## 4 Results and Discussion
### Artificial Neural Network Model
The procedure for dividing the observations was carried out completely randomly. The simulation model was developed using an algorithm based on an artificial multilevel neural network of the feed-forward type, with one hidden layer (with 10 neurons) and an output that represents the sound absorption coefficient of the material. During training, at each step the simulation results are compared with those obtained from the measurements. This allows you to calculate the forecast error. This error is then used to adjust the weights of the connections, trying to minimize an error function. The adjustment of the weights is carried out as follows: first the error function derivatives are calculated with respect to the weights. Derivatives are subsequently used to calculate the new net weights. For weight regulation, the Backpropagation algorithm is the most used technique. This method uses gradient descent to search for the minimum of the error function with respect to the weights [34]. The gradient descent method identifies the direction of the maximum increase/decrease of the error function. In this work for the regulation of weights, a variant of the conjugate gradient methods, the scaled conjugated gradient (SCG) backpropagation algorithm [35], was used. SCG returns linear convergence in most problems, returning high performance with at least one order of magnitude faster than the generic Backpropagation algorithm. This result is obtained by exploiting a step-size scaling mechanism. In this way, SCG avoids a long search per line to learn the iteration--this makes it the fastest algorithm among those most widely used. Figure 8 shows the model architecture based on neural networks. Figure 8: Architecture of artificial neural network-based model. Figure 8 shows the structure of each layer of the neural network. The input layer consists of seven data inputs as follows: three types of fragments (TypeA = only wooden, TypeB = mixed, TypeC = only bark), thickness of the samples, resistivity, porosity, and frequency. The hidden layer is made up of ten neurons. Finally, an output level with only one output is returned (sound adsorption coefficient). In Figure 8, the shape of the connections visually represents the strength of the weight: the greater the thickness of the line, the greater the weight. Indeed, the colors of the lines suggest the sign of the connection: black-positive; gray-negative [36; 37]. Table 3 shows the RMSE, MAE and the Person's correlation coefficient calculated for the prediction model. From the analysis of Table 3, we can see that the artificial neural network model has a decidedly low error and a high correlation between simulated data and measured data. Compared to the results obtained with the Hamet model (Table 2), we have obtained much better values. To understand how much the simulation model manages to predict the trend of the sound absorption coefficient with the frequency, we can display the measured and simulated values to compare the results (Figure 9). Let us analyze in detail the results obtained with the numerical simulation by comparing them with those obtained from the measurements with the Kundt tube. The specimens obtained by assembling only the wooden parts show excellent results for the specimen with a thickness of 4 cm. The simulated data curve fits almost perfectly on that of the measured data. Slight discrepancies occur at the high \begin{table}
\begin{tabular}{c c c} \hline \hline
**RMSE** & **MAE** & **Person’s Correlation Coefficient** \\ \hline
0.036 & 0.028 & 0.986 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: RMSE, MAE and the Person’s correlation coefficient for the prediction model. Figure 9: Simulated versus measured sound absorption coefficients. The figure shows a 4 cm thick sample (**a,c,e**) and 8 cm thick sample (**b,d,f**) for only the wooden part (**a,b**), mixed (**c,d**), and only bark (**e,f**). frequencies. In addition, for the 8 cm thick specimen, there is a slight underestimation of the simulated sound absorption coefficient at the peak of the bell curve.