Probability Density Analysis of Nonlinear Random Ship Rolling

Ship rolling in random waves is a complicated nonlinear motion that contributes substantially to ship instability and capsizing.The finite element method(FEM)is employed in this paper to solve the Fokker Planck(FP)equations numerically for homoclinic and heteroclinic ship rolling under random waves described as periodic and Gaussian white noise excitations.The transient joint probability density functions(PDFs)and marginal PDFs of the rolling responses are also obtained.The effects of stimulation strength on ship rolling are further investigated from a probabilistic standpoint.The homoclinic ship rolling has two rolling states,the connection between the two peaks of the PDF is observed when the periodic excitation amplitude or the noise intensity is large,and the PDF is remarkably distributed in phase space.These phenomena increase the possibility of a random jump in ship motion states and the uncertainty of ship rolling,and the ship may lose stability due to unforeseeable facts or conditions.Meanwhile,only one rolling state is observed when the ship is in heteroclinic rolling.As the periodic excitation amplitude grows,the PDF concentration increases and drifts away from the beginning location,suggesting that the ship rolling substantially changes in a cycle and its stability is low.The PDF becomes increasingly uniform and covers a large region as the noise intensity increases,reducing the certainty of ship rolling and navigation safety.The current numerical solutions and analyses may be applied to evaluate the stability of a rolling ship in irregular waves and capsize mechanisms.

A Semi-Analytical Method for the PDFs of A Ship Rolling in Random Oblique Waves

The PDFs(probability density functions) and probability of a ship rolling under the random parametric and forced excitations were studied by a semi-analytical method. The rolling motion equation of the ship in random oblique waves was established. The righting arm obtained by the numerical simulation was approximately fitted by an analytical function. The irregular waves were decomposed into two Gauss stationary random processes, and the CARMA(2, 1) model was used to fit the spectral density function of parametric and forced excitations. The stochastic energy envelope averaging method was used to solve the PDFs and the probability. The validity of the semi-analytical method was verified by the Monte Carlo method. The C11 ship was taken as an example, and the influences of the system parameters on the PDFs and probability were analyzed. The results show that the probability of ship rolling is affected by the characteristic wave height, wave length, and the heading angle. In order to provide proper advice for the ship’s manoeuvring, the parametric excitations should be considered appropriately when the ship navigates in the oblique seas.

大幅船舶横摇运动非线性附加质量惯性矩和阻尼矩特性的非参数识别

This study aims to investigate the nonlinear added mass moment of inertia and damping moment characteristics of largeamplitude ship roll motion based on transient motion data through the nonparametric system identification method.An inverse problem was formulated to solve the first-kind Volterra-type integral equation using sets of motion signal data.However,this numerical approach leads to solution instability due to noisy data.Regularization is a technique that can overcome the lack of stability;hence,Landweber’s regularization method was employed in this study.The L-curve criterion was used to select regularization parameters(number of iterations)that correspond to the accuracy of the inverse solution.The solution of this method is a discrete moment,which is the summation of nonlinear restoring,nonlinear damping,and nonlinear mass moment of inertia.A zero-crossing detection technique is used in the nonparametric system identification method on a pair of measured data of the angular velocity and angular acceleration of a ship,and the detections are matched with the inverse solution at the same discrete times.The procedure was demonstrated through a numerical model of a full nonlinear free-roll motion system in still water to examine and prove its accuracy.Results show that the method effectively and efficiently identified the functional form of the nonlinear added moment of inertia and damping moment.

Non-linearity Analysis of Ship Roll Gyro-stabilizer Control System

A gyro-stabilizer is the interesting system that it can apply to marine vessels for diminishes roll motion.Today it has potentially light weight with no hy­drodynamics drag and effective at zero forward speed.The twin-gyroscope was chosen.Almost,the modelling for designing the system use linear model that it might not comprehensive mission requirement such as high sea condition.The non-linearity analysis was proved by comparison the re­sults between linear and non-linear model of gyro-stabilizer throughout fre­quency domain also same wave input,constrains and limitations.Moreover,they were cross checked by simulating in time domain.The comparison of interested of linear and non-linear close loop model in frequency domain has demonstrated the similar characteristics but gave different values at same frequency obviously.The results were confirmed again by simulation in irregular beam sea on time domain and they demonstrate the difference of behavior of both systems while the gyro-stabilizers are switching on and off.From the resulting analysis,the non-linear gyro-stabilizer model gives more real results that correspond to more accuracy in a designing gyro-sta­bilizer control system for various amplitudes and frequencies operating condition especially high sea condition.