## 3 Results
### Association Rule Mining: Extraction and Analysis
#### 3.2.1 Concrete Cover Thickness  
Examples of measurements along the \(X\)-axis obtained for six different \(h\) are shown in Figure 14.  
The association rules derived from the investigations into concrete cover thickness (\(h\)) exhibited a robust and unambiguous nature. The high confidence level can be attributed to the fact that variations in cover thickness were implemented with a relatively large increment of 10 mm during measurements. This substantial confidence level indicates the potential to detect variations smaller than 10 mm with high reliability. The fundamental association rules on variations in concrete cover thickness are summarized in Table 2.  
The derived, basic association rules can be expressed as follows:  
If (\(h\uparrow\)), then (\(A\) (\(B_{\mathrm{x}}\)) \(\downarrow\)) [_support_ = 100%, _confidence_ = 57%]. Furthermore, the algorithm is capable of identifying more complex association rules, such as the following:  
If (\(h\uparrow\)), then (\(O\) (\(B_{\mathrm{x}}\))--and \(O\) (\(B_{\mathrm{y}}\)) \(\downarrow\) and \(O\) (\(B_{\mathrm{z}}\)) \(\uparrow\)) [_support_ = 56%, _confidence_ = 57%]. The analysis of association rules facilitates the rapid detection of all relations between the changes in the examined physical parameter and variations in the features of measurement waveforms. However, it does not permit the investigation of numerical dependencies. The data presented in Table 2 indicate that variations in concrete cover thickness (\(h\)) have a pronounced effect on the shapes, amplitudes, and offsets of the waveforms of magnetic induction spatial components (\(B_{\mathrm{x}}\), \(B_{\mathrm{y}}\), \(B_{\mathrm{z}}\)). One of the two exceptions is \(O\) (\(B_{\mathrm{z}}\)), with an ambiguous association rule. Moreover, in the case of the \(B_{\mathrm{x}}\) parameter, the offset remains constant and is equal to the value of \(B_{\mathrm{x}}\) measured directly above the reinforcing bar. The independence of the \(O\) (\(B_{\mathrm{x}}\)) attribute value from one of the parameters represents a significant advantage in the identification process. The subsequent step after identifying association rules involves examining numerical relationships. Figure 15 illustrates the relationship between the waveform shape and concrete cover thickness. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline _Feature_ & **A (\(B_{\mathrm{x}}\))** & **C (\(B_{\mathrm{y}}\))** & **O (\(B_{\mathrm{y}}\))  
The subsequent step in examining the numerical dependencies involves characterizing the waveform shape through specific features. In this context, the coordinates of extrema and inflection points along the \(X\)-axis can be utilized as descriptive metrics. An illustrative example of this approach is presented in Figure 16, which demonstrates how the coordinates of the maximum value vary with changes in \(h\). The coordinates of the waveform peak exhibit a linear dependence on the cover thickness. However, this parameter is highly susceptible to noise, as waveform values near the peak vary minimally, making them sensitive to noise impact. The relationship between concrete cover thickness and offset is shown in Figure 17.  
The relationship between offset and concrete cover thickness is characterized by a non-linear pattern, as demonstrated in Figure 17. Additionally, this relationship exhibits non-monotonic characteristics for component \(B_{\mathrm{z}}\). The concrete cover's thickness significantly influences the waveform's amplitude value. The shape of the amplitude variation curve as a function of cover thickness (\(h\)) is consistent across all spatial magnetic induction (\(B\)) components, as depicted in Figure 18.  
Figure 16: Statistical characterization of the variation in the position of the maximum waveform \(B_{\mathrm{x}}\) as a function of concrete cover thickness: (**a**) raw data; (**b**) filtered data.