## 3 Study on Instantaneous Phase of an Active Lamb Wave Monitoring Signal
### Experiment of the Instantaneous Phase of Monitoring Signal Model
As shown in Figure 3b-d, the effect is manifested in two aspects: one is whether the instantaneous phase of the superimposed scattering signal is larger or smaller than the original instantaneous phase; the other is the degree of the instantaneous phase change after the superimposed scattering signal. As shown in Figure 3b, when the superposition site was between the maximum and the minimum, the instantaneous phase of the signal was smaller than the original instantaneous phase. As shown in Figure 3c, when the superposition site was between the minimum and the maximum, the instantaneous phase of the signal was larger than the original instantaneous phase. When the superposition site was again between the maximum and minimum, as shown in Figure 3d, the instantaneous phase was again smaller than the original instantaneous phase. When the superposition site was again between the minimum and the maximum, the instantaneous phase was again larger than the original instantaneous phase. From the description above, it can be concluded that whether the instantaneous phase becomes larger or smaller is absolutely determined by the extreme interval of the superposition location. The instantaneous phase distortion trend can be obtained from Figure 3b-d. When the scattering wave and the direct wave tended to be antiphase, the instantaneous phase deformation increased gradually; on the contrary, the deformation tended to slow down. The above experimental phenomenon would be repeated if the scattering wave continues to shift to the right. In Figure 3e,f, the effect of scattering wave attenuation on the instantaneous phase is illustrated. The experimental results show that the attenuation degree could not change the size relationship between the instantaneous phase after superimposing the scattering wave and the original instantaneous phase, but it mainly affected the time range of instantaneous phase deformation. When \(\alpha\) was large, the range of the instantaneous phase deformation spreading along the time axis was also larger; on the contrary, the range along the time axis was smaller. Similar results could be obtained at the other superposition site. The following conclusions can be drawn from the analysis of the instantaneous phase change shown in Figure 3. When the superposition location was between the maximum and the minimum, the instantaneous phase of the monitoring signal model became larger than that of the direct wave. When the superposition location was between the minimum and the maximum, the instantaneous phase of the monitoring signal model became smaller than that of the direct wave. When the superposition site made the scattering wave and the direct wave tend to be antiphase, the instantaneous phase deformation of the monitoring signal model became larger. The attenuation degree of the scattering wave only affected the range of the instantaneous phase deformation on the time axis and did not change the size relationship. Figure 3: The experiment of the instantaneous phase change of the monitoring signal model. (**a**) Subfigure (**I**) shows the direct wave and the scattering wave, and subfigure (**II**) shows the instantaneous  
phase of the direct wave. (**b**) The superposition site occurred between the maximum and minimum. Subfigure **(I)** shows the superposition, and subfigures **(II,III)** show the instantaneous phase change and a locally enlarged view. (**c**) The superposition site occurred between the minimum and maximum. Explanations of the subfigures are the same as (**b**). (**d**) The superposition site returns between the maximum and minimum. Explanations of the subfigures are the same as (**b**). (**e**) The instantaneous phase change with the attenuation coefficient increase when the superposition site occurred between the minimum and maximum. Subfigure **(I)** shows 10 scattering signals with different attenuation coefficients and superposition sites, and subfigures **(II,III)** show the instantaneous phase change and a locally enlarged view.