A new reliability analysis method is proposed for time-dependent problems with limit-state functions of input random variables, input random processes and explicit in time using the total probability theorem and the concept of composite limit state. The input random processes are assumed Gaussian. They are expressed in terms of standard normal variables using a spectral decomposition method. The total probability theorem is employed to calculate the time-dependent probability of failure using a time-dependent conditional probability which is computed accurately and efficiently in the standard normal space using FORM and a composite limit state of linear instantaneous limit states. If the dimensionality of the total probability theorem integral (equal to the number of input random variables) is small, we can easily calculate it using Gauss quadrature numerical integration. Otherwise, simple Monte Carlo simulation or adaptive importance sampling is used based on a pre-built Kriging metamodel of the conditional probability. An example from the literature on the design of a hydrokinetic turbine blade under time-dependent river flow load demonstrates all developments.
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ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 17–20, 2014
Buffalo, New York, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-4632-2
PROCEEDINGS PAPER
Time-Dependent Reliability Analysis Using the Total Probability Theorem Available to Purchase
Zissimos P. Mourelatos,
Zissimos P. Mourelatos
Oakland University, Rochester, MI
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Monica Majcher,
Monica Majcher
Oakland University, Rochester, MI
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Vijitashwa Pandey,
Vijitashwa Pandey
Oakland University, Rochester, MI
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Igor Baseski
Igor Baseski
Oakland University, Rochester, MI
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Zissimos P. Mourelatos
Oakland University, Rochester, MI
Monica Majcher
Oakland University, Rochester, MI
Vijitashwa Pandey
Oakland University, Rochester, MI
Igor Baseski
Oakland University, Rochester, MI
Paper No:
DETC2014-35078, V02BT03A052; 13 pages
Published Online:
January 13, 2015
Citation
Mourelatos, ZP, Majcher, M, Pandey, V, & Baseski, I. "Time-Dependent Reliability Analysis Using the Total Probability Theorem." Proceedings of the ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 2B: 40th Design Automation Conference. Buffalo, New York, USA. August 17–20, 2014. V02BT03A052. ASME. https://doi.org/10.1115/DETC2014-35078
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