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Search Results (1,663)

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Keywords = second-order networks

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18 pages, 1245 KB  
Article
A Coordinated Planning Method for Flexible Distribution Networks Oriented Toward Power Supply Restoration and Resilience Enhancement
by Man Xia, Botao Peng, Bei Li, Lin Gan, Jiayan Liu and Gang Lin
Processes 2026, 14(2), 218; https://doi.org/10.3390/pr14020218 - 8 Jan 2026
Abstract
In recent years, the increasing frequency of extreme weather events, the large-scale integration of distributed generation into distribution networks, and the widespread application of new power electronic devices have posed severe challenges to the security of power supply in distribution networks. To enhance [...] Read more.
In recent years, the increasing frequency of extreme weather events, the large-scale integration of distributed generation into distribution networks, and the widespread application of new power electronic devices have posed severe challenges to the security of power supply in distribution networks. To enhance the power supply reliability of the distribution network while considering its economic efficiency, this paper proposes a collaborative planning method for a flexible distribution network focused on power supply restoration and resilience enhancement In this method, a planning model for flexible distribution networks is established by optimally determining the siting and sizing of soft open point (SOP), with the objective of minimizing the annual comprehensive cost of the distribution network under multiple operational and planning constraints. Second-order cone programming (SOCP) relaxation and polyhedral approximation-based linearization techniques are employed to reformulate and solve the model, thereby obtaining the optimal siting and sizing Case for SOPs. Finally, simulations are conducted on a modified IEEE 33-bus test system to verify the effectiveness of the proposed method. The results show that, through appropriate siting and sizing of SOPs, outage loss costs can be significantly reduced, nodal voltage profiles can be improved, and load support can be provided to de-energized areas, leading to a reduction of more than 70% in the annual comprehensive cost of the distribution network and an improvement in the system reliability index from 99% to 99.999%, thus effectively enhancing both the economic efficiency and reliability of the distribution system. Full article
(This article belongs to the Section Energy Systems)
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26 pages, 9984 KB  
Article
Multi-Fidelity Data and Prior-Enhanced Physics-Informed Neural Networks for Multi-Parameter Identification of Prestressed Concrete Beams with Unquantifiable Noise
by Yuping Zhang, Yifan Yang, Yubo Hu and Zengwei Guo
Appl. Sci. 2026, 16(2), 608; https://doi.org/10.3390/app16020608 - 7 Jan 2026
Abstract
Although PINNs have demonstrated strong predictive capabilities in forward problems, their performance in inverse problems remains inadequate, largely due to unquantifiable noise encountered during the multi-parameter identification of prestressed concrete beams. Experimental measurements are often noisy, sparse, or asymmetric, while numerical or analytical [...] Read more.
Although PINNs have demonstrated strong predictive capabilities in forward problems, their performance in inverse problems remains inadequate, largely due to unquantifiable noise encountered during the multi-parameter identification of prestressed concrete beams. Experimental measurements are often noisy, sparse, or asymmetric, while numerical or analytical models, although physically consistent, are typically approximate and lack regularization from well-defined multi-fidelity data. To address this limitation, this paper proposed a multi-fidelity data and prior-enhanced physics-informed neural network (MF-rPINN), which integrates multi-fidelity data with physics prior relational constraints to guide parameter identification using only sparse experimental observations. The MF-rPINN architecture is designed to enforce consistency between each training iteration and a prescribed set of experimental measurements, while embedding the second-order displacement function into the loss function. Experimental results demonstrate that the proposed MF-rPINN achieves accurate parameter identification even under noisy and incomplete observations, owing to the combined regularization effects of governing physical laws and the second-order displacement prior. The minimum relative errors of the elastic modulus are −6.49% and −9.32% under different and identical loading conditions, respectively, while the minimum relative errors of the prestress force are 0.65% and 4.51%. Compared with classical analytical approaches, MF-rPINN exhibits superior robustness and is capable of predicting continuous displacement fields of prestressed concrete beams while simultaneously identifying prestress force and elastic modulus. These advantages highlight the potential of MF-rPINN as a reliable surrogate modeling tool for practical engineering applications. Full article
(This article belongs to the Section Civil Engineering)
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40 pages, 6176 KB  
Article
Price-Calibrated Network Loss–Carbon Emission Co-Optimization for Radial Active Distribution Networks via DistFlow-Based MISOCP Reconfiguration
by Ziyan Li, Yongjie Wang, Yang Si and Xiaobin Gao
Sustainability 2026, 18(1), 544; https://doi.org/10.3390/su18010544 - 5 Jan 2026
Viewed by 119
Abstract
Active distribution networks (ADNs) with high DER penetration require coordinated decisions to ensure voltage security, limit losses, and support low-carbon targets. However, most reconfiguration-centric studies prioritize loss/cost and rarely integrate carbon pricing and emission accounting into a unified framework with verifiable optimality. This [...] Read more.
Active distribution networks (ADNs) with high DER penetration require coordinated decisions to ensure voltage security, limit losses, and support low-carbon targets. However, most reconfiguration-centric studies prioritize loss/cost and rarely integrate carbon pricing and emission accounting into a unified framework with verifiable optimality. This study develops a DistFlow-based mixed-integer second-order cone programming (MISOCP) model that co-optimizes feeder reconfiguration and resource active/reactive dispatch under a price-calibrated loss–emission objective. The framework coordinates PV/WT generation, MTs, aggregated PHEVs (V2G), and reactive-support devices (SVCs and switched capacitor banks (CBs)) and is solved by commercial CPLEX to global optimality for the SOCP-relaxed problem. On the IEEE 33-bus feeder, device coordination reduces losses from 0.203 MW to 0.0382 MW (81.18%) and CO2 emissions from 2.3872 to 0.3433 tCO2 (85.62%), while reducing operating cost from CNY 354.9357 to CNY 56.6271 (84.05%). Enabling reconfiguration further reduces losses to 0.0205 MW (89.90%), emissions to 0.2580 tCO2 (89.19%), and operating cost to CNY 37.4677 (89.44%), while keeping voltages within 0.99–1.01 p.u. Relative to device-only operation, reconfiguration yields 46.34% loss reduction, 24.85% emission reduction, and 33.83% operating-cost reduction. The mixed-integer optimality gap is ~10−7, and the solution quality for the original non-convex model depends on the tightness of the SOCP relaxation, which is numerically tight in the cases we studied. These results show interpretable technical and environmental gains via coordinated dispatch and topology control in radial ADNs at scale. Full article
(This article belongs to the Special Issue Sustainable Management for Distributed Energy Resources)
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17 pages, 2897 KB  
Article
Green Hybrid Biopolymeric Beads for Efficient Removal of Copper Ions from Aqueous Solutions: Experimental Studies Assisted by Monte Carlo Simulation
by Ilias Barrak, Ikrame Ayouch, Zineb Kassab, Youness Abdellaoui, Jaber Raissouni, Said Sair, Mounir El Achaby and Khalid Draoui
Analytica 2026, 7(1), 5; https://doi.org/10.3390/analytica7010005 - 5 Jan 2026
Viewed by 154
Abstract
The objective of this research is to develop environmentally friendly, risk-free and effective adsorbent composite beads that remove Cu(II) ions from aqueous solutions using cost-effective biopolymers (Carboxymethylcellulose (CMC) and sodium alginate (AL)). The synthesized hydrogel beads (AL@CMC) were dried using two drying modes, [...] Read more.
The objective of this research is to develop environmentally friendly, risk-free and effective adsorbent composite beads that remove Cu(II) ions from aqueous solutions using cost-effective biopolymers (Carboxymethylcellulose (CMC) and sodium alginate (AL)). The synthesized hydrogel beads (AL@CMC) were dried using two drying modes, namely air-drying and freeze-drying, and characterized using scanning electron microscopy (SEM), Fourier Transform Infrared Spectroscopy (FT-IR), and Brunauer–Emmett–Teller (BET) analysis. The study investigated factors such as pH, adsorbent dosage, reaction time, Cu(II) ions concentration, and temperature to elucidate the adsorption mechanisms involved in removing copper ions. The results indicated that the hydrogel exhibited a maximum adsorption capacity of 99.05 mg·g−1, which is highly competitive compared to previous studies; the AL@CMC beads prepared in this work show a significantly higher adsorption capacity, improved stability due to the interpenetrated biopolymer network, and a clear enhancement from freeze-drying, which greatly increases porosity and active surface area. In addition, the pseudo-second-order nonlinear kinetic model best described the experimental data, implying the chemical nature of the adsorption process. Furthermore, the thermodynamic studies revealed that the adsorption process was endothermic, spontaneous, and homogenous. A Monte Carlo simulation model was utilized to ensure compatibility with the adsorption mechanism, in order to delve deeper into the intricacies of the adsorption process and gain a more comprehensive understanding of its underlying mechanisms and behavior. In conclusion, the prepared hydrogel beads proved to be an effective adsorbent for efficiently removing copper ions, making them a promising solution for addressing Cu(II) ion pollution. Full article
(This article belongs to the Section Sample Pretreatment and Extraction)
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22 pages, 5960 KB  
Article
JFDet: Joint Fusion and Detection for Multimodal Remote Sensing Imagery
by Wenhao Xu and You Yang
Remote Sens. 2026, 18(1), 176; https://doi.org/10.3390/rs18010176 - 5 Jan 2026
Viewed by 95
Abstract
Multimodal remote sensing imagery, such as visible and infrared data, offers crucial complementary information that is vital for time-sensitive emergency applications like search and rescue or disaster monitoring, where robust detection under adverse conditions is essential. However, existing methods’ object detection performance is [...] Read more.
Multimodal remote sensing imagery, such as visible and infrared data, offers crucial complementary information that is vital for time-sensitive emergency applications like search and rescue or disaster monitoring, where robust detection under adverse conditions is essential. However, existing methods’ object detection performance is often suboptimal due to task-independent fusion and inherent modality inconsistency. To address this issue, we propose a joint fusion and detection approach for multimodal remote sensing imagery (JFDet). First, a gradient-enhanced residual module (GERM) is introduced to combine dense feature connections with gradient residual pathways, effectively enhancing structural representation and fine-grained texture details in fused images. For robust detection, we introduce a second-order channel attention (SOCA) mechanism and design a multi-scale contextual feature-encoding (MCFE) module to capture higher-order semantic dependencies, enrich multi-scale contextual information, and thereby improve the recognition of small and variably scaled objects. Furthermore, a dual-loss feedback strategy propagates detection loss to the fusion network, enabling adaptive synergy between low-level fusion and high-level detection. Experiments on the VEDAI and FLIR-ADAS datasets demonstrate that the proposed detection-driven fusion framework significantly improves both fusion quality and detection accuracy compared with state-of-the-art methods, highlighting its effectiveness and high potential for mission-critical multimodal remote sensing and time-sensitive application. Full article
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24 pages, 2236 KB  
Article
Radar HRRP Sequence Target Recognition Based on a Lightweight Spatiotemporal Fusion Network
by Xiang Li, Yitao Su, Xiaobin Zhao, Junjun Yin and Jian Yang
Sensors 2026, 26(1), 334; https://doi.org/10.3390/s26010334 - 4 Jan 2026
Viewed by 196
Abstract
High-resolution range profile (HRRP) sequence recognition in radar automatic target recognition faces several practical challenges, including severe category imbalance, degradation of robustness under complex and variable operating conditions, and strict requirements for lightweight models suitable for real-time deployment on resource-limited platforms. To address [...] Read more.
High-resolution range profile (HRRP) sequence recognition in radar automatic target recognition faces several practical challenges, including severe category imbalance, degradation of robustness under complex and variable operating conditions, and strict requirements for lightweight models suitable for real-time deployment on resource-limited platforms. To address these problems, this paper proposes a lightweight spatiotemporal fusion-based (LSTF) HRRP sequence target recognition method. First, a lightweight Transformer encoder based on group linear transformations (TGLT) is designed to effectively model temporal dynamics while significantly reducing parameter size and computation, making it suitable for edge-device applications. Second, a transform-domain spatial feature extraction network is introduced, combining the fractional Fourier transform with an enhanced squeeze-and-excitation fully convolutional network (FSCN). This design fully exploits multi-domain spatial information and enhances class separability by leveraging discriminative scattering-energy distributions at specific fractional orders. Finally, an adaptive focal loss with label smoothing (AFL-LS) is constructed to dynamically adjust class weights for improved performance on long-tail classes, while label smoothing alleviates overfitting and enhances generalization. Experiments on the MSTAR and CVDomes datasets demonstrate that the proposed method consistently outperforms existing baseline approaches across three representative scenarios. Full article
(This article belongs to the Special Issue Radar Target Detection, Imaging and Recognition)
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22 pages, 1784 KB  
Article
Automated Severity and Breathiness Assessment of Disordered Speech Using a Speech Foundation Model
by Vahid Ashkanichenarlogh, Arman Hassanpour and Vijay Parsa
Information 2026, 17(1), 32; https://doi.org/10.3390/info17010032 - 3 Jan 2026
Viewed by 117
Abstract
In this study, we propose a novel automated model for speech quality estimation that objectively evaluates perceptual dysphonia severity and breathiness in audio samples, demonstrating strong correlation with expert ratings. The proposed model integrates Whisper encoder embeddings with Mel spectrograms augmented by second-order [...] Read more.
In this study, we propose a novel automated model for speech quality estimation that objectively evaluates perceptual dysphonia severity and breathiness in audio samples, demonstrating strong correlation with expert ratings. The proposed model integrates Whisper encoder embeddings with Mel spectrograms augmented by second-order delta features combined with a sequential-attention fusion network feature mapping path. This hybrid approach enhances the model’s sensitivity to phonetic, high-level feature representation, and spectral variations, enabling more accurate predictions of perceptual speech quality. A sequential-attention fusion network feature mapping module captures long-range dependencies through the multi-head attention network, while LSTM layers refine the learned representations by modeling temporal dynamics. Comparative analysis against state-of-the-art methods for dysphonia assessment demonstrates our model’s better correlation with clinician’s judgments across test samples. Our findings underscore the effectiveness of ASR-derived embeddings alongside the deep feature mapping structure in disordered speech quality assessment, offering a promising pathway for advancing automated evaluation systems. Full article
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15 pages, 1295 KB  
Article
Two-Stage Wiener-Physically-Informed-Neural-Network (W-PINN) AI Methodology for Highly Dynamic and Highly Complex Static Processes
by Dillon G. Hurd, Yuderka T. González, Jacob Oyler, Spencer Wolfe, Monica H. Lamm and Derrick K. Rollins
Stats 2026, 9(1), 6; https://doi.org/10.3390/stats9010006 - 1 Jan 2026
Viewed by 223
Abstract
Our new Theoretically Dynamic Regression (TDR) modeling methodology was recently applied in three types of real data modeling cases using physically based dynamic model structures with low-order linear regression static functions. Two of the modeling cases achieved the validation set modeling [...] Read more.
Our new Theoretically Dynamic Regression (TDR) modeling methodology was recently applied in three types of real data modeling cases using physically based dynamic model structures with low-order linear regression static functions. Two of the modeling cases achieved the validation set modeling goal of rfit,val  0.9. However, the third case, consisting of eleven (11) type one (1) sensor glucose data sets, and thus, eleven individual models, all fail considerably short of this modeling goal and the average  rfit,val, r¯fit,val = 0.68. For this case, the dynamic forms are highly complex 60 min forecast, second-order-plus-dead-time-plus-lead (SOPDTPL) structures, and the static form is a twelve (12) input first-order linear regression structure. Using these dynamic structure results, the objective is to significantly increase  rfit for each of the eleven (11) modeling cases using the recently developed Wiener-Physically-Informed-Neural-Network (W-PINN) approach as the static modeling structure. Two W-PINN stage-two static structures are evaluated–one developed using the JMP® Pro Version 16, Artificial Neural Network (ANN) toolbox and the other developed using a novel ANN methodology coded in Python version, 3.12.3. The JMP r¯fit,val = 0.74 with a maximum of 0.84. The Python r¯fit,val = 0.82 with a maximum of 0.93. Incorporating bias correction, using current and past SGC residuals, the Python estimator improved the average r¯fit,val from 0.82 to 0.87 with the maximum still 0.93. Full article
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19 pages, 4790 KB  
Article
Hierarchical Fuzzy Adaptive Observer-Based Fault-Tolerant Consensus Tracking for High-Order Nonlinear Multi-Agent Systems Under Actuator and Sensor Faults
by Lei Zhao and Shiming Chen
Sensors 2026, 26(1), 252; https://doi.org/10.3390/s26010252 - 31 Dec 2025
Viewed by 300
Abstract
This paper investigates the consensus tracking problem for a class of high-order nonlinear multi-agent systems subject to actuator faults, sensor faults, unknown disturbances, and model uncertainties. To effectively address this problem, a hierarchical fault-tolerant control framework with fuzzy adaptive mechanisms is proposed. First, [...] Read more.
This paper investigates the consensus tracking problem for a class of high-order nonlinear multi-agent systems subject to actuator faults, sensor faults, unknown disturbances, and model uncertainties. To effectively address this problem, a hierarchical fault-tolerant control framework with fuzzy adaptive mechanisms is proposed. First, a distributed output predictor based on a finite-time differentiator is constructed for each follower to estimate the leader’s output trajectory and to prevent fault propagation across the network. Second, a novel state and actuator-fault observer is designed to reconstruct unmeasured states and detect actuator faults in real time. Third, a sensor-fault compensation strategy is integrated into a backstepping procedure, resulting in a fuzzy adaptive consensus-tracking controller. This controller guarantees the uniform boundedness of all closed-loop signals and ensures that the tracking error converges to a small neighborhood of the origin. Finally, numerical simulations validate the effectiveness and robustness of the proposed method in the presence of multiple simultaneous faults and disturbances. Full article
(This article belongs to the Special Issue Sensor-Based Fault Diagnosis and Prognosis)
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26 pages, 6899 KB  
Article
When RNN Meets CNN and ViT: The Development of a Hybrid U-Net for Medical Image Segmentation
by Ziru Wang and Ziyang Wang
Fractal Fract. 2026, 10(1), 18; https://doi.org/10.3390/fractalfract10010018 - 28 Dec 2025
Viewed by 409
Abstract
Deep learning for semantic segmentation has made significant advances in recent years, achieving state-of-the-art performance. Medical image segmentation, as a key component of healthcare systems, plays a vital role in the diagnosis and treatment planning of diseases. Due to the fractal and scale-invariant [...] Read more.
Deep learning for semantic segmentation has made significant advances in recent years, achieving state-of-the-art performance. Medical image segmentation, as a key component of healthcare systems, plays a vital role in the diagnosis and treatment planning of diseases. Due to the fractal and scale-invariant nature of biological structures, effective medical image segmentation requires models capable of capturing hierarchical and self-similar representations across multiple spatial scales. In this paper, a Recurrent Neural Network (RNN) is explored within the Convolutional Neural Network (CNN) and Vision Transformer (ViT)-based hybrid U-shape network, named RCV-UNet. First, the ViT-based layer was developed in the bottleneck to effectively capture the global context of an image and establish long-range dependencies through the self-attention mechanism. Second, recurrent residual convolutional blocks (RRCBs) were introduced in both the encoder and decoder to enhance the ability to capture local features and preserve fine details. Third, by integrating the global feature extraction capability of ViT with the local feature enhancement strength of RRCBs, RCV-UNet achieved promising global consistency and boundary refinement, addressing key challenges in medical image segmentation. From a fractal–fractional perspective, the multi-scale encoder–decoder hierarchy and attention-driven aggregation in RCV-UNet naturally accommodate fractal-like, scale-invariant regularity, while the recurrent and residual connections approximate fractional-order dynamics in feature propagation, enabling continuous and memory-aware representation learning. The proposed RCV-UNet was evaluated on four different modalities of images, including CT, MRI, Dermoscopy, and ultrasound, using the Synapse, ACDC, ISIC 2018, and BUSI datasets. Experimental results demonstrate that RCV-UNet outperforms other popular baseline methods, achieving strong performance across different segmentation tasks. The code of the proposed method will be made publicly available. Full article
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22 pages, 1451 KB  
Article
Design of Decoupling Control Based TSK Fuzzy Brain-Imitated Neural Network for Underactuated Systems with Uncertainty
by Duc Hung Pham and V. T. Mai
Mathematics 2026, 14(1), 102; https://doi.org/10.3390/math14010102 - 26 Dec 2025
Viewed by 205
Abstract
This paper proposes a Takagi–Sugeno–Kang Elliptic Type-2 Fuzzy Brain-Imitated Neural Network (TET2FNN)-based decoupling control strategy for nonlinear underactuated mechanical systems subject to uncertainties. A sliding-mode framework is employed to construct a decoupled control architecture, in which an intermediate variable is introduced to separate [...] Read more.
This paper proposes a Takagi–Sugeno–Kang Elliptic Type-2 Fuzzy Brain-Imitated Neural Network (TET2FNN)-based decoupling control strategy for nonlinear underactuated mechanical systems subject to uncertainties. A sliding-mode framework is employed to construct a decoupled control architecture, in which an intermediate variable is introduced to separate two second-order sliding surfaces, thereby forming a decoupled slip surface. The TET2FNN acts as the main controller and approximates the ideal control law online, while a robust compensator is incorporated to suppress approximation errors and guarantee closed-loop stability. Simulation studies conducted on a double inverted pendulum system demonstrate that the proposed method achieves improved tracking accuracy and disturbance rejection compared with representative state-of-the-art controllers. Furthermore, the computational burden remains reasonable, indicating that the proposed scheme is suitable for real-time implementation and practical nonlinear control applications. Full article
(This article belongs to the Special Issue Intelligent Control and Applications of Nonlinear Dynamic System)
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24 pages, 7261 KB  
Article
IFIANet: Frequency Attention Network for Time–Frequency in sEMG-Based Motion Intent Recognition
by Gang Zheng, Jiankai Lin, Jiawei Zhang, Heming Jia, Jiayang Tang and Longtao Shi
Sensors 2026, 26(1), 169; https://doi.org/10.3390/s26010169 - 26 Dec 2025
Viewed by 303
Abstract
Lower limb exoskeleton systems require accurate recognition of the wearer’s movement intentions prior to action execution in order to achieve natural and smooth human–machine interaction. Surface electromyography (sEMG) signals can reflect neural activation of muscles before movement onset, making them a key physiological [...] Read more.
Lower limb exoskeleton systems require accurate recognition of the wearer’s movement intentions prior to action execution in order to achieve natural and smooth human–machine interaction. Surface electromyography (sEMG) signals can reflect neural activation of muscles before movement onset, making them a key physiological source for movement intention recognition. To improve sEMG-based recognition performance, this study proposes an innovative deep learning framework, IFIANet. First, a CNN–TCN-based spatiotemporal feature learning network is constructed, which efficiently models and represents multi-scale temporal–frequency features while effectively reducing model parameter complexity. Second, an IFIA (Frequency-Informed Integration Attention) module is designed to incorporate global frequency information, compensating for frequency components potentially lost during time–frequency transformations, thereby enhancing the discriminability and robustness of temporal–frequency features. Extensive ablation and comparative experiments on the publicly available MyPredict1 dataset demonstrate that the proposed framework maintains stable performance across different prediction times and achieves over 82% average recognition accuracy in within-experiments involving nine participants. The results indicate that IFIANet effectively fuses local temporal–frequency features with global frequency priors, providing an efficient and reliable approach for sEMG-based movement intention recognition and intelligent control of exoskeleton systems. Full article
(This article belongs to the Special Issue Advanced Sensors for Human Health Management)
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9 pages, 1306 KB  
Article
A Frequency- and Power-Dependent Semi-Analytical Model for Wideband RF Energy Harvesting Rectifiers
by Sadık Zuhur
Micromachines 2026, 17(1), 30; https://doi.org/10.3390/mi17010030 - 26 Dec 2025
Viewed by 166
Abstract
In this study, a new semi-analytical model was developed that can calculate the output voltage of low-power microwave rectifiers as a function of frequency and input power. The model integrates diode rectification characteristics and frequency-dependent impedance mismatches within the same mathematical structure. Defined [...] Read more.
In this study, a new semi-analytical model was developed that can calculate the output voltage of low-power microwave rectifiers as a function of frequency and input power. The model integrates diode rectification characteristics and frequency-dependent impedance mismatches within the same mathematical structure. Defined by second-order polynomial expressions for input power and frequency, the model directly incorporates reflection coefficient (S11) data into the equations to account for frequency-dependent power losses caused by impedance mismatch, thereby improving calculation accuracy under wide-band conditions. To validate the model, a wide-band rectifier prototype with an FR4-based T-type matching network and a voltage doubler structure was designed and manufactured. Model calculations showed over 95% agreement with simulation results and closely followed the measured output voltage trends over the 0.5–3 GHz frequency range and input power levels from −12 dBm to 0 dBm. The proposed model provides a design-oriented and computationally efficient tool for wide-band, low-power RF energy harvesting and wireless power transfer applications, enabling rapid evaluation of impedance matching strategies with reduced reliance on electromagnetic simulations. Full article
(This article belongs to the Special Issue Micro-Energy Harvesting Technologies and Self-Powered Sensing Systems)
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22 pages, 3335 KB  
Article
Estimate Laplacian Spectral Properties of Large-Scale Networks by Random Walks and Graph Transformation
by Changlei Zhan, Xiangyu Li and Jie Chen
Mathematics 2026, 14(1), 26; https://doi.org/10.3390/math14010026 - 21 Dec 2025
Viewed by 199
Abstract
For network graphs, numerous graph features are intimately linked to eigenvalues of the Laplacian matrix, such as connectivity and diameter. Thus, it is very important to solve eigenvalues of the Laplacian matrix for graphs. Similarly, for higher-order networks, eigenvalues of combinatorial Laplacian matrices [...] Read more.
For network graphs, numerous graph features are intimately linked to eigenvalues of the Laplacian matrix, such as connectivity and diameter. Thus, it is very important to solve eigenvalues of the Laplacian matrix for graphs. Similarly, for higher-order networks, eigenvalues of combinatorial Laplacian matrices are also important for invariants of graphs. However, for large-scale networks, it is difficult to calculate eigenvalues of the Laplacian matrix directly because it is either very difficult to obtain the whole network structure or requires a lot of computing resources. Therefore, this article makes the following contributions. Firstly, this paper proposes a random walk approach for estimating the bounds of the greatest eigenvalues of Laplacian matrices for large-scale networks. Considering the relationship between the spectral moments of the adjacency matrix and the closed paths in the network, we utilize the relationship between the adjacency matrix and the Laplacian matrix to establish the relationship between the Laplacian matrix and the closed paths. Then, we employ equiprobable random walks to sample the large graph to obtain the small graph. Through algebraic topology knowledge, we obtain the bounds of the largest eigenvalue of the Laplacian matrix of the large graph by using Laplacian spectral moments of the small graph. Secondly, for high-order networks, this paper proposes a method based on random walks and graph transformations. The graph transformation we propose mainly converts graphs with second-order simplices into ordinary weighted graphs, thereby transforming the problem of solving the spectral moments of the second-order combined Laplacian matrix into solving the spectral moments of the adjacency matrix. Then, we use the aforementioned random walk method to solve bounds of the greatest eigenvalue of the second-order combinatorial Laplacian matrix. Finally, by comparing the proposed method with existing algorithms in synthetic and real networks, its accuracy and superiority are demonstrated. Full article
(This article belongs to the Special Issue Dynamic Analysis and Decision-Making in Complex Networks)
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11 pages, 3245 KB  
Article
A Breathable, Low-Cost, and Highly Stretchable Medical-Textile Strain Sensor for Human Motion and Plant Growth Monitoring
by Shilei Liu, Xin Wang, Xingze Chen, Zhixiang He, Linpeng Liu and Xiaohu Jiang
Sensors 2026, 26(1), 44; https://doi.org/10.3390/s26010044 - 20 Dec 2025
Viewed by 365
Abstract
Flexible strain sensors capable of conformal integration with living organisms are essential for advanced wearable electronics, human–machine interaction, and plant health. However, many existing sensors require complex fabrication or rely on non-breathable elastomer substrates that interfere with the physiological microenvironment of skin or [...] Read more.
Flexible strain sensors capable of conformal integration with living organisms are essential for advanced wearable electronics, human–machine interaction, and plant health. However, many existing sensors require complex fabrication or rely on non-breathable elastomer substrates that interfere with the physiological microenvironment of skin or plant tissues. Here, we present a low-cost, breathable, and highly stretchable strain sensor constructed from biomedical materials, in which a double-layer medical elastic bandage serves as the porous substrate and an intermediate conductive medical elastic tape impregnated with carbon nanotubes (CNTs) ink acts as the sensing layer. Owing to the hierarchical textile porosity and the deformable CNTs percolation network, the sensor achieves a wide strain range of 100%, a gauge factor of up to 2.72, and excellent nonlinear second-order fitting (R2 = 0.997). The bandage substrate provides superior air permeability, allowing long-term attachment without obstructing moisture and gas exchange, which is particularly important for maintaining skin comfort and preventing disturbances to plant epidermal physiology. Demonstrations in human joint-motion monitoring and real-time plant growth detection highlight the device’s versatility and biological compatibility. This work offers a simple, low-cost yet effective alternative to sophisticated strain sensors designed for human monitoring and plant growth monitoring, providing a scalable route toward multifunctional wearable sensing platforms. Full article
(This article belongs to the Special Issue Materials and Devices for Flexible Electronics in Sensor Applications)
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