RESPONSE OF DYNAMIC SYSTEMS TO POISSON WHITE NOISE

Abstract

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 indentically distributed pulses arriving in time according to a Poisson counting process. The method is based on the observation that the system experiences free vibrations between consecutive pulses of the input. Two algorithms 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 binomial white noise is an independent time series with a fixed time step that can be zero with a finite probability. The time step of the first and second algorithms are random and deterministic, respectively. The algorithms are used to calculate transition probabilities and estimate response statistics. Numerical examples are presented to demonstrate the proposed method of response and reliability analysis.