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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References
Price W G, Bishop R E D. Probabilistic Theory of Ship Dynamics[M]. London: Chapman and Hall,1974.
Tikhonov V I. The distribution of the duration of excursions of normal fluctuations[A]. In: Kuznetsov P I, Stratonovick R L, Tikhonov V I Eds. Non-Linear Transformations of Stochastic Processes[C]. Oxford: Pergamon,1965,354-367.
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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