### Numéro : 2792 - Year : 2023

# Sea waves & ship movements extreme values

**Julien MORESVE, ***Naval Group – Nantes, France*

Waves and associated ship movements are random processes that are well described in the literature and in industry standards.

In problems of naval engineer, the question often arises of the model of maxima to be used to size ship structures, installations, or limit/authorize naval operations (landing of helicopters, launching and recovery of boats, etc...).

Conventional approaches involve modelling the open sea surface with a wave spectrum, calculating the ship’s response to that wave spectrum, and then using statistical distribution models to predict maximum values.

However, this evaluation of the maximum is based on the knowledge of the standard deviation of the hypothetically measurable motion over an infinite time in constant meteorological conditions (RMS value, Root Mean Square), a theoretical hypothesis rarely realized.

Although acceptable for the assessment of permanent features, intrinsic to the criterion to be assessed (such as the seaworthiness of vessels), this approach is sometimes discussed between naval architects and naval aeronautics offices whose problem is to define maximum motion models for air operations (take-off/landing of aircraft). Indeed, a model of the maximum linked to the observation time horizon interferes with the evaluation of the acceptable conditions for the landing of a helicopter, limits which must be applicable regardless of the duration of the operation. Using a Rayleigh model (Weibul order 2) we are forced to set the probability of dreaded events whose acceptability is difficult to judge according to the criticality of the operations.

Here we examine another approach, inspired by the Italian studies of the GPD (Generalized Pareto Distribution) which describes the distribution of extreme values used for the prediction of rare phenomena (tides, floods, etc.) with Poisson’s law instead of Gaussian’s law.

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