Influence of Mathematical Modelling of Knowledge Application to the Transfer of Radionuclides in the Environment

Workshop on the Evaluation of Uncertainties in Relation to Severe Accidents and Level II Probabilistic Safety Analysis, Cadarache (FRANCE), 7-9 Novembre 2005

Eric Chojnacki(1), Catherine Mercat-Rommens(2), Cédric Baudrit(3).

Although Monte-Carlo methods provide extremely flexible and powerful techniques for solving many of the uncertainty propagation problems encountered in safety analysis, these methods present two major drawbacks. Like most methods based on probability theory, Monte-Carlo methods need a lot of knowledge. Indeed to determine the probability law associated to each uncertain parameter, it is necessary to have collected a considerable amount of data or to make assumptions in the place of such empirical information. Moreover, to perform a Monte-Carlo simulation, it is also required to provide information about all the possible dependencies between the uncertain parameters. Unfortunately, in practice, such information is rarely fully available and the impact of the assumptions made to mitigate this lack of knowledge can deteriorate the relevance of the decision-making.
To overcome both kinds of limitations, the French Institute for Radiological Protection and Nuclear Safety (IRSN) in collaboration with BRGM, INERIS and University of Toulouse intends to experiment recent advances in Dempster Shafer theory. The purpose of this paper is to introduce our developments of this theory through the example of the transfer of a radionuclide in the environment. In particular, it will be shown that fuzzy numbers are a natural way to represent current state of radioecological knowledge because they can be considered equivalent to a family of probability distributions instead of a single one. Thus, the use of fuzzy numbers in uncertainty analysis allows to avoid the subjectivity which may exist in the choice of a single probability distribution. Afterwards, we will see how the Dempster-Shafer theory provides an unified theoretical framework allowing both the use of probability functions for stochastic uncertainties modelling and fuzzy numbers for epistemic uncertainties modelling.

It will also be shown that the stochastic independence assumption often taken by default in Monte-Carlo applications may lead to an artificial reduction of evaluated uncertainty ranges. On the contrary, the notion of epistemic independency, taken by default in fuzzy calculations, may lead to an artificial extension of evaluated uncertainty ranges. In this way, it appears that the epistemic independency is more related to an ignorance of stochastic dependencies than an assumption of stochastic independency.
The results obtained from our example with this uncertainty methodology can be extended to other realistic studies as far as the nature of monotonicity between uncertain variables and the response is known. Such kind of uncertainty methodologies seems to us the only possibility to warrant the robustness of Monte-Carlo simulation in case of incomplete knowledge.

(1) : IRSN
(2) : RSN/DEI/SESURE
(3) : Université Paul Sabatier de Toulouse