# Triple Validation of Calibrated Building Energy Models with Different Air Infiltration Values
## 2 Methodology
### Triple Validation  
The validation phase was divided into three steps based on thermal indicators (temperature and energy consumption) and indoor air quality values (air infiltration expressed as CO\({}_{2}\) values). The case study model configuration (free oscillation periods) allowed us to isolate the building envelope's performance without any other interference. Thus, the \"real conditions\" represent the apartment's natural thermal response to internal and external conditions, including ambient temperature fluctuations, air infiltration, and internal heat storage or losses.  
_First step:_ Evaluate the agreement between simulated and measured indoor temperatures during the free oscillation period. Indoor temperatures are a consequence of the building's energy balance, reflecting the indoor space's response to various external (weather) and internal (loads) influences [60]. This variable was used to calibrate the models, as explained in Section 2.7, and to assess their performance. In this step, both the baseline model and the calibrated models were evaluated by comparing their simulated temperature values with the measured data. The uncertainty analysis was based on the statistical criteria established by CIBSE TM63: Operational performance: Building performance modeling [61]. The Mean Absolute Error (MAE) and the Root Mean Squared Error (RMSE) indices were used to calibrate the models and must be \(\leqslant\)1.00 and \(\leqslant\)1.50, respectively. Additionally, the correlation coefficient (R\({}^{2}\)) assessed the similarity in the patterns or trends between the real data and the simulated results and must be \(\geqslant\)75%.  
_Second step:_ Assess the total simulated energy consumption during the free oscillation period. Once the building envelope is calibrated, energy gains and losses can be quantified, which enables a direct evaluation of the building's energy demand. Given that we are working with free oscillation periods with no internal loads (e.g., appliances or occupants), any simulated energy use under these settings should theoretically be minimal. Therefore, the calibrated model with the lowest simulated energy consumption value was therefore considered the most accurate representation of the actual conditions in the living room, as it best reflects parameters such as capacitance, internal mass, and infiltration.  
_Third step:_ Validate the infiltration models according to the American Society for Testing Material (ASTM) D5157: Standard Guide for Statistical Evaluation of Indoor Air Quality (IAQ) Model [62] requirements. Since our study focuses on dynamic infiltration using a CO\({}_{2}\) decay curve, we selected this standard to evaluate the accuracy of both predicted and measured CO\({}_{2}\) concentrations. This approach enables a comprehensive assessment of the infiltration models. The method used to generate the site-specific coefficients was previously validated in earlier studies, as explained in Section 1.1. However, in this study, the approach is repeated using different data. Additionally, the parameterized air leakage area determined during the classic model calibration was validated against empirical data, a step that has never been performed before and is crucial for verifying whether it leads to an accurate infiltration model.  
ASTM D5157 requires the use of three statistical instruments for assessing agreement and two for assessing bias. These instruments are as follows: R\({}^{2}\)\(\geqslant\) 0.90; NMSE \(\leqslant\) 0.25; the slope of the line of regression, m, should be within the range of 0.75 to 1.25; FB \(\leqslant\) 0.25, and FS \(\leqslant\) 0.50. The standard stipulates that all criteria must be met consistently across both training and checking periods to confirm that the model's performance is satisfactory.  
The explained steps are summarized in Figure 7. Models that satisfy most of the validation criteria are considered the most accurate.