Probability density function of roll amplitude for parametric rolling using moment equation

For the ship stability estimation and ship design, it is helpful to know the probability of the roll amplitude exceeding a certain threshold. Therefore, it is necessary to obtain the probability density function of the roll amplitude. In this study, first, we derive the moment values of roll amplitude by combining the moment equations and the linearity of expectation. With this, we propose a method to estimate the probability density function of the roll amplitude by using the obtained moment values. The results of our proposed method are compared to those obtained from Monte Carlo simulations. When the higher-order cumulant neglect closure method is used, the moment values resulting from the moment equations are close to the results of corresponding Monte Carlo simulations. In addition, our proposed method for deriving the probability density function of the roll amplitude is validated by comparison with Monte Carlo simulation results. In conclusion, we can state that the proposed methods for deriving the moments and the probability density function of the roll amplitude are available for practical use cases.

Subjects

Moment equation

Parametric rolling

Probability density function

Roll amplitude

DDC Class

519: Applied Mathematics, Probabilities

623: Military Engineering and Marine Engineering

Lizenz

https://creativecommons.org/licenses/by/4.0/

Name

s00773-024-01006-2.pdf

Type

Main Article

Size

2 MB

Format

Adobe PDF

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Probability density function of roll amplitude for parametric rolling using moment equation