Roll Motion Equation Research Articles

Input saturated [formula omitted] optimal control to mitigate DTMB 5415 combatant roll motion using anti roll gyro stabilizer

Despite technological advances, rolling motion is the most critical motion for the stability and survivability of ships. This study examines the possibility of using Anti Roll Gyrostabilizer System (ARGS) as a control actuation system to mitigate the roll motion of the DTMB 5415. In the scope of conceptual study, state space model of the DTMB 5415 Combatant Warship has been obtained. Then, ARGS dynamics have been integrated into the roll motion dynamics. Parameters of the DTMB 5415 and actuator are identified from the literature. Comparing experimental and numerical studies in the literature have also expanded the damping term parameters in the equation of roll motion. However, a Monte Carlo analysis is carried out to define the preliminary parameters of ARGS. An actuator-saturated Linear Matrix Inequality (LMI) Full State-Feedback H∞ Optimal Controller is tested for this design iteration. The results are also contrasted with the requirements that military ships must meet. Ship roll amplitudes have significantly decreased (over 95% for various sea conditions) and have complied with STANAG 4154 standards. The 1 radian Precession Angle limit has not been overshot. Continuous and discrete-time control rules are implemented, thus demonstrating the applicability of this actuation and control method are shown.

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.

Theoretical Analysis Method for Roll Motion of Popup Data Communication Beacons

The popup data communication beacon (PDCB) can send data to the shore and ships through the BeiDou navigation satellite system (BDS) when it surfaces. The data can be collected by a deep-sea landing vehicle (DSLV) and transmitted using a magnetic induction coil. PDCBs can reduce the cost of DSLV recovery and redeployment. Whether the data can be successfully sent mainly depends on the outlet height and roll angle of the PDCB. Thus, accurately assessing the effect of the roll angle on data transmission is crucial. In this study, first, the differential equation of roll motion was preliminarily established using the small-amplitude wave theory along with the shape characteristics of the PDCB. Next, the nonlinear term of the recovery moment was processed using the Linz Ted Poincaré method. Then, the wave current force was analyzed using the Morrison theoretical formula along with an additional inertia moment calculation formula that is suitable for slender cylindrical small buoys. Finally, the theoretical calculation results were verified using the computational fluid dynamics (CFD) method and pool test. The roll angle error of the theoretical calculation was within 5%. Thus, the heave and roll response of PDCBs can be evaluated using theoretical calculation methods. The proposed calculation formula of additional inertia moment has guiding significance for the further optimization of the structure.

Formulation of ship roll damping models from free-decay data

Estimation of roll damping of a ship is essential to the prediction of its response in waves. The formulation of ship roll damping models from experiment or CFD data involves two parts: the determination of the model form and the calculation of the model coefficients, and both have significant influences on damping accuracy. To improve the roll motion prediction of a particular ship, this paper made an investigation of the typical damping models and its influence factors based on benchmark experiment data. The results show that the typical damping models can not reflect the fluid physics of roll motion. A conclusion is given that all roll angle, angular roll velocity, and angular roll acceleration should be considered in damping model determination. For the convenience of solving the roll motion equation, damping models with angle and angular velocity as independent variables are proposed due to the coupling of the angle, angular velocity, and the angular acceleration in roll. A procedure of damping model formulation is developed based on the Prony-SS method which was introduced into roll damping identification recently. Examples that follow the procedure show good performance. Furthermore, forward speed and flow memory effects on ship roll damping are discussed.

CFD database method for roll response of damaged ship during quasi-steady flooding in beam waves

A database method is proposed to predict the roll response of a damaged ship upon quasi-steady flooding in regular beam waves. To construct the hydrodynamic database, the hydrodynamic loads acting on the damaged ship are decomposed into wave excitation moment and motion-induced moment, which are calculated based on computational fluid dynamics (CFD). The wave excitation moments for different wave frequencies are formulated using the high-order trigonometric function. The ship hydrodynamic coefficients (i.e., added moment of inertia and damping coefficient) for different roll frequencies and amplitudes are regressed from the motion-induced moment and then used as samples for database construction by cubic spline interpolation. The Runge-Kutta method is employed to solve the ship's roll motion equation, in which the hydrodynamic coefficients are updated according to the roll amplitude in real time. To test the performance of the present method, the roll motion responses of a damaged frigate DTMB-5415 are computed. The results obtained by the database method are in good agreement with the CFD results and experimental data. The characteristics of motion-induced moment, roll hydrodynamic coefficients and wave excitation moment are analyzed. In addition, the influence of various factors (e.g., sensitivity of mesh and time step, order of regression method, interval of sample points and type of load decomposition model) on the computation accuracy are also discussed. Compared to directly performing CFD simulation of damaged ship motion in waves, the proposed database method can predict the ship's roll response with high efficiency and acceptable accuracy.

An investigation into the nonlinear effects in the roll motion of 2-D bodies by SPH method

Nonlinear effects in the roll motion of a 2–D body in the free surface are investigated by utilizing the Smoothed Particle Hydrodynamics (SPH) method. The continuity and Navier–Stokes equations are solved by employing the Weakly Compressible SPH (WCSPH) approach and our in-house code, which relies on the accumulated development process through the authors’ previous works including the fluid–solid coupling modeling by viscous penalty technique, (Tofighi et al. (2015)), and a hybrid Velocity-Variance Free Surface (VFS) and Artificial Particle Displacement (APD) algorithm (Ozbulut et al., 2014, 2018, 2020; Kolukisa et al., 2020). In this work, the GPU parallelization of the code is performed, to mitigate the computational burdens of the relatively high number of particles due to the long wavelengths generated by the roll motion of the cylinder. Presently, an alternative and exact approach in reducing the equation of roll motion with quadratic damping term is introduced. In parallel to this approach, a quadratic regression equation approximating the hydrodynamic roll moment is also employed. Aside from hydrodynamic coefficients, with linear and quadratic damping coefficients, vortex flow characteristics are also presented, qualitatively and quantitatively. It is understood from the results that, with the present capability, the WCSPH approach introduced is able to disclose nonlinearities inherently exist in the roll motion of oscillatory bodies in the free surface.

NONLINEAR ROLLING STABILITY AND CHAOS RESEARCH OF TRIMARAN VESSEL WITH VARIABLE LAY-OUTS IN REGULAR AND IRREGULAR WAVES UNDER WIND LOAD

The trimaran vessel rolls strongly at low forward speed and may capsize in high sea conditions due to chaos and loss of stability, which is not usually considered in conventional limit-based criteria. In order to perfect the method of measuring roll performance of trimaran, a set of nonlinear roll motion stability analysis method based on Lyapunov and Melnikov theory was established. The nonlinear roll motion equation was constructed by CFD and high-order polynomial fitting method. The wave force threshold of rolling chaos in regular waves is calculated by Gauss-Legendre numerical integration method. The limited significant wave height of rolling chaos in random sea conditions is deduced by the phase space transfer rate, and the complex effect of wind load is superposed in the calculation. The influence of trimaran configuration on the roll system is analyzed through the state differentiation of homoclinic and heteroclinic orbit in phase portrait. The calculation of the maximum Lyapunov exponent further verified the applicability of Melnikov method, and the topological structure change of gradual failure of the rolling system is analyzed by the erosion of safe basin. The complex changes of the nonlinear damping coefficient and the nonlinear restoring moment coefficient caused by the change of the transverse lay-outs between the main hull and side hull have a significant influence on chaos and stability, and the existence of wind load has a certain weakening effect on the stability and symmetry of the system. The conclusion also further indicates the importance of the lay-outs to the dynamic stability of the trimaran vessel, which is significant for its seakeeping design.

Parameter Identification of Roll Motion Equation of Ship in Regular Wave Using Opposition Based Learning Gaussian Bare Bone Imperialist Competition Algorithm

In this paper, a new method is proposed to identify the parameters of roll motion equation using the response data of ship in regular waves. The proposed method is based on the fact that if the estimated parameters are close to the true parameters, then, its response are also close to the true response. Therefore, the parameter identification is achieved via minimizing the mean square error between the true response and the estimated response. To effectively solving the parameter minimization problem, an improved imperialist competition algorithm (ICA), called opposition based learning Gaussian bare bone imperialist competition algorithm (OBL‐GBBICA) is proposed. The proposed OBL‐GBBICA integrates the opposition learning and Gaussian sampling technique into ICA to enhance its exploration ability and speed up its convergence. Experimental results show that the proposed method can accurately identify the parameters of roll motion equation. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Online Prediction of Ship Roll Motion in Waves Based on Auto-Moving Gird Search-Least Square Support Vector Machine

A novel method based on auto-moving grid search-least square support vector machine (AGS-LSSVM) is proposed for online predicting ship roll motion in waves. To verify the method, simulation data are used, which are obtained by solving the second-order nonlinear differential equation of ship roll motion using the fourth-order Runge–Kutta method, while the Pierson–Moskowitz spectrum (P–M spectrum) is used to simulate the irregular waves. Combining the sliding time window with the least square support vector machine (LS-SVM), the samples in the time window are used to train the LS-SVM model, and the model hyperparameters are optimized online by the auto-moving grid search (AGS) method. The trained model is used to predict the roll motion in the next 30 seconds, and the prediction results are compared with the simulation data. It is shown that the AGS-LSSVM is an effective method for online predicting ship roll motion in waves.

Nonlinear roll damping parameter identification using free-decay data

A common practice for evaluating the nonlinear damping in ship roll motion is to perform a free-decay experiment. Although various methods have been developed to estimate the coefficients of a nonlinear damping model, these methods are limited to certain and relatively simple models. In addition, the performances of these methods have been greatly affected by the random noise embedded in the measured data. In this article, an efficient and versatile parameter identification method, applicable to rather general nonlinear damping and restoring models, to estimate nonlinear damping coefficients from contaminated free-decay data is proposed. The proposed method approximates the roll motion as complex exponentials by using the Prony-SS method. Because the Prony-SS method has a build-in noise rejection mechanism via the usage of truncated singular value decomposition, random noise in the measured data could be largely removed. Based on the analytical complex exponential representation of free-decay data, the damping coefficients can be easily estimated from the nonlinear equation of roll motion by using a least-square technique. Numerical examples demonstrate the effectiveness of the proposed method, even when the simulated data are significantly corrupted by random noise. Furthermore, the developed method performs well when nonlinear restoring parameters are also treated as unknown.

Effect of Bilge Keels Position On Roll Motion Performance Of Traditional Wooden Boat

The most ship accidents occurred on size between 35GT and 500GT, including traditional wooden boats. The accidents were dominated by capsizing due to bad weather. Therefore the safety of traditional wooden boats needs to be improved. This paper discusses the position of bilge keels and their impact on the roll motion performance of an Indonesian traditional wooden boat. The roll damping is determined by a roll decay test with three different positions of bilge keels, namely 15 degrees, 30 degrees, and 45 degrees. The roll amplitude is determined in the frequency domain by solving the uncoupled nonlinear roll motion equation with an effective wave slope coefficient calculated using the simplified Froude-Krylov assumption of roll exciting moment. The bilge keels position with the angle of 15 degrees reduced the roll amplitude of 18% while the position with an angle of 30 degrees decreases the roll amplitude by 7% of roll amplitude without bilge keels. The bilge keels position with an angle of 45 degrees reduced the roll amplitude by 2% of those without bilge keels. The natural roll period was not significantly affected by the bilge keels position. The bilge keels position with an angle of 15 degrees is the most effective position to reduce the roll amplitude.

Prediction of a ship roll added mass moment of inertia using numerical simulation

Prediction of a ship's roll motion in parametric roll and dead ship condition using CFD and experiments is time consuming and expensive, while a reliable equation based method can drastically decrease the computation time. The commonly used roll motion equation contains roll mass and added mass moment of inertia, damping and restoring terms and associated coefficients. Improving the prediction of these coefficients increases the accuracy of the method. There is a lack of precise calculation for the roll added mass moment of inertia, which is commonly estimated using semi-empirical techniques and as a percentage of the roll mass moment of inertia coefficient. This paper presents a new method to determine the roll added mass moment of inertia using CFD simulations based on a harmonic excitation roll motion technique and the results are compared against Bhattacharyya's method. The influences of excitation frequency, Froude number, roll angle and appendages on the roll motion characteristics and the roll added mass moment of inertia coefficient are investigated. In addition, the roll added mass moment of inertia coefficients on the model scale and full scale ship are computed to investigate the scale effect.

Nonparametric identification of nonlinear ship roll motion by using the motion response in irregular waves

In order to precisely predict the nonlinear roll motion of ships at sea, it is important to determine the nonlinear damping and restoring moment as accurately as possible. In this paper, a nonlinear mathematical model is used to describe the nonlinear roll motion of ships at sea. A novel nonparametric identification method based on a combination of random decrement technique (RDT) and support vector regression (SVR) is used to identify the nonlinear damping and restoring moments in the mathematical model simultaneously by using only the random rolling responses of ships in irregular waves. In the identification method, RDT is first used to derive the random decrement equation as well as the auto- and cross-correlation equations based on the established mathematical models, and the random decrement signatures are also obtained from the random roll responses. Then SVR is applied to identify the damping and restoring moments in the roll motion equation. For the purpose of verifying the applicability, accuracy and generalization ability of the identification method, it is applied to analyzing the simulated data with different wave excitations. The identification results show that the identification method can be applied to identify the damping and restoring moments of the nonlinear roll motion using the random responses of ships in irregular waves.

Modelling and Simulation Analysis of Rolling Motion of Spherical Robot

This paper presents the findings of modelling, control and analysis of the spherical rolling robot based on pendulum driven within the simulation environment. The spherical robot is modelled using Lagrange function based on the equation of rolling motion. PD-type Fuzzy logic controller (FLC) was designed to control the position of the spherical robot where 25 rules were constructed to control the rolling motion of spherical robot. It was then integrated with the model developed in Simulink-Matlab environment. The output scaling factor (output gain) of the FLC was heuristically tuned to improve the system performance. The simulation results show that the FLC managed to eliminate the overshoot response and demonstrated better performance with 29.67% increasing in settling time to reach 0.01% of steady state error.

Parameter identification for nonlinear damping coefficient from large-amplitude ship roll motion using wavelets

In this paper, we have introduced an efficient Legendre wavelet spectral method (LWSM) to ship roll motion model for investigating the nonlinear damping coefficients. The accuracy of the proposed method is assessed by rolling with an initial amplitude using nonlinear type of equations. To the best of our knowledge until now there is no rigorous wavelet solution has been reported for the above model. Convergence analysis of the proposed method is discussed. The operational matrix of derivative is utilized to convert a ship roll motion equation into a set of algebraic equations. Accurate coefficients can be easily obtained for large rolling angles up to the amplitude at the maximum value of the restoring moment using wavelets. Some numerical examples are given to show the validity and applicability of the proposed wavelet method. Moreover the use of Legendre wavelets is found to be simple,flexible, accurate, efficient and small computation cost.

Parameter Estimation of Equation of Non-linear Ship Roll Motion by Using Evolutionary Computation

Parameter Estimation of Equation of Non-linear Ship Roll Motion by Using Evolutionary Computation

Influence of variable acceleration on parametric roll motion of a container ship

Ship operators increase or decrease thrust force of ships to avoid parametric roll motion. These operations cause varying acceleration values. In this study, influence of variable acceleration and deceleration of ships on roll motion is investigated in longitudinal waves. The method which is referred as simple model is utilized for analysis. Simple Model is one degree of freedom nonlinear parametric roll motion equation which contains changing velocity and restoring moment in waves with respect to time. Ship velocities in waves are predicted by XFlow software for various thrust forces. Results indicate that variable acceleration has significant effect on parametric roll phenomenon.

Parameter identification of nonlinear roll motion equation for floating structures in irregular waves

In order to predict the roll motion of a floating structure in irregular waves accurately, it is crucial to estimate the unknown damping coefficients and restoring moment coefficients in the nonlinear roll motion equation. In this paper, a parameter identification method based on a combination of random decrement technique and support vector regression (SVR) is proposed to identify the coefficients in the roll motion equation of a floating structure by using the measured roll response in irregular waves. Case studies based on the simulation data and model test data respectively are designed to validate the applicability and validity of the identification method. Firstly, the roll motion of a vessel is simulated by using the known coefficients from literature, and the simulated data are used to identify the coefficients in the roll motion equation. The identified coefficients are compared with the known values to validate the applicability of the identification method. Then the roll motion is predicted by using the identified coefficients. The prediction results are compared with the simulated data, and good agreement is achieved. Secondly, the model test data of a FPSO are used to identify the coefficients in the roll motion equation. Then the random decrement signature of the roll motion is predicted by using the identified coefficients and compared with that obtained from the model test data, and satisfactory agreement is achieved. From this study, it is shown that the identification method can be effectively applied to identify the coefficients in the nonlinear roll motion equation in irregular waves.

SVR-based identification of nonlinear roll motion equation for FPSOs in regular waves

A novel system identification method, Support Vector Regression (SVR), is proposed for identifying the nonlinear roll motion equation of a FPSO vessel in regular waves. Firstly, the roll motion of a vessel is simulated, and the simulated data are used to identify the parameters in the roll motion equation. Then the roll motion is predicted by using the identified parameters, and the prediction results are compared with the simulated data to verify the identification method. Secondly, model test data of a FPSO vessel are used to identify the parameters in the roll motion equation. The roll motion is predicted by using the identified parameters and compared with the model test data. In addition, by using the model test data, the time histories of the nonlinear damping and restoring moments in the non-parametric roll motion equation are identified and the identified results are used to predict roll motion. Comparison of the prediction results with the model test data shows the validity of the identification method in identifying the non-parametric roll motion equation. It is shown that the SVR-based identification method can be effectively applied to parametric and non-parametric identification of the nonlinear roll motion equation.

The System Identification Analysis of the Rolling Motion Model for the Unmanned Boat

In this paper, the author took an unmanned planting boat as the object of study and conducted a series of roll decay test on condition that the ship model was in different drafts and tilt angle. The author established eight kinds of mathematical model of roll decay motion model system identification by making a cross combination of linear or nonlinear righting moment and linear or nonlinear damping. Based on the principle of system identification, the author established the optimization calculation of the objective function. Then the author adapted the genetic algorithm of system identification program based on Visual Basic 6.0 and got eight kinds of identification programs. By identifying respectively the test data of the roll motion of the unmanned planting boat, the author confirmed the feasibility of the adapted program. Comparing large drafts and tilt angle identification results, the author found a reasonable hydrostatic roll motion equation of the unmanned planing boat in the case of large drafts and tilt angle, and made a preliminary analysis.