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Statistical Property of Threshold-Crossing for Zero-Mean-Valued, Narrow-Banded Gaussian Processes

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Abstract

Based on a comprehensive discussion of the calculation method for the threshold-crossing statistics of zero mean valued, narrow banded Gaussian processes of various practical engineering problems, including the threshold-crossing probability, average number of crossing events per unit time, mean threshold-crossing duration and amplitude, a new simple numerical procedure is proposed for the efficient evaluation of mean threshold-crossing duration. A new dimensionless parameter, called the threshold-crossing intensity, is defined as a measure of the threshold-crossing severity, which is equal to the ratio of the product of average number of crossing events per unit time and mean threshold-crossing duration and amplitude over the threshold. It is found, by the calculation results for various combinations of stochastic processes and different thresholds, that the threshold-crossing intensity, irrelevant of the threshold and spectral density of the process, is dependent only on the threshold-crossing probability.

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He, Wz., Yuan, Ms. Statistical Property of Threshold-Crossing for Zero-Mean-Valued, Narrow-Banded Gaussian Processes. Applied Mathematics and Mechanics 22, 701–710 (2001). https://doi.org/10.1023/A:1016366421928

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  • DOI: https://doi.org/10.1023/A:1016366421928

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