2015
DOI: 10.4271/2015-01-0425
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An Efficient Method to Calculate the Failure Rate of Dynamic Systems with Random Parameters Using the Total Probability Theorem

Abstract: Using the total probability theorem, we propose a method to calculate the failure rate of a linear vibratory system with random parameters excited by stationary Gaussian processes. The response of such a system is non-stationary because of the randomness of the input parameters. A space-filling design, such as optimal symmetric Latin hypercube sampling or maximin, is first used to sample the input parameter space. For each design point, the output process is stationary and Gaussian. We present two approaches t… Show more

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Cited by 4 publications
(1 citation statement)
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“…To solve the first passage problem in time-variant reliability analysis involving stationary random processes, Singh et al [49] developed an importance sampling approach to calculate the cumulative probability of failure. Recently, some researchers have utilized metamodeling techniques [50][51][52] to alleviate the computational burden of time-variant reliability analysis. With the consideration of parametric uncertainty, Hu et al [53] construct surrogate models for evaluating the timeinstantaneous reliability index, and then identify the time-instantaneous most probable points using the fast integration method.…”
Section: Time-dependent Reliability Analysis and Rbdomentioning
confidence: 99%
“…To solve the first passage problem in time-variant reliability analysis involving stationary random processes, Singh et al [49] developed an importance sampling approach to calculate the cumulative probability of failure. Recently, some researchers have utilized metamodeling techniques [50][51][52] to alleviate the computational burden of time-variant reliability analysis. With the consideration of parametric uncertainty, Hu et al [53] construct surrogate models for evaluating the timeinstantaneous reliability index, and then identify the time-instantaneous most probable points using the fast integration method.…”
Section: Time-dependent Reliability Analysis and Rbdomentioning
confidence: 99%