# Triple Validation of Calibrated Building Energy Models with Different Air Infiltration Values
## 3 Results and Discussions
### \(\text{CO}_{2}\) Validation  
Finally, the infiltration models were evaluated according to the ASTM D5157 criteria and Table 9 presents the statistical results of each model. The baseline and classic models did not meet the standard requirements outlined in ASTM D5157, with the baseline model presenting R2 values as low as 0.17 during the training period. While the baseline model's poor performance was expected due to its minimal infiltration value, the classic model's under-performance was surprising given its accurate temperature predictions. This model effectively represented temperature by using inaccurate parameter values as its air leakage area value led to an inadequate infiltration model, thereby addressing the third research question. During the checking period, the R2 value of the ELA REG model is 0.92, which is 130% higher than the 0.40 of the classic model. These correlation values between measured and simulated \(\text{CO}_{2}\) levels are clearly illustrated in Figure 10.  
Figure 10: Correlation graphs of measured and predicted \(\text{CO}_{2}\) curves for baseline, classic, and ELA REG models during the training (**a**) and checking (**b**) periods. As presented in Section 1.1, many studies calibrate the infiltration value in BEM to improve accuracy, using different objective functions such as temperature [39; 40; 41], energy consumption [38], and multi-objective calibration using temperature and relative humidity [43]. These studies achieve accurate calibrated models and demonstrate the impact of infiltration data on model outcomes. However, unlike our approach, most previous studies lack empirical validation of calibrated values, making it challenging to assess their physical accuracy. Our results, based on empirical air infiltration data, reveal the limitation of using arbitrary infiltration values. Although these values may deliver good model performance, they may not precisely represent air infiltration in the case study. This study's triple validation approach demonstrated the importance of empirical air infiltration data for accurate BEM calibration. As a highly sensitive parameter, air infiltration needs precise tuning to ensure reliable model performance, as shown by the energy consumption graphs and CO\({}_{2}\) prediction curves. Accurate air leakage data not only enhance model reliability but also align model parameters with real-world conditions, thereby improving overall model fidelity. Figure 11 summarizes these findings, illustrating the superiority of calibrated models with empirical air infiltration and providing a more intuitive understanding of the study's results. For building retrofit projects focused on reducing air infiltration through the building envelope, it is essential to use building energy models or digital twins that accurately represent air leakage. Otherwise, energy conservation measures and retrofit solutions targeting envelope's infiltration may be imprecise and ineffective, as seen in the study evaluating retrofit effectiveness on indoor air quality and energy use [13]. Figure 11: Summary of the results of this study. \begin{table}
\begin{tabular}{l l c c c c c c c c} \hline \hline
**Model** & **Period** & \(\overline{C_{a}}\)**(ppm)** & \(\overline{C_{p}}\)**(ppm)** & \(\mathbf{R^{2}}\) & \(\mathbf{m}\) & \(\mathbf{b}\) & \(\mathbf{b/\overline{C_{a}}}\)**(\%)** & **NMSE** & **FB** & **FS** \\ \hline Baseline & Training & 1038.95 & 1409.17 & 0.17 & 0.30 & 1092.10 & 1.05 & 0.13 & 0.30 & \(-0.58\) \\  & Checking & 1068.00 & 1540.62 & 0.25 & 0.14 & 1384.30 & 1.30 & 0.18 & 0.36 & \(-1.72\) \\ \hline Classic & Training & 1038.95 & 414.85 & 0.54 & 1.06 & \(-707.44\) & \(-0.68\) & 1.07 & \(-0.86\) & 0.74 \\  & Checking & 1068.00 & 399.60 & 0.40 & 0.80 & \(-445.94\) & \(-0.42\) & 1.26 & \(-0.91\) & 0.52 \\ \hline ELA REG & Training & 1038.95 & 1058.41 & 0.96 & 0.98 & 35.97 & 0.03 & 0.00 & 0.02 & \(-0.03\) \\  & Checking & 1068.00 & 1097.40 & 0.92 & 0.86 & 155.90 & 0.15 & 0.01 & 0.03 & \(-0.18\) \\ \hline \hline \end{tabular}
\end{table}