An Integral Equation Method for the First-Passage Problem in Random Vibration

The first-passage problem for a nonstationary stochastic process is formulated as an integral identity, which produces known bounds and series expansions as special cases, while approximation of the kernel leads to an integral equation for the first-passage probability density function. An accurate, explicit approximation formula for the kernel is derived, and the influence of uni or multi modal frequency content of the process is investigated.

Numerical results provide comparisons with simulation results and alternative methods for narrow band processes, and also the case of a multimodal, nonstationary process is dealt with.