## 5 Validation Results and Discussion  
The reported graphs in Figure 5 show the amplitude reduction ratio and the phase shift of a tested wall with different thermal capacities. Looking at Figure 5, it is possible to deduce that the model was accurate for a broad range of air changes, which largely comprehends the values that are currently used in common applications. The model generates accurate results for any value of the internal thermal capacity referred to the unit area of the walls being tested, M, assuming, as previously said, values of 2, 15, and 25 [k]/m\({}^{2}\)K].  
Regarding the graphs, it is easy to understand the positive effect of the air changes on the amplitude of the temperature oscillations: The amplitude of the temperature oscillations almost halved when the air changes were varied from 0.5 to 10. Besides, for air changes lower than 5, the net reduction of the amplitude of oscillation was affected to a larger extent by the thermal capacity of the room content.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Wall Configuration** & **Area (m\({}^{2}\))** & **Layer Material** & \begin{tabular}{c} **Thickness** \\ **of Layers** \\ **(m)** \\ \end{tabular} & \
\begin{tabular}{c} **Density \(\rho\)** \\ **(kg/m\({}^{3}\)) of** \\ **Layers** \\ \end{tabular} &
\begin{tabular}{c} **Thermal** \\ **Conductivity** \\ **(W/m K) of Layers** \\ \end{tabular} \\ \hline
1-Hollow block & 2.62 \(\times\) 2.62 & Concrete & 0.203 & 1858 & 0.486 \\ uninsulated & 2.62 \(\times\) 2.62 & Concrete & 0.02 & 1858 & 0.486 \\
2-Hollow block & 2.62 \(\times\) 2.62 & Perlite loose fill & 0.163 & 96 & 0.048 \\ insulated & & Concrete & 0.02 & 1858 & 0.486 \\
3-Block brick cavity & 2.62 \(\times\) 2.62 & Air space & 0.051 & 1.246 & 0.025 \\  & & Clay brick & 0.102 & 2419 & 1.275 \\
4-Block brick cavity & 2.62 \(\times\) 2.62 & Perlite insulation & 0.051 & 96 & 0.048 \\ insulated & & Clay brick & 0.102 & 2419 & 1.275 \\  & & Gypsum board fiber & 0.013 & 785 & 0.163 \\
5-Wood frame & 2.62 \(\times\) 2.62 & Blanket ins. & 0.102 & 68 & 0.053 \\  & & Plywood & 0.016 & 607 & 0.114 \\  & & Gypsum board fiber & 0.013 & 785 & 0.163 \\  & & Blanket ins & 0.102 & 68 & 0.053 \\
6-Wood frame & 2.62 \(\times\) 2.62 & Plywood & 0.016 & 607 & 0.114 \\  & & Air space & 0.025 & 1.246 & 0.025 \\  & & Clay brick & 0.102 & 2419 & 1.275 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Wall characteristics [40].  
Figure 4: Apparatus schematic (modified from [40]).  
Figure 6 reports the measured value and the corresponding numerical results, in order to highlight the accuracy of the model.  
Figure 5: The amplitude reduction ratio and time lag different heat capacity: (**a**) M = 2; (**b**) M = 15; and (**c**) M = 25.  
Figure 6: Comparison between calculated and measured data: (**a**) Time lag; and (**b**) amplitude reduction.  
The accuracy of the predictive model was evaluated according to two criteria: The fractions of data predicted to within \(\pm\)20%, called \(\phi\), and the mean absolute percent error, _MAPE_, defined by Equation (13):  
\[MAPE=\frac{100}{n}\sum_{t=1}^{n}\left|\frac{A_{t}-F_{t}}{A_{t}}\right| \tag{13}\]  
here \(A_{t}\) is the measured value and \(F_{t}\) is the calculated value.  
The calculation of these two quantities shows that for the time lag simulation \(\phi\) = 0.762 and _MAPE_ = 15.6%, whereas for the amplitude reduction simulation \(\phi\) = 1 and _MAPE_ = 5.1%; for the simulated amplitude reduction results, the fraction of data predicted to within \(\pm\)10% was equal to 0.81.