Uncertainty quantification and global sensitivity analysis with dependent inputs parameters: Application to a basic 2D-hydraulic model

Abstract

Hydraulic models include many uncertainties related to model parameters. Uncertainty Quantification (UQ) and Global Sensitivity Analysis (GSA) allow to quantify these uncertainties and identify the most influent parameters. To use traditional methods of UQ and GSA, the inputs must be independent. Therefore, this research aims to show that the dependence between inputs should not be neglected in uncertainty studies. To illustrate this, we used a simple hydraulic model built with TELEMAC-2D, representing a hypothetical linear river protected by a dyke that can break. The methodology is completed following these steps: the uncertain inputs and the outputs of interest are identified. Then, the inputs margins are defined through a statistical analysis using real dataset. The dependence structure between inputs is figured using copulas. Kriging metamodels are used to increase the number of experiences in a short time period. Finally, UQ and GSA are achieved. Regarding the UQ results, the outputs distribution is different if the inputs are considered dependent or not, whereas regarding the GSA, some parameters, usually considered non-influent in the hypothesis of independent inputs, have a real impact on the outputs. These results suggest that it could be interesting to consider the dependencies between inputs for “real” applications.

Keywords

• Dependent parameters
• uncertainty quantification
• global sensitivity analysis
• 2D hydraulic model
• copula
• metamodel