# Energy Performance Forecasting of Residential Buildings Using Fuzzy Approaches
## 4 Results and Discussion
### Fuzzy Approaches Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model [Reference]**} & \multicolumn{3}{c}{**Cooling Load**} & \multicolumn{3}{c}{**Heating Load**} \\ \cline{2-7}  & **MAE** & **RMSE** & **SI** & **MAE** & **RMSE** & **SI** \\ \hline IRLS [17] & 2.21 & 3.38 & 1 & 2.14 & 3.14 & 0.99 \\ RF [17] & 1.42 & 2.57 & 0.47 & 0.51 & 1.01 & 0.19 \\ SVR [19] & 0.89 & 1.65 & 0 & 0.24 & 0.35 & 0 \\ GLR [19] & 1.29 & 1.74 & 0.18 & 0.79 & 1.04 & 0.26 \\ CHAID [19] & 1.17 & 1.86 & 0.17 & 0.47 & 0.91 & 0.16 \\ CART [20] & 1.31 & 1.94 & 0.24 & 0.73 & 1.11 & 0.26 \\ SVM [20] & 2.10 & 2.49 & 0.70 & 2.19 & 2.49 & 0.88 \\ RBFNN [20] & 1.30 & 1.69 & 0.17 & 0.51 & 0.67 & 0.13 \\ BPNN [20] & 1.92 & 2.63 & 0.67 & 1.61 & 2.25 & 0.69 \\ MARS [20] & 1.12 & 1.65 & 0.09 & 0.53 & 0.68 & 0.13 \\ GSGP [21] & 1.47 & 2.36 & 0.42 & 1.31 & 1.06 & 0.40 \\ GSGP-LS [21] & 1.37 & 2.36 & 0.39 & 1.26 & 1.04 & 0.38 \\ GSGP-LS-LIN [21] & 1.18 & 2.04 & 0.22 & 0.51 & 0.79 & 0.15 \\ ANFIS & 1.03 & 1.76 & 0.08 & 0.37 & 0.52 & 0.06 \\ FIR & 1.09 & 1.72 & 0.09 & 0.35 & 0.49 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RMSE (root mean square prediction errors), MAE (mean absolute prediction errors) and SI (synthesis index) obtained by all the machine learning methodologies, including the fuzzy approaches, ANFIS and FIR, at the bottom of the table. Near the name of each model the reference of the paper is included. The best prediction performances are highlighted. to get equivalent performances than FIR for CL, but quite worse for HL. The remaining 12 modelling methodologies have results that are far away from the ones obtained by SVR, FIR and ANFIS. Figure 9 shows the synthesis indices, SI, obtained for all the modelling methodologies. From this figure it can be seen that IRLS, SVM and BPNN have by far the lowest performance, with SI values higher than 0.65. GSGP and GSGP-LS techniques have poor indices too, i.e., SI values around 0.40. Finally, RF, GLR, CHAID, CART, RBFNN and GSGP-LS-LIN obtain better results than the aforementioned methodologies, with SI values usually lower than 0.24 for CL and 0.26 for HL. However, these results are still away from the values obtained by fuzzy approaches and SVR methodology that are lower than 0.1. Figure 10 shows real versus predicted ANFIS and FIR results for HL and CL models. In both cases we present the fold that gives larger RMSE, in order to show that even for the worse prediction results, the difference from the real data is almost indistinguishable, especially in the case of the heating load model. Each point in Figure 10 represents a building. Both models perform well for the task at hand. However, it is important to note the huge difference in computational time between the model identification/training process of ANFIS and FIR methodologies. While ANFIS needs more than 7 h to perform a unique run (for a whole 10-fold CV), FIR needs only a few minutes to perform the same task, both running on the same machine (Intel Core2 Duo, 3 GHz, 4 GB of RAM). Comparing RMSE versus MAE errors, we can conclude that for both outputs, HL and CL, there is variation in the errors, since \(RMSE>MAE\). However, this variation is not sizeable enough to indicate the presence of very significant errors. Therefore, a first contribution of this research is to show that fuzzy approaches, like ANFIS and FIR, are good alternatives to estimate energy performance of residential buildings based on some building design parameters. Moreover, the fuzzy approaches studied here, have shown better throughput than twelve powerful machine learning approaches well suited for prediction problems. Figure 9: Synthesis indices (SI) of all machine learning methodologies for the heating load (top figure) and the cooling load (bottom figure). Values lower than 0.1 correspond only to SVR, ANFIS and FIR.