Cycle Amplitude Distributions for Gaussian Processes  Exact and Approximative
Results
Georg Lindgren and K. Bertram Broberg
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2003
ISSN 14039338

Abstract:

Wave cycles, i.e. pairs of local maxima and minima, play an important role
in many engineering fields. Many cycle definitions are used for specific
purposes, such as cresttrough cycles in wave studies in ocean engineering
and rainflow cycles for fatigue life predicition in mechanical engineering.
The simplest cycle, that of a pair of local maximum and the following local
minimum is also of interest as a basis for the study of more complicated
cycles. This paper presents and illustrates modern computational tools for
the analysis of different cycle distributions for stationary Gaussian processes
with general spectrum. It is shown that numerically exact but slow methods
will produce distributions in almost complete agreement with simulated data,
but also that approximate and quick methods work well in most cases.


Of special interest is the relation between the cycle average and the cycle
amplitude for the simple maximumminimum cycle and its implication for the
corresponding amplitude. It is observed that for a Gaussian process with
rectangular box spectrum, these quantities are almost independent and that
the amplitude is not far from a Rayleigh distribution. It will also be shown
that

had there been a Gaussian process where exact independence hold then the
amplitude would have had an exact Rayleigh distribution. Unfortunately no
such Gaussian process exists.




Key words:

cresttrough waves, maxmin waves, rainflow cycles, random fatigue, spectral
density, stationary Gaussian process, wave period distribution
