## 4 Results and Discussion
### Artificial Neural Network Model  
Successful prediction of data using machine learning-based algorithms essentially depends on the quality of the input data. In fact, the input data may present anomalies that in the processing phase can introduce false trends that jeopardize the prediction capacity of the model. For this reason, these anomalies must be identified and corrected in the preprocessing phase. In fact, it is necessary to identify possible anomalies such as the possible presence of any missing attributes or records, or the presence of records without values. Furthermore, since the input data contains very different variables (thickness, resistivity, porosity, frequency, sound absorption coefficient), the resizing of the data is required. This is because the input variables are characterized by different units of measurement and therefore have very different ranges of values. The standardization of variables is crucial in statistics and data analysis. It allows us to compare variables that show different distributions, or variables with different units of measurement. In standardization, a double normalization is performed: first, the average of the distribution is subtracted from each data, therefore this difference is divided by the standard deviation of the distribution. Thus, the uniqueness of the points and the relative distances from any other point are preserved. This procedure transforms the original data into deviations from the average, and since the algebraic sum of the deviations from the average is equal to zero, it is deduced that all the standardized variables have an average of zero value. On the other hand, each gap from the mean is divided by the standard deviation of the initial variable, which means that the standard deviation of any standardized variable is equal to 1. In this work, the z score standardization has been adopted. In this way, the mean of the column was subtracted from each value in it and the result was divided by the standard deviation of the column. The Equation (11) has been applied:  
\[x_{scaled}=\frac{x-mean\ (x)}{sd\ (x)} \tag{11}\]  
In the Equation (2),  
* _mean (x)_ represent the mean of the variable x
* _sd (x)_ is the standard deviation of the variable x  
As mentioned above, standardization involves a scaling which determines the following properties:  
* _mean = 0_
* _standard deviation = 1_  
Standardization means that above average values will become positive scores, while below average values will become negative scores. Furthermore, the score obtained is dimensionless, simply by \begin{table}
\begin{tabular}{c c c} \hline
**RMSE** & **MAE** & **Person’s Correlation Coefficient** \\ \hline
0.300 & 0.253 & 0.666 \\ \hline \end{tabular}
\end{table} 
Table 2: RMSE, MAE and the Person’s correlation coefficient for the Hamet model. subtracting the mean of the distribution and dividing the result by the standard deviation of the same [25]. The purpose of this study is to produce a neural networks-based algorithm to forecast the values of the sound absorption coefficient, known to be some characteristics of the material under examination. To measure algorithm performance, model validation must be performed. It consists in verifying the model's predictive ability using previously unused input data. The validation of the model is necessary to avoid the excess adaptation of the model; this happens when the model adapts to the observed data that has excessive parameters with respect to the observations. To get around this, we can divide the data into two subsets. The first data set, called the training set, will be used in the training phase; the second data set, called the test set, will be used in the model validation phase. The precision that we will obtain using the test data set will provide us with a measure of the model's performance. For our needs, the input data was divided into two sets as follows: 70% of the data for training (3923 observations), and the remaining 30% of the data for validation (1681 observations).