## 3 Adaptive Time-Frequency Analysis
### Variational Mode Decomposition and Optimization Models
#### 3.2.2 Successive Variational Mode Decomposition  
Definition  
Successive variational mode decomposition (SVMD) is a signal decomposition method proposed by [PERSON] and [PERSON] [90] that does not require prior knowledge of the number of modes in the signal. Through an iterative optimization process, SVMD decomposes the signal into multiple intrinsic mode functions (IMFs), each representing a specific frequency component of the signal. Application  
Research on the underlying principles of self-adaptive variational mode decomposition (SVMD) has yielded comprehensive findings and in-depth insights [91]. One such method is the self-adjusting SVMD, which adaptively updates the mode number K and penalty parameter \(\alpha\) based on the energy ratio and frequency-domain mode orthogonality, thereby addressing the issues of parameter selection and poor adaptability in the original variational mode decomposition (VMD). Ref. [90] introduces a novel signal decomposition approach termed continuous variational mode decomposition (also abbreviated as SVMD in this context) that obviates the need for prior knowledge of the number of signal modes and boasts lower computational complexity and higher robustness. In terms of lateral development, SVMD has been integrated with other network models. One example is a milling chatter detection method based on SVMD and a deep attention information fusion network, which extracts chatter features from multi-channel time-series signal data for detection [92]. It can also be combined with the instantaneous linear mixture model, resulting in the SMVMD method, which adaptively extracts joint or common modes from multi-channel signals. Furthermore, SVMD has been combined with other signal processing techniques. An improved Wigner-Ville distribution method based on SVMD [93] is used for the time-frequency analysis of multicomponent signals, reducing cross-terms and enhancing signal reconstruction accuracy. In [94], a new method called narrowband constraint-enhanced continuous variational mode decomposition (NCESVMD) is proposed which improves signal decomposition by introducing a minimum bandwidth constraint. Given the inherent characteristics of SVMD, parameter optimization is also a crucial aspect of optimizing the model. In [95], an ultra-weak fiber Bragg grating (UWFBG) hydrophone array-enhanced distributed acoustic sensing (DAS) system based on optimized SVMD and matched interference methods is proposed for noise resistance, with SVMD parameters optimized using the RIME algorithm. Ref. [96] demonstrates the combination of spatial dependency recursive sample entropy and improved wavelet thresholding for noise reduction. In [97], researchers introduce a dual-end traveling wave fault location method based on SVMD and frequency-dependent propagation velocity. This method extracts the intrinsic mode functions of the signal through SVMD and uses the Teager energy operator to determine the arrival time of the traveling wave. Additionally, researchers have designed adaptive SVMD algorithms that dynamically adjust decomposition parameters based on signal characteristics to avoid falling into local optimal solutions. Strength and Weakness  
* [noitemsep,topsep=0 pt]
* Insensitive to initial values and successive extraction
* Prone to getting trapped in local optimal solutions
* Limited parallelism resulting in low real-time efficiency Unlike the traditional variational mode decomposition method, SVMD (successive variational mode decomposition) extracts signals by successively implementing the variational mode decomposition technique. SVMD decomposes multicomponent signals into a series of band-limited intrinsic mode functions (IMFs) in a successive manner, whereas in the VMD method, modes are extracted concurrently. This successive approach eliminates the need for prior knowledge of the number of modes to be extracted, which is a significant advantage in practical applications where the mode count may be unknown or variable [90].