Short-time FORM analysis for extreme roll motion prediction in beam seas

This paper presents an efficient computational method to predict extreme roll motions by the First Order Reliability Method (FORM). The method facilitates accurate estimation of the reliability index distribution by short time domain calculations. The calculations are based on the transfer function of roll motion together with an equivalent linear damping for the estimation of the most probable largest roll motion using nonlinear time domain simulations. The linearization of the damping gives rise to an inconsistency (a “time shift”) in the time series evaluation. Thus, in order to account for this nonlinear effect, when evaluating the most probable largest roll motions, a method to correct the time shift from the linear solution is proposed. Two different container ships in beam seas and zero forward speed are used to demonstrate the effectiveness of the method. It is also shown that a further reduction of computational efforts is attained by using the Karhunen-Loeve wave representation based on Prolate Spheroidal Wave Functions (PSWF)