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25 pages, 111771 KB  
Article
Wind-Resistance Stability Analysis of a Magnetic Adhesion Wall-Climbing Obstacle-Crossing Robot for Offshore Wind Turbines
by Jun Liu, Shaojie Jing, Yongsheng Yang and Shiteng Yang
J. Mar. Sci. Eng. 2026, 14(16), 1528; https://doi.org/10.3390/jmse14161528 - 18 Aug 2026
Viewed by 188
Abstract
To address the challenges of adsorption instability and obstacle-crossing difficulties faced by wall-climbing robots in the harsh operation and maintenance (O&M) environment of offshore wind turbine (OWT) towers, this paper presents the design of a magnetic-adhesive wall-climbing robot with a planetary-gear configuration and [...] Read more.
To address the challenges of adsorption instability and obstacle-crossing difficulties faced by wall-climbing robots in the harsh operation and maintenance (O&M) environment of offshore wind turbine (OWT) towers, this paper presents the design of a magnetic-adhesive wall-climbing robot with a planetary-gear configuration and investigates its wind resistance stability. First, the magnetic circuit layout is optimized through finite element analysis, revealing that the F-16 continuous planetary configuration (16 poles) effectively suppresses magnetic flux leakage and forms an integrated magnetic pad, maintaining adsorption force at a large air gap of 20 mm, thereby enhancing magnetic robustness during obstacle crossing and making it the optimal choice for high-load offshore conditions. Second, an unsteady flow field model based on the Kaimal turbulence spectrum is constructed to analyze aerodynamic loads. Fluid–structure interaction (FSI) simulations demonstrate that at a height of 30 m, the turbulence integral scale matches the robot dimensions, and combined with the Venturi effect of gap jet flow, this leads to peak turbulence intensity and pitching moment, creating a hazardous, pronounced aerodynamic amplification condition. Finally, an anti-slip stability model is established, revealing that vertical wall climbing represents the critical loading scenario; the magnetic adhesion system must deliver a total adsorption force of no less than 1000 N to resist a 35 m/s wind speed under low-friction conditions, providing a quantitative design basis for anti-wind safety. This study integrates magnetic circuit optimization, turbulence-resolved aerodynamics, and macroscopic anti-slip mechanics, offering theoretical support and engineering guidance for the safe deployment of intelligent O&M equipment for offshore wind power. Bench-scale measurements of magnetic adhesion force, friction coefficient, and translation force fluctuation support the exponential-decay magnetic model and the multi-wheel phase-interleaving concept; however, the current 4 × 16-pole prototype delivers ~627 N at the 2 mm working gap, below the 1000 N design target. The design methodology is therefore validated, while the current physical configuration requires further iteration of the working gap or magnet grade before it can be considered operationally adequate. Full article
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18 pages, 19803 KB  
Article
Performance Analysis and Experimental Validation of Outer-Rotor Permanent Magnet Synchronous Motors for Drone Propulsion Systems
by Min-Mo Koo and Hyeon-Jae Shin
Energies 2026, 19(16), 3845; https://doi.org/10.3390/en19163845 - 17 Aug 2026
Viewed by 224
Abstract
As the drone industry expands rapidly, the demand for high-performance propulsion systems with high power density, superior energy efficiency, and lightweight characteristics has grown significantly. Outer-rotor permanent magnet synchronous motors (OR-PMSMs) are particularly well-suited for drone propulsion, due to their superior torque density [...] Read more.
As the drone industry expands rapidly, the demand for high-performance propulsion systems with high power density, superior energy efficiency, and lightweight characteristics has grown significantly. Outer-rotor permanent magnet synchronous motors (OR-PMSMs) are particularly well-suited for drone propulsion, due to their superior torque density and efficient thermal management, compared to inner-rotor structures. However, achieving accurate performance prediction during the initial design phase remains challenging due to complex electromagnetic phenomena. This paper proposes an analytical methodology using the subdomain method to evaluate the electromagnetic performance of OR-PMSMs, specifically accounting for slotting effects caused by stator geometry. Rather than focusing on complex optimization algorithms, this study prioritizes comprehensive performance evaluation and experimental validation. Key electromagnetic parameters and circuit constants—including air-gap flux density, back-EMF, winding resistance, inductance, and electromagnetic torque—are calculated efficiently using the proposed analytical model. To complement the limitations of analytical formulation regarding core saturation and flux leakage, the finite element method (FEM) is conducted for comparative evaluation. Furthermore, a physical prototype of the OR-PMSMs for drone propulsion was fabricated, and experimental tests were performed to validate the analytical and numerical results. The analytical predictions demonstrate strong agreement with both the FEM simulations and experimental measurements, confirming the accuracy and reliability of the proposed framework. Consequently, this study addresses the inherent constraints of conventional analytical methods and provides a computationally efficient, yet precise, evaluation procedure, serving as valuable baseline data for the design and development of high-efficiency, lightweight drone propulsion motors. Full article
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20 pages, 2319 KB  
Article
A Whale Optimization Algorithm Based on Oscillatory Convergence and Diversity Variation for Complex Defect Profile Inversion in Oil and Gas Pipelines
by Wanjun Han, Senxiang Lu and Jingwen Bai
Mathematics 2026, 14(15), 2820; https://doi.org/10.3390/math14152820 - 5 Aug 2026
Viewed by 232
Abstract
Magnetic leakage detection is one of the most commonly used methods for pipeline inspection, which mainly uses magnetic sensors to detect the magnetic leakage field on the internal and external surfaces of the pipeline to determine whether there are defects in the pipeline. [...] Read more.
Magnetic leakage detection is one of the most commonly used methods for pipeline inspection, which mainly uses magnetic sensors to detect the magnetic leakage field on the internal and external surfaces of the pipeline to determine whether there are defects in the pipeline. The defect quantification algorithm includes a forward model and an optimization algorithm, in which the estimation of target defects using optimization algorithms is one of the key aspects of defect inversion. Most of the existing optimization algorithms are based on particle swarm algorithms (PSOs) and genetic algorithms (GAs), which are prone to premature problems and have low convergence accuracy. To address the problems in the process of defect inversion, this paper proposes a new inversion algorithm, which obtains part of the prior knowledge from the application context of defect inversion, and adopts the decay oscillation function as the nonlinear convergence factor based on the whale optimization algorithm (WOA). In addition, referring to the concepts of “genetic” and “mutation” in the GA, a diversity variation strategy based on dynamic step size is designed. The algorithm designed has the advantages of fast operation and high search accuracy. At the end of the paper, two sets of experiments are designed to compare the improved WOA with other existing optimization algorithms. The results demonstrate that the algorithm is significantly superior to other algorithms, both in the ideal case of simulation experiments and in the practical application of defect inversion. Full article
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25 pages, 10819 KB  
Article
A Magnetic–Inductive Dual-Channel Inspection Method with Spatial Registration for Defect Characterization in Ferromagnetic Materials
by Jindao Qiu and Senxiang Lu
Machines 2026, 14(8), 867; https://doi.org/10.3390/machines14080867 - 1 Aug 2026
Viewed by 284
Abstract
Shallow defects in ferromagnetic components may produce weak and unstable magnetic flux leakage responses in compact inspection devices, whereas an inductive response alone does not provide the same depth-related magnetic information. To obtain complementary defect information, this study proposes a magnetic–inductive dual-channel inspection [...] Read more.
Shallow defects in ferromagnetic components may produce weak and unstable magnetic flux leakage responses in compact inspection devices, whereas an inductive response alone does not provide the same depth-related magnetic information. To obtain complementary defect information, this study proposes a magnetic–inductive dual-channel inspection method that integrates an MLX90393 three-axis digital magnetic sensor with a PCB planar spiral coil and an LDC1612 inductance-to-digital converter. Because the two sensing units are physically separated on the detection board, peak-position offset analysis and spatial registration were introduced to associate their responses to the same defect region. Controlled experiments were conducted on a laboratory pipeline inspection platform using a Q235 defect specimen installed at the internal inspection position of the pipe. The defects were machined on the inner surface, which was also the inspection surface. For each defect, five motor-driven axial scans were performed at 10 mm/s, with 400 samples acquired at 100 Hz during each 4 s scan. Response amplitude, signal-to-noise ratio, peak position, and repeatability were evaluated. For the square-hole defects, the magnetic response amplitude decreased from 675.0 to 98.5 a.u. as the depth ratio decreased from 50% to 10%, while the magnetic-channel SNR decreased from 30.5 to 4.7. For the 10% depth defect, the inductive channel retained an average SNR of 434.4 and a coefficient of variation of 0.23%, providing a stable auxiliary response. However, the pre-registration peak-position offset measured for this shallow defect was 21.2±20.9 sampling points, indicating substantial uncertainty in using a single magnetic extremum for scan-specific registration when the magnetic response was weak. These results demonstrate that the two channels provide different and complementary information under controlled laboratory conditions, while further validation is required for irregular corrosion, other ferromagnetic components, and practical inspection conditions. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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8 pages, 7360 KB  
Proceeding Paper
Modeling and Simulation of Planar Transformer for Flyback Converter
by Hristo Ibrishimov, Dimitar Arnaudov and Milko Yovchev
Eng. Proc. 2026, 150(1), 86; https://doi.org/10.3390/engproc2026150086 - 30 Jul 2026
Viewed by 262
Abstract
In this paper, the design of a planar transformer for a flyback converter and modeling using the finite element method are presented. Results are obtained for primary and secondary winding inductance, transformer leakage inductance, winding parasitic capacitances, winding current density, magnetic flux density, [...] Read more.
In this paper, the design of a planar transformer for a flyback converter and modeling using the finite element method are presented. Results are obtained for primary and secondary winding inductance, transformer leakage inductance, winding parasitic capacitances, winding current density, magnetic flux density, and distribution of magnetic field lines. A simulation of the operation of the converter in the continuous current mode and in border mode was made to validate the obtained electrical parameters. Full article
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42 pages, 3136 KB  
Article
New DTMOS-Based Charge- and Flux-Controlled Memtranstor Emulators
by Predrag Petrović
Appl. Sci. 2026, 16(15), 7551; https://doi.org/10.3390/app16157551 - 29 Jul 2026
Viewed by 256
Abstract
Memtranstors are emerging higher-order memory elements that establish a state-dependent constitutive relationship between electric charge and magnetic flux, making them attractive for adaptive analog electronics, neuromorphic computing, nonlinear dynamical systems, and memory-enabled signal processing applications. However, existing memtranstor emulators predominantly rely on operational [...] Read more.
Memtranstors are emerging higher-order memory elements that establish a state-dependent constitutive relationship between electric charge and magnetic flux, making them attractive for adaptive analog electronics, neuromorphic computing, nonlinear dynamical systems, and memory-enabled signal processing applications. However, existing memtranstor emulators predominantly rely on operational amplifiers, analog multipliers, current conveyors, or behavioral models, leading to increased circuit complexity and limited suitability for monolithic CMOS integration. This paper presents a unified transistor-level dynamic-threshold MOS (DTMOS) framework for realizing both charge-controlled and flux-controlled memtranstor emulators. The proposed architectures synthesize direct and inverse memtranstances through capacitive state integration, state-dependent DTMOS conductance modulation, and current-domain affine processing, thereby eliminating the need for composite active building blocks. Closed-form analytical expressions are derived for both constitutive relations and explicitly related to transistor-level parameters, bias conditions, and state-storage elements. The theoretical framework is further supported by comprehensive analyses of channel-length modulation, finite output resistance, device mismatch, DTMOS body-effect deviations, leakage mechanisms, pseudo-resistor non-idealities, parasitic capacitances, and small-signal stability. Cadence Virtuoso simulations performed in a 180 nm triple-well CMOS technology validate the analytical predictions and demonstrate the characteristic butterfly shaped pinched hysteresis loops of both emulators. The proposed circuits operate from a single 0.8 V supply while dissipating approximately 22 μW and 36 μW for the charge-controlled and flux-controlled realizations, respectively, and exhibit electronic tunability, together with robustness against process and temperature variations. Representative implementations of reconfigurable frequency-selective circuits and a memtranstor-based envelope detector further demonstrate the practical applicability of the proposed architectures. To the best of the author’s knowledge, this work presents the first unified transistor-level DTMOS constitutive synthesis framework for realizing both direct and inverse memtranstive behavior, providing a scalable foundation for future adaptive mixed-signal integrated circuits, programmable analog memory systems, neuromorphic hardware, and in-memory computing platforms. Full article
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33 pages, 11168 KB  
Review
Non-Destructive Testing Technology for Shallow Subsurface Defects in Rails: A Review with Focus on Ultrasonic Surface Wave Methods
by Tianyu Song, Lisha Peng, Songling Huang, Zijing Huang, Qibo Feng and Hongyu Sun
Sensors 2026, 26(14), 4614; https://doi.org/10.3390/s26144614 - 21 Jul 2026
Viewed by 628
Abstract
With increasing rail traffic intensity, reliable detection of shallow subsurface rail damage is essential for operational safety. This critical narrative review evaluates non-destructive testing technologies relevant to defects whose active crack front or principal scattering zone lies within the upper approximately 0.5–10 mm [...] Read more.
With increasing rail traffic intensity, reliable detection of shallow subsurface rail damage is essential for operational safety. This critical narrative review evaluates non-destructive testing technologies relevant to defects whose active crack front or principal scattering zone lies within the upper approximately 0.5–10 mm of the rail, while treating the 10–15 mm range as a transition to deeper-defect verification. Magnetic flux leakage, magnetic particle inspection, visual inspection, eddy current testing, and conventional ultrasonic testing are first examined as screening or confirmatory comparators. The review then focuses on four ultrasonic surface-wave excitation routes—contact piezoelectric, active air-coupled, electromagnetic acoustic, and laser ultrasonic—and distinguishes source-specific laboratory capability from demonstrated field evidence. Because the cited studies use different defect geometries, rail conditions, sensor configurations, speeds, and decision criteria, their numerical values are reported as source-conditioned evidence rather than as a normalized ranking. An engineering decision matrix links defect depth and size, inspection speed, surface condition, and noise environment to a recommended screening–confirmation workflow. The synthesis identifies contact piezoelectric UT/PAUT as the most mature quantitative confirmation route, while EMAT, air-coupled UT, and laser UT retain method-specific advantages but require stronger natural-defect and in-service validation. Full article
(This article belongs to the Section Industrial Sensors)
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25 pages, 6176 KB  
Article
RIME-ICEEMDAN-WPD-Based Denoising for MFL Sensor Signals in Pipeline Defect Detection
by Di Yin, Ruoxi Bai, Funing Qi and Yanbao Guo
Processes 2026, 14(14), 2294; https://doi.org/10.3390/pr14142294 - 14 Jul 2026
Viewed by 392
Abstract
Magnetic Flux Leakage (MFL) sensors are pivotal for the non-destructive inspection of oil and gas pipelines. However, the accuracy of defect quantification is severely compromised by pervasive noise in field-acquired MFL sensor signals, leading to substantial measurement uncertainty. To address this, we introduce [...] Read more.
Magnetic Flux Leakage (MFL) sensors are pivotal for the non-destructive inspection of oil and gas pipelines. However, the accuracy of defect quantification is severely compromised by pervasive noise in field-acquired MFL sensor signals, leading to substantial measurement uncertainty. To address this, we introduce a novel hybrid denoising framework that synergizes Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN) and Wavelet Packet Decomposition (WPD). The key innovation is the employment of the Rime Optimization Algorithm (RIME) to automatically fine-tune the critical parameters of ICEEMDAN—the signal-to-noise ratio (SNR) and the number of noise additions—thereby customizing the decomposition for superior sensor signal enhancement. This optimization effectively suppresses mode aliasing and yields intrinsic mode functions that faithfully represent underlying defect features. The framework’s efficacy is rigorously validated through mathematical modeling, COMSOL Multiphysics 6.3-based finite element simulation, and real-field MFL sensor data. Results demonstrate remarkable improvements in sensor signal quality: a 53.69% increase in the SNR and reductions of 61.03% in MAE and 62.05% in RMSE over conventional methods. Crucially, the method achieved a Feature Preservation Rate (FPR) of 97.18% on simulated defects, underscoring its exceptional capability to retain critical metrological features for defect sizing. This work provides a robust signal-processing framework that significantly advances the measurement fidelity of MFL sensors, enabling more reliable pipeline integrity assessment. Full article
(This article belongs to the Section AI-Enabled Process Engineering)
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33 pages, 2014 KB  
Review
Detection and Analysis of Conveyor Belt Damage: A Review of Sensing Technologies and Signal-Based Approaches
by Aleksandra Rzeszowska, Ryszard Błażej and Leszek Jurdziak
Sensors 2026, 26(14), 4453; https://doi.org/10.3390/s26144453 - 13 Jul 2026
Viewed by 803
Abstract
Conveyor belts constitute critical components of bulk material handling systems, and their reliable operation directly affects process continuity, operational safety, and maintenance costs in industrial environments. Increasing requirements regarding system reliability and predictive maintenance have stimulated the development of advanced diagnostic methods for [...] Read more.
Conveyor belts constitute critical components of bulk material handling systems, and their reliable operation directly affects process continuity, operational safety, and maintenance costs in industrial environments. Increasing requirements regarding system reliability and predictive maintenance have stimulated the development of advanced diagnostic methods for conveyor belt condition monitoring. This review presents a comprehensive analysis of conveyor belt damage detection and diagnostic approaches, with particular emphasis on sensing technologies and signal-based methodologies. The paper discusses major conveyor belt degradation mechanisms and analyzes their representation in diagnostic data obtained using different sensing modalities. Current developments in machine vision systems, magnetic methods based on magnetic flux leakage, ultrasonic techniques, and X-ray imaging are critically reviewed together with signal preprocessing procedures, feature extraction strategies, and damage classification approaches. Particular attention is devoted to the transition from conventional signal processing techniques toward machine learning and deep learning methods enabling automated feature representation and fault identification. The analysis indicates that despite substantial progress in sensing technologies and artificial intelligence, most existing solutions remain strongly sensor-specific and limited to individual data modalities. Key research gaps include the lack of unified damage representation frameworks, limited benchmark datasets, and the insufficient integration of multimodal sensing information. Future progress will likely depend on the development of integrated diagnostic ecosystems combining heterogeneous sensing technologies, advanced feature representation methods, and intelligent decision-support systems. Full article
(This article belongs to the Special Issue Feature Review Papers in Fault Diagnosis & Sensors)
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21 pages, 15423 KB  
Article
Periodic Motion Characteristics of a Magnetic Suspended Dual-Rotor System with Nonlinear Bearing Effects
by Mingzheng Liu, Nianxian Wang, Xinyuan Chen, Yuan Xu, Yingjie Ding and Qiwei Wang
Sensors 2026, 26(14), 4400; https://doi.org/10.3390/s26144400 - 10 Jul 2026
Viewed by 408
Abstract
To investigate the nonlinear dynamic characteristics of magnetic suspended dual-rotor systems, this study examines periodic and quasi-periodic responses induced by bearing nonlinearities, including flux leakage and magnetic saturation effects. A nonlinear dynamic model is established using the finite element method, incorporating unbalance excitation [...] Read more.
To investigate the nonlinear dynamic characteristics of magnetic suspended dual-rotor systems, this study examines periodic and quasi-periodic responses induced by bearing nonlinearities, including flux leakage and magnetic saturation effects. A nonlinear dynamic model is established using the finite element method, incorporating unbalance excitation and nonlinear bearing forces. A comprehensive parametric analysis is conducted to evaluate the effects of rotational speed, initial stiffness, and initial damping on the system’s dynamic responses and bifurcation behavior. The results reveal the occurrence of period-5 and quasi-periodic vibrations under nonlinear bearing conditions. In the quasi-periodic regime, low-frequency components dominate, and the force–current characteristics of the magnetic bearings spread over a wider band, reflecting a multi-valued force–current relationship. Furthermore, decreasing initial stiffness and increasing damping advance the onset of quasi-periodic responses and reduce the corresponding critical rotational speed. Notably, through real-time control adjustment, quasi-periodic motion can be converted into periodic motion, thereby distinguishing the system from conventional mechanically supported rotor systems. Experimental results obtained from a magnetic suspended dual-rotor test rig validate both the bearing-force model and the dynamic model, and further reveal periodic variations in system response under different speed ratios. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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30 pages, 11826 KB  
Article
Eddy-Current-Induced Waveform Reconstruction by Metallic Probe Carriers in Magnetic Flux Leakage Inspection
by Xiaoyuan Jiang, Bohan Jia and Yanhua Sun
Sensors 2026, 26(13), 4312; https://doi.org/10.3390/s26134312 - 7 Jul 2026
Viewed by 420
Abstract
Metallic probe carriers are commonly used in magnetic flux leakage (MFL) inspection to support sensing elements and maintain lift-off, but a conductive carrier located near the sensor can act as an active electromagnetic boundary. This study investigates the carrier-induced waveform reconstruction caused by [...] Read more.
Metallic probe carriers are commonly used in magnetic flux leakage (MFL) inspection to support sensing elements and maintain lift-off, but a conductive carrier located near the sensor can act as an active electromagnetic boundary. This study investigates the carrier-induced waveform reconstruction caused by such a conductive near-field boundary. A theoretical model is developed to describe the induced current, secondary magnetic field, and relaxation-related downstream memory generated when the carrier moves through a non-uniform leakage field. Transient finite-element simulations are used to examine the effects of carrier material, scanning speed, and concave carrier geometry. Compared with the air reference, aluminum and copper carriers produce stage-dependent waveform reconstruction, including valley modification, peak modulation, feature-position shift, and trailing-side extension. The quantitative waveform-deviation indicators increase with increasing speed and are further regulated by carrier geometry. Experimental results based on repeated magnetic response events confirm amplitude suppression, non-zero residual after amplitude matching, response broadening, and enhanced trailing asymmetry. These results demonstrate that the metallic probe carrier is not an electromagnetically transparent holder but an active near-field conductive boundary that should be considered in probe-carrier design and MFL signal interpretation. Full article
(This article belongs to the Section Physical Sensors)
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21 pages, 12091 KB  
Article
Research on Pipeline Magnetic Flux Leakage Testing Defect Classification Based on Generate Expansion and Dual-Channel Vision Transformer
by Xulai Zhu, Yuxiang Zhang, Qiansheng Fang, Jin Jiang, Nana Zhang, Shiheng Tang and Gongquan Zhang
Appl. Sci. 2026, 16(12), 6214; https://doi.org/10.3390/app16126214 - 19 Jun 2026
Viewed by 342
Abstract
Magnetic flux leakage (MFL) testing is a vital non-destructive testing method used to identify defects in oil and gas pipelines and critical components. However, variations in defect geometry and testing conditions can lead to inaccurate data and imbalanced feature distributions, which compromise detection [...] Read more.
Magnetic flux leakage (MFL) testing is a vital non-destructive testing method used to identify defects in oil and gas pipelines and critical components. However, variations in defect geometry and testing conditions can lead to inaccurate data and imbalanced feature distributions, which compromise detection outcomes. To address these challenges, this paper presents a defect classification approach for MFL testing based on generating expansion and the Dual-Channel Vision Transformer (DC-ViT). First, COMSOL finite element software (version 6.1) was used to simulate magnetic flux leakage for different types of pipeline defects. Axial and radial dual-channel signals were extracted to create the initial dataset. Next, a Conditional Variational Autoencoder (CVAE) was used for Generate Expansion to effectively mitigate sample scarcity and defect category imbalance. Finally, the DC-ViT model was constructed and trained using the Generate Expansion dataset as input to achieve multidimensional feature fusion and classification prediction for defects. Experimental results demonstrate 97.97% detection accuracy. The DC-ViT model outperforms traditional convolutional neural networks and single-channel models in terms of accuracy, precision, recall, and F1-score. These results validate the method’s effectiveness and robustness in complex defect scenarios and offer a novel approach to magnetic leakage signal detection. Full article
(This article belongs to the Section Computing and Artificial Intelligence)
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34 pages, 2043 KB  
Article
Matching of Multi-Run MFL In-Line Inspection Data Based on Dynamic Thresholds and Adaptive Anchor-Based Segmentation
by Shuo Zhang, Senxiang Lu, Yichen Liu and Liuqing He
Mathematics 2026, 14(12), 2200; https://doi.org/10.3390/math14122200 - 18 Jun 2026
Viewed by 283
Abstract
Matching of multi-run magnetic flux leakage (MFL) in-line inspection data for oil and gas pipelines provides an essential basis for defect evolution analysis, corrosion growth assessment, and integrity management. However, in practical engineering applications, inconsistencies in total measured mileage, differences in the number [...] Read more.
Matching of multi-run magnetic flux leakage (MFL) in-line inspection data for oil and gas pipelines provides an essential basis for defect evolution analysis, corrosion growth assessment, and integrity management. However, in practical engineering applications, inconsistencies in total measured mileage, differences in the number of key points, and cumulative mileage errors across different inspection runs significantly increase the difficulty of data matching. To address these issues, this study proposes a report-level matching framework for multi-run MFL in-line inspection data that combines key-point alignment with defect matching. The proposed method improves the adaptability of defect matching under complex defect-size and spatial-distribution conditions through a dynamic-threshold mechanism and mitigates the influence of cumulative mileage errors on the matching results in later pipeline sections when large total mileage discrepancies exist between inspection runs through an adaptive anchor-based segmentation mechanism. Experiments based on multi-run MFL in-line inspection data from two actual pipelines demonstrate that the proposed method can achieve stable key-point and defect correspondence in scenarios with both small and large total mileage differences, thereby providing a basis for subsequent defect growth analysis. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
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16 pages, 3246 KB  
Article
Analytical Modeling and Analysis of High-Torque-Density Three-Segment Halbach Array PM Machine by Considering Leakage Flux
by Jinlin Huang, Qingfeng Sun and Chen Wang
Machines 2026, 14(6), 683; https://doi.org/10.3390/machines14060683 - 12 Jun 2026
Viewed by 425
Abstract
Conventional finite element method (FEM) has a complex model and a long optimization time for Halbach array PM machines. This paper proposes a hybrid analytical method that combines the subdomain method (SM) and the magnetic circuit method (MEC) for analyzing a high-torque-density, three-segment [...] Read more.
Conventional finite element method (FEM) has a complex model and a long optimization time for Halbach array PM machines. This paper proposes a hybrid analytical method that combines the subdomain method (SM) and the magnetic circuit method (MEC) for analyzing a high-torque-density, three-segment Halbach array rotor permanent magnet (PM) machine, accounting for Halbach array magnetization and end leakage flux. Firstly, to address the challenge posed by complex PM shapes in the Halbach array PM machine, a novel subdivision equivalence method is conducted. Then, the magnetic equivalent circuit (MEC) of the stator and rotor is established, and the axial leakage flux and nonlinearity of the iron core are taken into account. In addition, electromagnetic performance, such as air gap flux density, cogging torque, electromagnetic torque, and back electromotive force (back-EMF), is obtained based on the proposed hybrid analytical model. The analytical results are verified by using the finite element method (FEM), and the results show that the error is less than 2%. Finally, a 15 kW prototype PM machine with a Halbach array PM rotor is manufactured and tested, and the results validate the accuracy and efficiency of the analytical method. Full article
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28 pages, 6635 KB  
Article
Advanced Fault Detection of Permanent Magnet Faults in Offshore Wind Turbine Generators Using Finite Element Analysis and Deep Transfer Learning
by Hüseyin Tayyer Canseven, Mustafa Ercire, Merve Cömert, Abdurrahman Ünsal and Nur Sarma
Machines 2026, 14(6), 665; https://doi.org/10.3390/machines14060665 - 8 Jun 2026
Cited by 2 | Viewed by 450
Abstract
As the offshore wind industry scales toward 15 MW capacity, the reliability of Direct-Drive Permanent Magnet Synchronous Generators (DD-PMSGs) becomes critical. However, real-world run-to-failure data for these massive, multi-pole machines is virtually non-existent, creating a barrier for developing effective data-driven diagnostic systems. This [...] Read more.
As the offshore wind industry scales toward 15 MW capacity, the reliability of Direct-Drive Permanent Magnet Synchronous Generators (DD-PMSGs) becomes critical. However, real-world run-to-failure data for these massive, multi-pole machines is virtually non-existent, creating a barrier for developing effective data-driven diagnostic systems. This study proposes a high-fidelity framework for detecting permanent magnet faults in the International Energy Agency (IEA) 15 MW Reference Wind Turbine. Using Finite Element Analysis (FEA), a dataset (magnetic flux and back electromotive-force (EMF)) capturing the electromagnetic signatures of healthy and faulty states of a PMSG under varying severities is generated. To improve the power of computer vision, 1D time-series signals were transformed into 2D images. Specifically, Gramian Angular Fields (GAFs) and Recurrence Plots (RPs) were applied to magnetic flux density signals, while Markov Transition Fields (MTFs) were applied to back-EMF signals. These representations were then fused into multi-channel Red-Green-Blue (RGB) images and processed via a ResNet-18 Deep Transfer Learning model using a strictly non-overlapping, leakage-free dataset partitioning strategy. The proposed framework achieved a classification accuracy of 99.45% on noise-free data. Furthermore, robustness testing under varying levels of Additive White Gaussian Noise (AWGN) (30 dB, 40 dB, and 50 dB Signal-to-Noise Ratio (SNR)) demonstrated sustained high performance, maintaining over 90% accuracy even under severe 30 dB noise conditions. Comparative analysis proved that this multi-channel fusion significantly outperforms single-channel encoding methods, which collapse under heavy noise, validating the scalability of the framework and applicability for next-generation condition monitoring in harsh offshore environments. Full article
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