# Empirical Approach to Defect Detection Probability by Acoustic Emission Testing
## 4 Results and Discussion
### Results of Estimating Type II Error Probability  
Figure 12 shows the POD values versus detection threshold and various values of the defect coordinate x (x = 1..\(L\)) calculated for Nclust = 5 and the distance between the sensors L = 5 m. The POD depends significantly on the threshold value. For threshold values of 40 dB, 45 dB, and more than 48 dB the POD value is 95%, 83%, and less than 50% respectively, for the case when a defect is placed in the middle between the sensors (\(x\) = 2.5 m).  
The dependence of the POD on the coordinate x is less significant. The highest POD is reached when the defect is placed in the middle between the sensors. When the defect is displaced from the central part, the probability decreases. For example, at a threshold of 40 dB and 45 dB the POD decreases by 5% and 35%, respectively, when the defect coordinate changes from \(x\) = 2.5 m to \(x\) = 0.5 m  
Figure 11: Result of AE source location with different amplitude thresholds: 30 dB (**a**), 35 dB (**b**) and 40 dB (**c**).  
Figure 12: Dependence of POD vs. threshold value thr and crack’s coordinate x.  
Figure 13 shows the dependence of POD on the amplitude discrimination threshold for \(L=5\) m at different values of \(N^{clust}\), which determines the number of located events. The probability of a fatigue crack detection decreases with an increase in the threshold \(thr\), and the rate of decrease initially becomes higher with the increase of \(N^{clust}\).  
The probability of AE signal detection for steel 45 is significantly higher than for steel 09G2S. The maximum value of the discrimination threshold, which ensures reliable defect detection, is 10 dB higher for steel 45 than for steel 09G2S. Therefore, fatigue cracks in steel 45 can be detected at a higher noise level. For example, with a detection threshold of 40 dB and a distance between the sensors \(L=5\) m, the probability of detecting a fatigue crack in steel 45 is 8% higher than in steel 09G2S, and at a threshold of 45 dB, typical for noisy objects, the probability of detection for steel 45 is higher by 32%.  
Calculating the probability of fatigue crack detection at different distances between the AE sensors was carried out according to the algorithm described in Section 3.2. The probability of fatigue crack detection versus testing zone length, given by a distance between the AE sensors is shown in Figure 14. The calculation was carried out for a single-layer waveguide, not in contact with a liquid.  
The probability of detecting a fatigue crack in steel 45 is significantly higher at any distance between the AE sensors. For example, with a minimum threshold value of 30 dB,  
Figure 14: The probability of detection of a fatigue crack for steels 09G2S (a) and 45 (b).  
Figure 13: Probability of fatigue crack detection depending on the threshold value for different \(N^{clust}\) for steels 09G2S (**a**) and 45 (**b**).  
the detection probability of 0.95 corresponds to the \(L\) = 8 m for steel 09G2S and \(L\) = 16 m for steel 45.  
Comparing the probabilities of detecting fatigue cracks for different distances between the sensors, it can be noted that at \(L\) = 10 m the probability of detecting cracks in 09G2S and 45 steel is approximately the same, and at \(L\) = 15 m the probability of detecting a crack in 45 steel is approximately 20% higher. However, a further comparison is impractical, since at \(L\) > 20 m the probability of detecting a crack in 09G2S steel is less than 50%.