Long-term prediction of nonlinear ship roll motion using RAO

This study proposes two practical methods for estimating the long-term probability of the exceedance distribution of ship roll motion with nonlinear damping. One is based on our previously proposed RTP method, which is applicable to nonlinear roll motion but requires iterative computation of the response amplitude operator (RAO) of roll motion. In this work, we add a technique that eliminates iterative calculations without any loss of accuracy, thereby improving the practicality of the RTP method. The second is a simplified method called the wave height-iteration method, which can be performed using general linear long-term prediction tools without any dedicated programs. Both methods consist of a simple procedure based on the RAO of the roll motion considering nonlinear damping, which can easily be computed by linear seakeeping codes, and are extremely easy to implement. The results of numerical validation demonstrate that both are effective and practical methods for estimating the long-term distribution of the nonlinear roll motion. Furthermore, they can be applied not only to ship roll motion but also to other nonlinear responses, as long as the nonlinearity in irregular waves can be approximated by the nonlinearity in regular waves.