Statistical Estimation of Extreme Roll Responses in Short Crested Irregular Head Seas

This paper addresses how to effectively estimate, using Design Loads Generator (DLG), the extreme value distribution of parametric roll responses for a given operating condition with a specified exposure time. The DLG approach, which efficiently determines an ensemble of the random phase vectors of seaways associated with the extreme value distribution of a Gaussian stochastic process, is employed to find the phase vectors associated with the extreme value distribution of a derived process. This novel mathematical process, combined with the DLG approach, efficiently constructs extrema of time-varying metacentric height (or GM) groups. The ensemble of GM groups represents rare instances of parametric excitation in short crested irregular seaways. The associated short duration irregular seaways are then utilized as inputs to a high fidelity nonlinear hydrodynamic computation system to get the statistics of extreme parametric roll responses of a C11 container hull form. Since these statistics represent the lower bound of the “true” extreme value distribution of the roll responses for the given exposure period, a useful engineering procedure to refine the statistics is proposed. While the main theme of the paper is the estimation of the distribution of extreme responses without long-term Monte Carlo simulations, extensive Monte Carlo simulations are conducted to generate comparable results in short crested irregular head seas. Results are also discussed in relation to previously published research. The DLG approach shows significant promise in predicting the statistics of extreme parametric roll.