## 4 Results and Discussion
### Comparison of Experimental and Simulated Results
In this context, Figure 6 shows the difference between the measured and simulated contrast values during the days of experimentation, calculated using the surface temperatures from Figure 5. The contrast values obtained by the numerical simulation are aligned to those calculated from the measurements performed by the IRT thermal camera, even with the temperature differences reported in the previous figure. The amplitude of the simulated contrast followed the periodic variation of the gradients through the days that the experiments were carried out, where gradients were small for the autumn and winter months (April, June, and July) compared to the spring and summer months (November and February). The Pearson Correlation (R), the Mean Bias Error (MBE), and the Mean Absolute Error (MAE) were calculated to assess the covariability and the deviation among the simulated results from the FEM model and the observed results from the IRT experiments (Table 3). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Experiment**} & \multicolumn{3}{c}{**Healthy Area Temperature**} & \multicolumn{3}{c}{**Damaged Area Temperature**} & \multicolumn{3}{c}{**Thermal Gradient**} \\ \cline{2-10}  & **R** & **MBE (\({}^{\circ}\)C)** & **MAE (\({}^{\circ}\)C)** & **R** & **MBE (\({}^{\circ}\)C)** & **MAE (\({}^{\circ}\)C)** & **R** & **MBE (\({}^{\circ}\)C)** & **MAE (\({}^{\circ}\)C)** \\ \hline
22 November 2018 & 0.98 & 0.02 & 3.07 & 0.98 & 0.31 & 3.37 & 0.97 & 0.29 & 0.51 \\
23 February 2019 & 0.97 & 0.20 & 2.17 & 0.97 & 0.63 & 2.46 & 0.97 & 0.48 & 0.51 \\
18 April 2019 & 0.99 & \(-\)0.93 & 4.21 & 0.99 & \(-\)0.55 & 4.36 & 0.98 & 0.38 & 0.47 \\
14 June 2019 & 0.96 & 2.51 & 2.78 & 0.97 & 2.73 & 2.96 & 0.97 & 0.22 & 0.29 \\
6 July 2019 & 0.98 & 3.24 & 3.95 & 0.98 & 3.82 & 4.38 & 0.97 & 0.58 & 0.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: R, MBE, and MAE for the surface temperatures and thermal gradients measured and simulated in the daily experiments. Figure 5: Comparison of surface temperatures measured in the IRT experiment and simulated by the FEM. The MBE measures the overall bias of the model, and MAE measures the absolute extent of the errors without considering their directions [45]. Table 3 shows that in most cases, the MBE produced positive values for the surface temperatures and thermal gradient, indicating that the model has a trend to overestimate the experimental results. An exception is seen in April, where MBE showed that the model underestimates the surface temperatures. However, thermal gradients were constantly overestimated. These trends can be confirmed by looking at the curves in Figures 5 and 6. The MAE is greater for the surface temperatures simulations, with averages differences ranging from 2.17 \({}^{\circ}\)C to 4.38 \({}^{\circ}\)C. However, the absolute error is under 0.6 \({}^{\circ}\)C in all thermal gradient tests, which indicates that the contrast between healthy and damaged areas is convergent, despite the surface temperature differences. Therefore, these results are aligned with the findings of previous studies [23; 24; 32; 33; 34; 35], where the numerical simulation presented the capability of reproducing the thermal gradients measured in the thermographic inspections using passive heating. [PERSON] and [PERSON] [32] reported the deviation measurements for the thermal contrast between their model and the experimental results. The correlation indices (R) were between 0.70 and 0.92, and the contrast differences (MBE) and absolute error (MAE) were below 1 \({}^{\circ}\)C. [PERSON] et al. [24] also calculated the correlation coefficient (R) between FEM simulation results and IRT measurements of the concrete surface temperature using three different thermal cameras, obtaining results above 0.97 in all cases. In this sense, we confirm the authors' conclusion that the FEM can represent a tool to predict the concrete surface temperatures and support practical IRT inspections.