## 3 Adaptive Time-Frequency Analysis
### Empirical Mode Decomposition and Optimization Models
#### 3.1.2 Ensemble Empirical Mode Decomposition  
Definition  
Ensemble empirical mode decomposition (EEMD) is an improved method of empirical mode decomposition designed to address the mode mixing issue that may arise when EMD processes signals. EEMD adds white noise of a certain amplitude to the signal to be analyzed and performs multiple EMD decompositions, which are then averaged to obtain more stable and accurate intrinsic mode functions. EEMD retains the adaptive characteristics of EMD, enabling decomposition based on the local characteristic time scales of the signal itself. Application  
Researchers have adopted data-driven models such as EEMD-RF, EEMD-ANN, and EEMD-GBM for precise prediction and conducted sensitivity analyses to understand model behavior [50]. Another study employed a method that combined EEMD with SVM [51]. Similarly, the W-EEMD-ARIMA model achieved the same objective [52]. A method using the EEMD-ANN model for prediction has been proposed, aiming to address inherent challenges in prediction, such as difficulties in model construction, low prediction accuracy, and high computational intensity [53]. EEMD exhibits good denoising performance. The effectiveness of the EEMD-based denoising method proposed in [54] was compared with various wavelet transform-based threshold denoising methods, demonstrating the potential of EEMD in signal denoising applications. A study combined the EEMD-independent component analysis (ICA) method to effectively remove artifacts [55]. Furthermore, several innovative models and applications have emerged. For example, an ensemble empirical mode decomposition-temporal convolutional network (EEMD-TCN) machine learning method has been employed in relevant research [56]. Strength and Weakness  
* Alleviates the mode mixing issue by adding Gaussian white noise
* Residual noise contamination and energy non-conservation  
Ensemble empirical mode decomposition (EEMD), as an enhanced version of classical empirical mode decomposition (EMD), demonstrates unique application value in structural health signal processing while facing several limitations that require urgent resolution. Its core advantage lies in effectively alleviating the mode mixing issue caused by signal intermittency in traditional EMD through multiple additions of Gaussian white noise to the original signal and ensemble averaging. For instance, in the analysis of bridge vibration signals with multiple damage sources, EEMD can separate high-frequency transient components from crack propagation and low-frequency modulated signals from bolt loosening into distinct intrinsic mode functions (IMFs), significantly improving the accuracy of damage feature extraction. This noise-assisted mechanism not only enhances decomposition stability but also preserves EMD's adaptability, enabling it to process nonlinear, non-stationary signals, such as acoustic emission signals from composite material delamination or dynamic structural responses under seismic excitation, without predefined basis functions. Furthermore, the decomposed IMFs possess clear multi-scale physical meanings: high-frequency components typically correspond to transient features of localized structural damage (e.g., impact components in early-stage gearbox faults), while low-frequency components reflect global structural vibration modes, providing reliable references for the early detection of fatigue cracks in wind turbine blades [57]. However, the engineering application of EEMD still faces multiple challenges. First, its performance heavily depends on manually set noise intensity and decomposition iterations. Improper parameter selection may lead to signal features being obscured by noise or incomplete modal separation. For example, in rail crack monitoring, excessive noise amplitude settings could contaminate high-frequency IMFs related to damage, compromising diagnostic accuracy.