## 2 Measuring Systems, Materials and Methods
### Methodology
#### 2.1.1 Feature Extraction  
Studies on magnetic and eddy current methods [34, 40, 44] have shown that simultaneously identifying three parameters from the same dataset presents a significant challenge. The effectiveness of the identification largely depends on the feature extraction techniques employed to characterize the waveform attributes. In the process of attribute extraction, it is crucial to consider specific conditions and limitations, including:  
* The number of attributes used in the model should be kept to a minimum to reduce the impact of the curse of dimensionality;
* The attributes should be independent and demonstrate low correlation with each other. When attributes are dependent or exhibit high correlation, they can exacerbate the curse of dimensionality without providing meaningful knowledge;
* The attributes included in the model must accurately represent the shape and characteristics of the measured waveforms. The study of attribute extraction is performed iteratively, adhering to the methodology described in [44]. Each subsequent method is developed based on enhancements from earlier versions. Each one presents unique strengths, limitations, and weaknesses. Figure 3 presents the development of these methods. Dividing the domain of the independent variable into equal intervals is an elemental method for extracting features from the waveform. Attributes are created by saving amplitude values (attributes) for subsequent positions (equally spaced from each other) on the independent variable. The positions are evenly spaced apart. While the method is straightforward, many attributes are needed to reflect the waveform's shape accurately. Experiments have demonstrated that treating amplitude as an individual feature can significantly enhance identification accuracy. In these instances, shape attributes are derived from the normalized waveform and separated from the amplitude value. This approach is referred to as equal intervals with normalization. In the following research phase, the extraction method for the shape attributes is enhanced. The technique is called equal intervals in the amplitude domain. This method involves dividing the vertical axis into equal intervals. The sampling frequency of attributes is proportional to the derivative of the waveform and increases in areas where the waveform rises more steeply. This modification enables a more precise depiction of the waveform's shape using fewer attributes. However, if the tested waveform is not monotonic, multiple abscissa values can be assigned to a single amplitude value. The primary benefit of all three feature extraction methods through equal dividing is the ability to extract attributes without requiring initial knowledge or testing the  
Figure 3: Development evolution of techniques for extracting features from waveforms. Figure 2: Methodology for knowledge acquisition from NDT measurement data based on the CRISP-DM model. association rules between waveforms and structure physical parameters. Prior understanding of the studied process is also not necessary. This makes these techniques highly universal and applicable in most contexts. The methods can be utilized as an intermediate step in the development (e.g., before using the characteristic point method to define characteristic points). On the other hand, a notable drawback of these methods is the necessity to extract many features to capture the shape of the waveform. This causes problems connected to the curse of dimensionality. As the number of features grows, the required number of records (database size) should increase exponentially. Moreover, obtained shape attributes are usually highly correlated. As a result, it is essential to reduce the number of features (usually, the number of attributes should be smaller than five). The reduction process requires time, experience, and knowledge about the tools that can be used (filtering, aggregation, wrappers, principal component analysis, rough set theory [57; 58], etc.).