## 5 Results and Discussions
### Magnitude-Based and Energy-Based DIs in Time Domain  
The intensity of damage-reflected wave energy is taken as a sensitive indicator to determine the orientation of fatigue cracks, as correlated in which the strongest reflection is captured perpendicular to the direction of incidence. With the increase of the incidence angle of the guided waves, the intensity of the crack-reflected signal energy declines quickly. Based on this, the actuator-sensor paths are selected by extracting signal features associated with higher intensity energy [30], the gained signals also have a higher signal-to-noise ratio. Therefore, the investigations successively select the actuator-sensor paths A\({}_{1}\)-S\({}_{4}\), A\({}_{2}\)-S\({}_{5}\), A\({}_{3}\)-S\({}_{6}\), A\({}_{2}\)-S\({}_{4}\), and A\({}_{2}\)-S\({}_{6}\) as representative paths in the time-frequency domain, as displayed in Figures 7-10. On this condition, the different paths A\({}_{1}\)-S\({}_{4}\), A\({}_{2}\)-S\({}_{5}\), and A\({}_{3}\)-S\({}_{6}\) are perpendicular to the crack orientation with a fixed crack length of 1.0 cm. Similarly, A\({}_{2}\)-S\({}_{4}\), A\({}_{2}\)-S\({}_{5}\), and A\({}_{2}\)-S\({}_{6}\) are selected as the comparison paths of A\({}_{1}\)-S\({}_{4}\), A\({}_{2}\)-S\({}_{5}\), and A\({}_{3}\)-S\({}_{6}\), the magnitude variations of the extracted S0 mode in the time domain are presented in Figure 7.  
Figure 7: The magnitude of measured signals with different actuator–sensor paths in the time domain (**a**) A\({}_{1}\)–S\({}_{4}\), A\({}_{2}\)–S\({}_{5}\), and A\({}_{3}\)–S\({}_{6}\) paths; (**b**) A\({}_{2}\)–S\({}_{4}\), A\({}_{2}\)–S\({}_{5}\), and A\({}_{2}\)–S\({}_{6}\) paths.  
The normalized magnitude-based and energy-based DIs in the time domain are calculated by Equations (2) and (4). As shown in Figure 8, in cases where the crack of the A\({}_{1}\)-S\({}_{4}\) actuator-sensor path propagates from 0.0 cm to 3.0 cm, the A\({}_{2}\)-S\({}_{5}\) actuator-sensor path propagates from 0.0 cm to 8.0 cm, or the A\({}_{3}\)-S\({}_{6}\) actuator-sensor path propagates from 0.0 cm to 12.0 cm, there are no obvious variations in the DIs with some negligible fluctuations. The detection features of magnitude-based and energy-based DIs are substantially restricted to evaluate the fatigue crack, in case that the crack size is comparable with the probing wavelength. It is also found that the temporal features of guided waves are fairly limited to characterize the fatigue crack growth near the actuator-sensor paths with high sensitivity. When the progressive crack is large enough or near the actuator-sensor paths, with an increase of the fatigue crack, the remarkable DIs can be obtained. On the contrary, when the extended  
Figure 8: The magnitude and energy DIs of different actuator-sensor paths in the time domain (**a**) Normalized magnitude-based DIs of the A\({}_{1}\)–S\({}_{4}\), A\({}_{2}\)–S\({}_{5}\), and A\({}_{3}\)–S\({}_{6}\) paths; (**b**) Normalized energy-based DIs of the A\({}_{1}\)–S\({}_{4}\), A\({}_{2}\)–S\({}_{5}\), and A\({}_{3}\)–S\({}_{6}\) paths; (**c**) Normalized magnitude-based DIs of the A\({}_{2}\)–S\({}_{4}\), A\({}_{2}\)–S\({}_{5}\), and A\({}_{2}\)–S\({}_{6}\) paths; (**d**) Normalized energy-based DIs of the A\({}_{2}\)–S\({}_{4}\), A\({}_{2}\)–S\({}_{5}\), and A\({}_{2}\)–S\({}_{6}\) paths.  
Figure 9: The amplitude of signals with different actuator–sensor paths in the frequency domain (**a**) A\({}_{1}\)–S\({}_{4}\), A\({}_{2}\)–S\({}_{5}\), and A\({}_{3}\)–S\({}_{6}\) paths; (**b**) A\({}_{2}\)–S\({}_{4}\), A\({}_{2}\)–S\({}_{5}\), and A\({}_{2}\)–S\({}_{6}\) paths.  
fatigue crack locates far from the actuator-sensor paths, it shows that the DIs are less sensitive to characterizing the crack variations without significant changes.