Research On The Probability Of A Ship Roll Under Parametric And Forced Excitation In Random Oblique Waves

So far,along with the development of the maritime transport vessel,which is more and more large,high technology and high performance,the complete stability requirement of the ship in random oblique waves is an important foundation to ensure the safety of the ship.IMO has developed the second generation of complete stability criteria for the ship parametric rolling phenomenon.In this paper,the PDF(probability density function)of a ship roll response under parametric and forced excitation in random wave is mainly studied.First of all,the stochastic ocean condition is simplified by using spectral analysis method,and the random wave rising is treated as a narrow band random process.Use the probability model(second-order controlled autoregressive moving average model)to accurately approximate the random sea condition,and obtain the autocorrelation function of the random sea condition.Secondly,considering the nonlinear damping,ship speed,heading angle and random wave,an analytic function was used to approximate the righting arm function obtained by the numerical simulation.The rolling motion equation of ship under parametric and forced excitation in oblique waves was established.Next,the PDF and probability of ship roll motion response are solved by the analytical method(the stochastic averaging method of energy envelope)and the numerical method(Monte Carlo method)respectively.The analytical method treats ship roll motion process under parametric and forced excitation as the diffused Markov process,the FPK equation of the transfer PDF of the system energy H was obtained by the stochastic averaging method,the stable PDFs of the energy level H and the maximal roll amplitudes b(H)corresponding to the each energy levels H were solved analytically.The numerical method is directly using the Runge-Kutta method to solve the differential equation of ship roll motion under parametric and forced excitation in the oblique wave.And a large number of response sample values are calculated based on the Monte Carlo principle to obtain the numerical solution of PDF of the rolling response.By comparing the results of the two methods,the correctness of the analytical method and the numerical method are also verified.Taking C11 container ship as an example,this paper has calculated the PDF of ship roll response and analyzed the parameter sensitivity of the rolling response probability.Mainly considered the effects of wave parameters(characteristic wave height and characteristic wavelength)and the ship navigation parameters(heading angle and speed).