**Optimal sensor location for inverse heat conduction
problem in multilayered building walls**

Julien Berger^{1, ⋆}, Suelen
Gasparin^{2}, Dariusz
Ucinski^{3}

^{⋆} : julien.berger@univ-lr.fr

^{1} Laboratoire des
Sciences de l’Ingénieur pour l’Environnement (LaSIE), UMR 7356 CNRS, La
Rochelle Université, CNRS, 17000, La Rochelle, France

^{2} Cerema, BPE Project
team, 44200 Nantes, France

^{3} Institute of Control
and Computation Engineering, University of Zielona Góra

**Mots clés :** parameter estimation problem, Practical
identifiability, inverse heat conduction problem, optimal experiment
design, sensor position

**Résumé :**

The estimation of wall thermal properties through an inverse problem
procedure enables to increase the reliability of the model predictions
for building energy efficiency. Nevertheless, it requires defining an
experimental campaign to obtain on-site observations for existing
buildings. The quality of the estimated parameter strongly depends on
the quality of the experimental data used for the parameter
identification. Pronzato highlights the relation between the experiment
design and the precision of the retrieved parameters. The design of
experiments enables to search for the optimal measurement plan. It
ensures the highest precision of the parameter to be estimated. For
on-site measurement in buildings, the design of experiments seeks to
answer the following questions: How many sensors do we need? What is the
sensor position *χ* in the
wall?

The Optimal Experiment Design (OED) methodology enables us to answer those questions. For example, Nenamorokov et al. searched the OED for the estimation of radiation properties. Artyukhin and Budnik inspected the optimal sensor location and their quantity in the inverse heat conduction boundary problem. More recently the optimal heating period and the duration of the experiment were investigated for the thermal conductivity estimation in building walls. In this paper, the OED methodology is used to answer the above-mentioned questions for a real case study. The unknown parameter is the thermal conductivity of each wall layer of an existing French house.

doi : https://doi.org/10.25855/SFT2022-034

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