Investigation of stochastic nonlinear dynamics of ocean engineering systems through path integration

Offshore structures operate in an uncertain environment under unsteady wave loads and also involve geometrical and material imperfections as well as parametric uncertainties. Additionally, there is sampling uncertainty and statistical uncertainty inherent in the response of these structures. These uncertainties have a significant impact on forecasting of the response unless the uncertainty is handled in a probabilistic manner. The present study tries to underline the importance by modelling the uncertainty through Weiner process by recasting the differential equations as stochastic differential ones. The stochastic differential equations are solved in an Ito framework using the Milstein scheme of solution. The study shows that there is a significant variation vis-à-vis the deterministic responses unless the modelling is done in a proper framework. Some of the sea states for numerical exposition are chosen which represent rogue waves. The importance of such framework is shown through three numerical illustrations: the response of tension leg platform with various parametric cases, a Mathieu-type instability problem and a three degree of freedom jacket structure. The efficacy of the Milstein method in handling a range of ocean nonlinear problems is brought out through these illustrations.