Estimation of acceleration probability density function for parametric rolling using PLIM

As previously reported, container loss due to severe roll angles and high acceleration is still a problem for container ships. In this paper, the roll's angular acceleration is explored. First, the acceleration is divided into two components. The PDF line integral method (PLIM) is used to obtain the probability density function (PDF) of each acceleration component. We point out that it is inappropriate to obtain the joint PDF of roll angle and rate via the standard transformation from roll energy to roll angle-roll rate. Furthermore, we suggest a method for calculating the joint PDF of roll angle and effective wave elevation. Although theoretically calculating the PDF of roll angular acceleration is attempted, the theory differs from the Monte Carlo simulation (MCS) result. Therefore, it is necessary to study an alternative way to obtain a reasonable PDF of roll angular acceleration. Finally, the PDF of cargo lateral acceleration is derived, showing that the proposed theory agrees well with the MCS result. In comparison to our previous results using the PLIM method, the computation of acceleration for large roll motion is much more difficult. This leads to new challenges.