A method is developed for finding response statistics and reliability
for a non-linear system subjected to Poisson white noise. The Poisson
white noise can be viewed as a sequence of independent identically dis
tributed pulses arriving in time according to a Poisson counting proce
ss. The method is based on the observation that the system experiences
free vibrations between consecutive pulses of the input. Two algorith
ms are used for analysis. The first uses the definition of the Poisson
white noise and the second is based on an approximate representation
of the Poisson white noise, referred to as binomial white noise. The b
inomial white noise is an independent time series with a fixed time st
ep that can be zero with a finite probability. The time step of the fi
rst and second algorithms are random and deterministic, respectively.
The algorithms are used to calculate transition probabilities and esti
mate response statistics. Numerical examples are presented to demonstr
ate the proposed method of response and reliability analysis. (C) 1996
Academic Press Limited