On some reliability applications of Rice's formula for the intensity of level crossings
type: Item
instance of: scholarly article
title: On some reliability applications of Rice's formula for the intensity of level crossings
zbMATH Open document ID: 1003.60049
DOI: 10.1023/A:1017942408501
author: Igor Rychlik
published in: Extremes
publication date: 2002-11-21T00:00:00Z
review text: The author proves that the Rice formula for the expected number of crossing a fixed level \(u\) by a stationary Gaussian process \(X(t)\) holds for almost all \(u\) if \(E |\dot X(0)|<\infty\). The proof is based on the Banach theorem which relates the variation of a function and the number of crossings of a fixed level by the graph of this function. It is demonstrated that this a.s. result is sufficient for applications in modeling the size of stress due to slams that occur when a ship proceeds in rough seas, a wave crest height and a fatigue of metals.
Mathematics Subject Classification ID: 60G70
Mathematics Subject Classification ID: 90B25
zbMATH DE Number: 1833852
zbMATH Keywords: fatigue
zbMATH Keywords: rainflow damage
zbMATH Keywords: wave height
Wikidata QID: Q56771086
MaRDI profile type: Publication
full work available at URL: a:1017942408501
OpenAlex ID: W131316833
description: scientific article; zbMATH DE number 1833852