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

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

doi:10.1061/9780784413609.186

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

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

University of Nottingham

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

1 Citation (SciVal)

146 Downloads (Pure)

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 language	English
Title of host publication	Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management
Subtitle of host publication	Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA)
Editors	Michael Beer, Sui-Kui Au, Jim W. Hall
Place of Publication	Reston, Virginia, USA
Publisher	American Society of Civil Engineers (ASCE)
Pages	1856-1865
Number of pages	10
ISBN (Print)	9780784413609
DOIs	https://doi.org/10.1061/9780784413609.186
Publication status	Published - 7 Jul 2014
Event	2nd 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 2014 → 16 Jul 2014

Conference

Conference	2nd International Conference on Vulnerability and Risk Analysis and Management, ICVRAM 2014 and the 6th International Symposium on Uncertainty Modeling and Analysis, ISUMA 2014
Country/Territory	UK United Kingdom
City	Liverpool
Period	13/07/14 → 16/07/14

ASJC Scopus subject areas

Safety, Risk, Reliability and Quality

Access to Document

10.1061/9780784413609.186

Wilson_ICVRAM_2013
The final publication is available at ascelibrary.org via https://doi.org/10.1061/9780784413609.186.
Accepted author manuscript, 104 KB

Cite this

Wilson, L. R. M., Hopcraft, K. I., & Jakeman, E. (2014). The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes. In M. Beer, S.-K. Au, & J. W. Hall (Eds.), Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management: Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA) (pp. 1856-1865). American Society of Civil Engineers (ASCE). https://doi.org/10.1061/9780784413609.186

The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes. / Wilson, Lorna R.M.; Hopcraft, Keith I.; Jakeman, Eric.
Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management: Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). ed. / Michael Beer; Sui-Kui Au; Jim W. Hall. Reston, Virginia, USA: American Society of Civil Engineers (ASCE), 2014. p. 1856-1865.

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

Wilson, LRM, Hopcraft, KI & Jakeman, E 2014, The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes. in M Beer, S-K Au & JW Hall (eds), Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management: Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). American Society of Civil Engineers (ASCE), Reston, Virginia, USA, pp. 1856-1865, 2nd 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, 13/07/14. https://doi.org/10.1061/9780784413609.186

Wilson LRM, Hopcraft KI, Jakeman E. The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes. In Beer M, Au SK, Hall JW, editors, Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management: Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). Reston, Virginia, USA: American Society of Civil Engineers (ASCE). 2014. p. 1856-1865 doi: 10.1061/9780784413609.186

Wilson, Lorna R.M. ; Hopcraft, Keith I. ; Jakeman, Eric. / The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes. Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management: Proceedings of the Second International Conference on Vulnerability and Risk Analysis and Management (ICVRAM) and the Sixth International Symposium on Uncertainty Modeling and Analysis (ISUMA). editor / Michael Beer ; Sui-Kui Au ; Jim W. Hall. Reston, Virginia, USA : American Society of Civil Engineers (ASCE), 2014. pp. 1856-1865

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AB - 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.

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

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