Estimation of extreme slamming pressures using the non-uniform Fourier phase distributions of a design loads generator

Slamming pressures are predicted using a nonlinear ship motion program whose input is an ensemble of short wave trains tailored to produce a large, linear pitch response. These short wave trains are calculated via a design methodology that first creates short time series containing a specified, large ship response and then back-calculates the incident wave trains using linear systems theory. The background simulations and theory used to create these short time series are presented here. Monte Carlo simulation of moderately rare events of a random process indicate the random Fourier component phase PDFs are non-uniform, non-identically distributed, and dependent on the rarity of the target event. These PDFs are modeled using a single parameter, Modified Gaussian distribution and used to generate design time series with a given expected value at a specific time. To predict rare events without resorting to Monte Carlo simulation, the parameters of the Modified Gaussian distributions are calculated via characteristic function comparison. The characteristic functions compare a target PDF calculated from extreme value theory to a PDF based on a discrete Fourier representation of the stochastic process with non-uniform component phases. The comparison to extreme value theory helps to quantify the risk associated with rare events.