## 2 Measuring System, Materials and Methods
### Methodology
#### 2.1.3 Features Extraction  
The simultaneous identification of three different parameters based on the same data is a complex and challenging issue. Various changes in the structure can exert remarkably similar effects on the measurement waveform. For instance, a change in concrete cover thickness may influence the results similarly to a simultaneous change in the diameter and type of steel. Extensive research on magnetic and eddy current methods [7; 44] has shown that a critical factor for effective identification is the method of feature extraction used to determine the attributes that describe the waveform. During the extraction process, special attention should be paid to the following limitations and conditions:  
* The number of attributes utilized in the model should be minimized to mitigate the curse of dimensionality. * The attributes incorporated into the model must accurately reflect the shape and parameters of the measured waveforms. * The attributes should be independent of one another and exhibit a possibly low correlation. Dependent or highly correlated attributes exacerbate the curse of dimensionality without providing substantial valuable knowledge [7; 44]. Although determining attributes that describe the waveform is essential for effective identification, this process is often undervalued. The research conducted in this domain followed an iterative approach consistent with the CRISP-DM model. Consequently, six general methods for attribute determination were considered. While each successive method was developed through enhancements of its predecessors, each possessed specific advantages and may be optimal depending on the specifics and goals of the research problem. The evolution of these methods is illustrated in Figure 5.  
Figure 4: Methodology for knowledge acquisition from NDT measurement data based on the CRISP-DM model. The simplest method to extract signal or waveform features involves dividing the domain of the independent variable into equal intervals. Amplitude values (attributes) are read for subsequent positions (equally spaced from each other) on the independent variable. The method's concept is similar to resampling. The procedure is straightforward to implement, but to accurately reflect the shape of the waveform, numerous attributes must be defined. Past research on both eddy current and magnetic methods [7, 44] has proven that significant improvements in identification accuracy are achieved by determining the amplitude as a separate attribute. Then, the waveform is normalized, and the features are extracted from the normalized curve. This sequence of actions allows the decoupling of shape attributes from amplitude attributes. However, even better results are obtained by dividing the domain of the amplitude into equal intervals. This modification (in this method, instead of dividing the independent variable on the abscissa axis, the ordinate axis was segmented into equal intervals) enables an automatic increase in the frequency of attribute sampling in regions where the waveform amplitude changes faster (proportionally to the derivative of the waveform), thereby facilitating a more accurate representation of the waveform's shape. A drawback of this solution is the potential for assigning more than one abscissa axis value to a given amplitude value. The foremost advantage of all three methods for determining attributes through equal partitioning is their capacity to derive attributes without understanding the association rules between waveforms and structural parameters. Therefore, prior knowledge of the studied process is not a prerequisite. Consequently, these methods can be broadly applied across various contexts and are well-suited for an intermediate step in developing final identification models. Conversely, a significant limitation of these approaches is the requirement to generate a substantial number of features to accurately represent the waveform's shape.