Engineering analysis with probability boxes: A review on computational methods

•Imprecise probabilities allow for explicitly taking epistemic uncertainty into account.•P-boxes are of interest for engineering analysis due to their mathematical straightforward description.•An overview of methods for construction of p-boxes based on available information is given.•The state-of-th...

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Published in:	Structural safety Vol. 93; p. 102092
Main Authors:	Faes, Matthias G.R., Daub, Marco, Marelli, Stefano, Patelli, Edoardo, Beer, Michael
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier Ltd 01.11.2021 Elsevier BV
Subjects:	Boxes Computer applications Distribution functions Imprecise probability Literature review P-boxes Probability Probability distribution Propagation Random variables Reliability analysis Reliability engineering Statistical analysis Structural reliability Surrogate modelling Uncertainty Upper bounds Literature review P-boxes Reliability analysis Imprecise probability Surrogate modelling
ISSN:	0167-4730, 1879-3355
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Abstract	•Imprecise probabilities allow for explicitly taking epistemic uncertainty into account.•P-boxes are of interest for engineering analysis due to their mathematical straightforward description.•An overview of methods for construction of p-boxes based on available information is given.•The state-of-the-art in propagation schemes for p-boxes is discussed. The consideration of imprecise probability in engineering analysis to account for missing, vague or incomplete data in the description of model uncertainties is a fast-growing field of research. Probability-boxes (p-boxes) are of particular interest in an engineering context, since they offer a mathematically straightforward description of imprecise probabilities, as well as allow for an intuitive visualisation. In essence, p-boxes are defined via lower and upper bounds on the cumulative distribution function of a random variable whose exact probability distribution is unknown. However, the propagation of p-boxes on model inputs towards bounds on probabilistic measures describing the uncertainty on the model responses is numerically still very demanding, and hence is subject of intensive research. In order to provide an overview on the available methods, this paper gives a state-of-the art review for the modelling and propagation of p-boxes with a special focus on structural reliability analysis.
AbstractList	The consideration of imprecise probability in engineering analysis to account for missing, vague or incomplete data in the description of model uncertainties is a fast-growing field of research. Probability-boxes (p-boxes) are of particular interest in an engineering context, since they offer a mathematically straightforward description of imprecise probabilities, as well as allow for an intuitive visualisation. In essence, p-boxes are defined via lower and upper bounds on the cumulative distribution function of a random variable whose exact probability distribution is unknown. However, the propagation of p-boxes on model inputs towards bounds on probabilistic measures describing the uncertainty on the model responses is numerically still very demanding, and hence is subject of intensive research. In order to provide an overview on the available methods, this paper gives a state-of-the art review for the modelling and propagation of p-boxes with a special focus on structural reliability analysis. •Imprecise probabilities allow for explicitly taking epistemic uncertainty into account.•P-boxes are of interest for engineering analysis due to their mathematical straightforward description.•An overview of methods for construction of p-boxes based on available information is given.•The state-of-the-art in propagation schemes for p-boxes is discussed. The consideration of imprecise probability in engineering analysis to account for missing, vague or incomplete data in the description of model uncertainties is a fast-growing field of research. Probability-boxes (p-boxes) are of particular interest in an engineering context, since they offer a mathematically straightforward description of imprecise probabilities, as well as allow for an intuitive visualisation. In essence, p-boxes are defined via lower and upper bounds on the cumulative distribution function of a random variable whose exact probability distribution is unknown. However, the propagation of p-boxes on model inputs towards bounds on probabilistic measures describing the uncertainty on the model responses is numerically still very demanding, and hence is subject of intensive research. In order to provide an overview on the available methods, this paper gives a state-of-the art review for the modelling and propagation of p-boxes with a special focus on structural reliability analysis.
ArticleNumber	102092
Author	Faes, Matthias G.R. Daub, Marco Patelli, Edoardo Beer, Michael Marelli, Stefano
Author_xml	– sequence: 1 givenname: Matthias G.R. surname: Faes fullname: Faes, Matthias G.R. email: Matthias.faes@kuleuven.be organization: KU Leuven, Jan De Nayerlaan 5, 2860 Sint-Katelijne-Waver, Belgium – sequence: 2 givenname: Marco surname: Daub fullname: Daub, Marco organization: ETH Zürich, Stefano-Franscini-Platz 5, 8093 Zürich, Switzerland – sequence: 3 givenname: Stefano surname: Marelli fullname: Marelli, Stefano organization: ETH Zürich, Stefano-Franscini-Platz 5, 8093 Zürich, Switzerland – sequence: 4 givenname: Edoardo surname: Patelli fullname: Patelli, Edoardo organization: Strathclyde University, Department of Civil and Environmental Engineering, Glasgow, United Kingdom – sequence: 5 givenname: Michael surname: Beer fullname: Beer, Michael organization: Institute for Risk and Reliability, Leibniz Universität Hannover, Callinstr. 34, 30167 Hannover, Germany
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Snippet	•Imprecise probabilities allow for explicitly taking epistemic uncertainty into account.•P-boxes are of interest for engineering analysis due to their... The consideration of imprecise probability in engineering analysis to account for missing, vague or incomplete data in the description of model uncertainties...
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SubjectTerms	Boxes Computer applications Distribution functions Imprecise probability Literature review P-boxes Probability Probability distribution Propagation Random variables Reliability analysis Reliability engineering Statistical analysis Structural reliability Surrogate modelling Uncertainty Upper bounds
Title	Engineering analysis with probability boxes: A review on computational methods
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Volume	93
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