On the First Excursion Probability in Stationary Narrow-Band Random Vibration

Abstract

Dealing with a stationary narrow-band Gaussian process X(t) with mean zero, this paper derives a number of approximate solutions on the basis of the point-process approach. In particular, upper and lower bounds sharper than those presently available are established, an approximation based on the Markov point process is obtained, and the clump size approach is also used for approximation. These approximations are checked with the result of the semisimulation performed by Crandall, et al. [11]. Some remarks are also made on the use of the principle of maximum entropy.