Stochastic seakeeping analysis of nonlinear ship rolling dynamics under non-stationary and irregular sea states

This paper presents an efficient semi-analytical methodology for quantifying the capsizing risk and seakeeping performance of ships undergoing nonlinear rolling motions under realistic, non-white sea-wave excitations. The dynamic response is captured through a comprehensive and physically consistent nonlinear formulation that incorporates both softening and hardening restoring moment characteristics, nonlinear hydrodynamic damping mechanisms, and evolutionary stochastic wave loads representative of complex maritime environments. By leveraging a refined blend of stochastic averaging and statistical linearization techniques, the study yields computationally efficient, time-dependent seakeeping probability estimates, rigorously accounting for the critical behaviors of both bounded and unbounded ship roll motions, including those associated with negative stiffness regions, through an appropriately tailored, non-stationary response amplitude probability density function (PDF). A notable advancement of the proposed framework lies in its robust capability to address stochastic sea-wave excitations with time-varying intensity and frequency content, thereby accurately reflecting the evolving nature of real-world open-sea environments. Numerical analyses across a range of case studies, validated against benchmark Monte Carlo simulations, demonstrate the accuracy and efficiency of the methodology, underscoring its promise as a practical performance-based tool for evaluating vessel stability and seakeeping under dynamic and uncertain maritime operational scenarios.