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Search Results (584)

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Keywords = nonlinear frequency modulation

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18 pages, 9246 KB  
Article
Optical Vector Analysis Based on Serrodyne Modulation for Arbitrary Responses
by Yonggang Luo, Hongwei Zou, Zhi Xiao and Zenghui Chen
Photonics 2026, 13(9), 893; https://doi.org/10.3390/photonics13090893 (registering DOI) - 21 Sep 2026
Abstract
An optical vector analysis (OVA) based on serrodyne modulation is proposed and numerically verified by simulations. In the proposed OVA, serrodyne modulation is implemented using a dual-parallel dual-drive Mach–Zehnder modulator to generate asymmetric optical double-sideband (ODSB) signals including a frequency-shifted optical carrier. The [...] Read more.
An optical vector analysis (OVA) based on serrodyne modulation is proposed and numerically verified by simulations. In the proposed OVA, serrodyne modulation is implemented using a dual-parallel dual-drive Mach–Zehnder modulator to generate asymmetric optical double-sideband (ODSB) signals including a frequency-shifted optical carrier. The generated signals subsequently propagate through the optical device under test (ODUT). Owing to the asymmetric ODSB structure, the proposed OVA is inherently immune to errors induced by the nonlinearity of the electro-optic modulator (EOM). Consequently, the responses of the ODUT can be accurately obtained by processing the frequency-shifted photocurrent, which is converted from the frequency-shifted carrier and the two desired sidebands. Furthermore, the proposed approach overcomes the limitation of conventional optical single-sideband-based OVA in characterizing bandpass responses. Through numerical simulations, the frequency responses of a uniform fiber Bragg grating, a Fabry–Perot cavity, and a bandpass filter are obtained within a bandwidth of 20 GHz. The proposed OVA provides an approach for characterization of optical devices and integrated microwave photonics systems. Full article
(This article belongs to the Special Issue Advanced Optoelectronic Systems)
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56 pages, 5422 KB  
Article
Distributed Quantum-Assisted Multi-SAPF Architecture Based on Deterministic Current Control and Asynchronous QUBO–QAOA–VQE Supervisory Optimization
by Marian Gaiceanu, Razvan Buhosu, George-Andrei Marin and Marius George Solomon
Electronics 2026, 15(18), 4288; https://doi.org/10.3390/electronics15184288 (registering DOI) - 19 Sep 2026
Abstract
The increasing penetration of nonlinear industrial loads, distributed renewable generation, and intelligent electrical infrastructures requires active power filters capable of simultaneously providing high-performance harmonic mitigation, reactive power compensation, coordinated operation of multiple converters, and deterministic real-time implementation. Conventional centralized shunt active power filters [...] Read more.
The increasing penetration of nonlinear industrial loads, distributed renewable generation, and intelligent electrical infrastructures requires active power filters capable of simultaneously providing high-performance harmonic mitigation, reactive power compensation, coordinated operation of multiple converters, and deterministic real-time implementation. Conventional centralized shunt active power filters (SAPFs) exhibit limited scalability, while optimization-based approaches often compromise deterministic execution because of their computational complexity. To address these challenges, this paper proposes a Distributed Quantum Multi-Shunt Active Power Filter (Quantum Multi-SAPF) that combines deterministic-based local current control with asynchronous quantum-assisted supervisory optimization. The proposed architecture employs four distributed SAPF units operating under a hierarchical cyber–physical framework. The lower control layer, implemented on a MATLAB R2026a, includes all fast electrical functions—signal acquisition, SOGI-based synchronization, Clarke transformation, instantaneous pq current reference generation, current regulation, interleaved PWM modulation, and protection—which are executed deterministically at a switching frequency of 15 kHz. The upper supervisory layer operates asynchronously at 20 Hz and formulates converter coordination as a quadratic unconstrained binary optimization (QUBO) problem solved using Quantum Approximate Optimization Algorithm (QAOA) allocation together with Variational Quantum Eigensolver (VQE) predictive correction. This multi-rate architecture separates fast electrical dynamics from slow supervisory optimization, ensuring that uncertain optimization latency does not affect converter stability. The proposed controller is validated through comprehensive switching-level simulations on the MATLAB R2026a platform. Numerical results demonstrate a reduction in source current total harmonic distortion from 24.615% to 0.142%, corresponding to a 99.423% harmonic reduction, while improving the source power factor to 0.99999 and achieving 99.999% reactive power compensation. The distributed four-SAPF synchronization network maintains coherent phase alignment among all converter units throughout the simulation, thereby supporting coordinated compensation and balanced current sharing. This synchronized operation contributes to highly accurate compensation current tracking, with an RMS tracking error of only 0.026 A, while limiting the source current unbalance to 0.026%. These results confirm the effectiveness of the distributed synchronization and local control architecture in maintaining coordinated and balanced operation of the four parallel SAPFs. The proposed interleaved modulation strategy, combined with optimized current sharing, maintains balanced converter utilization while suppressing circulating currents without requiring a dedicated circulating current controller. The proposed Distributed Quantum Multi-SAPF establishes a scalable framework that combines deterministic industrial control with quantum-assisted supervisory optimization. The architecture provides high harmonic compensation capability, near-unity power factor, balanced converter utilization, comprehensive Safe Operating Area supervision, and practical industrial feasibility, making it a promising solution for future smart grids, renewable energy integration, electric vehicle charging infrastructures, and intelligent power quality conditioning systems. Full article
(This article belongs to the Special Issue Renewable Energy Integration and Energy Management in Smart Grid)
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28 pages, 3054 KB  
Article
A Lightweight Forest Fire Detection Model with Multi-Granularity Vision-Language Enhancement
by Yifan Ma, Weifeng Shan, Yanwei Sui and Mengyu Wang
Fire 2026, 9(9), 409; https://doi.org/10.3390/fire9090409 (registering DOI) - 19 Sep 2026
Abstract
In recent years, Unmanned Aerial Vehicle (UAV)-based object detection technology has demonstrated immense potential for forest fire monitoring in complex environments. However, constrained by the drastic multi-scale variations in fire targets, severe background interference, and the limited computational resources of edge devices, existing [...] Read more.
In recent years, Unmanned Aerial Vehicle (UAV)-based object detection technology has demonstrated immense potential for forest fire monitoring in complex environments. However, constrained by the drastic multi-scale variations in fire targets, severe background interference, and the limited computational resources of edge devices, existing object detection models struggle to strike a balance between detection accuracy and inference efficiency. To systematically address the aforementioned issues, this paper proposes MVLFireNet, a lightweight and real-time forest fire detection model driven by multi-granularity vision-language enhancement. First, a Multi-scale Spatial-Aware attention (MSA) module is proposed to capture global long-range dependencies while explicitly preserving the high-frequency two-dimensional spatial features of weak fire spots and smoke edges. Second, a Cross-Modulation Fusion (CMF) module is designed to replace the traditional passive feature concatenation with bidirectional nonlinear conditional modulation, thereby achieving active denoising and compensation for both deep high-level semantics and shallow spatial details. Finally, a Multi-granularity Vision-Language Enhancement (MVLE) branch is innovatively introduced to inject robust semantic discriminative capabilities into visual features via a hierarchical text alignment enhancement mechanism covering both global scenes and local targets. Furthermore, FSDataset-VL, the first large-scale multi-granularity text-image dataset tailored for forest fire detection, is constructed. Extensive experiments on FSDataset-VL demonstrate that MVLFireNet, with merely 2.41 million parameters, achieves mAP@0.5 and mAP@0.5:0.95 of 86.3% and 54.8%, respectively, both representing the highest performance among all comparative models. Under the mAP evaluation framework, it attains an optimal balance between detection accuracy and computational efficiency, thereby providing an efficient solution for UAV-based forest fire monitoring in complex environments. Full article
(This article belongs to the Special Issue Intelligent Forest Fire Prediction and Detection: 2nd Edition)
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25 pages, 16325 KB  
Article
A Chirp-Rate-Driven Adaptive Window Chirplet Transform and Its Application in Bearing Fault Diagnosis
by Zhonghao Liu, Gang Yu and Tian Ran Lin
Machines 2026, 14(9), 1055; https://doi.org/10.3390/machines14091055 - 16 Sep 2026
Viewed by 68
Abstract
In this paper, we propose an instantaneous chirp-rate-driven adaptive window Chirplet transform algorithm for the analysis of strong time-varying nonlinear frequency-modulated signals with uncorrelated components. In this approach, the length of the sliding window in the Chirplet transform is dynamically adjusted according to [...] Read more.
In this paper, we propose an instantaneous chirp-rate-driven adaptive window Chirplet transform algorithm for the analysis of strong time-varying nonlinear frequency-modulated signals with uncorrelated components. In this approach, the length of the sliding window in the Chirplet transform is dynamically adjusted according to the estimated instantaneous chirp rate of each signal component of an initial time–frequency result from short-time Fourier transform (STFT). A boundary constraint determined from the modal support intervals of the signal is utilized to restrain the allowable searching frequency range of the instantaneous frequency (IF) trajectories and incorporated into a cost-function-based IF extraction method to improve accuracy in the IF estimation. The effectiveness of the proposed algorithm is validated using a simulated nonlinear frequency-modulated (FM) signal with two uncorrelated components, and two sets of experimental bearing vibration signals. It is shown that the proposed algorithm can accurately track the frequency modulation of a strong FM signal dynamically to render an accurate estimation of the IFs and modal amplitudes of a strong FM signal. A comparison study also verifies that the proposed algorithm can produce a better energy-concentrated time–frequency result compared to other commonly employed time–frequency analysis techniques, particularly when the signal is contaminated by noise. Full article
(This article belongs to the Special Issue Artificial Intelligence in Wind Energy Optimization Design)
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21 pages, 3278 KB  
Article
Integrating Dynamic Graph Representation and Reinforcement Learning for Portfolio Optimization
by Wensheng Wang and Qingbo Cheng
Systems 2026, 14(9), 1161; https://doi.org/10.3390/systems14091161 - 16 Sep 2026
Viewed by 93
Abstract
The complex dependency relationships and high-frequency, time-varying characteristics of financial market data pose many challenges to portfolio optimization. To address these problems, this paper proposes a robust portfolio optimization framework—dynamic graph reinforcement learning (DyGRL)—by integrating dynamic graph representation and reinforcement learning. The framework [...] Read more.
The complex dependency relationships and high-frequency, time-varying characteristics of financial market data pose many challenges to portfolio optimization. To address these problems, this paper proposes a robust portfolio optimization framework—dynamic graph reinforcement learning (DyGRL)—by integrating dynamic graph representation and reinforcement learning. The framework incorporates a dynamic graph construction module, which uses distance correlation coefficients to capture nonlinear dependencies among stocks and applies the triangulated maximally filtered graph method to remove redundant connections. Furthermore, DyGRL incorporates a mask reconstruction mechanism into dynamic graph learning to construct a graph representation learning module, which learns robust stock representations. Finally, a soft actor-critic-based decision network is introduced for portfolio weight optimization. Experimental results based on 5-min high-frequency data from the NDX and CSI300 markets from September 2016 to August 2025 show that, compared with the best-performing baseline method, DyGRL improves annualized returns by 3.21% and 1.43%, respectively. Moreover, the moving block bootstrap test confirms that the improvement in Sharpe ratio is statistically significant. The comprehensive results indicate that DyGRL can effectively improve portfolio performance and demonstrate the effectiveness of the proposed scheme. Full article
(This article belongs to the Section Systems Practice in Social Science)
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14 pages, 5640 KB  
Article
Nonlinear Carrier Dynamics and Optical Response of Lanthanum-Doped Barium Stannate
by Viktoriia E. Babicheva, Heungsoo Kim and Evgeniya H. Lock
Nanomaterials 2026, 16(18), 1156; https://doi.org/10.3390/nano16181156 - 15 Sep 2026
Viewed by 184
Abstract
Lanthanum-doped barium stannate (LBSO) is an emerging transparent conducting oxide with high carrier mobility and tunable plasmonic properties in the infrared regime. In this work, we investigate the nonlinear electromagnetic response of LBSO using a linearized collisionless Boltzmann model that captures the field-induced [...] Read more.
Lanthanum-doped barium stannate (LBSO) is an emerging transparent conducting oxide with high carrier mobility and tunable plasmonic properties in the infrared regime. In this work, we investigate the nonlinear electromagnetic response of LBSO using a linearized collisionless Boltzmann model that captures the field-induced modification of the carrier distribution function. We experimentally realize LBSO thin films with controlled carrier concentration and optical properties tailored for epsilon-near-zero operation. Analytical expressions for the nonlinear plasma frequency and permittivity reveal their dependence on carrier concentration, temperature, and optical excitation. An excitation-driven reduction in the effective plasma frequency is accompanied by significant changes in the permittivity spectrum. The results demonstrate that the LBSO metasurface exhibits strong optical tunability under near-infrared excitation, with significant modulation of its reflection and transmission characteristics. These findings provide physical insight into the nonlinear carrier dynamics in LBSO and establish a framework for designing tunable photonic devices based on transparent conducting oxides. Full article
(This article belongs to the Special Issue Advances in Nanophotonics and Optical Metasurfaces)
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19 pages, 2771 KB  
Article
The Interaction of Wind-Generated Gravity Water Wave Groups with Capillary-Gravity Wave Groups: Coupled Nonlinear Schrödinger Equations
by Montri Maleewong and Roger Grimshaw
Fluids 2026, 11(9), 231; https://doi.org/10.3390/fluids11090231 - 13 Sep 2026
Viewed by 121
Abstract
The nonlinear Schrödinger equation is a well-known and much-studied canonical equation for weakly nonlinear wave groups. In the context of wind-generated water waves, an additional wind forcing term can be added. It is asymptotically derived for the slowly varying amplitude of a sinusoidal [...] Read more.
The nonlinear Schrödinger equation is a well-known and much-studied canonical equation for weakly nonlinear wave groups. In the context of wind-generated water waves, an additional wind forcing term can be added. It is asymptotically derived for the slowly varying amplitude of a sinusoidal wave, with a dominant wavenumber and frequency. When two such wave groups are present, the asymptotic outcome is two coupled nonlinear Schrödinger equations, with coupling through a nonlinear term in each equation. In this article we examine this scenario, in a one horizontal space dimension setting, when one wave is a gravity wind-driven water wave, and the other is a capillary-gravity wave. For this coupled system, we present an analysis of modulation instability and a suite of numerical simulations analogous to those presented previously for the forced nonlinear Schrödinger equation. Full article
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27 pages, 42222 KB  
Article
Geo-XAI Reveals Wildfire Risk Driver Differences and Spatial Heterogeneity Between Drought and Non-Drought Periods in Southwest China Mountains
by Fuwen Li, Wenlong Yang, Jiangxia Ye, Lei Kong, Xiaojie Yin, Xun Zhao, Weili Kou, Zhichao Huang, Xinkun Zhu, Zhou Mao and Yiping Xu
Remote Sens. 2026, 18(18), 3089; https://doi.org/10.3390/rs18183089 - 9 Sep 2026
Viewed by 182
Abstract
Global warming has increased the frequency of droughts, further complicating wildfire susceptibility assessment in topographically complex mountainous regions. However, the factors associated with wildfire occurrence and their nonlinear spatial responses under contrasting drought conditions remain poorly understood. To address this knowledge gap, we [...] Read more.
Global warming has increased the frequency of droughts, further complicating wildfire susceptibility assessment in topographically complex mountainous regions. However, the factors associated with wildfire occurrence and their nonlinear spatial responses under contrasting drought conditions remain poorly understood. To address this knowledge gap, we conducted a case study in a fire-prone mountainous region of southwestern China. Drought and non-drought periods were identified using the Standardized Precipitation Evapotranspiration Index (SPEI) and run theory. Using historical wildfire records from 2006 to 2020 and 16 wildfire drivers, we developed three machine-learning models and applied GeoShapley to quantify the contributions of key predictors and characterize their spatial dynamics under different drought conditions. The results showed that the Extreme Gradient Boosting (XGB) model achieved the best predictive performance (AUC = 0.85–0.91) and effectively captured the spatial patterns of wildfire susceptibility. Meteorological variables consistently emerged as the dominant controls on wildfire occurrence, although their relative importance and functional effects differed substantially between drought and non-drought conditions. GeoShapley analysis further revealed pronounced spatial heterogeneity in the effects of the major drivers, with these spatial patterns further modulated by drought conditions. In particular, during drought periods, the local geographical context amplified the spatial interaction effect of precipitation, resulting in a stronger risk-enhancing effect than during non-drought periods. By decomposing variable contributions into non-spatial main effects and spatially explicit interaction effects, this study reveals how the effects of wildfire drivers vary spatially under contrasting drought conditions and provides a robust framework for targeted wildfire mitigation in complex mountainous landscapes. Full article
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22 pages, 46210 KB  
Article
Frequency-Modulated Spiral Manifold: A Model for Temporal Knowledge Graph Completion
by Xindong You, Kai Long, Zhaojun Wang, Likun Lu and Kai Zhang
Mathematics 2026, 14(17), 3234; https://doi.org/10.3390/math14173234 - 7 Sep 2026
Viewed by 243
Abstract
Temporal knowledge graph completion (TKGC) infers missing facts by modeling the temporal evolution of relations. Existing methods typically encode time through low-dimensional geometric transformations or frequency-domain decomposition. However, periodically recurring relations can still be mapped to overlapping trajectories in the same two-dimensional working [...] Read more.
Temporal knowledge graph completion (TKGC) infers missing facts by modeling the temporal evolution of relations. Existing methods typically encode time through low-dimensional geometric transformations or frequency-domain decomposition. However, periodically recurring relations can still be mapped to overlapping trajectories in the same two-dimensional working space, which may reduce temporal separability and produce conflicting optimization signals. To address this limitation, we propose the Frequency-Modulated Spiral Manifold (FMSM) model, which includes the following: (1) a relation-adaptive spectral partition and relation-dimension gate for fusing long- and short-term relation channels; (2) an independent global phase embedding and nonlinear spiral push that lift entangled planar trajectories onto separated three-dimensional manifold layers; and (3) a spiral norm regularizer that stabilizes temporal evolution while preserving valid burst signals. The artificial-intelligence contribution of FMSM is a phase-conditioned spectral-geometric representation that separates recurring temporal facts while retaining multi-scale relation dynamics. Its engineering application is the completion of time-stamped event records for dynamic knowledge-based decision-support systems. Experiments on ICEWS14, ICEWS05-15, and GDELT show that, compared with the strongest reported baseline TeRDy, FMSM yields relative MRR improvements of 0.62%, 0.86%, and 13.28%. Full article
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26 pages, 15695 KB  
Article
Impacts of Urbanization on Compound Heat and Drought Events in the Beijing–Tianjin–Hebei Region Based on Explainable Machine Learning
by Ping Jiang, Jianjun Wu, Lei Zhou, Ruimeng Tang, Jianhua Yang and Minghui Lu
Land 2026, 15(9), 1649; https://doi.org/10.3390/land15091649 - 5 Sep 2026
Viewed by 316
Abstract
Compound heat and drought events (CHDEs) are occurring more frequently due to climate change. However, the role of urbanization as a key driver of climate change in modulating these events remains poorly quantified. Hence, this study evaluates the impacts of urbanization on CHDE [...] Read more.
Compound heat and drought events (CHDEs) are occurring more frequently due to climate change. However, the role of urbanization as a key driver of climate change in modulating these events remains poorly quantified. Hence, this study evaluates the impacts of urbanization on CHDE frequency, duration, and severity using a daily scale analytical framework, and further quantifies the key influencing factors contributing to these impacts using explainable machine learning. The results revealed that: (1) the urban expansion rates ranged from 0.06% to 22.92% per decade in the Beijing–Tianjin–Hebei (BTH) region. Concurrently, the frequency, duration, and severity of CHDEs exhibited overall upward trends, with rates of 0.11, 1.45, and 0.06 per decade, respectively. (2) Urban stations exhibited more apparent upward trends in the frequency, duration, and severity of CHDEs than rural stations. Urbanization contributed to these increases in CHDEs, with its greatest contribution to duration (44.0%), followed by severity (39.1%) and frequency (33.6%). (3) The explainable machine learning analysis revealed that the attributes of CHDEs are driven by multiple urban and climatic factors under urbanization. While enhanced Tmean and UHI consistently intensified CHDEs, changes in urban underlying surfaces manifest complex non-linear relationships with CHDE attributes. Notably, BV and UrbF amplified the duration and severity of CHDEs more strongly than frequency. These findings suggest that urbanization may primarily amplify the duration and severity of CHDEs through enhanced thermal conditions and surface modification, highlighting the need to prioritize heat mitigation and urban land-use regulation in climate adaptation planning. Full article
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57 pages, 6417 KB  
Article
State-Dependent Coefficients in Electrical-Engineering Pedagogy: A Comparative Metrological and Coupling-Theory Audit with a Reserved Paraformer Test Section
by Esa Ruoho, Jukka Kortela and Michael Gasik
Foundations 2026, 6(3), 34; https://doi.org/10.3390/foundations6030034 - 3 Sep 2026
Viewed by 635
Abstract
Introductory and intermediate electrical-engineering education commonly models fundamental circuit and device parameters, including inductance, capacitance, resistance, permeability, permittivity, conductivity, characteristic impedance, transformer turns ratio, machine constants, amplifier gain, resonant frequency, propagation velocity, and mutual inductance, as numerical constants. While this approximation is valid [...] Read more.
Introductory and intermediate electrical-engineering education commonly models fundamental circuit and device parameters, including inductance, capacitance, resistance, permeability, permittivity, conductivity, characteristic impedance, transformer turns ratio, machine constants, amplifier gain, resonant frequency, propagation velocity, and mutual inductance, as numerical constants. While this approximation is valid within the intended small-signal operating regime, it becomes methodologically incomplete when these coefficients exhibit measurable state dependence. This paper presents a comparative audit of thirteen such coefficients by systematically contrasting their textbook formulations with the established engineering literature and interpreting the results through two complementary frameworks: the JCGM GUM-6:2020 measurement-model methodology for omitted effects, and the Heckmann–Nye/Gasik multidomain coupling architecture for multi-axis physical interactions. The analysis demonstrates that mainstream engineering practice routinely exploits state-dependent coefficients without invoking new physical laws, and that relaxing the constant-coefficient assumption naturally introduces physically meaningful terms, including the inductive contribution IdL/dt, the capacitive counterpart VdC/dt, and the mutual-inductance term i2dM/dt. The principal scientific contribution is the development and experimental validation of a unified theoretical and engineering framework for high-power resonant transformers and orthogonal Metglas AMCC-1000 paraformers. The proposed approach combines a new physics-based modal theory of octave (2:1) parametric excitation with simultaneous optimization of magnetic-core resonance, electrical resonance, nonlinear inductance modulation, resonant conductor lengths selected as integer multiples of the operating resonant wavelength, multi-stranded high-frequency Litz-wire windings, resonant capacitor synthesis, and the nonlinear magnetic characteristics of the AMCC-1000 amorphous core. The modal analysis demonstrates how coupled resonant eigenmodes and engineered state-dependent inductance can be used to satisfy the conditions for stable octave parametric excitation. Experimental results obtained from both the symmetric two-leg resonant transformer and the orthogonal paraformer are in close agreement with analytical predictions and numerical simulations, thereby validating both the proposed electromagnetic design methodology and the underlying modal theory. Full article
(This article belongs to the Section Mathematical Sciences)
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15 pages, 3361 KB  
Article
Experimental Study of a Digital Feedback Fluxgate Magnetometer Using a Fifth-Order Single-Loop 1-Bit Sigma–Delta Modulator
by Shang Lv, Jindong Wang, Yiteng Zhang and Xuanming Cui
Sensors 2026, 26(17), 5592; https://doi.org/10.3390/s26175592 - 3 Sep 2026
Viewed by 345
Abstract
Digital fluxgate magnetometers have been widely used in deep space exploration due to their low noise, high sensitivity, and high reliability. This paper presents a digital fluxgate magnetometer using a fifth-order single-loop 1-bit Sigma–Delta modulator. With a consistent system structure, measurement range, test [...] Read more.
Digital fluxgate magnetometers have been widely used in deep space exploration due to their low noise, high sensitivity, and high reliability. This paper presents a digital fluxgate magnetometer using a fifth-order single-loop 1-bit Sigma–Delta modulator. With a consistent system structure, measurement range, test setup, and calculation method, the characteristics of magnetic field measurement noise and non-linear error are obtained under four OSR configurations through simulation analysis and experimental testing. The test results show that within the range of ±65,000 nT, the system achieves its optimal performance with a non-linearity of 0.024%, an RMS noise of 0.106 nT, and a noise power spectral density of 5.7 pT·Hz−1/2 at 1 Hz. These results indicate that increasing the OSR can effectively improve the performance of this digital fluxgate magnetometer, enabling high linearity and low noise measurement in Earth’s magnetic field. Full article
(This article belongs to the Section Physical Sensors)
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31 pages, 12563 KB  
Article
Fractional-Order State Feedback Controller to Suppress the Nonlinear Self-Excited Oscillations: Accurate Analytical and Numerical Solution
by Nasser. A. Saeed, Lei Hou and Turki J. Alqurashi
Mathematics 2026, 14(17), 3106; https://doi.org/10.3390/math14173106 - 29 Aug 2026
Viewed by 355
Abstract
In this work, an accurate analytical solution is developed for a harmonically excited self-excited nonlinear oscillator under fractional-order state feedback control using a modified version of the Traditional Multiple Scales Method (TMSM), termed the Detuned Multiple Scale Method (DMSM). In contrast to the [...] Read more.
In this work, an accurate analytical solution is developed for a harmonically excited self-excited nonlinear oscillator under fractional-order state feedback control using a modified version of the Traditional Multiple Scales Method (TMSM), termed the Detuned Multiple Scale Method (DMSM). In contrast to the TMSM, which perturbs the nonlinear system about its linear natural frequency, the DMSM perturbs the system implicitly about its amplitude-dependent response frequency. Based on this formulation, reduced-order amplitude–phase modulation equations for the considered fractional-order system are derived and compared with those obtained by TMSM. It is found that the DMSM yields exactly the same backbone curve as that obtained using the first-order Harmonic Balance Method (HBM), whereas the TMSM provides only its leading-order approximation. In addition, the DMSM reveals that the effective linear and nonlinear damping and stiffness coefficients depend on the amplitude-dependent response frequency, unlike the TMSM, where they depend on the fixed linear natural frequency. Furthermore, it is shown that the TMSM detuning term represents only the first-order approximation of the exact detuning term obtained by the DMSM. Accordingly, the considered fractional-order system is analyzed using the DMSM in comparison with the TMSM through Frequency Response Curves (FRCs), bifurcation diagrams, and stability charts. The system dynamics are investigated for different fractional-order derivatives under weak, moderate, and strong feedback gains. Moreover, a Runge–Kutta Grünwald–Letnikov (RK–GL) algorithm is developed and validated for fractional-order simulations, and all obtained FRCs are numerically verified. The numerical results clearly demonstrate that the proposed DMSM maintains excellent agreement with the numerical results not only near the primary linear resonance condition, but also over a wide range of excitation frequencies under weak, moderate, and strong feedback gains. In contrast, the TMSM fails to preserve this level of accuracy and may produce misleading predictions, especially under strong feedback and large detuning conditions. Extracting reduced-order amplitude–phase equations using the DMSM provides highly accurate analytical predictions along with deep physical insight into system dynamics, which, despite their accuracy in steady-state solutions, offer limited insight into transient behavior and the overall evolution of the response. Full article
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20 pages, 2580 KB  
Article
A Hybrid Attention-Enhanced Transformer for Short-Term Attitude Vibration Prediction of Robotic Aerial Work Platforms
by Jiayu Guo, Mingming Lv, Mengyao Si, Haonan Hu and Wei Zhong
Machines 2026, 14(9), 964; https://doi.org/10.3390/machines14090964 - 25 Aug 2026
Viewed by 326
Abstract
Robotic Aerial Work Platforms (RAWPs) are subjected to multi-source excitations including wind gusts and inertial loads, which result in strongly nonlinear and time-varying coupled triaxial attitude vibrations. Conventional recurrent architectures such as LSTM and GRU suffer from gradient vanishing when processing long sequences, [...] Read more.
Robotic Aerial Work Platforms (RAWPs) are subjected to multi-source excitations including wind gusts and inertial loads, which result in strongly nonlinear and time-varying coupled triaxial attitude vibrations. Conventional recurrent architectures such as LSTM and GRU suffer from gradient vanishing when processing long sequences, while Transformer utilize self-attention mechanisms to learn simple periodic correlations; however, the vibrations in RAWPs exhibit a complex time-series pattern composed of low-frequency oscillations superimposed with high-frequency impacts and accumulates errors through autoregressive decoding. To address these limitations, this paper proposes an improved Transformer model featuring dual-channel periodic positional encoding and global–local hybrid multi-head attention for one-shot multi-step long-sequence prediction of RAWPs attitude vibrations. The proposed method designs a dual-channel independent sine–cosine positional encoding with a tunable periodic modulation factor to explicitly embed the multi-scale periodicity priors of vibration signals and introduces a global–local hybrid attention mechanism that parallelly extracts transient amplitude impact features in the time domain and periodic fluctuation features in the frequency domain. A full-scale aerial experimental platform is established to collect triaxial vibration data under two operating conditions at a sampling frequency of 20 Hz. The results determine the optimal periodic modulation factor and input window length, and ablation studies validate the synergistic gains of the two proposed modules. Comparative results demonstrate that the proposed model achieves substantially reduced prediction errors. In terms of pitch angle, the proposed model achieves a performance improvement of 53.89% over Transformer, 52.11% over LSTM, and 57.67% over GRU. The proposed model effectively provides a reliable data-driven prediction framework for attitude monitoring and active vibration suppression of aerial work platforms. Full article
(This article belongs to the Section Machine Design and Theory)
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33 pages, 1132 KB  
Article
Delay-Modulated Nonlinear Stochastic Mode Veering in Inertially Coupled Vibration Systems
by Lili Zhang, Zikun Han and Qiubao Wang
Entropy 2026, 28(9), 952; https://doi.org/10.3390/e28090952 - 24 Aug 2026
Viewed by 198
Abstract
Mode veering is a modal-interaction phenomenon found in vibration systems. For inertially coupled structures, the combined influence of coupling delay, nonlinear restoring force, and stochastic coupling perturbation remain insufficiently understood. This work analyzes an inertially coupled two-coordinate prototype in which a discrete delay, [...] Read more.
Mode veering is a modal-interaction phenomenon found in vibration systems. For inertially coupled structures, the combined influence of coupling delay, nonlinear restoring force, and stochastic coupling perturbation remain insufficiently understood. This work analyzes an inertially coupled two-coordinate prototype in which a discrete delay, a delayed cubic stiffness, and positive multiplicative stochastic modulation all enter through the same relative-coordinate coupling channel. We formulate the delayed linear spectrum through a quasi-polynomial characteristic equation. We also characterize the veering by the two positive-frequency characteristic-root branches descending from the mechanical modes. Coupling delay shifts the veering center, alters the minimum frequency gap, and moves the tracked rightmost roots toward the stability boundary. An analytical imaginary-axis-crossing criterion is derived to determine the delay-induced stability boundary of the deterministic linearized system, and the resulting boundary is independently validated by direct multi-start characteristic-root searches and Chebyshev-collocation approximation of the DDE generator. A fixed-reference modal-coordinate representation identifies the off-diagonal modal terms associated with branch exchange while retaining the full delayed characteristic equation. A first-harmonic treatment of the delayed cubic term can yield an amplitude-dependent nonlinear veering backbone. For the stochastic problem, frozen lognormal coupling samples and a time-dependent Ornstein–Uhlenbeck-driven multiplier are constructed from the same unit-mean positive lognormal marginal law. The former is used to quantify realization-wise spectral broadening, whereas the latter retains temporal correlation and is used to evaluate finite-time branch residence and pathwise delayed-work statistics. The pathwise energy balance reveals that the delayed relative-coordinate work rate is sign-indefinite. This provides a common energy-transfer mechanism through which delay, nonlinearity, and stochastic modulation reshape mode veering in the inertially coupled system. Full article
(This article belongs to the Section Complexity)
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