Identifiability and identification of a pollution source in a river by using a semi-discretized model

Nathalie Verdiere (1) , Ghislaine Joly-Blanchard (2) , Lilianne Denis-Vidal (2)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre
2 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

The aim of this paper is to identify the localization and the flow rate of a pollution source in a river by measuring the concentration of a substrate giving significant information. This concentration is assumed to be measured in two points of the river. The simplest model of such a problem consists in a parabolic partial derivative equation. We propose to discretize this P.D.E. in space, which leads to a system of differential equations in time. Then, the analysis of identifiability is carried out using an approach based on differential algebra. A numerical parameter estimation is inferred from this procedure, which gives a first parameter estimate without a priori knowledge about unknown parameters.

Mots clés: semi-discretized model; Identifiability; Parameter Identification; Application to Pollution

Domaines: Systèmes dynamiques [math.DS]

Nathalie Verdiere, Ghislaine Joly-Blanchard, Lilianne Denis-Vidal. Identifiability and identification of a pollution source in a river by using a semi-discretized model. 2010. ⟨hal-00696683⟩