Offshore structures are exposed to random wave loading in the ocean environment, and hence the probability distribution of the extreme values of their response to wave loading is of great value in the design of these structures. Due to nonlinearity of the drag component of Morison wave loading and also due to intermittency of wave loading on members in the splash zone, the response is often non-Gaussian; therefore, simple techniques for derivation of their extreme response probability distributions are not available. However, according to a recent paper, in the absence of current, the response of an offshore structure exposed to Morison wave loading, can be approximated by the response of an equivalent finite-memory nonlinear system (FMNS). These models can then be used, with great efficiency, to determine the probability distribution of response extreme values. In this paper, the progress made so far in extending these FMNS models to account for the effect of current on response is discussed.

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