Stability, control and reliability of a ship crane payload motion

This paper investigates the stochastic dynamics, stability and control of a ship-based crane payload motion, as well as the first time passage type of failure. The simplified nonlinear model of the payload motion is considered, where the excitation of a suspension point is imposed due to the heaving motion of waves. The latter enters the system parametrically, leading to a Mathieu type nonlinear equation. The stability boundaries are numerically calculated, using the Lyapunov exponent approach. The control strategy, based on the feedback bang-bang control policy, is implemented to minimize the load's swinging motion. Finally, the first time passage problem is addressed employing Monte-Carlo sampling of the failure process.