Estimation of Extreme Roll Motion Using the First Order Reliability Method
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Extreme value statistics can often be based on the assumption that exceedance events of a high threshold level are statistically independent and identically distributed (i.i.d. process), which further implies the Poisson assumption to be valid. This makes it possible to express the extreme response statistics through the mean up-crossing rate. For non-linear processes, analytic expressions of the mean up-crossing rate do not in general exist. Reliable statistics of mean up-crossing rate based on the brute-force approach, e.g. Monte Carlo simulation (MCS) require long time domain simulations considering a number of different ensemble input. The associated computations can be very time consuming especially when a detailed physical (e.g. hydrodynamic) model is applied. The First Order Reliability Method (FORM) has previously been found efficient for estimation of extreme value prediction of stationary stochastic time domain processes, However, if the non-linearity in a response is significant, the accuracy of the FORM linearized mean up-crossing rate can be limited. The present work attempts to improve the extreme value prediction for non-linear parametric roll motions of ships based on applications of the FORM approach and suggests a model for the mean up-crossing rate for strong non-linear response, validated by comparing with MCS results.