Extreme value predictions using FORM for ship roll motions

Abstract

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Estimation of Extreme Roll Motion Using the First Order Reliability Method

“…A comparison between X tju à ð Þ Linear and Xðtju Ã Þ provides an indication of how close the FORM linearization is to the real limit state surface GðuÞ around the design point u à . Choi and Jensen (2019) have investigated the accuracy of Eq. (6) for two types of ship roll motions: dead ship conditions in beam sea and parametric rolling in longcrested head sea.…”

“…Radiation forces are calculated by using the impulse response function approach, and the nonlinearities are considered in the damping, the Froude-Krylov and restoring forces. The waves are generated using JONSWAP spectrum with the significant wave height of 3.25 m, and the zero up-crossing period of 13.1 s. Further details can be found in Choi and Jensen (2019). The probability Density Function (PDF) of the calculated roll response are shown in Fig.…”

“…The First Order Reliability Method (FORM) can be used to determine the reliability index and it has been shown in several papers that often a good agreement is found as compared to direct Monte Carlo Simulations (MCS), e.g. Der Kiureghian (2000), Jensen (2015), Choi et al (2019) and Jensen et al (2017). The reason is that the reliability index is calculated using the exact non-linear limit state function.…”

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

“…Principal particulars of the ships, named as Ship #1 (Panamax) and Ship #2 (Postpanamax), are listed in Table 1. The still water transverse metacentric height, GMsw, are taken from the references, see Choi and Jensen [19] and Jensen…”

“…Therefore, another linearization of the damping is used in proposal 2 T  .It is based on an assumed sinusoidal motion of the instantaneous roll angle, also the linear roll natural frequency ω0 in Eqs (17). and (21) is replaced by the instantaneous roll natural period ωnl, Eq (19)…”