Ocean engineers are routinely faced with design problems for coastal and deepwater structures that must survive a wide range of environmental conditions. One of the most challenging problems in the field of ocean engineering is the accurate characterization and modeling of the interaction of ocean waves with these offshore structures. The random characteristic of ocean environment requires engineers to consider the effects of random variability of the pertinent variables in their predictive models and design processes. Thus, for ocean engineering purposes, one needs to have accurate estimates of the probability distribution of the key random variables that will be used in sensitivity studies, reliability analysis, and risk assessment in the design process.

In this study, a family of semi-empirical probability distribution is developed based on the quadratic transformation of linear random variable assuming that the linear random variable follows a Rayleigh distribution law. The estimates of model parameters are obtained from two moment based parameter estimation methods, i.e. method of moments and method of linear moments. The studied semi-empirical distribution can be applied to estimate the probability distribution of a wide range of non-linear random variables in the fields of ocean wave mechanics and wave-structure interaction. As examples, the application of the semi-empirical model in estimation of probability distribution of: a) ocean wave power, b) ocean wave crests interacting with an offshore structure is illustrated. For this purpose, numerically generated timeseries and experimentally measured data sets are utilized.

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