## 4 Results and Discussion
### Strain-Driven Comparison of PoD\({}_{A}\) and PoD\({}_{E}\)  
Detectability of the cracking activities in the concrete specimen was determined by calculating PoD values. Here, PoDs were calculated based on the second signal response PoD approach using two AE parameters, amplitude and energy distributions associated with the magnitude of damage. Figure 7 presents the PoDs of all AE activities based on both amplitudes and energies. The PoD curve typically represents the detectability and usually denotes the intensity or power. As seen from the amplitude-based PoD\({}_{\text{A}}\) variation with respect to signal amplitude, detectability of the activities starts from 15% at 40 dB of threshold and reaches 85% at 59 dB, becoming 100% from 73 dB onwards. Using this trend, it is possible to plot the PoDs of activities less than the threshold. Even though there might be mathematical PoD values before the threshold level, there is no actual detectability. Figure 6: AE hit rate and strain rate with respect to concrete strain. Figure 7: Amplitude- and energy-based detectability of concrete cracking activities: (**a**) PoD\({}_{\text{A}}\) and (**b**) PoD\({}_{\text{E}}\) curves. Considering energy-based PoD calculation of PoD\({}_{\text{E}}\), on the other hand, since the energy scale is considerably broader compared to the amplitude scale (Figure 5), PoD\({}_{\text{E}}\) values calculated based on energy started the detectability of the activities at more than 40% even at the lowest energy levels and swiftly ascended to 100%. This phenomenon can be explained by the calculation method of the AE energy. As the energy measures the area under the rectified envelope and is dependent upon both signal amplitude and duration, it is conceivable that two signals with identical amplitudes may exhibit different AE energies. In this context, the attenuation factor also influences both the duration and energy of the signal. Therefore, even weak signals close to the threshold are susceptible to yielding a detectability of approximately 40% by the energy-based PoD approach. For this reason, it is also necessary to evaluate PoD\({}_{\text{E}}\) with respect to the signal amplitude effect. Since multiple energy values could be measured for different signals having the same amplitude, average PoD\({}_{\text{E}}\) values were calculated for each signal using the PoD curves, and Figure 8 was then constructed based on these calculations. The situation mentioned above, as the energy-based detectability approach, is more clearly observed by examining PoD\({}_{\text{E}}\) with respect to signal amplitude. In this matching seen in Figure 8a, even for amplitude values below 40 dB, PoD\({}_{\text{E}}\) gives a seemingly unrealistic high detection rate of more than 40%. Figure 8b represents the relationship between PoD\({}_{\text{A}}\) and PoD\({}_{\text{E}}\) values of the same activities. As seen, between signals whose amplitude ranges from 40 dB to 57 dB, PoD\({}_{\text{A}}\) provides a wide range of detection probabilities, from 20% to 80%, while PoD\({}_{\text{E}}\) offers an average detection probability ranging between approximately 44% and 49% within this range. This suggests that PoD\({}_{\text{E}}\) may be more reliable in detecting low and closely similar amplitude AE signals, or micro-damages, consistently during early threats. On the other hand, for instance, to achieve a 75% successful detection rate, PoD\({}_{\text{A}}\) requires a signal as low as 55 dB, whereas PoD\({}_{\text{E}}\) requires signals up to 72 dB to reach the same level of detection. Accordingly, it may be considered that PoD\({}_{\text{E}}\) could be more reliable. However, it should be noted that the remarkably high PoD\({}_{\text{E}}\) values for low amplitudes resulted from misconceptions arising from energy calculations. To evaluate the performances of PoD\({}_{\text{A}}\) and PoD\({}_{\text{E}}\) at critical turning points of TP1 and TP2 that were observed in both amplitude and energy distributions and the AE hit rate curve, their trend lines were also investigated.