# Triple Validation of Calibrated Building Energy Models with Different Air Infiltration Values
## 3 Results and Discussions
### Temperature Validation  
As shown in Table 8, all calibrated models outperformed the baseline model, with improvements of approximately 31% in MAE, 25% in RMSE, and 20% in R\({}^{2}\) when comparing the best-performing training model (classic) to the baseline. These findings confirm the necessity of model calibration for accurately representing indoor conditions. Despite variations in capacitance, internal mass, and air infiltration among the calibrated models, their performance during the training period was nearly identical.  
The checking period serves as the most critical evaluation phase to assess the reliability of the models and their ability to generalize over a different time frame. In this period, although the classic model still met the CIBSE TM63 criteria, incorporating empirical infiltration data surpassed at predicting indoor temperatures over a period five times longer than the training phase. The ELA REG model achieved the lowest MAE (0.68) and the lowest RMSE (0.89), marking a 29% and 26% reduction, respectively, compared to the classic model. While R\({}^{2}\) values showed minimal variation among the calibrated models, those with empirical infiltration data produced the highest R\({}^{2}\) scores, with a 3.80% difference between the top-performing decay model and the lowest-scoring classic model. The strong performance of the decay and ELA REG models highlights their robustness and emphasizes the value of using in situ infiltration data in the calibration process. These results are clearly illustrated in the scatter plots (see Figure 8), which show the agreement between measured and simulated temperatures for all models. The decay and ELA REG are the most precise ones, generating points closest to the line of equality (a 45\({}^{\circ}\) line where the predicted values equal the observed values). It is important to note that, although the decay model has a schedule of infiltration values specific to the time steps where there was decay, it still delivers good results when extrapolated over a longer period. This may be due to the incorporation of an empirical value as sensitive as air infiltration into the calibration process, which allows other parameters, such as capacitance and internal mass, to more accurately represent the conditions of the case study.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{Model} & \multirow{2}{*}{Capacitance} & \multirow{2}{*}{Internal Mass} & \multicolumn{3}{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 & **6** & **80** & **130** & 0.00044 & 0.00027 \\ Decay & **20.50** & **68.50** & - & - & - \\ ELA REG & **21.50** & **70.50** & 2.1183 & 0.02414 & 2.78721 \\ \hline \hline \end{tabular}
\end{table}
Table 7: In bold: calibrated values of capacitance, internal mass, and \(A_{L}\) coefficient of the classic model.  
\begin{table}
\begin{tabular}{l|c c|c c|c c|c c} \hline \hline  & \multicolumn{4}{c}{Training Period} & \multicolumn{4}{c}{Checking Period} \\ \cline{2-9}  & Baseline & Classic & Decay & ELA REG & Baseline & Classic & Decay & ELA REG \\ \hline MAE & **1.06** & 0.73 & 0.71 & 0.71 & 1.18 & 0.96 & 0.69 & 0.68 \\ RMSE & **1.27** & 0.95 & 0.91 & 0.91 & 1.45 & 1.21 & 0.90 & 0.89 \\ R\({}^{2}\) & **65.95\%** & **79.63\%** & **79.18\%** & **78.94\%** & **62.15\%** & **75.01\%** & **77.97\%** & **77.64\%** \\ \hline \hline \end{tabular}
\end{table}
Table 8: Statistical index results of the adjustment between measured and simulated temperature data in the training and checking periods. Red values indicate the poorest performance, while green values represent the best according to CIBSE TM63 criteria. Yellow and orange values represent intermediate levels, with yellow closer to optimal and orange closer to poor performance.  
Figure 8: Scatter plots of measured and simulated temperature values for baseline, classic, decay, and ELA REG models during the training (**a**) and checking (**b**) periods.