The Influence of Oscillatory Correlation on the Zero Crossings of Gaussian Processes
Publication: Vulnerability, Uncertainty, and Risk: Quantification, Mitigation, and Management
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.
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© 2014 American Society of Civil Engineers.
History
Published online: Jul 7, 2014
ASCE Technical Topics:
- Continuum mechanics
- Correlation
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Gaussian process
- Mathematics
- Methodology (by type)
- Models (by type)
- Motion (dynamics)
- Numerical models
- Oscillations
- Probability
- Research methods (by type)
- Solid mechanics
- Statistics
- Stochastic processes
- Verification
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