Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T19:16:48.320Z Has data issue: false hasContentIssue false
  • English
  • Français

Regression approximations of wavelength and amplitude distributions

Published online by Cambridge University Press:  01 July 2016

Igor Rychlik
Igor Rychlik*
Affiliation:
University of Lund
*
∗Postal address: Department of Mathematical Statistics, University of Lund, Box 118, S-221 00 Lund, Sweden.
Get access Rights & Permissions [Opens in a new window]

Abstract

A regression approximation of wavelength and amplitude distribution in an almost surely continuous process η (t), is based on a successively more detailed decomposition, η (t) = η n(t) + Δn(t), into one regression term η n on n suitably chosen random quantities, and one residual process Δn. The distances between crossings, maxima, etc., are then approximated by the corresponding quantities in the regression term, and explicit expressions given for the densities of these quantities.

Keywords

CROSSINGSFATIGUEMAXIMAPERIODS ANALYSISSLEPIAN MODEL PROCESSWAVE-HEIGHT
Type
Research Article
Information
Advances in Applied Probability , Volume 19 , Issue 2 , June 1987 , pp. 396 - 430
Copyright
Copyright © Applied Probability Trust 1987 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Research supported in part by the National Swedish Board for Technical Development under contract No 83-3042.

References

1. Bulinskaya, E. V. (1961) On the mean number of crossings of a level by a stationary Gaussian process. Theory Prob. Appl. 6, 435–438.Google Scholar
2. Cavanié, A., Arhan, M. and Ezraty, R. (1976) A statistical relationship between individual heights and periods of storm waves. Proc. BOSS’ 76, 354–360.Google Scholar
3. Cramér, H. and Leadbetter, M. R. (1967) Stationary and Related Stochastic Processes. Wiley, New York.Google Scholar
4. Kac, M. and Slepian, D. (1959) Large excursions of Gaussian processes. Ann. Math. Statist. 30, 1215–1228.Google Scholar
5. Leadbetter, M. R., Lindgren, G. and Rootzen, H. (1983) Extremes and Related Properties of Random Sequences and Processes. Springer-Verlag, New York.Google Scholar
6. Lindgren, G. (1972) Wave-length and amplitude in Gaussian noise. Adv. Appl. Prob. 4, 81–108.Google Scholar
7. Lindgren, G. (1984) Use and structure of Slepian model processes for prediction and detection in crossing and extreme value theory. Proc. NATO ASI on Statistical Extremes and Applications , Vimeiro 1983. Reidel, Dordrecht, 261–284.CrossRefGoogle Scholar
8. Lindgren, G. and Holmström, K. (1978) WAMP–a computer program for wave-length and amplitude analysis of Gaussian waves. Univ. Umeå Statist. Res. Rep. 1978: 9, 1–45.Google Scholar
9. Lindgren, G. and Rychlik, I. (1982) Wave characteristic distributions for Gaussian waves–wave-length, amplitude, and steepness. Ocean Engng. 9, 411–432.Google Scholar
10. Longuet-Higgins, M. S. (1983) On the joint distribution of wave periods and amplitudes in a random wave field. Proc. R. Soc. London A389, 241–258.Google Scholar
11. Marcus, M. B. (1977) Level crossings of a stochastic process with absolutely continuous sample paths. Ann. Prob. 5, 52–71.Google Scholar
12. Rice, S. O. (1944), (1945) Mathematical analysis of random noise. Bell System. Tech. J. 23, 282–332; 24, 46-156.Google Scholar
13. Rice, J. R. and Beer, F. P. (1965) On the distribution of rises and falls in a continuous random process. J. Basic Engineering, ASME, Ser. D 87, 398–404.Google Scholar
14. Rychlik, I. (1987) Joint distribution of successive zero crossing distances in stationary Gaussian processes. J. Appl. Prob. 24 (2).Google Scholar
15. Rychlik, I. (1986) Rain flow cycle distribution for a stationary Gaussian load process. Univ. Lund Statist. Res. Rep. 4, 1–36.Google Scholar