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

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 dimensionaless 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.