Objective Parametric rolling is a typical dynamic stability failure mode, involving strong nonlinear dynamics and random wave excitation loads. China Classification Society (CCS) has issued the “Guidelines for Assessment of the Second Generation of Intact Stability of Ships”, which established the assessment methods and technical requirements. Prediction of dynamic stability of ships under complex sea state is a major scientific issue in the field of safe navigation. Stability discrimination methods based on deterministic waves cannot accurately identify the instability domain in random waves.

Method In this paper, considering the combination of external excitation and parametric excitation, the single-degree-of-freedom equation of roll motion is established with nonlinear damping force and nonlinear restoring force. Assuming that the pitch and heave motions of the ship in waves are quasi-static processes, the roll restoring moment is calculated numerically based on the strip theory. The righting arm is fitted with polynomial expression under different wave directions to accurately describe the roll motion characteristic. The dynamic stability of nonlinear roll motion in random waves are investigated based on stochastic analysis method. The improved stochastic averaging method of energy envelope (ISAM-E) is introduced which accounts for the difference in frequency components of rolling motion induced by parametric excitation and external excitation. ISAM-E is applicable to the analysis of nonlinear rolling motion under narrow-band spectra. Based on the first passage theory, the first passage probability of the stochastic roll motion is calculated with given boundary conditions and initial conditions.

Results Based on the first passage probability approach, the C11 container ship is taken as an example, the probabilities of the roll response exceeding 25° are calculated for full wave directions. The entire sea areas are divided into three parts, including high stability, medium stability, and low stability regions. This method can accurately identify the random sea conditions where the rolling response amplitude exceeds 25°.

Conclusion The occurrence mechanism of parametric rolling and dynamic stability assessment are deeply explored with application of stochastic averaging method and first passage theory. The methods proposed in this paper significantly improve the computational efficiency without considering the non-ergodicity. More information for stochastic stability of roll motion under different wave directions can be provided.