## 3 Magnetic Adaptive Testing  
A special method of magnetic measurement, the so-called magnetic adaptive testing (MAT), was recently developed. MAT belongs to the family of magnetic hysteresis measurement techniques, but in contrast to the conventional hysteresis technique, minor magnetic hysteresis loops are measured instead of the major hysteresis loop. By applying this technique, a large data pool is generated, and those elements of this data pool that are the best characteristics of the investigated material degradation are taken into account. A detailed description of this technique is given in Ref. [13]. It is shown in this work that the MAT method results in more sensitive and more reliable parameters than traditional magnetic hysteresis measurement does. Furthermore, magnetic saturation of the measured samples is not necessary, which is a very important advantage in practical applications. In this measurement, the series of minor magnetic hysteresis loops is measured. Demagnetization of samples is conducted before each measurement by decreasing the amplitude of the alternating magnetizing field. The amplitude of the magnetizing current with a triangular waveform is then increased step by step. This linearly increasing magnetizing field generates a voltage signal in the pick-up coil, which is proportional to the differential permeability of the measured sample. These measured permeability loops are the input for the further data evaluation. All points of the loops give information about the magnetic behavior of the sample. Using the measured data, an evaluation process is applied: Matrices are calculated from the permeability data. All matrix elements are compared with the same element of the reference sample. In this way, a large data pool that magnetically characterizes the investigated sample is calculated. These magnetic descriptors are taken as functions of any independent parameter that describes the material degradation due to any external influence. Within MAT evaluation, those descriptors are chosen to best characterize the actual material degradation. These parameters can be taken either from the permeability matrix (\(\mu\) matrix) obtained directly from measured permeability data, or from the hysteresis matrix, which is the integrated permeability along the field \(h_{\mathrm{z}}\), or from the derivative of the permeability (\(\mu^{\prime}\) matrix) with respect to the magnetic field (second derivative of the magnetic induction with respect to the field). Each MAT descriptor is characterized by the actual (\(h_{\mathrm{z}}\), \(h_{\mathrm{b}}\)) pairs, where \(h_{\mathrm{b}}\) is the minor loop amplitude. Special care has always been taken by determining both the optimal MAT descriptor of maximal sensitivity with respect to the independent parameter (degradation parameter) and the maximal reproducibility of the descriptor. This optimization depends on the actual material. Once the best parameter is chosen, the same parameter is used for each sample and in future measurements for all other similar samples. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**C** & **Mn** & **Si** & **S** & **P** & **Cr** & **Ni** & **Mo** & **Cu** \\ \hline
0.201 & 0.578 & 0.27 & 0.0085 & 0.0091 & 0.372 & 0.668 & 0.599 & 0.0472 \\ \hline \end{tabular}
\end{table} 
Table 2: The amount of polluting elements of base metal A508 Cl2 other than the chemical components indicated by the standard (wt.%). In the following sections, we use the term \"optimally chosen MAT descriptor\" without going into details about the exact matrix element. This is the descriptor, chosen from the calculated data pool, that results in the best correlation between the magnetic and independent parameters (Vickers hardness). The measured specimens were magnetized by a yoke placed on top of the sample. A half transformer core, made of laminated Fe-Si sheets, was used as the magnetizing yoke. A pick-up coil and an exciting coil were used, wound on the legs of the yoke.