## 3 Adaptive Time-Frequency Analysis
### Application  
Multivariate ensemble empirical mode decomposition (MEEMD) effectively addresses the complexity and non-stationarity of signals by decomposing composite waves into distinct components, thereby facilitating the examination of their spatiotemporal heterogeneity and separation characteristics [58]. Research has also leveraged this attribute, employing MEEMD to manage the non-linear and non-stationary nature of normalized difference vegetation index (NDVI) data, integrating MEEMD with the geographically and temporally weighted regression (GTWR) method [59]. Innovatively, MEEMD has been applied to non-destructive testing. By processing data obtained from pulsed thermography with MEEMD, signals of different frequency components can be separated. Due to the differences in thermal responses between defective and non-defective regions, the decomposition by MEEMD better highlights these discrepancies, thereby enabling non-destructive testing and enhancing the accuracy and reliability of detection [60]. A method combining MEEMD and Prony [61], wherein MEEMD decomposes the signal and introduces permutation entropy to detect randomness followed by the reconstruction of the remaining intrinsic mode function (IMF) components, has also made innovative progress. Furthermore, MEEMD is extensively utilized for prediction [62]. A sequence prediction method based on the MEEMD-long short-term memory (LSTM) network model has been proposed. Another prediction approach employs a model based on MEEMD, LSTM, and multilayer perceptron (MLP) [63]. MEEMD initially decomposes the data, LSTM handles the dynamic changes in time series, and MLP models complex nonlinear relationships. The synergy of these three enhances prediction accuracy and stability under different conditions and data characteristics. A prediction model based on improved MEEMD and a quasi-affine transformation (QUATRE)-optimized bidirectional long short-term memory (BILSTM) network has also been developed. In this model, MEEMD processes photovoltaic output data to extract key features, QUATRE optimizes these features, and BILSTM captures forward and backward dependencies in time series data. Simultaneously, MEEMD is applied to fault detection. A rotor fault detection method based on MEEMD energy entropy and an artificial neural network (ANN) has been developed. MEEMD decomposes the operational signals of the rotor and calculates energy entropy to construct a feature vector reflecting the energy distribution characteristics of the signal [64]. Another fault diagnosis method for reciprocating machinery based on improved MEEMD-SqueezeNet has also been proposed [65]. Researchers have further optimized MEEMD focusing on the crucial issue of noise in signal processing. To address the noise reduction problem in tunnel blasting vibration signals, a complete method based on MEEMD and least mean squares (LMS) has been developed. Additionally, a method combining MEEMD and singular value decomposition (SVD) is used to remove noise from high slope deformation data. MEEMD is employed for the initial decomposition of high slope deformation data, and SVD further processes the decomposed matrix to effectively eliminate noise, fully preserving the intrinsic details of the deformation data and providing a more accurate basis for subsequent data analysis and processing [66]. Strength and Weakness
* Suppression of modal aliasing and fusion of multi-physical field signals
* Parameter sensitivity, residual noise, and endpoint effect
* Algorithm generalization and poor adaptability to extreme working conditions  
On the one hand, MEEMD (multivariate ensemble empirical mode decomposition) possesses multiple advantages. First, it excels in mode mixing suppression and computational efficiency enhancement.