舶非线性随机横摇运动倾覆过程和安全域问题.考虑非线性阻尼、非线性复原力矩和随机波浪,建立了随机横浪中船舶运动的随机非线性微分方程.考虑两参数海浪谱和不同的有义波高,计算随机波浪力矩,采用简谐加速度数值计算方法求解随机微分方程,进行了随机倾覆过程的数值模拟.考虑船舶运动的瞬时状态,发展了胞映射方法计算随机非线性横摇运动安全域的方法,并编制了计算机程序.模拟了一条渔船不同有义波高作用下横摇倾覆过程,考虑不同的初始条件及随机波浪参数,在初始值平面上采用胞映射法构造了渔船航行的安全域.波高较小时,安全域是一个连续的区域;随着有义波高增大,安全域面积减小并且不再连续,倾覆域和安全域相互包围.计算结果表明,船舶运动的瞬时状态对安全域具有重要影响,而且随机海浪中安全域具有随机特性.