# Heat Loss Coefficient Estimation Applied to Existing Buildings through Machine Learning Models
## 3 Results and Discussion
### HLC Estimation Analysis
Lastly, in Sample 3 (see Figure 4c), an intermediate value of the HLC (2.46 kW/K) that came from the lowest average difference between indoor and outdoor temperatures (12.05 K) and the lowest average thermal demand (29.70 kW) was obtained. On the other hand, in the case of Sample 1, where the calculated HLC was 2.75 kW/K, the MLP neural network was the most accurate model (see Table 4). While this algorithm obtained an average absolute variation rate of 6.50%, the XGBoost and SVR models were only able to obtain an average absolute variation greater than 10% (12.52.% and 12.16%, respectively). Thus, the average HLC value estimated by MLP (2.90 kW/K) is the closest to the measured HLC value. Table 4 shows that all models obtained a higher average estimation than the calculated one (the same situation as in Section 3.1). Additionally, in relation to the variation rate dispersion, the MLP neural network was the one with the lowest variability among the errors (\(\pm\)4.5). However, in general, all models showed a significant high standard deviation. In Sample 2 the calculated HLC was 2.15 kW/K, and in relation to the average absolute variation values, the most accurate model was the MLP neural network (4.08%), but close to the SVR model (5.68%). As in the thermal demand section, the XGBoost model performed worse with an average absolute variation rate of 8.40% (see Table 4). Therefore, the HLC values estimated by the SVR and MLP models are very close to the calculated HLC value; while the average value obtained by SVR is 2.08 kW/K, the average value estimated for MLP is 2.23 kW/K. With respect to the dispersion of variation rate data and, as in Sample 1, \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Sample 1—HLC\({}_{\text{calculated}}\) = 2.750**} & \multicolumn{2}{c}{**Sample 2—HLC\({}_{\text{calculated}}\) = 2.146**} & \multicolumn{2}{c}{**Sample 3–HLC\({}_{\text{calculated}}\) = 2.464**} \\ \cline{2-10}  & **HLC\({}_{\text{estimated}}\)** & **\% Variation** & **SD** & **HLC\({}_{\text{estimated}}\)** & **\% Variation** & **SD** & **HLC\({}_{\text{estimated}}\)** & **\% Variation** & **SD** \\ \hline XGBoost & 3.094 & 12.517 & 5.224 & 2.327 & 8.404 & 4.759 & 3.032 & 23.052 & 4.473 \\ SVR & 3.070 & 12.158 & 7.677 & 2.082 & 5.680 & 4.813 & 2.800 & 13.600 & 5.049 \\ MLP & 2.901 & 6.505 & 4.500 & 2.232 & 4.083 & 2.966 & 2.458 & 4.966 & 3.702 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Numerical results of the HLC estimations for all validation samples. The values shown summarize the performance of each of the models through 10 repetitions of the experiment. The mean of the absolute variation rates (together with the standard deviation), the mean of the estimated HLC values and the calculated HLC are presented. Figure 4: Summary of the thermal conditions of each of the validation samples: (**a**) Sample 1; (**b**) Sample 2; (**c**) Sample 3. Solar radiation and indoor and outdoor temperatures affecting the analysed building during the specific time periods are represented. Table 4 shows that the MLP neural network was the most stable model with a standard deviation below \(\pm\)3. The other models presented values above \(\pm\)4. Regarding Sample 3, in which the measured HLC was 2.46 kW/K, the MLP neural network was again the model with the best average performance. While the XGBoost and SVR algorithms presented average absolute variation of 23.05% and 13.60%, respectively, the MLP model showed an average absolute variation of 4.97% (see Table 4). Therefore, the average HLC value from the MLP estimations (2.46 kW/K) was much closer to the calculated HLC value than those obtained by the other models. In addition, in this sample, all models obtained a high variability in their results: all standard deviations were higher than \(\pm\)3.5. In this situation, the MLP neural network was the model with the lowest dispersion among its errors (\(\pm\)3.70).