  This study is concerned with the estimation of long-term fatigue damage for a
floating offshore wind turbine. With the ultimate goal of efficient evaluation
of fatigue limit states for floating offshore wind turbine systems, a detailed
computational framework is introduced and used to develop a surrogate model
using Gaussian process regression. The surrogate model, at first, relies only
on a small subset of representative sea states and, then, is supplemented by
the evaluation of additional sea states that leads to efficient convergence and
accurate prediction of fatigue damage. A 5-MW offshore wind turbine supported
by a semi-submersible floating platform is selected to demonstrate the proposed
framework. The fore-aft bending moment at the turbine tower base and the
fairlead tension in the windward mooring line are used for evaluation. Metocean
data provide information on joint statistics of the wind and wave along with
their relative likelihoods for the installation site in the Mediterranean Sea,
near the coast of Sicily. \textcolor{black}{A coupled frequency-domain model}
provides needed power spectra for the desired response processes. The proposed
approach offers an efficient and accurate alternative to the exhaustive
evaluation of a larger number of sea states and, as such, avoids excessive
response simulations.
