Envelope Crossing Rate and First Passage Probability

by Wen-Fang Wu, Natl Taiwan Univ, Taiwan,

Abstract: Various definitions of the envelope of a random response process are discussed. The statistical properties of the random envelope process based on these definitions are then derived and compared with one another. Among these properties, the expected envelope crossing rate is directly related to the reliability of the random response against the first passage failure. The reliabilities of five stationary narrow-band random processes are studied from empirical formulas based on various envelope definitions as well as from numerical simulations. It is concluded that an envelope defined by S.H. Crandall and W.D. Mark associated with the assumption that envelope crossings occur according to a Poisson process usually results in rather accurate and conservative approximations for the reliabilities against the double-sided first passage failure of narrow-band random processes.

Subject Headings: Failure analysis | Terminology and definition | Numerical models | Statistics | Stationary processes | Empirical equations | Approximation methods

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