零均值、窄带高斯过程的过阀特性

对工程实际中经常遇到的零均值、窄带高斯过程过阀问题的统计特性作了系统的讨论,包括过阀概率、过阀平均次数、平均过阀延续时间和平均过阀幅值。提出了一种新的数值方法来计算平均过阀延续时间,该方法简单明了、使用方便。定义了一种度量过阀严重程度的新指标,称为“过阀强度”,等于单位时间过阀平均次数、平均过阀延续时间和平均过阀幅值三项乘积与阀值之比。大量的随机过程和阀值的组合计算结果表明,过阀强度仅仅与过阀概率有关,而与阀值大小、随机过程的谱密度无关,该规律深入地揭示了过阀特性的内在联系。

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.