The Safety Assessment of Civil Ships Against Capsizing Based on the Probability Analysis of Multiple Threshold-Crossings of Stochastic Sea Waves

Abstract This paper investigates the impact of threshold-crossing events on ship capsizing through a probabilistic model that predicts random wave heights. Utilizing statistical data from wave height observations, this paper proposes that random waves can be approximated and modeled using the Wiener process, employing autocorrelation function identification and probabilistic statistical verification methods. The threshold-crossing duration of a random wave is just the period of the wave exceeds a given threshold, which can reflect the frequency property of the stochastic sea waves. And the probability distribution of the period can theoretically be determined using the derived probability density function for the time interval between any two adjacent crossings of the Wiener process and a threshold. Based on the above theories, the capsizing probabilities of a civil ship sailing in different wave areas are analyzed under different safety thresholds considering certain ratios of the ship's intrinsic period and wave period. The research results can provide a reference for the anti-overturning design of the ships under the action of random waves.