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Search Results (18,275)

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Keywords = non-linear systems

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17 pages, 3154 KB  
Article
Embedded MOX-Based Volatilomic Sensing for Real-Time Classification of Plant-Based Milk Beverages
by Elisabetta Poeta, Veronica Sberveglieri and Estefanía Núñez-Carmona
Sensors 2026, 26(6), 1976; https://doi.org/10.3390/s26061976 (registering DOI) - 21 Mar 2026
Abstract
The increasing diffusion of plant-based milk alternatives poses new challenges at the intersection of food safety and consumer experience, particularly regarding allergen cross-contamination and beverage performance during preparation. Traditional quality control strategies are typically confined to upstream production stages and are unable to [...] Read more.
The increasing diffusion of plant-based milk alternatives poses new challenges at the intersection of food safety and consumer experience, particularly regarding allergen cross-contamination and beverage performance during preparation. Traditional quality control strategies are typically confined to upstream production stages and are unable to address individualized risks and sensory variability at the point of consumption. In this study, we propose an embedded volatilomic sensing approach that combines metal oxide semiconductor (MOX) sensor arrays with lightweight artificial intelligence algorithms to enable real-time, on-device decision-making. The volatilome of four commercially available plant-based milk beverages (oat, almond, soy, and coconut) was characterized using GC–MS/SPME as a reference method, while a MOX-based electronic nose provided rapid, non-destructive sensing of volatile fingerprints. Linear Discriminant Analysis demonstrated clear discrimination among beverage types based on their volatile signatures, supporting the use of MOX sensor arrays as functional descriptors of compositional identity and process-related variability. Beyond beverage classification, the proposed framework is designed to support future implementation of (i) screening for anomalous volatilomic patterns potentially compatible with accidental cow’s milk carryover in shared preparation settings and (ii) adaptive tuning of preparation parameters (e.g., foaming-related settings) in smart beverage systems. The results highlight the role of embedded volatilomic intelligence as a unifying layer between personalized risk-aware screening and sensory-oriented process control, paving the way for intelligent food-processing appliances capable of autonomous, real-time adaptation at the point of consumption. Full article
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27 pages, 425 KB  
Article
The Impact of Energy Transition on CO2 Emissions in BRICS Nations: Evidence from Linear and Nonlinear Approaches
by Nyiko Worship Hlongwane and Hlalefang Khobai
Sustainability 2026, 18(6), 3109; https://doi.org/10.3390/su18063109 (registering DOI) - 21 Mar 2026
Abstract
The impact of the shift in energy systems on CO2 emissions in BRICS nations plays a crucial role in mitigating climate change and advancing sustainable development goals. This study examines how changes in the composition of the energy mix influence CO2 [...] Read more.
The impact of the shift in energy systems on CO2 emissions in BRICS nations plays a crucial role in mitigating climate change and advancing sustainable development goals. This study examines how changes in the composition of the energy mix influence CO2 emissions in BRICS countries, and further evaluates the relationships among energy transition, economic growth, urbanization, trade openness, population growth, and CO2 emissions. Drawing on panel data from 1990 to 2023 and applying both linear and nonlinear PMG models, the study investigates how energy transition asymmetrically influences CO2 emissions in both the short and long run. In the short run, the linear PMG results show that energy transition helps reduce CO2 emissions in the UAE, South Africa, India, and Brazil, while it is associated with increased emissions in China, Egypt, Ethiopia, Indonesia, Iran, and Russia, while also decreasing on average for all in the long-run period based on the linear PMG. The impact of energy transition on CO2 emissions in BRICS nations is complex and heterogeneous from the nonlinear PMG. In the short run, positive energy transition shocks reduce emissions in most countries (UAE, Brazil, China, Egypt, Ethiopia, and South Africa), but increase emissions in others (Indonesia, India, Iran, and Russia). Negative shocks also have mixed effects. However, in the long run, positive energy transition shocks lead to a 0.019% decrease in CO2 emissions, while negative shocks increase emissions by 0.018%, indicating a nuanced relationship between energy transition and emissions. Urbanization, population growth, and economic expansion exhibit diverse effects on CO2 emissions across the BRICS group. The results imply that policymakers should implement a comprehensive policy mix that elevates the role of energy transition, sustainable urban development, and green investment to curb CO2 emissions. Tailored, country-specific measures are required to account for national circumstances and the asymmetric links between energy transition and emissions. The study underlines the importance of international collaboration in tackling climate change and advancing sustainable development, and stresses that customized strategies for each BRICS member are essential in order to achieve long-term environmental sustainability. Full article
54 pages, 54419 KB  
Article
An Investigation into Uncertainty Quantification of Shallow Foundation Failure Mechanisms in Horizontally Stratified Layered Soil Strata
by Ambrosios-Antonios Savvides
Appl. Sci. 2026, 16(6), 3051; https://doi.org/10.3390/app16063051 (registering DOI) - 21 Mar 2026
Abstract
In light of the evolution of computer science and computational mechanics, an uncertainty analysis of engineering systems has become increasingly feasible. In this paper, the failure of shallow foundations in layered soil continua is examined. It is shown that Gaussian input distributions lead [...] Read more.
In light of the evolution of computer science and computational mechanics, an uncertainty analysis of engineering systems has become increasingly feasible. In this paper, the failure of shallow foundations in layered soil continua is examined. It is shown that Gaussian input distributions lead to approximately Gaussian output response distributions even in the presence of an extensive nonlinear relationship between them. Soil configurations that provide larger average values and higher output variability in terms of bearing capacity force are those in which cohesive, stronger soils such as clays exist in the upper layers. Configurations with sandy soils in the upper layers, in several cases, provide greater average values of maximum displacements, rotations, and output variation. In this paper, the probabilities of the Meyerhof spline onset point are also estimated. Therefore, the proposed framework can support shallow foundation design decisions. Full article
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26 pages, 3482 KB  
Review
Advances in Magnetic and Electrochemical Techniques for Monitoring Corrosion and Microstructural Degradation in Steels
by Polyxeni Vourna, Pinelopi P. Falara, Aphrodite Ktena, Evangelos V. Hristoforou and Nikolaos D. Papadopoulos
Metals 2026, 16(3), 352; https://doi.org/10.3390/met16030352 (registering DOI) - 21 Mar 2026
Abstract
Steels remain among the most widely used structural and engineering materials in modern infrastructure, energy systems, and industrial facilities. Their long-term reliability depends critically on the early detection of corrosion damage and microstructural degradation. This review surveys recent advances in two complementary families [...] Read more.
Steels remain among the most widely used structural and engineering materials in modern infrastructure, energy systems, and industrial facilities. Their long-term reliability depends critically on the early detection of corrosion damage and microstructural degradation. This review surveys recent advances in two complementary families of non-destructive evaluation (NDE) methods: magnetic techniques, including magnetic Barkhausen noise (MBN), magnetic flux leakage (MFL), eddy current testing (ECT), and magnetic hysteresis analysis; and electrochemical methods including electrochemical impedance spectroscopy (EIS), linear polarization resistance (LPR), scanning vibrating electrode technique (SVET), and electrochemical noise (EN). Recent progress in sensor miniaturization, signal processing algorithms, and multi-technique integration is reviewed. Particular attention is given to the sensitivity of these methods to microstructural changes reported in the literature, including carbide dissolution, phase transformations, temper embrittlement, and sensitization in stainless steels, as well as to the conditions under which such sensitivity has been demonstrated. The potential synergy between magnetic and electrochemical monitoring is discussed as a possible pathway toward more robust, condition-based maintenance frameworks. Challenges related to field deployment, environmental interference, calibration, and data interpretation are identified, and future directions—including machine learning-assisted analysis and multi-physics sensor arrays—are outlined. Full article
19 pages, 1711 KB  
Article
Joint Planning Method for Soft Open Points and Energy Storage in Hybrid Distribution Networks Based on Improved DC Power Flow
by Wei Luo, Chenwei Zhang, Xionghui Han, Fang Chen, Zhenyu Lv and Yuntao Zhang
Processes 2026, 14(6), 1013; https://doi.org/10.3390/pr14061013 (registering DOI) - 21 Mar 2026
Abstract
Intelligent soft open points (SOPs) and energy storage systems (ESSs) are effective ways to absorb distributed new energy in the spatial and temporal dimensions, and play an important role in improving the new-energy-carrying capacity of distribution networks. Existing planning models for SOPs and [...] Read more.
Intelligent soft open points (SOPs) and energy storage systems (ESSs) are effective ways to absorb distributed new energy in the spatial and temporal dimensions, and play an important role in improving the new-energy-carrying capacity of distribution networks. Existing planning models for SOPs and ESSs in distribution networks are often nonlinear and non-convex, and are usually transformed into a mixed-integer second-order cone optimization (MISOCP) model. However, this transformation often needs stringent relaxation conditions, and the solution speed and convergence performance of the model are poor. These disadvantages make traditional MISOCP models unsuitable for optimal planning for complex hybrid networks. To overcome these limitations, a joint planning method for AC/DC hybrid networks based on an improved DC power flow (IDCPF) algorithm is proposed in this paper. The proposed method transforms the original nonlinear model into an approximate linear model, improving the solution speed and accuracy of the model. The effectiveness of the proposed method is validated through case studies on an improved AC/DC 43-node network, which demonstrates the accuracy and numerical stability of the planning model. Full article
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14 pages, 255 KB  
Article
Racial and Ethnic Differences in Labor Duration and Cesarean Indications Among Low-Risk Nulliparous Term Singleton Vertex Births: A Retrospective Analysis
by Elizabeth Mollard, Huijun Xiao, James Bena, Constance Cottrell and Maeve Hopkins
J. Clin. Med. 2026, 15(6), 2418; https://doi.org/10.3390/jcm15062418 (registering DOI) - 21 Mar 2026
Abstract
Background/Objectives: Racial and ethnic disparities in cesarean birth and labor management persist in the United States, including among individuals considered low risk. Understanding variation in labor progression and cesarean indications within low-risk nulliparous, term, singleton, vertex (NTSV) births may help clarify potential contributors [...] Read more.
Background/Objectives: Racial and ethnic disparities in cesarean birth and labor management persist in the United States, including among individuals considered low risk. Understanding variation in labor progression and cesarean indications within low-risk nulliparous, term, singleton, vertex (NTSV) births may help clarify potential contributors to inequities. This study examined differences in cesarean rates, cesarean indications, and labor duration by race and ethnicity in a low-risk NTSV cohort. Methods: We conducted a retrospective secondary analysis of electronic medical record data from 13,231 low-risk NTSV births within a Midwestern academic health system. Multivariable logistic regression models were used to evaluate the likelihood of cesarean birth and cesarean indications by race and ethnicity, adjusting for maternal age, gestational age, body mass index, insurance type, and labor onset. Linear regression models examined differences in first-stage, second-stage, and total labor duration. Interaction terms assessed whether associations varied by labor onset. Results: The overall cesarean rate was 29%. Absolute cesarean rates were higher among non-Hispanic Black and Hispanic individuals compared with non-Hispanic White individuals; however, these differences were not statistically significant after adjustment. Labor duration differed significantly by race and ethnicity. Non-Hispanic Black and Hispanic individuals experienced longer median first-stage and total labor durations compared with non-Hispanic White individuals; however, second-stage duration was markedly shorter among non-Hispanic Black individuals. Among induced labors resulting in cesarean birth, non-Hispanic Black and Hispanic individuals had increased odds of cesarean for early arrest of dilation, although these findings should be interpreted as hypothesis-generating, given data limitations in labor onset documentation. Body mass index was positively associated with likelihood of cesarean. Conclusions: In this low-risk NTSV cohort, adjusted cesarean rates did not differ significantly by race or ethnicity; however, differences in labor duration and cesarean indication were observed. These findings underscore the importance of continued investigation into labor management practices and structural contributors to obstetric inequities. Full article
(This article belongs to the Section Obstetrics & Gynecology)
25 pages, 4571 KB  
Article
A Hybrid Deep Learning Framework with CEEMDAN, Multi-Scale CNN, and Multi-Head Attention for Building Load Forecasting
by Limin Wang, Dezheng Wei, Jumin Zhao, Wei Gao and Dengao Li
Buildings 2026, 16(6), 1248; https://doi.org/10.3390/buildings16061248 (registering DOI) - 21 Mar 2026
Abstract
Accurate building load forecasting is essential for smart grid and energy management, yet nonlinearity, non-stationarity, and multi-scale characteristics of load data challenge traditional methods. To address these issues, we propose a hybrid deep learning framework, CEEMDAN-MultiScale-CNN-BiLSTM-MultiAttention. First, Complete Ensemble Empirical Mode Decomposition with [...] Read more.
Accurate building load forecasting is essential for smart grid and energy management, yet nonlinearity, non-stationarity, and multi-scale characteristics of load data challenge traditional methods. To address these issues, we propose a hybrid deep learning framework, CEEMDAN-MultiScale-CNN-BiLSTM-MultiAttention. First, Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) decomposes the load sequence into intrinsic mode functions (IMFs), mitigating mode mixing and complexity. Then, a MultiScale Convolutional Neural Network extracts multi-scale local features from each IMF. A Bidirectional Long Short-Term Memory network captures bidirectional temporal dependencies, and a Multi-Attention mechanism dynamically emphasizes critical time steps and feature channels, enhancing interpretability and prediction. The framework is validated on the Building Data Genome Project 2 dataset, achieving a Mean Absolute Percentage Error (MAPE) of 2.6464% and a coefficient of determination R2 of 0.8999, outperforming mainstream methods across multiple metrics. The main contributions are: (1) a hybrid framework integrating CEEMDAN, multi-scale feature extraction, and attention mechanisms to handle nonlinearity and non-stationarity; (2) a MultiScale-CNN to capture multi-scale temporal features and adapt to multi-frequency components; (3) a Multi-Attention mechanism to dynamically focus on key time steps and channels, improving accuracy and robustness. This work provides an effective solution for building load forecasting in complex energy systems. Full article
31 pages, 13353 KB  
Article
The Lateral Control of Unmanned Vehicles Based on Neural Network Identification and a Fast Tube Model Predictive Control Algorithm
by Yong Dai and Zhichen Zhou
Sensors 2026, 26(6), 1973; https://doi.org/10.3390/s26061973 (registering DOI) - 21 Mar 2026
Abstract
In traditional vehicle trajectory tracking processes, the dynamic model of the vehicle may not accurately represent complex and nonlinear vehicle behaviors. Moreover, conventional control methods may perform poorly when dealing with system uncertainties and disturbances, facing challenges in real-time computation. To address these [...] Read more.
In traditional vehicle trajectory tracking processes, the dynamic model of the vehicle may not accurately represent complex and nonlinear vehicle behaviors. Moreover, conventional control methods may perform poorly when dealing with system uncertainties and disturbances, facing challenges in real-time computation. To address these issues, this paper proposes an autonomous driving control method based on control-affine feedforward neural network (CAFNN) and fast tube model predictive control (tube-MPC). This method utilizes CAFNN for system dynamic identification, replacing traditional mathematical modeling with data-driven neural network pattern recognition to more accurately describe the vehicle’s nonlinear dynamic characteristics. On this basis, the proposed tube-MPC structure is divided into two parts: nominal MPC and sliding mode control (SMC). The nominal MPC controller associates the MPC problem with a linear complementarity problem (LCP) using a ramp function, enabling rapid computation of the quadratic programming (QP) solution through piecewise affine (PWA) functions; the auxiliary SMC controller employs multi-power sliding mode reaching laws to enhance the system’s robustness against external disturbances and model uncertainties. This control strategy demonstrates high accuracy and stability in vehicle trajectory tracking under complex road conditions, providing strong support for the advancement of autonomous driving technology. Full article
(This article belongs to the Section Vehicular Sensing)
17 pages, 491 KB  
Article
Deep Robust Moving Horizon Estimation for Nonlinear Multi-Rate Systems
by Rusheng Wang, Songtao Wen and Bo Chen
Sensors 2026, 26(6), 1967; https://doi.org/10.3390/s26061967 (registering DOI) - 21 Mar 2026
Abstract
In this paper, a moving horizon estimation (MHE)-based state estimation problem is studied for asynchronous multi-rate nonlinear systems. First, the asynchronous multi-rate system is transformed into a synchronous system at measurement sampling points through pseudo-measurement synchronization modeling. Secondly, a MHE strategy with a [...] Read more.
In this paper, a moving horizon estimation (MHE)-based state estimation problem is studied for asynchronous multi-rate nonlinear systems. First, the asynchronous multi-rate system is transformed into a synchronous system at measurement sampling points through pseudo-measurement synchronization modeling. Secondly, a MHE strategy with a time-discounted quadratic objective is proposed. Under the detectability assumption, the exponential stability of the proposed MHE is established via the Lyapunov method, and the corresponding linear matrix inequality (LMI) constraints are derived. Moreover, to address the model mismatch after synchronization, a deep learning-based framework is proposed to approximate and learn the weighting parameters of the MHE. Then, barrier-function regularization is introduced to enforce the aforementioned LMI feasibility conditions, keeping the learned weights within the feasible region throughout training. Finally, the result is illustrated by a target tracking example. Full article
(This article belongs to the Special Issue Recent Developments in Wireless Network Technology)
19 pages, 6847 KB  
Article
Refined Modeling and Failure Mechanisms of Distribution Pole–Line Systems Considering Nonlinear Wind–Rain Coupling
by Bin Chen, Hao Chen, Yufeng Guo, Lichaozheng Qin, Naixuan Zhu, Xinyao Zheng and Jiangtao Zeng
Electronics 2026, 15(6), 1314; https://doi.org/10.3390/electronics15061314 (registering DOI) - 21 Mar 2026
Abstract
Existing standards for distribution network safety under combined typhoon–rain hazards often overlook the nonlinear coupling effects induced by rain impact. To address this issue, this paper proposes a refined modeling and threshold-based failure assessment framework for distribution pole–line systems under coupled wind–rain loading. [...] Read more.
Existing standards for distribution network safety under combined typhoon–rain hazards often overlook the nonlinear coupling effects induced by rain impact. To address this issue, this paper proposes a refined modeling and threshold-based failure assessment framework for distribution pole–line systems under coupled wind–rain loading. A full dynamic model is established by integrating a multi-point spatiotemporally coherent wind field with raindrop impact effects, and the coupled time-domain response of the system is then simulated. The results indicate that wind–rain coupling significantly amplifies the dynamic response, with nonlinear energy accumulation occurring at the pole base. Under the analyzed extreme case, this amplification causes the pole-base stress to first exceed the collapse threshold within the simulated duration, indicating that neglecting rain loads may lead to a non-conservative assessment of system safety. In addition, the results reveal differentiated failure characteristics among components: conductors are primarily associated with functional flashover risk, whereas poles are more directly exposed to structural failure demand. These findings provide a preliminary analytical basis for the differential reinforcement and resilience enhancement of coastal distribution networks. Full article
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23 pages, 923 KB  
Review
From Beat to Risk: How Heart Rate Variability Predicts Arrhythmias in Type 2 Diabetes
by Amelian Madalin Bobu, Ștefania-Teodora Duca, Andrei Ionut Cucu, Diana Alina Avieriței, Cosmina-Georgiana Ponor, Maria-Ruxandra Cepoi, Sandu Cucută, Bianca-Ana Dmour, Claudia Florida Costea, Gina Botnariu and Irina-Iuliana Costache-Enache
Life 2026, 16(3), 520; https://doi.org/10.3390/life16030520 (registering DOI) - 21 Mar 2026
Abstract
Type 2 diabetes mellitus is associated with major cardiovascular complications, including cardiac autonomic neuropathy, which contributes to sympathetic–parasympathetic imbalance and increases susceptibility to arrhythmias and sudden cardiac death. Heart rate variability, assessed through R–R intervals on electrocardiography and 24 h Holter monitoring, represents [...] Read more.
Type 2 diabetes mellitus is associated with major cardiovascular complications, including cardiac autonomic neuropathy, which contributes to sympathetic–parasympathetic imbalance and increases susceptibility to arrhythmias and sudden cardiac death. Heart rate variability, assessed through R–R intervals on electrocardiography and 24 h Holter monitoring, represents a sensitive, non-invasive marker of autonomic dysfunction and arrhythmogenic risk. In patients with type 2 diabetes mellitus, chronic hyperglycaemia, oxidative stress, and metabolic inflammation lead to early impairment of the autonomic nervous system, manifested by consistent reductions in SDNN, RMSSD, pNN50, total power, and the high-frequency component, indicating diminished parasympathetic tone and sympathetic predominance. Nonlinear HRV indices demonstrate a loss of complexity and fractal organisation, providing additional prognostic value beyond conventional time- and frequency-domain analyses. Reduced HRV correlates with the severity of cardiac autonomic neuropathy, duration of diabetes, and poor glycaemic control, identifying patients with increased arrhythmogenic vulnerability. HRV analysis enables prediction of arrhythmic risk, facilitating the identification of high-risk individuals and guiding personalised interventions. The integration of HRV assessment into routine clinical practice may improve the early detection of subclinical autonomic neuropathy and optimise cardiovascular risk stratification and management in patients with type 2 diabetes mellitus. Full article
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36 pages, 1374 KB  
Article
Control Strategies for DC Motor Systems Driving Nonlinear Loads in Mechatronic Applications
by Asma Al-Tamimi, Fadwa Al-Momani, Mohammad Salah, Suleiman Banihani and Ahmad Al-Jarrah
Actuators 2026, 15(3), 175; https://doi.org/10.3390/act15030175 - 20 Mar 2026
Abstract
DC motors are widely used in mechatronic systems; however, their performance degrades significantly in the presence of nonlinear mechanical loads, parameter variations and sensing uncertainties. This paper proposes three control strategies (i.e., PID, optimal, and hybrid controllers) for discrete-time DC motor systems to [...] Read more.
DC motors are widely used in mechatronic systems; however, their performance degrades significantly in the presence of nonlinear mechanical loads, parameter variations and sensing uncertainties. This paper proposes three control strategies (i.e., PID, optimal, and hybrid controllers) for discrete-time DC motor systems to overcome the disturbances caused by nonlinear mechanical loads and parameter variations. Optimal control of nonlinear discrete-time systems is formally characterized by the Hamilton–Jacobi–Bellman (HJB) equation, whose analytical solution is generally intractable. To address this challenge, a learning-based optimal control strategy based on the Heuristic Dynamic Programming (HDP) framework is developed to approximate the HJB equation, supported by a formal convergence proof. For that purpose, Neural Networks (NNs) are employed to approximate both the cost function and the optimal control policy, enabling near-optimal performance with manageable computational complexity. Although the resulting optimal control achieves fast convergence, it may introduce overshoot and steady-state offset under nonlinear disturbances. To address this limitation, a hybrid control framework is proposed, where nonlinear optimal corrections are integrated with the robustness and adaptability of Proportional–Integral–Derivative (PID) control through error-dependent gating and gain-scheduling mechanisms. A structured evaluation framework is conducted, including nominal analysis, motor-parameter stress testing across nine nonlinear scenarios, controller-design sensitivity analysis, and stochastic measurement-noise assessment under filtered sensing conditions. Results demonstrate that the hybrid controller preserves transient speeds within 5–10% of the optimal controller while effectively eliminating overshoot and steady-state offset under nominal conditions. The hybrid design reduces the accumulated tracking error by more than 95% compared to the optimal controller, while incurring only negligible additional control effort. Under aggressive supply-sag disturbances, the hybrid controller significantly limits peak deviation and reduces accumulated tracking error by over 90%, while maintaining comparable control cost. Overall, the hybrid framework provides a convergence-proven and practically deployable control solution that combines near-optimal convergence speed with robust, overshoot-free performance for intelligent motion-control and robotics applications. Full article
(This article belongs to the Section Control Systems)
19 pages, 563 KB  
Article
Integrated Optimization of Routing, Scheduling, Charging, and Platooning for a Mixed Fleet of Electric and Conventional Trucks
by Danesh Hosseinpanahi, Jialu Yang, Bo Zou and Jane Lin
Future Transp. 2026, 6(2), 68; https://doi.org/10.3390/futuretransp6020068 - 20 Mar 2026
Abstract
The integration of truck platooning and electrification presents a promising avenue for improving operational efficiency and environmental sustainability in freight transportation. Realizing the energy and cost saving as well as emission reduction benefits requires a holistic design of truck routing, scheduling, and platooning [...] Read more.
The integration of truck platooning and electrification presents a promising avenue for improving operational efficiency and environmental sustainability in freight transportation. Realizing the energy and cost saving as well as emission reduction benefits requires a holistic design of truck routing, scheduling, and platooning strategies that account for practical operational constraints. This study investigates the integrated planning problem of routing, scheduling, and platooning for a mixed fleet of conventional trucks (CTs) and electric trucks (ETs), referred to as mixed fleet truck platooning (MFTP) problem. The MFTP incorporates charging scheduling and key operational factors, such as platooning leader–follower positioning under the battery constraints of ETs, charging station availability and capacity, and the positional configuration of trucks within a platoon. The objective is to minimize the total operation cost of the MFTP system, including charging cost, fuel cost, travel labor cost, charging labor cost, and platoon formation labor cost, while ensuring timely arrivals across multiple origin–destination (OD) pairs. The proposed MFTP is formulated as a novel mixed-integer linear program (MILP). Extensive numerical experiments on the simplified Illinois interstate highway network are conducted to examine the effectiveness and efficiency of the proposed model. Numerical results show that incorporating platooning reduces the total operational cost by 7.6% relative to the non-platooning scenario. The findings also shed some light on planning mixed fleets of CTs and ETs with platooning, offering valuable managerial insights for decision-makers. Full article
26 pages, 2028 KB  
Article
Stability Dependence on Inertia in the Driven Damped Pendulum: A Master Control Parameter Analysis
by Alexander N. Pisarchik
Mathematics 2026, 14(6), 1060; https://doi.org/10.3390/math14061060 - 20 Mar 2026
Abstract
The driven damped pendulum is a foundational model in nonlinear dynamics, with applications ranging from Josephson junctions to MEMS oscillators. Conventional dimensionless treatments obscure the common physical origin of damping and driving in the inertia coefficient. Here we restore this dependence and establish [...] Read more.
The driven damped pendulum is a foundational model in nonlinear dynamics, with applications ranging from Josephson junctions to MEMS oscillators. Conventional dimensionless treatments obscure the common physical origin of damping and driving in the inertia coefficient. Here we restore this dependence and establish inertia as a master control parameter governing stability, resonance, and bifurcations. Through linear analysis and perturbation theory, we derive universal scaling laws revealing a fundamental dichotomy: quantities at resonance—peak amplitude and nonlinear frequency shift—are independent of inertia due to exact algebraic cancellation between the inertia dependence of the effective driving amplitude and effective damping coefficient. Off resonance, however, amplitude scales inversely with inertia, bandwidth narrows proportionally, and the bistability threshold exhibits an even steeper dependence. A critical inertia separates underdamped from overdamped regimes, yielding non-monotonic relaxation times that maximize attractor memory at extreme inertia values. These scaling laws provide design guidelines: low inertia promotes broadband response for energy harvesting; high inertia suppresses off-resonant vibrations for precision timing and quantum applications. By establishing inertia as a physically realizable path through parameter space, this work unifies disparate phenomena and provides a framework for understanding stability in inertial-driven systems. Full article
(This article belongs to the Special Issue Mathematical Modelling of Nonlinear Dynamical Systems)
16 pages, 7170 KB  
Article
Aberration-Conditioned Attention-Driven Centroid Localization: From Simulation Mechanism to Double-Spot Experiment
by Zhonghao Zhao, Jia Hou, Yuanting Liu, Anwei Liu and Zhiping He
Photonics 2026, 13(3), 304; https://doi.org/10.3390/photonics13030304 (registering DOI) - 20 Mar 2026
Abstract
In size, weight, and power (SWaP)-constrained optical systems, such as spaceborne LiDAR, high-precision centroid localization often relies on focal-plane measurements without dedicated wavefront sensors. Under such conditions, the nonlinear coupling between optical aberrations and sensor noise introduces systematic bias that is difficult to [...] Read more.
In size, weight, and power (SWaP)-constrained optical systems, such as spaceborne LiDAR, high-precision centroid localization often relies on focal-plane measurements without dedicated wavefront sensors. Under such conditions, the nonlinear coupling between optical aberrations and sensor noise introduces systematic bias that is difficult to mitigate using conventional centroiding methods. To address this issue, we propose a physics-conditioned feature correction framework based on an aberration-conditioned attention mechanism. A hybrid CNN–Transformer architecture is employed to predict and compensate for systematic centroid bias. Specifically, convolutional layers encode the degraded spot morphology, while a multi-head attention mechanism leverages Seidel aberration coefficients to adaptively modulate spatial features for precise regression. Given the unavailability of absolute ground-truth coordinates in empirical scenarios, a physics-consistent simulation framework based on scalar diffraction theory is constructed to generate synthetic data for supervised learning. Simulation results indicate that the proposed method objectively reduces anisotropic systematic bias, achieving a localization root-mean-square error (RMSE) of 0.011 to 0.021 pixels, and maintains stable sub-pixel accuracy even under a 10% empirical prior perturbation. To evaluate generalization performance and engineering reliability, a wedge-based double-spot platform is developed to verify physical consistency via geometric invariance. Experimental results demonstrate a measured spacing standard deviation (SD) of 0.015 to 0.039 pixels. This validates the framework’s transferability from theoretical simulation to controlled physical measurements, providing an algorithmic foundation for precision optical metrology in hardware-constrained environments. Full article
(This article belongs to the Special Issue Advancements in Optics and Laser Measurement)
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