In this study, a method for predicting the extreme value distribution of the Vertical Bending Moment (VBM) in a flexible ship under a given short-term sea state is presented. The First Order Reliability Method (FORM) is introduced to evaluate the Probability of Exceedances (PoEs) of extreme VBM levels. The Karhunen-Loeve (KL) representation of stochastic ocean wave is adopted in lieu of the normal wave representation using the trigonometric components, by introducing the Prolate Spheroidal Wave Functions (PSWFs) to formulate the wave elevations. By this means, reduction of the number of stochastic variables to reproduce ocean wave is expected, which in turn the number of computations required during FORM based prediction phases is significantly reduced. In this study, the Reduced Order Model (ROM), which was developed in our previous studies, is used to yield the time-domain VBMs along with the hydroelastic (whipping) component in a ship. Two different short-term sea states, moderate and severe ones, are assumed. The FORM based predictions using PSWF for normal wave-induced VBM are then validated by comparing with those using the normal trigonometric wave representation and Monte Carlo Simulations (MCSs). Through a series of numerical demonstrations, the computational efficiency of the FORM based prediction using PSWF is presented. Then, the validation is extended to the severe sea state where the whipping vibration contributes to the extreme VBM level to a large degree, and finally the conclusions are given.
- First order reliability method
- Most probable wave episode
- Vertical bending moments
- Prolate Spheroidal Wave Functions