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.     

Robust adaptive control of underactuated ships on a linear course with comfort

This paper addresses an important problem in ship control application—the robust stabilization of underactuated ships on a linear course with comfort. Specifically, we develop a multivariable controller to stabilize ocean surface ships without a sway actuator on a linear course and to reduce roll and pitch simultaneously. The controller adapts to unknown parameters of the ship and constant environmental disturbances induced by wave, ocean current and wind. It is also robust to time-varying environmental disturbances, time-varying change in ship parameters and other motions of the ship such as surge and heave. The roll and pitch can be made arbitrarily small while the heading angle and sway are kept to be in reasonably small bounds. The controller development is based on Lyapunov’s direct method and backstepping technique. A Lipschitz continuous projection algorithm is used to update the estimate of the unknown parameters to avoid the parameters’ drift due to time-varying environmental disturbances. Simulations on a full-scale catamaran illustrate the effectiveness of our proposed controller.     

Static and dynamic aspects of a capsize phenomenon

Capsizing of ships constitutes a primary group of casualties that leads to loss of life and money. Unfortunately, its mechanism has yet to be fully resolved due to underlying complex dynamics and parameters. Upon studying the causes in more detail, designing safer ships against capsizing may become a reality. In the present study, a relatively different approach called “reserve of stability” or “stability margins” which utilizes both statical and nonlinear dynamical aspects of stability is employed to analyze ship hydrodynamics. For this purpose a nonlinear roll model in beam waves has been implemented. In order to apply the theory, a capsized vessel is chosen to be analyzed in terms of stability. The necessary data about the vessel at the time of capsizing were collected from the published work found in the naval architecture literature. Suggestions are made based on the results of the analysis to improve ship stability qualities in a seaway.     

On the track keeping and roll reduction of the ship in random waves using different sliding mode controllers

In the paper, an autopilot system composed of sliding mode controller and line-of-sight guidance technique are adopted to navigate the ship in random waves by altering the rudder deflection. Two kinds of sliding mode controller are considered; one is the separate system including sway–yaw control and roll control, the other is the compact system considering sway–roll–yaw control altogether. Both track keeping and roll reduction are accomplished by rudder control and the design parameters of controller are optimized by genetic algorithm. The present simulation results show both the separate controller and the compact controller work quite well, either for track keeping or roll reduction while the ship is sailing in random waves. However, the separate controller is recommended due to its simplicity.     

A study of the angle dependence of roll damping moment

The angle dependence of the roll damping moment is investigated by analysing experimentally obtained free roll decay records. Two ship models were used with and without bilge keels, also results with forward speed were obtained. The analysis indicate strong angle dependence and explains why the quadratic and cubic velocity dependent damping moments are successful in many cases.     

Solution of the nonlinear roll model by a generalized asymptotic method

Mathematical modeling of the nonlinear roll motion of ships is one subject widely dealt with in nonlinear ship dynamics. This paper investigates setting up a form of nonlinear roll motion model and developing its periodic solution by the generalized Krylov–Bogoliubov asymptotic method in the time domain. In this model, nonlinearities are introduced through damping and restoring terms. The restoring term is approximated as a third-order odd polynomial whereas the quadratic term is favored to represent the nonlinear damping. The ship is assumed to be under the influence of a sinusoidal exciting force. Although the method is expressible to contain any order of the perturbing term, a single degree is chosen to avoid cumbersome mathematical complexity. In order to improve the solution a first-order correction term is also included. Moreover, a numerical example is carried out for a small vessel in order to validate the solution scheme.     

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.     

Study on coupling effects of ship motion and sloshing

This study considers the coupling effects of ship motion and sloshing. The linear ship motion is solved using an impulse-response-function (IRF) method, while the nonlinear sloshing flow is simulated using a finite-difference method. The IRF method requires the frequency-domain solution prior to conversion to time domain, but the computational effort is much less than that of direct time-domain approaches. The developed scheme is verified by comparing the motion RAOs between the frequency-domain solution and the solution obtained by the IRF method. Furthermore, a soft-spring concept and linear roll damping are implemented to predict more realistic motions of surge, sway, yaw, and roll. For the simulation of sloshing flow in liquid tanks, a physics-based numerical approach adopted by Kim [2001. Numerical simulation of sloshing flows with impact load. Applied Ocean Research 23, 53–62] and Kim et al. [2004. Numerical study on slosh-induced impact pressures on three-dimensional prismatic tanks. Applied Ocean Research 26, 213–226] is applied. In particular, the present method focuses on the simulation of the global motion of sloshing flow, ignoring some local phenomena. The sloshing-induced forces and moments are added to wave-excitation forces and moments, and then the corresponding body motion is obtained. The developed schemes are applied for two problems: the sway motion of a box-type barge with rectangular tanks and the roll motion of a modified S175 hull with rectangular anti-rolling tank. Motion RAOs are compared with existing results, showing fair agreement. It is found that the nonlinearity of sloshing flow is very important in coupling analysis. Due to the nonlinearity of sloshing flow, ship motion shows a strong sensitivity to wave slope.     

Using wavelet transforms to analyze nonlinear ship rolling and heave-roll coupling

The use of wavelet transforms is explored to investigate the nonlinear dynamical characteristics of ship roll and coupled heave-roll motion. The harmonic character, double period character and chaotic character are observed via a time–frequency window of the wavelet transform. Typical wave parameters in different stability regions are considered. Features such as restoring rolling, divergence rolling, steady state and chaotic responses of ship roll are obtained as well. The investigation in this paper not only highlights the feasibility of using wavelet transforms in the analysis of nonlinear dynamic characteristics of ship rolling in waves, but also shows how it could enhance the analysis abilities.     

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.     

Estimation of survival probability for a ship in beam seas using the safe basin

The purpose of this paper is to analyze the nonlinear ship roll motion equation and the main parameters that induce ship capsizing in beam seas, estimate the survival probability of a ferry in random seas and to find out a risk assessment method for the ship’s intact stability. A single degree of freedom (1-DOF) dynamic system of ship rolling in beam seas is investigated and the nonlinear differential equation is solved in the time domain by the fourth order Runge-Kutta algorithm. The survival probability of a ferry in beam seas is investigated using the theory of “safe basin”. The survival probability is calculated by estimating erosion of “safe basin” during ship rolling motion by Monte Carlo simulations. From the results it can be concluded that the survival probability of a ship in beam sea condition can be predicted by combining Monte Carlo simulations and the theory of “safe basin”.     

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.     

A time-domain method to evaluate the use of moving weights to reduce the roll motion of a ship

A method to evaluate the use of actively controlled moving weights on board ships to reduce roll motion is developed. The weights can simulate in principle anti-roll-tank systems, or they can be considered a possible anti-roll device in their own right. The ship, the moving weight, and the control device are considered components of a single dynamic system. The full eight-degree-of-freedom set of coupled governing equations for the complete dynamic system is derived. And a three-degree-of-freedom non-linear approximation for the roll motion only (MOTSIM) is derived from these eight equations. The reduced set of equations is used to determine the influence of various parameters and to evaluate control strategies. A PID controller is developed to command the position of the weight and a servomechanism model is used to predict its actual position. Then, the moving-weight system is incorporated into LAMP (Large–Amplitude–Motion Program), a computer code that integrates the governing equations of the sea and the motion of the ship interactively and simultaneously and predicts the motion of the ship in the time domain. A comparison of the results from the two simulations shows that there is fairly good correlation between the simple and complex models, but the simple model is a little optimistic in predicting the effectiveness of the moving-weight system. The results predict that the moving-weight system can be an excellent roll-suppressing device when the moving weight is as small as 1% of the displacement of the ship and the maximum distance the weight moves is as small as 15% of the half-beam.     

Transient behavior of towed cable systems during ship turning maneuvers

The dynamic behavior of a towed cable system that results from the tow ship changing course from a straight-tow trajectory to one involving steady circular turning at a constant radius is examined. For large-radius ship turns, the vehicle trajectory and vehicle depth assumed, monotonically and exponentially, the large-radius steady-state turning solution of Chapman [Chapman, D.A., 1984. The towed cable behavior during ship turning manoeuvers. Ocean Engineering 11, 327–361]. For small-radius ship turns, the vehicle trajectory initially followed a corkscrew pattern with the vehicle depth oscillating about and eventually decaying to the steady-state turning solution of Chapman (1984). The change between monotonic and oscillatory behavior in the time history of the vehicle depth was well defined and offered an alternate measure to Chapman's (1984) critical radius for the transition point between large-radius and small-radius behavior. For steady circular turning in the presence of current, there was no longer a steady-state turning solution. Instead, the vehicle depth oscillated with amplitude that was a function of the ship-turning radius and the ship speed. The dynamics of a single 360° turn and a 180° U-turn are discussed in terms of the transients of the steady turning maneuver. For a single 360° large-radius ship turn, the behavior was marked by the vehicle dropping to the steady-state turning depth predicted by Chapman (1984) and then rising back to the initial, straight-tow equilibrium depth once the turn was completed. For small ship-turning radius, the vehicle dropped to a depth corresponding to the first trough of the oscillatory time series of the steady turning maneuver before returning to the straight-tow equilibrium depth once the turn was completed. For some ship-turning radii, this resulted in a maximum vehicle depth that was greater than the steady-state turning depth. For a 180° turn and ship-turning radius less than the length of the tow cable, the vehicle never reached the steady-state turning depth.     

On the development of ship anti-roll tanks

This paper reviews the development of ship anti-roll tanks from the 1880s to the present day including their modelling and control strategies. Mention is also made of other ship roll stabilization systems and the application of the technology to stabilization of other structures. The potential for the use of roll stabilization tanks on modern, high speed multi-hull craft which also have a low speed operational requirement is also discussed.     

Adaptive ship roll mitigation by using a U-tube tank

Active control of ship roll motion with proportional and derivative controller, linear quadratic regulator, generalized predictive control (GPC), and deadbeat predictive control, is studied by using a U-tube water tank. For the predictive control, system identification is applied to update the parameters of linear ship roll model with U-tube tank when the ship dynamics changes. Numerical simulations show that GPC has the best performance and the U-tube tank is effective in ship roll mitigation.     

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.