Bayesian calibration of a numerical code for prediction

Carmassi, Mathieu; Barbillon, Pierre; Chiodetti, Matthieu; Keller, Merlin; Parent, Eric

Journal de la société française de statistique, Tome 160 (2019) no. 1, pp. 1-30.

Field experiments are often difficult and expensive to carry out. To bypass these issues, industrial companies have developed computational codes. These codes are intended to be representative of the physical system, but come with a certain number of problems. Despite continuous code development, the difference between the code outputs and experiments can remain significant. Two kinds of uncertainties are observed. The first one comes from the difference between the physical phenomenon and the values recorded experimentally. The second concerns the gap between the code and the physical system. To reduce this difference, often named model bias, discrepancy, or model error, computer codes are generally complexified in order to make them more realistic. These improvements increase the computational cost of the code. Moreover, a code often depends on user-defined parameters in order to match field data as closely as possible. This estimation task is called calibration. This paper proposes a review of Bayesian calibration methods and is based on an application case which makes it possible to discuss the various methodological choices and to illustrate their divergences. This example is based on a code used to predict the power of a photovoltaic plant.

Les difficultés de mise en œuvre d’expériences de terrain ou de laboratoire, ainsi que les coûts associés, conduisent les sociétés industrielles à se tourner vers des codes numériques de calcul. Ces codes, censés être représentatifs des phénomènes physiques en jeu, entraînent néanmoins tout un cortège de problèmes. Le premier de ces problèmes provient de la volonté de prédire la réalité à partir d’un modèle informatique. En effet, le code doit être représentatif du phénomène et, par conséquent, être capable de simuler des données proches de la réalité. Or, malgré le constant développement du réalisme de ces codes, des erreurs de prédiction subsistent. Elles sont de deux natures différentes. La première provient de la différence entre le phénomène physique et les valeurs relevées expérimentalement. La deuxième concerne l’écart entre le code développé et le phénomène physique. Pour diminuer cet écart, souvent qualifié de biais ou d’erreur de modèle, les développeurs complexifient en général les codes, les rendant très chronophages dans certains cas. De plus, le code dépend de paramètres à fixer par l’utilisateur qui doivent être choisis pour correspondre au mieux aux données de terrain. L’estimation de ces paramètres propres au code s’appelle le calage. Ce papier propose une revue des méthodes de calage bayésien et s’appuie sur un cas d’application qui permet de discuter les divers choix méthodologiques et d’illustrer leurs divergences. Cet exemple s’appuie sur un code de calcul servant à prédire la puissance d’une centrale photovoltaïque.

Keywords: Centrale photovoltaïque, Calage bayésien, Quantification d’incertitudes, Code numérique
Mot clés : Photovoltaic power plant, Bayesian calibration, Uncertainty quantification, Numerical code

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