Modelling

Efficient and safe path planning is the core prerequisite for realizing the autonomous crushing operation of the hydraulic crushing robotic arm in the mine chute. Foundational sampling-based algorithms, specifically standard RRT* and Informed RRT*, have problems such as unattainable targets, high computational redundancy, and hydraulic commutation shock in this highly constrained context. Therefore, this paper proposes a novel path planning method based on an improved Informed RRT* algorithm. Firstly, an axis-aligned bounding box (AABB) is constructed to approximately replace the obstacles, which not only facilitates collision detection but also enables the end of the robotic arm to accurately reach the target point. Secondly, an adaptive hierarchical strategy based on inverse kinematics perception and an artificial potential field guidance mechanism are used to construct the elevated obstacle-crossing corridor, achieving dimensionality-reduced path search and reducing ineffective collision detection. Finally, cubic non-uniform B-spline and seven-segment S-shaped velocity planning are combined to complete trajectory smoothing. Simulation results show that the success rate of the proposed planning algorithm is 100%, the number of generated nodes is reduced by 90.1%, and the trajectory achieves C² continuity, providing command-level smoothing to act as a feedforward mitigation against potential hydraulic oscillations. Path-planning experiments are carried out on the hydraulic crushing robotic arm, and the average positioning error of the end robotic arm reaching position is 30 mm, meeting the accuracy requirements and providing a reliable solution for the safe operation of heavy-duty robotic arms. Full article

Background: To elucidate the hydraulic response, progressive deformation, and wetting-induced swelling effects of high-fill expansive soil slopes throughout the rainfall–cessation process. Methods: A high-fill expansive soil slope in Jianshui, Yunnan Province, China, was selected as the study case. A three-dimensional coupled saturated–unsaturated seepage and wetting-induced swelling model was established to simulate the evolution of pore-water pressure, displacement, maximum shear strain increment, and factor of safety during 24 h of continuous rainfall followed by 48 h without rainfall. Results: During rainfall, the shallow part of the slope exhibited a pronounced pore-water pressure response. Displacement and shear strain were mainly concentrated in the middle and lower portions of the slope, near the platform transitions, and around the slope toe. Throughout the rainfall–cessation process, the factor of safety generally exhibited a decreasing trend. Wetting-induced swelling further intensified slope deformation and shear strain concentration. At 72 h, the maximum total displacement increased from 92.5 mm without considering wetting-induced swelling to 139.0 mm when wetting-induced swelling was considered, representing an increase of approximately 50.3%. After rainfall ceased, pore-water pressure and displacement remained essentially stable when wetting-induced swelling was neglected. When wetting-induced swelling was considered, matric suction increased during approximately the first 0–9 h after rainfall cessation, whereas slope displacement continued to increase after the end of rainfall and gradually stabilized only after approximately 9 h. These results indicate that the hydraulic state and deformation of the slope continued to adjust after rainfall cessation. Conclusions: Wetting-induced swelling not only increased shear deformation and reduced slope stability but also altered the post-rainfall displacement response, causing deformation adjustment to persist after rainfall cessation. Neglecting wetting-induced swelling, or evaluating slope stability solely at the end of rainfall, may therefore underestimate the actual slope deformation and overlook the continued evolution of pore-water pressure and displacement, ultimately leading to an underestimation of the final deformation magnitude and potential instability risk. Full article

This paper investigates prescribed-performance containment control of nonlinear multi-agent systems with multiple leaders under a fixed directed graph. To reconcile follower-specific physical containment envelopes, multi-leader targets determined by the communication graph, and the virtual errors available for distributed feedback, the inverse-Laplacian transfer principle is used to construct sufficient virtual-error bounds. Nonlinear evaluation and convex averaging also generate a possibly nonvanishing nonlinear averaging residual at the containment target. The controller therefore couples the allocated barrier feedback with a directional robust term that dominates this residual in the Lyapunov estimate. For every maximal Filippov solution, a barrier Lyapunov analysis based on an improper integral establishes forward completeness, invariance of the allocated virtual and prescribed physical envelopes, and asymptotic physical containment. Finally, simulation studies across multiple configurations and two direct comparisons with existing methods verify the theoretical results. Full article

This study addresses the challenges of slow attenuation and significant hazards associated with explosive shock waves confined within conventional underground tunnel walls. A novel serrated passive shock-attenuating tunnel design is proposed, grounded in the principle of viscous dissipation within the boundary layer. The investigation encompasses both experimental analyses and numerical simulations. The study found that shock waves in smooth tunnels primarily propagate as one-dimensional plane waves, resulting in concentrated energy and gradual attenuation. Conversely, the serrated tunnel geometry generated a continuous reflection, scattered and vortex formation due to abrupt geometric discontinuities, led to distortion and fragmentation of the shock front and the emergence of a three-dimensional discrete pressure field. Through turbulent dissipation mechanisms, energy is rapidly transformed into small-scale vortices, effectively reducing wave velocity and markedly diminishing the forward peak pressure. Under conditions of high-equivalent explosions, the serrated structure demonstrates enhanced efficacy in energy dissipation and peak pressure attenuation, significantly curtailed the effective propagation distance of high-pressure shock waves. Optimization of the serration spacing identified 30 cm as the optimal interval, minimizing stress peaks both centrally and at the tunnel entrance, thereby maximizing wave attenuation. Comparative analysis between simulation and experimental was resulted that corroborates the wave-attenuation performance of the serrated design, offering a critical foundation for the development of blast-resistant underground structures. Full article

Many scientific and engineering domains, including machine learning, software engineering, operations research, and logistics optimization, are characterized by a fragmented landscape of problem variants, methodological approaches, and application-specific requirements. This diversity makes it difficult to systematically understand, compare, and select appropriate solution approaches, particularly when real-world industry needs must be translated into formal problem definitions and scientific methods. The Electric Vehicle Routing Problem (EVRP) provides a representative example: the literature spans numerous problem variants and a wide range of exact, heuristic, learning-based, and hybrid methods, yet there is no clear structure for linking practical requirements to relevant solution approaches through scientific evidence. We propose a dual-taxonomy framework that structures problem features and solution features as complementary conceptual spaces. Using this structure, industry requirements and scientific publications are annotated with shared taxonomy elements. Publications provide traceable links between problem features and solution methods reported in the mapped literature, while requirements provide an industry-facing entry point into the problem space. In a real-world EVRP case study, we demonstrate how the framework can support method exploration, reveal mismatches between industrial needs and the mapped research corpus, and identify gaps in the requirement set, taxonomy, and analyzed literature corpus. This provides a transparent and extensible pathway from practical problem descriptions to relevant scientific evidence and candidate solution approaches. Full article

Accurate and computationally efficient numerical modelling of shallow-water flows is essential for flood prediction and hydrodynamic risk assessment. This study develops an implicit finite-difference scheme for the numerical solution of the two-dimensional shallow-water equations. First, the main numerical approaches used for shallow-water modelling, including finite-difference, finite-volume, finite-element, and discontinuous Galerkin methods, are analysed in terms of accuracy, stability, treatment of discontinuities, and computational requirements. Based on this analysis, an implicit finite-difference formulation is developed that uses central approximations for spatial derivatives and averages flow variables at cell boundaries. The nonlinear terms are treated using Newton linearization, resulting in an iterative scheme that allows larger time steps than explicit formulations constrained by the Courant–Friedrichs–Lewy condition. The proposed method is implemented in MATLAB as a computational module for two-dimensional hydrodynamic simulations. Its performance is demonstrated on a test problem that describes the propagation of an initially localised disturbance in a rectangular computational domain with rigid boundaries. The numerical results demonstrate stable wave propagation, conservation of the modelled flow dynamics, and physically consistent boundary reflections. The developed approach provides a computational basis for further integration of shallow-water hydrodynamic models with spatial data and geographic information systems for flood forecasting and risk assessment. The implicit scheme allowed the release of time steps $\Delta t = 0.1, 0.5$ and 0.9, which significantly exceeds the limit stability of the explicit scheme, which, due to the Courant–Friedrichs–Lévy conditions, was limited to the value Δt ≤ 0.01. The simulation results show that the developed scheme provides stable wave growth and physically correct separation from impermeable boundaries for all investigated time step indicators. The obtained water depth profiles at times $t = 10, 15, 20$ and 25 s illustrate the correct evolution of the initial combustion: the wave front expands symmetrically while preserving the conservative properties of the model hydrodynamics. The numerical solution demonstrates the accuracy and robustness of the proposed implicit finite-difference scheme, even when using time steps that are almost two orders of magnitude larger than those allowed by explicit methods. The results confirm that the developed approach is a robust and computationally efficient tool for hydrodynamic modelling, intended for further integration with geographic information systems in behaviour prediction and risk assessment tasks. Full article

This paper presents an analytical—mechanistic model for determining local friction and normal force components acting on the rake and flank surfaces during oblique cutting. The proposed formulation integrates the tool geometry by considering both the constructive angles of the cutting tool and the functional angles resulting from the cutting conditions, including cutting speed, feed rate, and depth of cut. The transformation from the oblique cutting coordinate system to the dynamometer reference system is performed using successive rotation matrices based on Euler angles. The model is formulated as a system of three equations with four unknown local force components $\left(F,F_N,F_{\alpha },F_{N\alpha }\right)$, which is analytically resolved by combining the measured cutting force components $\left(F_x,F_y,F_z\right)$ with an experimentally determined friction coefficient. The geometric direction parameters derived from the Euler angles enable the decomposition of the measured global forces into local friction and normal force components acting on the active tool surfaces. The model is further extended to functional geometry by accounting for changes in the effective tool orientation under actual cutting conditions. The internal consistency of the proposed formulation is supported through several particular cases, including orthogonal cutting and zero-angle geometry. Experimental validation was carried out using P20 carbide inserts and AISI 1045 steel. The obtained results showed good agreement between the analytically reconstructed force components, the measured cutting forces, and the friction coefficient values identified experimentally, supporting the applicability of the proposed model for local force evaluation in oblique cutting. Full article

The end-winding insulation structure of stator windings in pumped-storage generator units is complex, with pronounced electric field concentration under out-of-phase conditions, making them critical concerns in insulation design and condition-based maintenance. Although the finite element method (FEM) offers reliable accuracy, the strong nonlinearity of the anti-corona layer results in a computation time exceeding 10⁴ seconds per single solution, rendering it impractical for parameter optimization and rapid on-site assessment. This paper proposes a fast prediction method for end-region potential distribution based on a deep neural network (DNN). Taking a 334 MW unit as the research object, a three-dimensional electroquasistatic finite element model with six stator coils is established and validated through power-frequency withstand voltage and ultraviolet imaging experiments. Training samples are generated via design of experiments (DoE), and a multilayer DNN surrogate model with a 7-dimensional input (comprising 3D spatial coordinates and four physical parameters) and a 1-dimensional output is constructed to directly reconstruct the spatial potential field at the end region. The results demonstrate that the surrogate model achieves a maximum relative error of less than 2% along the entire path compared with the high-fidelity FEM solutions, with a single prediction time of approximately 38 s—representing a speedup factor of approximately 272—while also exhibiting good generalization capability. This method provides a feasible technical approach for rapid reconstruction of end-region field distribution and optimization of insulation structures. Full article

Installed-capacity shares are widely used to describe power-sector transition, but per-kWh life cycle assessment (LCA) depends on delivered generation. This study develops and tests a static, annual-average generation-weighted structural diagnostic framework linking capacity-to-generation conversion, technology impact factors, scenario simulation, uncertainty analysis, optimization-boundary diagnostics, and regional proxy analysis. The lcpy Simple LCA capacity mix supplies six pedagogical S0–S5 stress-test scenarios, while UK official capacity and generation observations provide a 2020–2024 observational backcast. Relative to raw capacity shares, fixed 2024 capacity-factor weighting reduces mean generation-share error by 60.1%, and a prior-year capacity-factor model reduces it by 72.3%; these improvements are interpreted as arithmetic and structural evidence, not as evidence of dispatch-model forecasting skill. In the scenario set, generation weighting lowers GWP100 by 13.55–22.59%; the low-fossil S2 scenario gives the lowest GWP100, 0.09011 kg CO₂-eq kWh⁻¹, 50.01% below S0, and remains lowest in the tested climate-change sensitivity analyses. Multi-indicator rankings are less stable, with S2, S3, and S4 forming a low-burden group rather than a method-invariant optimum. Applying the same weighted-sum calculation to 2024 generation structures for China, the UK, and the EU gives a central-proxy China GWP100 of 0.7497 kg CO₂-eq kWh⁻¹; this is a proxy-based structural diagnostic, not a validated regionalized LCA. The results relocate the assessment focus from installed capacity to delivered generation while identifying time-varying utilization and region-specific inventories as necessary extensions. Full article

Water-decking can buffer and redistribute borehole loading, but the coupled effects of axial charge segmentation, radial decoupling, and peripheral-hole spacing across scales remain insufficiently quantified. A cross-scale three-dimensional multi-material Arbitrary Lagrangian–Eulerian (ALE) framework coupled with the Riedel–Hiermaier–Thoma (RHT) damage model was developed for intact granite and applied at single-hole, double-hole, and full-face scales following specimen-scale calibration and numerical consistency checks. Increasing the segment count from four to six reduced the charge-section peak pressure from 283.0 to 257.0 MPa while increasing the water-section peak from 24.5 to 50.7 MPa. Increasing the radial decoupling coefficient from 1.00 to 1.31 reduced the numerical damage span from 55.6 to 33.7 cm. The spacing–decoupling assessment identified the six-segment configuration with K_d = 1.31 and 65 cm spacing as a condition-specific combination that maintained inter-hole damage connectivity while limiting outward disturbance. In the full-face model, multi-hole stress-wave interaction occurred at approximately 0.48–0.52 ms. The D ≥ 0.19 and D ≥ 0.90 damaged regions occupied 2.154% and 0.348% of the representative section, respectively. These results support a sequential axial–radial–spatial regulation framework linking pressure redistribution and inter-hole interaction to full-face stress and damage evolution, providing a basis for smooth-blasting parameter selection under the investigated intact-granite conditions. Full article

Valve-controlled hydraulic servo systems have been broadly utilized in applications requiring fast response and high power, where input constraints represent one of the major limitations on control performance. To tackle this problem, this study proposes an adaptive asymptotic tracking control method considering input constraints. First, a nonlinear mathematical model of the valve-controlled hydraulic servo system is established and transformed into an integrator form to facilitate controller derivation. Second, a tracking controller is designed based on the robust integral of the sign of the error (RISE) method, and an adaptive law for the robust gain is developed. This method not only realizes asymptotic tracking but also guarantees that the control input magnitude remains within the prescribed bounds. The controller stability is rigorously analyzed via Lyapunov theory. Finally, the validity of the proposed control method is confirmed by comparative simulations. The results show that the amplitude of the control input can be effectively limited, and the tracking accuracy is further improved. Full article

Proppant transport and placement in rough fractures strongly influence hydraulic fracture conductivity, while the mechanisms by which fracture-wall heterogeneity affects particle migration and deposition remain insufficiently understood. In this study, a Eulerian–Eulerian two-fluid model coupled with fractal fracture reconstruction is developed to investigate proppant transport and placement in rough fractures. Rough fracture surfaces with different fractal dimensions are generated using the spectral synthesis method, and a modified cosine-weighted transition algorithm is proposed to improve geometric continuity and mesh stability between the inlet and rough fracture regions. The effects of fracture roughness, injection velocity, particle size, particle density, and sand concentration on sand-bank evolution are systematically investigated. The results reveal that fracture roughness has a non-monotonic influence on proppant deposition: moderate roughness enhances near-wall disturbances and particle resuspension, reducing sand-bank accumulation, whereas excessive roughness increases particle interception, collision, and local flow disturbance, resulting in localized deposition. Increasing injection velocity from 0.15 to 0.8 m/s decreases the equilibrium sand-bank height by approximately 44%. Increasing particle diameter from 0.25 to 0.85 mm increases the maximum sand-bank height from 2.23 to 25.64 cm, while increasing sand concentration from 1 to 10 increases the maximum sand-bank height from 3.97 to 15.01 cm. Although rough and smooth fractures have identical average apertures, roughness-induced contraction–expansion channels redistribute particle trajectories and promote deeper fracture placement. This study provides insights into proppant transport mechanisms in heterogeneous fractures. Full article

Particulate matter from small-scale combustion systems remains a concern, as fine and submicron particles are difficult to remove by inertial separation alone. Electrostatic precipitators (ESP) are a promising option for this application. However, the effective aerodynamic utilization of the available collecting area depends on the internal distribution of particle-laden flue gas. This study numerically investigates the gas-flow distribution and aerodynamic particle transport in a four-tube ESP, designed to increase the collecting surface area relative to a conventional tubular arrangement. Three geometrical configurations were evaluated using computational fluid dynamics: a basic four-tube model without flow guidance, a model with nine radial inserts, and a model with a screw-type guiding structure positioned in the T-junction region. The basic geometry showed strongly non-uniform flow distribution, with a maximum-to-minimum tube-average velocity ratio of 3.31 and a coefficient of variation of approximately 51%. Radial inserts reduced these values to 1.95 and 27%, respectively, while the screw-type structure provided the most uniform distribution, with corresponding values of 1.75 and 20%. Particle-velocity fields indicated that the guiding elements promoted a more even particle supply to the four tubes. The results demonstrate that inlet-flow conditioning is essential for the effective aerodynamic utilization of the enlarged collecting area in multi-tube ESPs. Full article

Digital volume correlation (DVC) is widely used to extract internal displacement and strain fields from X-ray computed tomography (XCT) data, yet the limits imposed by the material’s own texture remain poorly quantified. This paper quantifies the individual and combined effects of particle volume fraction, particle geometry, and imaging noise on DVC accuracy. Sixteen specimens with prescribed volume fractions (0.25–10%) and particle shapes (spherical and angular) were generated using the discrete element method (DEM), loaded elastically in uniaxial compression, and converted into synthetic three-dimensional image datasets with and without additive Gaussian noise. Global DVC was performed in AVIZO and compared against the exact DEM ground truth. Under noise-free conditions, mean nodal displacement errors fall below 5% once the volume fraction exceeds 1%, whereas errors of 10–25% occur below this value; adding Gaussian noise with a variance of 0.001 raises the practical threshold to approximately 4%. Angular particles consistently outperform spherical particles at an equal volume fraction, a difference explained quantitatively by their 1.4-times-larger specific interfacial area and correspondingly higher image gradient. Median filtering favours spherical microstructures, whereas the Non-Local Means filter performs consistently across all microstructures. The results provide a priori guidelines for assessing DVC feasibility directly from microstructural descriptors. Full article

Modern manufacturing enterprises are increasingly transitioning to multi-variety, small-batch production. This shift introduces significant scheduling challenges, particularly due to the job hierarchy constraints inherent in assembling multi-level intermediate parts. Furthermore, non-machining preparation times—such as tool switching, material handling, and equipment standby—significantly impact production efficiency. To address these challenges, this paper investigates the flexible job shop batch scheduling problem by integrating order and operation consolidation under strict job hierarchy constraints. To mathematically formulate the scheduling problem with non-serial operation precedence networks and dynamic batching, we develop a mixed-integer programming model. The primary objective is to simultaneously minimize the maximum completion time (makespan) and total tardiness. To solve this efficiently, an Improved Grey Wolf Optimization (IGWO) algorithm is proposed. The algorithm features a novel two-tier coding scheme tailored for consolidation logic and employs a hybrid population initialization strategy to enhance initial solution quality. Moreover, it improves the standard hunting mechanism, utilizes Variable Neighborhood Search (VNS) for local exploitation, and independently applies a Simulated Annealing (SA) dynamic acceptance mechanism to balance global exploration and local exploitation. Extensive experiments using small-, medium-, and large-scale industrial data from a power station valve manufacturer validate the effectiveness of the proposed model and algorithm in optimizing complex batch scheduling schemes. Full article

This study presents a numerical investigation of natural convection in a two-dimensional inclined square cavity filled with air and subjected to differential heating. The effects of the Rayleigh number and cavity inclination on heat transfer and flow behavior were investigated for 10³ ≤ Ra ≤ 10⁹ and inclination angles of 0°, 15°, 30°, and 45°. The dimensionless Navier–Stokes and energy equations were solved using the finite-element method under the Boussinesq approximation with a steady laminar formulation. A structured quadrilateral mesh with boundary-layer refinement was employed near the differentially heated walls. Mesh-refinement tests and comparisons with benchmark data for the classical square cavity were used to assess the numerical accuracy of the model. The results show that the average Nusselt number increases with the Rayleigh number, reflecting the progressive intensification of buoyancy-driven heat transfer. The effect of inclination is non-monotonic and depends on the Rayleigh number. At Ra = 10⁴, the highest average Nusselt number is obtained at 45°, whereas for Ra ≥ 10⁵, the maximum is consistently observed at 15°. At Ra = 10⁹, the average Nusselt number is 54.475, 55.617, 53.224, and 49.408 for inclination angles of 0°, 15°, 30°, and 45°, respectively. The results indicate that moderate cavity inclination can enhance heat transfer by favorably modifying the interaction between buoyancy and the imposed thermal gradient, whereas larger inclinations progressively reduce the heat-transfer rate. The present results provide a systematic characterization of the coupled effects of Rayleigh number and cavity inclination within the scope of the steady two-dimensional formulation considered. Full article

The large-scale integration of renewable energy has compelled coal-fired power plants to operate under deep peak-shaving conditions, significantly increasing the failure risk of Circulating Fluidized Bed (CFB) boiler heating surfaces due to severe thermal and pressure fluctuations. To address the limitations of traditional static risk evaluations, this study proposes a novel dynamic risk assessment framework integrating a Spatial–Temporal Graph Convolutional Network (STGCN) and a Dynamic Bayesian Network (DBN). The STGCN, enhanced with an operation-adaptive dynamic cross-attention delay module, predicts spatiotemporal temperature and pressure variations across the high-temperature heating surfaces. The predicted variables are incorporated into the DBN as dynamic evidence, which utilizes Noisy-OR logic and an embedded Weibull physical degradation model to continuously quantify cumulative failure probabilities. Case study results demonstrate that the STGCN outperforms traditional LSTM and RNN baselines in prediction accuracy. Furthermore, the DBN effectively maps the distinct degradation characteristics of individual boiler components, accurately identifying the water wall and superheater as having the highest failure risks and the largest fluctuations in marginal failure probability during rapid load cycling. This integrated data-driven approach provides highly accurate, real-time risk predictions, offering essential decision-making support for the predictive maintenance and safe flexible operation of CFB boilers. Full article

Accurate AFM nanoindentation analysis requires models that account for the rounded apex of real pyramidal indenters. Although exact force-indentation equations for n-sided blunt pyramids exist, their numerical complexity limits routine use. In this work, a simple closed-form analytical approximation is developed that directly relates force to indentation depth for blunt pyramidal indenters. The method employs first-order Maclaurin series expansions of the geometric terms and the generic indentation differential equation, yielding a closed-form second-degree polynomial expression that is readily implemented in AFM data analysis. Comparison with the exact solutions showed that the approximation error decreases with indentation depth and is governed by the pyramid geometry rather than the tip radius. Simulated and experimental AFM data confirmed accurate Young’s modulus estimation above a geometry-dependent validity threshold. For a four-sided blunt pyramidal indenter, the proposed criterion predicts minimum indentation depths ranging from approximately $10.4 R_c$ for θ = 15° to 2.4 $R_c$ for θ = 45° where $R_c$ is the tip radius and θ is the pyramid’s semi-included angle. Application of the model to simulated AFM datasets yielded Young’s modulus values between 18.5 and 19.8 kPa for a true modulus of 20 kPa, corresponding to errors below 8% in all examined cases. Furthermore, the closed-form equation provided very good agreement with AFM nanoindentation data obtained from human prostate cancer cells. It is also shown that the generic derived equation includes the case of a spheroconical indenter as a limiting case. Young’s modulus is obtained directly from the quadratic coefficient, eliminating the need for tip-radius calibration. In addition, the formulation is applicable to heterogeneous materials, providing an effective local modulus through the weighted mean value theorem for integrals. The approach offers a practical and computationally efficient alternative for AFM data processing, improving the robustness of modulus estimation for soft biological materials. Full article

Accurate prediction of pile base resistance is essential for the safe and economical design of deep foundations, particularly in soft soils where load-transfer mechanisms are highly nonlinear and uncertain. This study develops a comparative, probabilistic, and interpretable machine learning framework for predicting pile unit base resistance using five input variables: applied load, settlement, effective pile length, axial stiffness, and SPT value. A Gaussian Process Regression model with an automatic relevance determination (ARD) Exponential kernel achieved the best performance, with RMSE = 262.11 kPa, R² = 0.943 on an independent test set, and 95% prediction intervals with 96.46% coverage. Beyond record-level evaluation, a leave-one-pile-out validation (the first grouped validation applied to this database) showed harder generalization to entirely unseen piles, driven mainly by a per-pile level offset rather than shape mismatch (within-pile correlation = 0.975). A sequential next-stage scheme, calibrating this level from a pile’s early loading stages, then predicted its remaining segments with consistently strong agreement (Willmott’s d = 0.76–0.83), supporting practical extension of partial load tests. Interpretability was assessed using ARD, SHAP, permutation/ablation importance, and partial dependence/accumulated local effects analysis, identifying settlement as the dominant predictor. The framework combines accuracy, calibrated uncertainty, interpretability, and validated segment-level extrapolation for reliability-oriented pile assessment. Full article