# Triple Validation of Calibrated Building Energy Models with Different Air Infiltration Values
## 2 Methodology
### Model Calibration Process  
As mentioned in the Introduction, the model calibration method carried out in this study was developed by authors in previous works [40; 45; 46]. This method adjusts parameters such as capacitance, internal mass, and air infiltration to optimize the agreement between measured and simulated indoor temperatures. Varying these parameters led to different model configurations. Table 6 presents the parameter values assigned to each baseline and to models that will be calibrated. In the classic model, the ELA coefficients were selected based on the E\({}^{+}\) InputOutput document: values of \(C_{s}\) = 0.00044 and \(C_{w}\) = 0.00027 were chosen as the maximum number of stories available and shelter class (both equal to 3), corresponding to a \"Typical shelter caused by other buildings across the street\" [59]. The baseline model shares the same \(C_{s}\) and \(C_{w}\) values as the classic model but has an \(A_{L}\) value of 0.001 cm\({}^{2}\). Unlike the other models, the baseline model was not calibrated. This allows us to compare its original characteristics with those of the newly generated, calibrated models to assess the level of adjustment achieved. For the REG models, we calibrated using the three E\({}^{+}\) infiltration models: the ELA REG model, the DFR REG model, and the IFC REG model, each with its respective regressed coefficients. Similar to the REG models, in the decay model, only the capacitance and internal mass were calibrated. Since the decay model includes a schedule of calculated infiltration, there was no need to calibrate this parameter. Unlike the regression of E\({}^{+}\) model coefficients, the calibrated models were trained using 16% of the available data (1148 ten-minute time steps) and evaluated on 84% (5879 ten-minute time steps). The training period aligns with that used for the regression of the infiltration models, ensuring that the air leakage area for the classic model was determined \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{Model} & \multirow{2}{*}{Capacitance} & \multirow{2}{*}{Internal Mass} & \multicolumn{2}{c}{Zone Infiltration: Effective Leakage Area} \\ \cline{3-6}  & & & \(A_{L}\) & \(C_{s}\) & \(C_{w}\) \\ \hline Baseline & 1 & 1 & 0.001 & 0.00044 & 0.00027 \\ Classic & **Calibrated** & **Calibrated** & **Calibrated** & 0.00044 & 0.00027 \\ Decay & **Calibrated** & **Calibrated** & - & - & - \\ ELA REG & **Calibrated** & **Calibrated** & **REG** & **REG** & **REG** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Composition of baseline and calibrated models with known parameter values for capacitance, internal mass, and ELA infiltration model coefficients. Parameters to be determined through calibration are labeled as “Calibrated”, while those obtained through mathematical regression based on tracer gas data are labeled as “REG”. \begin{table}
\begin{tabular}{c c c c c|c c c c} \hline \hline  & \multicolumn{3}{c}{**In Situ Data**} & \multicolumn{3}{c}{**Weather Station Data**} \\ \hline  & T\_db & RH & T\_dp & WS & **GHR** & DHR & WD & **AP** \\  & **(°C)** & **(°C)** & **(m/s)** & **(W/m\({}^{2}\))** & **(W/m\({}^{2}\))** & **(°)** & **(Pa)** \\ \hline Mean value & 13.14 & 56.53 & 4.07 & 0.15 & 143.66 & 10.96 & 1.00 & 97.0077.50 \\ Min. value & -1.10 & 15.83 & -9.50 & 0.00 & 0.51 & 0.59 & 1.00 & 95.380.00 \\ Max. value & 28.70 & 90.71 & 14.70 & 2.30 & 1194.56 & 186.76 & 1.00 & 96.870.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Weather data gathered from in situ and weather station sensors from 10 February 2023 until 26 April 2023.  
over the same period in which the site-specific coefficients were calculated. The evaluation period was more extensive than in the regression process as it included all available temperature data during free oscillation periods when the apartment was unoccupied and unaffected by occupant behavior. The model is considered calibrated once it meets the validation period in both training and checking periods.