Extreme and first excursion probability
Journal
Journal of the Chinese Institute of Engineers,Series A/Chung-kuo Kung Ch'eng Hsuch K'an
Journal Volume
12
Journal Issue
4
Pages
519-528
Date Issued
1989
Author(s)
Abstract
The extreme value problem is related to the first excursion problem in random vibration analysis. In the present paper, Gumbel’s order statistics and the asymptotic theory of statistical extremes are applied directly to the peak distribution function of a stationary random process in order to find the probability distribution of the extremal value within a certain time interval. The extreme value distribution of a random process obtained from this approach is compared with results from some classical methods. It is concluded that the present approach can be applied not only to a narrow-band process but also to a wide-band process for which the classical methods usually use several approximations to find the approximate results. The second part of this paper deals with the first excursion probability. A semi-empirical formula based on results of the first part and a correlation time consideration are proposed. Three examples, which include a narrow-band process, a wide-band process and a uniformly modulated process, are studied. The results are compared favorably with either simulation results or those obtained from other methods. © 1989 Taylor & Francis Group, LLC.
SDGs
Type
journal article