On the probability estimates of broaching in irregular waves by direct counting on intensive repeated simulations

Abstract

In the study, surf-riding and broaching in irregular waves are simulated using a previously developed 6-DOF numerical model. Cases in irregular waves with various speeds and wave directions are chosen for intensive repeated simulations. During the simulation, the instantaneous celerity calculated using the Hilbert transform is used to identify the “high run”. The direct counting scheme is applied on the simulation results to acquire the estimate of probability of high run, yaw exceedance within high run, yaw exceedance under “likely broaching”, and unconditional yaw exceedance. It is found that the ship capsizes after experiencing a relatively long duration of high run, which suggests correlation between capsizing and high run. High run in irregular wave is proved to be a good representation of surf-riding as they are highly related. The occurrence of broaching is strongly related with the wave angle. When the wave angle reaches 30°, the total time duration of yaw exceedance within high run can account for as much as 30%–50% of total time duration of high run under ±5°-yaw-exceeding and 5%–15% under ±10°-yaw-exceeding, especially for high Fn. The probability estimates of yaw exceedance under “likely broaching” can account for as much as 60% of those of yaw exceedance within high run using ±5°-yaw-exceeding and only 10% using ±5°-yaw-exceeding, which indicates ±5°-yaw-exceeding is not sufficient, as the yaw angle is too small and broaching is masked by a large amount of “normal” yaw motions. As Fn increasing, yaw exceedance after high run will become majority in unconditional yaw exceedances.