  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.
