# A Method of Barkhausen Noise Feature Extraction Based on an Adaptive Threshold
## 3 Results  
### Adaptive Pulse Count Feature  
As shown in Figure 8, the pulse count with different thresholds as a function of stress and standard deviation of every feature are shown. With Table 1 and Figure 9, in the case of large stress (130 MPa and 150 MPa tensile and compressive stress), thresholds of 0.038, 0.036 and 0.034  
However, it is difficult to manually find the appropriate threshold, so a genetic algorithm is used in this paper. After optimization by GA, when the threshold is 0.0249, the sum of standard deviation is the lowest, which is 0.1501. The sum of standard deviation varies with genetic generation as shown in Figure 10; it can be found that the genetic algorithm can find the optimal threshold in about 70 generations.  
Since the sum of standard deviation can only reflect the fluctuation range of the whole feature, it cannot reflect the distinguishing degree of features for different stress conditions. The paper proposes a new criterion 'overlap' for judging the distinguishing degree of features. Figure 11 depicts the calculation method of 'overlap'. Assume _stress_2 is greater than _stress_1(tensile stress) or _stress_2 is less than _stress_1(compressive stress), 'overlap' can be divided into three cases in Figure 11 and be calculated by Equation (2), where \(S1_{up}\) and \(S1_{low}\) are the upper and lower limits of the feature change under the condition of _stress_1, \(S2_{up}\) and \(S2_{low}\) are the upper and lower limits of the feature change under the  
\begin{table}
\begin{tabular}{c c c c} \hline
**Threshold** & **Sum of Standard Deviation** & **Threshold** & **Sum of Standard Deviation** \\ \hline
0.020 & 0.1794 & 0.030 & 0.1652 \\
0.022 & 0.1675 & 0.032 & 0.1685 \\
0.024 & 0.1600 & 0.034 & 0.1753 \\
0.026 & 0.1585 & 0.036 & 0.1781 \\
0.028 & 0.1554 & 0.038 & 0.1797 \\ \hline \end{tabular}
\end{table}
Table 1: Sum of the standard deviation of the pulse count feature with different thresholds.  
Figure 10: The sum of standard deviation varies with genetic generation.  
Figure 9: Distinction of pulse count feature with different thresholds.  
condition of _stress_2. The lower the 'overlap', the greater the ability of this feature to distinguish from different stress conditions.  
\[overlap=\left\{\begin{array}{ccc}0&,&S2_{low}>S1_{up}\\ S1_{up}-S2_{low}&,&S1_{low}<S2_{low}<S1_{up}\text{ \ and \ }S2_{up}>S1_{up}\\ S2_{up}-S2_{low}&,&S1_{low}<S2_{low}<S1_{up}\text{ \ and \ }S2_{up}<S1_{up}\\ 1&,&S1_{low}<S2_{up}<S1_{up}\text{ \ and \ }S2_{low}>S1_{low}\\ 1&,&S1_{low}<S2_{up}<S1_{up}\text{ \ and \ }S2_{low}<S1_{low}\\ 1&,&S2_{up}>S1_{up}\text{ \ and \ }S2_{low}<S1_{low}\\ \end{array}\right. \tag{2}\]  
Table 2 shows the sum of overlap of the pulse count feature with different thresholds. When the threshold is 0.020, the sum of overlap is equal to 0, which indicates that this threshold is more suitable for stress detection than other ten thresholds. If there is a case where 'overlap' of multiple pulse count features with different thresholds is 0, the feature with the lowest sum of standard deviation can be selected as the most optimal threshold. After optimization by the genetic algorithm, when the threshold is 0.0230, 'overlap' is 0 and sum of standard deviation is 0.1633, which is the lowest.