Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (6): 701-710.

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STATISTICAL PROPERTY OF THRESHOLD-CROSSING FOR ZERO-MEAN-VALUED, NARROW-BANDED GAUSSIAN PROCESSES

HE Wu-zhou, YUAN Ming-shun   

  1. Department of Hydraulic and Hydropower Engineering, Tsinghua University, Beijing 100084, P.R.China
  • Received:1998-11-04 Revised:1999-11-08 Online:2001-06-18 Published:2001-06-18

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.

2010 MSC Number: 

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