Approximation to First Passage Probability

In the theory of random vibration, a problem of considerable practical importance is to determine the probability, called first passage or first excursion probability, that the structural response will pass out of safety bounds or thresholds for the first time within a specified time interval. Within the framework of point process approach, a recurrence solution for approximating the first passage probability of a Gaussian random process, stationary or nonstationary, is suggested herein. Numerical results of the present approximation are displayed along with the results of other approximations. It is shown that the accuracy of the present approximation is satisfactory compared with the results of numerical simulation.