The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes

Lorna R.M. Wilson, Keith I. Hopcraft, Eric Jakeman

Research output: Chapter or section in a book/report/conference proceedingChapter in a published conference proceeding

1 Citation (SciVal)
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Abstract

The problem of zero-crossings is of great historical prevalence and promises extensive application. The challenge is to identify the Probability Density Function (PDF) for the times between successive zero-crossings of a stochastic process. In this paper, we address the zero-crossing problem for a Gaussian process and investigate the effect of introducing oscillations into the prescribed auto-correlation function. Statistics for the number of zero-crossings occurring within a set time period are calculated and verified by simulations of the process. We find that highly oscillatory auto-correlation functions cause realizations of the stochastic process to become increasingly 'regular' or 'deterministic'. Zeros occur at more regular intervals, implying that the inter-event PDF has an exponential tail with large persistence exponent. The persistence exponent exhibits a complex phenomenology that is strongly influenced by the oscillatory nature of the auto-correlation function. Comparison is made between the theoretical predictions and numerical simulation results.

Original languageEnglish
Title of host publicationVulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management
Subtitle of host publicationProceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA)
EditorsMichael Beer, Sui-Kui Au, Jim W. Hall
Place of PublicationReston, Virginia, USA
PublisherAmerican Society of Civil Engineers (ASCE)
Pages1856-1865
Number of pages10
ISBN (Print)9780784413609
DOIs
Publication statusPublished - 7 Jul 2014
Event2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014 - Liverpool, UK United Kingdom
Duration: 13 Jul 201416 Jul 2014

Conference

Conference2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014
Country/TerritoryUK United Kingdom
CityLiverpool
Period13/07/1416/07/14

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality

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