Predictive Motion Envelopes for Offshore Logistics via α-Cut Intervals

Offshore logistics operations must continuously balance safety, fuel efficiency, and emissions reduction while navigating under uncertain and highly variable sea states. To address this challenge, we present an α-cut interval framework in which environmental uncertainties, specifically wave height and wind speed, are modeled as fuzzy numbers. Their corresponding α-level intervals are systematically propagated through a discrete vessel dynamics model, focusing on surge and heave responses. This procedure generates families of nested motion envelopes that tighten monotonically with increasing α, thereby producing deterministic yet progressively refined safety bounds without relying on full probabilistic distributions. A case study off the Karnataka coast is used to demonstrate the approach for a 20 km offshore supply voyage. Route planning constrained by α-envelopes ensures adherence to vessel structural and stability limits while enabling optimized transit speed. Comparative evaluation indicates that, relative to standard interval analysis, α-cut propagation substantially reduces over-conservatism, while against Monte Carlo-based envelopes it achieves similar coverage with significantly lower computational effort. Sensitivity analyses further quantify the influence of α-grid resolution, membership-function design, and hydrodynamic coupling coefficients on envelope width, fuel use, and emissions. In the tested scenario, higher α levels allow up to ~15% reduction in worst-case energy consumption and nearly 10% reduction in CO₂ emissions, all while preserving safety margins. Overall, the proposed framework is transparent, computationally efficient, and easily integrable into digital-twin-enabled operational workflows, providing a practical and sustainable decision-support tool for adaptive offshore logistics planning.