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Representation and propagation of uncertainty involving imprecision and randomness: application to risk assessment related to polluted sites and soils

Cédric BAUDRIT, doctorate thesis of the University of Toulouse III Paul Sabatier, speciality: computer science, 198p, defended on the 19th October 2005

Document type > *Mémoire/HDR/Thesis

Keywords > polluted site, radioecology, uncertainty


Authors > BAUDRIT Cédric

Publication Date > 19/10/2005


Currently, decisions pertaining to the management of potentially polluted sites very often rely on the evaluation of risks for man and the environment. This evaluation is carried out with the help of models which simulate the transfer of pollutants from a source to a vulnerable target, for different scenarios of exposure. The selection of parameter values of these models is based as much as possible on the data collected at the time of on-site investigations (phase of diagnosis). However, due to time and financial constraints, information regarding model parameters is often incomplete and imprecise. This leads to uncertainty that needs to be accounted for the decision-making process.

Uncertainty regarding model parameters may have essentially two origins. It may arise from randomness due to natural variability resulting from heterogeneity of population or the fluctuations of a quantity in time. Or it may be caused by imprecision due to a lack of information resulting, for example, from systematic measurement errors or expert opinions. In risk assessment, no distinction is traditionally made between these two types of uncertainty, both being represented by means of a single probability distribution.

So, uncertainty in risk assessment models is generally addressed within a purely probabilistic framework. This approach comes down to assuming that knowledge regarding model parameters is always of random nature (variability). Such knowledge is represented by single probability distributions typically propagated through the risk model using the Monte-Carlo technique. Even if this approach is well-known, the difficulty is to avoid an arbitrary choice of the shape of probability distributions asssigned to model parameters. Indeed in the context of risk assessment related to pollutant exposure, knowledge of some parameters is often imprecise or incomplete. The use of single probability distribution to represent this type of knowledge becomes subjective and partly arbitrary, and it is more natural to use intervals.

However, the available information is often richer than an interval but less rich than a probability distribution. In practice, while information regarding variability is best conveyed using probability distributions, information regarding imprecision is more faithfull conveyed using probability families encoded either by p-boxes (lower & upper cumulative distribution functions) or by possibility distributions (also called fuzzy intervals) or yet by random intervals using the belief functions of Dempster-Shafer.

The first objective of this work is to propose practical representation methods according to available information regarding model parameters by using possibility, probability and random sets. The second one is to propose different methods for propagating variability and imprecision information through risk model by trying to take into account dependency between model parameters. Lastly, these alternative methods are tested on simplified real cases, with a view to provide useful inputs for the decision-making process.

- Dose calculation : Transfer of a radioactive pollutant (strontium) from the deposit to
man, through the consumption of food (cow's milk).
- Toxic risk related to the accidental spill of trichloroethylene (TCE) into an aquifer
(semi-analytical model) .
- Risk for health related to grounds polluted by lead due to the presence of factories.

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