Statistical Analysis of Crests and Maxima in Gaussian Seas
Jesper Rydén
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology
2002
ISBN 916285108X
LUTFMS10162002

Abstract:

An important problem in ocean engineering is to find distributions for
characteristic wave parameters. For windgenerated water waves at deep water,
a Gaussian distribution for the wavesurface 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 hoggingbending 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 nonlinear filter used in fatigue

analysis is investigated. An approximation in the frequency domain of the
filter is proposed; it is found by a computerintensive 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