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Keywords = time–space discretization models

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29 pages, 4163 KB  
Article
Fast Computation and Model Order Reduction of the Friction Stir Welding Process with POD-DEIM
by Joshua Kay and Zilong Song
AppliedMath 2026, 6(9), 148; https://doi.org/10.3390/appliedmath6090148 (registering DOI) - 5 Sep 2026
Abstract
Friction stir welding (FSW) is a solid-state manufacturing process widely used in joining aluminum and other metal workpieces. The FSW process can be modeled by a coupled system of non-Newtonian Navier–Stokes and heat-transfer equations. However, solving this non-linear system with high accuracy requires [...] Read more.
Friction stir welding (FSW) is a solid-state manufacturing process widely used in joining aluminum and other metal workpieces. The FSW process can be modeled by a coupled system of non-Newtonian Navier–Stokes and heat-transfer equations. However, solving this non-linear system with high accuracy requires significant computational power. This work refines the system by introducing corrected coefficients and new treatments for boundary conditions near the tool. Then, model order reduction, including the Proper Orthogonal Decomposition (POD) and Discrete Empirical Interpolation Method (DEIM), is applied to efficiently solve the FSW system in a low-dimensional space. To enhance accuracy and effectiveness, two novel treatments have been adopted for the POD and DEIM models: the introduction of preconditioner matrices to avoid large condition numbers and the use of indicator matrices to generate the non-linear data. For different cases regarding operating parameters, the results show that the DEIM model dramatically speeds up the computation (e.g., over 250 times faster compared with the full model) while maintaining accuracy. This makes simulations of the FSW process more accessible and easily combined with machine learning techniques in future study. Full article
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34 pages, 17039 KB  
Article
Binary-Encoded Transformable Modular Component Method for Structural Crack Identification
by Yifei Wang and Xiaojun Wang
Mathematics 2026, 14(17), 3136; https://doi.org/10.3390/math14173136 - 1 Sep 2026
Viewed by 213
Abstract
Accurate identification of complex crack networks with branching and intersecting topologies remains a challenge in aerospace and civil engineering. Conventional non-destructive testing techniques are constrained by limited coverage and equipment access requirements, while model-based inverse methods face the curse of dimensionality and high [...] Read more.
Accurate identification of complex crack networks with branching and intersecting topologies remains a challenge in aerospace and civil engineering. Conventional non-destructive testing techniques are constrained by limited coverage and equipment access requirements, while model-based inverse methods face the curse of dimensionality and high computational cost when characterizing intricate crack morphologies. To address these limitations, a Binary-encoded Transformable Modular Component (BTMC) method is proposed, which abstracts complex crack morphologies into combinations of modular components representing elementary crack topological operations and encodes their parameters into a unified binary genotype. This representation converts the high-dimensional continuous inverse problem into a discrete combinatorial optimization task over a bounded search space, and the extended finite element method is coupled with a genetic algorithm for forward analysis and parameter optimization. Numerical simulations covering non-intersecting cracks, intersecting networks, and irregular morphologies beyond the component library demonstrate that the method maintains stable identification accuracy under measurement noise up to 10%. Experimental verification on a metal tensile plate and a wing surface curved-shell structure confirms that the identified configurations are mechanically consistent with the measurements, with the strain-response error on the wing surface reduced from 8.67% for the traditional genetic algorithm to 2.27% for BTMC. Across all test cases, the BTMC method converges in fewer generations with a total identification time of approximately 16 min on average, which provides a computationally efficient framework for online structural health monitoring of aircraft structures. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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38 pages, 1017 KB  
Article
Stochastic Wolbachia Dynamics: Persistence, Invariant Measures, and Probability-Based Release Strategies
by Eddy A. Kwessi
Axioms 2026, 15(9), 654; https://doi.org/10.3390/axioms15090654 - 1 Sep 2026
Viewed by 168
Abstract
We develop a stochastic discrete-time framework for Wolbachia invasion in mosquito populations under environmental variability. Starting from a deterministic frequency-dependent difference equation with an Allee-type threshold, we consider the random iteration Xn+1=FΘn(Xn) [...] Read more.
We develop a stochastic discrete-time framework for Wolbachia invasion in mosquito populations under environmental variability. Starting from a deterministic frequency-dependent difference equation with an Allee-type threshold, we consider the random iteration Xn+1=FΘn(Xn), where Θn represents fluctuations in fitness cost, cytoplasmic incompatibility, and maternal transmission. We establish existence, uniqueness, positivity, forward invariance of [0,1], continuity, and pathwise order preservation, and formulate the model as a random dynamical system. Under independent environmental forcing, the process is Markovian; the associated Markov operator is Feller, and compactness of the state space implies the existence of invariant probability measures. Local behavior near extinction is characterized by the stochastic Lyapunov exponent λ=Elog(1M)(1Sf), with λ<0 yielding local exponential stability of the Wolbachia-free state. We further introduce finite-horizon establishment probabilities and probability-based release thresholds, whose monotonicity follows from the pathwise comparison principle. Numerical simulations show how the magnitude, source, and dependence structure of environmental variability affect invasion probabilities and release requirements. The framework combines nonlinear difference equations, random dynamical systems, Markov operators, invariant measure theory, and stochastic stability in a unified analysis of threshold-dependent Wolbachia invasion. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics, 2nd Edition)
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44 pages, 1693 KB  
Article
Posterior Communicating Artery Aneurysm Microsurgery: PComA-CORE, an Anatomy-Informed Explainable AI Framework for Complexity, Neurovascular Risk, Oculomotor Recovery and Functional Outcome
by Matei Șerban, Corneliu Toader, Alexandru Vlad Ciurea, Leon Dănăilă and Răzvan-Adrian Covache-Busuioc
Med. Sci. 2026, 14(5), 528; https://doi.org/10.3390/medsci14050528 - 28 Aug 2026
Viewed by 146
Abstract
The posterior communicating artery (PComA) aneurysm is a challenging microsurgical problem due to multiple factors. These include the technical complexity of the surgery itself, potential injury to blood vessels during surgery, recovery of cranial nerve function, and overall neurological outcome after the operation. [...] Read more.
The posterior communicating artery (PComA) aneurysm is a challenging microsurgical problem due to multiple factors. These include the technical complexity of the surgery itself, potential injury to blood vessels during surgery, recovery of cranial nerve function, and overall neurological outcome after the operation. These are all related to the area where the PComA aneurysm is located, but they have fundamentally different biological determinants. Prior methods of describing aneurysms do not adequately describe how the relationships of the internal carotid artery (ICA) and PComA/P1 configuration influence the proximity of the aneurysm to other important structures such as the perforating arteries, the anterior choroidal artery (AChA), cranial nerve III (CN III), and the surgical corridor. We created PComA-CORE, an artificial intelligence-based framework designed to evaluate whether the elements of experienced microsurgeons’ thought processes can be measured individually while still maintaining temporally valid predictions, human interpretability, and explicit estimates of predictive uncertainty. Methods: Using a highly detailed database of clinical, radiographic, anatomical, intraoperative, and longitudinal data from 687 adult patients who underwent microsurgical clipping of PComA aneurysms over the period 1997–2026, we applied PComA-CORE to predict separately: Microsurgical Complexity (C); Oculomotor Recovery (O); Neurovascular Preservation Risk (R); and Expected 90-Day Functional Outcome (E). The models used cases from 1997–2020 (n = 564) for development and cases from 2021–2026 (n = 123) for temporal evaluation. Several architectures, including penalized regression, machine-learning techniques, interpretable machine learning, and ensembles, were compared using nested cross-validation, discrimination metrics, calibration metrics, decision-curve analysis, explainability measures, uncertainty-aware prediction, inter-observer reproducibility, and model-to-score distillation. Results: Four discrete predictive architectures were identified by PComA-CORE. PComA-C was found to be highly dependent upon anatomy because the specific geometric characteristics of individual vascular segments and the presence or incorporation of branches around the aneurysm strongly influenced temporal predictions. PComA-R was found to behave as a distributed susceptibility phenotype based on neurovascular attributes rather than a deterministic injury model and achieved a temporal AUC of 0.703. Among patients with preoperative CN III palsy, PComA-O identified that recovery primarily depended upon the time course of neurological dysfunction and structural deformation of the affected nerve. Temporal validation was not feasible given the small number of recent non-recovery events. Conversely, PComA-E showed that global functional outcome continued to depend predominantly upon clinical neurological severity, with a temporally evaluated penalized model achieving an AUC of 0.878. Uncertainty-aware predictions indicated that some cases would benefit from greater caution in interpretation. High-resolution anatomical phenotypes demonstrated good inter-observer reproducibility. Score distillation demonstrated that simplification preserved predictive information, but did so differently depending on the endpoint. Conclusions: The problem of predicting the consequences of clipping a PComA aneurysm is multidimensional and does not exist as a single “risk” prediction problem. Technical complexity, neurovascular vulnerability, neural recovery, and global disability each exist within distinct predictive spaces and require different levels of anatomical detail and/or computational complexity. PComA-CORE establishes a human-supervised framework to transform expert microsurgical thought processes into explicit, reproducible, uncertainty-aware, and clinically interpretable representations. While prospective multicenter validation will be needed prior to clinical use, it has the potential to establish a basis for explainable AI, precision cerebrovascular neurosurgery, anatomy-informed risk stratification, and clinically interpretable decision-support systems in complex aneurysm surgery. Full article
(This article belongs to the Section Neurosciences)
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22 pages, 1395 KB  
Article
Projection Neural Dynamics for Inverse Variational Inequality Problems: Stability Analysis and Applications to Sparse Signal Recovery
by Vajahat Karim Khan, Mohd. Sarfaraz, Hafiz Farooq Ahmad and Md. Kalimuddin Ahmad
Mathematics 2026, 14(17), 3083; https://doi.org/10.3390/math14173083 - 27 Aug 2026
Viewed by 273
Abstract
In this work, we develop a projection neural network based on a second-order dynamical model (SO-PDM) for solving inverse variational inequality problems (IVIPs) in Hilbert spaces. The proposed framework incorporates inertial and damping components, resulting in improved convergence behavior while ensuring feasibility through [...] Read more.
In this work, we develop a projection neural network based on a second-order dynamical model (SO-PDM) for solving inverse variational inequality problems (IVIPs) in Hilbert spaces. The proposed framework incorporates inertial and damping components, resulting in improved convergence behavior while ensuring feasibility through a projection operator. Under the Lipschitz continuity assumption on the operator, the proposed SO-PDM admits a unique global trajectory. Under the additional strong monotonicity assumption and suitable parameter conditions, convergence to the unique solution of the IVIP is established. A discrete-time formulation is derived via a finite-difference scheme, leading to a projection-based inertial algorithm with relaxation. Under suitable parameter conditions, the algorithm is shown to converge linearly to the unique solution of the IVIP, and under an additional parameter condition, the global asymptotic stability of the continuous-time SO-PDM is established via Lyapunov analysis. Furthermore, a numerical comparison in a higher-dimensional setting shows that the proposed algorithm converges faster and attains higher accuracy than the existing first-order projection method. Numerical experiments further confirm the effectiveness and stability of the proposed SO-PDM, including its application to sparse signal recovery in compressed sensing. Full article
(This article belongs to the Section C: Mathematical Analysis)
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35 pages, 5447 KB  
Article
Bayesian-Optimized Surrogate Framework for Cost-Effective Design of Composite Steel–Concrete Beams
by Iuan Brandão Ferreira, Markssuel Teixeira Marvila, Marília Gonçalves Marques and Leonardo Carvalho Mesquita
Buildings 2026, 16(17), 3430; https://doi.org/10.3390/buildings16173430 - 27 Aug 2026
Viewed by 268
Abstract
Structural design codes provide safe procedures for verifying steel–concrete composite beams but do not directly guide engineers toward cost-effective configurations. This study aims to develop and evaluate a surrogate-assisted framework that combines a Multilayer Perceptron neural network with Bayesian Optimization for the preliminary [...] Read more.
Structural design codes provide safe procedures for verifying steel–concrete composite beams but do not directly guide engineers toward cost-effective configurations. This study aims to develop and evaluate a surrogate-assisted framework that combines a Multilayer Perceptron neural network with Bayesian Optimization for the preliminary flexural-resistance and material-cost optimization of simply supported steel–concrete composite beams designed according to the Brazilian code NBR 8800. A dataset containing 20,000 beam configurations and 15 input variables was generated using a Python-based analytical routine that implements the NBR 8800 provisions for the positive bending resistance of composite beams. The generated dataset was used to train a Multilayer Perceptron neural network to predict the design bending resistance. The trained surrogate model was then integrated with Bayesian Optimization to search a discrete design space comprising commercial steel profiles, concrete slab thicknesses, shear connector quantities, and connector diameters. The selected neural network architecture achieved validation MAE and RMSE values of 2.128 kN·m and 3.013 kN·m, respectively, with an R2 of 0.9999. In ten benchmark scenarios, the BO–MLP framework identified candidate solutions using only 60 objective-function evaluations. This corresponds to 3% of the evaluation budget adopted for GA and PSO and approximately 0.057% of the configurations examined by exhaustive search. Despite this limited sampling budget, the resulting candidate solutions presented an average optimality gap of approximately 12.1% relative to the global reference. In computational terms, GA and PSO required approximately 4.1 and 4.9 times the execution time of BO–MLP, respectively, while exhaustive search required approximately 18.4 times the execution time. Overall, the proposed framework offers a computationally efficient means of exploring discrete composite-beam configurations and identifying cost-competitive candidate solutions. Direct NBR 8800 verification showed that seven of the ten selected candidates satisfied the resistance requirement, while three presented resistance-to-demand ratios slightly below unity. Therefore, the framework should be used as a preliminary screening tool, with the selected configurations subsequently verified using the complete code-based procedure. Within the restricted structural domain investigated, the framework can support preliminary decisions related to positive bending resistance and material cost. Full article
(This article belongs to the Section Building Structures)
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23 pages, 5480 KB  
Article
Prediction of Waterjet Cutting Depth Under Multi-Field Coupling Based on Zero-Shot Learning
by Feifei Lu, Yu Qiu, Dong Fan and Weiming Chen
Technologies 2026, 14(9), 527; https://doi.org/10.3390/technologies14090527 - 27 Aug 2026
Viewed by 214
Abstract
Sudden collapse accidents in mine roadways occur frequently, and post-disaster emergency rescue faces major challenges in terms of safety and efficiency. Therefore, efficient demolition equipment and intelligent prediction methods are urgently needed. Abrasive waterjet technology has considerable potential for complex disaster environments owing [...] Read more.
Sudden collapse accidents in mine roadways occur frequently, and post-disaster emergency rescue faces major challenges in terms of safety and efficiency. Therefore, efficient demolition equipment and intelligent prediction methods are urgently needed. Abrasive waterjet technology has considerable potential for complex disaster environments owing to its high efficiency, environmental friendliness, and cold-cutting characteristics. However, its cutting performance is affected by multiple coupled factors, including jet parameters, material properties, and environmental conditions. This makes accurate prediction difficult, especially under extreme or unseen operating conditions where available samples are limited. To address this problem, this study proposes a zero-shot learning-based multi-physics coupling prediction framework for the “jet–material–environment–effect” relationship. The framework is designed to predict abrasive waterjet cutting performance under unseen working conditions. First, a multi-factor cutting-performance dataset is constructed through a hierarchical experimental design. A generative adversarial network (GAN) is then introduced to expand the sample space and compensate for the discrete nature and limited distributional coverage of the experimental data. Second, a lightweight self-attention mechanism is employed to model high-dimensional input features globally, thereby improving the model’s ability to capture complex feature interactions. Finally, a joint loss function is designed to collaboratively optimize the generation and prediction processes. The experimental results show that the proposed model achieves a prediction accuracy of 98.3% on the test set, with a coefficient of determination R2 of 0.967, outperforming WOA-SVM, BP neural network, EML, and Transformer models. The inference response time is approximately 3.2 s, indicating good engineering applicability. The results demonstrate that GAN effectively expands the sample space and improves model generalization, while the LightTransformer structure provides advantages in modeling high-dimensional coupled inputs. The proposed method can provide theoretical support and technical reference for intelligent demolition rescue and cutting-depth prediction under mine disaster conditions. Full article
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0 pages, 44245 KB  
Article
A Simulation-Based Dynamic Path Planning Approach for Low-Altitude Unmanned Aerial Vehicles in Inspection Scenarios
by Changqi Yang, Hongjie Hu and Yi Ai
Drones 2026, 10(9), 644; https://doi.org/10.3390/drones10090644 - 25 Aug 2026
Viewed by 241
Abstract
Traditional target-oriented task allocation and path planning methods often struggle to balance real-time responsiveness to dynamic task alterations with multi-UAV cooperative operations in complex urban environments under meteorological disturbances. To address these challenges, this paper proposes a dynamic path planning method for low-altitude [...] Read more.
Traditional target-oriented task allocation and path planning methods often struggle to balance real-time responsiveness to dynamic task alterations with multi-UAV cooperative operations in complex urban environments under meteorological disturbances. To address these challenges, this paper proposes a dynamic path planning method for low-altitude Unmanned Aerial Vehicles (UAVs) tailored for urban inspection missions. Integrating an improved Discrete Particle Swarm Optimization (DPSO) algorithm with a decoupled Soft Actor–Critic (SAC) and B-spline smoothing framework, the proposed approach optimizes upper-level task allocation and lower-level trajectory planning within a 3D joint meteorological-obstacle feasible region. For task scheduling, an improved DPSO algorithm embedded with a spatial topology guidance mechanism dynamically coordinates task flows governed by Poisson processes. effectively addressing the spatial blindness and fragmented route assignments typical of conventional discrete optimization. Concurrently, local trajectory replanning executes receding-horizon spatial exploration via SAC deep reinforcement learning, followed by B-spline refinement to strictly enforce UAV kinematic limits, systematically bridging continuous-space exploration with low-level flight compliance to overcome the kinematic infeasibility common in pure learning-based models. Validated through extensive Monte Carlo comparative simulations (N=50) and further verified by a high-fidelity AirSim dynamic physics engine, the results demonstrate that: (1) The improved DPSO constrains the average response latency for high-priority emergency tasks to within 40 s even under 50 concurrent dynamic tasks. (2) The lower-level replanning achieves an average execution time of 3.60±0.18 s and a path success rate of 95.8±1.2%, in numerical tests, while maintaining a 96.2% kinematic feasibility rate under realistic rigid-body inertia and aerodynamic drag. While the current 3.60 s latency presents a potential bottleneck for millisecond-level dynamic emergency reactions, the developed framework offers a highly effective and safe closed-loop dynamic scheduling solution that lays a rigorous computational foundation for low-altitude urban inspections. Full article
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26 pages, 4234 KB  
Article
A Piecewise Stationary Spectral Model for Walking Crowd–Structure Interaction
by Jinping Wang, Gaoyang Zhu and Zekun Xu
Buildings 2026, 16(17), 3364; https://doi.org/10.3390/buildings16173364 - 24 Aug 2026
Viewed by 328
Abstract
Pedestrian-induced vibration is a critical serviceability concern for flexible structures such as footbridges and long-span floors. Existing human–structure interaction models commonly rely on single-degree-of-freedom simplifications and time-domain simulations, making them less suitable for frequency-domain analysis. This paper proposes a spectral analysis model for [...] Read more.
Pedestrian-induced vibration is a critical serviceability concern for flexible structures such as footbridges and long-span floors. Existing human–structure interaction models commonly rely on single-degree-of-freedom simplifications and time-domain simulations, making them less suitable for frequency-domain analysis. This paper proposes a spectral analysis model for crowd-structure interaction vibration under unrestricted pedestrian traffic. The structure was formulated as a multi-degree-of-freedom modal system, whereas each pedestrian is represented by an independent spring–mass–damper system. To address the time-varying nature of moving crowds, a piecewise stationary assumption was introduced: the continuous walking path was discretized into fixed position groups, within each of which a time-invariant coupled equation of motion was established. The response spectra obtained for different position groups were combined using residence-time weighting, thereby allowing nonuniform walking speeds to be considered. The corresponding frequency response function was derived using the state–space method, and the structural acceleration power spectral density and root mean square responses were obtained by incorporating an unrestricted crowd walking load spectral model. Comparisons with field measurements from two footbridges demonstrated reasonable agreement. The resulting framework offers an efficient frequency-domain approach for vibration serviceability assessment under unrestricted pedestrian traffic. Full article
(This article belongs to the Section Building Structures)
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51 pages, 9382 KB  
Article
A Novel Lightweight Transformer-Free Neuro-Scattering Mamba-KAN Architecture for Respiratory Sound Classification
by Florin Bogdan and Mihaela-Ruxandra Lascu
Appl. Sci. 2026, 16(16), 8342; https://doi.org/10.3390/app16168342 - 21 Aug 2026
Viewed by 193
Abstract
Automated pulmonary auscultation demands rapid and reliable anomaly detection. Contemporary deep learning frameworks frequently face deployment barriers due to their reliance on memory-intensive Transformer mechanisms and high-cost processing hardware. Addressing this limitation, the present study introduces the Neuro Scatter Mamba Kolmogorov–Arnold Neural Network [...] Read more.
Automated pulmonary auscultation demands rapid and reliable anomaly detection. Contemporary deep learning frameworks frequently face deployment barriers due to their reliance on memory-intensive Transformer mechanisms and high-cost processing hardware. Addressing this limitation, the present study introduces the Neuro Scatter Mamba Kolmogorov–Arnold Neural Network (NSMK-Net), a lightweight, Transformer-free architecture. The model integrates 1D Wavelet Scattering, bi-directional Selective State Space Models (Mamba), and Kolmogorov–Arnold Networks (KAN). By substituting quadratic self-attention with continuous-time differential discretization, the framework achieves very good computational efficiency under severe hardware constraints. Model optimization followed an eco-friendly “Green-AI” methodology, successfully converging on a standard 4 GB VRAM graphics unit. Regarding real-world deployment, the finalized architecture can be considered as a possible candidate for future “Edge-AI” applications, because it requires only 0.34 MB of parameter storage (89,342 parameters) and executes inference in approximately 48 milliseconds per respiratory cycle. Evaluated on the SPRSound dataset, the proposed model achieved a cycle-level accuracy of 84.67% (Macro-F1: 0.48). When tested under the strict official 60/40 partition of the ICBHI 2017 dataset, the network delivered a global accuracy of 41.56% (Macro-F1: 0.31) alongside an official reported ICBHI Score of 49.38%. These metrics indicate a stable detection capability when processing highly imbalanced clinical data. By replacing fixed activation nodes with learnable edge non-linearities and utilizing linear sequence memory, this new structural approach reduces the dependency on high-end hardware for medical acoustic processing. Full article
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61 pages, 8382 KB  
Review
A Review of Machine Learning Applications in Monitoring Data Processing for Underground Engineering
by Mingfei Li, Yongjun Zhang, Yu Wang and Yan Wang
Buildings 2026, 16(16), 3285; https://doi.org/10.3390/buildings16163285 - 18 Aug 2026
Viewed by 354
Abstract
With the acceleration of global urbanization and the large-scale development of underground spaces, underground engineering faces extremely complex and variable geological environments and high-risk construction disturbances. The widespread application of the Internet of Things and novel sensing technologies has given rise to structural [...] Read more.
With the acceleration of global urbanization and the large-scale development of underground spaces, underground engineering faces extremely complex and variable geological environments and high-risk construction disturbances. The widespread application of the Internet of Things and novel sensing technologies has given rise to structural health monitoring data increasingly characterized by massive volume, high dimensionality, multi-source heterogeneity, and strong spatiotemporal coupling. Traditional data processing methods based on mechanical analysis, empirical formulas, or numerical simulation have increasingly exposed limitations of insufficient accuracy, lengthy computation times, and weak generalization capability when confronted with such engineering big data. Machine learning and deep learning technologies, by virtue of their superior nonlinear mapping capability, advantages in feature extraction from massive data, and flexible architectural design, provide solutions for efficient knowledge extraction and intelligent assessment of underground engineering monitoring data. This paper reviews the current application status and frontier advances of machine learning technologies in the field of underground engineering monitoring data processing in recent years. First, the development trajectory of analytical algorithms evolving from classical shallow machine learning, through temporal and spatial deep learning, to physics-data dual-driven approaches is delineated. Second, targeting the critical challenges of missing field data and sparse sensor deployment, spatiotemporal fusion imputation techniques and spatial reconstruction methods incorporating mechanical prior knowledge are thoroughly evaluated, elucidating the paradigm shift in monitoring philosophy from discrete point-based alarming to inference-augmented sparse sensing that approximates full-field state awareness through model-dependent estimation rather than direct measurement. Third, the applications of machine learning in underground structural deformation mechanism interpretation, key influencing factor identification based on explainable artificial intelligence (AI), and rapid back-analysis of geomechanical parameters are summarized. Finally, composite network architectures and physics-constrained guidance strategies for non-stationary deformation time series prediction under complex and variable working conditions are discussed. A methodological audit of the 73 included studies—of which 33 enter the quantitative comparison tables—reveals that 26 of the 33 audited studies (78.8%) validate exclusively on single-project data, only 1 study conducts rigorous out-of-distribution generalization testing, and none of the 33 studies (0%) provides uncertainty quantification. These findings highlight cross-project generalization and probabilistic prediction as important methodological challenges. This paper aims to provide theoretical references and methodological guidance for safety early warning, intelligent construction, and full life-cycle health management of underground engineering. Full article
(This article belongs to the Section Construction Management, and Computers & Digitization)
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28 pages, 1674 KB  
Article
An Efficient and Stable Numerical Scheme for Three-Dimensional Riemann–Liouville Time-Fractional Integro-Differential Equations
by Quan Tang, Ziyang Luo and Shuo Wang
Fractal Fract. 2026, 10(8), 570; https://doi.org/10.3390/fractalfract10080570 - 18 Aug 2026
Viewed by 202
Abstract
Three-dimensional Riemann–Liouville time-fractional integro-differential equations provide useful prototype models for diffusion and transport processes with temporal memory and weakly singular hereditary effects. Their numerical solution is challenging because of the nonlocal fractional derivative, history-dependent fractional integral term, and large-scale discrete systems arising from [...] Read more.
Three-dimensional Riemann–Liouville time-fractional integro-differential equations provide useful prototype models for diffusion and transport processes with temporal memory and weakly singular hereditary effects. Their numerical solution is challenging because of the nonlocal fractional derivative, history-dependent fractional integral term, and large-scale discrete systems arising from three-dimensional spatial discretization. In this work, an efficient high-order compact finite difference scheme is developed for solving such problems. The Riemann–Liouville fractional derivative is approximated by the weighted and shifted Grünwald difference formula, the fractional integral term is discretized by the product trapezoidal formula, and the Laplace operator is approximated by compact difference operators. The proposed scheme achieves second-order accuracy in time and fourth-order accuracy in space. Moreover, the solvability, stability, and convergence of the fully discrete three-dimensional scheme are analyzed under suitable regularity assumptions. Numerical experiments, including examples with smooth and non-smooth solutions, verify the theoretical convergence orders and demonstrate the effectiveness of the proposed method for different fractional parameters. Full article
(This article belongs to the Special Issue Advanced Numerical Methods for Fractional Functional Models)
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32 pages, 6635 KB  
Article
Design of a Risk Assessment Model for Grassroots Agricultural Product Quality and Safety Based on Bayesian Networks and Evidential Reasoning
by Yijia Qiu and Yuheng Li
Symmetry 2026, 18(8), 1382; https://doi.org/10.3390/sym18081382 - 17 Aug 2026
Viewed by 212
Abstract
The quality and safety supervision of agricultural products at the grassroots level has long faced the triple superposition dilemma of small-sample sampling, multi-source evidence conflict, and risk chain evolution. Although existing data-driven models have considerable accuracy, they are difficult to leverage for intervention [...] Read more.
The quality and safety supervision of agricultural products at the grassroots level has long faced the triple superposition dilemma of small-sample sampling, multi-source evidence conflict, and risk chain evolution. Although existing data-driven models have considerable accuracy, they are difficult to leverage for intervention decisions, and the simple serial connection of traditional Bayesian networks and evidence theory cannot respond to dynamic scenarios. Aiming at this research gap, this paper constructs a dynamic risk assessment model, CIBE-DR, that deeply couples Bayesian networks with evidential reasoning. It contains three core innovations. First, the structure learning method of the causally identifiable Bayesian network embeds a graded do-calculus identifiability score covering both back-door and front-door criteria into the BDeu scoring function and combines this reward with an expert-prior divergence penalty that breaks Markov equivalence so as to realize the transition from relevance modeling to intervention decision modeling. Second, the conflict-aware adaptive evidence synthesis rule orthogonally decomposes multi-source conflict into an epistemic component and an ontological component, which are modeled respectively by Tsallis belief entropy and abductive inference over a discrete twenty-seven-point heterogeneity hypothesis space and are then fused under a reparameterized Dempster–Yager interpolation in which the two endpoints recover the two named rules under a single consistent interpretation. Third, the bidirectional closed-loop coupling mechanism between BN and ER realizes the mutual calibration between the conditional probability table and the evidence credibility prior under a Lyapunov monotone descent argument with the explicit Lipschitz bound Lθ ≤ 0.028 < 1, endowing the model with time-varying self-correction ability. Based on experiments on 156,847 sampling samples from counties and townships in East China, Central China, and Southwest China from 2021 to 2024, the proposed method achieved the best value in six of the seven evaluation indicators, with a minority recall of 0.864 ± 0.014, an intervention effect estimation error of 0.063 ± 0.005, and a dynamic response delay of 2.8 ± 0.3 days, significantly ahead of eleven mainstream baselines under the McNemar test on classification (p < 0.001) and the Wilcoxon signed-rank test on intervention-effect estimation (p < 0.001). The only indicator on which CIBE-DR does not lead is overall accuracy, which is 0.002 lower than that of Transformer; this difference does not reach statistical significance under the McNemar test (p = 0.32) and does not weaken the value of grassroots supervision in the strong-imbalance scenario where the positive rate is only 1.04%. The robustness advantage of the model is particularly prominent in the scenarios of sparse data, adversarial perturbation, and prior-graph incompleteness, and the intervention-effect estimates were additionally validated against two post-2022 policy interventions with absolute deviations of 1.4 and 1.2 percentage points respectively. These results verify the product gain and grassroots deployability of the three mechanisms. Full article
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21 pages, 2981 KB  
Article
Traveling-Wave Fault Location in Distribution Networks Based on Rank-Correlation and Random Forest
by Yifan Yu, Sizu Hou, Yao Sang and Qiwei Xue
Energies 2026, 19(16), 3782; https://doi.org/10.3390/en19163782 - 12 Aug 2026
Viewed by 225
Abstract
Traveling-wave fault location in distribution networks confronts two fundamental challenges: insufficient robustness of the cost function against heavy-tailed synchronization noise, and the location-resolution bottleneck imposed by the discrete search step. Starting from first physical principles, we identify that faulty-branch identity is encoded in [...] Read more.
Traveling-wave fault location in distribution networks confronts two fundamental challenges: insufficient robustness of the cost function against heavy-tailed synchronization noise, and the location-resolution bottleneck imposed by the discrete search step. Starting from first physical principles, we identify that faulty-branch identity is encoded in the ordering pattern of multi-terminal TW arrival times rather than in their absolute values. Building on this insight, we propose a faulty-branch identification and precise fault-location method that integrates amplitude-assisted rank correlation (AAC) features with random forest (RF). At the theoretical level, we employ Hampel’s finite-sample breakdown-point framework to quantitatively establish that the L2 cost function has an asymptotic breakdown point of zero, whereas the Spearman rank correlation coefficient attains an asymptotic breakdown point of 0.5—providing a rigorous robustness justification for replacing the L2 residual with a rank-consistency cost. At the algorithmic level, the method consists of a three-stage inference pipeline: AAC computes a joint rank correlation cost for every line section across the network and extracts a 42-dimensional feature vector encompassing cost statistics, timing residuals, and topological attributes; feature selection is performed via fused ranking, which combines Pearson correlation, point-biserial correlation, and RF out-of-bag permutation importance through a weighted harmonic mean; the RF classifier directly performs branch identification over the full edge space, and the RF regressor predicts the coarse-location residual from local cost-terrain statistical features along the correctly identified branch, breaking through the 20 m search-step resolution bottleneck. We construct a five-layer physical noise model covering wavefront detection, time synchronization, wave-velocity deviation, reflected-wave misdetection, and terminal failure. Experiments on three structurally distinct 10 kV radial distribution network topologies, each with 5000 independently generated fault samples, demonstrate that branch identification accuracy remains stably above 94%, and residual correction reduces the mean location error from approximately 60 m to approximately 40 m—an improvement exceeding 30%—confirming the effectiveness of the physics–data hybrid framework for TW fault location in distribution networks. Full article
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25 pages, 5138 KB  
Article
Tracks of Coincidence: How Climate and Human Presence Shape the Fossil Footprint Record
by Matthew R. Bennett and Sally C. Reynolds
Foss. Stud. 2026, 4(3), 22; https://doi.org/10.3390/fossils4030022 - 11 Aug 2026
Viewed by 213
Abstract
Fossil human footprints provide direct evidence of past presence and behaviour, yet the processes governing their preservation remain poorly understood. In particular, it remains unclear whether repeated footprint-bearing surfaces reflect population abundance and occupation continuity, or instead arise through environmental and taphonomic filtering. [...] Read more.
Fossil human footprints provide direct evidence of past presence and behaviour, yet the processes governing their preservation remain poorly understood. In particular, it remains unclear whether repeated footprint-bearing surfaces reflect population abundance and occupation continuity, or instead arise through environmental and taphonomic filtering. This study addresses the problem using an agent-based model (ABM) of footprint formation and preservation within a dynamic lake-margin environment. The model simulates interactions between human activity, basin morphology, and time-varying hydrological conditions under contrasting climate forcing regimes and occupation structures. Preservation is treated as a probabilistic process occurring when wetting events coincide with sufficient footprint availability, allowing analysis within an environmental–behavioural state space. Results show that the footprint record is highly sensitive to the temporal organisation of climate variability, with different forcing regimes producing distinct preservation architectures even under comparable mean environmental conditions. Basin geometry exerts a fundamental control, with basins that are not too steep or shallow maximising shoreline mobility and preservation potential, while behavioural organisation shapes how footprints are distributed relative to preservation windows. In contrast, population size alone exerts comparatively limited influence. Comparison with artefact accumulation highlights a key contrast: artefacts integrate behaviour across time, whereas footprints are preserved episodically, capturing short-lived snapshots of activity. Footprint-bearing surfaces should therefore not be interpreted as direct proxies for population size or occupation continuity, but as discrete sampling events generated through the intersection of human activity and transient preservation opportunity. More broadly, the model suggests that fossil footprint assemblages are emergent products of coupled behavioural, geomorphic, and environmental systems, providing a framework for more robust interpretation of the human footprint record. Full article
(This article belongs to the Special Issue New Directions in the Study of Vertebrate Trace Fossils)
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