Probability Density Functions for Nonlinear Random Waves and Responses

Ulla Botelho Machado

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
Nonlinear waves have been a research topic for a long time, but have not yet entered common ocean engineering practice. In this article the problem of calculating the probability density function (pdf) for nonlinear waves is investigated. The `saddlepoint approximation' is applied to a second-order wave model to estimate the pdf. The performance of the approximation is compared with the performances of the more commonly used models, for different types of input spectra. In addition, a non-parametric transformation model, with extrapolation of the level crossing intensity, is proposed to estimate the pdf. One simulation and three different data sets are used to investigate the performance of the model.
Key words:
Nonlinear random waves, probability density function, saddlepoint approximation, POT method