## 3 Adaptive Time-Frequency Analysis
### Application
By adopting a multivariate signal ensemble decomposition strategy and incorporating a median operator to integrate and average the decomposition results of multiple signal sets, MEEMD effectively reduces spurious components induced by the addition of random noise in EMD (ensemble empirical mode decomposition). Second, it enhances multi-physical field signal fusion and robustness. The multivariate signal ensemble nature of MEEMD enables it to process multi-channel sensor data simultaneously (such as vibration, acoustic emission, and fiber optic sensing). Through joint analysis of the time-frequency characteristics of signals from different physical fields, it strengthens its identification capability for complex damage patterns (such as the coexistence of composite delamination and metal fatigue). Experiments demonstrate that when applied to the diagnosis of composite damages in wind turbine blades, MEEMD can reduce the false alarm rate, significantly outperforming the single-channel EEMD method [67]. Furthermore, its adaptive noise bandwidth design dynamically adjusts to different signal characteristics (such as high-frequency transients or low-frequency slow variations), avoiding the masking of signal features by fixed-bandwidth noise. Additionally, computational cost optimization and real-time performance improvement are achieved. By optimizing the ensemble averaging strategy (for example, through stage-wise averaging instead of global averaging), MEEMD shortens the computation time while maintaining decomposition accuracy [68]. This improvement is particularly suitable for long-term health monitoring scenarios, such as dam deformation analysis or aerospace structural fatigue assessment. The main technical challenges of MEEMD are as follows: First, parameter sensitivity and residual noise persistence. The performance of MEEMD still relies on a manually set noise bandwidth and number of ensemble trials. If the noise bandwidth is too wide, it may introduce high-frequency artifacts; if it is too narrow, then it may result in incomplete mode separation. For instance, in rail crack monitoring, improper noise parameter settings can contaminate damage-related high-frequency IMFs (intrinsic mode functions) with noise, reducing the signal-to-noise ratio [58]. Moreover, multiple overlays of limited-bandwidth noise may lead to the accumulation of low-frequency residual noise, necessitating post-processing with wavelet threshold denoising or energy compensation algorithms. Second, endpoint effects can distort the decomposition results, and the method shows poor adaptability to extreme conditions, such as high-temperature or high-humidity environments where signals may be severely affected. Although MEEMD partially suppresses endpoint distortions through local mean prediction (such as the OFCEEMDAN algorithm), under extreme conditions of strong impact loads or abrupt signal amplitude changes (such as building responses during earthquakes), envelope fitting errors may still cause IMF boundary frequency shifts, affecting damage localization accuracy. Experiments indicate that modal energy leakage in such cases can reach a significant level, which may have a negative impact on the accuracy of signal decomposition. Third, hardware resource constraintsand algorithm generalization limitations. The multi-channel data processing requirements of MEEMD significantly increase memory usage, posing challenges to the hardware resources of embedded devices (such as wireless sensor nodes). For example, when compared to standard FPGA-implemented modules implemented for single signal processing, FPGA-implemented MEEMD modules require an additional 20% of logic units for multi-signal synchronous processing, which limits their promotion in low-power scenarios [68]. Furthermore, the algorithm's generalization capability for non-stationary signals still needs verification; in particular, the decomposition stability under multi-physical field coupling (such as the combined effect of temperature and strain) has not been fully investigated.