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

Abstract

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.

Uncertainty propagation in a model for the estimation of the ground level concentration of dioxin/furans emitted from a waste gasification plant

“…Finally, notice that both PMC and HMC methods have been applied under the simplifying assumption of independence of the parameters C D and V F , although they are expected to be somehow correlated. Future developments of this work may thus include investigating the effects of the dependence between these parameters on the uncertainty propagation results, for example resorting to the approach suggested in (Pedroni and Zio 2012).…”

A Critical Discussion and Practical Recommendations on Some Issues Relevant to the Nonprobabilistic Treatment of Uncertainty in Engineering Risk Assessment

“…Among the alternative approaches mentioned above, that based on possibility theory is by many considered one of the most attractive for extending the risk assessment framework in practice. In this article, we focus on this approach for the following reasons: (i) the power it offers for the coherent representation of uncertainty under poor information (as testified to by the large amount of literature in the field, see above); (ii) its relative mathematical simplicity; (iii) its connection with fuzzy sets and fuzzy logic, as conceptualized and put forward by Zadeh: actually, in his original view possibility distributions were meant to provide a graded semantics to natural language statements, which makes them particularly suitable for quantitatively translating (possibly vague, qualitative, and imprecise) expert opinions; and, finally, (iv) the experience of the authors themselves in dealing and computing with possibility distributions . One the other hand, it is worth remembering that possibility theory is only one of the possible “alternatives” to the incorporation of uncertainty into an analysis (see the approaches mentioned above).…”

“…In this context, the main objective of this article is to show in a systematic and comprehensive framework how some conceptual and technical issues on the treatment of uncertainty in risk assessment (items (1)‒(4) above) can be effectively tackled outside the probabilistic setting: practically speaking, different approaches and methods will be recommended for efficiently addressing each of issues (1)‒(4) listed above; classical probability theory tools as well as alternative, nonprobabilistic ones (in particular, possibility theory) are considered. The recommendations are “informed” by (i) a critical review of the literature approaches to solving the specific issues and (ii) the research work of the authors on addressing these issues: with respect to the latter item (ii), some of the considerations are based on results contained in articles previously published by the authors; other conclusions are instead drawn from analyses originally presented in this article (e.g., part of the work related to the issue of Bayesian updating).…”

Empirical Comparison of Two Methods for the Bayesian Update of the Parameters of Probability Distributions in a Two-Level Hybrid Probabilistic-Possibilistic Uncertainty Framework for Risk Assessment

“…Notice that the distributions for Z c have been obtained by propagating the two-level mixed probabilistic and possibilistic uncertainty through the mathematical model by means of a hybrid Monte Carlo (MC) and Fuzzy Interval Analysis (FIA) approach. This method combines the MC technique [Kalos and Withlock, 1986] with the extension principle of fuzzy set theory [Guyonnet et al, 2003;Aral, 2004 and in two hierarchical, repeated steps [Baudrit et al, 2008;Kentel and Aral, 2005;Beer, 2004 andMoller et al, 2003 andPedroni and Zio, 2012;: the reader is…”