## 3 Results and Discussion  
### Comparison between Measurements and Predictions  
The ANN model is trained and validated with 80 and 10 standardized laboratory measurements, respectively. In addition, 10 measurements are employed for testing the accuracy in prediction of airborne sound reduction curves. The acoustic behavior of each wall (in dB) in \(1/3\)-octave frequencies (50 Hz-5 kHz) is used as a dependent variable. Predicted and measured airborne curves of test facade walls are shown in Figure 3. It is significant that predicted and measured insulation curves are close, with some deviations in certain cases. The deviations between predicted and measured curves increase in some samples in low and/or high frequency bands. The smallest deviation is notable in facade #3 with a \(RMSE\) value of 2.19 dB, while the largest is 5.73 dB in facade #10 which has slightly complex configuration. At high frequencies (1.25-3 kHz), a significant gap is observed in the results. The later frequency range usually includes the critical frequency of lightweight constructions. This frequency is also called coincidence frequency, at which occurs a match between the wavelength of the bending wave in the plate and incident acoustic wavelength which is projected onto the plate [17]. A good coupling or matching means that the structure will efficiently and easily radiate sound at and above this frequency [65]. In addition, similar variations are visible at frequencies lower than 200 Hz, e.g., facades #1, #8 and #9. That can happen due to the effect of first eigenfrequencies or fundamental resonances [17]. It is also observed that the trend of certain estimated curves becomes smoother in bands close to low resonances and/or critical frequencies. This reveals that the main difficulties in estimation of sound reduction values are appeared near those bands. Similar problems with ANN models were also reported in other studies [25; 45]. Table 3 represents root-mean-square errors (RMSE) in the prediction of airborne sound reduction curves. It also includes the calculated single-number quantities (SNQ), \(R_{w}\) and \(R_{wPredicted}\), that corresponds to each curve. The highest error is up to 3 dB (facade #7), while the model can predict the same weighted values for facade #3 and #6. In addition, the calculated and predicted correlation terms \(C_{100-3150}\) and \(C_{50-5000}\), which are presented in Table 3, show a maximum difference of 4 dB in facade #5. Figure 4 depicts normalized error deviation values (in interval \([-1,1]\)). The highest error variations are located at high frequencies (1.25-5 kHz) (e.g., facade #2, #7 and #10). In  
Figure 3: Predicted and measured airborne sound reduction index curves of test facades. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Facade no.**} & \multicolumn{1}{c}{\(RMSE\) **(dB)**} & \multicolumn{1}{c}{\(R_{w}\) **(dB)**} & \multicolumn{1}{c}{\(C_{100-3150}\)} & \multicolumn{1}{c}{\(C_{50-5000}\)} & \multicolumn{1}{c}{\(R_{wPred}\) **(dB)**} & \multicolumn{1}{c}{\(C_{Pred}\) **100-3150**} & \multicolumn{1}{c}{\(C_{Pred}\) **50-5000**} \\ \hline
1 & 3.42 & 39 & \(-4\) & \(-3\) & 40 & \(-3\) & \(-3\) \\
2 & 5.48 & 46 & \(-2\) & \(-2\) & 48 & \(-1\) & \(-1\) \\
3 & 2.19 & 53 & \(-4\) & \(-6\) & 53 & \(-4\) & \(-6\) \\
4 & 2.92 & 50 & \(-3\) & \(-4\) & 51 & \(-6\) & \(-6\) \\
5 & 5.62 & 52 & \(-2\) & \(-2\) & 51 & \(-6\) & \(-6\) \\
6 & 4.48 & 55 & \(-4\) & \(-4\) & 55 & \(-5\) & \(-5\) \\
7 & 5.59 & 48 & \(-1\) & \(-1\) & 51 & \(-2\) & \(1\) \\
8 & 3.01 & 65 & \(-5\) & \(-7\) & 67 & \(-4\) & \(-5\) \\
9 & 4.12 & 37 & \(-4\) & \(-3\) & 38 & \(-1\) & \(-1\) \\
10 & 5.73 & 49 & \(-3\) & \(-3\) & 47 & \(-2\) & \(-1\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Predicted and measured weighted sound reduction indices of test facades. low frequency bands (50-200 Hz), the model shows certain gaps between measured and predicted curves, such as facade #5 and #9.