# A Method of Barkhausen Noise Feature Extraction Based on an Adaptive Threshold
## 2 Experiment  
Based on previous work [4], specimens used in the experiment are made of Q235 steel, which is a standard material in industrial manufacturing. A four-point bending platform is used to generate applied stress. The applied tensile and compressive stress is limited in the range of 0-150 MPa to avoid plastic deformation. Figure 1: Illustration of ‘pulse count’ and ‘event’ of MBN signals. Figure 2: Illustration of full width at 25, 50 and 75% of the maximum amplitude. The block diagram of the MBN measurement system is shown in Figure 3. To obtain MBN signals, the function generator provides low frequency excitation (triangle wave at 5 Hz) which is amplified by a bi-polar power amplifier (LPA05B). The MBN signals are detected using a pick-up air-coil (with 3000 turns of 0.07 mm diameter wire), which are amplified (30 dB gain), band pass filtered (2-40 kHz), and sampled at 200 kHz frequency by A/D converter (14-bit A/D resolution, DAQ2010). In addition, the excitation voltage is acquired using a second channel synchronously. An example of MBN signal and excitation signal are shown in Figure 4.  
In the experiment, five cycles of MBN signals are sampled under the same stress condition, so the number of MBN signals is 10. Figure 5 shows pulse count as a function of stress when threshold = 0.05, the negative stress represents compressive stress, and the positive stress represents tensile stress. Figure 4: Example of an MBN signal and excitation signal. The red curve is the excitation signal and the blue one is the MBN signal. Figure 5: Example of pulse count as a function of stress when threshold = 0.05. Figure 3: Magnetic Barkhausen noise (MBN) measurement systems. MBN features are normalized for the reason that it is feasible to compare the features of different thresholds. The range of normalized features is between [0,1]. The normalized equation is as follows:  
\[y_{i}=\frac{x_{i}-x_{min}}{x_{max}-x_{min}} \tag{1}\]  
where \(x_{i}\) is the \(i\)th feature of MBN under different stress conditions, \(x_{min}\) is the minimum value of features, \(x_{max}\) is the maximum value of features, \(y_{i}\) is the result of normalization. Figure 6 shows the difference of pulse count before and after normalization with different thresholds as a function of stress. The x-axis represents different thresholds from 0.050 to 0.032. The pulse count values are changed from \(-\)150 MPa to 150 MPa with each threshold, which is equivalent to Figure 5 under different stress conditions. The number of MBN signals under the same stress condition is 10 (five cycles) and the number of stress conditions is 11 (\(-\)150 MPa-150 MPa). The standard deviation of the pulse count feature of 10 MBN signals (under the same stress) can be calculated. So sum of the standard deviations is defined by the sum of the standard deviations in the 11 stress conditions. A genetic algorithm is an optimization technique with the basic idea derived from biological evolution [5; 6; 7]. The algorithm is based on the population of chromosomes that achieves a global optimal solution by selection, crossover and mutation. The parameters of the genetic algorithm in the paper are set as follows: Population size (\(N\)pop = 40), the number of generations (\(N\)gen = 300) and the probabilities of crossover (\(pc\) = 0.8) and mutation (\(pm\) = 0.05), because only one optimal threshold  
Figure 6: Diagram of pulse count before and after normalization with different thresholds as a function of stress. needs to be found in this article. Npop determines the search number of thresholds, which is set to 40. Ngen determines the number of iterations of algorithm. _pc_ determines the crossover probability of binary chromosome. Two-point crossover is used in the paper, which picks two crossover points from the parent chromosomes randomly. _pm_ determines the probability of altering one or more gene values in a chromosome [8]. We use this genetic algorithm to choose an appropriate threshold for MBN signal features.