Studies on Stochastic Parametric Roll of Ship with Stochastic Averaging Method

The paper studies the parametric stochastic roll motion in the random waves. The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed. Random sea surface is treated as a narrow-band stochastic process, and the stochastic parametric excitation is studied based on the effective wave theory. The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function. By using the stochastic averaging method, the differential equation of motion is transformed into Ito's stochastic differential equation. The steady-state probability density function of roll motion is obtained, and the results are validated with the numerical simulation and model test.     

Control of ship roll using passive and active anti-roll tanks

We numerically studied the full (six degrees of freedom) motion of a cargo ship without roll stabilizers in rough (sea state 5) conditions for multiple heading angles ranging from 0° (follower seas) to 180° (head seas). We found that the ship exhibits excessive roll motion in quartering (45° off the stern), beam, and head seas. Therefore, roll damping is critical in these conditions. We then investigated the performance of passive and active anti-roll tank (ART) systems and compared their performance in each of the three sea conditions. Each ART consists of three identical tanks, distributed along the centerline of the ship, each of which consists of two vertical ducts connected at the bottom with a horizontal duct. A pump is located at the middle of the horizontal duct of each tank. The pumps are switched on for active ARTs but switched off for passive ones. The loads (forces and moments) exerted on the ship by the ARTs are added to the hydrodynamic loads (e.g., due to pressure and viscous effects) and the thrust in the governing equations of motion of the ship. Whereas both passive and active ARTs are able to reduce the excessive roll motion, active ARTs outperform the passive ones from three perspectives. First, they are more effective in reducing the roll motion. Second, they require much less working liquid. Third, their performance is insensitive to their natural frequencies and, hence, to their geometric design. In addition, we found that head seas are most responsive to ARTs, which suggests that they are effective in mitigating parametric roll.     

Numerical simulation of ship stability for dynamic environment

The prediction of ship stability during the early stages of design is very important from the point of vessel’s safety. Out of the six motions of a ship, the critical motion leading to capsize of a vessel is the rolling motion. In the present study, particular attention is paid to the performance of a ship in beam sea. The linear ship response in waves is evaluated using strip theory. Critical condition in the rolling motion of a ship is when it is subjected to synchronous beam waves. In this paper, a nonlinear approach has been tried to predict the roll response of a vessel. Various representations of damping and restoring terms found in the literature are investigated. A parametric investigation is undertaken to identify the effect of a number of key parameters like wave amplitude, wave frequency, metacentric height, etc.     

Simplified model for predicting the onset of parametric rolling

The world container fleet shows the fastest growth of any ship type. The infrastructure for loading and unloading container ships are also growing in many ports around the world. Such a trend is due to the fact that the containerized transportation is becoming more and more attractive due to many factors. The increasing demand in container transportation is met by use of more number of container ships including Post-Panamax and Malacca-max containers. Loss of containers in seas and accidents of container vessels are reported from many parts of seas. New generation containers are severely hit by parametric rolling. Pure loss of stability, due to exponential increase of roll in either broaching—to or head sea conditions, is called parametric rolling, is subjected to rigorous investigation by many researchers. Algebraic expression based on well known Duffing's method is proposed for solutions in parametric rolling. The variation in GM and damping values from trough to crest conditions associated with bow flare immersion and emergence in head sea conditions with pitch resonance with the heading waves are said to be the prime reason for parametric rolling. A simple model to predict the beginning of parametric rolling is described in this paper.     

The optimization of ship weather-routing algorithm based on the composite influence of multi-dynamic elements

This study proposes a ship weather-routing algorithm based on the composite influence of multi-dynamic elements for determining the optimized ship routes. The three-dimensional modified isochrone (3DMI) method utilizing the recursive forward technique and floating grid system for the ship tracks is adopted. The great circle sailing (GCR) is considered as the reference route in the earth coordinate system. Illustrative optimized ship routes on the North Pacific Ocean have been determined and presented based on the realistic constraints, such as the presence of land boundaries, non-navigable sea, seaway influences, roll response as well as ship speed loss. The proposed calculation method is effective for optimizing results by adjusting the weighting factors in the objective functions. The merits of the proposed method can be summarized as: (1) the navigability of the route can be analyzed dynamically to acquire the optimal route; (2) adopting multi-dynamic elements as weighting factors has the benefits in energy efficiency, time-saving and minimum voyage distance; and (3) an ability to enhance speed performance and to incorporate safety concern in a dynamic environment.     

船舶随浪运动稳性仿真计算

本文利用Ｌｉａｐｕｎｏｖ理论，研究了船舶在规则波浪运动的稳性；利用摄动理论，求解出船舶运动响应；并讨论了船舶横摇与垂荡运动频率、最大横摇角和波浪要素对稳性曲线ＧＺ的影响，以及流体动压力对稳性曲线的修正，从而给计算船舶在随浪中的稳性提供了一种方法。     

Application of advanced system identification technique to extract roll damping from model tests in order to accurately predict roll motions

In this paper our previously developed advanced system identification technique [1] has been applied to extract the frequency dependent roll damping from a series of model tests run in irregular (random) waves. It is shown that this methodology accurately models the roll damping which can then be used to produce accurate predictions of the ships roll motion. These roll motion predictions are not only more accurate than the potential flow predictions but more accurate than potential flow models corrected using either empirical prediction methods [2] and even those corrected using roll damping obtained from free decay sallying experiments. This methodology has the potential to significantly improve roll motion prediction during full scale at sea trails of vessels in order to dramatically improve safety of critical operations such as helicopter landing or ship to ship cargo transfer.     

Design of passive anti-roll tanks for roll stabilization in the nonlinear range

The best way of reducing roll motion is by increasing roll damping. Bilge keels are the most common devices for increasing roll damping. If more control is required, anti-roll tanks and fins are used. Tanks have the advantage of being able to function when the ship is not underway. Our objective is to develop design procedures for passive tanks for roll reduction in rough seas. This paper focuses on the design of passive U-tube tanks. The tank-liquid equation of motion is integrated simultaneously with the six-degree-of-freedom (6DOF) equations of the ship motion. The coupled set of equations is solved by using the Large Amplitude Motion Program ‘LAMP’, which is a three-dimensional time-domain simulation of the motion of ships in waves. The unstabilized and stabilized roll motions of a S60-70 ship with forward speed and beam waves have been analyzed. For high-amplitude waves, the unstabilized roll angle exhibits typical nonlinear phenomena: a shift in the resonance frequency, multi-valued responses, and jumps. The performance of a S60-70 ship with a passive tank is investigated in various sea states with different encounter wave directions. It is found that passive anti-roll tanks tuned in the linear or nonlinear ranges are very effective in reducing the roll motion in the nonlinear range. The effect of the tank damping, frequency, and mass on the tank performance is studied. Also, it is found that passive anti-roll tanks are very effective in reducing the roll motion for ships having a pitch frequency that is nearly twice the roll frequency in sea states 5 and 6.     

On the parametric resonance of container ships

This work deals with parametric resonance which poses a great danger especially for container ships sailing in following or head seas. Important parameters that are effective in roll resonance are pointed out. For this purpose, a containership is taken as an example to analyze its stability in longitudinal waves based on the method worked out by American Bureau of Shipping (ABS). Unfavorable sailing conditions such as heading and speed, which directly depend on the environmental conditions, have been determined for this particular ship. These conditions may be reported to the master to guide him to keep his ship out of parametric resonance zones. Numerical details of the procedure have been worked out and provided as well.     

The application of the self-tuning neural network PID controller on the ship roll reduction in random waves

In this paper, we present a mathematical model including seakeeping and maneuvering characteristics to analyze the roll reduction for a ship traveling with the stabilizer fin in random waves. The self-tuning PID controller based on the neural network theory is applied to adjust optimal stabilizer fin angles to reduce the ship roll motion in waves. Two multilayer neural networks, including the system identification neural network (NN1) and the parameter self-tuning neural network (NN2), are adopted in the study. The present control technique can save the time for searching the optimal PID gains in any sea states. The simulation results show that the present developed self-tuning PID control scheme based on the neural network theory is indeed quite practical and sufficient for the ship roll reduction in the realistic sea.     

Subharmonic oscillations in nonlinear rolling

In this paper the rolling motion of a ship is examined with particular regard to the possibility of obtaining oscillations which are subharmonic to the excitation frequency. Three different mechanisms are found to be responsible for this phenomenon, the importance of which has already been recognized in the context of ship stability. The first is related to a strong symmetric or non-symmetric nonlinearity in the righting arm. The second is linked to the harmonic composition of sea waves and the third to the well known parametric excitation caused by coupling between different ship motions in a following sea.The onset of subharmonics is related to a threshold value for the excitation strongly depending on damping. The more appropriate analytical methods for a theoretical study of each mechanism are suggested.     

Wind Farm Support Vessel Extreme Roll Assessment While Docking in the Bohai Sea

Robust prediction of extreme motions during wind farm support vessel(WFSV)operation is an important safety concern that requires further extensive research as offshore wind energy industry sector widens.In particular,it is important to study the safety of operation in random sea conditions during WFSV docking against the wind tower,while workers are able to get on the tower.Docking is performed by thrusting vessel fender against wind tower(an alternative docking way by hinging is not studied here).In this paper,the finite element software AQWA has been used to analyze vessel response due to hydrodynamic wave loads,acting on a specific maintenance ship under actual sea conditions.Excessive roll may occur during certain sea conditions,especially in the beam sea,posing a risk to the crew transfer operation.The Bohai Sea is the area of diverse industrial activities such as offshore oil production,wave and wind power generation,etc.This paper advocates a novel method for estimating extreme roll statistics,based on Monte Carlo simulations(or measurements).The ACER(averaged conditional exceedance rate)method and its modification are presented in brief detail in Appendix.The proposed methodology provides an accurate extreme value prediction,utilizing available data efficiently.In this study the estimated return level values,obtained by ACER method,are compared with the corresponding return level values obtained by Gumbel method.Based on the overall performance of the proposed method,it is concluded that the ACER method can provide more robust and accurate prediction of the extreme vessel roll.The described approach may be well used at the vessel design stage,while defining optimal boat parameters would minimize potential roll.     

A 3D fully coupled analysis of nonlinear sloshing and ship motion

This study investigates the coupling effects of six degrees of freedom in ship motion with fluid oscillation inside a three-dimensional rectangular container using a novel time domain simulation scheme. During the time marching, the tank-sloshing algorithm is coupled with the vessel-motion algorithm so that the influence of tank sloshing on vessel motions and vice versa can be assessed. Several factors influencing the dynamic behavior of tank–liquid system due to moving ship are also investigated. These factors include container parameters, environmental settings such as the significant wave height, current velocity as well as the direction of wind, wave and flow current acting on the ship. The nonlinear sloshing is studied using a finite element model whereas nonlinear ship motion is simulated using a hybrid marine control system. Computed roll response is compared with the existing results, showing fair agreement. Although the two hull forms and the sea states are not identical, the numerical result shows the same trend of the roll motion when the anti-rolling tanks are considered. Thus, the numerical approach presented in this paper is expected to be very useful and realistic in evaluating the coupling effects of nonlinear sloshing and 6-DOF ship motion.     

A multiscale analysis of nonlinear rolling

A new analysis of nonlinear rolling carried out by the multiscale perturbation method is herewith presented. The behaviour of a ship in a regular beam sea is considered and approximate analytical solutions in three nonlinear resonance regions are obtained. These concern the transient and the steady state roll oscillations. The latter fits in well with a previous one obtained through the averaging method and with the results of the numerical simulation.The obtained results appear to be particularly convenient due to their major mathematical simplicity. Moreover, they allow a simple estimation of the maximum roll amplitudes predictable for a given excitation intensity.     

Estimation of the Roll Hydrodynamic Moment Model of a Ship by Using the System Identification Method and the Free Running Model Test

When a fast container ship or a naval vessel turns, accompanying roll motions occur. This roll effect must be considered in the horizontal equations of the motion of the ship to predict the maneuverability of the ship properly. In this paper, a new method for determining a model structure of the hydrodynamic roll moment acting on a ship and for estimating the hydrodynamic coefficients is proposed. The method utilizes a system identification technique with the data from sea trial tests or from free running model (FRM) tests. To obtain motion data that is applied to the proposed algorithm, an FRM of a large container ship was developed. Using this model ship, standard maneuvering tests were carried out on a small body of water out of doors. A hydrodynamic roll moment model was constructed utilizing the data from turning circle tests and a 20-20 zig-zag test. This was then confirmed through a 10-10 zig-zag test. It was concluded that a model structure of the hydrodynamic roll moment model could be established without difficulty through a system identification method and FRM tests.     

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.     

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.     

A synthetic aperture radar sea surface distribution estimation by n-order Bézier curve and its application in ship detection

To dates,most ship detection approaches for single-pol synthetic aperture radar(SAR) imagery try to ensure a constant false-alarm rate(CFAR).A high performance ship detector relies on two key components:an accurate estimation to a sea surface distribution and a fine designed CFAR algorithm.First,a novel nonparametric sea surface distribution estimation method is developed based on n-order Bézier curve.To estimate the sea surface distribution using n-order Bézier curve,an explicit analytical solution is derived based on a least square optimization,and the optimal selection also is presented to two essential parameters,the order n of Bézier curve and the number m of sample points.Next,to validate the ship detection performance of the estimated sea surface distribution,the estimated sea surface distribution by n-order Bézier curve is combined with a cell averaging CFAR(CA-CFAR).To eliminate the possible interfering ship targets in background window,an improved automatic censoring method is applied.Comprehensive experiments prove that in terms of sea surface estimation performance,the proposed method is as good as a traditional nonparametric Parzen window kernel method,and in most cases,outperforms two widely used parametric methods,K and G0 models.In terms of computation speed,a major advantage of the proposed estimation method is the time consuming only depended on the number m of sample points while independent of imagery size,which makes it can achieve a significant speed improvement to the Parzen window kernel method,and in some cases,it is even faster than two parametric methods.In terms of ship detection performance,the experiments show that the ship detector which constructed by the proposed sea surface distribution model and the given CA-CFAR algorithm has wide adaptability to different SAR sensors,resolutions and sea surface homogeneities and obtains a leading performance on the test dataset.     

Head-wave parametric rolling of a surface combatant

Complementary CFD, towing tank EFD, and nonlinear dynamics approach study of parametric roll for the ONR Tumblehome surface combatant both with and without bilge keels is presented. The investigations without bilge keels include a wide range of conditions. CFD closely agrees with EFD for resistance, sinkage, and trim except for Fr>0.5 which may be due to free surface and/or turbulence modeling. CFD shows fairly close agreement with EFD for forward-speed roll decay in calm water, although damping is over/under predicted for largest/smaller GM. Most importantly CFD shows remarkably close agreement with EFD for forward-speed parametric roll in head waves for GM=0.038 and 0.033 m, although CFD predicts larger instability zones at high and low Fr, respectively. The CFD and EFD results are analyzed with consideration ship motion theory and compared with Mathieu equation and nonlinear dynamics approaches. Nonlinear dynamics approaches are in qualitative agreement with CFD and EFD. The CFD and nonlinear dynamics approach results were blind in that the actual EFD radius of gyration k_xx was not known a priori.