# Comparison of Measurement Possibilities by Non-Invasive Reflectometric Sensors and Invasive Probes
## 4 Discussion  
### Regression Model  
The graphs in Figure 4 present the relationships obtained on the basis of the results presented in Tables 1-6. The graphs show the average permittivity readings from the five measurements for all examined moisture contents and the confidence intervals. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Moisture \(\mathbf{w}\) [\%]**} & \multicolumn{5}{c}{**Apparent Permititivity \(\varepsilon\) [-]**} \\ \cline{2-6}  & \(\mathbf{\epsilon_{1}}\) & \(\mathbf{\epsilon_{2}}\) & \(\mathbf{\epsilon_{3}}\) & \(\mathbf{\epsilon_{4}}\) & \(\mathbf{\epsilon_{5}}\) \\ \hline
0 & 3.11 & 3.32 & 3.27 & 3.31 & 3.43 \\
10 & 3.72 & 3.76 & 3.87 & 3.94 & 3.84 \\
20 & 5.11 & 5.24 & 5.42 & 5.30 & 5.36 \\
30 & 6.75 & 6.81 & 6.99 & 6.85 & 6.86 \\
40 & 8.82 & 8.96 & 9.10 & 9.12 & 8.96 \\
50 & 10.53 & 10.28 & 10.05 & 9.96 & 10.18 \\
55 & 12.65 & 12.49 & 12.88 & 12.72 & 12.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of the apparent permittivity \(\varepsilon\) measurements with the S2 surface sensor for different values of moisture \(\mathbf{w}\); 600 c.c. sample. Figure 4: Relationship between the apparent permittivity reads determined with the use of the FP/mts invasive probe and the non-invasive probe and the moisture content of class 400 c.c. and 600 c.c. samples. The graphs in Figure 4 confirmed the relationship between the apparent permittivity and the moisture content of the material. The effect of the apparent bulk density of the material was not high, and the different regression courses resulted from the fact that the two materials had different water absorption capacity, i.e., a maximum of 55% for the aerated concrete 600 and a maximum of 69% for the aerated concrete 400, which was a consequence of the different structure of the porous medium. There were differences in the permittivity readings between the invasive probes and the surface sensors, which resulted from their construction and the type of contact between the measuring element and the material. In the case of the invasive probes, the measuring rods were inserted into the material, whereas in the case of the surface sensors, they were in contact with the surface of the material. The invasive probes read the permittivity of the tested material, and the apparent permittivity read by the sensors S1 and S2 was the average value of the apparent permittivity of the tested material as well as of the housing from which the sensor was made. As a consequence, in the case of the invasive sensors for dry material, the average apparent permittivity value was 1.17 [-] for the cellular concrete 400 and 1.1 [-] for the cellular concrete 600. However, in the case of the S1 and S2 probes, they were 3.60 [-] and 3.66 [-] for the concrete 400 and 3.36 [-] and 3.29 [-] for the concrete 600. For the maximum saturation of the 400 cellular concrete sample, the apparent permittivity result when measured with an invasive probe exceeded 20 [-]. On the basis of the measurements, the obtained data and the adopted polynomial regression model described by formula (1), the values of the \(\beta_{1}\)\(\beta_{2}\) and \(\beta_{3}\) estimators were calculated for the individual sensor models and the classes of cellular concrete. These values are summarized in Tables 7 and 8. In Table 7, it can be seen that the measurement error expressed as RMSE in the case of 400 c.c. was the highest when using the S1 non-invasive sensor. On the other hand, the values of the determination coefficient R\({}^{2}\) were similar for all analyzed sensors and exceeded the value of 0.98, which proved a very good fit of the adopted model to the dependence tested. In turn, in the case of class 600 c.c., the RMSE error values presented in  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Sensor** & \(\beta_{1}\) & \(\beta_{2}\) & \(\beta_{3}\) & **R\({}^{2}\)** & **F Statistic** & **\%mass** & **  
Table 8 were the highest for the invasive measurement by the FP/mts probe. As in the case of the 400 c.c.