Bounds on the Probability of Failure in Random Vibration
- 1 January 1982
- journal article
- research article
- Published by Taylor & Francis in Journal of Structural Mechanics
- Vol. 10 (1) , 67-91
- https://doi.org/10.1080/03601218208907402
Abstract
A new method to construct upper and lower bounds for the failure probability of a structure exposed to random excitations is presented. The method is based on an extension of the classical inclusion-exclusion series of Rice where the main idea is to take into consideration only realizations which are in the safe area at a number of previous instants of time. By a numerical example it is demonstrated that this method may lead to rather sharp bounds.Keywords
This publication has 12 references indexed in Scilit:
- Vector-Process Models for System ReliabilityJournal of the Engineering Mechanics Division, 1977
- An Upper Bound on the Failure Probability for Linear StructuresJournal of Applied Mechanics, 1973
- Maximum Structural Response to Seismic ExcitationsJournal of the Engineering Mechanics Division, 1970
- Model-Free Design of Aseismic StructuresJournal of the Engineering Mechanics Division, 1970
- On the Bound of First Excursion ProbabilityJournal of the Engineering Mechanics Division, 1969
- An approach to the first-passage problem in random vibrationJournal of Sound and Vibration, 1968
- On the Number of Exits Across the Boundary of a Region by a Vector Stochastic ProcessTheory of Probability and Its Applications, 1968
- Probability of Structural Failure Under Random LoadingJournal of the Engineering Mechanics Division, 1964
- The One-Sided Barrier Problem for Gaussian NoiseBell System Technical Journal, 1962
- Continuous Generalizations of Chebyshev’s InequalityTheory of Probability and Its Applications, 1958