Ship Roll Motion Research Articles

Experimental and numerical investigations on responses of ship rolling motion coupled with liquid sloshing inside three tanks with and without baffles

Rolling response of a floating production storage and offloading coupled with sloshing inside three liquid tanks with and without baffles under different wave periods is analyzed experimentally in a towing tank. The main focuses of this study are to examine the effect of baffles on natural period and amplitude of ship rolling motion coupled sloshing for various tank filling depths. The experimental results show that baffles decrease the natural period of ship rolling motion for low filling conditions (20% and 30%). However, when the filling depths are high (e.g., 60% and 70%), the natural period is increased due to the installation of the baffles. The changing of natural period is revealed quantitatively by the change of the sloshing-induced added mass calculated by the numerical potential flow model. The amplitude of ship rolling motion coupled with sloshing without baffles reveals two typical phenomena, namely the anti-rolling effect at low filling conditions and the enhanced-rolling effect at high filling conditions, depending on the dominant factor between the hydrostatic and the hydrodynamic forces. Baffles are effective in suppressing the amplitude of ship rolling motion, especially at its natural period. Their effect is more obvious for low filling condition than that for high filling conditions. This is because baffles are more effective in stopping the fluid inside the tanks from flowing to the inclined side when the filling depth is low. It is also found that baffles can decrease the sloshing-induced mass at low filling conditions and increase that at middle and high filling conditions. The above-mentioned changes are the reasons for the decrease and increase in the natural period of ship rolling motion at low and high filling conditions, respectively, due to the application of baffles.

An insight about roll damping within the second generation intact stability criteria

AbstractDespite the recognized complexity to estimate the damping influence on ship roll motion, some efficient semi-empirical methodologies have been developed along the years to this purpose. CFD methods, in principle the most appropriate tools to predict roll damping, are not a favorite option in preliminary design at present due to their implications in terms of complexity and computational time. In this paper, an integration of the semi-empirical Ikeda’s simplified method has been formulated with modification of the bilge keels and lift components, following a contribution found in the literature and relevant for Ro–Ro ships. Moreover, with focus on damping evaluation, the second generation intact stability criteria (SGISc) have been investigated: the second-level vulnerability criteria for dead ship condition and parametric roll have been applied to a Ro–Ro passenger ship. Both the consolidated and the new proposed roll damping prediction methods have been implemented in order to appreciate their effects on the final outcome.

Multi-objective model predictive control for ship roll motion with gyrostabilizers

Ships are prone to significant roll motion while sailing in adverse conditions, posing a serious threat to ship safety and maneuverability. Therefore, effective ship motion control is crucial. Integrating the MPC control algorithm with a gyrostabilizer can effectively achieve this goal. To evaluate and compare control strategies, a multi-objective model predictive control is proposed that integrates considerations of ship motion, safety, and energy consumption to conduct the operation concurrently. By assigning different weights to these factors, the study aims to discern the varying impacts on control effectiveness. The response of ship roll motion in beam waves is evaluated through roll hydrodynamic modelling, accounting for wave memory effects. A state-space model of ship and gyrostabilizers is proposed to represent their dynamic interaction and response to external moment. Subsequently, the influence of different weightings in the multi-objective model predictive control is compared, and the control performances of a frigate under different wave conditions are analyzed respectively. The multi-objective model predictive control, with varied weight assignments, leads to distinct reductions in roll motions. This investigation offers valuable insights into controlling roll motion in beam wave conditions, effectively reducing motion under varying sea conditions, and providing alternative guidance tailored to user preferences.

Research on parametric roll of the polar environmental transport ship based on time-domain Rankine panel method

In this study, the roll damping of a polar environmental transport ship (PETS) is estimated using viscous CFD method, and the parametric roll is simulated based on time-domain Rankine panel method. This method's reliability is validated by contrasting the simulation results with the experimental data of C11 container ship. The roll damping of C11 container ship is estimated using CFD method and improved Ikeda's method, respectively. Then, the time-domain Rankine panel method is adopted to simulate the roll motions of C11 container ship, and the simulation results are contrasted with experimental data. It confirms that the roll damping is calculated by CFD method and the roll motions of ships are simulated based on time-domain Rankine panel method has good applicability. Finally, the influence of wave steepness, wavelength, and the ratio of encounter frequency ωe to natural roll frequency ωroll on the parametric roll of PETS are studied. It is found that the maximum roll angle of PETS increases along with wave steepness. As the wavelength increases, the possibility of parametric roll for PETS is also increasing. When the parametric roll of PETS occurs, the ωe/ωroll tends to increase.

Probabilistic solution of non-linear random ship roll motion by data-driven method

In this paper, a data-driven method is employed to investigate the probability density function (PDF) of nonlinear stochastic ship roll motion. The mathematical model of ship roll motion comprises a linear term with cubic damping and a nonlinear restoring moment represented as an odd-degree polynomial up to the fifth order. The data-driven method integrates maximum entropy, the pseudo-inverse algorithm, and a backpropagation (BP) neural network to obtain the PDF. The process begins with simulating data for the nonlinear stochastic system, followed by dimensional analysis to identify dimensionless parameter clusters. Optimization algorithms are then employed to solve for the coefficients, leading to the development of a BP neural network model trained to predict the PDF across various system characteristics and excitation intensities. The method's effectiveness is validated with Monte Carlo simulations, demonstrating high accuracy and reduced sensitivity to parameter variations.

A dynamic modelling method for the naval gun under the influence of random wave excitation and servo system

ABSTRACT This paper proposed a mechanical–electrical-hydraulic coupling dynamic modelling method for naval guns coupled with multiple nonlinear factors. The ship's rocking motion equation is derived based on the wave spectrum formula to introduce the influence of random wave excitation into the vibration analysis of naval guns. An efficient gear transmission model of the servo system is developed using a multibody contact-based model to control the computational cost and based on the tooth stiffness theory, the time-varying mesh stiffnesses are considered. The dynamic results show that the ship's rolling motion will have more influence on gun dynamic characteristics than the pitching motion. Though under the control of servo systems, the adverse influence of the ship's rocking motion on cradle motion is basically eliminated. The instantaneous residual disturbances of the cradle increase for the driving torque saturation and the residual disturbances of the cradle will increase gradually with the ship's rocking motion increasing.

Study on numerical simulation and mitigation of parametric rolling in a container ship under head waves

To investigate the parametric rolling motion of container ships navigating in head seas, this study utilizes the unsteady RANS approach combined with dynamic overlapping grid technology to simulate parametric roll in a container ship under the coupled motions of roll, pitch, and heave. Initially, the model was validated against experimental results, demonstrating good agreement and thus confirming the reliability of the computational method. Furthermore, the paper investigates the impacts of the initial roll angle, encounter frequency, and the addition of bilge keels on parametric rolling. The research findings indicate that the initial angles of rolling impact the duration needed to attain a steady roll condition, yet they have minimal effect on the amplitude post-stabilization. The likelihood of parametric rolling arises when the frequency of encounters doubles that of the ship's inherent roll frequency. Furthermore, the likelihood of parametric rolling escalates when the wavelengths approach the length of the ship. Installing bilge keels markedly reduces the parametric rolling movement in vessels, and the occurrence of parametric rolling is also delayed.

ALGORITHM FOR ESTIMATING THE PARAMETRIC ROLL MOTIONS

For a ship, both synchronous and parametric roll motions can be modelled by nonlinear second-order differential equations with the roll angle as dependent variable and the nonlinearities coming from the damping and restoring moments. In the absence of exact solution techniques, approximate solutions for such equations can be obtained, in principle, analytically or numerically. In this paper, we focused on a fast and accurate recursive scheme based on the segmentation of the time domain into a fine grid of intervals of equal lengths. Due to the smallness of each time subinterval, a reset of the terms of the initial nonlinear equation of motion allows replacing it with a linear one in which the constant coefficients represent approximate values of the former variable coefficients in the middle of each subinterval. The linear equation is solved via the Laplace transform and the resulting solution together with its first derivatives is used to generate the iterative algorithm. This technique was applied to the case of two typical roll equations. The first describes the synchronous roll of a vehicle ferry model equipped or not with bilge keels while the second estimates the parametric roll of a container ship model. In both cases, the analyzed recursive algorithm not only generated results in full agreement with those provided by the ode45 solver in Matlab but also lead to a gain in computation time and offered more flexibility in imposing some restrictive conditions associated, for example, with exceeding some oscillation amplitudes or to the ship capsizing. Key words: synchronous and parametric ship rolling, iterative scheme

Four-DOF Maneuvering Motion of a Container Ship in Shallow Water Based on CFD Approach

With the continuous increase in ship size combined with the generally slower increase in the sizes of waterways, the need for the prediction of ship maneuvering in shallow waterways continues to attract attention from the international scientific community. Ship behavior in shallow water is relevant in seabed effects that result in changing the hydrodynamic forces acting on a ship. In this study, the maneuvering characteristics of a container ship with four degrees of freedom in shallow water are analyzed. The Reynolds-Averaged Navier Stokes approach in Ansys Fluent code is used to produce the maneuvering coefficients through the simulations of forward running, static drift, static heel, circular motion, the combined motions, and the pure roll motion of the KRISO container ship. The maneuvering characteristics of the ship are estimated for evaluating the ship behaviors in shallow-water conditions. The obtained results show that the roll has a significant decrease and the ship’s turning diameter has a significant increase when the ship operates in a shallow waterway. The predictions of the maneuvering characteristics of the ship are in good agreement with those of free-running model tests, indicating that the numerical simulation based on the Computational Fluid Dynamics method has compromising capability to predict the maneuvering derivatives and the four-DOF ship maneuvering motion in shallow water as well.

A novel stochastic approach to investigate the probabilistic characteristics of the ship roll system with sinusoidal restoring force

A novel constrained optimization-oriented exponential–polynomial–closure (CO-EPC) method is developed to investigate the ship roll-motion with non-smooth damping and sinusoidal restoring moments under stochastic wave excitations. The ’non-smooth damping’ and ’sinusoidal restoring moments’ refer to the damping force and restoring force of the system, respectively, which are mathematically expressed using non-smooth and sinusoidal functions. The propagation of uncertainty in the system is governed by the Fokker–Plank–Kolmogorov (FPK) equation, as the presence of stochastic wave excitation induces Markovian behavior in the system responses. The solution of FPK must meet the non-negativity, normalization, and limitation attributes. To fulfill these essential requirements, a novel method has been developed. By deriving the moment functions of the non-smooth terms (for the damping moment part) and the sine terms (for the restoring moment part), the complicated FPK equation is solved. Through two case studies, it is found that the CO-EPC approach demonstrates superior efficiency compared to Monte Carlo simulation and produces more accurate solutions in contrast to the Gaussian closure method. These findings support the effectiveness of CO-EPC in studying the ship roll motion problem under stochastic wave excitations.

Определение нелинейных сил второго порядка, возникающих при поперечно-горизонтальных, вертикальных и бортовых колебаниях накрененных шпангоутных контуров

В статье рассматривается определение нелинейных сил и моментов второго порядка для различных изолированных видов качки на основании применения двухмерной потенциальной теории. Приводится сравнение результатов расчета нелинейных сил и моментов соответствующих видов качки при использовании классического и модифицированного методов интегральных уравнений для жидкости как неограниченной, так и ограниченной глубины. Результаты расчетов, полученные при использовании модифицированных методов, сопоставляются с результатами расчетов, полученных классическими методами. Показано удовлетворительное согласование результатов расчета между собой в большинстве случаев. Представлено исследование влияния угла накренения различных типов шпангоутных контуров на величину нелинейных сил и моментов второго порядка. Делается вывод о целесообразности дальнейшего использования модифицированного метода интегральных уравнений в условиях мелководья при определении нелинейных сил и моментов, действующих на накрененные контура. The article considers the calculation of second-order non-linear forces and moments for various isolated types of ship motions based on the application of two-dimensional potential theory. The calculation results of non-linear forces and moments are given for the corresponding types of ship motions using classical and modified methods of integral equations for fluid of both infinite depth and in shallow waters. The calculation results obtained using modified methods are compared with the calculation results obtained by classical methods. Most of the time, calculation yields a satisfying result. An investigation of the heel angle influence for the various types of frame sections on the values of second-order non-linear forces and moments is shown. The conclusion is made about the expediency of further use of the modified method of integral equations in shallow water conditions when determining nonlinear forces and moments acting on heeled contours.

An enhanced hybrid scheme for ship roll prediction using support vector regression and TVF-EMD

In order to represent the complex characteristics of ship roll motion such as nonlinearity, uncertainty, and time-varying dynamics thus improving the ship roll prediction accuracy, an enhanced hybrid prediction scheme is proposed by using improved swarm intelligent optimization, time series decomposition, and machine learning. Firstly, the novel time-varying filtering-based empirical mode decomposition (TVF-EMD) is employed to decompose the ship roll motion data into multiple mode components with dynamic time-varying characteristics, which immunes of the mode mixing and intermittency problems of traditional empirical mode decomposition (EMD). Then, the support vector regression is utilized to train and predict mode components. Finally, the predicted results of individual components are reconstructed to achieve the final ship roll prediction angles. To avoid the unfavorable influence of manual parameter selection for TVF-EMD, an improved black widow optimization algorithm is employed to optimize the parameter configuration. The feasibility and effectiveness of the enhanced hybrid model are validated by ship roll prediction simulation based on the measured data of M.V. YuKun at sea. The experimental results show that the enhanced hybrid scheme can improve the prediction accuracy of ship roll motion and outrank those by using methods of EMD, ensemble empirical mode decomposition, and variational mode decomposition.

Comparison of stochastic stability boundaries for parametrically forced systems with application to ship rolling motion

Numerous accidents caused by parametric rolling have been reported on container ships and pure car carriers (PCCs). Considering this dangerous phenomenon, the parametric rolling in irregular seas is examined in this paper based on the stability of the systems origin, which corresponds to the upright condition of the vessel. It provides a novel theoretical explanation of the instability mechanism for two cases: white-noise parametric excitation and colored-noise parametric excitation. Moreover, the authors confirm the usefulness of the previously provided formulae by Roberts and Dostal by means of numerical examples.

Rapid prediction of damaged ship roll motion responses in beam waves based on stacking algorithm

Rapid prediction of damaged ship roll motion responses in beam waves based on stacking algorithm

Stochastic bifurcation and chaos study for nonlinear ship rolling motion with random excitation and delayed feedback controls

In this paper, we investigate the stochastic dynamics of a class of nonlinear ship rolling motion with multiplicative noise under both displacement and velocity delay feedback controls. The Itoˆ-stochastic differential equation for the amplitude and phase of the roll motion is derived using the stochastic center manifold method and stochastic average method. Subsequently, the stochastic stability and bifurcation behaviors of the system are analyzed. Furthermore, using the stationary probability density method, we derive the parameter conditions for the occurrence of stochastic D-bifurcation and stochastic P-bifurcation. We also analyze the properties and shape changes of the system’s probability density function under different parameters through numerical simulation. It has been determined that the system exhibits stochastic bifurcation behavior, specifically P-bifurcation and D-bifurcation. The validity of the method is verified by a numerical model. The theoretical chaos threshold of the system is determined using the random Melnikov method, and the impact of delayed feedback parameters on the chaotic motion of the system is analyzed by combining the bifurcation diagram, phase portrait, and time series.

Premonition-driven deep learning model for short-term ship violent roll motion prediction based on the hull attitude premonition mechanism

Ship transit forecasting can provide advanced movement information to a multidimensional wave motion compensation system. However, traditional deep learning models based on data-driven or physical data have difficulty in accurately predicting the rapid variations in ship motion attitudes that frequently occur in complex ocean environments. Therefore, a premonition-driven deep learning model is proposed in this paper to significantly improve the prediction accuracy of ship violent roll motion. This model applies precursor information to predict premonitory values of ship prospective motion attitudes based on an integrated statistical regression model and then employs these premonitory values to revise the outputs of the deep learning time series model. First, a hull attitude premonition mechanism is presented based on biological premonition cognitive behaviour, which captures the correlation relationships between extreme values by downgrading the globally continuous time series prediction problem to a time-independent regression problem. The corresponding methods for predicting local extreme values and deep feedforward neural network cluster are established based on these correlation relationships between the extreme values to achieve precise premonitory values. Second, the time and amplitude variables of the extreme angle values are transformed to countdown time variables and sequential sets of premonitory angle values. Two types of premonition units and their respective premonitory long short-term memory neural networks are constructed to upgrade the regression problem to a globally continuous time series prediction problem. Finally, a single-step output recurrent strategy is applied to forecast the short-term ship motion attitude for fifteen seconds by considering eleven initially predicted points across the two datasets. In sixty-six simulation experiments, the mean absolute error, root mean squared error, and mean absolute percentage error of the premonition-driven long short-term memory neural networks are considerably lower than those of traditional deep learning models. These simulation experiments verify that the premonition-driven deep learning model can effectively forecast short-term violent ship roll motion and provide safeguards for cargo transfer.

Short-term ship roll motion prediction using the encoder–decoder Bi-LSTM with teacher forcing

The safety of maritime operations has become a paramount concern with the advancement of intelligent ships. Ship stability and safety are directly impacted by roll motion, making the prediction of short-term ship roll motion pivotal for assisting navigators in making timely adjustments and averting hazardous roll conditions. However, predicting ship roll motion poses challenges due to nonlinear dynamics. This study aims to predict short-term ship roll motion by leveraging the encoder–decoder structure of Bidirectional Long Short-Term Memory Networks (Bi-LSTM) with teacher forcing. The model is accomplished by employing an encoder–decoder structure to map input sequences to output sequences of varying lengths, and employing teacher forcing to enhance the network’s ability to extract information. To refine and analyze the prediction model, aspects such as the quantity of training data to guarantee model generalization, establishing apposite length relationships between input and output sequences, and assessing the model performance in various sea states are investigated. Additionally, comparative experiments assessing roll motion prediction for intervals of 10s, 30 s, 60 s, and 120 s are conducted to substantiate the necessity and effectiveness of the proposed network. The dataset originates from a commercial professional simulator developed by the Norwegian company Offshore Simulator Center AS (OSC).

Short-Term Prediction of Ship Roll Motion in Waves Based on Convolutional Neural Network

In this study, a short-term prediction method for ship roll motion in waves based on convolutional neural network (CNN) is presented. Firstly, based on the ship roll motion equation, the data for free roll attenuation motion in still water, roll motion in regular waves, and roll motion excited by irregular waves are simulated, respectively. Secondly, the simulation data is normalized and preprocessed, and then the time-sliding window technique is applied to construct the training and testing sample sets. Thirdly, the CNN model is trained by learning from the constructed training sample sets, and the well-trained CNN model is applied to predict the roll motion. To validate the CNN model’s prediction accuracy and effectiveness, a comparison between the forecasted results and the simulation data is conducted. Meanwhile, the predicted results are also compared with that of the long-short-term memory (LSTM) neural network. The research results demonstrate that CNN can effectively achieve accurate prediction of ship roll motion in waves, and its prediction accuracy is the same as that of the LSTM neural network.

A data-driven, scenario-based human evacuation model for passenger ships addressing hybrid uncertainty

In a disaster at sea, the safe and timely removal of passengers from the ship is paramount. Here, a human evacuation plan enables passengers to be swiftly displaced from a risk area to one less so. Despite existing research on evacuation planning, there is a need for a more comprehensive model that considers various uncertainties and factors. This paper proposes an optimization evacuation model that balances uncertain variables, including passenger walking speed and travel distance, and deterministic factors like deck layout, door capacity, initial density, and corridor traffic flow. The model also accounts for varying starting locations and two levels of awareness—alert and non-alert. The model utilizes a data-driven technique, i.e., the k-means algorithm, to cluster historical data on speeds and generate scenarios. An adjustment scheme is applied to account for the ship's rolling motion, affecting passenger speeds during the evacuation planning period. Travel distance scenarios are produced to capture the impact of different route choices per passenger. A risk-neutral two-stage programming model is constructed to handle uncertainties. The model is tested on multiple problems for a passenger ship deck in day and night modes, revealing valuable managerial insights for the maritime safety sector.

Non-stationary probabilistic analysis of non-linear ship roll motion due to modulated periodic and random excitations

This paper is about the study on the non-stationary probability density function (PDF) solution of the non-linear ship rolling system under modulated periodic and random excitations. The quadratic and cubic damping terms are introduced to describe the non-linear damping moment and the power terms in state variables are adopted to describe the righting moment in the ship rolling system, respectively. The relevant Fokker–Planck–Kolmogorov (FPK) equation of the ship rolling system is constructed and the non-stationary probabilistic solutions are obtained by the presented solution procedure. In the solution process, the time variable t is introduced to the traditional exponential-polynomial-closure (EPC) method to obtain the non-stationary PDF solutions of the ship rolling system. The obtained non-stationary PDF solutions of the non-linear ship rolling systems demonstrate that the presented solution procedure can give high solution accuracy even in the PDF tails when they are compared with Monte Carlo simulation (MCS). Moreover, owing to the strong system nonlinearity and the interaction of the periodic excitation and random excitation, the achieved non-stationary PDF solutions of the system responses can deviate significantly from the Gaussian PDF. It is also found that the PDFs of responses are not even symmetrical about the means of responses due to the interaction of the periodic excitation and the random excitation even if the system only contains odd nonlinear terms. In addition, the computational efficiency is increased by over five hundred times by the presented solution procedure compared to MCS.