Parameter identification for the shallow water equations using modal decomposition | Identification de paramètres pour les équations de l'hydraulique à surface libre à l'aide de la décomposition modale
2007
Wu, Qingfang | Amin, Saurabh | Munier, Simon | Bayen, Alexandre | Litrico, Xavier | Belaud, Gilles | DPT OF CIVIL AND ENVIRONMENTAL ENGINEERING U.C. BERKELEY USA ; Partenaires IRSTEA ; Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA)-Institut national de recherche en sciences et technologies pour l'environnement et l'agriculture (IRSTEA) | Gestion de l'Eau, Acteurs, Usages (UMR G-EAU) ; Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Centre international d'études supérieures en sciences agronomiques (Montpellier SupAgro)-AgroParisTech-Centre national du machinisme agricole, du génie rural, des eaux et forêts (CEMAGREF)-Institut de Recherche pour le Développement (IRD [Occitanie])-Centre International de Hautes Etudes Agronomiques Méditerranéennes - Institut Agronomique Méditerranéen de Montpellier (CIHEAM-IAMM) ; Centre International de Hautes Études Agronomiques Méditerranéennes (CIHEAM)-Centre International de Hautes Études Agronomiques Méditerranéennes (CIHEAM)
[Departement_IRSTEA]RE [TR1_IRSTEA]GES / TRANSCAN
Show more [+] Less [-]English. A parameter identification problem for systems governed by first-order, linear hyperbolic partial differential equations subjected to periodic forcing is investigated. The problem is posed as a PDE constrained optimization problem with data of the problem given by the measured input and output variables at the boundary of the domain. By using the governing equations in the frequency domain, a spatially dependent transfer matrix relating the input variables to the output variables is obtained. It is shown that by considering a finite number of dominant oscillatory modes of the input, an accurate representation of the output can be obtained. This converts the original PDE constrained optimization problem to one without any constraints. The optimal parameters can be identified using standard nonlinear programming. The utility of the proposed approach is illustrated by considering a river reach in the SacramentoSan-Joaquin Delta, California, that is subjected to tidal forcing. The dynamics of the reach are modeled by linearized Saint-Venant equations. The available data is the flow variables measured upstream and downstream of the reach. The parameter identification problem is to estimate the average free-surface width, the bed slope, the friction coefficient and the steady-state boundary conditions. It is shown that the estimated model gives an accurate prediction of the flow variables at an intermediate location within the reach.
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