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Keywords = measurement error correction

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30 pages, 2523 KB  
Article
A Combined Error-Compensation and Adaptive Third-Order PLL Demodulation Method for TMR-Based Magnetic Encoders
by Yue Xin, Jia Cui, Haifeng Wei and Li Lui
Electronics 2026, 15(4), 860; https://doi.org/10.3390/electronics15040860 - 18 Feb 2026
Abstract
TMR-based magnetic encoders provide sensitive SIN/COS signals, but practical accuracy is degraded by channel mismatch and decoder dynamics. This study evaluates an end-to-end embedded implementation on a PMSM (Permanent Magnet Synchronous Motor) bench. We consider amplitude mismatch, quadrature non-orthogonality, and harmonic/noise disturbances in [...] Read more.
TMR-based magnetic encoders provide sensitive SIN/COS signals, but practical accuracy is degraded by channel mismatch and decoder dynamics. This study evaluates an end-to-end embedded implementation on a PMSM (Permanent Magnet Synchronous Motor) bench. We consider amplitude mismatch, quadrature non-orthogonality, and harmonic/noise disturbances in the measured differential channels. We implement a lightweight compensation chain, including fixed-window moving-average filtering, min–max amplitude normalization, and correlation-based quadrature identification with sample-shift correction. We then compare four demodulation configurations under identical sampling and reference alignment to a 24-bit encoder: (A0) conventional second-order PLL (phase locked loop), (A1) compensation + open-loop atan2, (A2) compensation + fixed-ωn third-order PLL, and (A3) compensation + adaptive-ωn third-order PLL. Experiments with a TMR3081 sensor and an STM32 controller show clear differences among A0–A3. In steady operation, A3 removes the DC bias observed with A0 and keeps the angle error within approximately ±0.3° in the evaluated steady window. During commutation and ramp-like segments, PLL-based tracking (A0/A2/A3) is more robust than open-loop atan2 (A1), and bandwidth adaptation in A3 improves the acquisition–noise trade-off within the preset ωn bounds. These results are reported for this prototype and the tested parameter settings. Full article
16 pages, 9023 KB  
Article
Optimising Camera–ChArUco Geometry for Motion Compensation in Standing Equine CT: A CT-Motivated Benchtop Study
by Cosimo Aliani, Cosimo Lorenzetto Bologna, Piergiorgio Francia and Leonardo Bocchi
Sensors 2026, 26(4), 1310; https://doi.org/10.3390/s26041310 - 18 Feb 2026
Abstract
Standing equine computed tomography (CT) acquisitions are susceptible to residual postural sway, which can introduce view-inconsistent motion and degrade image quality. External optical tracking based on ChArUco fiducials is a promising, low-cost strategy to enable projection-wise motion compensation, yet quantitative guidance on how [...] Read more.
Standing equine computed tomography (CT) acquisitions are susceptible to residual postural sway, which can introduce view-inconsistent motion and degrade image quality. External optical tracking based on ChArUco fiducials is a promising, low-cost strategy to enable projection-wise motion compensation, yet quantitative guidance on how camera–marker geometry affects pose-estimation performance remains limited. This CT-motivated benchtop study characterizes how the relative camera–ChArUco configuration influences both the accuracy (bias with respect to ground truth) and the precision (repeatability) of pose estimates obtained from RGB images using OpenCV ChArUco detection and reprojection-error minimization to estimate the rigid camera-to-board transformation. Controlled experiments systematically varied acquisition protocol (continuous repeated estimates at fixed pose versus cyclic repositioning), viewing angle over a wide angular range at two working distances, and camera-to-board distance over multiple depth settings. Ground truth for angular configurations was defined by a stepper-motor rotation stage, while distance ground truth was obtained by ruler measurements. Performance was summarized via mean absolute error and standard deviation across repeated measurements, complemented by variance-based statistical testing with multiple-comparison correction. Cyclic repositioning did not yield evidence of increased variability relative to continuous acquisitions, supporting view-by-view sampling. Viewing angle induced a consistent accuracy–precision trade-off for rotations: frontal views minimized mean error but exhibited higher variability, whereas oblique views reduced jitter at the expense of increased bias. Increasing working distance reduced repeatability, most prominently for depth-related components. Overall, these findings provide pre-clinical guidance for selecting camera/marker placement (moderately oblique viewpoints, limited working distance, sufficient image footprint) before in-scanner and in-vivo validation for standing equine CT motion compensation. Full article
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21 pages, 1287 KB  
Article
Machine Learning Calibration of Smartphone-Based Infrared Thermal Cameras: Improved Bias and Persistent Random Error
by Jayroop Ramesh, Tom Loney, Stefan Du Plessis, Homero Rivas, Assim Sagahyroon, Fadi Aloul and Thomas Boillat
Sensors 2026, 26(4), 1295; https://doi.org/10.3390/s26041295 - 17 Feb 2026
Viewed by 68
Abstract
Low-cost, smartphone-based thermal cameras offer unprecedented accessibility for physiological monitoring, yet their validity and reliability for absolute skin temperature measurement in clinical settings remain contentious. This study aims to quantify the agreement and repeatability of a widely used smartphone thermal camera, the FLIR [...] Read more.
Low-cost, smartphone-based thermal cameras offer unprecedented accessibility for physiological monitoring, yet their validity and reliability for absolute skin temperature measurement in clinical settings remain contentious. This study aims to quantify the agreement and repeatability of a widely used smartphone thermal camera, the FLIR One Pro, against a consumer-grade, non-contact infrared thermometer, the iHealth PT3. A method comparison study was conducted with 40 healthy adult participants, yielding a total of 2400 temperature measurements. Skin temperature of the hand dorsum was measured concurrently with the FLIR One Pro and the iHealth PT3. The protocol involved two rounds: Round 1 (R1) in a stable, static environment to assess baseline repeatability, and Round 2 (R2) in a dynamic environment mimicking clinical repositioning. The performance of the instruments was compared using paired t-tests for mean differences and Bland–Altman analysis for assessing agreement. The iHealth PT3 demonstrated superior precision, with an average intra-participant standard deviation (SD) of 0.030 °C in R1 and 0.092 °C in R2. In stark contrast, the FLIR One Pro exhibited significantly higher variability, with an average SD of 0.34 °C in R1 and 0.30 °C in R2. Bland–Altman analysis revealed a substantial mean bias of −1.42 °C in R1 and −1.15 °C, with critically wide 95% limits of agreement ranges of ≈6 °C. The substantial systematic bias and poor agreement of the FLIR One Pro far exceed both its manufacturer-stated accuracy and clinically acceptable error margins for absolute temperature measurement. To further examine whether calibration could mitigate these deficiencies, we applied a suite of ten machine learning regressors to map FLIR readings onto iHealth PT3 values. Calibration reduced systematic bias across all models, with Quantile Gradient-Boosted Regression Trees achieving the lowest MAE (1.162 °C). The Extra Trees model yielded the lowest RMSE (1.792 °C) and the highest explained variance (R2 = 0.152), yet this relatively low value confirms that the device’s high intrinsic variability limits the effectiveness of algorithmic correction. As such the device has limited utility for longitudinal patient monitoring or for diagnostic decisions that rely on precise, absolute temperature thresholds. These findings inform medical practitioners in low-resource settings of the profound limitations of using this device as a standalone clinical thermometer and emphasize that algorithmic correction cannot compensate for fundamental hardware and measurement noise constraints. Full article
(This article belongs to the Special Issue AI-Based Sensing and Imaging Applications)
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31 pages, 10739 KB  
Article
Multi-Point Contact Dynamics of a Novel Self-Centring Mechanism for In-Space Robotic Assembly
by Yuanxin Wang, Jiafu Liu, Shujie Ma, Jianping Jiang, Yuanyuan Li and Xing Wang
Aerospace 2026, 13(2), 188; https://doi.org/10.3390/aerospace13020188 - 16 Feb 2026
Viewed by 76
Abstract
Autonomous in-space assembly using a free-flying robot can lead to residual vibrations and positioning errors of the target modules during the grasping process. This places stringent demands on end-effectors, which must tolerate large misalignments while maintaining high positioning accuracy. In this regard, this [...] Read more.
Autonomous in-space assembly using a free-flying robot can lead to residual vibrations and positioning errors of the target modules during the grasping process. This places stringent demands on end-effectors, which must tolerate large misalignments while maintaining high positioning accuracy. In this regard, this paper presents a novel self-centring mechanism, which consists of two self-centring fingers mounted on the end-effector and a double V-groove mechanism attached to the target module. The proposed compact structural design passively corrects substantial parallel offsets and angular misalignments between the end-effector and the module. A multi-point contact model consistent with this mechanism is then developed using the virtual sphere layer method to describe the self-centring process. This model incorporates a normal contact force model and a three-dimensional bristle frictional force model to characterise the multi-point bouncing contact behaviours during the self-centring process. Numerical simulations and experimental tests involving the grasping of a module with a single robotic arm confirm that the self-centring mechanism effectively eliminates initial misalignments, achieving sub-millimetre positioning accuracy. The measured parallel offsets and contact forces align closely with numerical predictions, with minor discrepancies attributed to environmental noise and vibrations from the elastic bungees in the gravity compensation system. Finally, the self-centring mechanism is applied to grasp two modules with a dual-arm robot in the Space Proximity Operations Test facility. The centroid displacements of the robot closely match the simulation results, further validating the accuracy of the proposed multi-point contact model. Full article
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21 pages, 869 KB  
Article
Low-Cost CO2 Sensors: On-Site Performance Evaluation and Co-Location Correction Procedure for Reliable Ventilation Assessments in Schools
by David Honan, John Garvey, John Littlewood, Matthew Horrigan and John Gallagher
Sensors 2026, 26(4), 1265; https://doi.org/10.3390/s26041265 - 15 Feb 2026
Viewed by 255
Abstract
Adequate ventilation is essential for maintaining indoor environmental quality in schools, where ventilation standards are often based on an indoor concentration of human-generated carbon dioxide (CO2) above ambient levels. Low-cost non-dispersive infrared (NDIR) CO2 sensors offer a practical solution for [...] Read more.
Adequate ventilation is essential for maintaining indoor environmental quality in schools, where ventilation standards are often based on an indoor concentration of human-generated carbon dioxide (CO2) above ambient levels. Low-cost non-dispersive infrared (NDIR) CO2 sensors offer a practical solution for ventilation monitoring, yet variability between sensors can compromise accuracy, particularly when applications depend on the determination of precise concentration differences. This study evaluates the performance of twenty-three low-cost CO2 sensors, developing normalisation functions to improve comparability across sensors, introducing an accessible methodology for on-site sensor calibration without the need for laboratory-grade reference equipment. The sensors were co-located for three independent test periods in 2025 representing typical school internal conditions in Ireland. Pre-normalisation analysis showed strong linearity (coefficient of determination (R2) = 0.999) but notable variability, with a mean root mean square error (RMSE) of 18.3 ppm and 0.45% of measurements outside manufacturers stated accuracy. Normalisation models were trained and validated using a leave-one-period-out approach. Regression-based correction yielded the greatest improvement, reducing RMSE by 16%. When applied to the full dataset, final correction factors reduced RMSE by 27%, out-of-range measurements by 43%, and proportional bias by 31%. Corrected sensors demonstrated highly consistent performance, particularly within the CO2 ranges most relevant for classroom ventilation assessment, with an RMSE = 7.4 parts per million (ppm) at ambient concentrations and 11.9 ppm at concentrations below 1500 ppm. Field-based co-location in the deployment environment across full CO2 cycles, combined with a network-derived global reference, produced effective correction factors. Performance declined marginally above 1500 ppm and during dynamic occupancy, while overall accuracy remained strong. The study presents a practical and accessible methodology for evaluating and normalising low-cost CO2 sensors without specialised laboratory equipment, supporting reliable ventilation assessments in schools. Full article
(This article belongs to the Section Environmental Sensing)
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26 pages, 4779 KB  
Article
A Day–Night-Differentiated Method for Sea Surface Temperature Retrieval with Emissivity Correction
by Caixia Gao, Qinghua Zhang, Yaru Meng, Yun Wang, Wan Li, Enyu Zhao and Yongguang Zhao
Remote Sens. 2026, 18(4), 604; https://doi.org/10.3390/rs18040604 - 14 Feb 2026
Viewed by 141
Abstract
Sea surface temperature (SST) is widely used to characterize marine productivity, environmental pollution, and climate variability, and is commonly derived from thermal infrared measurements obtained by optical satellite sensors. However, accurately retrieving large-scale SSTs remains challenging due to the complexity of air–sea coupling [...] Read more.
Sea surface temperature (SST) is widely used to characterize marine productivity, environmental pollution, and climate variability, and is commonly derived from thermal infrared measurements obtained by optical satellite sensors. However, accurately retrieving large-scale SSTs remains challenging due to the complexity of air–sea coupling processes and the difficulty of accurately obtaining key intermediate parameters. This study proposes a day–night-differentiated SST retrieval method with emissivity correction rather than treating it as a fixed value. Specifically, radiance characteristics from the mid-infrared band are integrated alongside those from thermal infrared bands. The retrieved SSTs are then validated against the MODIS SST product and in situ measurements. The results demonstrate strong consistency between the retrieved SST and the MODIS SST product, with overall root mean square errors (RMSEs) of 0.66 K and 0.82 K for daytime and nighttime, respectively. In winter the RMSEs improve to 0.37 K (day) and 0.42 K (night). In situ validation against Argo measurements in 2019 shows that the RMSEs of the retrieved SSTs are approximately 0.26 K for both day and night. This confirms the efficacy of the proposed SST retrieval approach, providing a feasible solution for high-precision SST retrieval in high-latitude regions with large view zenith angles. Full article
31 pages, 3427 KB  
Article
A Data-Driven Method Based on Feature Engineering and Physics-Constrained LSTM-EKF for Lithium-Ion Battery SOC Estimation
by Yujuan Sun, Shaoyuan You, Fangfang Hu and Jiuyu Du
Batteries 2026, 12(2), 64; https://doi.org/10.3390/batteries12020064 - 14 Feb 2026
Viewed by 132
Abstract
Accurate estimation of the State of Charge (SOC) for lithium-ion batteries is a core function of the Battery Management System (BMS). However, LiFePO4 batteries present specific challenges for SOC estimation due to the characteristic plateau in their open-circuit voltage (OCV) versus SOC [...] Read more.
Accurate estimation of the State of Charge (SOC) for lithium-ion batteries is a core function of the Battery Management System (BMS). However, LiFePO4 batteries present specific challenges for SOC estimation due to the characteristic plateau in their open-circuit voltage (OCV) versus SOC relationship. Moreover, data-driven estimation approaches often face significant difficulties stemming from measurement noise and interference, the highly nonlinear internal dynamics of the battery, and the time-varying nature of key battery parameters. To address these issues, this paper proposes a Long Short-Term Memory (LSTM) model integrated with feature engineering, physical constraints, and the Extended Kalman Filter (EKF). First, the model’s temporal perception of the historical charge–discharge states of the battery is enhanced through the fusion of temporal voltage information. Second, a post-processing strategy based on physical laws is designed, utilizing the Particle Swarm Optimization (PSO) algorithm to search for optimal correction factors. Finally, the SOC obtained from the previous steps serves as the observation input to EKF filtering, enabling a probabilistically weighted fusion of the data-driven model output and the EKF to improve the model’s dynamic tracking performance. When applied to SOC estimation of LiFePO4 batteries under various operating conditions and temperatures ranging from 0 °C to 50 °C, the proposed model achieves average Mean Absolute Error (MAE) and Root Mean Square Error (RMSE) as low as 0.46% and 0.56%, respectively. These results demonstrate the model’s excellent robustness, adaptability, and dynamic tracking capability. Additionally, the proposed approach only requires derived features from existing input data without the need for additional sensors, and the model exhibits low memory usage, showing considerable potential for practical BMS implementation. Furthermore, this study offers an effective technical pathway for state estimation under a “physical information–data-driven–filter fusion” framework, enabling accurate SOC estimation of lithium-ion batteries across multiple operating scenarios. Full article
35 pages, 2579 KB  
Article
Geospatial–Temporal Quantification of Tectonically Constrained Marble Resources Within the Wadi El Shati Extensional Regime via Multi-Sensor Sentinel and DEM Data Fusion
by Mahmood Salem Dhabaa, Ahmed Gaber and Adel Kamel Mohammed
Geosciences 2026, 16(2), 81; https://doi.org/10.3390/geosciences16020081 - 14 Feb 2026
Viewed by 110
Abstract
This study addresses a critical knowledge gap in quantifying strategic mineral resources within hyper-arid, tectonically complex terrains by establishing a recursive framework that reconciles deterministic resource estimation with the nonlinear dynamics of tectonically mediated metamorphic systems. Using Libya’s Wadi El Shati as a [...] Read more.
This study addresses a critical knowledge gap in quantifying strategic mineral resources within hyper-arid, tectonically complex terrains by establishing a recursive framework that reconciles deterministic resource estimation with the nonlinear dynamics of tectonically mediated metamorphic systems. Using Libya’s Wadi El Shati as a case study, legacy lithological misclassifications are rectified through the fusion of Sentinel-1 Synthetic Aperture Radar, Sentinel-2 multispectral imagery, and Digital Elevation Model analytics within a unified geospatial workflow. The methodology synergizes atmospherically corrected optical data, processed via supervised Maximum Likelihood Classification, with calibrated radar-derived structural lineaments. Classified marble-bearing zones within the Al Mahruqah Formation are integrated with DEM data and field-validated thickness measurements using Triangulated Irregular Network models to resolve surface–subsurface dependencies and compute volumes. The results demonstrate a 91% lithological classification accuracy, rectifying a 22% error in legacy maps. Structural analysis of 1213 lineaments confirms a dominant NE–SW extensional regime (σ3) that facilitated fluid conduits. The quantified marble-bearing horizon spans ~334 km2 with a volume of 6.0 km3 (±9%). Spatial analysis reveals a causal link between high-grade marble clusters, basaltic intrusions, and NE–SW fault systems, refining models of contact metamorphism in rift-related settings. Full article
24 pages, 3572 KB  
Article
Integrated Wavefront Detection for Large-Aperture Segmented Planar Mirrors: Concept & Principle
by Rui Sun, Qichang An and Xiaoxia Wu
Photonics 2026, 13(2), 189; https://doi.org/10.3390/photonics13020189 - 14 Feb 2026
Viewed by 98
Abstract
Planar mirrors play a crucial role in autocollimation testing and optical beam relay systems of telescopes and other fields. However, for the next-generation large-aperture telescopes, typical monolithic planar mirrors fall short in meeting anticipated performance requirements, owing to their high costs and fabrication [...] Read more.
Planar mirrors play a crucial role in autocollimation testing and optical beam relay systems of telescopes and other fields. However, for the next-generation large-aperture telescopes, typical monolithic planar mirrors fall short in meeting anticipated performance requirements, owing to their high costs and fabrication limitations. Here, a new integrated multimodal testing method for 3–4m-class segmented planar mirrors is proposed. The presented system utilizes an innovative keystone architecture with a central mirror and keystone-shaped segments, which is superior to the traditional hexagonal architecture. To facilitate rapid coarse alignment, a machine vision system based on edge detection is investigated. Furthermore, the dispersed fringe technique is used for robust co-phasing. By using a segmented planar mirror designed with sub-aperture stitching strategy and combining local apertures, the system cost was reduced and high-precision measurement was achieved. Eventually, the alignment, co-focus and co-phasing measurements based on the proposed concept were completed, and the transfer characteristics were determined by analyzing the Optical Transfer Function (OTF). Test data shows co-phasing accuracy of better than 30 nm RMS (root-mean-square) and alignment accuracy less than 10 arcseconds. In addition, the system uses small-aperture mirrors in autocollimation testing to facilitate flexible alignment and testing of individual segments. The test optical path is configured to match the effective focal length of the system under test, and the optical lever effect of reflectors enhances the alignment sensitivity. The method combines autocollimation and wavefront sensing which allows the approach to provide high-precision control of co-focus, co-phasing, and surface errors correction. Full article
(This article belongs to the Special Issue Advances in Optical Fiber Sensing Technology)
16 pages, 4562 KB  
Article
Design and Verification of Non-Intrusive Current Transformer with PCB Coils in Reverse-Series Connection
by Xunan Ding, Juheng Wang, Chenchen Han, Xiao Chen and Jingang Wang
Designs 2026, 10(1), 20; https://doi.org/10.3390/designs10010020 - 13 Feb 2026
Viewed by 147
Abstract
Accurate and reliable current measurement is a key prerequisite for ensuring the safe operation of power systems. Conventional through-core and wound current transformers require power outage for installation or modification of line structures, which are plagued by high installation difficulty and cost, and [...] Read more.
Accurate and reliable current measurement is a key prerequisite for ensuring the safe operation of power systems. Conventional through-core and wound current transformers require power outage for installation or modification of line structures, which are plagued by high installation difficulty and cost, and fail to meet the digital development needs of smart grids. To address the demand for non-intrusive installation of current transformers, this paper proposes a non-intrusive current transformer with PCB coils in reverse-series connection. First, a magnetic coupling current calculation model is established to design a reverse-series double-layer coil structure, and a mathematical model of the equivalent circuit for the sensing and measurement system is constructed. The influence of circuit parameters on the output response is analyzed, yielding an optimization method for the system operating state and completing the hardware circuit design. Subsequently, a simulation model of the reverse-series double-layer coil is built to calculate and analyze the amplitude-frequency characteristics, steady-state and transient performance, as well as anti-interference capability of the transformer. The results demonstrate that the designed transformer, combined with an active integrating circuit, achieves an upper cutoff frequency of 13,169 Hz and a lower cutoff frequency approaching 0 Hz, which satisfies the requirements of wide-frequency measurement while ensuring high sensitivity and anti-interference capability. Finally, a current-sensing experiment platform is built for comparative verification with conventional invasive current transformers. Experimental results show that after correction with a proportional coefficient of 1.317, the fitting squared error is only 0.0038. The linearity remains excellent under different conditions with a wide dynamic measurement range, and the phase error is less than 15°. Within the range of 2–120% of the rated current, the ratio error is less than 0.9%, indicating high measurement accuracy. This study provides a new high-precision and convenient method for current measurement in smart grids. Full article
(This article belongs to the Section Electrical Engineering Design)
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13 pages, 1818 KB  
Article
Adaptive Multi-Tiered Intraday Load Forecasting Strategy with Real-Time Error Correction
by Aleksandar Selakov, Zoran Janković, Aleksandar Bošković, Slađana Turudić, Zoran Pajić and Srđan Vukmirović
Energies 2026, 19(4), 953; https://doi.org/10.3390/en19040953 - 12 Feb 2026
Viewed by 88
Abstract
This paper presents an adaptive short-term intraday load forecasting strategy designed for the operational requirements of transmission and distribution system operators. Standard forecasting approaches often report strong performance on selected periods, yet real utility operations require accurate predictions for every day and every [...] Read more.
This paper presents an adaptive short-term intraday load forecasting strategy designed for the operational requirements of transmission and distribution system operators. Standard forecasting approaches often report strong performance on selected periods, yet real utility operations require accurate predictions for every day and every hour of the year. Deviations during the operating day, caused by unexpected changes in consumer behavior, introduce forecasting errors and financial risk. To address this problem, we propose a multi-tiered forecasting model that selects the base method according to the availability of historically similar days. When many similar days exist, the model uses a pretrained artificial neural network, while linear regression is applied under moderate similarity conditions, and an arithmetic mean is used when only a few similar days are available. A real-time delta correction layer is applied in all cases, using recent intraday measurements to forecast short-term error and adjust the baseline output. This approach enables rapid adaptation to atypical days and intraday anomalies. Testing on five years of utility data demonstrates that the method maintains consistently low MAPE across all days and all hours, providing the level of accuracy needed for intraday market operations and system balancing. Full article
(This article belongs to the Special Issue Advanced Load Forecasting Technologies for Power Systems)
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27 pages, 4240 KB  
Article
Robust State Estimation of Power System Based on Unscented Kalman Filter with Fractional-Order Adaptive Generalized Cross Correlation Entropy
by Yan Huang, Shangyong Wen, Hongyan Xin and Chaohui Xin
Mathematics 2026, 14(4), 642; https://doi.org/10.3390/math14040642 - 12 Feb 2026
Viewed by 128
Abstract
With the high penetration of power electronic devices, modern power systems exhibit complex fractional-order dynamic characteristics. Addressing this, along with the prevalent issues of multi-modal non-Gaussian noise, outliers, and sudden load changes, a fractional-order adaptive generalized cross correlation entropy unscented Kalman filter (FO-AGCCE-UKF) [...] Read more.
With the high penetration of power electronic devices, modern power systems exhibit complex fractional-order dynamic characteristics. Addressing this, along with the prevalent issues of multi-modal non-Gaussian noise, outliers, and sudden load changes, a fractional-order adaptive generalized cross correlation entropy unscented Kalman filter (FO-AGCCE-UKF) method is proposed in this paper. First, acknowledging that traditional integer-order models overlook the cumulative effects of historical states, a fractional-order (FO) discrete-time state-space model is constructed based on the Grünwald–Letnikov definition. This model accurately characterizes the long-memory and non-locality properties of power systems, thereby improving modeling accuracy during transient processes. Second, to mitigate the impact of non-Gaussian noise and outliers, the generalized cross correlation entropy (GCCE) criterion is adopted to replace the traditional mean square error (MSE) criterion. Combined with statistical linearization techniques, a novel recursive filtering framework is derived to enhance robustness against heavy-tailed noise. Furthermore, to address the time-varying and unknown statistical properties of process and measurement noise, an adaptive update mechanism for noise covariance matrices is introduced, which corrects noise parameters online based on innovation sequences. Simulation experiments and comparative analysis on multiple power systems of different scales demonstrate that the proposed method not only exhibits superior anti-interference capability in mixed-Gaussian noise environments but also achieves a faster convergence speed and higher tracking accuracy during dynamic events such as sudden load changes. Full article
(This article belongs to the Special Issue Fractional Order Systems and Its Applications)
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9 pages, 2986 KB  
Article
Research on Phase Correction of Spatial Heterodyne Interferogram Based on Recurrent Neural Network
by Yongying Gan, Zhen Wang, Tingli Song, Zhi Li, Song Ye and Xinqiang Wang
Atmosphere 2026, 17(2), 186; https://doi.org/10.3390/atmos17020186 - 11 Feb 2026
Viewed by 120
Abstract
The spatial heterodyne spectrometer, used in gas and mineral detection, requires phase error correction for data accuracy. Traditionally, this needs ground-based system calibration. In space, however, environmental changes can alter instrument parameters, making recalibration of the phase error surface difficult. Therefore, there is [...] Read more.
The spatial heterodyne spectrometer, used in gas and mineral detection, requires phase error correction for data accuracy. Traditionally, this needs ground-based system calibration. In space, however, environmental changes can alter instrument parameters, making recalibration of the phase error surface difficult. Therefore, there is an urgent need to develop a novel phase correction method that does not require measuring the phase error surface. This study focuses on the phase errors in the interferogram and establishes a predictive model using a recurrent neural network by analyzing the relationship between spectra with errors and those without errors, thereby achieving correction of the error-containing spectra. The results indicate that, in the absence of known phase errors, the recurrent neural network can effectively perform phase error correction, yielding corrected spectra that align closely with the profiles of error-free spectra, while significantly reducing residuals and standard deviations. Compared to convolutional methods, the recurrent neural network approach demonstrates superior correction efficacy and good applicability. Therefore, the recurrent neural network method can be effectively applied to phase correction for various types of spatial heterodyne interferograms. Full article
(This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling)
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18 pages, 3428 KB  
Article
Influence of Electrode Distribution in a Multi-Electrode Electromagnetic Flow Measurement System on the Measurement of Velocity Field in Asymmetric Flow Sections
by Xu Liu, Yuntong Jia, Lu Liu, Jiacheng Cai, Bing Zhang, Zeqiang Shi, Bangbang Han and Genqiang Jing
Energies 2026, 19(4), 928; https://doi.org/10.3390/en19040928 - 10 Feb 2026
Viewed by 200
Abstract
This paper mainly conducts research on the electrode distribution of the multi-electrode electromagnetic flow measurement system. Through simulation work, the weight function of the area to which the electrodes on the pipeline cross-section belong with respect to the potential difference is roughly obtained. [...] Read more.
This paper mainly conducts research on the electrode distribution of the multi-electrode electromagnetic flow measurement system. Through simulation work, the weight function of the area to which the electrodes on the pipeline cross-section belong with respect to the potential difference is roughly obtained. Moreover, by comparing the simulation data with the actual experimental data, the correctness of the simulation work is verified. Tikhonov regularization is utilized to inversely solve the average velocity of the electrode area, and the TR-CNN algorithm is established to refine the velocity field of the pipeline cross-section in question. It mainly introduces the influence of different electrode placement methods on the potential difference. The results show that it has a relatively small impact on the velocity distribution of the fluid cross-section before flowing through the elbow, and the potential difference is highly sensitive to the velocity in the area where the magnetic induction coil and the electrodes are relatively close. The Pitot tube is used to conduct verification measurements on the fluid velocity field in the pipeline. The results indicate that as the measurement points are farther away from the elbow, the “skewing” phenomenon of the fluid flow velocity gradually weakens. In terms of prediction performance, the mean square error (MSE) of the cross-section error is approximately 0.015, and the mean absolute error (MAE) is about 0.095. These error indicators jointly demonstrate that the system has a relatively high measurement accuracy in practical applications. Full article
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17 pages, 4637 KB  
Article
An Approach for Spectrum Extraction Based on Canny Operator-Enabled Adaptive Edge Extraction and Centroid Localization
by Ao Li, Xinlan Ge, Zeyu Gao, Qiang Yuan, Yong Chen, Chao Yang, Licheng Zhu, Shiqing Ma, Shuai Wang and Ping Yang
Photonics 2026, 13(2), 169; https://doi.org/10.3390/photonics13020169 - 10 Feb 2026
Viewed by 184
Abstract
In adaptive optics systems, high spatial resolution detection is a core prerequisite for achieving accurate wavefront correction. High spatial resolution wavefront measurement based on the traditional Shack-Hartmann technique is limited by the density of the microlens array. In contrast, off-axis digital holography technology [...] Read more.
In adaptive optics systems, high spatial resolution detection is a core prerequisite for achieving accurate wavefront correction. High spatial resolution wavefront measurement based on the traditional Shack-Hartmann technique is limited by the density of the microlens array. In contrast, off-axis digital holography technology is applied in wavefront measurement systems of adaptive optics systems due to its advantages of high spatial resolution, non-contact measurement, and full-field measurement. However, during the demodulation of its interference fringes, the accurate extraction of the complex amplitude of the +1st-order diffraction order directly determines the precision of wavefront reconstruction. Traditional frequency-domain filtering methods suffer from drawbacks such as reliance on manual threshold setting, poor adaptability to irregular spectra, and localization deviations caused by multi-region interference, making it difficult to meet the dynamic application requirements of adaptive optics. To address these issues, this study proposes a spectrum extraction method based on the Canny operator for adaptive edge extraction and centroid localization. The method first locks the rough range of the +1st-order spectrum through multi-stage peak screening, then achieves complete segmentation of spectrum spots by combining adaptive histogram equalization with edge closing and filling, resolves centroid indexing errors via maximum connected component screening, and ultimately accomplishes accurate extraction through Gaussian window filtering. Simulation experimental results show that, in comparison with two classical spectrum filtering methods, the centroid estimation error of the proposed method remains below 0.245 pixels under different noise intensity conditions. Moreover, the root mean square error of the residual wavefront corresponding to the reconstructed wavefront of the proposed method is reduced by 89.0% and 87.2% compared with those of the two classical methods, respectively. We further carried out measurement experiments based on a self-developed atmospheric turbulence test bench. The experimental results demonstrate that the proposed method exhibits higher-precision spectral centroid localization capability, which provides a reliable technical support for the high-precision measurement of dynamic distortion induced by atmospheric turbulence. Full article
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