## 4 Pressure Characteristics on the Gate Panel
### The Pressure Distribution Characteristics on the Gate Panel
#### 4.1.2 Ihhtr Analysis of Pressure  
It is essential to determine whether the load follows a smooth random process or a non-smooth random process, and assessing the degree of non-smoothness is a prerequisite for conducting further analyses. In this study, we enhanced the conventional HHT by replacing the EMD method with improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) for signal decomposition. Subsequently, we utilized this method to analyze the smoothness of a typical water fluctuating pressure during a time-domain process. The ICEEMDAN decomposition of the fluctuating pressure at the P2 measurement point near the bottom of the gate at a small opening (e = 10%) produced the IMF components and spectra depicted in Figure 9.  
As depicted in Figure 9, the ICEEMDAN decomposition follows a descending order of frequency from the original signal decomposition to extract the modal components from low to high, culminating in the Res component, representing the trend term of the original signal. This process is characteristic of time-domain data for water flow fluctuating pressure, which exhibits weak non-stationarity and can be approximated as stationary. Figure 8: Pressure distribution at measuring points of the gate panel at different upstream reservoir levels: (**a**) time-average pressure; (**b**) fluctuating pressure. Each modal component signal exhibited a more pronounced periodic pattern compared to the original signal. According to the theory of turbulence mechanics, the low-frequency segment of the signal corresponds to larger scales of vortices within turbulent flow, while the high-frequency segment corresponds to smaller scales of vortices. Consequently, the scales of vortex levels, represented by the transition from low-order to high-order components, gradually increase. Upon analyzing the IMF4 to IMF6 modal components, we observed a modal aliasing phenomenon resulting from the decomposition. Similar characteristic time-scale waveforms appeared in IMF4 and IMF5, as indicated by the blue dashed box, and this phenomenon persisted and was transmitted to higher orders, evident in the red dashed box in IMF5 and IMF6. It was shown that the blue characteristic waveforms in IMF4 and the red characteristic waveforms in IMF5 exhibited significant differences in time scales compared to the other positional characteristics, but both contained the same components found in IMF5. The presence of identical amplitude components at a specific frequency across the different component signals suggests the existence of vortices of comparable scales within vortex bodies of varying scale levels. The local amplitude of a single signal oscillates over time, representing the continuous variation in a specific vortex scale. This phenomenon reflects the development, mixing, and attenuation processes of vortices of various scales within the vortex structure. The diffusion and mixing of vortices across adjacent scales directly result in the pulsation of fluctuating pressure, which is of significant importance for understanding the mechanisms of turbulent mixing and energy transfer. The IMF components derived from the decomposition of the measured fluctuating pressure signals in this paper using ICEEMDAN were subjected to Hilbert transformation to obtain their instantaneous frequencies and amplitudes. Subsequently, the instantaneous frequencies of all components, weighted by their amplitudes, were plotted on a time-frequency plane, resulting in a three-dimensional spectrogram depicting the signal's time-frequency-amplitude (energy) characteristics, as shown in Figure 10. Additionally, Figure 10 illustrates the Hilbert spectrum of the fluctuating pressure signal measured at point P2 near the bottom edge of the gate under a small opening condition (e = 10%). The frequencies of all modal components of fluctuating pressure were observed to be within 25 Hz, with the high-energy region frequencies confined to 20 Hz or below. Overall, a distinct low-frequency characteristic was evident.