Vector Process Out‐Crossing as Parallel System Sensitivity Measure
- 1 October 1991
- journal article
- Published by American Society of Civil Engineers (ASCE) in Journal of Engineering Mechanics
- Vol. 117 (10), 2201-2220
- https://doi.org/10.1061/(asce)0733-9399(1991)117:10(2201)
Abstract
The mean rate of vector processes out‐crossing safe domains is calculated using methods from time‐independent reliability theory. The method is founded on a result for scalar up‐crossing derived by Madsen. The out‐crossing is formulated as a zero down‐crossing of a continuously differentiable scalar process, and the mean crossing rate is obtained as a sensitivity measure of the probability for an associated parallel system domain. The vector process may be Gaussian, non‐Gaussian, stationary or nonstationary, and the failure function defining the boundary of the safe domain may be time‐dependent. A method for calculation of the expected number of crossings in a time interval through the introduction of an auxiliary uniformly distributed variable is presented. For stochastic failure surfaces the ensemble averaged rate is determined. A closed‐form expression for the mean crossing rate of a nonstationary Gaussian vector process crossing into a time‐dependent convex polyhedral set is derived. The method is demonstrated to give good results by examples.Keywords
This publication has 21 references indexed in Scilit:
- Probability Integration by Directional SimulationJournal of Engineering Mechanics, 1988
- New light on first- and second-order reliability methodsStructural Safety, 1987
- Second‐Order Reliability ApproximationsJournal of Engineering Mechanics, 1987
- Sensitivity Measures in Structural Reliability AnalysisLecture Notes in Engineering, 1987
- Asymptotic crossing rate of Gaussian vector processes into intersections of failure domainsProbabilistic Engineering Mechanics, 1986
- Crossings of Non‐Gaussian Translation ProcessesJournal of Engineering Mechanics, 1984
- Gaussian Outcrossings from Safe Convex PolyhedronsJournal of Engineering Mechanics, 1983
- Non-Normal Dependent Vectors in Structural SafetyJournal of the Engineering Mechanics Division, 1981
- Characteristics of Excursions above a High Level for a Gaussian Process and Its EnvelopeTheory of Probability and Its Applications, 1969
- On the Number of Exits Across the Boundary of a Region by a Vector Stochastic ProcessTheory of Probability and Its Applications, 1968