## 2 HHT-Based Signal Processing and Active Lamb Wave Based Monitoring Method
### Active Lamb Wave Based Monitoring Method  
Various damages inside a structure increase the stress concentration and crack probability, and damage boundaries cause scattering of the propagation waves in a structure. Thus, a damage scattering wave can be considered as a wave that comes from another signal source. The active Lamb wave based monitoring of plate structural health is based on this principle. In the active monitoring of a plate structure, if a waveform excited by the actuator encounters damage on its propagation path, then scattering occurs. In that case, the signal received by the sensor is composed of the scattering wave and direct wave, as shown in Figure 1a. It should be noted that the damage location is not on the straight line with the actuator and sensor as two points. In practice, as for a secondarywave source, the amplitude of a damage scattering wave attenuates significantly, and no change in the waveform can be observed after the superposition with the direct wave. The active Lamb wave based monitoring system adopted in this paper was developed by the Structural Health Monitoring and Forecasting Group of the State Key Laboratory of Mechanics and Control of Mechanical Structures at Nanjing University of Aeronautics and Astronautics (NUAA). It includes the wave excitation module, the switch control module, the charge amplifier module, and the data acquisition module, as shown in Figure 1b. The actuators and sensors are both piezoelectric patches (PZTs) [26]. The excitation signal of the actuators is a tone burst signal, and its mathematical expression is given by  
\[\mathrm{u(t)}=\mathrm{A}\times\left[\mathrm{H(t)}-\mathrm{H(t-n/f_{c})} \right]\times\left(1-\cos 2\pi\mathrm{f_{c}}\,\mathrm{t/n}\right)\times\sin 2\pi \mathrm{f_{c}}\mathrm{t} \tag{6}\]  
where A represents the signal amplitude modulation, f\({}_{c}\) denotes the center frequency, n is the number of signal wave peaks, and H(t) denotes the Heaviside step function [8].  
The experimental system used for the active Lamb wave based monitoring of the plate structure is presented in Figure 2. The excitation signal had a center frequency of 150 kHz and five peaks as shown in Figure 2a. As shown in Figure 2b, there were three wave packets in the plate response. Wave packet 1 occurred at the same time as the excitation signal, and it apparently denoted crosstalk. Thus, it could be neglected. Wave packet 2 represented the propagation wave of the excitation signal in the plate structure. Wave packet 3 could also be ignored because it had relatively low energy and was mainly composed of the signals reflected by the plate structure edges. Therefore, Wave packet 2 was considered to be a response of the plate structure to the excitation signal, and it was easily identifiable in the sensing signal. The wavelet transform of the signals is shown in Figure 2c,d, wherein it can be seen that Wave packet 2 almost maintained a consistent center frequency with the excitation signal. A tone burst signal was adopted as the excitation signal, mainly because of the high identification degree of its response in the plate as well as its simple waveform structure.  
Figure 1: The active monitoring principle and the active monitoring system. (**a**) Schematic diagram of the active monitoring principle of a plate structure; (**b**) Structural diagram of an active Lamb wave based monitoring system.  
Furthermore, the center frequency of the excitation signal could also be regulated to acquire a relatively ideal response wave in the plate structure, which not only facilitated the extraction of the signal time-frequency parameters but also reduced the interferences of parameter comparisons before and after damage. In this study, Wave packet 2 in Figure 2b was taken as the research object, and the HHT time-frequency processing technology was used to analyze its instantaneous phase and marginal spectrum before and after damage.