Statistical Analysis of Crests and Maxima in Gaussian Seas

Jesper Rydén

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology
2002

ISBN 91-628-5108-X
LUTFMS--1016--2002


Abstract:
An important problem in ocean engineering is to find distributions for characteristic wave parameters. For wind-generated water waves at deep water, a Gaussian distribution for the wave-surface elevation is considered a reasonable model. Within the Gaussian assumption, extensions of Rice's formula can be applied to formulate explicit expressions for the distributions in the ergodic, or Palm, sense. This framework also allows for modelling with (Gaussian) random fields, which is one of the topics in this thesis. The explicit expressions need to be evaluated numerically which is possible to do once the covariance structure of the probabilistic model is known.
In the papers of this thesis, a main theme is the joint distribution of wavelength and amplitude; this distribution is not easily obtained from measured time records. Distributions are deduced for different representations of the sea state, e.g. including directionality of waves. Where possible, comparisons with empirical field data are made and demonstrate good agreement. The derived joint distribution is applied to compute the distribution of the hogging-bending moment midships of a floating vessel. The problem of finding the distribution for high wave crests is also addressed, and its relation to wave groups is investigated. Further, the topic of filtering records is discussed. The rainflow filter, a non-linear filter used in fatigue
analysis is investigated. An approximation in the frequency domain of the filter is proposed; it is found by a computer-intensive method involving i.a. spectral simulation. For the distribution of high crests, this linear approximation works well.
Keywords:
Gaussian fields, random waves, wave height, wave length, Rice's formula, rainflow cycle, fatigue