## 3 Results
### Parameter Identification
#### 3.2.2 Rebar Diameter  
The diameter (\(D\)) of the rebar can be regarded as a discrete parameter that affects almost all attributes. Table 9 presents the basic association rules. The weak association rules presented in Table 9 indicate that identifying this parameter is difficult. A change in the rebar diameter by 2 mm affects all attributes except the offset \(B_{\text{x}}\). In the case of the eddy current (EC) method, the confidence parameter indicates that the identification will probably be based on the \(d_{\text{s}}\) feature. In contrast, in the case of the magnetic flux leakage (MFL) method, the offset parameters (not present in the EC method) and some amplitudes will play a significant role in the identification model (in addition to the ds parameters). The changes in \(d_{\text{x}}\) are small. Therefore, this parameter may not be useful, especially for larger cover thicknesses, where noise becomes more important. Figures 22 and 23 illustrate example results obtained for samples with varying rebar diameters. The results in Figure 22 support the conclusions drawn from the basic association \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \(h\) (mm) & **20** & **30** & **40** & **50** & **60** & **70** \\ \hline Correctness of the identification (\%) & 100 & 100 & 100 & 100 & 100 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Correctness of the concrete cover identification—magnetic method, step of 10 mm. Figure 21: Amplitude as a function of concrete cover thickness. (**a**) Eddy current method; (**b**) magnetic flux leakage method. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{_Feature_} & \multicolumn{4}{c}{**EC—magnitude**} & \multicolumn{4}{c}{**MFL—\(B_{\text{X}}\) waveform**} \\ \cline{2-9}  & \(A\) & \(d_{x}\) & \(d_{s}\) & \(A\) & \(O\) & \(d_{x}\) & \(d_{s}\) \\ \hline \multirow{2}{*}{_Change_} & \(\downarrow\) & \(\uparrow\) & \(\uparrow\) & \(\uparrow\) & - & \(\uparrow\) & \(\uparrow\) \\ \hline _CONFIDENCE_ (\%) & 69 & 83 & 90 & 88 & 92 & 84 & 61 \\ \hline \multirow{2}{*}{_Support_ (\%)_} & 33 & 33 & 33 & 57 & 57 & 57 & 57 \\ \cline{2-9}  & \multicolumn{4}{c}{**MFL—\(B_{\text{Y}}\) waveform**} & \multicolumn{4}{c}{**MFL—\(B_{\text{Z}}\) waveform**} \\ \cline{2-9}  & \(A\) & \(O\) & \(d_{x}\) & \(d_{s}\) & \(A\) & \(O\) & \(d_{x}\) & \(d_{s}\) \\ \hline _Change_ & \(\uparrow\) & \(\uparrow\) & - & \(\uparrow\) & \(\uparrow\) & \(\uparrow\) & - & \(\uparrow\) \\ \hline _CONFIDENCE_ (\%) & 83 & 99 & 58 & 100 & 90 & 86 & 74 & 83 \\ \hline _Support_ (\%) & 57 & 57 & 57 & 57 & 57 & 57 & 57 & 57 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Basic association rules for assessing changes in rebar diameter (\(\Delta D\) = 2 mm \(\uparrow\)). rules presented in Table 5, indicating that the diameter affects nearly all attributes, albeit with minimal variations. The changes in the \(d_{\text{s}}\) parameter are both significant and linear as a function of \(D\). At the same time, changes in the \(d_{\text{x}}\) parameter are also linear with respect to \(D\), but they are relatively small. A more thorough analysis indicates that a 2 mm change in diameter has effects comparable to a 2 mm change in concrete cover thickness. Similar to the concrete cover thickness, further analyses were conducted. The optimal model for the EC method included all three attributes. For the MFL method, the model utilized the aggregated amplitude, \(d_{\text{s}}(B_{\text{y}})\), and \(O(B_{\text{y}})\). Including the aggregated offset could also be considered, as it slightly enhances the results for larger cover thicknesses, although it negatively impacts performance for smaller thicknesses. The classification results are illustrated in Figure 24.  
Figure 24: Results of rebar diameter identification derived from both methods across all transducers. Figure 22: EC—waveforms obtained for different rebar diameters; (**a**) raw data, (**b**) normalized data.