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35 pages, 6347 KB  
Article
Design, Development, and Laboratory Validation of a Low-Cost Multi-Sensor System for Bridge Structural Health Monitoring with Scour-Related Environmental Sensing
by Matilde Bidone, Mauro Aimar, Marco Civera, Alessio Carullo and Alberto Vallan
Sensors 2026, 26(18), 5957; https://doi.org/10.3390/s26185957 (registering DOI) - 20 Sep 2026
Abstract
This paper reports the design, development and laboratory validation of a low-cost multi-sensor system for bridge Structural Health Monitoring with complementary scour-related environmental sensing. The proposed sensing apparatus is intended for continuous dynamic (vibration-based) and quasi-static structural monitoring, in particular for bridge applications. [...] Read more.
This paper reports the design, development and laboratory validation of a low-cost multi-sensor system for bridge Structural Health Monitoring with complementary scour-related environmental sensing. The proposed sensing apparatus is intended for continuous dynamic (vibration-based) and quasi-static structural monitoring, in particular for bridge applications. It employs a distributed wired architecture comprising two custom printed circuit boards, BridgeWatch and EnvironMonitor. BridgeWatch nodes integrate MEMS accelerometers and gyroscopes, enabling acceleration measurements, quasi-static inclination estimates from gravity components, angular-rate measurements and structural surface-temperature acquisition. The EnvironMonitor node acquires wind, rainfall, air temperature, humidity and bridge water level; these variables provide environmental and hydrological context relevant to scour risk, without directly measuring riverbed elevation or scour depth. A Raspberry Pi coordinates acquisition, synchronisation and communication through RS485 and RS232 links. The hardware was implemented through custom PCB design and dedicated firmware. The principal contribution is the system-level integration of structural and environmental measurements in one open architecture. Laboratory validation comprised communication and synchronisation checks, shaker tests, a scaled structural benchmark, climatic-cell tests and environmental-input simulations. The results demonstrate functional acquisition and relevant dynamic-feature extraction under controlled conditions. These outcomes enable future full-scale in situ validation and testing on full-size case studies. Full article
(This article belongs to the Special Issue Recent Advances in Structural Health Monitoring of Bridges)
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12 pages, 20555 KB  
Article
A Gyroscope-Pendulum-Coupled Multilayer Triboelectric Nanogenerator for Omnidirectional Low-Frequency Ocean Wave Energy Harvesting
by Songhang Li, Zhenlong Xu, Zheming Zhang, Yiwen Zhu, Xiaohan Xu, Chengping Deng and Xinting Ge
Micromachines 2026, 17(9), 1010; https://doi.org/10.3390/mi17091010 - 26 Aug 2026
Viewed by 301
Abstract
Low-frequency, irregular water waves with continuously changing propagation directions are difficult to harvest efficiently using conventional power generation devices. This work proposes a gyroscope-pendulum-coupled multilayer triboelectric nanogenerator (GP-TENG), in which a multi-axis gyroscope mechanism, an inertial pendulum, and a helical-structured power generation module [...] Read more.
Low-frequency, irregular water waves with continuously changing propagation directions are difficult to harvest efficiently using conventional power generation devices. This work proposes a gyroscope-pendulum-coupled multilayer triboelectric nanogenerator (GP-TENG), in which a multi-axis gyroscope mechanism, an inertial pendulum, and a helical-structured power generation module are integrated inside a spherical floating body. The gyroscope joints enable the pendulum to respond to waves arriving from any horizontal direction, while the heave and tilting motions of the floating body jointly drive periodic contact and separation of the multilayer triboelectric materials. Motor-driven platform and water tank experiments were conducted to investigate the effects of the number of generating layers, excitation frequency, translational stroke, swing amplitude, and external resistance on the output performance. In the controlled translational tests, the maximum root-mean-square open-circuit voltage, short-circuit current, and transferred charge reached 98.6 V, 2.3 μA, and 242 nC, respectively, and a maximum output power of 16.3 μW was obtained at a load of 81 MΩ. In the water tank, the GP-TENG showed a stable response near 1.42 Hz, with maximum output power of 3.45 μW at a 60 MΩ load. The generator successfully charged the capacitor, lit up LEDs, and powered a commercial temperature and humidity sensor. These results indicate that the GP-TENG provides a compact and low-cost approach for omnidirectional low-frequency wave energy harvesting and a distributed power supply for low-power marine electronic devices. Full article
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27 pages, 3038 KB  
Article
A Denoising Algorithm for Maglev Gyro Jump Data Based on Bayesian Ensemble Time-Series Segmentation
by Binqiang Guo, Zhen Shi, Di Liu, Xinkang Hu, Gang Jiang and Tao Dang
Sensors 2026, 26(16), 5287; https://doi.org/10.3390/s26165287 - 20 Aug 2026
Viewed by 337
Abstract
High-precision tunnel breakthroughs depend critically on the north-seeking accuracy of maglev gyroscopes. However, external disturbances during underground construction often introduce abrupt jumps into rotor current signals, significantly reducing the orientation reliability. Existing signal-processing methods either require manually defined segmentation windows or apply identical [...] Read more.
High-precision tunnel breakthroughs depend critically on the north-seeking accuracy of maglev gyroscopes. However, external disturbances during underground construction often introduce abrupt jumps into rotor current signals, significantly reducing the orientation reliability. Existing signal-processing methods either require manually defined segmentation windows or apply identical denoising strategies to both stationary and disturbed signal intervals, resulting in limited adaptability and suboptimal denoising performance. To overcome these limitations, this study proposes an improved rotor current denoising algorithm based on the MAF-ARIMA framework by incorporating the Bayesian ensemble algorithm for abrupt change, seasonality, and trend (BEAST) and an optimized wavelet transform (OWT). First, the BEAST is employed to automatically detect the structural change point of the rotor current signal, enabling the adaptive segmentation of stationary and jump intervals without manual intervention. Subsequently, empirical mode decomposition is performed, and the OWT applies different denoising parameters to the dominant components of the stationary and jump segments according to their distinct fluctuation characteristics. Finally, moving-average smoothing is adopted to preserve the signal continuity at the segmentation boundary, while the autoregressive integrated moving average (ARIMA) model reconstructs the missing trend component of the jump interval to obtain the complete denoised signal. Comparative experiments using 12 field-collected rotor current datasets demonstrated that the proposed method reduced the standard deviation of the denoised signal by 70.96% and the absolute azimuth error by 50.36% compared with the raw signal, outperforming the optimized Hilbert–Huang transform, HSA-KS, and the original MAF-ARIMA algorithm. By introducing adaptive change-point detection and segment-specific denoising into the existing MAF-ARIMA framework, the proposed method significantly improves the adaptability and denoising performance of maglev gyro rotor current processing under complex tunnel construction environments while preserving the signal continuity and reconstruction accuracy. Full article
(This article belongs to the Section Physical Sensors)
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36 pages, 2823 KB  
Article
Observer-Based Hybrid Backstepping–Super-Twisting Control of a Twin Rotor MIMO System with Windowed Metaheuristic Gain Scheduling: Real-Time Tracking Experiments and Numerical Disturbance Analysis
by Azeddine Beloufa, Abderrahmane Kacimi, Souaad Tahraoui, Abderrahmane Senoussaoui, Abdelbasset Azzouz, Mehdi Houari Zaid and Jun-Jiat Tiang
Actuators 2026, 15(8), 453; https://doi.org/10.3390/act15080453 - 20 Aug 2026
Cited by 1 | Viewed by 240
Abstract
Twin Rotor Multi-Input Multi-Output (TRMS) platforms combine strong aerodynamic cross-coupling, gravitational loading on the vertical axis, friction-dominated horizontal dynamics, and systematic mismatch between idealised models and laboratory hardware. The platform provides only two optical encoders, so the angular rates and the rotor states [...] Read more.
Twin Rotor Multi-Input Multi-Output (TRMS) platforms combine strong aerodynamic cross-coupling, gravitational loading on the vertical axis, friction-dominated horizontal dynamics, and systematic mismatch between idealised models and laboratory hardware. The platform provides only two optical encoders, so the angular rates and the rotor states are unavailable for feedback. This paper presents an observer-based output-feedback architecture that addresses both difficulties. A high-gain observer built on the fully coupled six-state model, including the gyroscopic terms that the control design cannot retain, reconstructs the four unmeasured states from the two encoder angles. The reconstructed states drive a Hybrid Backstepping–Super-Twisting (B-STA) controller in which a second-order continuous sliding mode is embedded at the final recursive step through a composite surface. Because backstepping requires strict-feedback structure, which the centralised coupled model does not possess, the controller is synthesised on a decentralised design model and the residual coupling is rejected as a matched perturbation of the sliding variable. Closed-loop behaviour is analysed as a three-stage cascade covering observer error, sliding variable, and tracking error, yielding practical stability under bounded residuals with an explicit input-to-state gain. The residual bounds are evaluated numerically from the actuator saturation limit and the identified coefficients rather than assumed, and the resulting figures are shown to predict the marked difference in sliding-variable behaviour observed between the two axes. A second architecture applies a windowed Grey Wolf Optimiser (B-GWO) to the backstepping gains, in which each candidate is applied to the plant for a fixed test window, scored on its own accumulated integral of time-weighted absolute error, and followed by a settle window at the incumbent best. We prove that this windowing is a requirement rather than a convenience: a fitness evaluated at a single sample is common to all candidates, cancels from the population ranking, and reduces the search to the minimiser of its own regularisation term. Both schemes are implemented on a physical TRMS through a Simulink Desktop Real-Time interface at a control period of 10ms. On a 100s experimental run, B-STA attains a pitch tracking error of 0.0318rad RMS, 7.94% of the reference amplitude, and the lowest control energy on both axes among the strategies compared, reducing pitch control energy by 72.9% relative to a first-order Backstepping–Sliding Mode baseline recorded on the same interface. Numerical disturbance rejection tests on the fully coupled model confirm the mechanism: under a matched actuator step the super-twisting integrator state migrates to a new steady level that cancels the disturbance, driving the residual pitch error to 2×104rad, whereas the same recursive law without the second-order injection retains a permanent offset of 0.28rad. Full article
(This article belongs to the Section Control Systems)
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33 pages, 2920 KB  
Article
Characterizing the Operating Envelope of an Anomaly-Aware Adaptive EKF for GNSS-Denied USV Formation Relative Localization
by Ling Tan, Jianqiang Zhang, Yiping Liu, Pengfei Zhang and Xingda Li
J. Mar. Sci. Eng. 2026, 14(16), 1490; https://doi.org/10.3390/jmse14161490 - 11 Aug 2026
Viewed by 340
Abstract
Unmanned surface vehicle (USV) formations operating under GNSS denial require accurate relative localization using proprioceptive sensors and inter-vehicle ranging. This paper presents an anomaly-aware adaptive extended Kalman filter for four-USV formations using inertial measurements, compass, and ultra-wideband ranging, and systematically characterizes its operating [...] Read more.
Unmanned surface vehicle (USV) formations operating under GNSS denial require accurate relative localization using proprioceptive sensors and inter-vehicle ranging. This paper presents an anomaly-aware adaptive extended Kalman filter for four-USV formations using inertial measurements, compass, and ultra-wideband ranging, and systematically characterizes its operating envelope. Observability analysis establishes that S-curve maneuvering achieves structural rank 24, with only global translation unobservable, while straight-line motion leads to a rank deficiency of exactly seven dimensions All four gyroscope biases remain observable under both trajectories. The proposed filter integrates chi-square testing, cumulative sum (CUSUM) detection, and bias drift rate monitoring to trigger coordinated R adaptation and Q-boost mechanisms. Controlled experiments spanning outlier magnitudes and drift rates reveal three performance regimes, clean conditions with equivalent performance across all variants, moderate outliers [3σd,10σd] where the proposed method achieves 4.8–13.4% improvement, and extreme outliers where all robust methods converge. Critically, pure bias drift experiments expose a structural limitation of single-hypothesis, residual domain robustification within the tested drift range—all variants exhibit equivalent performance across the tested drift rates, analytically attributable to Kalman gain partitioning that distributes innovations between position and bias subspaces. The characterized operating envelope establishes that robust mechanisms provide measurable benefits for transient anomalies but encounter hard boundaries under persistent drift conditions, with all variants converging to equivalent performance across the tested range, necessitating multi-hypothesis or constraint-based approaches. Full article
(This article belongs to the Section Ocean Engineering)
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24 pages, 1479 KB  
Article
Motion-State-Aware Adaptive Step-Length Smartphone PDR for GPS-Denied Pedestrian Localization
by Huabang Liu, Wanfeng Dou and Hexing Wang
Sensors 2026, 26(15), 4915; https://doi.org/10.3390/s26154915 - 4 Aug 2026
Viewed by 319
Abstract
Smartphone-based pedestrian dead reckoning (PDR) provides an infrastructure-free solution for two-dimensional (2D) planar localization in GPS-denied environments, but its open-loop nature makes it sensitive to accumulated step-length and heading errors. These errors grow when pedestrian actions and phone carrying modes change, because conventional [...] Read more.
Smartphone-based pedestrian dead reckoning (PDR) provides an infrastructure-free solution for two-dimensional (2D) planar localization in GPS-denied environments, but its open-loop nature makes it sensitive to accumulated step-length and heading errors. These errors grow when pedestrian actions and phone carrying modes change, because conventional methods use a fixed step-length model with a constant Weinberg coefficient. This paper proposes a motion-state-aware PDR method with two key designs. First, a joint motion state defined by action type and carrying mode is recognized from smartphone sensor data using a random-forest classifier. Second, the Weinberg coefficient is modeled through two adaptive variants: a state-wise linear model as the main lightweight adaptation mechanism, and a Transformer-enhanced extension that uses historical step-feature sequences to provide additional temporal smoothing for the per-step coefficient K. Both variants keep the predicted coefficient inside the Weinberg equation to preserve the physical structure of step-length estimation, with offline training minimizing the distance error over each calibrated segment. Heading is estimated by fusing gyroscope increments and magnetometer observations to improve continuity under magnetic disturbance. Experiments on routes with frequent motion-state transitions, including a representative indoor corridor with magnetic disturbance and turns, compare a fixed-parameter baseline and two established adaptive step-length baselines against the proposed variants using coefficient-modeling diagnostics and trajectory-level metrics. More challenging deployments such as underground or multi-floor environments are left for future work. Full article
(This article belongs to the Special Issue Development and Challenges of Indoor Positioning and Localization)
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12 pages, 449 KB  
Review
Data-Driven Fusion Algorithms for Temperature-Drift Compensation of MEMS Gyroscopes: A Mini Review
by Haoze Lan and Yingjie Xu
Micromachines 2026, 17(8), 924; https://doi.org/10.3390/mi17080924 - 31 Jul 2026
Viewed by 1062
Abstract
Microelectromechanical systems (MEMS) gyroscopes are now standard rate sensors in inertial navigation, automotive electronics, industrial automation, and medical instrumentation because they are inexpensive, compact, and readily integrated. Their accuracy, however, degrades with temperature: damping and quadrature coupling change, and readout-electronics behavior shifts, producing [...] Read more.
Microelectromechanical systems (MEMS) gyroscopes are now standard rate sensors in inertial navigation, automotive electronics, industrial automation, and medical instrumentation because they are inexpensive, compact, and readily integrated. Their accuracy, however, degrades with temperature: damping and quadrature coupling change, and readout-electronics behavior shifts, producing temperature-dependent zero-rate-output drift, elevated random noise, and poorer long-term stability. Hardware- and structure-based temperature compensation address part of the problem but carry cost and generality penalties, which has moved recent work toward data-driven software-based temperature-drift compensation. This review focuses on the fusion algorithms that have come to dominate that literature, organized as a four-stage pipeline: signal decomposition, learning-based drift modeling, adaptive filtering, and signal reconstruction. We examine how optimizer-tuned variational mode decomposition and improved empirical-mode-decomposition variants separate temperature-related components from noise; how deep temporal networks and optimizer-coupled learners model the nonlinear, time-lagged drift; and how adaptive Kalman variants and time-frequency filtering reconstruct a stable output. We close by identifying four open problems that recur across the recent gyroscope-specific work—cross-device generalization, temperature hysteresis, embedded real-time deployment, and physics-informed lightweight modeling. Full article
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21 pages, 20472 KB  
Article
An Adaptive-Output Operational Amplifier for Electrostatic Closed-Loop MEMS Gyroscope Drive Circuits
by Xiaoqin Li, Wanting Rong, Diqun Yan, Xiali Han, Shanshan Wang, Wenbo Zhang, Hao Ye and Xiangyu Li
Micromachines 2026, 17(8), 900; https://doi.org/10.3390/mi17080900 - 27 Jul 2026
Viewed by 901
Abstract
To address the challenge that microelectromechanical system (MEMS) gyroscope electrostatic force-modulated closed-loop self-excited driving circuits experience significant dynamic variations in capacitive load and driving demand under different operating conditions, such as start-up, steady-state resonance maintenance, and environmental perturbations, making it difficult to simultaneously [...] Read more.
To address the challenge that microelectromechanical system (MEMS) gyroscope electrostatic force-modulated closed-loop self-excited driving circuits experience significant dynamic variations in capacitive load and driving demand under different operating conditions, such as start-up, steady-state resonance maintenance, and environmental perturbations, making it difficult to simultaneously achieve strong driving capability, stable oscillation, and low power consumption, this paper proposes a high-energy-efficiency adaptive output operational amplifier architecture. Based on a dynamic load-sensing mechanism, the design introduces a three-threshold decision scheme combining a high threshold, a low threshold, and a mid-supply reference voltage. By coordinating a continuous-time voltage detection circuit with a bidirectional shift register, the proposed approach enables accurate identification of the output state and the load level. A time-division-multiplexed two-stage control strategy is adopted to rapidly compensate for the drive capability under abrupt load changes, while proactively disabling redundant output units under steady-state conditions, thereby achieving power delivery on demand. The output stage employs a Class-AB push–pull structure integrating an improved low-leakage single-pole double-throw (SPDT) switch, which hard shuts off the power transistors in the non-operating state to effectively eliminate the subthreshold leakage current. Circuit simulations in a 0.18 μm CMOS process demonstrate that the proposed operational amplifier can adaptively regulate its output current in real time according to variations in the gyroscope driving demand, ensuring sufficient an electrostatic driving force and oscillation stability during transient conditions while significantly reducing static power consumption during the resonance steady state. The proposed design provides an effective solution for high-performance and high-energy-efficiency interface circuit design in MEMS gyroscope electrostatic force-modulated closed-loop self-excited driving systems. Full article
(This article belongs to the Special Issue MEMS Inertial Device, 3rd Edition)
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44 pages, 4342 KB  
Systematic Review
Floating Car Data in Transportation: A Survey of the Literature
by Sara Siverio, Roberto Ventura and Benedetto Barabino
Infrastructures 2026, 11(8), 257; https://doi.org/10.3390/infrastructures11080257 - 26 Jul 2026
Viewed by 698
Abstract
Floating Car Data (FCD) are increasingly used to analyse mobility patterns and support transport-system management, but the evidence remains fragmented across heterogeneous applications, sensing technologies, and data-processing methods, particularly regarding road-infrastructure monitoring. This study presents a systematic literature review and structured evidence map [...] Read more.
Floating Car Data (FCD) are increasingly used to analyse mobility patterns and support transport-system management, but the evidence remains fragmented across heterogeneous applications, sensing technologies, and data-processing methods, particularly regarding road-infrastructure monitoring. This study presents a systematic literature review and structured evidence map of FCD research published between 2010 and 2025. Following PRISMA methodology, Scopus and Google Scholar were searched using the exact expression “floating car data”. The search retrieved 2127 records; after bibliographic harmonisation, duplicate removal, title-and-abstract screening, full-text retrieval, and eligibility assessment, 165 publications were included. The studies were classified through a top-down framework covering application domain, sensing technology, processing approach, validation method, geographical region, deployment scale, and integration with Pavement Management Systems (PMSs). Traffic-state estimation and mobility-planning applications covered 100 publications (60.6%), whereas infrastructure monitoring was the primary domain in 20 studies (12.1%). GPS or GNSS data were used in 128 publications (77.6%), while accelerometers, gyroscopes, or inertial measurement units were reported in 29 studies (17.6%). Only 15 publications (9.1%) described operational or real-time deployment, and explicit PMS-oriented integration was identified in only 9 studies (5.5%). The findings show that FCD research is methodologically mature for traffic and mobility applications but remains comparatively fragmented for pavement-condition assessment. The review therefore proposes an operational pathway linking accelerometric data acquisition, preprocessing, normalization, fleet-level aggregation, validation, data fusion, and PMS decision-making. These results highlight that the principal research gap concerns not sensor availability, but the development of standardized, transferable, and operationally validated frameworks for network-wide pavement monitoring. Full article
(This article belongs to the Special Issue Sustainable Infrastructures for Urban Mobility, 2nd Edition)
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25 pages, 12058 KB  
Article
The Zeta Filter: Attitude Estimation Using Von Mises–Fisher Concentration Dynamics on S3
by Paweł Zalewski and Paweł Rzucidło
Inventions 2026, 11(4), 76; https://doi.org/10.3390/inventions11040076 - 24 Jul 2026
Viewed by 1110
Abstract
This paper presents an attitude filter that encodes both orientation and uncertainty in a single four-dimensional vector, requiring no covariance propagation or normalization constraints. The filter state is the natural parameter of the von Mises–Fisher (vMF) distribution on S3, whose exponential [...] Read more.
This paper presents an attitude filter that encodes both orientation and uncertainty in a single four-dimensional vector, requiring no covariance propagation or normalization constraints. The filter state is the natural parameter of the von Mises–Fisher (vMF) distribution on S3, whose exponential family structure reduces measurement updates to vector addition. Prediction is governed by a continuous-time ODE (Ordinary Differential Equation) that couples rotational kinematics with concentration decay. The QUEST-based construction of measurement natural parameters with a Fisher-information-matched concentration, an antipodal switching mechanism for the quaternion double cover, and a global exponential convergence analysis of the attitude error are described. The filter construction is left-invariant: it commutes with rotations of the reference frame, making the error dynamics trajectory-independent. The result is a filter with the computational simplicity of a complementary filter and the statistical grounding of Bayesian vMF fusion, operating entirely in unconstrained ℝ4 space. The filter is validated in simulation, on two recorded flights—including an evaluation against an EFIS attitude reference—and its computational cost is measured down to on-target microcontroller cycle counts. Gyroscope bias estimation is not included and is left to future work. Full article
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8 pages, 2470 KB  
Proceeding Paper
Integrated Assessment and Rehabilitation System for Hand Function
by Flavia-Iuliana Neculai, Andreea-Larisa Țiploiu, Mădălin Geru, Andreea Matei, Robert Fuior and Călin Corciovă
Eng. Proc. 2026, 148(1), 35; https://doi.org/10.3390/engproc2026148035 - 17 Jul 2026
Viewed by 283
Abstract
The hand is essential for performing everyday activities due to its structural and functional complexity. Injuries and various disorders affecting the hand may lead to significant motor deficits and reduced quality of life. In this context, we developed a system designed to support [...] Read more.
The hand is essential for performing everyday activities due to its structural and functional complexity. Injuries and various disorders affecting the hand may lead to significant motor deficits and reduced quality of life. In this context, we developed a system designed to support hand rehabilitation through both evaluation and therapy. The proposed solution combines a hardware component, based on accelerometer and gyroscope sensors connected to an Arduino Mega platform, with a software component consisting of two applications. The system records finger mobility comparing the collected data with physiological parameters and transmits the results via Bluetooth to a mobile application, which provides visual feedback regarding movement deficits. In addition, a secondary application includes a therapeutic game intended to support rehabilitation in an engaging interactive manner. Full article
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26 pages, 18614 KB  
Article
Sensor-Modality-Aware Human Activity Recognition with the Convolutional Tsetlin Machine: Interpretable and Resource-Efficient Neuro-Symbolic Learning
by Olga Tarasyuk, Anatoliy Gorbenko, Oleksandr Gordieiev, Artem Akulynichev, Rishad Shafik and Alex Yakovlev
Sensors 2026, 26(14), 4482; https://doi.org/10.3390/s26144482 - 15 Jul 2026
Viewed by 549
Abstract
Human activity recognition (HAR) based on smartphone and wearable sensor data is commonly addressed using statistical learning methods and deep neural networks that often provide strong predictive performance, but at the expense of limited interpretability and substantial computational and energy requirements. Such limitations [...] Read more.
Human activity recognition (HAR) based on smartphone and wearable sensor data is commonly addressed using statistical learning methods and deep neural networks that often provide strong predictive performance, but at the expense of limited interpretability and substantial computational and energy requirements. Such limitations reduce their suitability for deployment in practical sensing environments where model decisions must be transparent, verifiable and executable on resource-constrained devices. In this work, we investigate the Convolutional Tsetlin Machine (CTM) for multimodal HAR using only the raw inertial signals (9 × 128) of the UCI-HAR dataset, rather than its pre-computed 561-feature representation. The Tsetlin Machine is a novel neuro-symbolic machine learning approach that offers two important advantages over many conventional machine learning methods: (i) it learns logic-based decision rules that support human inspection and provide a transparent basis for analyzing model decisions, and (ii) it operates with comparatively low computational complexity, making it well suited to efficient and low-power on-device learning. The proposed study systematically analyses the contribution of different feature modalities by decomposing the inertial signals space into semantically defined subsets according to: (i) sensor source: accelerometer and gyroscope; (ii) signal group: gyroscope angular velocity, body and total acceleration (including gravity); (iii) coordinate axis: x, y and z. A separate CTM classifier was trained for each modality and its combinations in order to determine the relative discriminative value of each modality group for activity classification. In addition to predictive performance, the study emphasizes the interpretability of the CTM model ensured by expressing each decision in the form of propositional clauses, thereby enabling visualization and direct inspection of the modality-specific patterns supporting each activity class. Owing to its symbolic structure and modest computational demands, the CTM provides a principled framework for the design of explainable, resource-efficient and deployable HAR systems. The proposed work therefore contributes toward trustworthy multimodal sensing by jointly addressing predictive performance, interpretability and suitability for embedded and mobile platforms. Full article
(This article belongs to the Special Issue Multimodal Ubiquitous Sensing for Human-Centered Healthcare)
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31 pages, 7933 KB  
Review
High-Temperature Piezoelectric Gyroscopes for Harsh Industrial Environments: A Review of Materials, Structural Design, and Circuitry
by Xinyu Liu, Qingwei Liao, Shuhan Zhang, Yifan He, Meng Tang and Lei Qin
Coatings 2026, 16(7), 810; https://doi.org/10.3390/coatings16070810 - 7 Jul 2026
Viewed by 1359
Abstract
Severe shocks and vibrations are common in industrial settings (such as oil drilling at 200–300 °C and heavy machinery); high-temperature piezoelectric gyroscopes’ solid-state architecture provides remarkable shock and vibration tolerance as well as great reliability. This review covers the most recent advances in [...] Read more.
Severe shocks and vibrations are common in industrial settings (such as oil drilling at 200–300 °C and heavy machinery); high-temperature piezoelectric gyroscopes’ solid-state architecture provides remarkable shock and vibration tolerance as well as great reliability. This review covers the most recent advances in the creation of high-temperature piezoelectric gyroscopes from three angles: materials, structural design, and circuit design. First, it emphasises how optimising microstructures can greatly improve the materials’ temperature stability (e.g., PZT with d33 = 562 pC/N and LiNbO3 with Curie temperature ~1210 °C) and piezoelectric coefficient; second, it examines the structural design of piezoelectric gyroscopes based on MEMS/NEMS technology (such as disc-type, ring-type, and beam-type), showing that optimising resonance frequency matching and modal isolation techniques greatly improves the gyroscope’s zero-bias stability (down to 5°/h) and immunity to interference; and third, it summarises the efficacy of optimisation techniques like temperature self-compensation circuit design and structural symmetry design. According to research, problems like high-temperature material ageing (e.g., degradation above 120 °C for silicon-based devices) and the difficulty of system integration continue to limit current technology; in the future, performance bottlenecks will need to be removed through advancements in cross-scale manufacturing technologies and intelligent sensor fusion design. From a multidisciplinary standpoint, this study offers theoretical references and technical recommendations for the industrial use of high-temperature piezoelectric gyroscopes. Full article
(This article belongs to the Section Surface Characterization, Deposition and Modification)
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29 pages, 6556 KB  
Article
Thermal Characteristics and Dynamic Behavior of Auxiliary Bearings in a Vertical Magnetic Suspension System
by Xiaoxu Pang, Chongfeng Jiang, Zhixin Shen, Dingkang Zhu, Aosha Wang and Kaili Wang
Machines 2026, 14(7), 738; https://doi.org/10.3390/machines14070738 - 30 Jun 2026
Viewed by 543
Abstract
Auxiliary bearings in vertical magnetic suspension systems can suffer thermal damage and impact-induced failure during rotor drop events caused by instability. This study aims to clarify the coupled effects of collision, frictional heating, and transient heat transfer on auxiliary bearing response. Dynamic, thermodynamic, [...] Read more.
Auxiliary bearings in vertical magnetic suspension systems can suffer thermal damage and impact-induced failure during rotor drop events caused by instability. This study aims to clarify the coupled effects of collision, frictional heating, and transient heat transfer on auxiliary bearing response. Dynamic, thermodynamic, and finite element models were established to analyze impact behavior, frictional heating, and temperature-field evolution, and were validated using rotor-drop measurements of impact force, rotor displacement, and outer-ring temperature together with post-test damage observations. The results show that severe impact and friction rapidly convert rotor kinetic energy into thermal energy, producing a non-uniform temperature field in the auxiliary bearings. The highest temperature occurs in the inner ring, followed by the rolling elements and outer ring, with peak temperatures of 169.59 °C, 154.66 °C, and 94.79 °C, respectively. Owing to gravity, gyroscopic motion, and rotor inclination during drop, the upper auxiliary bearing experiences greater impact loads, a faster speed increase, and a higher peak temperature rise than the lower bearing. Experimental evidence, including thermal discoloration, wear positions, and component damage, agrees with the simulated high-temperature regions. These results support thermal-shock-resistant design, structural optimization, and operational safety assessment of auxiliary bearings. Full article
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18 pages, 2539 KB  
Article
Multi-Damping Mechanism Analysis and Quality Factor Optimization of Micromachined Disk Resonator Gyroscopes
by Ruotong Qi and Zhirui Liao
Micromachines 2026, 17(6), 727; https://doi.org/10.3390/mi17060727 - 16 Jun 2026
Viewed by 1234
Abstract
A high quality factor, denoted as the Q-factor, is crucial for micromachined disk resonator gyroscopes, commonly referred to as DRGs, to suppress thermomechanical noise and improve bias stability. However, the coupled energy dissipation mechanisms under low-pressure conditions impose significant limitations on further Q-factor [...] Read more.
A high quality factor, denoted as the Q-factor, is crucial for micromachined disk resonator gyroscopes, commonly referred to as DRGs, to suppress thermomechanical noise and improve bias stability. However, the coupled energy dissipation mechanisms under low-pressure conditions impose significant limitations on further Q-factor enhancement. This paper establishes a rigorous multiphysics damping analysis framework for DRGs and quantitatively investigates the contributions of air damping, thermoelastic damping, and anchor loss. A free-molecular squeeze-film damping model is derived based on kinetic gas theory and molecular energy transfer mechanisms, avoiding the continuous fluid assumption of the classical Reynolds equation, which fails in low-pressure regimes. Due to the highly symmetric ring structure and central anchor design, finite element method simulations reveal an extremely high anchor-loss-limited quality factor, Q_anchor, of approximately 1.85 × 1012, indicating negligible anchor-induced dissipation. Under an operating pressure of 0.1 Pa, air damping is validated as the absolute dominant energy dissipation mechanism with a gas quality factor, Q_air, of approximately 1.105 × 105, which is significantly lower than the thermoelastic damping quality factor, Q_TED, evaluated at 8.98 × 105. To break the classical trade-off between squeeze-film damping suppression and capacitive drive efficiency, a decoupled gap optimization strategy is proposed. By maintaining the drive electrode gap, gap_e, at 7.2 µm while increasing only the parasitic ring-to-suspended-mass gap, gap_m, to 12 µm, the squeeze-film-damping-limited Q-factor is improved by approximately 25% to 1.381 × 105 without degrading electromechanical coupling efficiency. In addition, the optimal anchor radius is determined to be approximately 160 µm. The proposed framework provides practical design guidance for high-Q DRGs and other MEMS resonant inertial sensors. Full article
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