Probabilistic fatigue assessment and optimal heading design of FOWT mooring systems under wind–wave misalignment

Floating offshore wind turbine (FOWT) mooring fatigue accumulates under ordinary operating conditions, where wind and waves are often misaligned. Previous studies typically represent this misalignment by a relative angle or a few fixed directional cases. Yet the three-line mooring is directionally anisotropic, making fairlead fatigue dependent on the absolute wind and wave directions. This study develops a probabilistic fatigue framework that preserves absolute directionality and exploits it to optimize platform heading. A D-vine copula represents the joint distribution of five metocean variables at fourteen Korean buoy sites, and fully coupled OrcaFlex simulations with separately specified wind and wave directions train a Gaussian-process surrogate for per-fairlead fatigue damage, enabling reliability analysis and a computationally inexpensive orientation sweep. Directional simplifications are not uniformly safe-sided and can alter the governing line; at Ulsan, the fully aligned assumption reduces the system reliability index from 2.01 to −4.09. At the three representative sites, misaligned states contribute most of the lifetime damage. At Chilbaldo, rotating the complete platform–mooring layout at the installation stage increases the system reliability index from 2.21 to 4.97. These results support retaining absolute directions in site-specific fatigue assessment and preliminary mooring-layout design.