A variance reducing multiplier for Monte Carlo integrations

Sobol, I. M.; Tutunnikov, A. V.

doi:10.1016/0895-7177(96)00042-8

Cited by 4 publications

(2 citation statements)

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“…When the number of samples is large enough, the MCS method can be regarded as accurate, and the results obtained by the MCS method are also used as a reference in this paper. 36,39,40 Based on the conventional hybrid reliability model, many computation methods have been derived, including MCS combined with the optimization strategy (MCSO), 23 unified uncertainty analysis based on the first-order reliability method (FORM-UUA), 24 surrogate model based methods (such as ALK-HRA), 38 and so forth.…”

Section: The Basic Theory Of the Conventional Hybrid Reliability Modelmentioning

confidence: 99%

“…where N is the total number of random variable samples, and

{\boldsymbol{y}}^{(j)}

is the j‐ th sample. When the number of samples is large enough, the MCS method can be regarded as accurate, and the results obtained by the MCS method are also used as a reference in this paper 36,39,40 …”

Section: Time‐dependent Reliability Analysis For Random and Interval ...mentioning

confidence: 99%

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Hybrid time‐dependent reliability analysis under a mixture of random and interval uncertainties

Zhou

Gao

et al. 2023

Numerical Meth Engineering

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A new time‐dependent reliability analysis model with a mixture of random variables and interval variables is proposed in this paper. First, samples of random variables are generated according to their probability density functions. Then, the samples are substituted into the performance function to obtain the interval processes corresponding to these samples. The reliability index of each interval process is computed to finally obtain the upper and lower bounds of failure probability. The adaptive Kriging surrogate model based on the global addition strategy is used in the calculation process to increase the computational efficiency. The accuracy of the computational strategy is demonstrated by a mathematical example and three engineering practical cases. The proposed new hybrid time‐dependent reliability model is compared to the conventional hybrid reliability model. The comparison results show that the proposed model is more convenient to implement than the conventional reliability model. It can accurately evaluate the reliability of the structure and can be applied to real‐world engineering practice thereby providing assistance and guidance for hybrid time‐dependent reliability analysis of structures.

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