Uncertainty analysis using evidence theory – confronting level-1 and level-2 approaches with data availability and computational constraints

Limbourg, Philipp; Rocquigny, Etienne de

doi:10.1016/j.ress.2010.01.005

Cited by 66 publications

(47 citation statements)

References 32 publications

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“…In extreme synthesis, the two main steps of the procedure are: 5,32,33 (1) sample N e random realizations Notice that the random samplings performed at steps (1) and (2) above may account for possible dependences existing between the epistemically-uncertain parameters and between the aleatory variables, respectively; on the other hand, such dependences can be obviously included in the analysis, only if they can be modeled within a classical MC framework. 63 Finally, notice that in this work standard MC simulation is used to propagate the aleatory uncertainties in step (2) above, which presupposes independence between the random variables.…”

Section: Two-dimensional Monte Carlo Methodsmentioning

confidence: 99%

“…The main steps of the procedure are: 5,32,33 (1) set i e = 1 (outer loop processing epistemic uncertainty by MC simulation); , respectively (i.e., as the two "extreme" CDFs that envelop all the N e CDFs generated in correspondence of the N e realizations of epistemic uncertainty).…”

Section: Appendix a Two-dimensional Monte Carlo Methodsmentioning

confidence: 99%

“…The former type of uncertainty is often referred to as objective, aleatory, stochastic whereas the latter is often referred to as subjective, epistemic, state of knowledge. [1][2][3][4] We are interested in the framework of two hierarchical levels of uncertainty, referred to as "level-2" setting: 5 the models of the aleatory events (e.g., the failure of a mechanical component, the variation of its geometrical dimensions and material properties, …)…”

Section: Introductionmentioning

confidence: 99%

“…[23][24][25][26] When both aleatory and epistemic uncertainties are represented by probability distributions, their propagation is carried out by a two-dimensional (or double) Monte Carlo (MC) simulation approach. 5,32,33 Instead, when a hybrid (probabilistic and possibilistic) uncertainty representation is considered, two approaches are here undertaken: (i) the hybrid MC and Fuzzy Interval Analysis (FIA) approach, b where the MC technique 34,35 is combined with the extension principle of fuzzy set theory, [36][37][38][39][40][41][42][43][44][45] within a "level-2" hierarchical setting; 24,[46][47][48][49][50][51] (ii) the Monte Carlo (MC)-based Dempster-Shafer (DS) approach employing Independent Random Sets (IRSs), c where the possibility distributions describing the epistemically-uncertain parameters are discretized into focal sets that are randomly and independently sampled by MC.…”

Section: Introductionmentioning

confidence: 99%

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Empirical Comparison of Methods for the Hierarchical Propagation of Hybrid Uncertainty in Risk Assessment, in Presence of Dependences

Pedroni

Zio

2012

Int. J. Unc. Fuzz. Knowl. Based Syst.

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Risk analysis models describing aleatory (i.e., random) events contain parameters (e.g., probabilities, failure rates, …) that are epistemically-uncertain, i.e., known with poor precision. Whereas aleatory uncertainty is always described by probability distributions, epistemic uncertainty may be represented in different ways (e.g., probabilistic or possibilistic), depending on the information and data available. The work presented in this paper addresses the issue of accounting for (in)dependence relationships between epistemically-uncertain parameters. When a probabilistic representation of epistemic uncertainty is considered, uncertainty propagation is carried out by a two-dimensional (or double) Monte Carlo (MC) simulation approach; instead, when possibility distributions are used, two approaches are undertaken: the hybrid MC and Fuzzy Interval Analysis (FIA) method and the MCbased Dempster-Shafer (DS) approach employing Independent Random Sets (IRSs). The objectives are: i) studying the effects of (in)dependence between the epistemically-uncertain parameters of the aleatory probability distributions (when a probabilistic/possibilistic representation of epistemic uncertainty is adopted) and ii) studying the effect of the probabilistic/possibilistic representation of epistemic uncertainty (when the state of dependence between the epistemic parameters is defined). The Dependency Bound Convolution (DBC) approach is then undertaken within a hierarchical setting of hybrid (probabilistic and possibilistic) uncertainty propagation, in order to account for all kinds of (possibly unknown) dependences between the random variables. The analyses are carried out with reference to two toy examples, built in such a way to allow performing a fair quantitative comparison between the methods, and evaluating their rationale and appropriateness in relation to risk analysis.

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Section: Two-dimensional Monte Carlo Methodsmentioning

confidence: 99%

Section: Appendix a Two-dimensional Monte Carlo Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Empirical Comparison of Methods for the Hierarchical Propagation of Hybrid Uncertainty in Risk Assessment, in Presence of Dependences

Pedroni

Zio

2012

Int. J. Unc. Fuzz. Knowl. Based Syst.

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“…Also these parameters are uncertain and the information to characterize them is drawn from experts. This framework of analysis where the aleatory and epistemic components of the uncertainty are separated into two hierarchical levels is often referred to as 'level 2' approach or setting [31]. This makes the present study different from other works of the literature, in which DSTE is embraced to treat epistemic uncertainty directly entering system reliability (e.g., [41]), i.e., with no stochastic variables.…”

Section: Introductionmentioning

confidence: 98%

Maintenance policy performance assessment in presence of imprecision based on Dempster–Shafer Theory of Evidence

Baraldi

Compare

Zio

2013

Information Sciences

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To cite this version:Piero Baraldi, Michele Compare, Enrico Zio. Maintenance policy performance assessment in presence of imprecision based on Dempster-Shafer Theory of Evidence. Information Sciences, Elsevier, 2013, 245, pp.112 -131 Abstract: The aim of this work is to assess the performance of a maintenance policy when a stochastic model of the life of the component of interest is known, but relies on parameters that are imprecisely known, and only through information elicited from experts. The case in which the information used to feed the model comes from a single expert has been investigated by the authors in a previous work. This paper deals with the different situation in which a number of experts are involved in the elicitation of the uncertain parameters; in particular, each expert provides an interval he/she believes containing the unknown value of the parameter which he/she is knowledgeable about. The different type of available information calls for the development of a different method to represent and propagate the associated uncertainty. Resorting to Probability theory to address this issue is questionable. Then, a technique based on the Dempster-Shafer Theory of Evidence (DSTE) is embraced in this work, which allows facing a practical case study concerning the check valve of a turbo-pump lubricating system in a Nuclear Power Plant. The output of such method consists of couples of Lower and Upper cumulative distributions describing the uncertainty in the maintenance performance indicators of interest (i.e., unavailability and costs), which accounts for both the aleatory and epistemic contributions.

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References – Part II

2014

Uncertainty in Risk Assessment

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Uncertainty analysis using evidence theory – confronting level-1 and level-2 approaches with data availability and computational constraints

Cited by 66 publications

References 32 publications

Empirical Comparison of Methods for the Hierarchical Propagation of Hybrid Uncertainty in Risk Assessment, in Presence of Dependences

Empirical Comparison of Methods for the Hierarchical Propagation of Hybrid Uncertainty in Risk Assessment, in Presence of Dependences

Maintenance policy performance assessment in presence of imprecision based on Dempster–Shafer Theory of Evidence

References – Part II

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