# Empirical Approach to Defect Detection Probability by Acoustic Emission Testing
The second reason is the absence of a direct correlation between AE data and defect size [12]. A defect in AE testing is considered not as a discontinuity, but as an active source of elastic waves. In the case of a crack, generation of AE waves may be caused by deformation and fractures as well as by friction between existing defective surfaces, but in the case of corrosion, the most powerful AE signals may be caused by concomitant processes, such as hydrogen bubble formation or corrosion products crumbling [13; 14]. The third reason is the complexity of the diagnostic data--a single defect can generate hundreds and even thousands of AE signals. It complicates formulating the defect detection criteria, unlike other NDT methods where the defect may be detected from a single signal when its amplitude exceeds a certain threshold. Due to the presence of residual stresses, generation of AE is also possible for defect-free structures, which contributes to the probability of making false detection of a defect (type I error). In the presence of a defect, signals corresponding to its growth must be identified against the background of external acoustic noise, which increases the probability of defect omission (type II error). One of the first approaches to assessing defect detection probability is described in [15; 16]. This approach represents a universal method for estimating POD in the case of fatigue destruction, but their implementation requires setting more than 20 quantitative a priori unknown parameters. An empirical method for assessing POD in composite materials is based on the distribution of AE hit amplitudes using a finite element model of the acoustic waveguide [17]. Various aspects are analyzed in [18; 19], with respect to POD at various stages of defect development and the likelihood of correctly assessing the defect hazard class. In [20; 21], a method for calculating POD in industrial objects made of ductile low-carbon steel is proposed. Based on the experimental data, the authors justify the need to scale the amplitude distribution by the crack step value, while POD turns out to be proportional to the crack size. The reliability of defect detection by the AE method in composite materials is also considered in [22], where the author compares the distribution of the defect's dimensions with the distribution of AE hit amplitudes and estimate the probability of making type I and II errors by comparing the discrimination threshold value with the quantile of the amplitude distribution. The problem of assessing POD in AE testing cannot be solved in general due to uncertain stress-strain conditions and a strong influence of the material microstructure. Partial decisions for POD estimation are possible but do not have a practical meaning. This study represents an attempt to make a reasonable generalization in assessing POD for AE testing. The proposed method allows estimating POD for the case of periodical AE inspection and for the steels of the pearlitic structural class. Periodic AE testing procedure is carried out for the decommissioned structures and, in contrast to structural health monitoring, assumes a certain regulated loading procedure, which represents a stepped pressure loading of the structure. With such organization of the testing procedure, the stress-strain state of the structure is not completely uncertain. Restrictions on the structural class of the investigated steels allow making more definite generalizations regarding the parameters of AE sources. In [12], it was proposed to predict the number of AE hits emitted by an object with crack during the loading procedure using the Palmer-Heald model, which represents the relationship of the number of AE hits vs. the applied load up to a multiplicative parameter \(D\), which is a constant of the inspected material.