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Keywords = variational mode decomposition

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17 pages, 2452 KB  
Article
Daily Runoff Series Prediction Using GWO Optimization and Secondary Decomposition: A Case Study of the Xujiang River Basin
by Qingyan Li, Manxin Quan, Xuwen Ouyang, Shumin Zhou, Xiling Zhang and Xiangui Lan
Water 2026, 18(8), 946; https://doi.org/10.3390/w18080946 - 15 Apr 2026
Abstract
Runoff time series often exhibit nonlinear and fluctuating characteristics, and their complexity has further increased with the intensification of global climate change; high-precision daily-scale forecasting remains a core challenge in the field of hydrological forecasting. Addressing the shortcomings of existing methods in terms [...] Read more.
Runoff time series often exhibit nonlinear and fluctuating characteristics, and their complexity has further increased with the intensification of global climate change; high-precision daily-scale forecasting remains a core challenge in the field of hydrological forecasting. Addressing the shortcomings of existing methods in terms of runoff feature extraction capabilities and limited forecasting accuracy, this paper aims to improve the accuracy of daily runoff forecasting in small watersheds by constructing a hybrid forecasting model that integrates optimization algorithms, signal decomposition, and deep learning models. Specifically, the original runoff data is first preliminarily decomposed using a variational mode decomposition (VMD) method optimized by the grey wolf optimization (GWO) algorithm. The mode components obtained from the decomposition are evaluated using Fuzzy Entropy (FE), and the selected high-entropy components (IMFs) are then input into a second-order decomposition using an optimized Wavelet Transform (WT) to further extract latent features. After decomposition, the mode components are reassembled; second, a bidirectional long short-term memory (BiLSTM) model for daily runoff prediction is constructed for each subcomponent, and the model’s hyperparameters are optimized using an optimization algorithm; finally, the prediction results are reconstructed to obtain the final output. Case studies were conducted using three hydrological stations—Nanfeng, Baiquan, and Shaziling—in the Xujiang River basin of the Fuhe River. The experimental results indicate that by incorporating an optimization mechanism and a two-stage decomposition strategy, the proposed model achieved an NSE of over 0.95 at all three stations. Compared to the baseline BiLSTM model, the proposed model reduced the RMSE by 76.69%, 75.82%, and 65.92% at the three stations, respectively, and reduced the MAE by 64.77%, 73.54%, and 50.46%, and NSE increased by 27.82%, 40.06%, and 38.02%, respectively. This demonstrates that the model exhibits excellent reliability and superiority in daily-scale runoff forecasting for small watersheds. Full article
(This article belongs to the Section Hydrology)
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13 pages, 950 KB  
Communication
All-LCP Terahertz Metasensor with Dual Quasi-BIC Resonances for Dual-Range Refractive Index Sensing
by Yan Zhang, Mengya Pan, Qiankai Hong, Shengyuan Shen, Conghui Guo, Yaping Li, Yanpeng Shi and Yifei Zhang
Biosensors 2026, 16(4), 221; https://doi.org/10.3390/bios16040221 - 15 Apr 2026
Abstract
Terahertz (THz) metasurface biosensors still encounter difficulties in simultaneously achieving high spectral resolution and stable readout across different refractive-index regimes. In this work, an all-liquid-crystal-polymer (LCP) THz metasensor supporting dual quasi-bound states in the continuum (quasi-BIC) resonances is proposed for regime-dependent refractive-index sensing. [...] Read more.
Terahertz (THz) metasurface biosensors still encounter difficulties in simultaneously achieving high spectral resolution and stable readout across different refractive-index regimes. In this work, an all-liquid-crystal-polymer (LCP) THz metasensor supporting dual quasi-bound states in the continuum (quasi-BIC) resonances is proposed for regime-dependent refractive-index sensing. By introducing structural asymmetry into a periodic LCP cubic-cluster metasurface, two pronounced resonances are generated with quality factors (Q factors) of 6811 and 2526, respectively. Near-field distributions and multipole decomposition analysis indicate that the two resonances possess distinct electromagnetic features, which result in different responses to surrounding dielectric perturbations. In the low-refractive-index range of 1.0–1.5, the two resonance frequencies exhibit a linear variation with refractive index, yielding sensitivities of 122 GHz/RIU and 179 GHz/RIU, respectively. These dual-mode linear responses further offer a foundation for concentration- and temperature-related evaluation through analyte refractive-index mapping. In the higher-refractive-index range of 1.5–1.8, the intermodal frequency difference shows improved linearity with refractive index compared with the individual resonance frequencies, enabling a differential readout scheme with enhanced robustness against common perturbations. The results demonstrate that the proposed all-LCP dual-quasi-BIC metasensor not only enables high-resolution THz refractive-index sensing, but also establishes a regime-dependent spectral readout approach for different dielectric-response intervals. Full article
(This article belongs to the Section Optical and Photonic Biosensors)
17 pages, 3278 KB  
Article
Research on Wind Storage Coordinated Frequency Control Considering Optimal Power Allocation of Hybrid Energy Storage System
by Zhenzhen Kong, Yun Sun, Nanwei Guo, Gaojun Meng, Kun Zhao and Yongzhe Yu
Electronics 2026, 15(8), 1629; https://doi.org/10.3390/electronics15081629 - 14 Apr 2026
Viewed by 48
Abstract
To mitigate the volatility and instability caused by large-scale wind power integration in new-type power systems, hybrid energy storage systems (HESSs) can offer effective frequency support to wind farms. This paper presents a coordinated wind storage frequency control strategy that incorporates optimal power [...] Read more.
To mitigate the volatility and instability caused by large-scale wind power integration in new-type power systems, hybrid energy storage systems (HESSs) can offer effective frequency support to wind farms. This paper presents a coordinated wind storage frequency control strategy that incorporates optimal power allocation within an HESS. First, wind power output is decomposed and reconstructed into low- and high-frequency components via variational mode decomposition (VMD) optimized with the multi-verse optimization (MVO) algorithm, followed by the establishment of a PI-based HESS frequency response model. Second, an SOC-aware flexible frequency division strategy is designed by coordinating the participation sequence of the wind turbine and the HESS. The regulation process is divided into three stages, namely, wind turbine regulation, joint wind storage regulation, and HESS-dominant regulation, to suppress frequency fluctuations induced by wind power variations. Finally, primary frequency regulation performance indices are proposed and validated in a three-machine, nine-bus system. The simulation results demonstrate that the coordinated use of different storage types within the HESS enhances the grid-connected stability of the wind storage system, while the incorporation of hybrid storage improves wind power utilization. Full article
(This article belongs to the Special Issue Modeling and Control of Power Converters for Power Systems)
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18 pages, 3157 KB  
Article
Deep Learning-Based Distributed Photovoltaic Power Generation Forecasting and Installation Potential Assessment
by Jun Chen, Jiawen You and Huafeng Cai
Sustainability 2026, 18(8), 3859; https://doi.org/10.3390/su18083859 - 14 Apr 2026
Viewed by 75
Abstract
Against the backdrop of the global energy structure accelerating its transition towards a clean and low-carbon model, rooftop-distributed photovoltaic (PV) systems are playing an increasingly prominent strategic role in urban energy supply systems, owing to their notable advantages such as environmental friendliness and [...] Read more.
Against the backdrop of the global energy structure accelerating its transition towards a clean and low-carbon model, rooftop-distributed photovoltaic (PV) systems are playing an increasingly prominent strategic role in urban energy supply systems, owing to their notable advantages such as environmental friendliness and high spatial utilization efficiency. Consequently, they are becoming a critical pillar in advancing urban energy transformation and enhancing sustainable development. This paper aims to explore deep learning-based techniques for assessing the potential of large-scale distributed PV installations. To accurately evaluate their dynamic power generation capability, a hybrid prediction model integrating variational mode decomposition (VMD), the mutual information (MI) method, and a cascaded xLSTM-Informer network is proposed. Firstly, the model preprocesses key meteorological sequences using VMD, decomposing them into modal components of different frequencies. Subsequently, the MI method is employed to extract critical sequences. Then, the xLSTM module is utilized to learn the long-term complex dependencies between meteorological conditions and PV power output, while the Informer network captures key global temporal patterns, achieving high-precision time-series forecasting of PV generation. Finally, employing the forecasted time-series power curve as the core input, a comprehensive analytical framework for PV installation potential is constructed, integrating assessments of technical feasibility, economic viability, and environmental performance. This framework aims to scientifically estimate the admissible installed capacity and system value of distributed PV systems, thereby providing a dynamic basis for decision-making in urban planning. Full article
(This article belongs to the Section Energy Sustainability)
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22 pages, 4144 KB  
Article
Multiscale Nonlinear Forecasting of Government Bond Yields and Volatility via a Hybrid VMD–LSTM Framework
by Yingjie Xu, Baojie Guo, Yifan Chen and Xiwei Liu
Mathematics 2026, 14(8), 1297; https://doi.org/10.3390/math14081297 - 13 Apr 2026
Viewed by 173
Abstract
Government bond yields and volatility exhibit nonlinearity, complexity, and noise, making accurate forecasting challenging for conventional econometric or deep learning models alone. This study develops a multiscale nonlinear forecasting framework that combines variational mode decomposition (VMD) with a long short-term memory (LSTM) model [...] Read more.
Government bond yields and volatility exhibit nonlinearity, complexity, and noise, making accurate forecasting challenging for conventional econometric or deep learning models alone. This study develops a multiscale nonlinear forecasting framework that combines variational mode decomposition (VMD) with a long short-term memory (LSTM) model to forecast China’s government bond yields and volatility. By decomposing the time series into trend, periodic, and disturbance components, the hybrid model effectively captures both linear and nonlinear patterns while mitigating overfitting. In the empirical analysis, five loss functions—MSE, RMSE, MAE, MAPE, SMAPE—and the DM test are used as evaluation criteria to compare the predictive performance of ARIMA, SVM, LSTM, VMD-SVM, and VMD-LSTM models. Using the yields and volatility of 3-year government bonds as the benchmark case and 1-year government bonds for robustness tests, the results indicate that the VMD-LSTM model achieves superior predictive accuracy, demonstrating its effectiveness and robustness. The proposed hybrid model offers a novel framework for government bond yield forecasting, providing valuable insights for monetary policy and financial risk monitoring. Full article
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22 pages, 1240 KB  
Article
Single-Ended Fault Location Method for DC Distribution Network Based on Bi-LSTM
by Jiamin Lv, Ying Wang, Mingshen Wang, Qikai Zhao and Manqian Yu
Energies 2026, 19(8), 1866; https://doi.org/10.3390/en19081866 - 10 Apr 2026
Viewed by 179
Abstract
When a line short-circuit fault occurs in a DC distribution network, the fault current rises quickly and affects a wide range, jeopardizing the safe operation of the system. In order to locate the fault quickly and accurately, this study proposes a fault localization [...] Read more.
When a line short-circuit fault occurs in a DC distribution network, the fault current rises quickly and affects a wide range, jeopardizing the safe operation of the system. In order to locate the fault quickly and accurately, this study proposes a fault localization method based on the Variational Mode Decomposition (VMD) and Bidirectional Long Short-Term Memory (Bi-LSTM) networks. First, the nonlinear relationship between the intrinsic principal frequency and fault distance is analyzed; then, the intrinsic principal frequency of the faulty traveling wave is extracted by using VMD, and the nonlinear relationship between the spectral energy of the principal frequency of the intrinsic frequency and the fault distance is fitted by training the Bi-LSTM network incorporating the attention mechanism. Finally, in response to the issue that a small amount of fault data in practical engineering is difficult to support the amount of data required for deep learning, a transfer learning method is used to locate the fault in the target domain. A small sample test of the target domain is carried out using the migration learning method. The experimental results show that the proposed method has high localization accuracy and good resistance to over-resistance and noise; compared with the traditional network training, the localization error based on migration learning is smaller, and the network convergence effect is better. Full article
(This article belongs to the Section F1: Electrical Power System)
19 pages, 6501 KB  
Article
Study on Near-Field Spectral Characteristics and Vibration Control of Multi-Hole Blasting Based on VMD
by Dasong Zhang, Hongyan Xu, Hui Chen, Jinggang Zhang, Sifan Wei, Yuanxiang Mu and Fei Gao
Appl. Sci. 2026, 16(8), 3665; https://doi.org/10.3390/app16083665 - 9 Apr 2026
Viewed by 231
Abstract
To explore the spectral characteristics of near-field vibration signals from multi-hole millisecond-delay blasting in open-pit mines and the modulation effect of delay time on blasting energy distribution, field blasting vibration tests with multi-gradient delays were conducted taking an open-pit coal mine in Xinjiang [...] Read more.
To explore the spectral characteristics of near-field vibration signals from multi-hole millisecond-delay blasting in open-pit mines and the modulation effect of delay time on blasting energy distribution, field blasting vibration tests with multi-gradient delays were conducted taking an open-pit coal mine in Xinjiang as the engineering background. Particle Swarm Optimization (PSO) optimized Variational Mode Decomposition (VMD) and Hilbert-Huang Transform (HHT) were introduced for the refined processing and frequency band energy ratio analysis of the measured signals, and field vibration control tests were subsequently carried out. The results show that compared with the traditional Empirical Mode Decomposition (EMD), the PSO-optimized VMD can effectively overcome the mode aliasing phenomenon. By extracting the high-frequency Intrinsic Mode Function (IMF7) that characterizes the instantaneous detonation impulse, the actual delay time was successfully inverted to be 10.47 ms. The inter-hole delay time significantly affects the time-frequency distribution of vibration energy. Under the 25 ms delay condition, the energy ratio of the high-frequency band is the highest, and the low-frequency energy accumulation degree is the lowest, which is most conducive to shortening the vibration duration and accelerating energy attenuation. Control tests further confirmed that adopting a 17 ms delay in the near-slope area can effectively control the peak particle velocity (PPV) in the near field, while adopting a 23 ms delay in the middle and far areas can further reduce the low-frequency energy concentration. The research results demonstrate a dynamic matching strategy for millisecond delays based on spatial distance differences, which has important guiding significance for realizing safe and efficient blasting vibration control in open-pit mines. Full article
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14 pages, 3957 KB  
Article
Feature Extraction of Gear Tooth Surface Fatigue Failure in Reducers Based on Vibration Signals
by Zhenbang Cheng, Zhengyu Liu, Yu Zhou and Hongxin Wang
Algorithms 2026, 19(4), 290; https://doi.org/10.3390/a19040290 - 9 Apr 2026
Viewed by 174
Abstract
Extracting periodic fault pulses caused by gear surface fatigue in reducers is often hindered by transmission path interference and strong background noise. Moreover, the traditional Variational Mode Decomposition (VMD) and Maximum Correlation Kurtosis Decomposition (MCKD) method rely on manual parameter selection, which limits [...] Read more.
Extracting periodic fault pulses caused by gear surface fatigue in reducers is often hindered by transmission path interference and strong background noise. Moreover, the traditional Variational Mode Decomposition (VMD) and Maximum Correlation Kurtosis Decomposition (MCKD) method rely on manual parameter selection, which limits its practicality. To address these issues, this paper proposes a parameter-adaptive VMD-MCKD method based on vibration signals for extracting gear surface fatigue fault features. Using the reciprocal of the peak indicator squared of decomposed signals as fitness functions, the method employs the global search capability of the Sparrow Search Algorithm to adaptively select optimal VMD-MCKD configurations. The optimized VMD-MCKD method is applied to decompose gear surface fatigue fault signals, effectively filtering out noise while highlighting periodic fault pulses caused by gear fatigue. Envelope demodulation is then performed to extract characteristic frequency components of gear surface fatigue faults. Experimental results demonstrate that the proposed method can adaptively extract periodic fault pulse components from strong noise environments, achieving a 2-fold improvement in signal kurtosis and enhanced robustness. Full article
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29 pages, 6506 KB  
Article
A Hybrid VMD–Informer Framework for Forecasting Volatile Pork Prices
by Xudong Lin, Guobao Liu, Zhiguo Du, Bin Wen, Zhihui Wu, Xianzhi Tu and Yongjie Zhang
Agriculture 2026, 16(8), 827; https://doi.org/10.3390/agriculture16080827 - 8 Apr 2026
Viewed by 275
Abstract
Accurate forecasting of pork prices is important yet challenging because pork price series are highly volatile and non-stationary. Existing hybrid forecasting models often rely on fixed-weight integration, which may limit their ability to adapt to multi-scale temporal variation and complex temporal dependencies. To [...] Read more.
Accurate forecasting of pork prices is important yet challenging because pork price series are highly volatile and non-stationary. Existing hybrid forecasting models often rely on fixed-weight integration, which may limit their ability to adapt to multi-scale temporal variation and complex temporal dependencies. To address these issues, this study proposes VMD–EMSA–HCTM–Informer, a hybrid forecasting framework that combines signal decomposition with an enhanced encoder–decoder architecture. Variational Mode Decomposition (VMD) is first used to reduce signal non-stationarity by extracting intrinsic mode functions. Within the Informer backbone, an Enhanced Multi-Scale Attention (EMSA) encoder is introduced to capture local fluctuations at different temporal scales, while a Hybrid Convolutional–Temporal Module (HCTM) decoder is used to strengthen temporal feature extraction and channel interaction modeling. Empirical evaluation was conducted on daily pork price data from the China Pig Industry Network and a large-scale intensive breeding enterprise in southern China over the period 2013–2025. Under the current experimental setting, the proposed framework achieved the lowest average errors among the compared baselines across five independent runs, with an average MAE of 0.4875 and an average MAPE of 3.0540%. These results suggest that the proposed framework provides a useful and relatively stable univariate forecasting approach for volatile pork prices. However, the findings should be interpreted within the scope of the present dataset and experimental design, and future work will extend the framework to multivariate forecasting with exogenous drivers and uncertainty quantification. Full article
(This article belongs to the Section Agricultural Economics, Policies and Rural Management)
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24 pages, 67497 KB  
Article
A Physics-Guided Dual-Stream Vibration Feature Fusion Network for Chatter-Induced Surface Mark Diagnosis in Wafer Thinning
by Heng Li, Hua Liu, Liang Zhu, Xiangyu Zhao, Lemiao Qiu and Shuyou Zhang
Machines 2026, 14(4), 404; https://doi.org/10.3390/machines14040404 - 7 Apr 2026
Viewed by 263
Abstract
Ultra-precision thinning of hard and brittle materials like monocrystalline silicon demands high dynamic stability in thinning spindle. To address the challenge of accurately detecting subtle spindle chatter anomalies in industrial environments characterized by high noise and limited data, this paper proposes a physics-guided [...] Read more.
Ultra-precision thinning of hard and brittle materials like monocrystalline silicon demands high dynamic stability in thinning spindle. To address the challenge of accurately detecting subtle spindle chatter anomalies in industrial environments characterized by high noise and limited data, this paper proposes a physics-guided dual-stream attention fusion transfer network (PG-AFNet). First, a physics-guided signal preprocessing method was developed. Using variational mode decomposition (VMD) and continuous wavelet transform (CWT) masking, one-dimensional dynamic features and high-frequency regions of interest (ROIs) rich in transient impact features were extracted. Second, the PG-AFNet architecture was designed. By introducing an attention mechanism, it achieves deep integration of one-dimensional purely dynamic sequences with two-dimensional spatiotemporal visual textures to capture surface damage features caused by subtle vibrations. Finally, systematic validations were conducted using a real silicon wafer thinning dataset with 197 real samples. By overcoming small-sample limitations via physical augmentation, PG-AFNet achieved an 82.45% (86.64% after data augmentation) diagnostic accuracy, significantly outperforming traditional baselines. Furthermore, a large-scale cross-load validation on the diverse CWRU dataset yielded an exceptional 99.68% accuracy under mixed-load conditions, conclusively verifying the model’s robust domain generalization. Lastly, a rigorous ablation study explicitly quantified the indispensable contributions of the physics-guided dual-stream architecture and attention fusion. This research provides a feasible theoretical foundation for intelligent surface quality monitoring in semiconductor hard-brittle material processing. Full article
(This article belongs to the Special Issue Monitoring and Control of Machining Processes)
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21 pages, 5751 KB  
Article
A Hybrid VMD-Transformer-BiLSTM Framework with Cross-Attention Fusion for Aileron Fault Diagnosis in UAVs
by Yang Song, Weihang Zheng, Xiaoyu Zhang and Rong Guo
Sensors 2026, 26(7), 2256; https://doi.org/10.3390/s26072256 - 6 Apr 2026
Viewed by 368
Abstract
Aileron fault diagnosis in fixed-wing unmanned aerial vehicles (UAVs) faces significant challenges due to strong noise, multi-modal coupling, and limited fault samples. This paper presents a hybrid fault diagnosis framework that integrates variational mode decomposition (VMD) with a cross-attention-based feature fusion mechanism. First, [...] Read more.
Aileron fault diagnosis in fixed-wing unmanned aerial vehicles (UAVs) faces significant challenges due to strong noise, multi-modal coupling, and limited fault samples. This paper presents a hybrid fault diagnosis framework that integrates variational mode decomposition (VMD) with a cross-attention-based feature fusion mechanism. First, residual signals are generated from UAV kinematic models and decomposed into multi-scale intrinsic mode functions (IMFs) using VMD to extract multiscale frequency-localized features. An integrated framework is then constructed, where Transformer encoders capture the global features and bidirectional long short-term memory (BiLSTM) networks extract local temporal dynamics. To effectively combine these complementary features, a cross-attention fusion module is designed to focus on the discriminative time-frequency features. Furthermore, a hybrid pooling strategy integrating max pooling and attention pooling is introduced to enhance classification robustness. Experiments on the AirLab failure and anomaly (ALFA) dataset demonstrate that the proposed method achieves 95.12% accuracy with improved fault separability, outperforming VMD + BiLSTM (87.66%), VMD + Transformer (86.89%), Transformer + BiLSTM (84.83%), Transformer (72.24%), CNN + LSTM (94.05%), and HDMTL (94.86%). Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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17 pages, 9423 KB  
Article
Photovoltaic Power Prediction Based on Multi-Source Environmental Information Fusion Using a VMD-ZOA-LSTM Hybrid Mode
by Zixiu Qin, Hai Wei, Xiaoning Deng, Yi Zhang and Xuecheng Wang
Processes 2026, 14(7), 1166; https://doi.org/10.3390/pr14071166 - 4 Apr 2026
Viewed by 304
Abstract
New energy power generation has become the first choice for low-carbon reform in the energy industry due to its emission reduction characteristics and environmental friendliness. However, due to the fluctuating nature of renewable energy, sustaining consistent reliability and secure performance within the power [...] Read more.
New energy power generation has become the first choice for low-carbon reform in the energy industry due to its emission reduction characteristics and environmental friendliness. However, due to the fluctuating nature of renewable energy, sustaining consistent reliability and secure performance within the power network has become increasingly challenging. A novel ensemble prediction scheme for photovoltaic (PV) output is presented, leveraging multi-source environmental data fusion to enhance forecast precision. The relationship between environmental variables and PV generation is quantitatively assessed using Pearson’s correlation coefficient to isolate the most influential factors. Subsequently, the PV time-series data are decomposed via variational mode decomposition (VMD) to extract multi-scale dynamic patterns. The refined features are then utilized within a long short-term memory (LSTM) network, whose parameters are adaptively optimized by the zebra optimization algorithm (ZOA). Historical datasets comprising environmental observations and corresponding PV generation records from a representative power station serve as the empirical basis. Results reveal that the VMD-ZOA-LSTM framework achieves the lowest RMSE and MAE, reducing errors by over 50% relative to comparative models. Furthermore, its R2 metric outperforms that of the baseline LSTM and VMD-LSTM configurations by 2.05% and 1.19%, respectively, thereby substantiating the efficiency and validity of the proposed modeling strategy. Full article
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26 pages, 27074 KB  
Article
Entropy-Driven Adaptive Decomposition and Linear-Complexity Score Attention: An AI-Powered Framework for Crude Oil Financial Market Forecasting
by Jiale He, Chuanming Ma, Shouyi Wang, Yifan Zhai and Qi Tang
Entropy 2026, 28(4), 392; https://doi.org/10.3390/e28040392 - 1 Apr 2026
Viewed by 359
Abstract
The crude oil market has obvious financial entropy, and there are characteristics such as continuous uncertainty, multi-scale fluctuations and nonlinear state transitions. These characteristics bring challenges to the traditional prediction method. In this context, in order to improve the accuracy of energy financial [...] Read more.
The crude oil market has obvious financial entropy, and there are characteristics such as continuous uncertainty, multi-scale fluctuations and nonlinear state transitions. These characteristics bring challenges to the traditional prediction method. In this context, in order to improve the accuracy of energy financial market prediction, this study proposes an artificial intelligence-driven hybrid prediction framework, ALA-VMD-CASA. This framework is divided into three stages. First, with the goal of minimizing envelope entropy, ALA is introduced to adaptively optimize the hyperparameters of VMD, so as to generate informative sub-modes with reduced entropy. Next, the parallel prediction of each sub-mode is carried out by using the score attention mechanism based on the CNN autoencoder, and its linear time complexity can capture volatility clustering and sudden price fluctuations. Finally, the final price prediction is generated through the aggregation component. The empirical experiment of Brent crude oil spot prices from 2010 to 2025 shows that the ALA-VMD-CASA framework is superior to benchmark models such as ARIMA, RW, RWWD, LSTM, GRU, Transformer and Informer. Compared with the best standalone model, the proposed framework reduces the mean square error by more than 63% and obtains a perfect win rate in expanding-window evaluations. These results prove that the proposed framework is effective and robust for modeling financial entropy and improving energy price forecasting. Full article
(This article belongs to the Special Issue Entropy, Artificial Intelligence and the Financial Markets)
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22 pages, 5107 KB  
Article
Adaptive Filtering Method for Low-SNR Rock Mass Fracture Microseismic Signals in Deep-Buried Tunnels Considering Noise Intrusion Characteristics
by Tao Lin, Weiwei Tao, Yakang Xu and Wenjing Niu
Geosciences 2026, 16(4), 143; https://doi.org/10.3390/geosciences16040143 - 1 Apr 2026
Viewed by 259
Abstract
Aiming at the problems of microseismic signals from rock mass fracture in deep-buried tunnels with low signal-to-noise ratio (SNR) suffering from coupled interference of multi-source noise, and traditional filtering methods having fixed parameters and poor processing effects on spectral aliasing, this study proposes [...] Read more.
Aiming at the problems of microseismic signals from rock mass fracture in deep-buried tunnels with low signal-to-noise ratio (SNR) suffering from coupled interference of multi-source noise, and traditional filtering methods having fixed parameters and poor processing effects on spectral aliasing, this study proposes a ternary coupled adaptive filtering method integrating the Sparrow Search Algorithm, Variational Mode Decomposition and Wavelet Threshold Denoising (SSA-VMD-DWT). First, the noise intrusion characteristics of low-SNR microseismic signals in deep-buried tunnels were analyzed, and the filtering difficulties of white noise, low-frequency noise, high-frequency noise and non-stationary noise were clarified. Subsequently, a parameter optimization framework with the Sparrow Search Algorithm (SSA) as the core was constructed to optimize the key parameters, including the penalty factor α and modal number K of Variational Mode Decomposition (VMD), as well as the wavelet basis and decomposition layers of Wavelet Threshold Denoising (DWT), respectively. A dual-index threshold decision function based on kurtosis and correlation coefficient, and a wavelet packet entropy weighted reconstruction algorithm were designed to realize the collaborative adaptive adjustment of decomposition depth and threshold rules. Finally, the performance of the algorithm was verified through simulation signal experiments and an engineering case of a deep-buried tunnel in Southwest China. The results show that for the simulated signal with a low SNR of 2 dB, the SNR is increased to 12.43 dB, and the root mean square error is reduced to 2.36 × 10−7 after denoising by this algorithm, which is significantly superior to the Empirical Mode Decomposition (EMD) and traditional DWT methods. In the engineering case, the information entropy of the filtered signal is the lowest among all methods, which can effectively suppress multi-band noise and retain the core characteristics of microseismic signals from rock mass fracture, solving the problems of spectral aliasing, detail loss and empirical parameter setting of traditional methods. This method provides a new technical paradigm for the processing of low-quality microseismic signals in deep tunnel engineering and can improve the accuracy of monitoring and early warning for rock mass dynamic disasters. Full article
(This article belongs to the Special Issue New Trends in Numerical Methods in Rock Mechanics)
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22 pages, 10589 KB  
Article
An Improved Fault Diagnosis Method for Diesel Engines Based on Optimized Variational Mode Decomposition and Transformer-SVM
by Xiaoxin Ma, Shuyao Tian, Xianbiao Zhan, Hao Yan and Kaibo Cui
Processes 2026, 14(7), 1131; https://doi.org/10.3390/pr14071131 - 31 Mar 2026
Viewed by 243
Abstract
Due to the non-stationary and nonlinear characteristics of diesel engine vibration signals, fault features cannot be fully extracted, which limits fault diagnosis performance. To address this issue, an improved fault diagnosis method combining optimized Variational Mode Decomposition with a Transformer and Support Vector [...] Read more.
Due to the non-stationary and nonlinear characteristics of diesel engine vibration signals, fault features cannot be fully extracted, which limits fault diagnosis performance. To address this issue, an improved fault diagnosis method combining optimized Variational Mode Decomposition with a Transformer and Support Vector Machine is proposed. An improved dung beetle optimization algorithm is employed to obtain optimal parameters for Variational Mode Decomposition. The envelope entropy minimization principle is applied to select the optimal intrinsic mode functions after Variational Mode Decomposition, achieving signal denoising. Analysis of variance is integrated for feature significance testing to screen critical features. The selected features are fed into a Transformer network for training. At the final classification stage, the traditional SoftMax classifier is replaced with a Support Vector Machine classifier. Full article
(This article belongs to the Special Issue AI-Driven Safe and High-Quality Development in Process Industries)
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