Advanced

Cycle range distributions for Gaussian processes - exact and approximative results

Lindgren, Georg LU and Broberg, Bertram (2004) In Extremes 7(1). p.69-89
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 crest-trough cycles in wave studies in ocean engineering and rainflow cycles for fatigue life prediction 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... (More)
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 crest-trough cycles in wave studies in ocean engineering and rainflow cycles for fatigue life prediction 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 dependence relation between the cycle average and the cycle range for the simple maximum-minimum cycle and its implication for the range distribution. It is observed that for a Gaussian process with rectangular box spectrum, these quantities are almost independent and that the range 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 range would have had an exact Rayleigh distribution. Unfortunately no such Gaussian process exists. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
random fatigue, spectral density, stationary Gaussian process, crest-trough waves, max-min waves, rainflow cycles, wave period distribution
in
Extremes
volume
7
issue
1
pages
69 - 89
publisher
Kluwer
external identifiers
  • scopus:17544372839
ISSN
1572-915X
DOI
10.1007/s10687-004-4729-3
language
English
LU publication?
yes
id
472af0ad-b255-480c-8729-3ebbbfb2a9dc (old id 581231)
date added to LUP
2007-10-24 19:24:53
date last changed
2017-03-15 13:27:00
@article{472af0ad-b255-480c-8729-3ebbbfb2a9dc,
  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 crest-trough cycles in wave studies in ocean engineering and rainflow cycles for fatigue life prediction 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. <br/><br>
<br/><br>
Of special interest is the dependence relation between the cycle average and the cycle range for the simple maximum-minimum cycle and its implication for the range distribution. It is observed that for a Gaussian process with rectangular box spectrum, these quantities are almost independent and that the range 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 range would have had an exact Rayleigh distribution. Unfortunately no such Gaussian process exists.},
  author       = {Lindgren, Georg and Broberg, Bertram},
  issn         = {1572-915X},
  keyword      = {random fatigue,spectral density,stationary Gaussian process,crest-trough waves,max-min waves,rainflow cycles,wave period distribution},
  language     = {eng},
  number       = {1},
  pages        = {69--89},
  publisher    = {Kluwer},
  series       = {Extremes},
  title        = {Cycle range distributions for Gaussian processes - exact and approximative results},
  url          = {http://dx.doi.org/10.1007/s10687-004-4729-3},
  volume       = {7},
  year         = {2004},
}