Modelling Under Risk and Uncertainty: An Introduction to Statistical, Phenomenological and Computational Methods

3.2 A Short Introduction to Gradual Illustrative Modelling Steps

Several approaches to uncertainty assessment are thus possible for one or other of these criteria: (1) demonstrating compliance with a design criterion, securing the fact that the installation is well protected up to a conventional specification or risk level; (2) optimising the design in a cost benefit (or expected utility) approach to the dike and the protection system in the face of potential accidental costs and adjustable investment costs. The gradual modelling steps in Section 2 will introduce different ways to solve those two decision-making problems on a mixed probabilistic-deterministic basis, gradually moving on to the more probabilistic. Two very elementary approaches will firstly be discarded, as being too poor to be retained.

Firstly, elementary engineering thinking might refer to a basic deterministic study. Consider the use of so-called 'penalised' values for each of the inputs. In fact, when the system model is monotonous, it is simple to understand that the highest value for the output over intervals of variation for each input component corresponds to the value computed at the lowest or highest input bound depending on the sense of monotony (increasing or decreasing):

(3.14)

where, for the hydro component:

(3.15)

Penalised values would typically be taken at the maximum historically observed, or an ...