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Register a new userGlobal sensitivity analysis with 2d hydraulic codes: applied protocol and practical tool
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Added by
Olivier Delestre
Publication date
2016
fields
Informatics Engineering
and research's language is
English
Authors
M Abily
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No Arabic abstract
Global Sensitivity Analysis (GSA) methods are useful tools to rank input parameters uncertainties regarding their impact on result variability. In practice, such type of approach is still at an exploratory level for studies relying on 2D Shallow Water Equations (SWE) codes as GSA requires specific tools and deals with important computational capacity. The aim of this paper is to provide both a protocol and a tool to carry out a GSA for 2D hydraulic modelling applications. A coupled tool between Prom{e}th{e}e (a parametric computation environment) and FullSWOF 2D (a code relying on 2D SWE) has been set up: Prom{e}th{e}e-FullSWOF 2D (P-FS). The main steps of our protocol are: i) to identify the 2D hydraulic code input parameters of interest and to assign them a probability density function, ii) to propagate uncertainties within the model, and iii) to rank the effects of each input parameter on the output of interest. For our study case, simulations of a river flood event were run with uncertainties introduced through three parameters using P-FS tool. Tests were performed on regular computational mesh, spatially discretizing an urban area, using up to 17.9 million of computational points. P-FS tool has been installed on a cluster for computation. Method and P-FS tool successfully allow the computation of Sobol indices maps. Keywords Uncertainty, flood hazard modelling, global sensitivity analysis, 2D shallow water equation, Sobol index. Analyse globale de sensibilit{e} en mod{e}lisation hydrauliqu{`e} a surface libre 2D : application dun protocole et d{e}veloppement doutils op{e}rationnels -- Les m{e}thodes danalyse de sensibilit{e} permettent de contr{^o}ler la robustesse des r{e}sultats de mod{e}lisation ainsi que didentifier le degr{e} dinfluence des param etres d entr{e}e sur le r{e}sultat en sortie dun mod ele. Le processus complet constitue une analyse globale de sensibilit{e} (GSA). Ce type dapproche pr{e}sente un grand int{e}r{^e}t pour analyser les incer-titudes de r{e}sultats de mod{e}lisation , mais est toujours a un stade exploratoire dans les etudes appliqu{e}es mettant en jeu des codes bas{e}s sur la r{e}solution bidimensionnelle des equations de Saint-Venant. En effet, l impl{e}mentation dune GSA est d{e}licate car elle
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Technologies such as aerial photogrammetry allow production of 3D topographic data including complex environments such as urban areas. Therefore, it is possible to create High Resolution (HR) Digital Elevation Models (DEM) incorporating thin above ground elements influencing overland flow paths. Even though this category of big data has a high level of accuracy, there are still errors in measurements and hypothesis under DEM elaboration. Moreover, operators look for optimizing spatial discretization resolution in order to improve flood models computation time. Errors in measurement, errors in DEM generation, and operator choices for inclusion of this data within 2D hydraulic model, might influence results of flood models simulations. These errors and hypothesis may influence significantly flood modelling results variability. The purpose of this study is to investigate uncertainties related to (i) the own error of high resolution topographic data, and (ii) the modeller choices when including topographic data in hydraulic codes. The aim is to perform a Global Sensitivity Analysis (GSA) which goes through a Monte-Carlo uncertainty propagation, to quantify impact of uncertainties, followed by a Sobol indices computation, to rank influence of identified parameters on result variability. A process using a coupling of an environment for parametric computation (Prom{e}th{e}e) and a code relying on 2D shallow water equations (FullSWOF 2D) has been developed (P-FS tool). The study has been performed over the lower part of the Var river valley using the estimated hydrograph of 1994 flood event. HR topographic data has been made available for the study area, which is 17.5 km 2 , by Nice municipality. Three uncertain parameters were studied: the measurement error (var. E), the level of details of above-ground element representation in DEM (buildings, sidewalks, etc.) (var. S), and the spatial discretization resolution (grid cell size for regular mesh) (var. R). Parameter var. E follows a probability density function, whereas parameters var. S and var. R. are discrete operator choices. Combining these parameters, a database of 2, 000 simulations has been produced using P-FS tool implemented on a high performance computing structure. In our study case, the output of interest is the maximal
Sensitivity indices are commonly used to quantity the relative inuence of any specic group of input variables on the output of a computer code. In this paper, we focus both on computer codes the output of which is a cumulative distribution function and on stochastic computer codes. We propose a way to perform a global sensitivity analysis for these kinds of computer codes. In the rst setting, we dene two indices: the rst one is based on Wasserstein Fr{e}chet means while the second one is based on the Hoeding decomposition of the indicators of Wasserstein balls. Further, when dealing with the stochastic computer codes, we dene an ideal version of the stochastic computer code thats ts into the frame of the rst setting. Finally, we deduce a procedure to realize a second level global sensitivity analysis, namely when one is interested in the sensitivity related to the input distributions rather than in the sensitivity related to the inputs themselves. Several numerical studies are proposed as illustrations in the dierent settings.
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In assignment problems, decision makers are often interested in not only the optimal assignment, but also the sensitivity of the optimal assignment to perturbations in the assignment weights. Typically, only perturbations to individual assignment weights are considered. We present a novel extension of the traditional sensitivity analysis by allowing for simultaneous variations in all assignment weights. Focusing on the bottleneck assignment problem, we provide two different methods of quantifying the sensitivity of the optimal assignment, and present algorithms for each. Numerical examples as well as a discussion of the complexity for all algorithms are provided.
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