Quantifying the motion–fatigue trade-off in low-frequency surge of semi-submersible floating offshore wind turbines via energy-to-stiffness scaling

Low-frequency surge in semi-submersible floating offshore wind turbines is driven by second-order difference-frequency wave loading and amplified by mooring restoring stiffness. Both mechanisms are well established, but their individual contributions under realistic irregular wave conditions have rarely been isolated systematically. A controlled parametric study of the OC4-DeepCwind platform in OpenFAST varies wave height, peak period, and mooring line length independently and in combination, using full difference-frequency QTF loading. Excitation intensity depends on the spectral availability of second-order forcing, while resonant amplification is governed by effective mooring stiffness. Within the parameter range studied, these contributions combine through near-linear variance superposition and collapse onto a compact non-dimensional energy-to-stiffness index. The scaling holds for peak periods below roughly 8 s; beyond this range, QTF-weighted excitation efficiency declines independently of wave energy. Surge and fairlead tension occupy separate frequency bands. Surge is low-frequency-dominated throughout, whereas fairlead tension is controlled by wave-frequency loading and stiffness-dependent load transmission. Fatigue is assessed using the Tovo–Benasciutti spectral method. The spectral decoupling produces a direct motion–fatigue conflict: the stiffest mooring yields the lowest surge but a fatigue indicator 19 times the baseline, with the critical fairlead reaching 284 times. No configuration resolves both objectives, a constraint invisible to surge amplitude alone. • Excitation and resonant amplification act as separable mechanisms in LF surge. • Second-order excitation and mooring stiffness collapse onto index Π s (T p ≲ 8 s). • Sub-linear Π s exponent (0.83) reflects damping and QTF-overlap variation, not noise. • Spectral decoupling of surge and fairlead tension drives a motion-fatigue trade-off. • No mooring stiffness minimises both LF surge and TB fatigue: a Pareto-type limit.