Evaluation of the reliability of building energy performance models for parameter estimation

Julien Berger (1) , Denys Dutykh (2, 3, 4)

1 LOCIE - LabOratoire proCédés énergIe bâtimEnt
2 LAMA - Laboratoire de Mathématiques
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc

The fidelity of a model relies both on its accuracy to predict the physical phenomena and its capability to estimate unknown parameters using observations. This article focuses on this second aspect by analyzing the reliability of two mathematical models proposed in the literature for the simulation of heat losses through building walls. The first one, named DuFort-Frankel (DF), is the classical heat diffusion equation combined with the DuFort-Frankel numerical scheme. The second is the so-called RC lumped approach, based on a simple ordinary differential equation to compute the temperature within the wall. The reliability is evaluated following a two stages method. First, samples of observations are generated using a pseudo-spectral numerical model for the heat diffusion equation with known input parameters. The results are then modified by adding a noise to simulate experimental measurements. Then, for each sample of observation, the parameter estimation problem is solved using one of the two mathematical models. The reliability is assessed based on the accuracy of the approach to recover the unknown parameter. Three case studies are considered for the estimation of (i) the heat capacity, (ii) the thermal conductivity or (iii) the heat transfer coefficient at the interface between the wall and the ambient air. For all cases, the DF mathematical model has a very satisfactory reliability to estimate the unknown parameters without any bias. However, the RC model lacks of fidelity and reliability. The error on the estimated parameter can reach 40% for the heat capacity, 80% for the thermal conductivity and 450% for the heat transfer coefficient.

Mots clés: building thermal performance; Mathematical Model reliability; parameter estimation problem; Thermal Circuit Model; Dufort-Frankel numerical model; Heat transfer; Du Fort-Frankel numerical model

Domaines: Thermique [physics.class-ph]; Physique Numérique [physics.comp-ph]; Thermique [physics.class-ph]; Optimisation et contrôle [math.OC]; Analyse numérique [math.NA]; Modélisation et simulation; Analyse numérique [cs.NA]

Julien Berger, Denys Dutykh. Evaluation of the reliability of building energy performance models for parameter estimation. Journal of Computational technologies, 2019, 24 (3), pp.4-32. ⟨10.25743/ICT.2019.24.3.002⟩. ⟨hal-02140452⟩