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 |
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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 | |
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 |
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Country/Territory | UK United Kingdom |
City | Liverpool |
Period | 13/07/14 → 16/07/14 |
ASJC Scopus subject areas
- Safety, Risk, Reliability and Quality