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.
Time-Dependent Reliability Analysis Using the Total Probability Theorem
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.
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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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