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🔥 Content Introduction
In the field of signal processing and data analysis, efficiently extracting signal features and decomposing complex signals has always been a hot topic and challenge. Multivariate Variational Mode Decomposition (MVMD), as an advanced signal decomposition technique, can decompose complex signals into multiple intrinsic mode functions (IMFs) with different characteristics, but it has certain limitations in parameter selection. The Whale Optimization Algorithm (WOA), with its excellent global optimization capability, provides a new approach for optimizing MVMD. The WOA-MVMD method, which combines WOA and MVMD, is becoming a powerful tool for solving many practical problems.
1. Algorithm Principles: Exploring the Secrets of WOA and MVMD
1.1 Whale Optimization Algorithm (WOA)
WOA is a meta-heuristic optimization algorithm inspired by the hunting behavior of humpback whales. When hunting, humpback whales use a “spiral bubble net” strategy. WOA simulates this process by surrounding the prey, spiraling upward to update positions, and randomly searching for prey in three stages to find the optimal solution. In the prey surrounding stage, the algorithm updates the whale’s position based on the current best solution, gradually approaching the prey; in the spiral upward position update stage, it uses logarithmic spirals to simulate the whale’s movement trajectory during hunting, achieving position updates; the random search for prey stage generates random positions to avoid the algorithm getting trapped in local optima, enhancing global search capability. With its simple principles and minimal parameter settings, WOA has demonstrated strong optimization performance in various fields such as function optimization and engineering design.
1.2 Multivariate Variational Mode Decomposition (MVMD)
MVMD is an adaptive signal decomposition method based on variational models. Compared to traditional signal decomposition methods, such as Empirical Mode Decomposition (EMD), it overcomes issues like mode mixing and can more accurately decompose complex signals into multiple intrinsic mode functions (IMFs) with specific frequency characteristics. MVMD transforms the signal decomposition problem into a variational constraint problem by constructing a variational model, using the Alternating Direction Method of Multipliers (ADMM) for iterative solving, thus obtaining each modal component. In practical applications, MVMD plays an important role in fault diagnosis, vibration signal analysis, etc., but the decomposition effect of this algorithm is sensitive to parameters such as the number of decomposed modes, making appropriate parameter settings key to achieving ideal decomposition results.
2. WOA-MVMD: Implementation Process of Algorithm Fusion
2.1 Determining Optimization Objectives and Parameters
When applying WOA to optimize MVMD, the first step is to clarify the optimization objectives. Typically, the optimization objectives are related evaluation metrics of each modal component after decomposition, such as minimizing reconstruction error to restore the original signal as closely as possible; or maximizing the kurtosis value of modal components to highlight impact features in the signal, facilitating applications like fault diagnosis. At the same time, it is necessary to determine the parameters that need to be optimized in MVMD, commonly including the number of decomposed modes K and the secondary penalty factor α.
2.2 Application of Whale Optimization Algorithm
The parameters of MVMD are encoded as the position vector of the whale, with each whale representing a set of parameter combinations for MVMD. During the iteration process of WOA, the fitness value of each whale is calculated based on the set optimization objectives, continuously updating the whale’s position through the three stages of surrounding prey, spiraling upward to update positions, and randomly searching for prey, i.e., adjusting the parameters of MVMD. After multiple iterations, when the algorithm meets the stopping conditions (such as reaching the maximum number of iterations or convergence of fitness values), the optimal whale position corresponding to the parameter combination is the optimized MVMD parameters.
2.3 Improved MVMD Decomposition
Substituting the optimized parameters into the MVMD algorithm, the original signal is decomposed. At this point, due to the optimization of parameters through WOA, MVMD can more accurately extract signal features, yielding decomposition results that better meet practical needs, enhancing the accuracy and reliability of analysis in applications such as signal denoising, feature extraction, and fault diagnosis.
⛳️ Running Results
📣 Sample Code
🔗 References
🎈 Some theoretical references are from online literature; if there is any infringement, please contact the author for removal.
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