Filtered Poisson Process for Random Vibration Problems

The problem considered is the probability of failure analysis of structures excited by randomly varying dynamic forces. A solution is given for the random filtered Poisson process model which has often been proposed to characterize dynamic forces associated with superposition of pulses including random wind, earthquake and highway vehicle loadings. A numerical procedure using the familiar Fourier series technique is used for inverting the characteristic functions of a Poisson process. This gave univariate and bivariate probability density distributions and crossing rates for the time-varying stress or deflection of a single degree-of-freedom system excited by forces described by the Poisson process. A new method for finding first-passage probabilities is also employed which is applicable to both Gaussian and Poisson processes and has been verified by simulation. A specific application is given for wind loaded structures. Results are presented in the form of reliability data showing the safety factor needed to achieve a specified overall failure probability.