Mixed aleatory and epistemic uncertainty quantification using fuzzy set theory

He, Yanyan; Mirzargar, Mahsa; Kirby, Robert M.

doi:10.1016/j.ijar.2015.07.002

Cited by 28 publications

(9 citation statements)

References 30 publications

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“…Recently, many methods were proposed to deal with epistemic uncertainty, such as fuzzy sets, information difference theory, interval analysis, evidence theory, etc. [20][21][22]. All these methods have their own desirable and undesirable features-such as the approach of evidence theory, especially the appropriateness of Dempster's rule for combining evidence, which is somewhat controversial [23].…”

Section: A P-box Methods Based On Bayesian Theorymentioning

confidence: 99%

System Reliability Assessment with Imprecise Probabilities

Yang

Huang

et al. 2019

Applied Sciences

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The exact statistical characteristics of some components may be unavailable because of the limited sample information in practical engineering. One challenge that system reliability analysis faces is dealing with limited sample sizes, which introduces the potential for a high level of uncertainty in the analysis results. In this paper, we propose a procedure for the reliability analysis of complex systems with a limited number of samples. Bayesian inference is used to estimate the parameter intervals of the life distributions of the components with a limited number of samples. Then, probability boxes (p-box) are constructed from the parameter intervals to represent the life distributions of the components with a limited number of samples. In addition, the theory of survival signature is applied to calculate the reliability of the system with a mixture of precise and imprecise knowledge of the life distributions of the components. Finally, two numerical examples are given to illustrate the validity of the methods.

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Section: A P-box Methods Based On Bayesian Theorymentioning

confidence: 99%

System Reliability Assessment with Imprecise Probabilities

Yang

Huang

et al. 2019

Applied Sciences

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show abstract

“…However, when considering pboxes in the input space, uncertainty propagation is more complex. A much lower number of methods have been developed for propagating p-boxes, amongst which are nested Monte Carlo algorithms (Eldred and Swiler, 2009;He et al, 2015) and interval-analysis-based algorithms . These algorithms require a large number of model evaluations to ensure an accurate estimate of the uncertainty in the QoIs.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty propagation of p-boxes using sparse polynomial chaos expansions

Schbi

Sudret

2017

Journal of Computational Physics

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In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making efficient quantification and propagation of uncertainties an important aspect. In this context, a typical workflow includes the characterization of the uncertainty in the input variables. In this paper, input variables are modelled by probability-boxes (p-boxes), accounting for both aleatory and epistemic uncertainty. The propagation of p-boxes leads to p-boxes of the output of the computational model. A two-level meta-modelling approach is proposed using non-intrusive sparse polynomial chaos expansions to surrogate the exact computational model and, hence, to facilitate the uncertainty quantification analysis. The capabilities of the proposed approach are illustrated through applications using a benchmark analytical function and two realistic engineering problem settings. They show that the proposed two-level approach allows for an accurate estimation of the statistics of the response quantity of interest using a small number of evaluations of the exact computational model. This is crucial in cases where the computational costs are dominated by the runs of high-fidelity computational models.

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“…A fuzzy-probability-based fault tree analysis is developed to overcome the limitation of fuzzy fault tree analysis in [9]. Algorithms constructing fuzzy probabilities to represent or model the mixed aleatory and epistemic uncertainty in a limited-size ensemble are proposed in [10]. A general method for estimating the bounds of the reliability of a system, where the input variables are described by random sets (probability distributions, probability boxes, or possibility distributions) is proposed in [11].…”

Section: Introductionmentioning

confidence: 99%

Imprecise reliability assessment of generating systems involving interval probability

Qiao

2017

IET Generation, Transmission & Distribution

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Mixed aleatory and epistemic uncertainty quantification using fuzzy set theory

Cited by 28 publications

References 30 publications

System Reliability Assessment with Imprecise Probabilities

System Reliability Assessment with Imprecise Probabilities

Uncertainty propagation of p-boxes using sparse polynomial chaos expansions

Imprecise reliability assessment of generating systems involving interval probability

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