Title : Robust inversion under uncertainty for risk analysis – application to the failure of defences against flooding
Beginning of thesis : 2020
End of thesis : 2023
Abstract : The risk of coastal or fluvial flooding is aggravated by the failure of defences (either natural like dunes or artificial like dykes). The study of flood hazard on the Dutch River System illustrates this (Curran et al, 2019), as do several events that occurred in the last decade such as the hurricane Katrina in 2005 in New Orleans (Sills et al, 2008). The failure of defences is a factor of flooding risk whose importance will keep increasing in the future because of climate change. Our analysis of coastal and river flooding takes into account the following variables:
- Controlled variables, related to the geometry and location of the flood protection embankments.
- Uncontrolled variables capturing the randomness of natural phenomena, such as hydrograph parameters for river flooding and offshore hydrodynamic conditions (e.g wave characteristics). These variables have known probabilistic laws.
- Drastically uncertain variables, that are uncontrolled and not well characterized neither probabilistically nor in regulations. They are related to the dyke breach parameters.
In this work, we investigate a mathematical procedure based on inversion to characterize the possible combinations of controlled parameters (named excursion set) that lead to flooding with a probability greater than a given threshold α, a standard safety limit. If the flooding event is defined as the water level at a specific location, modelled as the result of a function F, exceeding a threshold T, the probabilistic excursion set to be investigated can be defined as 
is a random variable giving the water level at a specific location for a combination of controlled parameters equal to xc.
Several questions are addressed:
- First, how to represent excursion sets when there are more than two controlled variables and some uncertain variables do not have a known density. Parallel coordinates plots are considered and the relationship between the probabilistic excursion set Sα and the random excursion set
, (where Xu represents the uncontrolled variables) is theoretically investigated. - Second, the numerical simulations of the flooding are expensive to compute (typically several hours): metamodeling techniques (mainly kriging aka Gaussian Process) combined with active learning specifically designed to the estimate of the excursion set are used to reduce the computational cost. The idea is to replace the numerical simulations with an inexpensive surrogate model, that interpolates a few simulations points which are iteratively chosen to reduce uncertainty in the identification of the excursion set.
- Third, the inversion needs to be robust in the sense that it needs to consider the random nature of the uncontrolled variables. We generalize previous studies that dealt with uncontrolled variables through a worst-case scenario (Richet, Bacchi, 2019) by considering rare events, as the threshold α previously introduced must be very small.
- Fourth, the drastically uncertain variables need to be integrated in the probabilistic framework. Thus, the inversion will be combined with an optimisation to investigate here the worst-case scenario, ie the scenario leading to the highest probability of flooding.
Keywords : Uncertainties, metamodeling, active learning, flooding risk
Thesis defense : Octobre 2023
Supervisor :
Rodolphe Le Riche : Directeur de recherche Mines Saint-Étienne, CNRS, Limos
- Didier Rullière : Chargé de Recherche Mines Saint-Étienne, Limos
Partners or/and funders : IRSN, BRGM
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Objectifs de développement durable concernés :
Publications
- Probabilistic studies of flood risk are essential for assessing the safety of vulnerable areas, particularly in the presence of industrial facilities such as nuclear ones. These studies are complex as they rely on costly hydraulic simulators and require numerous simulations to deal with very low probabilities. The communication of the probabilistic findings to a wide […]
- The risk of coastal or fluvial flooding is aggravated by the failure of defences (either natural like dunes or artificial like dykes). The study of flood hazard on the Dutch River System illustrates this (Curran et al., 2019) along with several events that occurred in the last decade such as the hurricane Katrina in 2005 […]
- Visualization is an essential operation when assessing the risk of rare events such as coastal or river floodings. The goal is to display a few prototype events that best represent the probability law of the observed phenomenon, a task known as quantization. It becomes a challenge when data is expensive to generate and critical events […]
- The investigation of mixture models is a key to understand and visualize the distribution of multivariate data. Most mixture models approaches are based on likelihoods, and are not adapted to distribution with finite support or without a well-defined density function. This study proposes the Augmented Quantization method, which is a reformulation of the classical quantization […]
- Quantization summarizes continuous distributions by calculating a discrete approximation. Among the widely adopted methods for data quantization is Lloyd's algorithm, which partitions the space into Vorono\"i cells, that can be seen as clusters, and constructs a discrete distribution based on their centroids and probabilistic masses. Lloyd's algorithm estimates the optimal centroids in a minimal expected […]
- Quantization methods classically provide a discrete representation of a continuous set. This type of representation is relevant when the objective is the visualisation of weighted prototype elements representative of a continuous phenomenon. Nevertheless, more complex descriptions may be investigated. In this sense, mixture models identify subpopulations in a sample, arising from different distributions. The Gaussian […]
- Visualization is essential in the risk assessment of coastal or river flooding. In this work, we deal with expensive-to-evaluate hydraulic simulators, taking as random scalar inputs offshore meteo-oceanic conditions and dyke breach parameters, whereas the output is a flooding map. The challenge is to display a few prototype maps representing at best the probability law […]
- These slides constitute a 12h introductory course on global optimization. The course starts with basic concepts specific to global optimization and different from those underlying local optimization algorithms. A selection of 6 algorithms is then presented: random search, randomly restarted local searches, simulated annealing, CMA-ES and Bayesian Optimization. This selection is meant to cover the […]
- The risk of coastal or fluvial flooding is aggravated by the failure of defences (either natural like dunes or artificial like dykes). The study of flood hazard on the Dutch River System illustrates this (Curran et al., 2019) along with several events that occurred in the last decade such as the hurricane Katrina in 2005 […]
Actualité
- Ce rapport met en lumière la contribution significative de l’Institut Fayol de Mines Saint-Étienne au Consortium CIROQUO, avec la participation active de Didier Rullière, Charlie Sire, Tanguy Appriou, Xavier Bay, Rodolphe Le Riche, ainsi que d’anciens membres de Mines Saint-Etienne. … Lire la Suite →
- Le Consortium CIROQUO de Recherche et Industrie, publie son rapport d’Activité 2021-2024 Ce rapport met en lumière la contribution significative de l’Institut Fayol de Mines Saint-Étienne au Consortium CIROQUO, avec la participation active de Didier Rullière, Charlie Sire, Tanguy Appriou, … Lire la Suite →
- Le consortium CIROQUO (Consortium Industrie Recherche pour l’Optimisation et la QUantification d’incertitude pour les données Onéreuses) auquel participe Mines Saint-Etienne a tenu ses journées d’automne chez Stellantis Poissy les 23 et 24 novembre derniers. A cette occasion, plusieurs doctorants de … Lire la Suite →
- C’est la gageure que s’est proposé de relever Charlie Sire, doctorant à Mines Saint-Etienne, avec des chercheurs de l’IRSN (Yann Richet et Lucie Pheulpin), du BRGM (Jérémy Rohmer) et Rodolphe Le Riche et Didier Rullière, chercheurs à l’Institut Fayol. La visualisation sous forme … Lire la Suite →
- L’Institut Fayol de Mines Saint-Etienne bien représenté dans les réseaux de l’IFIP (International Federation for Information Processing) Cette année encore, Khaled Medini, chercheur à l’Institut Henri Fayol, IMT, membre du laboratoire LIMOS a poursuivi son implication, commencée il y a … Lire la Suite →