Accurate fault localization in power transmission line with wind penetration using variational mode decomposition and CNN-GRU architecture

High-precision laser ultrasonic VMD-TFM imaging of surface defects on rough surfaces of additive manufactured Ti-6Al-4V.

Collaborative optimization operation method of electrical-thermal‑hydrogen multi-energy storage system based on variable mode decomposition

Improving multi-step drought forecasting in Atlantic Canada through variational mode decomposition and machine learning: The role of sand-cat swarm optimization technique in kernel ridge regression

To address the limitation of harmonic monitoring on the low-voltage side of distribution networks, this paper proposes a multi-source harmonic estimation method based on variational mode decomposition. The method integrates short-term test data with long-term power data. First, dominant harmonic users are identified through a strategy that combines Fisher optimal segmentation and derivative dynamic time warping. Second, an electrical data transformation approach is designed by combining variational mode decomposition with Gramian angular fields, which maps the power signals of dominant harmonic users and low-voltage side harmonic signals into pseudo-color Gramian power images and grayscale Gramian harmonic images, respectively. Finally, an improved PSRGAN (pix2pix-super-resolution generative adversarial network) model is constructed to train and learn from these images, establishing the mapping relationship between power data and low-voltage side harmonic data of the distribution network, thereby enabling the migration and generation of long-term low-voltage side harmonic monitoring data. Simulation cases and field measurements validate the effectiveness and accuracy of the proposed method in multi-source harmonic scenarios. Moreover, the required data are easily accessible, demonstrating strong potential for engineering applications.

With the rapid penetration of photovoltaic (PV) generation into modern power grids, accurate and robust ultra-short-term PV power forecasting is increasingly important for real-time dispatch and frequency regulation. However, PV power series are volatile, nonlinear, and uncertain at short time scales, challenging conventional methods. This paper proposes a hybrid ultra-short-term forecasting framework that integrates secondary decomposition with advanced learning models. First, key features are screened and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) decomposes PV power into intrinsic mode functions (IMFs). Sample entropy quantifies IMF complexity, and K-means clusters IMFs into high- and low-frequency components. High-frequency components are further decomposed by Black-winged Kite Algorithm (BKA)-Variational Mode Decomposition (VMD) to enhance stationarity and reduce manual parameter tuning. The resulting high-frequency sub-signals are predicted using Online Kernel Extreme Learning Machine (OKELM), while low-frequency components are modeled by a Convolutional Neural Network (CNN)-Echo State Network (ESN) to capture spatiotemporal patterns. Final ultra-short-term forecasts are obtained via additive reconstruction. Experiments on datasets from the Ningxia PV station (China) and the Desert Knowledge Australia (DKA) Solar Energy Centre achieve [Formula: see text] values of 99.6987% and 99.0635% in comparative and validation experiments, respectively, demonstrating high accuracy across different geographic locations and seasons. Improved PV power forecasting reduces uncertainty, supports grid stability, enables more efficient dispatch and reserve scheduling, and lowers operating costs and curtailment.

Accurate pump energy consumption forecasting in long-distance water supply systems (LWSS) is crucial for operational scheduling optimisation and demand response. However, nonlinear variations in pump parameters during long-term operation often degrade the forecasting accuracy. To address this, this study proposes a novel hybrid framework, CV-CBiLSTM-Att, which integrates Chaos Particle Swarm Optimization (CPSO)-tuned Variational Mode Decomposition (VMD) with a deep learning network, utilising hydraulic flow rate as the primary predictor to capture the intrinsic nonlinear relationship between flow dynamics and pump energy consumption. Specifically, the CPSO algorithm is employed to minimise envelope entropy, globally searching for the optimal decomposition mode number (K) and penalty factor (α). This adaptive decomposition effectively disentangles the non-stationary flow rate signal into band-limited Intrinsic Mode Functions (IMFs), avoiding mode mixing and residual noise. Subsequently, a Convolutional Neural Network (CNN) extracts local invariant features from the multiscale IMFs, while a Bidirectional Long Short-Term Memory (BiLSTM) network captures long-range temporal dependencies. Crucially, an Attention mechanism is integrated to assign adaptive weights to pivotal hidden states, thereby enhancing the model's sensitivity to peak-valley transitions. Validated against 11 benchmark models using real-world LWSS operational data, the proposed framework demonstrates superior robustness. Experimental results indicate that the CV-CBiLSTM-Att model reduces the Root Mean Square Error (RMSE) by 68.06% compared to the baseline LSTM. Further, the model exhibits exceptional distributional consistency, achieving a Nash-Sutcliffe Efficiency (NSE) of 0.972, a Kling-Gupta Efficiency (KGE) of 0.976, and a negligible systematic bias (PBIAS < 0.1%), confirming its stability in capturing peak-to-valley energy dynamics. These findings verify that the proposed framework offers a highly accurate and reliable approach for energy management in LWSS.

Abstract Short-term air traffic flow prediction is crucial for urban air traffic management, increasingly recognized for its potential to reduce controller workload and enhance aviation safety in high-density metropolitan regions. Extensive research has been conducted in this area, yet these studies confront challenges such as the uncertainty, time variability, and sequential randomness of air traffic data, which obstruct precise short-term flow predictions. To address these issues, this research proposes a Multi-tiered Decomposition and Integration Model (MDIV), optimized through Variational Mode Decomposition, based on the actual operational conditions of airport terminal areas. Initially, an Optimized Variational Mode Decomposition approach is utilized to mitigate the noise impact on traffic flow data, considering its characteristics, complexity, and evolving patterns. Subsequently, a Multi-Level Integration Model is introduced to enhance the accuracy of long-term predictions. The simulation experiment shows that the MDIV model's performance on datasets, when compared with machine learning models and other benchmarks, demonstrates superior prediction accuracy, making it particularly effective for forecasting short-term air traffic flows in urban terminal areas. It provides the foundation for the digital construction of urban air traffic management and promotes the construction of humanmachine intelligent city.

Wind power generation exhibits pronounced volatility and intermittency, and direct grid connection may cause instability in grid frequency. To address this issue, this paper proposes an optimisation strategy for hybrid energy storage systems to mitigate wind power fluctuations, integrating lithium-ion batteries with supercapacitors within wind power systems. Firstly, the grid-connected power of wind turbines and the reference power of the energy storage system are determined through dynamic weight adjustment using a weighted filtering algorithm combining adaptive exponential smoothing and recursive averaging algorithms. Secondly, the fish-eagle optimisation algorithm is employed to refine variational modal decomposition parameters. The modal components derived from decomposing the energy storage system’s reference power are converted into Hilbert marginal spectra. Following determination of the cut-off frequency, high-frequency signal components are managed by supercapacitors, while low-frequency components are handled by lithium-ion batteries. Finally, an optimised configuration model for the hybrid energy storage system is constructed to minimise the annual lifecycle target cost. Case study analysis demonstrates that this approach effectively smooths fluctuations in wind power output while fully leveraging the complementary characteristics of both energy storage types, achieving a balance between system economics and overall performance.

This study presents an analytical comparison of three meta-heuristic optimization-based signal processing frameworks based on variational mode decomposition (VMD): particle swarm optimization-VMD (PSO-VMD), grey wolf optimizer-VMD (GWO-VMD), and whale optimization algorithm-VMD (WOA-VMD). The authors performed 44 milling experiments under variable machining parameters (spindle speed 500–3000 r/min; feed rate 20–120 mm/min; depth of cut 0.3–1.8 mm). The acoustic signals generated by each experiment were captured with a high-sensitivity microphone. The authors applied the three meta-heuristics to optimize the VMD parameters. The hybrid optimization-VMD methods were employed to adaptively adjust the parameters to efficiently decompose complex machining signals. Among the three methods, PSO-VMD produced the best results due to optimal convergence when selecting a mode number ( K = 8) and alpha values (range of 150–4300). The extracted intrinsic mode functions (IMFs) produced the tooth passing frequency (TPF) and its harmonics and the dominant chatter frequency (923 Hz) as well as two sidebands (1423 Hz &amp; 2248 Hz). Using multiscale permutation entropy (MPE) to analyze the time series data of the IMF components enabled the identification of stable versus unstable cutting regimes as well as the identification of significant changes in entropy as machining conditions changed. The authors report that PSO-VMD was superior to both GWO-VMD and WOA-VMD in terms of modal separation, spectral clarity and robustness to noise with a fitness score of 0.0657 being reported for PSO-VMD vs. 0.0703 for GWO-VMD and 0.0841 for WOA-VMD. The application of the PSO-VMD-MPE framework provides a viable, interpretable and computationally efficient methodology to monitor chatter in real-time within IoT-enabled machining environments.

The proliferation of Unmanned Aerial Vehicles (UAVs) poses a significant challenge for ISAR imaging. Conventional multi-target imaging methods, such as sequential CLEAN-based techniques, are often hindered by error propagation and sensitivity to noise, leading to degraded performance or even imaging failure, especially at low SNR. To address these issues, this paper proposes a novel robust imaging framework. The framework is built upon two key innovations: a partitioned block-wise compensation mechanism integrated with PSO for simultaneous and precise motion parameters estimation of multiple targets, which avoids local optima and error accumulation; and the application of Sequential Variational Mode Decomposition (SVMD) to adaptively separate and reconstruct signals, thereby suppressing inter-target aliasing and noise interference overlooked in prior studies. Simulations and measured-data experiments confirm that the proposed method maintains clear focusing and superior image quality even at low SNR, outperforming existing techniques in terms of image entropy, contrast, and resolution. This paper provides a robust and effective solution for high-resolution radar surveillance in complex multi-target scenarios.

ABSTRACT This study proposes short-term load forecasting scheme for integrated energy systems based on deep learning networks and evolutionary algorithm, in which the CNN-BiGRU-Attention model that integrates variational mode decomposition and crested porcupine optimization is presented for load forecasting. Extracting spatial features of load data through CNN (Convolutional Neural Networks, CNN), capturing temporal features through BiGRU (Bidirectional Gated Recurrent Unit, BiGRU) network, and enhancing key information weights through attention mechanism. Using variational mode decomposition technology to perform modal decomposition on the original load effectively eliminates random noise and extracts trend terms and harmonic components. Innovatively introducing crested porcupine optimization algorithm to adaptively optimize hyperparameters such as training times, number of neurons, and learning rate of BiGRU. The simulation results show that compared with the current prediction model, the proposed model has better load forecasting accuracy and stable error distribution, indicating that the model has superior performance. Verified the effectiveness of the model in spatiotemporal feature fusion and parameter optimization.

This paper tackles the challenge of accurately diagnosing rolling bearing faults under limited data conditions by introducing an integrated deep learning framework that synergistically combines Temporal Convolutional Networks (TCN), Bidirectional Gated Recurrent Unit (BiGRU), Attention mechanism, and Deep Q-Network (DQN)-based reinforcement learning. Conventional approaches frequently exhibit overfitting and poor generalization when labeled fault data is scarce. To address this limitation, our model leverages TCN’s capacity for parallelized long-term dependency modeling, BiGRU’s capability to capture bidirectional contextual features, and the Attention mechanism’s adaptive feature weighting capability. Unlike traditional methods that rely on static architectures or manual tuning, this study innovatively introduces a Deep Q-Network (DQN) agent as an external controller. This design theoretically enables the dynamic self-optimization of hyperparameters and network structures during training, ensuring robust convergence even under severe data scarcity. Additionally, a reinforcement learning strategy dynamically optimizes hyperparameters and network architecture during training, thereby enhancing convergence and robustness under data scarcity. The framework integrates advanced signal processing techniques, including Variational Mode Decomposition (VMD) for noise-resistant signal decomposition and maximum singular value energy entropy for effective feature fusion. Experimental results on benchmark bearing fault datasets demonstrate that the proposed model achieves a detection rate (DR) exceeding 80% with an error threshold of 0.195 and 90% with an error threshold of 0.2, significantly outperforming comparative models including LVQ, CNN, LSTM, and standalone TCN-BiGRU-Attention. Notably, at a 30% training sample size, the model improves DR by 3.21% and reduces the false alarm rate (FAR) by 4.13% compared to baseline methods. These results validate the method’s efficacy in achieving high diagnostic accuracy and stability under data-limited scenarios, providing a practical solution for intelligent fault diagnosis in industrial applications.

Ranging method of weak lidar signal based on manta ray foraging optimization and variational modal decomposition

Wildfire spots analysis and forecasting: Evaluation of univariate and multivariate based on variational mode decomposition models

A novel method based on variational mode decomposition for lie detection

Colony predation algorithm-based variational mode decomposition for multilevel color image segmentation with chaotic and simulated annealing techniques

A two-stage adaptive multivariate variational mode decomposition method for noise reduction

Multivariate variational mode decomposition combined with discrete Fourier transform and lightweight Mixture-of-Experts models for predicting multivariate time series with strong volatility

Adaptive successive variational mode decomposition for denoising ECG and arterial pulse waves