For a vessel in open seas, the sudden indirect excitation of roll motions due to waves from the front or rear leads to dangerous situations, sometimes even capsizing. We derive a general non-linear model, which is appropriate for the analysis of parametric excited roll motions in head or following random seas. The irregular waves are modelled in terms of a continuous time autoregressive moving average process. The resulting model of stochastic differential equations is investigated numerically by Local Statistical Linearization. The necessary stochastic moments and their derivatives are computed using Itoˆ’s differential rule and Gaussian closure.
