A new reliability analysis method is proposed for time-dependent problems with explicit in time limit-state functions of input random variables and input random processes 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 time-dependent conditional probabilities which are computed accurately and efficiently in the standard normal space using the first-order reliability method (FORM) and a composite limit state of linear instantaneous limit states. If the dimensionality of the total probability theorem integral is small, we can easily calculate it using Gauss quadrature numerical integration. Otherwise, simple Monte Carlo simulation (MCS) or adaptive importance sampling are used based on a Kriging metamodel of the conditional probabilities. 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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March 2015
Research-Article
Time-Dependent Reliability Analysis Using the Total Probability Theorem
Zissimos P. Mourelatos,
Zissimos P. Mourelatos
1
Mechanical Engineering Department,
e-mail: mourelat@oakland.edu
Oakland University
,2200 N. Squirrel Road
,Rochester, MI 48309
e-mail: mourelat@oakland.edu
1Corresponding author.
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Monica Majcher,
Monica Majcher
Mechanical Engineering Department,
e-mail: mtmajch2@oakland.edu
Oakland University
,2200 N. Squirrel Road
,Rochester, MI 48309
e-mail: mtmajch2@oakland.edu
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Vijitashwa Pandey,
Vijitashwa Pandey
Mechanical Engineering Department,
e-mail: pandey2@oakland.edu
Oakland University
,2200 N. Squirrel Road
,Rochester, MI 48309
e-mail: pandey2@oakland.edu
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Igor Baseski
Igor Baseski
Mechanical Engineering Department,
e-mail: ibaseski@oakland.edu
Oakland University
,2200 N. Squirrel Road
,Rochester, MI 48309
e-mail: ibaseski@oakland.edu
Search for other works by this author on:
Zissimos P. Mourelatos
Mechanical Engineering Department,
e-mail: mourelat@oakland.edu
Oakland University
,2200 N. Squirrel Road
,Rochester, MI 48309
e-mail: mourelat@oakland.edu
Monica Majcher
Mechanical Engineering Department,
e-mail: mtmajch2@oakland.edu
Oakland University
,2200 N. Squirrel Road
,Rochester, MI 48309
e-mail: mtmajch2@oakland.edu
Vijitashwa Pandey
Mechanical Engineering Department,
e-mail: pandey2@oakland.edu
Oakland University
,2200 N. Squirrel Road
,Rochester, MI 48309
e-mail: pandey2@oakland.edu
Igor Baseski
Mechanical Engineering Department,
e-mail: ibaseski@oakland.edu
Oakland University
,2200 N. Squirrel Road
,Rochester, MI 48309
e-mail: ibaseski@oakland.edu
1Corresponding author.
Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received July 11, 2014; final manuscript received November 28, 2014; published online January 9, 2015. Assoc. Editor: Xiaoping Du.
J. Mech. Des. Mar 2015, 137(3): 031405 (8 pages)
Published Online: March 1, 2015
Article history
Received:
July 11, 2014
Revision Received:
November 28, 2014
Online:
January 9, 2015
Citation
Mourelatos, Z. P., Majcher, M., Pandey, V., and Baseski, I. (March 1, 2015). "Time-Dependent Reliability Analysis Using the Total Probability Theorem." ASME. J. Mech. Des. March 2015; 137(3): 031405. https://doi.org/10.1115/1.4029326
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