# Triple Validation of Calibrated Building Energy Models with Different Air Infiltration Values
## 3 Results and Discussions
### Energy Consumption Validation  
Ideally, models should exhibit minimal simulated energy consumption during both training and checking periods due to the lack of indoor loads during the free oscillation calibration process. Figure 9 clearly demonstrates that the models with the lowest simulated energy consumption during both periods are the baseline, decay, and ELA REG models. However, the configuration of the baseline model significantly reduces the infiltration value and, as a result, leads to an inaccurate representation of the impact of air infiltration on energy consumption. This model uses default values for capacitance and internal mass, which do not reflect the actual characteristics of the space. Moreover, although this model simulates low energy consumption, it fails to capture the overall thermal behavior of the case study, as it has not produced precise temperature simulation indices.  
In contrast, the decay and ELA REG models incorporate empirical infiltration values and have also demonstrated low energy consumption in the results, with results of 14.39 kWh and 14.77 kWh during the training period, respectively. This represents approximately 31% less energy consumption compared to the classic model (21.01 kWh) while achieving similar temperature results during this period. In the checking period, the decay and ELA REG models presented values approximately 3% and 12% higher than the baseline model, respectively, and 31% and 25% lower than the classic model. This indicates that incorporating empirical air leakage data enhances the model's realism, thereby addressing the first research question. Moreover, it highlights the importance of a comprehensive evaluation of the model, as relying solely on temperature data to assess model performance might be insufficient to capture the improvements that the inclusion of calculated air leakage values may provide.  
It is notable that the energy simulation did not show zero energy consumption, as would be expected if the model had perfect envelope parameters [46]. This residual energy use likely results from minor thermal imbalances in the building envelope, reflecting small heat gains or losses due to factors such as thermal conduction, absorbed solar radiation, or material characterization errors. These minimal values are not from active HVAC loads but represent natural thermal dynamics within the structure, which still slightly influence the model's energy consumption calculations.  
A remarkable finding is that the ELA REG model's energy consumption values are only 2.6% and 8.5% higher, respectively, in training and checking periods, compared to the decay model. They also have similar performance in temperature. This supports the second research question by demonstrating the effectiveness of mathematical regression in identifying optimal coefficients for this case study, resulting in air leakage values as accurate as those introduced into the decay model. While the ELA REG model generation has been validated for indoor air quality in previous works, these results confirm its suitability for thermal performance as well. This is a positive outcome, as models utilizing site-specific coefficients enable the extrapolation of infiltration models beyond the training period.  
Figure 9: Total energy consumption of the four building energy models during the training (**a**) and checking (**b**) periods.