The mean crossing rate of a stochastic process out-crossing a safe domain is calculated using methods from time-independent reliability theory. The method is developed from Madsen’s formula which expresses the mean up-crossing rate of a scalar process through a specified level as a parallel system sensitivity measure. The method is applicable to stationary as well as nonstationary stochastic vector processes provided the random variables describing the process and the time-derivative process at time t can be mapped jointly into a set of independent standardized random normal variables. This is identical to the restriction imposed on the random variables using the first and second-order reliability methods (FORM, SORM), and is not very restrictive. Thus, quite general stochastic models can be treated. Also, closed-form results have been developed. In this paper the mean crossing rate for the stationary Gaussian process crossing into a polyhedral convex set is given. The method is demonstrated to give good results by examples.
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Parallel System Approach for Vector Out-Crossing Available to Purchase
O̸. Hagen
A.S. Veritas Research, Ho̸vik, Norway
L. Tvedt
A.S. Veritas Research, Ho̸vik, Norway
J. Offshore Mech. Arct. Eng. May 1992, 114(2): 122-128 (7 pages)
Published Online: May 1, 1992
Article history
Received:
January 21, 1992
Online:
June 12, 2008
Citation
Hagen, O., and Tvedt, L. (May 1, 1992). "Parallel System Approach for Vector Out-Crossing." ASME. J. Offshore Mech. Arct. Eng. May 1992; 114(2): 122–128. https://doi.org/10.1115/1.2919959
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