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22 pages, 68640 KB  
Article
Real-Time Terrain Recognition for Quadruped Robots Using Proprioceptive Sensors and Temporal Convolutional Networks
by Tzu-Hsiu Chang, Minyechil Alehegn Tefera, Jun-Ming Cheng, Tsung-Ming Fang, Chin-Sheng Chen, Chia-Jen Lin, Peng-Chun Peng, Chao-Ching Ho, Tzu-Hsuan Tsai, Cherng-Yuh Su, Shih-Hao Chang, Pai-Yen Chen, Hsiang-Wei Ho and Ching-Yuan Chang
Sensors 2026, 26(13), 4050; https://doi.org/10.3390/s26134050 (registering DOI) - 25 Jun 2026
Abstract
In this article, we propose a novel real-time terrain recognition and slip estimation method for quadruped robots using proprioceptive sensors and temporal convolutional networks (TCNs). As quadruped robots are increasingly deployed in complex environments, accurate terrain understanding is crucial. External sensors can be [...] Read more.
In this article, we propose a novel real-time terrain recognition and slip estimation method for quadruped robots using proprioceptive sensors and temporal convolutional networks (TCNs). As quadruped robots are increasingly deployed in complex environments, accurate terrain understanding is crucial. External sensors can be affected by lighting variations, occlusion, reflective surfaces, and others. To overcome these challenges, we propose a proprioceptive sensing-based complementary perception module with a TCN, enabling reliable real-time terrain recognition while reducing dependence on external perception. The TCN model effectively captures temporal dependencies in sensor signals, enabling precise and robust detection. The framework is validated through extensive real-world experiments and deployed on an embedded edge computing platform for real-time operation. Results show that the proposed TCN method achieves 98.8% recognition accuracy, outperforming the baseline models compared in this study. In addition, this study analyzes how locomotion speed and environmental conditions affect slip in quadruped robots. These findings confirm that quadruped robots can not only recognize terrain types but also detect surface states, enabling safer and more adaptive locomotion. Therefore, the proposed system is a cost-effective, robust, and low-latency solution for real-time terrain recognition, providing a strong foundation for future deployment across more diverse terrains. Full article
(This article belongs to the Special Issue Intelligent Robots: Control and Sensing)
30 pages, 1266 KB  
Article
Strain-Based Monitoring Methodology and Numerical Validation for the Evaluation of Transverse Connection Condition in Precast Multi-Girder Bridges
by Wenhao Zheng, Han Wei, Jiehua Jiang and Wanheng Li
Sensors 2026, 26(13), 4043; https://doi.org/10.3390/s26134043 (registering DOI) - 25 Jun 2026
Abstract
Precast multi-girder bridges are widely utilized in highway infrastructure but are susceptible to transverse connection deterioration, which can lead to single-girder load-bearing failures. Existing structural health monitoring methods based on the correlation of total dynamic strain responses often fail to identify early-stage damage [...] Read more.
Precast multi-girder bridges are widely utilized in highway infrastructure but are susceptible to transverse connection deterioration, which can lead to single-girder load-bearing failures. Existing structural health monitoring methods based on the correlation of total dynamic strain responses often fail to identify early-stage damage due to the static masking effect, where dominant, in-phase quasi-static components overshadow subtle, damage-sensitive dynamic features. To overcome this limitation, this paper proposes a novel condition indicator based on the correlation of high-frequency dynamic strain increments. An online streaming processing pipeline is developed, incorporating automated single-vehicle crossing event extraction, frequency-targeted signal decoupling, and indicator smoothing. Theoretical derivations on a dual-beam model demonstrate that the proposed indicator is a structural-intrinsic metric, exhibiting high sensitivity to joint stiffness while remaining robust against variations in vehicle weight and speed. Numerical simulations on an 8-slab finite element bridge model under stochastic traffic flow further verify the effectiveness of the framework. Results indicate that the proposed indicator can localize both progressive degradation and sudden brittle failures. Additionally, the method maintains reliability down to a signal-to-noise ratio of 30dB and robustness to hyper-parameter selection. While the current framework is established based purely on numerical validation and has not yet been tested using real bridge strain data, it shows numerical feasibility and provides a solid theoretical and algorithmic foundation for the automated condition evaluation of precast multi-girder bridges, supporting future field validation for both long-term maintenance and emergency response. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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24 pages, 8829 KB  
Article
Narrow Shielded Spaces: Analysis of BDS Navigation Signal Feature Establishment and Spectrum Map Network Design
by Heng Zhang, Baoguo Yu, Shuguo Pan, Chuanzhen Sheng, Shiyuan Liu, Jianqiang Cheng and Shitong Du
Electronics 2026, 15(13), 2799; https://doi.org/10.3390/electronics15132799 (registering DOI) - 25 Jun 2026
Abstract
Long and narrow shielded confined spaces, represented by traffic tunnels and underground utility tunnels, constitute critical application scenarios for indoor and underground positioning services. Despite their relatively simple geometric configurations, such environments suffer from severe spatial distortion of geometric dilution of precision (GDOP). [...] Read more.
Long and narrow shielded confined spaces, represented by traffic tunnels and underground utility tunnels, constitute critical application scenarios for indoor and underground positioning services. Despite their relatively simple geometric configurations, such environments suffer from severe spatial distortion of geometric dilution of precision (GDOP). Coupled with pervasive low-elevation signal propagation and intensive multipath reflection effects, conventional BeiDou Navigation Satellite System (BDS) positioning services are unable to provide continuous and reliable coverage in these scenarios. To date, existing research on high-precision pseudolite positioning for narrow confined spaces remains largely confined to theoretical analysis and laboratory experimental verification, while systematic studies on application-oriented signal atlas feature network design are significantly insufficient, forming a prominent gap that restricts the practical engineering deployment of relevant technologies. To address the aforementioned technical bottlenecks, this paper proposes a novel BDS pseudolite signal atlas network design method to improve the continuity, stability and comprehensive positioning performance in spatially distorted narrow shielded environments. Field vehicular tests were carried out in actual engineering tunnels and underground utility tunnels to systematically analyze the variation characteristics of raw BDS pseudolite observation data, including pseudorange, carrier phase, carrier-to-noise ratio (C/N0) and Doppler shift. The test results verified that kinematic Doppler parameters exhibited outstanding stability in complex shielded environments with strong multipath interference. On this basis, a spatial feature model based on kinematic Doppler measurements was constructed, and wavelet denoising technology was adopted to extract effective typical spatial feature parameters. Combined with the deterministic one-to-one mapping relationship between Doppler peak characteristics and spatial positions, a multi-peak kinematic Doppler atlas was established, which eliminates the dependence on pre-deployment data collection, dedicated database construction and offline model training. Furthermore, comprehensively considering multi-dimensional constraints such as spatial environment scale, carrier dynamic characteristics and terminal output rate, the atlas network scheme was optimized to achieve a balanced trade-off among positioning detection accuracy, absolute positioning precision and suppression of the pseudolite near-far effect. Comparative experimental results demonstrate that the proposed BDS pseudolite atlas network effectively resolves the inherent GNSS positioning difficulty in long and narrow shielded spaces. Benefiting from the rational spectral peak configuration strategy, the system can satisfy the continuous and stable positioning requirements of multiple carrier types including motor vehicles and railway locomotives under variable motion speeds and terminal output rates. This study provides a robust and feasible technical solution for high-precision BDS positioning services in long and narrow shielded confined spaces, and holds favorable engineering application prospects for underground navigation scenarios. Full article
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20 pages, 10872 KB  
Article
Study on Centrifugal Spreading Characteristics of Pellet Feed Based on Discrete Element Method
by Leilei Chen, Zirui Wu, Zhijian Li, Qingsong Hu, Tianli Ma and Jun Li
Appl. Sci. 2026, 16(13), 6367; https://doi.org/10.3390/app16136367 (registering DOI) - 25 Jun 2026
Abstract
To clarify the spreading law of river crab pellet feed in a centrifugal spreading mechanism and provide a physical basis for the path planning of automatic feeding boats, this study took 4.0 mm sinking extruded river crab feed as the research object. A [...] Read more.
To clarify the spreading law of river crab pellet feed in a centrifugal spreading mechanism and provide a physical basis for the path planning of automatic feeding boats, this study took 4.0 mm sinking extruded river crab feed as the research object. A systematic research method combining physical experiments and Discrete Element Method (DEM) simulation was established. Physical experiments were conducted to calibrate the intrinsic parameters (density, Poisson’s ratio, elastic modulus) and contact parameters (friction coefficients and restitution coefficients between feed and 304 stainless steel/ABS plastic, as well as between feed particles) of the pellet feed. On this basis, a DEM simulation model of a vibration blanking-dual disc centrifugal spreading mechanism was constructed using the multi-sphere aggregation method and the Hertz-Mindlin (no-slip) contact model. A Central Composite Design (CCD) response surface experiment was employed to investigate the spreading law, with boat speed (0.5–1.5 m/s) and spreading disc rotation speed (800–1000 rpm) as independent variables, and unilateral spreading width (W), track superposition uniformity (ω), and transverse coefficient of variation (Cv) as response indicators to characterize spreading range and particle distribution. The results showed that the spreading disc rotation speed had an extremely significant effect (p < 0.0001) on all three response indicators, while boat speed had no significant effect. The feed exhibited a characteristic double fan-shaped superposition distribution pattern. Through multi-objective optimization, the optimal operational parameters were determined as a boat speed of 1.0 m/s and a spreading disc rotation speed of 879 rpm, yielding a unilateral spreading width of 2.9 m, a track superposition uniformity of 88.31%, and a transverse coefficient of variation of 8.33%. This study establishes a quantitative method for analyzing feed spreading characteristics and clarifies the spreading range and particle distribution law, providing a reliable physical basis for full-coverage path planning of crab pond feeding boats. Full article
(This article belongs to the Section Agricultural Science and Technology)
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25 pages, 1717 KB  
Article
Task Engagement in Matrix Reasoning Performance: A Cross-Cultural Investigation in China and the United Kingdom
by Rui Wang, Kastoori Kalaivanan, Jiani Ren, Shen-Hsing Annabel Chen and Chew Lee Teo
J. Intell. 2026, 14(7), 117; https://doi.org/10.3390/jintelligence14070117 (registering DOI) - 25 Jun 2026
Abstract
Matrix reasoning tasks remain among the most widely used instruments for assessing abstract reasoning and are often assumed to be culturally neutral. However, this assumption has been challenged by studies reporting significant cross-cultural variation in performance on nonverbal matrix reasoning tasks, even when [...] Read more.
Matrix reasoning tasks remain among the most widely used instruments for assessing abstract reasoning and are often assumed to be culturally neutral. However, this assumption has been challenged by studies reporting significant cross-cultural variation in performance on nonverbal matrix reasoning tasks, even when groups show comparable performance on verbal measures of general cognitive ability. One plausible reason is that many matrix reasoning tasks rely primarily on accuracy-based performance metrics while providing limited insight into response timing and task engagement during problem solving. The present study examined the Matrix Reasoning Item Bank (MaRs-IB), a new online matrix reasoning instrument integrating both accuracy and response time, in 458 participants from China and the UK. Results demonstrated strong psychometric properties across both cultural contexts, while also revealing systematic between-group differences in overall task performance. Chinese participants were generally slower but more accurate, whereas UK participants responded more quickly with lower overall accuracy. Rather than reflecting a classical speed–accuracy trade-off, these patterns may indicate cross-cultural variation in persistence, deliberative engagement, and the metacognitive regulation of cognitive effort during reasoning tasks. In particular, Chinese participants allocated more time before responding and persisted longer on challenging task items, whereas UK participants demonstrated relatively faster responding and shorter response times on more challenging items. These findings suggest that cross-cultural differences in matrix reasoning performance may reflect not only differences in observed performance levels, but also variation in how participants allocate time and sustain engagement during cognitively demanding tasks. Full article
(This article belongs to the Special Issue How Culture Impacts the Process of Cognitive Assessment)
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23 pages, 6923 KB  
Article
Electric Bicycle Series Arc Fault Identification Method Based on Improved PCA and SVM
by Kai Yang, Jiaqi Chen, Zuxuan Yang, Ziyu Ma and Rencheng Zhang
Sensors 2026, 26(13), 4018; https://doi.org/10.3390/s26134018 (registering DOI) - 24 Jun 2026
Abstract
Electric bicycles are popular due to their environmental benefits and convenience. However, electric bicycle fires caused by series arc faults remain a serious safety concern. This study focuses on series arc fault identification for electric bicycles under complex operating conditions, covering state of [...] Read more.
Electric bicycles are popular due to their environmental benefits and convenience. However, electric bicycle fires caused by series arc faults remain a serious safety concern. This study focuses on series arc fault identification for electric bicycles under complex operating conditions, covering state of charge (SoC), torque, and speed variations, and simultaneously considers normal state, DC-side series arc fault, and AC-side series arc fault conditions. Five time-domain features, namely root mean square (RMS), standard deviation (STD), skewness (SK), kurtosis (KUR), and current amplitude (CA), and three frequency-domain features, namely amplitude–frequency energy (AFE), amplitude–frequency mean (AFM), and amplitude–frequency kurtosis (AFK), are extracted. An improved principal component analysis (PCA)-based feature fusion method transforms the eight original time–frequency features into a five-dimensional PCA-fused feature representation consisting of PC1, PC2, PC3, fused PC4–PC7, and PC8. The fused features are classified using a radial basis function (RBF)-support vector machine (SVM) model. The proposed method achieves 98.68% test accuracy, 0.9869 Macro-F1, and 0.9931 Macro-AUC. A classifier comparison and feature-level latency analysis are also provided to clarify the accuracy–cost tradeoff and deployment feasibility. The results indicate that the proposed method can provide an interpretable and lightweight solution for electric bicycle controllers, battery management systems (BMSs), and onboard safety-monitoring applications. Full article
17 pages, 1701 KB  
Article
Uncertainties of Estimating the Conductive Heat Flux at a Pavement Surface
by Chan Huang and Chuanchong Wei
Infrastructures 2026, 11(7), 216; https://doi.org/10.3390/infrastructures11070216 (registering DOI) - 24 Jun 2026
Abstract
Conductive heat flux (G) at pavement surfaces plays a vital role in managing internal temperature variations. G can be calculated either as the residual of solar absorption, heat convection, and long-wave radiation, or as the product of thermal conductivity and the [...] Read more.
Conductive heat flux (G) at pavement surfaces plays a vital role in managing internal temperature variations. G can be calculated either as the residual of solar absorption, heat convection, and long-wave radiation, or as the product of thermal conductivity and the temperature gradient near the surface. Both methods, however, are subject to uncertainties due to measurement parameters. For the two methods, this study formulates the uncertainty of the conductive heat flux at the pavement surface. The experiment was designed to measure pavement interior temperatures and external weather data so that the uncertainties of the two methods can be quantified and compared. It was found that ∆G estimated by the residual method is significantly higher than that calculated using conductivity and temperature gradient. The key factors influencing ∆G in the residual method, in order, are wind speed, incident solar radiation, and reflectivity, with other factors such as surface and air temperatures, relative humidity, and emissivity having minimal impact. In contrast, the primary contributors to ∆G in the conductivity and temperature gradient method are the temperature gradient and thermal conductivity. The residual method is crucial for predicting pavement temperatures when no pre-installed temperature sensors are available, and enhancing wind speed measurement precision can significantly reduce the uncertainty of G. The study finds that the approach of estimating G through conductivity and temperature gradient showed lower uncertainty than the residual method, particularly in complex urban environments. Full article
(This article belongs to the Special Issue Sustainable Road Infrastructure: Safety, Performance and Resilience)
22 pages, 10106 KB  
Article
Designing and Evaluating a Neural Network-Based Control Strategy for a PMSM-Driven Electric Vehicle Under Various Driving Cycles
by Elmehdi Ennajih, Hakim Allali, Abdelhadi Ennajih, Ezzitouni Jarmouni and Hind Tarout
World Electr. Veh. J. 2026, 17(7), 327; https://doi.org/10.3390/wevj17070327 (registering DOI) - 24 Jun 2026
Abstract
In light of the rapid development of the electric vehicle market, permanent magnet synchronous motors (PMSMs) are becoming essential components of propulsion systems. This is due to their high efficiency, remarkable power density, and ability to deliver high torque over a wide speed [...] Read more.
In light of the rapid development of the electric vehicle market, permanent magnet synchronous motors (PMSMs) are becoming essential components of propulsion systems. This is due to their high efficiency, remarkable power density, and ability to deliver high torque over a wide speed range. However, the optimal control of these motors under dynamic conditions remains a major challenge due to system nonlinearities, parameter variations, and external disturbances. Conventional strategies such as field-oriented control (FOC), direct torque control (DTC), and fuzzy logic control (FLC) show variable performance in terms of current quality, robustness, and energy efficiency. To overcome these limitations, this study proposes an intelligent control strategy based on artificial neural networks (ANNs), which ensures efficient operation and high control performance under various operating conditions. This approach leverages the learning capabilities of deep neural networks to improve control accuracy, system stability, and overall energy performance. The results obtained show a significant reduction in the current’s total harmonic distortion (THD) as well as an improvement in the stator’s current quality and the electromagnetic torque’s dynamic behavior compared to conventional methods. This improvement reduces overall losses in the electric drive system, thereby contributing to increased vehicle energy efficiency. As a result, the electric vehicle’s range is extended, and the dynamic performance of the PMSM is optimized. These results confirm the potential of artificial intelligence techniques for developing intelligent, robust, and adaptive control systems designed for modern electric propulsion applications. Full article
(This article belongs to the Section Energy Supply and Sustainability)
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23 pages, 1990 KB  
Article
Time-Optimal Trajectory Planning Method for Servo PMSM Based on Short-Term Dynamic Feasible Region Constraint
by Hui Li, Jianfu Li, Xuewei Xiang, Peng Jiang, Bin Yuan and Renkuan Liu
Sensors 2026, 26(13), 4010; https://doi.org/10.3390/s26134010 (registering DOI) - 24 Jun 2026
Abstract
Aiming at addressing the problem whereby the traditional time-optimal trajectory planning based on the steady-state torque–speed characteristic cannot fully exploit the short-term dynamic output performance of the servo permanent magnet synchronous motor (SPMSM), a time-optimal trajectory planning method for the SPMSM based on [...] Read more.
Aiming at addressing the problem whereby the traditional time-optimal trajectory planning based on the steady-state torque–speed characteristic cannot fully exploit the short-term dynamic output performance of the servo permanent magnet synchronous motor (SPMSM), a time-optimal trajectory planning method for the SPMSM based on the short-term dynamic feasible region constraint is proposed to effectively improve the response speed. Firstly, the dynamic trapezoidal domain operation boundary is obtained by analyzing the motor working point variation curve and considering factors such as the working temperature and trajectory control, which constitutes the torque–speed value and the dynamic constraint mechanism of trajectory planning. Secondly, based on the energy consumption model, the average thermal power is used to represent the torque overload limit condition, and a dynamic constraint method based on the short-term dynamic torque–speed operation boundary is proposed. Then, in order to reduce the computational load in the online millisecond-level response, a time-optimal trajectory optimization algorithm based on sequential least squares is proposed to calibrate the positioning time of the time-optimal trajectory under different working temperatures and angles. Finally, a simulation and experimental comparisons of the time-optimal trajectories under different angles and working temperatures are carried out to verify the effectiveness of the proposed method. Full article
31 pages, 22249 KB  
Article
Sectional Differences in Stratum Response and Construction Parameter Sensitivity During River-Crossing Double-Line Shield Tunneling
by Yintao Chen, Zhongxiang Lu, Jingwei Li, Kaifang Yang and Lifeng Wang
Buildings 2026, 16(13), 2493; https://doi.org/10.3390/buildings16132493 (registering DOI) - 24 Jun 2026
Abstract
To reveal the differences in stratum response among different environmental sections and the influences of key construction parameters on deep soil deformation during river-crossing double-line shield tunneling, the paper takes the East Genshan Road River-Crossing Tunnel as the engineering case, and systematically investigates [...] Read more.
To reveal the differences in stratum response among different environmental sections and the influences of key construction parameters on deep soil deformation during river-crossing double-line shield tunneling, the paper takes the East Genshan Road River-Crossing Tunnel as the engineering case, and systematically investigates the stratum responses of the onshore and riverbed sections as well as the effects of construction parameters via field monitoring, measured construction parameter data and three-dimensional finite element simulation based on ABAQUS. The simulation results suggest that, compared with the onshore section, the riverbed section may present larger cumulative displacement, more intense deep soil response and a wider influence range of transverse settlement under the investigated high-water-pressure and saturated soft-soil conditions. These differences are more reasonably interpreted as the combined effects of burial depth, stratum composition, mechanical properties, hydraulic boundary conditions, surface boundary constraints and overburden conditions. Among these factors, the high-water-pressure and saturated soft-soil environment may contribute to the enhanced disturbance diffusion and cumulative deformation response observed in the riverbed section. The longitudinal displacement evolution of the riverbed section presents obvious stratified transmission characteristics, and its transverse settlement trough shows a typical double-peak W-shaped distribution with larger peak values, wider trough profile and slower far-field attenuation. The single-factor parametric analysis suggests that, within the investigated parameter ranges, cutterhead torque produced the largest absolute settlement variation, followed by total shield thrust and tunneling speed. The results of this study can provide a reference basis for settlement control and construction parameter optimization of river-crossing double-line shield tunneling in high-water-pressure and saturated soft soil strata. Full article
(This article belongs to the Section Construction Management, and Computers & Digitization)
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19 pages, 5984 KB  
Article
Grating-Based Fiber-Optic Sensing Using a Single Packaged FBG for Boundary-Dependent Motor Vibration-State Transitions
by Cheng-Yu Lin, Pei-Chung Liu, Cheng-Kai Yao, Shao-Chi Huang, Shi-Jia Huang, Sheng-Jie Chen and Peng-Chun Peng
Sensors 2026, 26(13), 3994; https://doi.org/10.3390/s26133994 (registering DOI) - 24 Jun 2026
Abstract
This study demonstrates single-channel fiber Bragg grating (FBG) sensing for relative vibration-state monitoring of a motor–support system under angle-dependent boundary conditions. A packaged FBG accelerometer-type sensing unit was mounted on the motor–support structure, and the reflected Bragg wavelength was recorded as a one-dimensional [...] Read more.
This study demonstrates single-channel fiber Bragg grating (FBG) sensing for relative vibration-state monitoring of a motor–support system under angle-dependent boundary conditions. A packaged FBG accelerometer-type sensing unit was mounted on the motor–support structure, and the reflected Bragg wavelength was recorded as a one-dimensional optical vibration response. Because the sensor was installed away from the rotating shaft, the measured wavelength fluctuation was interpreted as a coupled vibration-sensitive response of the motor, fixture, sensor package, bonding condition, and changing boundary state, rather than as a calibrated shaft speed or absolute acceleration signal. Adaptive variational mode decomposition (AVMD) was applied to track the time-varying narrowband spectral-response trajectory of the Bragg-wavelength signal. In parallel, raw wavelength windows were supplied to LSTM, 1D-CNN, and CNN–LSTM autoencoders to evaluate waveform departures from learned nominal fixed-angle behavior. The fixed-angle results showed stable but distinguishable optical vibration responses under different boundary states, whereas the dynamic angle-transition records produced local trajectory changes and alarm-candidate intervals. Baseline and autoencoder comparisons further clarified the trade-off between transition coverage and false-alarm tendency. The RMS threshold baseline was more sensitive to transition-related amplitude changes but produced more false alarms, whereas the CNN–LSTM autoencoder provided the most selective response among the tested autoencoder branches. The results are interpreted as task-specific evidence for relative vibration-state transition monitoring rather than as general motor fault diagnosis. Overall, the framework demonstrates a compact FBG-based route for relative vibration-state transition monitoring when speed references, dense sensor layouts, and labeled fault data are unavailable. Full article
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23 pages, 584 KB  
Article
Benchmarking Barren Plateau Mitigation Strategies in Quantum Neural Networks on Standard and Medical Image Datasets
by Maqsudur Rahman, Rui Liu, Anup Majumder, Pintu Chandra Paul, Kangtong Mo, Amena Begum, Kashmi Sultana, Nahida Akter, Lu Wei, Ye Zhang and Jun Zhuang
J. Imaging 2026, 12(7), 275; https://doi.org/10.3390/jimaging12070275 (registering DOI) - 23 Jun 2026
Abstract
Barren plateaus (BPs) pose a major trainability challenge for quantum neural networks (QNNs) by causing gradients to concentrate near zero as circuit size, depth, or expressibility increases. This study presents a comparative benchmark of 10 BP mitigation strategies across six qubit settings (2, [...] Read more.
Barren plateaus (BPs) pose a major trainability challenge for quantum neural networks (QNNs) by causing gradients to concentrate near zero as circuit size, depth, or expressibility increases. This study presents a comparative benchmark of 10 BP mitigation strategies across six qubit settings (2, 4, 8, 12, 16, and 20) and three datasets of increasing complexity: Iris, MNIST, and MedMNIST. The evaluated methods include eight initialization-based strategies (Beta, Gaussian, Uniform Norm, CNN-based initialization, He-normal, He-uniform, Xavier-normal, and Xavier-uniform), one model-based variational encoder, and one optimization-based time-nonlocal Fourier parameterization. Experiments were implemented using PennyLane 3.10 and PyTorch 2.5 with simulator backends. We evaluate trainability using gradient variance and training loss, and we clarify that the benchmark analyzes simulated QNN optimization behavior rather than hardware-noise-resilient or noisy-label learning. Across the tested two-layer circuit configurations, the mitigation strategies maintained measurable gradient variance and stable loss reduction, suggesting that severe barren plateau behavior was not observed under the benchmark conditions. CNN-based and Beta initialization showed strong empirical behavior in variance retention and convergence speed, while Gaussian initialization was comparatively weaker in higher-dimensional settings. The study provides a reproducible benchmark structure for comparing BP mitigation behavior and identifies important limitations related to circuit depth, hardware noise, feature encoding, and classification performance that should be addressed in future QNN benchmarking. Full article
(This article belongs to the Section Medical Imaging)
18 pages, 2613 KB  
Article
Diversity of Solitary Structures by the Application of Symbolic Neural Network-Based Approach: Exploring the Strain Wave Equation
by Usman Younas, Reem Abdullah Aljethi, Fengping Yao and Jan Muhammad
Mathematics 2026, 14(13), 2238; https://doi.org/10.3390/math14132238 (registering DOI) - 23 Jun 2026
Abstract
A novel modified generalized Riccati equation mapping neural network-based approach is the basic theme of this study by exploring the nonlinear dynamical characteristics of the the strain wave model’s soliton solutions, which govern wave propagation in micro structured solids. Strain waves are particularly [...] Read more.
A novel modified generalized Riccati equation mapping neural network-based approach is the basic theme of this study by exploring the nonlinear dynamical characteristics of the the strain wave model’s soliton solutions, which govern wave propagation in micro structured solids. Strain waves are particularly intriguing, since they preserve their form and speed throughout transmission. The nonlinear dynamical behaviors of strain waves may be modeled by partial differential equations in micro structured materials. In the realm of micro structured solids, there exists a class of phenomena that are referred to as micro strain waves. These waves arise in solids possessing intricate internal architectures, including periodic lattices, precisely engineered metamaterials Understanding these waves is key to designing more complex materials and new acoustic technologies. The activation function and the weight function of the neural network are assigned to each input layer, hidden layer and output layer and the neural network itself is a multi-layer computational network. Using the structure of the neural network, every neuron in the first hidden layer is given solutions to the Riccati equation, and the new highly expressive trial functions are generated in a systematic way. In this way, a large variety of exact soliton solutions are obtained, such as bright, dark, kink, and combined solitons as well as periodic and hyperbolic wave profiles. The influence of the essential physical and mathematical parameters is explored systematically using three-dimensional, two-dimensional and contour visualizations, which illustrate how parameter variations lead to changes in the amplitude, shape and stability of the wave structures. The solutions presented reveal the dynamic properties of micro strain solitons which leads to new avenues of investigation in the study of related nonlinear phenomena in micro structured solids. In a broader context, our results highlight the great potential of analytical techniques using neural networks as a powerful and versatile toolset to study complex nonlinear wave models within the applied sciences from acoustics to photonics to smart materials engineering. Full article
(This article belongs to the Special Issue Soliton Theory and Integrable Systems in Mathematical Physics)
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34 pages, 3799 KB  
Article
Simulation of 2D Shallow-Sea Acoustic Fields Using a Physics-Informed Residual Network
by Ziyue Wang, Lingyi Cong, Luotao Zhang, Shuyue Liu and Xiaobo Zhang
J. Mar. Sci. Eng. 2026, 14(13), 1154; https://doi.org/10.3390/jmse14131154 (registering DOI) - 23 Jun 2026
Abstract
Acoustic propagation in stratified shallow seas is governed by finite-depth waveguiding, impedance contrasts at the seawater–seabed interface, and coupled space–time wave dynamics. Conventional numerical solvers are accurate but often require detailed environmental priors, mesh generation, and explicit time marching, increasing the cost of [...] Read more.
Acoustic propagation in stratified shallow seas is governed by finite-depth waveguiding, impedance contrasts at the seawater–seabed interface, and coupled space–time wave dynamics. Conventional numerical solvers are accurate but often require detailed environmental priors, mesh generation, and explicit time marching, increasing the cost of simulations involving complex boundaries or repeated evaluations. This study proposes a physics-informed residual network (ResNet-PINN) for continuous simulation of two-dimensional acoustic fields in shallow-sea stratified media. The framework embeds a variable-density, variable-sound-speed acoustic pressure wave equation, initial and boundary constraints, and interface-focused collocation into network training. A Gaussian initial wave packet and temporal gating are incorporated through the output transformation to improve early-time physical consistency. The model is validated against SPECFEM2D simulations and a stratified semi-analytical modal benchmark. The results show that it captures source-region spreading, main wavefront evolution, and transmission–reflection structures near the seawater–seabed interface at an equivalent frequency of approximately 477 Hz. Supplementary tests with sloping and arched interfaces and modified boundary conditions indicate adaptability to smooth interface variations. Overall, the framework provides a physically consistent neural network strategy for continuous shallow-sea acoustic field simulation and a complementary basis for future extensions to higher-frequency propagation, more complex environments, and dynamically varying ocean conditions. Full article
24 pages, 11542 KB  
Article
Novel Silicone Rubber–Based Multi-Dimensional Filler Composite Electrode Materials for the Dielectric Elastomer Actuation Technology of Micro-Crawling Robots
by Yang Hong, Yun Yang, Zening Lin, Tao Jiang and Zirong Luo
Polymers 2026, 18(13), 1561; https://doi.org/10.3390/polym18131561 (registering DOI) - 23 Jun 2026
Abstract
Aiming to develop high-performance flexible electrode materials for dielectric elastomer actuation systems applied to micro-crawling robots, this study proposes multi-dimensional filler composite electrode materials with a methyl vinyl silicone rubber matrix. Three types of conductive fillers—namely, zero-dimensional super-conductive carbon black, one-dimensional single-walled carbon [...] Read more.
Aiming to develop high-performance flexible electrode materials for dielectric elastomer actuation systems applied to micro-crawling robots, this study proposes multi-dimensional filler composite electrode materials with a methyl vinyl silicone rubber matrix. Three types of conductive fillers—namely, zero-dimensional super-conductive carbon black, one-dimensional single-walled carbon nanotubes, and two-dimensional flaky micron-sized silver powder—were employed to construct a hierarchical multi-dimensional conductive network within the silicone rubber matrix via a three-stage fabrication strategy. The electrical conductivity and conductive stability of the as-prepared composite electrode materials were systematically investigated, where the intrinsic mechanisms and evolutionary laws of material electrical performance variations were analyzed. Furthermore, the effects of fillers with different dimensional morphologies on the comprehensive properties of the composites at each fabrication stage were explored, and the optimal filler dosage for each component was determined. Microstructural observations of the staged conductive network formation further verified the rationality of the stage-based functional design model. The optimized composite electrode delivers an initial electrical conductivity of 1.5 × 104 S/m, with only a 14.9% conductivity attenuation under 50% tensile strain, demonstrating excellent electromechanical stability. Moreover, a prototype micro-crawling robot was fabricated using the optimized composite electrode, achieving a maximum linear crawling speed of 8 mm/s. These experimental results validate the feasibility and superiority of the proposed multi-dimensional filler composite strategy. This work provides a novel technical approach for the design and development of high-performance flexible electrode materials for flexible electronic and micro-robotic actuation applications. Full article
(This article belongs to the Section Smart and Functional Polymers)
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