# Empirical Approach to Defect Detection Probability by Acoustic Emission Testing
## 5 Conclusions  
In this study, we have proposed a new approach to assessing the probability of fatigue cracks detection in structural steels during AE testing, based on an a priori estimation of AE signals emitted during crack growth with respect to the parameters of the acoustic waveguide and data registration, such as amplitude discrimination threshold and spatial filtration. We have implemented an empirical approach, i.e., the parameters of the AE source have been determined experimentally. However, the probabilistic assessment of the crack emissivity and the values of the AE signals amplitudes enables generalizing the results obtained for a class of steels with a ferrite-pearlite structure. The parameters of the AE source--the number of emitted signals during the growth of the crack (emissivity) and the amplitudes of the AE signals are estimated as random parameters (Figure 6). The parameters of the acoustic path, on the contrary, are considered deterministic using analytical modeling of dispersive propagation and frequency-dependent attenuation of AE waves. The integration of mathematical models of various types has been carried out (Figure 8), which allows calculating AE signal which corresponds to different values of the source parameters and reflecting the variability of the AE parameters observed during the testing procedure in an industrial environment. Due to a large number of random parameters, the calculation of the AE parameters using the empirical model is carried out about 10,000 times, until the estimated value of the probability stabilizes, i.e., the estimated value does not change by more than 0.05% within 100 iterations. The proposed approach is based on the statistical model of the source; therefore, it is more formal than the approach based on Paris law and the AE source theory [33] represented by [PERSON] [15]. In addition to the statistical basis, the present method utilizes a physical Palmer-Heald model, therefore being more reliable and specific than methods based on artificial neural networks [34] and deep learning technology [35]. The proposed method is relatively complex since it represents a common concept, which allows considering many factors influencing the AE test result. However, the method in its current state has several simplifications that should be revised in a more detailed examination or for more specific test conditions:  
* when calculating the probability of defect detection, it is assumed that the AE channels have the same sensitivity. However, in practice, the sensitivity may differ due to problems associated with the quality of the acoustic contact between the transducer  
Figure 19: Minimum values of the total error probability of a fatigue crack detection against the background of stationary uncorrelated (**a**), stationary correlated (**b**) and nonstationary frictional (**c**) noise. and the testing object; the information about testing structure--sensor coupling could be obtained during the calibration of the AE equipment,  
during data analysis, the authors rely on the amplitude distribution and the emissivity parameter, however, the use of precise broadband sensors allows considering information in the frequency domain, which, in turn, allows us to change the defect detection criterion, making it more reliable for solving specific problems. probability calculation is carried out only for a given detection criterion during standard data processing, including only threshold discrimination and standard location procedure. The proposed technique opens wide possibilities for POD assessment under various testing conditions. It is possible to consider the distance between the AE sensors, the magnitude of the maximum applied load, AE sensor parameters, noise characteristics, etc. For example, it was shown that for structures made of steel 09G2S, AE testing may provide 95% POD at 10 m distance between sensors and 30 dB detection threshold as well as at 5 m distance and 40 dB threshold.