✅ Author Profile: A Matlab simulation developer passionate about research, skilled in data processing, modeling simulation, program design, obtaining complete code, reproducing papers, and scientific simulation.
🍎 Previous reviews, follow the personal homepage:Matlab Research Studio
🍊 Personal motto: Investigate to gain knowledge, complete Matlab code and simulation consultation available via private message.
🔥 Content Introduction
1. Research Background
In the field of signal processing, Multivariate Variational Mode Decomposition (MVMD) is an advanced adaptive signal decomposition method that can decompose complex multivariate signals into multiple modal components with different characteristics. It is widely used in mechanical fault diagnosis, biomedical signal analysis, financial time series processing, and other fields. However, the MVMD algorithm faces challenges in practical applications, such as the difficulty in determining parameters, where the selection of key parameters like the number of decomposition modes directly affects the accuracy and effectiveness of the decomposition results. Inappropriate parameter settings may lead to modal aliasing, over-decomposition, or under-decomposition, reducing the quality of signal decomposition and subsequently affecting the reliability of tasks such as feature extraction and fault diagnosis based on signal decomposition.
The Sparrow Search Algorithm (SSA) is a novel population intelligence optimization algorithm that simulates the foraging and anti-predation behavior of sparrows for global optimization, possessing strong global search capabilities and convergence speed. Applying SSA to MVMD parameter optimization can leverage its efficient optimization characteristics to automatically search for the best parameter combinations for MVMD, enhancing the accuracy and reliability of signal decomposition, thus providing more effective technical support for related fields in signal processing.
2. Core Technical Principles
2.1 Sparrow Search Algorithm (SSA)
SSA simulates the role-switching between discoverers and followers during the foraging process of sparrows and their anti-predation behavior. In the algorithm, the sparrow population is divided into two categories: discoverers and followers. Discoverers are responsible for searching for areas rich in food resources in the solution space, possessing a larger search range and higher fitness, and update their positions according to the following formula:
2.2 Multivariate Variational Mode Decomposition (MVMD)
MVMD is developed based on Variational Mode Decomposition (VMD) for processing multivariate signals. Its core is to construct and solve a variational model that decomposes multivariate signals into multiple modal components. Each modal component corresponds to a specific center frequency and bandwidth. By optimizing the variational model, the sum of the estimated bandwidths of all modal components is minimized while ensuring that the decomposed modal components can accurately reconstruct the original multivariate signal.
Specifically, MVMD transforms the signal decomposition problem into a constrained variational problem. By introducing a quadratic penalty term and Lagrange multipliers, it is converted into an unconstrained variational problem, which is iteratively solved using the Alternating Direction Method of Multipliers (ADMM) to obtain each modal component and its corresponding center frequency, achieving adaptive decomposition of multivariate signals.
3. The Process of SSA Optimizing MVMD
3.1 Determining Optimization Parameters and Objective Function
In SSA-MVMD, the key parameters of MVMD (such as the number of decomposition modes
K etc.) are treated as variables in the search space of the SSA algorithm. The design of the objective function is crucial for optimization, typically based on the rationality and effectiveness of each modal component after signal decomposition. For example, the sum of the kurtosis of each modal component after decomposition can be chosen as the objective function, as kurtosis reflects the impact characteristics of the signal. The larger the sum of kurtosis, the more sufficient the extraction of impact features from the signal, indicating better decomposition results. The expression for the objective function is:
⛳️ Running Results
📣 Sample Code
🔗 References
🎈 Some theoretical references are from online literature; if there is any infringement, please contact the author for deletion.
👇 Follow me to receive a wealth of Matlab e-books and mathematical modeling materials
🏆 The team specializes in custom MATLAB simulation guidance across various research fields, helping to realize research dreams:
🌈 Improvements and applications of various intelligent optimization algorithms
Production scheduling, economic scheduling, assembly line scheduling, charging optimization, workshop scheduling, departure optimization, reservoir scheduling, three-dimensional packing, logistics site selection, cargo location optimization, bus scheduling optimization, charging station layout optimization, workshop layout optimization, container ship loading optimization, pump combination optimization, medical resource allocation optimization, facility layout optimization, visual domain base station and drone site selection optimization, knapsack problem, wind farm layout, time slot allocation optimization, optimal distributed generation unit allocation, multi-stage pipeline maintenance, factory-center-demand point three-level site selection problem, emergency supply distribution center site selection, base station site selection, road lamp post arrangement, hub node deployment, transmission line typhoon monitoring devices, container scheduling, unit optimization, investment portfolio optimization, cloud server combination optimization, antenna linear array distribution optimization, CVRP problem, VRPPD problem, multi-center VRP problem, multi-layer network VRP problem, multi-center multi-vehicle VRP problem, dynamic VRP problem, two-layer vehicle routing planning (2E-VRP), electric vehicle routing planning (EVRP), hybrid vehicle routing planning, mixed flow shop problem, order splitting scheduling problem, bus scheduling optimization problem, flight shuttle vehicle scheduling problem, site selection path planning problem, port scheduling, port bridge scheduling, parking space allocation, airport flight scheduling, leak source localization
🌈 Time series, regression, classification, clustering, and dimensionality reduction in machine learning and deep learning
2.1 BP time series, regression prediction, and classification
2.2 ENS voice neural network time series, regression prediction, and classification
2.3 SVM/CNN-SVM/LSSVM/RVM support vector machine series time series, regression prediction, and classification
2.4 CNN|TCN|GCN convolutional neural network series time series, regression prediction, and classification
2.5 ELM/KELM/RELM/DELM extreme learning machine series time series, regression prediction, and classification
2.6 GRU/Bi-GRU/CNN-GRU/CNN-BiGRU gated neural network time series, regression prediction, and classification
2.7 Elman recurrent neural network time series, regression prediction, and classification
2.8 LSTM/BiLSTM/CNN-LSTM/CNN-BiLSTM long short-term memory neural network series time series, regression prediction, and classification
2.9 RBF radial basis function neural network time series, regression prediction, and classification