First Passage of Nonstationary Random Processes

by Ross B. Corotis, Asst. Prof. of Civ. Engrg.; Northwestern Univ., Evanston, IL,
Erik H. Vanmarcke, Asst. Prof. of Civ. Engrg.; MIT, Cambridge, MA,
Allin C. Cornell, Assoc. Prof. of Civ. Engrg.; MIT, Cambridge, MA,

Serial Information: Journal of the Engineering Mechanics Division, 1972, Vol. 98, Issue 2, Pg. 401-414

Document Type: Journal Paper


A two-state Markov process for barrier passage statistics provides a more realistic model than the traditional Poisson process, especially for the response of a lightly-damped oscillator to broad-bank excitation. For high barrier levels the two give similar results. With the Markov model, first passage probability depends on the first three area moments of the process power spectral density. The concept of a time-dependent power spectrum conveniently describes the frequency decomposition of the response of an oscillator suddenly exposed to broad-band stationary excitation. Analytical expressions for time-dependent spectral moments lead to an evolutionary power spectral density shape parameter and improved first-passage results, especially for lightly-damped oscillators and short durations.

Subject Headings: Probability | Markov process | Power spectral density | Oscillations | Power plants | Excitation (physics) | Time dependence | Statistics

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