## 2 Methodology  
### Principle of the CEEMDAN Algorithm  
In this paper, we introduce the improved HHT based on ICEEMDAN for gate panel fluctuating pressure in order to capture fluctuating characteristics at different vortex scales. The ICEEMDAN algorithm is based on EMD. To address mode aliasing and the issue of many small-amplitude IMF components in the original EMD algorithm, the ICEEMDAN algorithm adds Gaussian white noise during the decomposition iteration. This process enhances anti-interference capability and partially solves the aforementioned problems. Compared with the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) algorithm, which uses the average of the IMF decomposed by multiple noisy signals as the IMF for each iteration [24], the ICEEMDAN algorithm uses the residuals of the previous iteration minus the average of residuals of multiple noisy signals of the current iteration as the IMF for the original signal iteration, which can further alleviate the phenomenon of noise residuals in the IMF, as well as the problem of modal mixing, and improve the decomposition effect. Therefore, in order to improve the analysis of time series, this paper uses the ICEEMDAN algorithm instead of the EMD used in HHT.  
Based on the EMD algorithm, ICEEMDAN adds a special white noise \(\eta_{i}\) with mean 0 and variance 1 to the decomposition process to decompose the signal x(t) into several IMF components and a residual function component. The ICEEMDAN method effectively mitigates the problems of residual noise and mode aliasing that may exist in the IMF of the EMD and EEMD algorithms. The ICEEMDAN decomposition process is as follows:  
1. The operator \(E_{k}(\cdot)\) in EMD decomposes the original signal \(x(t)\) in \(kth\) mode, and the operator \(\tau(\cdot)\) is used to generate the local mean of the signal.
2. Construct the additive noise signal \(x^{i}(t)=x(t)+\alpha_{0}E_{1}\big{(}\eta^{i}(t)\big{)}\) and compute the first-order residual \(\gamma_{1}=\big{\langle}\tau\big{(}x^{i}(t)\big{)}\big{\rangle}\). Where \(\alpha_{0}=\varphi_{0}std(x(t))/std\big{(}E_{k}\big{(}\eta^{i}(t)\big{)}\big{)}\) is added at the initial stage to remove noise and \(\varphi_{0}\) is the inverse of desired signal-to-noise ratio between the first additive noise signal and the analyzed signal. i denotes the number of times the noise is added, \(std\) denotes the standard deviation, and the operator \(\langle\cdot\rangle\) denotes averaging over the whole.
3. When k = 1, the 1 st IMF component is calculated as follows: IMF\({}_{2}(t)=x(t)-\gamma_{1}(t)\).
4. The 2 nd residuals and IMF components are obtained using the average of \(\gamma_{1}(t)+\alpha_{1}E_{2}\big{(}\eta^{i}(t)\big{)}\) local means as follows: \[\gamma_{2}(t)=\tau\Big{(}\gamma_{1}(t)+\alpha_{1}E_{2}\Big{(}\eta^{i}(t)\Big{)} \Big{)}\] (1) \[\text{IMF}_{2}(t)=\gamma_{1}(t)-\tau\Big{(}\gamma_{1}(t)+\alpha_{1}E_{2}\Big{(} \eta^{i}(t)\Big{)}\Big{)}\] (2) (5) Derivation of the kth mode is as follows: \[\gamma_{k}(t)=\tau\Big{(}\gamma_{k-1}(t)+\alpha_{k-1}E_{k}\Big{(}\eta^{i}(t) \Big{)}\Big{)}\] (3) \[\text{IMF}_{k}(t)=\gamma_{k-1}(t)-\gamma_{k}(t)\] (4) (6) Repeat step 5 to obtain all residuals and IMF components.