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37 pages, 1597 KB  
Article
Topology-Aware Graph Reinforcement Learning for Voltage-Reactive Power Control in Grid-Connected Microgrids
by Yunfei Zhang, Kefan Bao, Gaige Liang, Wennan Zhuang, Longlong Qiang, Difei Tang, Xiangyu Lu and Mingxiao Zhang
Electricity 2026, 7(2), 60; https://doi.org/10.3390/electricity7020060 (registering DOI) - 22 Jun 2026
Abstract
As the global energy transition accelerates, distribution systems are integrating increasing shares of inverter-interfaced renewables, making reliable voltage support a key operational requirement. In grid-connected microgrids, especially weak radial feeders in rural and remote areas, voltage-reactive power (Volt/Var) control must coordinate multiple inverters [...] Read more.
As the global energy transition accelerates, distribution systems are integrating increasing shares of inverter-interfaced renewables, making reliable voltage support a key operational requirement. In grid-connected microgrids, especially weak radial feeders in rural and remote areas, voltage-reactive power (Volt/Var) control must coordinate multiple inverters under uncertainty from photovoltaic (PV) intermittency, load volatility, and point-of-common-coupling (PCC) disturbances. Existing droop, model-based optimization, and non-graph reinforcement learning (RL) approaches often rely on fixed rules or do not explicitly exploit electrical topology, which limits adaptive coordination. To address this gap, we propose a topology-aware graph reinforcement learning framework for voltage-reactive power control in grid-connected microgrids under uncertainty. The method encodes node states with a graph convolutional network (GCN) and learns coordinated PV/storage reactive-power actions via proximal policy optimization (PPO) with a multi-objective reward balancing voltage quality, control effort, and action smoothness. In a controlled comparison against a multilayer perceptron (MLP)-PPO baseline with identical action space, reward, and PPO objective, our method reduces voltage violation rate (VVR) from 0.0316 ± 0.0086 to 0.0048 ± 0.0019. Additional validation on a modified IEEE 33-bus feeder further reduces VVR from 0.00726 for MLP-PPO and 0.02999 for Droop control to 0.00095, supporting the effectiveness of topology-aware state representation on a larger radial benchmark feeder. Full article
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23 pages, 13349 KB  
Article
Plastic Damage Evolution of Flexible Casing Pile Utilized in Karst Area Under Vertical Loading
by Tao Wu, Yueran Hao, Ying Wang, Lulu Zhang, Fengyu Zhang and Yunpeng Zhang
Appl. Sci. 2026, 16(12), 6252; https://doi.org/10.3390/app16126252 (registering DOI) - 22 Jun 2026
Abstract
Flexible casing piles can form locally enlarged sections by expanding flexible casings during concrete casting, thereby filling karst cavities and improving the adaptability and bearing capacity of pile foundations in karst areas. However, the damage evolution and failure mechanism of the enlarged section [...] Read more.
Flexible casing piles can form locally enlarged sections by expanding flexible casings during concrete casting, thereby filling karst cavities and improving the adaptability and bearing capacity of pile foundations in karst areas. However, the damage evolution and failure mechanism of the enlarged section under vertical loading remain insufficiently understood. In this study, a three-dimensional finite element model of a flexible casing pile was established using the Concrete Damaged Plasticity (CDP) model. The stress transfer, plastic strain development, and tensile–compressive damage evolution of the enlarged section under vertical static loading were investigated. The effects of karst cavity spacing, cavity number, and cavity diameter on the vertical bearing behavior were further analyzed. The results show that damage localization is governed by the transition zone between the pile shaft and the enlarged section, where plastic strain, tensile damage localization, and compressive damage accumulation develop in a coupled manner. Increasing the number and diameter of enlarged sections improves the ultimate bearing capacity, whereas cavity spacing mainly controls the interaction and synchronization of damage zones between adjacent enlarged sections. These findings establish a damage-based interpretation for identifying the failure-control region of flexible casing piles in karst cavities and provide a basis for bearing-capacity assessment and structural optimization. Full article
(This article belongs to the Section Civil Engineering)
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19 pages, 1338 KB  
Article
A Physics-Guided Symbolic Regression Framework for Multi-Resolution Dynamic Equivalent Modeling of Power Systems
by Mingyu Pang, Min Li, Wanlin Wang, Peng Shi, Zongsheng Zheng, Lai Yuan and Hongwen Tan
Electronics 2026, 15(12), 2733; https://doi.org/10.3390/electronics15122733 (registering DOI) - 22 Jun 2026
Abstract
The transition toward renewable-dominated power systems introduces significant complexity and nonlinearity, rendering traditional mechanism-based modeling computationally prohibitive for real-time security assessment. While data-driven approaches offer computational efficiency, they fundamentally lack physical interpretability and often exhibit generalization failures under rare, large-signal disturbances due to [...] Read more.
The transition toward renewable-dominated power systems introduces significant complexity and nonlinearity, rendering traditional mechanism-based modeling computationally prohibitive for real-time security assessment. While data-driven approaches offer computational efficiency, they fundamentally lack physical interpretability and often exhibit generalization failures under rare, large-signal disturbances due to the absence of intrinsic physical constraints. To bridge this gap, this paper proposes a Physics-Guided Symbolic Regression (PGSR) framework for constructing interpretable and robust dynamic equivalent models. The methodology embeds domain knowledge via topological masks and dimensional consistency rules to restrict the evolutionary search space to physically admissible manifolds. A multi-resolution extraction strategy based on the Pareto frontier is developed to autonomously identify both linear small-signal models and nonlinear large-signal formulations adaptable to varying analytical requirements. Furthermore, a post hoc verification stage based on Lyapunov stability theory ensures the dynamic validity and energy dissipation properties of the generated equations. A case study on the WSCC 9-bus system demonstrates that the proposed method accurately recovers the underlying Taylor-series structure of swing equations and significantly outperforms four data-driven baselines—including polynomial, kernel, and neural network models—in out-of-distribution generalization, achieving 12–42× lower trajectory error under unseen large perturbations. Full article
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18 pages, 914 KB  
Article
Fractal Characteristics of Coal Structure and Fluid Transport During Compression Failure Process
by Teng Teng and Wang Yuming
Fractal Fract. 2026, 10(6), 421; https://doi.org/10.3390/fractalfract10060421 (registering DOI) - 21 Jun 2026
Abstract
The fractal characteristics of coal pore–fracture networks and their evolution under compression are essential for predicting rock mass failure and fluid transport. This study combines micro-CT scanning with fractal theory and seepage mechanics to investigate the structural evolution of coal under uniaxial compression [...] Read more.
The fractal characteristics of coal pore–fracture networks and their evolution under compression are essential for predicting rock mass failure and fluid transport. This study combines micro-CT scanning with fractal theory and seepage mechanics to investigate the structural evolution of coal under uniaxial compression and its impact on fluid transport. CT scans were performed at four characteristic stages (initial, elastic, plastic, and failure) to reconstruct three-dimensional fracture networks. Quantitative analysis reveals that fracture porosity increases sequentially from 0.44% to 5.01%, with the failure stage reaching 11.4 times the initial value. Fracture length and aperture distributions follow power-law scaling, and their fractal dimensions exhibit distinct evolution patterns: length dimension increases from 2.43 to a peak of 2.56 in the plastic stage and then drops to 2.47 at failure, while aperture dimension decreases from 2.29 to a trough of 2.12 before rebounding to 2.26. These patterns reflect a dynamic adjustment of network complexity, transitioning from primary fractures to micro-fracture dominance and finally to main fracture coalescence. Based on the Knudsen number, three diffusion regimes of Fick, transition and Knudsen are identified. A fractal permeability model is developed by idealizing the pore space as tortuous capillaries, showing that permeability scales with the fourth power of the maximum pore diameter and is positively influenced by the fractal dimension and the number of large pores. Furthermore, a coupled seepage–stress model is derived, incorporating pressure transmission, shear transmission, and crack opening coefficients. The damage variable is expressed as a function of stress level and fractal dimension. These findings provide theoretical support for predicting gas transport and failure behavior in coal under coupled hydro-mechanical conditions. Full article
(This article belongs to the Special Issue Fractal and Fractional Modelling in Deep Mining and Geomechanics)
29 pages, 11979 KB  
Article
Direct Prestack Inversion of the Formation Pressure Coefficient for Deepwater Overpressured Reservoirs
by Hao Chen, Handong Huang, Gang Cui, Jun Liao, Jiahui Peng and Yaning Wu
J. Mar. Sci. Eng. 2026, 14(12), 1138; https://doi.org/10.3390/jmse14121138 (registering DOI) - 21 Jun 2026
Abstract
Accurate prediction of overpressured formations in deepwater is important for drilling safety and reservoir evaluation. However, conventional two-step inversion workflows are affected by cumulative errors and parameter crosstalk, which limits their ability to characterize the sharp pressure-transition interfaces at the top of overpressured [...] Read more.
Accurate prediction of overpressured formations in deepwater is important for drilling safety and reservoir evaluation. However, conventional two-step inversion workflows are affected by cumulative errors and parameter crosstalk, which limits their ability to characterize the sharp pressure-transition interfaces at the top of overpressured zones. In this study, we propose a direct prestack nonlinear inversion method for the formation pressure coefficient (λ), a dimensionless and drilling-relevant indicator of overpressure intensity. Unlike previous exact-Zoeppritz direct inversions that target effective stress or elastic moduli, here a single formation pressure coefficient drives the pressure-sensitive rock-physics chain—linking pore pressure, effective stress, and pore-space stiffness to the seismic response—thereby reducing the number of free inversion variables. This single-parameter mapping is then coupled with the exact Zoeppritz equation to build a nonlinear prestack forward operator, helping to reduce the parameter coupling and error propagation associated with conventional multiparameter inversion workflows. To describe the typical blocky structural features of overpressured strata, a nonconvex Lp-norm (0 < p < 1) regularization is introduced as a structural prior, and a decoupled optimization strategy combining the alternating direction method of multipliers (ADMM) and iteratively reweighted least squares (IRLS) is developed for a stable solution. In a single pseudo-well synthetic test, the proposed method achieved a higher correlation coefficient and lower root mean square error (RMSE) than the indirect workflow, indicating improved agreement with the reference formation-pressure-coefficient profile. Application to field seismic data from the Yinggehai Basin, South China Sea, shows that the method produces clearer pressure-transition boundaries and pressure-coefficient profiles more consistent with the available well constraints. These results suggest that, under the tested conditions, the proposed method can provide useful geophysical support for pressure prediction and the characterization of deepwater overpressured reservoirs. Full article
(This article belongs to the Special Issue Marine Well Logging and Reservoir Characterization)
26 pages, 6705 KB  
Article
Intelligent Analysis of the Geomechanical State of Rock Masses During Underground Mining
by Dmytro Babets, Amirbek Yerkinbekov, Serik Moldabayev, Samal Assylkhanova, Volodymyr Hnatushenko and Olena Sdvyzhkova
Mathematics 2026, 14(12), 2222; https://doi.org/10.3390/math14122222 (registering DOI) - 20 Jun 2026
Abstract
This study presents an intelligent framework for the analysis of multidimensional geomechanical states in underground mining systems based on numerical simulation and machine learning methods. A three-dimensional geomechanical model of the Zholymbet deposit was developed in the RS3 environment using the generalized Hoek–Brown [...] Read more.
This study presents an intelligent framework for the analysis of multidimensional geomechanical states in underground mining systems based on numerical simulation and machine learning methods. A three-dimensional geomechanical model of the Zholymbet deposit was developed in the RS3 environment using the generalized Hoek–Brown failure criterion. Numerical simulations were performed for representative mining scenarios characterized by complex excavation interaction and stress redistribution. The modelling results were transformed into a multidimensional geomechanical dataset containing stress, deformation, displacement, and yielding parameters. Principal component analysis (PCA) was applied to investigate the internal structure of the geomechanical state space and identify dominant patterns controlling the rock mass behavior. Clustering analysis revealed several geomechanical regimes corresponding to stable, transitional, and instability-prone conditions. Isolation Forest anomaly detection demonstrated that atypical geomechanical states are not randomly distributed but spatially localized near excavation systems and mining horizons. The obtained results indicate that hazardous geomechanical conditions are governed by complex interactions between stress concentration, deformation intensity, yielding processes, and excavation geometry. The proposed approach provides a basis for intelligent interpretation of large-scale numerical modelling results and may support geomechanical risk assessment in underground mining operations. Full article
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20 pages, 3179 KB  
Article
Robustness Analysis and Optimization Strategy of Urban Bus Network Based on Complex Network
by Zhiguo Shao, Yixin Zhang and Kexin Li
Sustainability 2026, 18(12), 6320; https://doi.org/10.3390/su18126320 (registering DOI) - 19 Jun 2026
Viewed by 186
Abstract
The bus system plays an important role in the urban public transportation infrastructure system, providing a convenient way for the masses to travel. However, the operational resilience and functional stability of urban transit systems are frequently jeopardized by a variety of internal disruptions [...] Read more.
The bus system plays an important role in the urban public transportation infrastructure system, providing a convenient way for the masses to travel. However, the operational resilience and functional stability of urban transit systems are frequently jeopardized by a variety of internal disruptions and external emergencies. Therefore, it is important to evaluate the robustness of urban bus networks. Based on the complex network theory, this research applies Space L and Space R methods to construct the bus stop network and bus line network models in Jinan, China. The topological characteristics of the two network models are studied, and the network robustness is analyzed using two attack strategies: random attack and deliberate attack. The robustness is optimized based on the network edge addition strategy. The results show that: (1) The bus stop network has a scale-free network property, but the bus stop network and the bus line network do not have the small-world network property. (2) The bus line network is more robust than the bus stop network when under attack, and the network under deliberate attack is more vulnerable than that under random attack. The maximum betweenness centrality node attack causes the most significant damage to the network. (3) Under random attack, both high betweenness centrality edge addition (HBA) and high degree edge addition (HDA) strategies are more effective at optimizing network robustness; under maximum degree node attack, both low betweenness centrality edge addition (LBA) and low degree edge addition (LDA) strategies are more effective on optimizing network robustness; under maximum betweenness centrality node attack, the LBA strategy has the best effect on optimizing network robustness. The research results can provide scientific guidance for the emergency scheduling and line optimization of urban public transportation system. Full article
(This article belongs to the Special Issue Sustainable Transportation Strategies for Urban and Regional Mobility)
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34 pages, 3776 KB  
Article
Spatial Coupling Characteristics and Driving Mechanisms of Population–Land–Housing Based on Multi-Source Data: A Case Study of Guangzhou, China
by Chunshan Zhou, Shuyuan Liu, Huiming Huang, Xiong He and Xiaodie Yuan
Land 2026, 15(6), 1085; https://doi.org/10.3390/land15061085 - 18 Jun 2026
Viewed by 86
Abstract
Against the backdrop of the transition of new-type urbanization towards high-quality development, the triple contradictions of population agglomeration, land constraints, and housing supply-demand imbalance have become increasingly prominent. The conventional binary framework of human–land relations can no longer meet the requirements of coordinated [...] Read more.
Against the backdrop of the transition of new-type urbanization towards high-quality development, the triple contradictions of population agglomeration, land constraints, and housing supply-demand imbalance have become increasingly prominent. The conventional binary framework of human–land relations can no longer meet the requirements of coordinated development within human settlement systems, creating an urgent need to examine the multi-system interactions among population, land, and housing in order to resolve spatial mismatch. Taking Guangzhou as a case study, this research integrates 2020 population census data, land-use data from the European Space Agency (ESA), housing-price data from the Anjuke platform, and multi-source data on related influencing factors, and conducts a systematic empirical analysis by combining coupling coordination analysis, a relative development model, and the geographical detector. The findings reveal that the coupling coordination level of population, land and housing in Guangzhou exhibits a concentric, ring-shaped distribution pattern with central agglomeration and peripheral decline. The relative development among the three systems can be classified into matching types including the core-differentiated type, the peripheral-imbalanced type, and the surrounding-equilibrium type. With respect to influencing factors, all pairwise interactions are of the bi-factor enhancement type, and the driving mechanism displays a three-stage dynamic evolution. This study enriches research on human–land relations, provides precise guidance for optimizing spatial allocation and alleviating housing mismatch conflicts in Guangzhou, and offers transferable practical experience for comparable cities in China seeking to advance the high-quality development of new-type urbanization. Full article
14 pages, 14389 KB  
Article
Proactive Early Warning of Vortex Ring State in Coaxial UAVs: A Physics-Informed Multimodal ViT-LSTM Approach
by Xiang Zhou, Jiawei Sun, Jiannan Zhao and Feng Shuang
Sensors 2026, 26(12), 3888; https://doi.org/10.3390/s26123888 (registering DOI) - 18 Jun 2026
Viewed by 184
Abstract
The Vortex Ring State (VRS) poses a catastrophic aerodynamic threat to coaxial dual-rotor unmanned aerial vehicles (UAVs). Traditional reactive detection mechanisms provide insufficient altitude for recovery, while existing data-driven diagnostics are severely bottlenecked by data leakage, extreme class imbalance, and a lack of [...] Read more.
The Vortex Ring State (VRS) poses a catastrophic aerodynamic threat to coaxial dual-rotor unmanned aerial vehicles (UAVs). Traditional reactive detection mechanisms provide insufficient altitude for recovery, while existing data-driven diagnostics are severely bottlenecked by data leakage, extreme class imbalance, and a lack of physical interpretability. To bridge these gaps, this paper proposes a physics-informed multimodal deep learning framework that transitions from post-occurrence detection to proactive early warning. We establish a 1.5 s precursor window—creating a three-class ordinal state space—to provide the flight control system with critical intervention time for differential rotor recovery. We developed a novel ViT-LSTM architecture (MTSF-Net) to fuse continuous seven-channel onboard-recorded data (comprising three-axis acceleration, three-axis angular velocity, and barometric vertical velocity), which are subsequently transformed into Continuous Wavelet Transform (CWT) spectrograms. To ensure real-time unidirectional inference while preserving absolute physical vibration scales across heterogeneous sensors, a Calibrated Benchmark Normalization (CBN) strategy is introduced. Furthermore, a Hybrid Ordinal Loss is proposed to mitigate the extreme sample imbalance (<0.5%) of the precursor state by penalizing asymmetric aerodynamic degradation. Evaluated under a strict sortie-based isolation protocol, the proposed system achieves an exceptional test accuracy of 98.26% and an unprecedented precursor recall of 100%. Notably, it completely eliminates fatal missed detections (VRS predicted as Normal) and false-positive VRS predictions triggered by precursor states. Finally, Gradient-weighted Class Activation Mapping (Grad-CAM) is utilized to verify that the multimodal sensor processing pipeline successfully anchors onto authentic physical vibration frequencies rather than artifactual noise, laying a rigorous, interpretable foundation for intelligent aviation safety systems. Full article
(This article belongs to the Special Issue Recent Trends and Advances in Intelligent Fault Diagnostics)
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22 pages, 6912 KB  
Article
Evaluation of Walnut (Juglans regia L.) Grafting Performance by Optimizing Methods and Execution Periods Using TOPSIS Multicriteria Analysis
by Cristina Zlati, Roxana Pașcu, Marius Florea, Marius Dascălu, Andromeda Pătrașcu Sonea and Mihai Istrate
Horticulturae 2026, 12(6), 742; https://doi.org/10.3390/horticulturae12060742 - 17 Jun 2026
Viewed by 349
Abstract
Walnut multiplication technology for obtaining high-quality planting material consists of grafting, followed by forcing bionts in protected spaces under controlled microclimatic conditions, and completed by acclimatization under field conditions. The present research substantiates the hypothesis that the use of protected spaces (polyethylene tunnels) [...] Read more.
Walnut multiplication technology for obtaining high-quality planting material consists of grafting, followed by forcing bionts in protected spaces under controlled microclimatic conditions, and completed by acclimatization under field conditions. The present research substantiates the hypothesis that the use of protected spaces (polyethylene tunnels) enables rigorous control of limiting factors. The main objectives of the paper are the comparative evaluation of two grafting methods (chip and patch budding) on the grafting success of eight native genotypes (‘Anica’, ‘Grădinar’, ‘Miroslava’, and ‘Velnița’, ‘Bălțăți’, ‘Belcești’, ‘Săbăuani’, and ‘Șorogari’) grafted on ‘Bălțați’ local biotype, determining the optimal moment of grafting by identifying the time window (April vs. August) that maximizes the success rate of the grafting association. The study, carried out from 2022 to 2024, evaluated the performance of chip and patch budding executed under high-tunnel conditions, quantifying the scion/rootstock growth, callus formation, and anatomical symbiont similarity through cross-sectional microscopy and image analysis software to measure vessel number, density, and diameter; the results are presented as the mean values of three annual repetitions across the experimental period. Preliminary results indicate a superior efficiency of the chip budding method, with a 51.3% success rate compared to 32.9% for the patch budding method. Another objective of the study was the ranking of the experimental variants. Thus, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), a multi-criteria decision analysis method, ranked the experimental variants and identified the chip budding performed in April (variant a1/b2) as the optimal solution across all analyzed physiological and morphological parameters. These findings are highly significant for the nursery sector, as they demonstrate that transitioning from unpredictable field conditions to controlled high-tunnel conditions stabilizes production outcomes. By establishing a clear methodological hierarchy and a precise chronological window, this study provides actionable guidelines to standardize walnut multiplication, mitigate seasonal climate risks, and substantially increase the output of high-quality certified planting material. Full article
(This article belongs to the Section Fruit Production Systems)
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33 pages, 981 KB  
Article
A Collision Mitigation Scheme for LoRa Networks Based on EKF-Based Backlog Estimation and NOMA-SIC Cooperation
by Zongliang Xu and Guicai Yu
Electronics 2026, 15(12), 2691; https://doi.org/10.3390/electronics15122691 - 17 Jun 2026
Viewed by 100
Abstract
In the LoRa (long-range) wide area network (LoRaWAN), Class A devices employ a pure ALOHA random access mechanism. Under large-scale access and bursty traffic conditions, severe packet collisions are likely, which reduces throughput and increases the packet loss rate. To address these issues, [...] Read more.
In the LoRa (long-range) wide area network (LoRaWAN), Class A devices employ a pure ALOHA random access mechanism. Under large-scale access and bursty traffic conditions, severe packet collisions are likely, which reduces throughput and increases the packet loss rate. To address these issues, herein, we propose a collision mitigation scheme integrating the extended Kalman filter (EKF) with nonorthogonal multiple access (NOMA). First, a nonlinear state-space model is constructed to capture the dynamic evolution of backlog nodes and the uncertainty of traffic arrivals. The backlog node number is modeled as the hidden state, while newly arrived and successfully decoded packets are incorporated into the state-transition equation. At the gateway, decoded packet counts and channel occupancy are treated as observations based on which a nonlinear mapping between system state and observable features is established. The EKF is then applied to recursively predict and correct, enabling real-time estimation of the backlog state. Accordingly, an adaptive backoff strategy is designed to adjust transmission probability based on the estimated optimal load. Furthermore, to mitigate packet loss caused by collisions, a power-domain NOMA scheme with successive interference cancelation (SIC) is introduced. Signals transmitted with different spreading factors (SFs) are decoupled into approximately independent processing branches by exploiting inter-SF quasi-orthogonality. To account for imperfect inter-SF orthogonality, cross-SF residual coupling coefficients are introduced to characterize leakage interference. For transmissions sharing the same SF, overlapping packets are successively decoded and recovered through a NOMA-SIC mechanism jointly constrained by the SINR-based decoding threshold, the power-domain separation requirement, the maximum number of resolvable SIC layers, and residual SIC interference. Accordingly, the proposed receiver architecture enhances the decoding and recovery capability for collided LoRa packets. Simulation results demonstrate that, under medium-to-high traffic loads, the proposed scheme significantly improves throughput and access success rate while effectively reducing collision probability and packet loss, thereby enhancing the overall robustness and efficiency of the LoRa network. Full article
(This article belongs to the Section Electronic Materials, Devices and Applications)
28 pages, 1570 KB  
Article
Risk Management of Underground Rail Transit: A Disaster Chain Network Analysis
by Jiajia Wang, Zhe Chen, Hao Chen and Xiangsheng Chen
Buildings 2026, 16(12), 2414; https://doi.org/10.3390/buildings16122414 - 17 Jun 2026
Viewed by 109
Abstract
In recent years, China’s urban underground rail transit has developed rapidly, and the development of underground space has become increasingly complex, exposing the system to multiple operational risks such as structural instability, excessive deformation, equipment failures and emergencies. Existing studies often evaluate individual [...] Read more.
In recent years, China’s urban underground rail transit has developed rapidly, and the development of underground space has become increasingly complex, exposing the system to multiple operational risks such as structural instability, excessive deformation, equipment failures and emergencies. Existing studies often evaluate individual hazards or isolated stakeholder risks, while insufficient attention has been paid to how sudden events interact and propagate as disaster chains. To address this gap, this study develops a disaster-chain network framework for operational risk management in underground rail transit. Twenty sudden disaster risk events are first identified through literature review, expert consultation, system investigation, and HAZOP (Hazard and Operability) analysis. A database of 595 historical events is then used to construct co-occurrence and adjacency matrices. And the Jaccard index is used only to quantify association strength, while temporal order, HAZOP-based causal screening, and expert verification are introduced to distinguish plausible triggering relationships from simple correlations. Network indicators, including degree, betweenness, modified clustering coefficient, path length, connectivity, and edge vulnerability, are applied to identify critical nodes and propagation paths. The results indicate that functional failure of civil structures, fire, and crowd stampede are the dominant risk nodes. The proposed framework provides a transparent and replicable basis for prioritizing monitoring, emergency response, and link-cutting mitigation measures. The findings are intended as system-specific decision support rather than universal risk rankings and should be updated when new local operational data become available. Full article
(This article belongs to the Special Issue Innovation and Technology in Sustainable Construction)
22 pages, 2360 KB  
Article
Fiber Bundle Learning: A Topological Framework for Classification Using Homology and Discrete Connections
by Arturo Tozzi
Int. J. Topol. 2026, 3(2), 12; https://doi.org/10.3390/ijt3020012 - 17 Jun 2026
Viewed by 193
Abstract
Many machine-learning tasks involve structured data whose geometry, local feature distributions, and global organization interact in ways that are not well captured by existing methods based on vectorization, graph metrics, or homological signatures. We introduce Fiber Bundle Learning (FBL), a topological framework that [...] Read more.
Many machine-learning tasks involve structured data whose geometry, local feature distributions, and global organization interact in ways that are not well captured by existing methods based on vectorization, graph metrics, or homological signatures. We introduce Fiber Bundle Learning (FBL), a topological framework that represents each data sample as a discrete fiber bundle and extracts a classification signature combining persistent homology, local feature geometry, and gluing structure. FBL builds a base space from the coarse geometry of each object, models local feature patches as fibers, and estimates transition maps between neighboring fibers to construct a discrete connection. From this representation, FBL computes a set of invariants: persistent homology of the base, fibers, and total space; holonomy obtained by transporting fiber states along cycles; curvature-like quantities measuring transition inconsistency; and discrete analogues of characteristic classes. These components are assembled into a fixed-length feature vector that can be used with any standard classifier. We show that FBL yields a signature with three desirable theoretical properties: stability under perturbations of geometry and local features, invariance under isometries and global fiber reparameterizations, and robustness to sampling noise. Our synthetic experiments show that FBL distinguishes twisted from untwisted bundles with identical homology, a distinction classical topological methods fail to capture. Additional tests quantify the system’s resistance to noise, its invariance to geometric transformations, and the contribution of each signature component. Taken together, our results indicate that representing data through fiber bundle structure may provide an effective tool for classifying complex, multi-level objects. Full article
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14 pages, 2659 KB  
Article
Topological Characterization of Molecular Energy Landscapes Using Sublevel-Set Persistent Homology
by Dairo José Hernández, Carlos Alberto Cadavid, Julio De Luque and David Fernández Bueno
Math. Comput. Appl. 2026, 31(3), 108; https://doi.org/10.3390/mca31030108 - 16 Jun 2026
Viewed by 147
Abstract
The study of conformational spaces and potential energy surface (PES) functions is fundamental for understanding the structural and dynamical properties of molecules with one or more rotational degrees of freedom. In this work, the topological characteristics of conformational spaces and PES functions are [...] Read more.
The study of conformational spaces and potential energy surface (PES) functions is fundamental for understanding the structural and dynamical properties of molecules with one or more rotational degrees of freedom. In this work, the topological characteristics of conformational spaces and PES functions are investigated for a set of molecules including ethane, butane, and butadiene, which possess one rotational degree of freedom, as well as n-pentane with two rotational degrees of freedom. Sublevel-set persistent homology was applied to the potential energy functions in order to characterize the topology of the associated energy landscapes. This approach allows for the identification of topological changes during the sublevel filtration process, which can be associated with the presence of critical points in the energy landscape, including minima (index 0), transition states (index-1), and maxima (index-2). Furthermore, the method provides information about the global connectivity and structural organization of the conformational landscape. The results show that sublevel-set persistent homology successfully reproduces the energy hierarchy and connectivity between molecular conformers, providing a coherent topological description of the molecular energy landscape. These findings demonstrate that persistent homology constitutes a useful framework for studying the topology of conformational spaces and potential energy surfaces in molecular systems. Full article
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22 pages, 8856 KB  
Article
Impacts of Urban Amenities on Socio-Spatial Differentiation: A Multiscale Analysis in Beijing
by Xianjia Jiang, Zhihong Li and Peng Cheng
Sustainability 2026, 18(12), 6183; https://doi.org/10.3390/su18126183 - 16 Jun 2026
Viewed by 118
Abstract
With the growing focus on people-centered urban development sustainability in megacities, urban amenities have emerged as an important factor consistently associated with residential differentiation and restructuring. Understanding how it relates to the structure of social space is essential to advancing spatial equity. The [...] Read more.
With the growing focus on people-centered urban development sustainability in megacities, urban amenities have emerged as an important factor consistently associated with residential differentiation and restructuring. Understanding how it relates to the structure of social space is essential to advancing spatial equity. The study developed an analytical framework that integrates functional characteristics and supply patterns and applied Multi-scale Geographically Weighted Regression (MGWR) to examine how amenities shaped socio-spatial differentiation within Beijing’s Fifth Ring Road from 2015 to 2025. The results indicate that socio-spatial differentiation showed a rise followed by a decline across the three time points examined, yet its spatial pattern maintained a stable agglomeration characteristic of “high in the core area and low in the peripheral areas.” Significant differences exist in the roles of amenities across different attributes and scales. Market-driven factors, represented by amenity density and amenity diversity, typically exert their influence over larger spatial scales and are generally associated with spatial mixing and provide baseline opportunities for potential social interaction. Attributes such as amenity publicness and amenity uniqueness, which are more influenced by institutional and capital factors, primarily operate at local scales. While they are often associated with exclusionary effects in traditional core areas, they are also consistent with a certain degree of spatial integration in some revitalized districts. This study offers a more nuanced explanation for understanding the socio-spatial restructuring of megacities in transition and provides empirical evidence for advancing more equitable and sustainable urban governance. Full article
(This article belongs to the Section Sustainable Urban and Rural Development)
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