Response and First Passage Probability of Non-linear Systems Subjected to Non-stationary Random Input

Abstract

An approximate method assuming partially Gaussian probability density functions is applied for the analysis of symmetric and non-symmetric non-linear systems subjected to non-stationary white noise. And the first passage probabilities are obtained by use of the assumed probability density functions, based upon the assumption of Poisson process of threshold crossings. In the numerical calculations and simulations, the usefulness of the method is demonstrated in comparison with the Gaussian method used often so far, and it is indicated that the estimation accuracy of the probability density is very important in the first passage problem.