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Search Results (843)

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22 pages, 5048 KB  
Article
Continuous Anchor-Confidence-Weighted UWB/IMU Localization for Unmanned Ground Vehicles in Structured Indoor Environments
by Yufei Yang and Wei Liu
Sensors 2026, 26(16), 5215; https://doi.org/10.3390/s26165215 - 17 Aug 2026
Viewed by 264
Abstract
In Global Navigation Satellite System (GNSS)-denied indoor environments, ultra-wideband (UWB) localization of unmanned ground vehicles (UGVs) is challenged by position-dependent anchor visibility and mixed line-of-sight (LOS)/non-line-of-sight (NLOS) ranging. This study proposes a soft continuous confidence weighting method within an adaptive Kalman filter (AKF)-based [...] Read more.
In Global Navigation Satellite System (GNSS)-denied indoor environments, ultra-wideband (UWB) localization of unmanned ground vehicles (UGVs) is challenged by position-dependent anchor visibility and mixed line-of-sight (LOS)/non-line-of-sight (NLOS) ranging. This study proposes a soft continuous confidence weighting method within an adaptive Kalman filter (AKF)-based UWB/inertial measurement unit (IMU) localization framework. The vehicle model uses motor pulse increments and IMU yaw-rate measurements as inputs and outputs vehicle position and heading estimates. Virtual forward–backward iteration converts inconsistencies between the current UWB ranges and tag–anchor geometry into terminal virtual-anchor displacements. A half-Gaussian function then maps each displacement to a continuous confidence coefficient. The resulting coefficients are incorporated into weighted least-squares (WLS) and AKF localization, while the UWB measurement-noise covariance is adaptively updated using the range innovations. The proposed method was evaluated through static calibration and dynamic localization experiments. These experiments compared soft and hard weighting schemes and assessed the contribution of AKF fusion. These results indicate that the method proposed in this study improves localization accuracy, robustness, and temporal continuity under position-dependent anchor visibility and mixed LOS/NLOS conditions. Full article
(This article belongs to the Section Navigation and Positioning)
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22 pages, 1796 KB  
Article
Power Optimization and Vibration Suppression Method for Wind Farms Based on Risk Assessment Under Sandstorm Conditions
by Jun Zhao, Yuxiang Li, Xueting Cheng, Juan Wei, Weiru Wang, Lu Liu and Yu Yang
Technologies 2026, 14(8), 510; https://doi.org/10.3390/technologies14080510 - 17 Aug 2026
Viewed by 83
Abstract
In response to the severe challenges posed by extreme sandstorm weather to the operational safety of WTs and grid stability, this paper proposes an MPC-based power optimization control strategy for WFs. Simulation results indicate that, compared with the traditional PD strategy, the proposed [...] Read more.
In response to the severe challenges posed by extreme sandstorm weather to the operational safety of WTs and grid stability, this paper proposes an MPC-based power optimization control strategy for WFs. Simulation results indicate that, compared with the traditional PD strategy, the proposed MPC strategy significantly reduces the active power fluctuations of individual WTs, smoothly tracks grid dispatch orders with an overall power tracking accuracy improvement, and effectively lowers the operational risk index of turbines across the farm (ranging from 6.90% to 57.14% for the ten evaluated turbines). Furthermore, the proposed strategy substantially mitigates the angular acceleration fluctuation amplitude of the drive train components (e.g., reducing peak angular accelerations of drive-train masses by up to 35%) and reduces the fore-aft and lateral displacement oscillations of the tower top (reducing peak displacement variations by approximately 25% and 40%, respectively), providing comprehensive structural load mitigation while ensuring WF power output stability and grid safety. This study provides a theoretical basis and technical approach for the intelligent operation and risk prevention and control of WFs under extreme meteorological conditions. Full article
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30 pages, 17301 KB  
Article
Design, Kinematic Control, and Implementation of a LEGO-Based Drawing Robot for Lissajous Curve Generation
by Attila Körei, Szilvia Szilágyi and Ingrida Vaičiulytė
Computers 2026, 15(8), 529; https://doi.org/10.3390/computers15080529 - 14 Aug 2026
Viewed by 158
Abstract
Lissajous figures are frequently studied and widely used objects in engineering and physics. Although these patterns are usually analysed using computer simulations or oscilloscopes, such tools may limit their educational value by covering the core physical processes that generate the curves. In order [...] Read more.
Lissajous figures are frequently studied and widely used objects in engineering and physics. Although these patterns are usually analysed using computer simulations or oscilloscopes, such tools may limit their educational value by covering the core physical processes that generate the curves. In order to address these problems, the design, kinematic validation, and prototyping of a dual-axis drawing robot were carried out on the LEGO Education SPIKE Prime platform. The hardware implementation centres on a LEGO-based dual Scotch yoke mechanism, which supports precise transformation of uniform circular motion into simple harmonic motion. This setup implements the superposition of two independent simple harmonic oscillations by simultaneously moving the paper tray along the x-axis and the pen along the y-axis. High-fidelity trajectories are achieved through a 40:1 worm gear reduction, which enables precise control of the parameter configuration. The phase shift can be manually set by adjustment levers. The robot’s geometry supports discrete amplitude settings of 8, 16, and 24 mm by adjusting the crankpin position. System control is managed by Python code that synchronises motor speeds and angular displacements according to frequency ratios. The research methodology used the Double Diamond design thinking framework, structuring development into four phases: identifying historical mechanical solutions, defining pedagogical and technical classroom requirements, iteratively developing the LEGO prototype, and testing the system through representative drawing experiments. Results show that the robot can reproduce a broad range of periodic Lissajous curves with high repeatability, and that its physical outputs show strong visual and mathematical correspondence to ideal trajectories simulated in the Desmos graphing calculator. The final prototype satisfies classroom constraints, providing a transparent, low-cost, modular STEAM tool that bridges the distance between abstract parametric equations and complex mechanical implementations. Full article
(This article belongs to the Special Issue STEAM Literacy and Computational Thinking in the Digital Era)
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22 pages, 21482 KB  
Article
Global Sensitivity Analysis of Platform-Mooring Responses for a 15 MW Semi-Submersible Floating Wind Turbine Based on PCE-Sobol and Spearman Methods
by Qiang Liu, Qunyi Wang, Xu Han, Xin Li, Chana Sinsabvarodom and Wei Shi
J. Mar. Sci. Eng. 2026, 14(16), 1457; https://doi.org/10.3390/jmse14161457 - 7 Aug 2026
Viewed by 231
Abstract
For large-scale floating offshore wind turbines, existing sensitivity studies have not fully addressed the combined effects of multiple uncertain input parameters on multiple output responses. Meanwhile, conventional Sobol indices quantify contribution magnitude but do not indicate effect direction. Based on the IEA 15 [...] Read more.
For large-scale floating offshore wind turbines, existing sensitivity studies have not fully addressed the combined effects of multiple uncertain input parameters on multiple output responses. Meanwhile, conventional Sobol indices quantify contribution magnitude but do not indicate effect direction. Based on the IEA 15 MW semi-submersible benchmark model, this study investigates the sensitivity of mooring tension and platform motion dynamic responses at a normal operating condition under power production. Integrated dynamic simulations were performed to generate response data. Eight uncertain parameters were considered, including the key mechanical and hydrodynamic coefficients of mooring lines as well as mass distribution and hydrodynamics-related key parameters for the platform. A polynomial chaos expansion surrogate model was used for the global sensitivity analysis, based on the Sobol index, Spearman coefficient, and a newly proposed modified Sobol index. The results indicate weak parameter interactions, with first-order Sobol indices dominating. The platform mass makes the largest contribution, with first-order Sobol indices approaching 1.0 for the mean tensions of all three mooring lines and 0.995 and 0.999 for the mean surge and heave displacements, respectively. The mooring line normal drag coefficient reaches a first-order Sobol index of 0.805 for the standard deviation of the upwind mooring line tension. The pitch response is influenced by multiple parameters. The Spearman coefficients confirmed the dominant parameters and identified their effect directions. By integrating variance contribution with effect direction, the modified Sobol index provides a more interpretable assessment of parameter effects. These findings can support parameter prioritization, mooring system design, and digital-twin model updating for floating offshore wind turbines. Full article
(This article belongs to the Special Issue Resilient Offshore Structures: Design, Analysis and Optimization)
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31 pages, 2565 KB  
Article
An Interaction-Aware NI-EA Framework for EV Charging-Station Siting: Source-Conditioned Robust Candidate Sets and Bounded Spatial Evidence in Dubai
by Ghassan Malkawi, Azmi Alazzam, Ahmed Abdelaziz Elsayed, Asem Omari, Said Badreddine, Bakeel Hussein, Mohammed Alhagyan and Abdelrahman Altigani
World Electr. Veh. J. 2026, 17(8), 411; https://doi.org/10.3390/wevj17080411 - 6 Aug 2026
Viewed by 238
Abstract
Public-data electric-vehicle charging-station siting needs a screening workflow that can use spatial proxies while keeping demand, grid-capacity, and implementation claims separate from the score. This study develops an interaction-aware Nonlinear Interaction–Einstein Aggregation (NI-EA) framework for Dubai and extends it with source-conditioned robust candidate-set [...] Read more.
Public-data electric-vehicle charging-station siting needs a screening workflow that can use spatial proxies while keeping demand, grid-capacity, and implementation claims separate from the score. This study develops an interaction-aware Nonlinear Interaction–Einstein Aggregation (NI-EA) framework for Dubai and extends it with source-conditioned robust candidate-set diagnostics. From 7410 admitted candidate/amenity records, 5097 inside-boundary candidates are scored using a candidate-derived activity-density proxy, a charger-coverage-gap proxy, and a grid-access proxy. The analysis compares NI-EA with WSM, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and Einstein aggregation; reconstructs a 63-scenario interaction/curvature/blending rank matrix; evaluates weighting, road-network, and official-DEWA source sensitivities; and reports necessary and possible top-K candidate sets, family-balanced finite-scenario acceptability, rank-displacement summaries, and bounded spatial-evidence context from official community, transport, parking, DEWA, and OpenStreetMap-derived sources. The baseline leader is S1421/Boonmax, while official-DEWA coordinate-source reconciliation changes the leader to S3473. Across the reconstructed interaction, weighting, road-network, and official-DEWA scenario families, the top-15 necessary core contains 12 candidates, and the top-15 possible envelope contains 18 candidates. Activity-radius and charger-count coverage alternatives are reported separately as proxy-definition sensitivities. TOPSIS has 0/15 top-15 overlap with NI-EA because it favors a different profile with much higher coverage-gap scores but low activity density. The reported output is therefore a source-conditioned planning shortlist and robustness audit, not an observed-demand map, feeder-capacity validation, financial feasibility assessment, or construction recommendation. Full article
(This article belongs to the Section Charging Infrastructure and Grid Integration)
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28 pages, 4107 KB  
Article
Critical-Material Recovery from U.S. Industrial Byproducts: A Scenario-Based Supply-Risk Analysis
by Abu Shahadat Md Ibrahim, Maxwell Fleming, Elif Bozkurt, Tom Brady and Ian Lange
Resources 2026, 15(8), 104; https://doi.org/10.3390/resources15080104 - 5 Aug 2026
Viewed by 367
Abstract
Recovery of critical materials from industrial byproducts is often presented as a near-term United States (U.S.) supply-security strategy, yet contained inventories, pilot output, announced capacity, and commercial production are not equivalent. This study evaluates eight U.S. pathways for gallium, germanium, tellurium, lithium, magnesium, [...] Read more.
Recovery of critical materials from industrial byproducts is often presented as a near-term United States (U.S.) supply-security strategy, yet contained inventories, pilot output, announced capacity, and commercial production are not equivalent. This study evaluates eight U.S. pathways for gallium, germanium, tellurium, lithium, magnesium, and cobalt, classified as operational, demonstration/pilot, announced target-year, or technical upper-bound cases. Facility- and stream-specific quantities were converted to qualifying domestic output and incorporated into same-stage material balances under explicit assumptions for utilization, eligibility, demand, and import displacement. Supply risk was calculated from the net import dependence and governance-adjusted production and trade concentration using a geometric index, with arithmetic formulations as robustness checks. The operational U.S. copper-refining tellurium pathway yielded the largest central reduction (49.29%). Announced 2030 Clarksville capacity reduced modeled risk by 13.87% for gallium and 8.75% for germanium, conditional on project completion, feed attribution, product qualification, utilization, and demand. All other central cases produced reductions of 4.63% or less; the current lithium demonstration, Stillwater cobalt, and aluminum-residue magnesium cases had negligible national effects. Policy support should therefore be differentiated by qualifying output, market scale, project maturity, and evidence quality rather than by contained material or nameplate capacity alone. Full article
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18 pages, 6519 KB  
Article
Collaborative Optimization of Dynamic Characteristics and Armature Structural Safety in Electromagnetic Repulsion Mechanisms
by Wenying Yang, Fansong Meng and Guofu Zhai
Energies 2026, 19(15), 3665; https://doi.org/10.3390/en19153665 - 4 Aug 2026
Viewed by 191
Abstract
As a driving mechanism, the electromagnetic repulsion mechanism has been widely used in mechanical switches, such as circuit breakers, current limiters, and bypass switches, owing to its high closing speed and large output force. The dynamic characteristics and structural safety of electromagnetic repulsion [...] Read more.
As a driving mechanism, the electromagnetic repulsion mechanism has been widely used in mechanical switches, such as circuit breakers, current limiters, and bypass switches, owing to its high closing speed and large output force. The dynamic characteristics and structural safety of electromagnetic repulsion mechanisms are critical to the stable and reliable operation of mechanical switches. However, the dynamic characteristics of electromagnetic repulsion mechanisms are affected by multiple factors, including coil parameters, energy storage parameters, armature structural dimensions, and air gaps. Moreover, strong coupling exists among these design variables. Parameter optimization that focuses solely on operating speed or electromagnetic force may lead to local stress concentration and edge vibration of the armature, thereby compromising the operational reliability of the mechanism. To address the difficulty in synergistically optimizing dynamic characteristics and structural safety, this paper proposes a two-stage optimization method that combines the series armature equivalent method, genetic algorithm-based multi-objective optimization, structural shape optimization, and topology optimization. In the first stage, a series armature equivalent model is established, and design parameters are optimized by the genetic algorithm to obtain a parameter combination that satisfies the requirements for displacement, closing speed, and operating time. In the second stage, under the constraints of dynamic performance, armature shape optimization, topology optimization, and combined shape–topology optimization are separately conducted to reduce edge vibration and local stress concentration of the armature. The dynamic characteristics, edge vibration displacement, and stress under different optimization schemes are comparatively analyzed. The results show that the proposed two-stage optimization method can effectively improve the structural response of the armature while ensuring that the dynamic characteristics of the mechanism satisfy the design requirements. In particular, after the combined optimization, the edge vibration of the armature is reduced to 41.8% of that before optimization, and the local stress concentration is significantly alleviated. The proposed optimization framework realizes the coordination between parameter design and armature structural optimization of electromagnetic repulsion mechanisms, providing a reference for improving the dynamic characteristics and structural reliability of electromagnetic repulsion mechanisms. Full article
(This article belongs to the Section F: Electrical Engineering)
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20 pages, 2383 KB  
Article
An Evidence-Weighted Multi-Rate Inertial Fusion Method for Industrial Load Displacement Reconstruction
by Peiyi Zhou, Weige Liang, Qizheng Zhou, Chi Li, Shiyan Sun and Jixin Song
Mathematics 2026, 14(15), 2779; https://doi.org/10.3390/math14152779 - 4 Aug 2026
Viewed by 230
Abstract
An evidence-weighted multi-rate inertial fusion method is proposed for load displacement reconstruction in high-vibration industrial transportation scenarios, where inertial displacement reconstruction is readily affected by acceleration bias, attitude error, vibration disturbance, and false zero-velocity decisions. Multi-rate inertial data and high-bandwidth vibration/impact observations are [...] Read more.
An evidence-weighted multi-rate inertial fusion method is proposed for load displacement reconstruction in high-vibration industrial transportation scenarios, where inertial displacement reconstruction is readily affected by acceleration bias, attitude error, vibration disturbance, and false zero-velocity decisions. Multi-rate inertial data and high-bandwidth vibration/impact observations are used. The main inertial channel is used for motion-dynamics modeling, low-frequency inertial and attitude information is used to constrain the trajectory trend, and high-bandwidth vibration and impact responses are converted into motion-veto evidence so that unreliable stationary decisions under high-vibration conditions can be weakened. A Dempster–Shafer-style evidence fusion model is adopted to estimate motion, stationary, and unknown confidence, and the stationary confidence is propagated to ZUPT gating, covariance weighting, multi-branch displacement fusion, and keyframe factor-graph optimization. The experimental results show that stable load displacement reconstruction can be achieved by the proposed method, while interpretable diagnostic information, including displacement, velocity, stationary probability, ZUPT triggering, residuals, and drift risk, is also output. A diagnosable and auditable framework for inertial displacement reconstruction is therefore provided for high-vibration industrial scenarios where external references are difficult to deploy. Full article
(This article belongs to the Special Issue Advanced Computational and Intelligent Methods in Signal Processing)
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23 pages, 6948 KB  
Article
MEMS Data-Driven Intelligent Identification of Rotation-Angle Response and Shear Band Position in Gravelly Soil Slopes
by Di Wu, Yongzhe Feng, Gurong Yao, Hualin Song, Zhiwen Lu and Ming Wu
Sensors 2026, 26(15), 4871; https://doi.org/10.3390/s26154871 - 2 Aug 2026
Viewed by 238
Abstract
Identifying shear band locations is essential for precursor recognition and early warning of progressive failure in gravelly soil slopes. However, conventional displacement monitoring methods mainly capture macroscopic slope deformation and remain limited in detecting internal localized deformation and the spatial evolution of shear [...] Read more.
Identifying shear band locations is essential for precursor recognition and early warning of progressive failure in gravelly soil slopes. However, conventional displacement monitoring methods mainly capture macroscopic slope deformation and remain limited in detecting internal localized deformation and the spatial evolution of shear bands. To address this limitation, this study proposes an MEMS data-driven framework for predicting spatial rotation-angle responses and locating potential shear bands in gravelly soil slopes, with the aim of enhancing the perception of internal shear deformation and detecting potential instability zones. First, scaled laboratory model tests were conducted under different gravel contents, and MEMS sensors were embedded within the slope to measure cumulative rotation-angle responses during shear band formation. Second, based on a DEM model incorporating particle geometric morphology, the spatial differentiation of the rotation-angle field during shear band evolution was analyzed, and the experimental results were further validated. Finally, a shear band localization framework integrating PDL-GAN-based data augmentation with PCA + Gaussian regional rotation-angle field prediction was established. Potential shear band locations were then indirectly localized based on the positive–negative partitioning and abrupt amplitude changes in the predicted rotation angles. The results show that the DEM simulations agree well with the cumulative rotation-angle responses obtained from the laboratory tests, with mean absolute percentage errors of 9.79%, 6.03%, and 3.84% under the T1, T2, and T3 conditions, respectively. Within the shear band influence zone, the upper monitoring points mainly exhibit negative rotation-angle accumulation, whereas the lower monitoring points primarily show positive rotation-angle responses. A larger absolute rotation angle indicates a stronger controlling effect of the shear band on the corresponding monitoring point. The PCA + Gaussian model demonstrates strong overall performance in regional rotation-angle prediction, with MAE, RMSE, and CRPS values of 0.0803, 0.1024, and 0.0801, respectively. The model preserves the dominant deformation mode of the rotation-angle field and provides probabilistic prediction outputs. The proposed method enables the prediction of internal rotation-angle responses and facilitates the localization of potential shear band locations in gravelly soil slopes, providing data-driven technical support for precursor recognition and intelligent early warning of progressive slope failure. Full article
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25 pages, 21504 KB  
Article
InSAR-Based Prediction of Time-Series Displacements Using a New Physics-Informed Neural Network with Prior Parameter Inversion
by Yucheng Xiang, Zidu Ouyang, Jingze Li, Zefa Yang, Guangcai Feng and Zelang Miao
Remote Sens. 2026, 18(15), 2516; https://doi.org/10.3390/rs18152516 - 2 Aug 2026
Viewed by 320
Abstract
Deep learning algorithms have become useful tools for predicting time-series displacements from historical displacements measured using interferometric synthetic aperture radar (InSAR) techniques. However, nearly all existing InSAR-related studies are based on data-driven deep learning algorithms, causing poor robustness, especially for long-term prediction with [...] Read more.
Deep learning algorithms have become useful tools for predicting time-series displacements from historical displacements measured using interferometric synthetic aperture radar (InSAR) techniques. However, nearly all existing InSAR-related studies are based on data-driven deep learning algorithms, causing poor robustness, especially for long-term prediction with small-scale training samples. In this study, we propose a new algorithm, named physics-informed neural network with prior parameter inversion (PINNPI), for InSAR-based prediction of time-series displacements. PINNPI is a hybrid data-driven and knowledge-guided deep learning network, where two coupled deep neural networks are first constructed for network training and parameter inversion of prior knowledge. The outputs of these two deep neural networks are coupled by an automatic differentiation module. By minimizing a hybrid physics-informed and data-driven loss function, the proposed network simultaneously models time-series displacement and estimates prior parameters. Subsequently, time-series displacements are predicted based on the trained networks and inverted parameters. The incorporation of physical knowledge into PINNPI enhances the capability of long-term displacement prediction with respect to data-driven learning algorithms. In addition, PINNPI effectively improves the poor robustness of classical PINNs, when prior parameters are unknown. Simulations and two real-world tests suggest that the accuracy of displacement prediction by PINNPI is, on average, 85% and 88% higher than that of classical data-driven deep learning and PINN algorithms, respectively. This work offers a new insight for predicting InSAR-based displacements associated with anthropogenic and geophysical activities. Full article
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20 pages, 11696 KB  
Article
Design of a Multi-Channel BiSS-C Asynchronous Acquisition and Synchronous Transmission Interface Based on FPGA
by Hao Du, Xinyi Li, Kaifu Zeng, Quan Feng, Wentao Zhang, Peiyuan Xiong, Huiying Gao and Zhe Zhou
Electronics 2026, 15(15), 3412; https://doi.org/10.3390/electronics15153412 - 1 Aug 2026
Viewed by 309
Abstract
Multi-channel synchronous data transmission interfaces are increasingly required to deliver higher accuracy, reliability, and cost efficiency for displacement measurement in industrial ultra-precision equipment and advanced manufacturing. The bidirectional serial synchronous continuous (BiSS-C) protocol is widely used for high-precision sensor data transfer due to [...] Read more.
Multi-channel synchronous data transmission interfaces are increasingly required to deliver higher accuracy, reliability, and cost efficiency for displacement measurement in industrial ultra-precision equipment and advanced manufacturing. The bidirectional serial synchronous continuous (BiSS-C) protocol is widely used for high-precision sensor data transfer due to its advantages of fast transmission speed, anti-interference capability, and low implementation cost. However, existing methods cannot effectively address data acquisition errors and decoding timing mismatches caused by inconsistent line delays between channels. This paper proposes a design for a multi-channel BiSS-C asynchronous acquisition and synchronous transmission interface based on FPGA. The proposed interface employs an asynchronous data acquisition mechanism based on majority voting to dynamically adapt to line delay and ensure reliable data acquisition. A barrier synchronization module is designed to eliminate the difference in decoding progress between channels and achieve synchronous output. Experimental verification through a laser interferometer displacement measurement system demonstrates that the proposed interface operates without CRC errors under multi-channel parallel operation. It supports a maximum clock frequency of 10 MHz and achieves a control cycle frequency above 10 kHz. The engineering practicality of the interface is further verified through displacement measurement experiments. Full article
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29 pages, 14521 KB  
Article
Energy Harvesting Based on Piezoelectric Patched Beams Under Moving-Mass Excitation
by El Mahdi Rhiate, Khawla Gaouzi, Farah Abdoun and Lahcen Azrar
Vibration 2026, 9(3), 47; https://doi.org/10.3390/vibration9030047 - 31 Jul 2026
Viewed by 347
Abstract
This paper develops a reduced-order electromechanical model for piezoelectric energy harvesting from a beam traversed by a moving mass. The beam is described by the Euler–Bernoulli theory, and the coupled equations of motion are derived through modal expansion combined with the linear piezoelectric [...] Read more.
This paper develops a reduced-order electromechanical model for piezoelectric energy harvesting from a beam traversed by a moving mass. The beam is described by the Euler–Bernoulli theory, and the coupled equations of motion are derived through modal expansion combined with the linear piezoelectric constitutive relations. Unlike most existing formulations, the model accounts for non-uniform transit by including moving-mass acceleration, accommodates an arbitrary number of piezoelectric patches distributed along the span, and incorporates von Kármán strain–displacement relations. So, moderately large deflections and mid-plane stretching as well as various boundary conditions may be investigated within the same framework. The resulting coupled nonlinear ordinary differential equations are integrated in time using a numerical solver. On the other hand, predictions of midpoint deflection, output voltage, and harvested power are validated against the COMSOL Multiphysics Finite element model. The experimental setup has been established, and a dedicated laboratory experiment provides additional verification under controlled conditions. Parametric analyses investigating the individual and combined effects of the mass ratio, velocity ratio, acceleration profile, patch length, patch position, number of patches, and external load resistance are elaborated. Distributed multi-patch configurations are shown to recover more energy than a single-centered patch once higher modes contribute appreciably to the response. Design charts relating the governing parameters to the harvested power are constructed for each set of support conditions. These results are intended to assist the preliminary sizing and placement of piezoelectric transducers on some practical energy harvesting applications. Full article
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28 pages, 67423 KB  
Article
Adaptive Inverse Control Using the Krasnosel’skii-Pokrovskii Model for Hysteresis Compensation in Piezoelectric Flexure Micro-Positioning Stage
by Yuansheng Chen, Hao Lou, Jian Wang and Shaona Liu
Micromachines 2026, 17(8), 917; https://doi.org/10.3390/mi17080917 - 30 Jul 2026
Viewed by 532
Abstract
Piezoelectric flexure micro-positioning stages are essential micromotion actuators for micro-assembly, atomic force microscopy and nano-manufacturing, but intrinsic hysteresis nonlinearity of piezoelectric stacks distorts the linear voltage-to-displacement mapping and induces significant micro-positioning errors. Conventional hysteresis compensation based on offline-calibrated Krasnosel’skii-Pokrovskii (KP) models cannot adapt [...] Read more.
Piezoelectric flexure micro-positioning stages are essential micromotion actuators for micro-assembly, atomic force microscopy and nano-manufacturing, but intrinsic hysteresis nonlinearity of piezoelectric stacks distorts the linear voltage-to-displacement mapping and induces significant micro-positioning errors. Conventional hysteresis compensation based on offline-calibrated Krasnosel’skii-Pokrovskii (KP) models cannot adapt to time-varying excitation, whereas state-of-the-art adaptive KP control requires auxiliary dynamic equations and imposes high computational overhead on miniature real-time controllers. To address these limitations, this paper develops a single-degree-of-freedom micromotion positioning device equipped with symmetric two-stage displacement amplification mechanisms and straight circular flexure hinges. ANSYS finite element simulations validate the mechanical stiffness, structural safety and linear amplification characteristic of the micro-positioning stage, achieving a maximum output stroke of 95.95 μm. A discretized KP hysteresis model is constructed to accurately capture the asymmetric rate-dependent hysteresis of piezoelectric stacks. On this basis, a lightweight adaptive inverse control framework is proposed, which realizes online tuning of KP weights through gradient descent iteration only relying on real-time position feedback, eliminating static pre-calibration and extra dynamic correction links. Tracking experiments under 0.1–2 Hz sinusoidal waveforms and 3–7 V variable-amplitude sinusoidal waveforms are implemented. Experimental results show that the proposed approach reduces the root-mean-square error (RMSE) by 7.41–85.65% and the mean absolute percentage error (MAPE) by 7.56–87.81% compared with uncompensated open-loop micromotion control. The combined micro-flexure mechanical design and adaptive hysteresis compensation strategy greatly improves positioning accuracy and anti-interference capacity, offering a low-computation technical route for high-performance micro-positioning systems. Full article
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16 pages, 6380 KB  
Article
Design and Optimization of High-Amplification-Ratio Micromanipulator Based on Compliant Mechanism
by Feng Zhao, Wentao Huang, Jianguo Liao, Xiaodong Chen, Fengchen Zhai and Xueyan Chen
Micromachines 2026, 17(8), 883; https://doi.org/10.3390/mi17080883 - 24 Jul 2026
Viewed by 271
Abstract
Displacement magnification (DM) is one of the key indicators to measure the performance of a micromanipulator. Based on the principle of triangle amplification, a series of three-stage displacement amplification (DA) micromanipulators is designed in this paper, which is driven by a piezoelectric actuator. [...] Read more.
Displacement magnification (DM) is one of the key indicators to measure the performance of a micromanipulator. Based on the principle of triangle amplification, a series of three-stage displacement amplification (DA) micromanipulators is designed in this paper, which is driven by a piezoelectric actuator. The mechanism is composed of a compound rhombus mechanism, a bridge mechanism and two parallelogram mechanisms. The compound rhombus mechanism is located at the front end and has high stiffness characteristics. The bridge mechanism is located at the back end and is connected to the parallelogram mechanism to realize the parallel output of the clamping end. The DM model of the mechanism is established. On this basis, the structural size optimization design is carried out. With the goal of maximizing the DM, the key geometric parameters such as the thickness and length of the hinge and the section size of the key rod are selected as the design variables. Considering the constraints of material strength and input stiffness, the parameters of the micromanipulator are optimized. The correctness of the optimization method is verified by finite element simulation and experimental test. The results show that the DM of the optimized micromanipulator is significantly improved under the premise of maintaining sufficient stiffness, which can effectively guide the performance improvement and structural design of the micromanipulator. Full article
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22 pages, 11236 KB  
Article
Velocity-Sensor-Based Dual-ESO Reconstruction for Feedforward–Feedback Low-Frequency Active Micro-Vibration Isolation
by Zhenyu Fan, Yong Xie, Yuzhang Zhu, Yi Le, Yifei Zhang, Rui Xiu, Xindong Liang, Liang Zhang and Jianjun Jia
Sensors 2026, 26(15), 4715; https://doi.org/10.3390/s26154715 - 24 Jul 2026
Viewed by 586
Abstract
Low-frequency base vibration transmitted through supporting platforms can degrade the stability of precision payloads, optical instruments, and inertial measurement systems. In velocity-sensor-based active isolation platforms, displacement-related feedback states are unavailable. Direct velocity integration can drift under sensor bias, while raw lower-platform velocity feedforward [...] Read more.
Low-frequency base vibration transmitted through supporting platforms can degrade the stability of precision payloads, optical instruments, and inertial measurement systems. In velocity-sensor-based active isolation platforms, displacement-related feedback states are unavailable. Direct velocity integration can drift under sensor bias, while raw lower-platform velocity feedforward can introduce measurement noise and out-of-band components. This paper proposes a dual extended state observer (ESO) reconstruction method combining equivalent-displacement feedback and lower-platform feedforward. The upper-platform ESO reconstructs feedback velocity and a bounded equivalent-displacement state, while the lower-platform ESO provides a smoothed velocity reference for feedforward compensation. The method was implemented on a plate-type active vibration isolation platform and evaluated using lower-to-upper-platform acceleration transmissibility over 0.1–10 Hz. Across three repeated 200 s records, the proposed ESO feedback–feedforward condition achieved an integrated input–output suppression ratio of 38.67±0.46 dB, reduced the upper-platform output acceleration RMS to (1.31±0.09)×107 g, and provided a 48.92±2.12 dB RMS reduction relative to the passive baseline. Direct nominal–measured comparisons further showed that the reduced model captured the dominant passive and feedback-controlled dynamics. These results demonstrate that low-frequency active micro-vibration isolation can be achieved using only velocity measurements, without additional displacement sensors. Full article
(This article belongs to the Section Physical Sensors)
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