Méthodes stochastiques non-intrusives pour l’analyse de la propagation d’incertitudes: Application aux écoulements des ruptures de barrages

Abstract

This thesis is a contribution to the uncertainties propagation analysis through numerical models of dam-break flows. The complexity of these phenomena and the relatively high computation time required by numerical solvers render the application of classical sampling methods such as Monte Carlo, Latin Hypercube Sampling (LHS), computationally cumbersome due to the high sample size that require such techniques to reach a satisfactory convergence. In this context, a novel non-intrusive approach named B-Splines Bézier Elements based Method (BSBEM) is proposed as an efficient tool for the uncertainty propagation analysis in physical hyperbolic problems. The generic character of the proposed approach allows it to be implemented for several engineering fields. The predictive efficiency of the BSBEM is first assessed and compared to the polynomial chaos expansion (PCE) and Monte Carlo (MC) methods using benchmark numerical examples and Stoker’s analytical solution for an idealized dam-break flow with discontinuous outputs. The proposed methodology is then applied to analyze the uncertainty propagation of a hypothetical failure of an actual dam (Batiscan River) located in the province of Québec (Canada). Three parameters, the input discharge, the Strickler roughness coefficient of the main channel, and the average breach width are considered as input random variables from which uncertainties may occur and propagate through the hydraulic numerical models. The obtained results reveal the ability of BSBEM to efficiently predict the statistical moments and probability distributions of the output quantities of interest represented in terms of the downstream discharge, water level, and front wave arrival time at different locations of the studied reach with smooth profiles, unlike those from the polynomial chaos expansion that showoscillatory behavior. Another contribution of this thesis concerns the proposal of a novel non-intrusive reduced order model technique named proper orthogonal decomposition-based B-Splines Bézier Elements Method (POD-BSBEM) for the uncertainty propagation analysis of stochastic time-dependent problems. The method uses a two-step proper orthogonal decomposition (POD) technique to extract the reduced basis. A third POD level is then applied to separate the time-dependent modes from the stochastic parametrized coefficients, which are approximated in the stochastic parameter space using B-splines basis functions defined in the corresponding Bézier element. The accuracy and the efficiency of the proposed method are assessed and compared to reduced-order model-based artificial neural network (POD-ANN) and the full-order model-based polynomial chaos expansion (Full-PCE) using benchmark steady-state and time-dependent problems. The POD-BSBEM is then applied to analyze the uncertainty propagation through a food wave flow stemming from a hypothetical dam break within a river with a complex bathymetry. The results confirm the ability of the POD-BSBEM to accurately predict the statistical moments of the output quantities of interest with a substantial speed-up for both offline and online stages compared to other techniques.

Date	16 Mar 2021
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Azzeddine Soulaïmani (Supervisor)