Un système d'aide au choix de modèles hydrologiques et hydrauliques pour simuler les réseaux d'assainissement : application aux modèles de propagation en conduite A decision support system for the choice of hydrological and hydraulics models in order to simulate urban drainage networks: application on flood routing models

Résumé

La nouvelle génération de logiciels destinés aux études d'assainissement dispose d'un nombre croissant de modèles hydrauliques et hydrologiques. Il en découle une augmentation des possibilités de choix parmi ces modèles qui complique la tâche des techniciens de l'assainissement. Pour limiter cette difficulté, nous suggérons d'introduire dans les logiciels des outils permettant d'aider les utilisateurs à choisir les modèles en adéquation avec le réseau à simuler. Dans cet article, nous nous intéresserons essentiellement aux modèles de propagation en conduite. Les modèles de propagation les plus usités sont un modèle basé sur les équations de Barré de Saint Venant et des modèles conceptuels nettement plus simples tels que le modèle Muskingum. Ces modèles présentent chacun des avantages et des inconvénients. Dans la pratique, plus un modèle est sophistiqué, mieux il est capable de représenter la réalité. En contrepartie, il est plus difficile à utiliser et nécessite davantage de données et des temps de calcul plus importants. Le problème qui se pose alors à l'utilisateur est de décider quel modèle utiliser. Pour régler ce problème, nous proposons un système d'aide au choix prenant en compte les caractéristiques du réseau étudié, les événements pluvieux simulés et le type d'étude réalisée. Les connaissances nécessaires pour cette aide au choix de modèles peuvent être de qualité variable. Pour mesurer la confiance à accorder à ces connaissances, il est nécessaire de prendre en compte les notions d'imprécision et d'incertitude. Cet état de fait nous a conduit, lors de l'élaboration de cet outil d'aide au choix des modèles de propagation en conduite, à définir un ensemble de règles utilisant la théorie des sous-ensembles flous.

Mots-clés:

• Aide à la décision,
• modèles de propagation,
• assainissement pluvial,
• sous-ensembles flous,
• système expert

Abstract

Most hydraulic and hydrologic softwares offer an increasing choice of models, each with its advantages and disadvantages. Generally, the more sophisticated the model, the better it can represent larger aspects of reality, but also the more difficult it is to use and the longer the data acquisition and calculation times are. In fact, the real difficulty lies in selecting the appropriate model to use. To answer this question, two subproblems must be solved :

- what is the validity field for each of the models, with respect to the network structure, operating conditions, type of rainfall, nature of problem, etc. ?

- once this information is available, what is the best way to ensure its usability, even by people who are not experts in hydrology or hydraulics ?

The first problem can be dealt with by analyzing the theoretical validity field of the different models. Nevertheless, this method raises certain difficulties. It requires a particularly thorough knowledge of the equations, algorithms and calculating artifices used in the software package. But, for various reasons, software designers generally refuse to supply this information. Until now, the solution to the second problem has only been addressed by means of scientific reports, communications or papers. The published data generally gives a global introduction to the validity field of each model. Experience shows that most software users do not have enough information on this subject, or, even if they do, do not use it correctly.

To work towards solving these two problems, we propose to introduce into the software packages a decision support system which can help to choose the best model according to the simulated network. In this paper, only the models for flow simulation will be taken into account. Presently, the most commonly used models are the more or less complete Barre de Saint Venant equations and more simple conceptual models like Muskingum model.

The major difficulty in solving the first subproblem, was mainly the collection and reformulation of pre-existing knowledge. Considerable bibliographical work had to be supplemented by interviews of experts and by complementary studies (Semsar, 1995) (Mottie, 1996). The result of these studies was the identification of a set of criteria related to the network (slope, fractal dimension, loop index, etc.) or to the working conditions depending on the rainfall event (fullness rate, travel rate, etc.).

The answer to the second problem was to develop an "intelligent" man-machine interface able to analyse the background of the simulation (values of the criteria) and to advise the user on the model to select. The knowledge required to build this decision support system can vary in both source and quality, so assessment of its reliability involve the notions of uncertainty and inaccuracy. The problem of uncertainty has been solved by associating uncertainty degrees to the rules. These degrees define a proposal's level of reliability. The approach to inaccuracy is based on the theory of fuzzy sets, according to which the membership of an element of a given set is not settled but relative. The validity of a given fact is represented by a value between 0 (false) and 1 (true). This value can be related to a variable by fuzzy rules, represented by trapezoidal intervals. By this way, each of the criteria has been represented by qualitative decision variables which allow the elaboration of qualitative rules, leading to a "probably better" decision. One more decision variable - the kind of study - has been added because the hydrograph at the outlet of the network is not necessarily the only criterion to be taken into account. Each of the decision variable is represented by one, two, or sometimes more possible qualitative characterisation(s), associated with a degree of possibility (not probability because the sum of all the possibilities is not necessarily equal to 1). The decision support system uses these variables in a set of rules to determine the degree of adequacy of each model. The development of this system shows us that the use of fuzzy sets and qualitative rules seems to be well adapted to represent the used knowledge.

The decision support system will be installed in a software package called CANOE developed by INSA de Lyon and SOGREAH.

In the future we envisage adding an explanatory unit to the decision support system. This study showed too that there is some lack in the knowledge about flow simulation models, so it seems useful to continue to study the validity field of each model.