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18 pages, 1998 KB  
Article
Experimental Study on Time-Frequency Analysis of Vibration Signals from an Active De-Icing Exciter on Transmission Lines
by Dongwang Fan, Bin Zhao, Mengxuan Li, Hao Wang and Lei Ding
Sensors 2026, 26(13), 4128; https://doi.org/10.3390/s26134128 - 30 Jun 2026
Viewed by 172
Abstract
In traditional mechanical de-icing technologies, the time-frequency evolution and spatial propagation mechanisms of transient high-frequency impact signals in flexible transmission lines remain unclear. To address this issue, transient impact responses were experimentally investigated using a full-scale transmission line model. An active de-icing exciter, [...] Read more.
In traditional mechanical de-icing technologies, the time-frequency evolution and spatial propagation mechanisms of transient high-frequency impact signals in flexible transmission lines remain unclear. To address this issue, transient impact responses were experimentally investigated using a full-scale transmission line model. An active de-icing exciter, featuring controllable impact energy and the potential for sustained online operation, was independently developed. High-frequency transient acceleration signals were acquired at multiple measurement points on a 20 m single-span line. The spatial distribution and time-frequency attenuation characteristics of the impact energy were quantitatively evaluated by extracting high-order time-domain statistical features, including root mean square, kurtosis, and crest factor, together with frequency-domain analyses based on Fast Fourier Transform (FFT) and wavelet entropy. The results indicate that: (1) The exciter generated highly impulsive transient responses, with a kurtosis up to 795.3 and a crest factor approaching 40. This suggests a strong local concentration of impact energy at the excitation source, which provides a dynamic basis for analyzing potential localized stress concentration and dynamic responses of the conductor system. (2) The transmission line structure exhibited a significant low-pass filtering effect on transient high-frequency shock waves. As the shock wave propagated towards the distal end, its high-frequency components above 30 Hz were substantially attenuated, likely due to internal dry friction within the stranded conductor. Consequently, the dominant frequency decreased to a low-frequency macroscopic sway of approximately 12 Hz, indicating a reduced risk of transmitting high-frequency shock loads to distal fittings and towers. (3) Under geometric nonlinear coupling, the vertical impact energy was partially transferred to the longitudinal and lateral directions during propagation, leading to sustained out-of-plane swaying. This study reveals the signal evolution characteristics of transient impacts in overhead transmission lines and provides experimental evidence for optimizing excitation parameters and assessing the engineering safety of active impact de-icing technologies. Full article
(This article belongs to the Section Electronic Sensors)
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29 pages, 2075 KB  
Article
A Multi-Criterion Selection of Hybrid Features in Mammographic Imaging for Early Computer-Assisted Sensing and Detection of Breast Cancer
by Amira J. Zaylaa, Lama N. Yassine and Silva Kourtian
Sensors 2026, 26(12), 3874; https://doi.org/10.3390/s26123874 - 18 Jun 2026
Viewed by 248
Abstract
Feature selection represents a critical step in developing accurate and interpretable models for early breast cancer detection. Despite extensive research in the field of mammographic image analysis, no consensus has yet been reached on the optimal feature subsets that distinguish normal from malignant [...] Read more.
Feature selection represents a critical step in developing accurate and interpretable models for early breast cancer detection. Despite extensive research in the field of mammographic image analysis, no consensus has yet been reached on the optimal feature subsets that distinguish normal from malignant tissues. To address this gap, the present study aims to identify the most discriminative and significant features through a comprehensive multi-criterion selection framework. The aim is to integrate, as new frameworks, different combinations of t-test, ANOVA, Mutual Information (MI), and Equal Grouping Methods (EGM) to rank 19 linear and nonlinear features extracted from mammographic images. The objective is to maximize feature relevance while minimizing redundancy and enhancing diagnostic and healthcare systems. Linear features were assessed alongside nonlinear descriptors. A framework combining t-test, ANOVA, and EGM, guided by MI relevance, was employed to balance feature contributions across categories. The experimental results demonstrated that hybrid feature selection significantly enhanced diagnostic accuracy using optimal linear and nonlinear attributes. The optimization results suggested using a hybrid of six linear and eight nonlinear features. Linear features were highly accurate for detecting cancer. Haralick entropy obtained the highest average accuracy and performance, 94.14% and 93.45%; followed by kurtosis, 93.49% and 92.59%; perimeter irregularity, 93.43% and 92.65%; skewness, 93.01% and 92.25%; and volume/area, 92.82% and 91.92%. Despite the reliable discriminative power of linear descriptors, their overall effectiveness in representing intricate tissue characteristics was limited. The comparison of statistical characteristics shows a distinct performance benefit of nonlinear descriptors over linear ones for detecting breast cancer. Nonlinear descriptors, however, showcased higher accuracy and performance, with an average accuracy of 97.81% in contrast to 94.43% for linear approaches. Local phase congruency achieved the top average accuracy and performance, 97.81% and 96.61%, respectively; succeeded by wavelet entropy, 97.62% and 96.42%; Laplacian spectrum features, 97.52% and 96.32%; nonlinear diffusion, 97.10% and 95.90%; and clustering coefficient, 96.70% and 95.50%; then Shannon, Tsallis, and Rényi entropies. The results indicate that statistically validated nonlinear characteristics significantly outperform linear ones across accuracy and performance measures. Their combination significantly improves the strength and discriminative power of computer-assisted breast cancer diagnostic systems, affirming their suitability for integration into sophisticated machine learning and deep learning models. The results also show that the new multi-criterion framework’s early detection performance surpassed that of the statistical and deep learning models explored, with an average of 98.6% accuracy, 98% sensitivity, 98.9% precision, and 98.4% F1 score of early detection of breast cancer. The incorporation of statistically validated nonlinear descriptors, particularly local phase congruency and wavelet entropy, improves the discriminative ability, robustness, and clinical understanding of breast cancer computer-assisted diagnostic systems. Overall, the proposed framework confirms that integrating hybrid features substantially enhances robustness and plays a pivotal role in computer-assisted breast cancer detection. These selected features may be fed to more advanced algorithms in the future, potentially yielding improved performance. Full article
(This article belongs to the Section Biomedical Sensors)
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20 pages, 9722 KB  
Article
Single-Photon Depth Reconstruction at Low Signal-Background Ratio Based on Four-Dimensional Attention Mechanism
by Senlin Feng, Tong Liu, Jianghua Cheng, Bang Cheng, Yahui Cai and Yunwang Zhang
Remote Sens. 2026, 18(12), 2006; https://doi.org/10.3390/rs18122006 - 16 Jun 2026
Viewed by 166
Abstract
Single-photon Light Detection and Ranging (LiDAR), which is capable of detecting single-photon signals, has developed rapidly in the field of long-range imaging. Due to the long detection range and limited laser power, the accumulated signal photons of single-photon LiDAR are extremely sparse. Meanwhile, [...] Read more.
Single-photon Light Detection and Ranging (LiDAR), which is capable of detecting single-photon signals, has developed rapidly in the field of long-range imaging. Due to the long detection range and limited laser power, the accumulated signal photons of single-photon LiDAR are extremely sparse. Meanwhile, the dark current counts, backscattering noise, and background noise of the single-photon detector are significant, resulting in an extremely low signal-background ratio of the detection data. However, existing algorithms struggle to accomplish the depth reconstruction on data with extremely low signal-to-background ratio (SBR). To address the challenges of complex spatiotemporal correlation and feature sparsity in long-range single-photon imaging depth reconstruction, we design a deep reconstruction algorithm based on a classification formulation, specifically tailored for single-echo detection scenarios. We propose a wavelet denoising preprocessing module and a four-dimensional attention module to learn the spatiotemporal correlations of the photon-counting cube data. Sawtooth-arranged dilated convolutions are utilized during the pixel-wise denoising process to extract sparse features, and non-local total variation regularization combined with cross-entropy is introduced as a joint loss function. For depth reconstruction of data with an SBR of 1:100, the root-mean-square error is less than 0.022 m, which is 66.72% lower than that of the best baseline algorithm. It also achieves promising depth reconstruction results on data with an SBR of 1:300. Full article
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16 pages, 5836 KB  
Article
Partial Discharge Signal Denoising for Gas-Insulated Switchgear Using Spearman Coefficient-Optimized VMD and Combined Filtering Algorithm
by Changxiong Xia, Wei Xie, Changfei Deng and Changjin Hao
Energies 2026, 19(12), 2805; https://doi.org/10.3390/en19122805 - 11 Jun 2026
Viewed by 200
Abstract
Partial discharge (PD) signals acquired from gas-insulated switchgear (GIS) are often severely contaminated by discrete-spectrum interference and periodic narrowband noise, which impairs the accuracy of subsequent fault diagnosis. This paper proposes a hybrid denoising method that integrates Spearman coefficient-optimized variational mode decomposition (S_VMD), [...] Read more.
Partial discharge (PD) signals acquired from gas-insulated switchgear (GIS) are often severely contaminated by discrete-spectrum interference and periodic narrowband noise, which impairs the accuracy of subsequent fault diagnosis. This paper proposes a hybrid denoising method that integrates Spearman coefficient-optimized variational mode decomposition (S_VMD), spatially related recursive sample entropy (Sdr_SampEn) for intrinsic mode function (IMF) classification, an improved wavelet threshold function, and Savitzky–Golay (SG) filtering. First, the Spearman correlation coefficient between the original signal and the reconstructed signal is used to adaptively determine the optimal mode number K of VMD, avoiding the over- and under-decomposition problems of conventional VMD. Second, Sdr_SampEn, which characterizes signal irregularity along both the Chebyshev distance and spatial direction of a recurrence plot, is employed to classify the obtained IMFs into noise-dominant and PD-dominant components, with the discrimination threshold calibrated as p = 1.94 at 0 dB. Third, an improved wavelet threshold function—continuous at the threshold and asymptotically unbiased—is applied to the noise-dominant components, while SG filtering is applied to the PD-dominant components, after which the denoised signal is reconstructed. The results demonstrate that the proposed method effectively suppresses both white and narrowband noise while preserving the detailed morphology of PD pulses. Full article
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25 pages, 3141 KB  
Article
Ground and Low-Altitude Target Classification in Cluttered Radar Remote Sensing via Velocity-Aware Multi-Feature Fusion
by Peilong Hu, Liyu Tian, Mengze Zhang and Zhongshan Zhang
Remote Sens. 2026, 18(11), 1788; https://doi.org/10.3390/rs18111788 - 1 Jun 2026
Viewed by 243
Abstract
Classification of ground and low-altitude targets in radar remote sensing is challenging because environmental clutter and noise can significantly degrade the discriminability of target echoes, especially under complex outdoor observation conditions. To improve the classification performance for humans, vehicles, and unmanned aerial vehicles [...] Read more.
Classification of ground and low-altitude targets in radar remote sensing is challenging because environmental clutter and noise can significantly degrade the discriminability of target echoes, especially under complex outdoor observation conditions. To improve the classification performance for humans, vehicles, and unmanned aerial vehicles (UAVs), this paper proposes a velocity-aware multi-feature fusion method based on measured radar echo data. First, radar echoes are preprocessed using a wavelet-decomposition-based strategy to suppress clutter and noise while preserving useful target information. Then, multiple complementary features, including wavelet packet energy distribution, spectral entropy, spectral standard deviation, temporal standard deviation, amplitude dispersion coefficient, and relative radar cross-section (RCS), are extracted to characterize the target echoes from different perspectives. Considering the influence of target velocity on Doppler distribution and class separability, the measured data are further divided into different velocity intervals for stratified classification. Based on the fused feature vectors, a long short-term memory (LSTM) network is employed to model feature relationships and perform target classification. Experiments conducted on real measured radar echo data demonstrate that the proposed method achieves classification accuracies of 97.82% for UAVs, 96.00% for vehicles, and a mean interval-level accuracy of 96.94%, indicating its effectiveness for ground and low-altitude target classification in cluttered radar remote sensing environments. Full article
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38 pages, 42009 KB  
Article
Urban Morphology-Oriented Streetscape Segmentation via Hierarchical Transformer and Frequency-Aware Feature Learning
by Xiyue Guan and Kejun Luo
Buildings 2026, 16(11), 2180; https://doi.org/10.3390/buildings16112180 - 29 May 2026
Viewed by 494
Abstract
Semantic segmentation of street-view imagery has become an important computational tool for urban morphological analysis and the evaluation of street spatial quality. However, existing methods still struggle in complex urban environments. Major challenges include large variations in building façade scales, degradation of boundary [...] Read more.
Semantic segmentation of street-view imagery has become an important computational tool for urban morphological analysis and the evaluation of street spatial quality. However, existing methods still struggle in complex urban environments. Major challenges include large variations in building façade scales, degradation of boundary information, and severe class imbalance. These issues limit the ability of current models to capture structurally meaningful urban forms. To address these challenges, this study proposes a high-resolution street-view segmentation framework, termed HieraWaveSeg. The model aims not only to improve pixel-level segmentation accuracy but also to enhance the interpretability of urban morphology through structured representations of street space. Specifically, a Hiera Transformer backbone is employed to capture hierarchical spatial semantics. A Path Aggregation Network is further introduced to strengthen cross-scale feature interaction and improve structural consistency in complex scenes. In addition, a Wave Fusion module based on the Haar wavelet transform is incorporated to preserve fine-grained architectural details by enhancing high-frequency boundary and texture information during decoding. Unlike conventional segmentation approaches that primarily focus on object recognition, this study introduces a morphology-oriented semantic reconfiguration strategy. This strategy reorganizes original categories into functionally meaningful urban units. As a result, the segmentation outputs can be more directly linked to urban morphological indicators, such as façade continuity, spatial enclosure, and interface permeability, thereby improving interpretability in architectural and urban design contexts. To further address class imbalance, a composite loss function combining weighted cross-entropy and Dice loss is adopted, together with a median frequency balancing strategy. Experimental results on the CamVid and Cityscapes datasets demonstrate that the proposed method consistently outperforms several state-of-the-art baselines in both segmentation accuracy and structural preservation. Beyond quantitative improvements, the results indicate that the proposed framework generates more coherent and morphologically meaningful urban representations, supporting further quantitative analysis in urban morphology and architectural studies. Full article
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20 pages, 2325 KB  
Article
Time-Frequency, Complexity, and Fractal Analyses of Hemoglobin and Deoxyhemoglobin Responses to Quantify Mechanisms of Actions of Cupping Therapy
by Nasrin Dabirian, Mansoureh Samadi, Amir Babaniamansour, Yameng Li, Manuel E. Hernandez and Yih-Kuen Jan
Entropy 2026, 28(6), 597; https://doi.org/10.3390/e28060597 - 27 May 2026
Viewed by 298
Abstract
Cupping therapy has been demonstrated to improve hemodynamic regulation. Existing studies have reported mean changes of oxyhemoglobin (OxyHb) and deoxyhemoglobin (DeoxyHb), which do not capture the multi-scale regulatory dynamics of the microvasculature. It is therefore unclear whether cupping therapy modulates the complexity and [...] Read more.
Cupping therapy has been demonstrated to improve hemodynamic regulation. Existing studies have reported mean changes of oxyhemoglobin (OxyHb) and deoxyhemoglobin (DeoxyHb), which do not capture the multi-scale regulatory dynamics of the microvasculature. It is therefore unclear whether cupping therapy modulates the complexity and fractal property of hemodynamic signals. The objective of this study was to examine complexity of hemodynamic response to cupping therapy. A 2 by 2 factorial design with repeated measures was used to examine the main effect of pressure (−225 and −300 mmHg) and duration (5 and 10 min) and their interaction. A near infrared spectroscopy (NIRS) was used to measure OxyHb and DeoxyHb concentrations before and after cupping therapy. A total of 18 healthy participants were enrolled in this study. The wavelet analysis, sample entropy and detrended fluctuation analysis (DFA) were used to quantify the oscillatory, complexity, and fractal scaling properties of OxyHb and DeoxyHb signals. A two-way ANOVA with Bonferroni correction was used to examine the main and interaction effects. The results demonstrated that the combined effects of pressure and duration, rather than either factor independently, were the primary determinants of the dynamic hemodynamic response to cupping therapy, with significant Pressure × Duration interactions observed in DeoxyHb myogenic wavelet power (F = 4.636, p = 0.046, η2p = 0.214), OxyHb (F = 5.704, p = 0.029, η2p = 0.251) and DeoxyHb (F = 6.600, p = 0.020, η2p = 0.280) sample entropy, and DeoxyHb DFA scaling exponent (F = 5.598, p = 0.030, η2p = 0.248). In addition, cupping pressure selectively modulated neurogenic DeoxyHb oscillatory power (F = 5.001, p = 0.039, η2p = 0.227), and cupping duration significantly altered the fractal scaling properties of DeoxyHb signals (F = 7.775, p = 0.013, η2p = 0.314). The findings indicate that the interaction of pressure and duration of cupping therapy could effectively modulate hemodynamic responses. To the best of our knowledge, this is the first study investigating the complexity of hemodynamic responses after cupping therapy. Full article
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22 pages, 1060 KB  
Article
Phase-Faithful Compression for Marine Parallel Phase-Shifting Digital Holography via Spatiotemporal Decomposition
by Xinran Liu and Haoran Meng
Appl. Sci. 2026, 16(10), 4879; https://doi.org/10.3390/app16104879 - 13 May 2026
Viewed by 282
Abstract
Continuous in situ marine holographic observation generates data volumes that challenge onboard storage and transmission. Parallel phase-shifting digital holography (PPSDH) is especially sensitive to compression because phase retrieval depends on consistent four-channel demodulation. We present a training-free spatiotemporal compression framework for sparse-particle marine [...] Read more.
Continuous in situ marine holographic observation generates data volumes that challenge onboard storage and transmission. Parallel phase-shifting digital holography (PPSDH) is especially sensitive to compression because phase retrieval depends on consistent four-channel demodulation. We present a training-free spatiotemporal compression framework for sparse-particle marine PPSDH sequences based on background–residual decomposition and a shared four-channel processing path. The background is coded once per temporal window by a discrete wavelet transform (DWT) followed by principal component analysis (PCA), and the dynamic residual is decorrelated by temporal principal component analysis before quantization and entropy coding. The framework is evaluated on three primary 64-frame marine PPSDH sequences using a common reconstruction-and-evaluation pipeline with wrapped-phase root-mean-square error (PhaseRMSE) as the primary metric and amplitude peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) as secondary references; expanded supplementary checks are also reported for nine additional selected 64-frame groups spanning sparse to transitional occupancy. On the primary sequence and within the high-fidelity achieved-rate overlap with the JPEG Pleno anchor codec INTERFERE, the proposed framework reduces PhaseRMSE by about 3.3-fold to 3.4-fold while increasing amplitude PSNR by about 11 dB and preserving amplitude SSIM above 0.99997. Lower-bitrate sweeps further quantify the rate–fidelity trade-off rather than claiming universal low-rate superiority. These results support BG–Res spatiotemporal coding as a practical phase-fidelity-oriented option for the tested sparse-to-transitional marine PPSDH conditions; extension to dense scenes, broader marine conditions, and downstream biological tasks requires separate validation. Full article
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18 pages, 27124 KB  
Article
Research on Plantar Signal Measurement and Foot Arch Classification
by Jinyu Zhu, Baoqing Nie and Chuanhao Yu
Electronics 2026, 15(10), 2051; https://doi.org/10.3390/electronics15102051 - 11 May 2026
Viewed by 356
Abstract
The foot arch functions as a dynamic biomechanical system, maintained by the integrated actions of bones, ligaments, and muscles. A large body of clinical evidence indicates that, in addition to congenital foot deformities, acquired variations in the foot arch caused by factors such [...] Read more.
The foot arch functions as a dynamic biomechanical system, maintained by the integrated actions of bones, ligaments, and muscles. A large body of clinical evidence indicates that, in addition to congenital foot deformities, acquired variations in the foot arch caused by factors such as poor gait, aging, weight, or injury can significantly affect quality of life. Early intervention upon detection of foot arch changes can help mitigate progression and prevent further deterioration. Despite the availability of multimodal sensor-integrated running platforms for gait analysis, such systems are inherently bulky and not conducive to routine walking measurement. To overcome the above limitations, this study employed a flexible plantar pressure insole with an integrated accelerometer and a dedicated acquisition circuit to capture plantar pressure and acceleration data. This smart insole system acquires plantar data, performs feature extraction via time–domain and wavelet analysis, and then employs machine learning to classify the foot arch type as a normal foot, flatfoot, or high-arched. A Random Forest classifier was then established to categorize foot arch types based on the collected data, which integrates numerous decision trees through bootstrap aggregation and random feature selection, with final classification determined by majority voting. A total of 30 volunteers participated, including 11 with normal arches, 11 with flat feet, and 8 with high arches. Compared with support vector machine, K nearest neighbors, and decision tree, the Random Forest achieved the highest recognition accuracy of 92%. This system reveals the patterns of plantar pressure distribution and acceleration fluctuations during walking across three foot arches and demonstrates that wavelet entropy can effectively quantify the changes in signal complexity included in foot arch differences. Compared with laboratory force plates, this system features lower cost and a smaller form factor, making it suitable for real-time monitoring. This system can lay the technical foundation for personalized foot orthopedics and health monitoring. Full article
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25 pages, 3616 KB  
Article
Simultaneous Decompositions of Two Sets of Five Quaternion Tensors and Applications in Color Videos Processing
by Zhuo-Heng He, Yu-Fei Jiang, Mei-Ling Deng and Shao-Wen Yu
Mathematics 2026, 14(9), 1558; https://doi.org/10.3390/math14091558 - 5 May 2026
Viewed by 365
Abstract
This paper extends the theory of equivalence canonical forms from quaternion matrices to quaternion tensors under the Einstein product. Motivated by recent results on the simultaneous decomposition of two specific configurations of five quaternion matrices, we establish a comprehensive framework for the corresponding [...] Read more.
This paper extends the theory of equivalence canonical forms from quaternion matrices to quaternion tensors under the Einstein product. Motivated by recent results on the simultaneous decomposition of two specific configurations of five quaternion matrices, we establish a comprehensive framework for the corresponding configurations of five quaternion tensors. The core approach leverages bijective transformation maps that establish isomorphisms between quaternion tensor spaces and matrix spaces, allowing us to systematically construct invertible transformation tensors that simultaneously reduce the given tensor quintuples to canonical forms consisting solely of binary entries (0 and 1). A detailed structural analysis of the resulting canonical tensor forms is provided, including explicit dimension formulas for all identity blocks derived from precise rank conditions. To demonstrate practical utility, we integrate the proposed tensor decomposition with the discrete wavelet transform to construct a color video encryption and decryption system. Experimental results confirm perfect reconstruction (PSNR exceeding 300 dB, SSIM equal to 1) and strong security performance: NPCR of 49.8%, UACI of 49.6%, information entropy of 0.9986 bits per pixel, adjacent pixel correlation below 0.03 in absolute value, and a key space exceeding 2512. The developed theory significantly extends the existing literature on quaternion tensor decompositions and provides powerful tools for multidimensional signal processing. Full article
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26 pages, 10500 KB  
Article
Lossless Frequency-Domain Image Encryption via 3D Exponential Hyper-Chaotic Map and Integer Lifting Wavelet Transform
by Xiangqun Shi, Yifan Su, Xiaole Yang, Wei Feng, Xian Zhang, Zhenhua Chen, Guangjun Wen and Heping Wen
Axioms 2026, 15(5), 315; https://doi.org/10.3390/axioms15050315 - 28 Apr 2026
Cited by 3 | Viewed by 496
Abstract
To resolve the inherent conflict between high robustness and strict reversibility in frequency-domain image encryption, as well as to eliminate data expansion caused by floating-point errors, this paper presents a novel lossless frequency-domain image encryption scheme via 3D exponential hyper-chaos and integer lifting [...] Read more.
To resolve the inherent conflict between high robustness and strict reversibility in frequency-domain image encryption, as well as to eliminate data expansion caused by floating-point errors, this paper presents a novel lossless frequency-domain image encryption scheme via 3D exponential hyper-chaos and integer lifting wavelet transform (ILWT). Firstly, a 3D hyper-chaotic exponential sine map (3D-HESM) is constructed by introducing nonlinear exponential coupling, providing a high-entropy keystream source with wider chaotic ranges than traditional maps. Secondly, to guarantee lossless reconstruction, the ILWT is employed to diffuse image coefficients in the frequency domain. By integrating modular arithmetic into the lifting steps, this transform confines coefficients within the finite integer ring, effectively solving the data expansion problem while maintaining perfect mathematical reversibility. Thirdly, an adaptive key generation protocol is designed by fusing SHA-512 with Singular Value Decomposition (SVD). Leveraging the geometric stability of singular values, this mechanism establishes a balance between extreme sensitivity to plaintext alterations and tolerance to channel noise. Experimental results and security analyses demonstrate that the proposed scheme achieves a vast key space and resists differential attacks. Furthermore, it exhibits superior robustness against data cropping and noise interference compared to state-of-the-art methods, validating its suitability for secure and lossless image transmission. Full article
(This article belongs to the Special Issue Nonlinear Dynamical System and Its Applications)
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37 pages, 64444 KB  
Article
A WTD-WOA-SVMD-Based Signal Processing Method for Stress Distortion Zones in Coiled Tubing
by Xu Luo, Huan Yang, Wenbo Jiang, Luqi Lin, An Mao and Li Kou
Processes 2026, 14(9), 1404; https://doi.org/10.3390/pr14091404 - 28 Apr 2026
Viewed by 433
Abstract
As critical equipment in the petroleum industry, coiled tubing is prone to safety hazards, including stress concentrations and fatigue failure, under complex operating conditions. An online enhanced metal magnetic memory detection method was employed to reduce noise in surface magnetic field signals from [...] Read more.
As critical equipment in the petroleum industry, coiled tubing is prone to safety hazards, including stress concentrations and fatigue failure, under complex operating conditions. An online enhanced metal magnetic memory detection method was employed to reduce noise in surface magnetic field signals from tubing subjected to 35 MPa of internal pressure across different fatigue cycles. Conventional signal processing methods have difficulty effectively extracting characteristic magnetic field signals in high-noise environments; therefore, a comprehensive comparison of the noise reduction effectiveness of five common signal processing techniques in stress-distorted regions was conducted, an in-depth analysis of the limitations of different methods was performed, and a hybrid noise reduction framework combining wavelet threshold denoising (WTD) and sequential variational modal decomposition (SVMD) was established. Concurrently, the whale optimization algorithm (WOA), which possesses global search capabilities and demonstrates good adaptability to multi-parameter coupling issues in hybrid denoising frameworks, was innovatively proposed for key parameter optimization. Using fuzzy entropy (FE) as an evaluation metric, the experimental results demonstrated that magnetic field signals in all directions achieved at least a 1.03% reduction in FE and a minimum increase of 33.1% in integrated side lobe ratio (ISLR). This provided effective technical support for reliably detecting stress-distortion zones on coiled-tubing surfaces and established the engineering necessity of implementing preventive maintenance. Full article
(This article belongs to the Section Process Control, Modeling and Optimization)
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23 pages, 2091 KB  
Article
A Photovoltaic Power Prediction Method Based on Wavelet Convolutional Neural Networks and Improved Transformer
by Yibo Zhou, Zihang Liu, Zhen Cheng, Hanglin Mi, Zhaoyang Qin and Kangyangyong Cao
Energies 2026, 19(9), 2040; https://doi.org/10.3390/en19092040 - 23 Apr 2026
Viewed by 470
Abstract
The output power of photovoltaic (PV) systems is influenced by various environmental factors, exhibiting strong nonlinearity and non-stationarity, which poses significant challenges for accurate forecasting. To address these issues, this paper proposes a short-term PV power forecasting method based on wavelet convolutional neural [...] Read more.
The output power of photovoltaic (PV) systems is influenced by various environmental factors, exhibiting strong nonlinearity and non-stationarity, which poses significant challenges for accurate forecasting. To address these issues, this paper proposes a short-term PV power forecasting method based on wavelet convolutional neural networks and an improved Transformer. First, the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is employed to decompose the original PV power sequence into several intrinsic mode functions (IMFs). Fuzzy entropy is then utilized to evaluate the complexity of each component, and subsequences with similar entropy values are reconstructed to reduce the non-stationarity of the original series. Subsequently, Pearson correlation coefficients and the maximal information coefficient (MIC) are applied to capture both linear and nonlinear relationships between each reconstructed component and meteorological features, enabling the selection of strongly correlated variables. On this basis, a wavelet convolutional network (WTConv) is introduced to perform multi-scale decomposition and frequency-band feature extraction on the reconstructed components by integrating wavelet transform with convolution operations, effectively expanding the receptive field and extracting deep-seated features of the sequences. Finally, an improved iTransformer model is adopted for time-series modeling, leveraging its inverted encoding structure and self-attention mechanism to fully capture long-term dependencies among multivariate variables. The proposed model is validated using actual power data from a PV plant in Ningxia, China, across four seasons. Comprehensive experiments, including ablation studies, comparative analyses, loss function convergence evaluation, and Diebold–Mariano significance tests, are conducted to thoroughly assess the model’s effectiveness and superiority. Experimental results demonstrate that the proposed model achieves excellent prediction accuracy and stability in spring, summer, autumn, and winter, showing strong potential for engineering applications. Full article
(This article belongs to the Section A2: Solar Energy and Photovoltaic Systems)
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25 pages, 7570 KB  
Article
Relationship of Multifractal and Entropic Properties of Global Seismic Noise with Major Earthquakes, 1997–2025
by Alexey Lyubushin and Eugeny Rodionov
Fractal Fract. 2026, 10(4), 267; https://doi.org/10.3390/fractalfract10040267 - 17 Apr 2026
Viewed by 696
Abstract
A method for analyzing long-term (1997–2025) continuous records of low-frequency global seismic noise measured at a network of 229 broadband seismic stations distributed across the Earth’s surface is proposed in this study. The method is based on the use of nonlinear multifractal and [...] Read more.
A method for analyzing long-term (1997–2025) continuous records of low-frequency global seismic noise measured at a network of 229 broadband seismic stations distributed across the Earth’s surface is proposed in this study. The method is based on the use of nonlinear multifractal and entropy statistics, evaluated daily in successive time intervals, of first-principal component analysis, correlation analysis, and parametric models of point process intensity. The relationships between changes in seismic noise properties and the response of noise properties to the irregularity of the Earth’s rotation with the sequence of strong earthquakes, including those of a predictive nature, are investigated. Full article
(This article belongs to the Special Issue Fractals in Earthquake and Atmospheric Science)
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17 pages, 2510 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
Viewed by 558
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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