## 2 Materials and Methods
### The Building Case-Study
\begin{table}
\begin{tabular}{l l l l} \hline \hline \multirow{2}{*}{**Building Element**} & \multicolumn{2}{c}{**Layers**} & \multirow{2}{*}{**Thickness [m]**} & \multirow{2}{*}{**Thermal Transmittance [W/(m\({}^{2}\) K]**]**} \\  & **(from Inside to Outside)** & & \\ \hline \multirow{4}{*}{Outer ceiling} & \multicolumn{2}{c}{Lime/gypsum plaster} & 0.020 & \\ \cline{2-4}  & Concrete & 0.200 & \\ \cline{2-4}  & Waterproofing layer & 0.004 & 2.68 \\ \cline{2-4}  & Tiles & 0.015 & \\ \hline \multirow{4}{*}{Outer floor (porch apt.)} & Floor tiles & 0.010 & \\ \cline{2-4}  & Lean concrete & 0.050 & \\ \cline{2-4}  & Hollow core concrete & 0.180 & 0.49 \\ \cline{2-4}  & Expanded polystyrene & 0.050 & \\ \cline{2-4}  & Lime/gypsum plaster & 0.020 & \\ \hline \multirow{4}{*}{Outer vertical walls} & \multicolumn{2}{c}{Lime/gypsum plaster} & 0.020 & \\ \cline{2-4}  & Hollow clay bricks & 0.100 & \\ \cline{2-4}  & Air Gap & 0.080 & 1.25 \\ \cline{2-4}  & Hollow concrete bricks & 0.100 & \\ \hline \multirow{4}{*}{Inner vertical walls} & \multicolumn{2}{c}{Lime/gypsum plaster} & 0.010 & \\ \cline{2-4}  & Hollow clay bricks & 0.100 & 2.10 \\ \cline{2-4}  & Line/gypsum plaster & 0.010 & \\ \hline \multirow{4}{*}{Inner ceiling and all other floors} & Floor tiles & 0.010 & \\ \cline{2-4}  & Lean concrete & 0.050 & 1.25 \\ \cline{2-4}  & Hollow core concrete & 0.180 & \\ \cline{2-4}  & Line/gypsum plaster & 0.020 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main constructive characteristics of the investigated building. Figure 2: Picture of the building case-study. In September 2017, two-sensors--Heat Cost Allocators (HCAs) and Thermostatic Radiator Valves (TRVs)--were installed on each radiator to comply with the EED obligation [16], transposed in Italy with the Legislative Decree 102/2014 and subsequent amendments and integrations [17]. To allow an optimal system operation, a variable speed circulation pump was installed in the central boiler room. Together with the HCAs and the TRVs, two temperature sensors were installed in the bedroom and in the living room of each dwelling, which are able to measure the daily average temperature of the room as an average of 24-h measurements with a 6-min acquisition frequency. Additionally, a main thermal energy meter was installed on the main distribution pipes downstream of the centralized boiler in order to measure the total energy consumption of the building. The installed heating powers have been estimated through the dimensional method [18; 19], after mapping the dimensions of all radiators, which was also required as preliminary action for the purposes of programming the HCAs. In the context of a specific project, survey questionnaires have been administrated to the inhabitants of the investigated building and on-field informative meetings have been organized, aimed at designing a suitable feedback strategy to enhance end-user's awareness. In particular, the analysis of surveys allowed authors to collect specific information about behavioral features which have been also meaningful for the present analysis, such as the ability to use thermostatic valves and chrono thermostat, and their feeling about indoor temperature in the apartment [20]. Table 2 contains the data related to the calculated installed heating power and the number of inhabitants of each apartment of the building case study.