Application of linear filter and moment equation for parametric rolling in irregular longitudinal waves

Parametric rolling is one of the dangerous dynamic phenomena. To discuss safety a vessel when phenomenon occurs, it important to estimate probability certain dynamical behavior ship with respect threshold level. In this paper, moment values are obtained by solving equations. Since stochastic differential equation (SDE) needed obtain equations, autoregressive moving average (ARMA) filter used. The effective wave modeled using 6th-order ARMA filter. addition, parametric excitation process non-memory transformation from relationship between GM and elevation. resulting system equations represented 8th-order Itô equation, which consists second-order SDE for motion wave. This has nonlinear components. Therefore, cumulant neglect closure method used as higher-order moments need be truncated. Furthermore, density function roll angle determined equation. Here, two types suggested have good agreement.