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The present study concerns the stern slamming load of container carriers, with stern bulb arrangement variation. First, a series of wedge drop tests were conducted using simple wedge models with fixed deadrise angles, and tests with the cross-section models of practical container carrier sterns were followed. The deadrise angle of the simple wedge ranged from 0° to 10°. The pressure measurement results of the simple wedge drop tests were distributed between empirical formula and analytic solution, so the experimental setup was validated. In the cases of practical hull cross-sections, the water entry of the bulb prior to that of the transom resulted in characteristic water film generation and delayed pressure peak appearance. The trapped air between the bulbs damped the pressure in the twin skeg hull case, reducing the pressure peak and causing the pressure oscillation during water entry.

Extreme value predictions of the roll motion of ships are considered within the framework of the First Order Reliability Method focusing on the applicability of the Poisson assumption for the peak value statistics. The examples considered are a ship rolling in dead sea condition under the combined action of waves and wind and a ship experiences parametric rolling.

Extreme value statistics can often be based on the assumption that exceedance events of a high threshold level are statistically independent and identically distributed (i.i.d. process), which further implies the Poisson assumption to be valid. This makes it possible to express the extreme response statistics through the mean up-crossing rate. For non-linear processes, analytic expressions of the mean up-crossing rate do not in general exist. Reliable statistics of mean up-crossing rate based on the brute-force approach, e.g. Monte Carlo simulation (MCS) require long time domain simulations considering a number of different ensemble input. The associated computations can be very time consuming especially when a detailed physical (e.g. hydrodynamic) model is applied. The First Order Reliability Method (FORM) has previously been found efficient for estimation of extreme value prediction of stationary stochastic time domain processes, However, if the non-linearity in a response is significant, the accuracy of the FORM linearized mean up-crossing rate can be limited.

The international Maritime Organization (IMO) Weather Criterion has proven to be the governing stability criteria regarding minimum metacentric height for e.g., small ferries and large passenger ships. The formulation of the Weather Criterion is based on some empirical relations derived many years ago for vessels not necessarily representative for current new buildings with large superstructures. Thus, it seems reasonable to investigate the possibility of capsizing in beam sea under the joint action of waves and wind using direct time domain simulations. This has already been done in several studies. Here, it is combined with the first order reliability method (FORM) to define possible combined critical wave and wind scenarios leading to capsize and corresponding probability of capsize. The FORM results for a fictitious vessel are compared with Monte Carlo simulations, and good agreement is found at a much lesser computational effort. Finally, the results for an existing small ferry will be discussed in the light of the current weather criterion. 1. Introduction Recently, the International Maritime Organization (IMO) has initiated a thorough revision of the intact stability rules in the framework of goal-based design, e.g., Peters et al. (2013). Several draft guidelines have been issued, e.g., SDC 1/INF.8 (IMO 2013) discussing in details the requirements for the hydrodynamic software to be applied including qualitative and quantitative assessment procedures. The focus so far has been mostly on failure modes related to the change of righting lever in waves, notably parametric rolling and pure loss of stability, whereas the dead ship behavior in beam sea still is based on the existing Weather Criterion issued by IMO (1985) as Resolution A.562. This criterion is based to a large extent on model tests of older hull forms and does not provide any probability of capsize for a given vessel, just a pass/no pass result. Furthermore, the wave environment is not explicitly specified in the criterion thus leading to the same requirement whether the ship is sailing in restricted areas or not. A very detailed and precise description of the drawbacks in the IMO Weather Criterion, as applied to modern ships, is given in Bulian and Francescutto (2004). In a recent study by Tompuri et al. (2015), a detailed investigation on application of the second generation intact stability criteria has been done. However, the criterion for dead ship condition is excluded from this thorough study because the criterion is thought to be still in the early phase of development.

Previous research has shown that the First Order Reliability Method (FORM) can be an efficient method for estimation of outcrossing rates and extreme value statistics for stationary stochastic processes. This is so also for bifurcation type of processes like parametric roll of ships. The present paper discusses this solution procedure with a focus on the computational efficiency of FORM as compared with Monte Carlo Simulation (MCS).

Uncertainties related to numerical modelling of parametric roll have been investigated by using a 6-DOFs model with nonlinear damping and roll restoring forces. At first, uncertainty on damping coefficients and its effect on the roll response is evaluated. Secondly, uncertainty due to the “effective (equivalent) wave” concept in calculation of restoring moment is studied. Finally, uncertainty to roll response from different methods of GZ calculation has been checked. It is found that the equivalent wave concept is sufficiently accurate for the purpose of GZ calculation. Two different GZ approximations give a good agreement with direct calculation method if relevant coefficients have been properly found in the fitting.

In this paper, submerged body dynamics model in vertical plane which can include the effect of free surface and wave is suggested to simulate the motions of submerged body moving beneath free surface precisely. A controller is designed, which can maintain a constant depth below the mean sea level and minimize the pitch angle. Numerical simulations show that the designed controller is effective on depth keeping and minimizing pitch angle in regular waves and irregular waves.

The IMO Weather Criterion has proven to be the governing stability criteria regarding minimum GM for e.g. small ferries and large passenger ships. The formulation of the Weather Criterion is based on some empirical relations derived many years ago for vessels not necessary representative for current new buildings with large superstructures. Thus it seems rea-sonable to investigate the possibility of capsizing in beam sea under the joint action of waves and wind using direct time domain simulations. This has already been done in several studies. Here it is combined with the First Order Reliability Method to define possible combined critical wave and wind scenarios leading to capsize and corresponding probability of capsize. The results for a fictitious vessel are compared with Monte Carlo simulation and good agreement is found at a much lesser computational effort. Finally, the results for a large container vessel and a small ferry will be discussed in the light of the current weather criterion.