## 4 Verification of the Artificial Neural Network  
The results of the experimental verification of an unidirectional multilayer neural network (with back error propagation, the conjugate gradient algorithm (CG), and the number of hidden layer neurons equal to 3), which was previously taught and tested based on the results of the research presented in [29], are presented below. A total of 15 result sets were accepted for verification. This network generated a mass humidity value \(U_{mc}\) at each point. These values were compared with the actual \(U_{m}\) values obtained experimentally using the gravimetric method. Figure 6 shows the relationship between \(U_{m}\) humidity obtained on the basis of gravimetric tests and \(U_{mc}\) humidity identified by the network for the experimental verification process. The obtained results show that the artificial neural network correctly mapped the verification data. This is evidenced by the location of points along the regression line, which correspond to the ideal mapping, and also the satisfactory value of the linear correlation coefficient \(R\) equal to 0.807. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Data set**} & **Height of the** & **Indication** & **Indication** & **Salt** & **Salt** & **Salt** & **Real Mass** \\  & **Measuring** & **of the** & **of the** & **Concentration** & **Concentration** & **Concentration** & **Concentration** \\  & **Point above** & **Dielectric** & **Meter** & **in the Wall** & **in the Wall** & **in the Wall** & **in the Wall** \\  & **Ground/Floor** & **Level [cm]** & \(\mathbf{X_{D}}\) **[-]** & \(\mathbf{X_{M}}\) **[-]** & \(\mathbf{X_{M}}\) **[-]** & \(\mathbf{X_{M}}\) **[-]** & \(\mathbf{X_{M}}\) **[-]** & \(\mathbf{X_{M}}\) **[-]** \\ \hline
1 & \(100\) & 135.00 & 58.40 & 0.04 & 0.20 & 0.10 & 8.32 \\ \hline
2 & 50 & 137.10 & 68.30 & 0.45 & 0.50 & 0.01 & 9.75 \\ \hline
3 & \(15\) & 130.00 & 72.50 & 0.50 & 0.20 & 0.30 & 6.87 \\ \hline
4 & \(100\) & 89.70 & 47.20 & 0.35 & 1.20 & 0.25 & 4.57 \\ \hline
5 & 100 & 89.30 & 35.80 & 0.02 & 0.20 & 0.00 & 5.50 \\ \hline
6 & 15 & 39.80 & 30.60 & 0.03 & 0.40 & 0.00 & 3.00 \\ \hline
7 & 10 & 133.60 & 73.40 & 0.50 & 0.45 & 0.50 & 7.21 \\ \hline
8 & 10 & 134.00 & 23.10 & 0.29 & 0.35 & 0.50 & 6.18 \\ \hline
9 & 50 & 104.00 & 35.70 & 0.22 & 0.45 & 0.05 & 4.00 \\ \hline
10 & 100 & 78.00 & 39.60 & 0.42 & 0.30 & 0.00 & 4.95 \\ \hline
11 & 50 & 87.60 & 31.00 & 0.03 & 0.30 & 0.01 & 4.17 \\ \hline
12 & 100 & 129.90 & 49.60 & 0.03 & 0.20 & 0.03 & 7.14 \\ \hline
13 & 100 & 34.60 & 24.10 & 0.10 & 0.25 & 0.03 & 2.01 \\ \hline
14 & 50 & 100.24 & 39.50 & 0.23 & 0.33 & 0.16 & 5.09 \\ \hline
15 & 10 & 111.06 & 51.16 & 0.27 & 0.44 & 0.21 & 6.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Test results of sets prepared for experimental verification of the artificial neural network. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Name and Symbol of the Characteristic**} & \multicolumn{5}{c}{**Parameter Symbol**} \\ \cline{2-7}  & \(\mathbf{X_{D}}\) **[-]** & \(\mathbf{X_{M}}\) **[-]** & \(\mathbf{A}\) **[\%]** & \(\mathbf{C}\) **[\%]** & \(\mathbf{S}\) **[\%]** & \(\mathbf{U_{m}}\) **[\%]** \\ \hline Average value \(\overline{x_{i}}\) & 34.60 & 23.10 & 0.02 & 0.20 & 0.00 & 2.01 \\ \hline Maximum value \(x_{\text{max}}\) & 137.10 & 73.40 & 0.50 & 1.20 & 0.50 & 9.75 \\ \hline Minimum value \(x_{\text{min}}\) & 102.26 & 45.33 & 0.23 & 0.38 & 0.14 & 5.68 \\ \hline Standard deviation \(S_{\text{x}}\) & 32.15 & 16.12 & 0.18 & 0.24 & 0.17 & 1.97 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: List of selected statistical characteristics of parameters. Table 4 presents a comparative comparison of the \(U_{m}\) and \(U_{mc}\) humidity values determined using the gravimetric method and by means of the artificial neural network, respectively. The results of the experimental verification presented in Table 3 indicate the correct identification of validation data.