Interval-Based Multi-Body Dynamics Simulation of Special-Purpose Vessels in Rough Sea Conditions

Vessel motions in offshore operations are heavily influenced by uncertain wave loads and hydrodynamic parameters. Yet, traditional deterministic or probabilistic models often fail to capture epistemic ambiguity when data are scarce. We introduce a fuzzy–set framework using α-cut interval analysis to represent imprecise wave heights, periods, added mass, damping, and stiffness as fuzzy numbers. These are incorporated into the multi-body equations of motion and solved via a fuzzy Runge–Kutta scheme across nested α-levels. A simulation architecture iterates over α-cuts and time-steps to produce interval bounds on heavy responses. A case study off the Karnataka coast, with realistic sea-state data for moderate and severe scenarios, yields heave-amplitude envelopes whose widths quantify response uncertainty. At mid-confidence (α = 0.5), moderate seas produce amplitudes of 8.30–9.65 m (± 15 %), while severe seas yield 7.15–8.90 m (± 22 %). Envelope narrowing as α→1 confirms that increased parameter confidence reduces prediction spread, and bias analysis against crisp baselines highlights the impact of imprecision on mean responses. This non-probabilistic approach provides interpretable, worst- and best-case motion bounds without requiring large datasets, offering marine engineers robust safety margins and guidance for targeted data collection and real-time uncertainty updating.