Stochastic modeling of long term wave induced responses of ship structures

This paper presents a procedure for evaluating the long term response distribution in ship structures. A specified travel route through given geographical areas during the lifetime of the ship is defined. The individual scatter diagrams, describing the relative occurrence of different sea states for the geographical areas, are weighted with respect to the relative time occupancy of the ship. A two-dimensional analytical distribution is fitted to the weighted scatter diagram over the lifetime.

Frequency response functions for all the sectorial forces are calculated for different ship speeds, heading angles and loading conditions, and fitted to a bi-cubic spline. The wave spectrum is defined by applying a gamma spectrum. The response spectrum is found using a linear frequency domain analysis. From the response spectrum, the peak distribution of the response in each short term period, conditioned on the loading condition, the ship speed and the wave heading direction is computed. The peak distribution over the lifetime is estimated by unconditioning with respect to sea states, maneuvering and loading condition.