## 1 Introduction
It was concluded that the sensitivity of the marginal spectrum to signal variation is higher than that of the spectrum. According to the above-mentioned literature, HHT performed well in the information processing of nonstationary signals. Namely, HHT could adaptively decompose a signal into a few components and process them by HT. The signal could be observed from the aspect of time-domain intrinsic sequence, time-frequency variation, and energy distribution, and thus the signal information could be described in more detail. Based on the previous two paragraphs, the following conclusions can be drawn: A Lamb wave is a typical nonstationary signal sensitive to structural damage, and HHT can be applied to nonstationary signal processing to extract the abnormal information that cannot be extracted by the conventional signal processing. The active monitoring method in this paper is based on the superposition of a damage scattering wave in the monitoring signal. There is a lack of research on the change of the monitoring signal caused by the scattering wave in the frequency domain or frequency-time domain. Compared with the signal characteristics of abnormal events in prior work (18; 19; 21; 22; 23; 24), in the active monitoring method in this paper, the scattering signal frequency is not only consistent with the frequency of monitoring signal but also far less than the energy of monitoring. Therefore, it is worth studying what changes the scattering signal causes in the monitoring signal. Some papers have carried out preliminary research on this; for example, one study (25) directly used a marginal spectrum to process monitoring signals and found that a marginal spectrum is more sensitive to a change of monitoring signals than spectrum. However, these papers did not explain the relationship between the scattering wave and the instantaneous parameter change of the monitoring signal nor did they answer why the EMD decomposition results of the same state monitoring signals were quite different. Thus, they could not be used to study changes before and after the damage. In this paper, the relationship between the scattering signal and the change in the signal instantaneous phase is studied, and the consistency of the signal EMD decomposition is solved, which makes it feasible to use the change in the instantaneous parameter characteristics of a single sensing signal to realize the active Lamb wave based monitoring of the plate structural health. The rest of this paper is organized as follows: In Section 2, HHT-based signal processing and the principle of active Lamb wave based monitoring of a plate structural health is presented. In Section 3, the monitoring signal model is established, and the relationship between the attenuation coefficient and superposition of the scattering wave and instantaneous phase change of the active Lamb wave is discussed. In Section 4, the change in the active Lamb wave marginal spectrum in the frequency domain caused by plate structure damage is analyzed. In Section 5, the relationship between the instantaneous phase change and the marginal spectrum change of a monitoring signal is discussed. Lastly, conclusions are drawn in Section 6.