## 2 Measuring Systems, Materials and Methods
### Methodology
#### 2.1.2 Extraction of Association Rules  
Exploring the relationships between the physical parameters of a structure and the waveform features obtained from NDT investigations is a difficult-to-standardize process. Various analytical methods can be employed to understand the association rules better and obtain the initial knowledge (Figure 4) necessary for further investigation. Algorithms for extracting association rules, such as Apriori, can be advantageous. The large number of features generated through equal division methods allows for a more in-depth analysis of these relationships, improving the understanding of the underlying processes and creating an effective classification algorithm [59; 60; 61; 62; 63].  
Unlike methods such as rough set theory, association rule extraction techniques are not employed for classification purposes (matching sets of predictors to specific values of the decision variable). The main objective of these algorithms is to demonstrate how changes in a physical parameter (such as an increase in cover thickness) will influence the waveform. However, similar to rough set theory, the method can be utilized for attribute selection. The initial step in exploring association rules during non-destructive testing (NDT) investigations involves constructing a database containing comparisons of original records. The compared records can differ by only one structural parameter, representing the smallest possible change. The compared parameters (both structure and waveform) can be categorized as increase (\(\uparrow\)), decrease (\(\downarrow\)), or no change (-). Finally, a rule can be formulated as follows (1):  
If (BODY), then (HEAD) [_support_, _confidence_]  
Figure 5: Attribute extraction with equal intervals in the domain of amplitude method.  
Figure 6: The definitions of amplitude and offset: (**a**) amplitude, (**b**) offset.  
where:  
BODY (A) is a change in a specific parameter of the structure;  
HEAD (B) is a change in a specific parameter of the waveform.  
The strength of the rule is assessed using two indicators: _support_ and _confidence_.  
_Support_ is a ratio of the number of records in which the rule is present to the total number of records in the database (D). This indicator is given as (2):  
\[\text{supp }(\text{A})=\frac{\#\{\text{d}_{\text{i}}\in\text{D}:\text{A}\subset \text{d}_{\text{i}}\}}{\#\text{D}}\approx\text{P}(\text{A}) \tag{2}\]  
The _confidence_ indicator is a conditional probability that the entire rule will be observed, contingent upon the presence of the BODY (A). This indicator is given as (3):  
\[\text{conf}(\text{A}\rightarrow\text{B})=\frac{\text{supp }(\text{A}\cup\text{B})}{\text{supp }(\text{A})}\approx\text{P}(\text{B}|\text{A}) \tag{3}\]  
The proposed method for discovering association rules closely resembles the traditional Apriori algorithm [59; 60; 61; 62; 63]. This approach is founded on the principle that significant rules are derived solely from frequent item sets. Such item sets must surpass the minimum support and confidence thresholds established by the investigator. In comparison to the classical algorithm, a few significant changes have been introduced:  
* Set A includes only the structure's physical parameters;
* Set B includes only the waveform's parameters;
* The BODY length equals 1; only one physical parameter (A) can change.  
The introduced modifications improve the algorithm's efficiency by reducing the search space for association rules.  
The algorithm of the designed method is shown in Figure 7.