# Triple Validation of Calibrated Building Energy Models with Different Air Infiltration Values
## 1 Introduction
### Context and Background Work
The study found that the calibration approaches with the highest accuracy were those with over 70% of their Pareto solutions having discrepancy indicators below 10%. The best results were achieved with CV(RMSE) applied to heating and cooling energy demands over weekly, monthly, and yearly datasets. Calibration using the C\(\chi^{2}\) error function with both energy demands and temperature data also showed a significant improvement in accuracy. Furthermore, it was observed that using yearly temperature and energy demand data for CV(RMSE) calibration enhanced the model's accuracy. Although various calibration approaches for white-box models exist, this study employed one of the 60 calibration approaches previously developed by other authors [40; 45; 46], which enhances building envelope characterization using data from in situ sensors, as outlined in the ASHRAE guidelines [36]. This inverse modeling approach is based on a white-box model that incorporates physics-based equations to represent the building's physical characteristics. Building construction details are input into the model based on available technical documentation, forming the baseline BEM. The goal of this calibration process is to determine an optimal set of three parameters that align the model with real-world conditions: air capacitance, internal mass, and air infiltration. These parameters are implemented in EnergyPlus as the following objects: ZoneAirCapacitance:TemperatureMultiplier, InternalMass, and ZoneInfiltration:EffectiveLeakageArea. Parameter values may become physically unrealistic after model calibration, compromising and limiting our understanding of the model's underlying physics [47]. Both air capacitance and internal mass are treated as black-box parameters, meaning their values may not have a direct physical interpretation and can be arbitrary [40]. However, to specifically address infiltration, the air leakage area (\(A_{L}\)) in the ELA equation is chosen for calibration due to its clear physical meaning, with ASHRAE providing the additional stack coefficient (\(C_{s}\)) and wind coefficient (\(C_{w}\)) used in this equation. The calibration process is executed using EnergyPlus 9.4 as the simulation engine, with iEPlus v1.7 + EA software [48] employed for optimization. iEPlus utilizes the Non-Dominated Sorting Genetic Algorithm (NSGA-II) [49] to identify the optimal set of parameters. This set is defined by a range of values for capacitance (dimensionless), internal mass (m2), and air leakage area (cm2), taking their magnitudes into account. If a model generated by these combinations achieves R2, MAE, and RMSE values that comply with CIBSE TM63 criteria for comparing measured and simulated indoor temperatures, the model is considered calibrated. If the model does not meet these criteria, a new set of values must be defined to rerun iEPlus and further refine the calibration. This iterative process is outlined in Figure 1 and continues until the statistical criteria are met, providing a straightforward and economical approach compared to other methods [45; 46]. To empirically validate the air infiltration values in the calibration process, we chose to carry out a tracer gas test to measure the in situ air leakage of a case study. The test followed the procedure in previous research [50; 51; 52] based on the E741 Standard Test Method for Determining Air Change in a Single Zone by Means of a Tracer Gas Dilution (ASTM E741) test method and requirements [53; 54]. It consisted of the CO2 concentration decay method [55], where the CO2 was injected via a fire extinguisher into an unoccupied, monitored space. Air infiltration rates were calculated using the decay Equation (A1) by tracking the relationship between the tracer gas injection and the concentration changes [56]. This procedure allowed for the determination of site-specific coefficients for the three empirical infiltration models in E\({}^{+}\) through mathematical regression analysis.