# Heat Loss Coefficient Estimation Applied to Existing Buildings through Machine Learning Models
## 3 Results and Discussion
### HLC Estimation Analysis  
The specific characteristics of each of the validation samples studied in this work are analysed in Table 3 and presented in Figure 4. Moreover, the results of the HLC estimations, based on the previous heating demand predictions, for each of the three validation samples are shown in this section in Table 4. Although estimated from the heating demand predictions during a weekend, the HLC is represented as a single number (see Equation (3)). As in the preceding section, the average performance of the different algorithms among the 10 trials is summarized in Table 4.  
First, Table 3 shows that the three validation samples fulfilled the conditions necessary to efficiently measure the HLC of the analysed building (see Section 2.3.2). Moreover, each of the samples has different HLC values. The main different thermal conditions of the samples, which caused slightly different HLC values, are also summarized in Table 3 and presented in Figure 4. The highest HLC value was obtained in Sample 1 (2.75 kW/K) due to the fact that the weight of the radiation gains, in relation to the heating demands, was the lowest among the samples (0.09%). This is related to the fact that the average thermal demand throughout this period was the highest and is a numerator value in the HLC formula (see Equation (3)). In addition, the average difference between indoor and outdoor temperatures, as shown in Figure 4a, was one of the smallest (12.48 K). These were the main reasons for obtaining a greater HLC \begin{table}
\begin{tabular}{l c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Sample 1**} & \multicolumn{4}{c}{**Sample 2**} & \multicolumn{4}{c}{**Sample 3**} \\ \cline{2-11}  & **CV(RMSE) (\%)** & **SD** & **NMBE (\%)** & **SD** & **CV(RMSE) (\%)** & **SD** & **NMBE (\%)** & **SD** & **CV(RMSE) (\%)** & **SD** & **NMBE (\%)** & **SD** \\ \hline XGBoost & 18.570 & 3940 & \(-\)12517 & 5.224 & 17.434 & 4.203 & \(-\)8.044 & 4.759 & 29.143 & 3.808 & \(-\)23.052 & 4.473 \\ SVR & 21.312 & 3710 & \(-\)11.627 & 8.460 & 16.607 & 2.417 & 2.987 & 6.819 & 21.596 & 3.581 & \(-\)13.600 & 5.049 \\ MLP & 19.839 & 2.409 & \(-\)5.491 & 5.693 & 17.381 & 2.301 & \(-\)4.012 & 3.061 & 21.543 & 2.331 & 0.253 & 6.189 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numerical results of the thermal demand predictions for all validation samples. The mean of the CV(RMSE) and the Normalized Mean Biased Error (NMBE) obtained through the 10 trials, besides the standard deviation (SD) of each of them, are presented. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multicolumn{2}{c}{**HLCcalculated(kW/K)**} & \(\overline{T_{int}-T_{out}}\) (K) & \(\overline{Q}\) (kW) & \(Rad/Q\) (\%) & \(\overline{T}^{\circ}{}_{initial}\) (K) & \(\overline{T}^{\circ}{}_{final}\) (K) \\ \hline Sample 1 & 2.750 & 12.476 & 34.313 & 0.091 & 289.671 & 288.127 \\ Sample 2 & 2.146 & 15.246 & 32.725 & 0.127 & 287.917 & 287.220 \\ Sample 3 & 2.464 & 12.053 & 29.704 & 0.232 & 289.402 & 287.741 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Thermal conditions of the three validation samples. These represent the mean difference between indoor and outdoor temperatures, the average heating demand (\(\overline{Q}\)), the solar radiation gain (Rad) over the thermal demand and the average temperatures (indoor and outdoor) at the start (\(\overline{T}^{\circ}{}_{initial}\)) and at the end of the period (\(\overline{T}^{\circ}{}_{final}\)). HLC, Heat Loss Coefficient. (see Table 3). On the other hand, Sample 2 is where the HLC value is the lowest (2.15 kW/K) because, as shown in Figure 4b, the average difference between indoor and outdoor temperatures was the largest (15.25 K). This value, which is in the denominator of the HLC formula, together with an average heating demand significantly lower than in Sample 1 (32.72 kW) reduces the calculated HLC value (see Table 3).