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Modelling

Modelling is an international, peer-reviewed, open access journal on theory and applications of modelling and simulation in engineering science, published bimonthly online by MDPI.

Quartile Ranking JCR - Q2 (Engineering, Multidisciplinary)

All Articles (445)

This paper addresses the optimization of electric vehicle (EV) charging facility configuration on highways by proposing a collaborative planning method that integrates driver anxiety psychology, mixed traffic flow dynamics, and service area queuing characteristics. By abstracting the road travel and service area replenishment processes into an integrated queuing network, a system analysis framework is constructed to characterize the coupling relationship of “facility supply, traffic assignment, and state feedback.” On this basis, a bi-level optimization model is established with the objective of minimizing the generalized total social cost. The upper level makes decisions on the coordinated quantities of fixed charging piles and mobile charging vehicles, while the lower level describes the stochastic user equilibrium behavior of drivers under the influence of real-time congestion and anxiety. To tackle the high-dimensional nonlinear nature of the model, an efficient solution algorithm based on simultaneous perturbation stochastic approximation (SPSA) is designed. A case study of the Nei-Yi Expressway demonstrates that compared with the traditional peak demand proportional allocation method, the proposed approach can better balance construction costs, operation and dispatching costs, and user travel experience under limited investment, significantly reducing waiting times and psychological anxiety costs. It provides theoretical methods and decision support for planning a resilient energy replenishment network that achieves “fixed facilities ensuring base load and mobile resources responding to peak demands.”

27 February 2026

Schematic diagram of the highway service network (queuing system). (Created using Microsoft PowerPoint 2016).

Neural Approach to Study the Vibration Behavior of Damaged Composite Rotating Beams

  • Patricia Rubio Herrero,
  • Belén Muñoz-Abella and
  • Lourdes Rubio
  • + 1 author

In recent decades, Artificial Neural Networks (ANNs) have become a robust tool for addressing complex engineering challenges. This paper implements an ANN-based methodology to determine the natural frequencies of rotating sandwich composite beams with core defects. The study focuses on the influence of rotation speed and defect characteristics (size and location) on a beam made of carbon fiber face-sheets and a honeycomb core, selected for its high strength-to-weight ratio in next-generation designs. The primary novelty lies in providing a simplified model that, through an ANN-based surrogate, establishes an automated and high-speed process for frequency prediction. This approach bypasses the prohibitive computational costs of 3D-FEM simulations, enabling near-instantaneous results essential for real-time Structural Health Monitoring (SHM) applications.

27 February 2026

Geometric model.

This paper investigates an Organic Rankine Cycle (ORC) system for low-to-medium temperature heat recovery using comparative thermodynamic, exergoeconomic and economic modelling. A working-fluid study considering environmental and thermodynamic perspectives is conducted. A 20 kW ORC unit is tested and used as a feasibility and trend-consistency reference to support the modelling assumptions and practical operating bounds. A parametric study then examines the effects of evaporator pressure, condensation temperature, superheat, subcooling and heat-exchanger pinch-point temperature differences on net power output, first- and second-law efficiencies, total product cost and total capital investment under prescribed boundary conditions. Multi-objective optimization is applied to identify Pareto-optimal trade-offs and representative compromise solutions. Results show an intermediate evaporator pressure maximizes net power output, while lower condensation temperature generally improves efficiency; superheat has limited efficiency impact but should ensure safe operation, and a small subcooling margin (around 3 °C) mitigates cavitation risk. The best overall performance is obtained with an evaporator pinch of 3 °C and a condenser pinch of 5–9 °C; tightening pinch constraints increases required heat-transfer area and makes heat exchangers the main cost bottleneck for high-efficiency solutions.

25 February 2026

Schematic of the ORC system and its coupling to external heat-source and heat-sink loops (geothermal brine shown as an example heat source). The evaporator acts as the coupling heat exchanger between the ORC working-fluid loop and the geothermal loop, while the condenser rejects heat to the external cooling loop. Arrows indicate flow directions and numbers denote the state points used in the thermodynamic calculations.

Reliable state-of-charge (SoC) estimation is crucial for safe and efficient battery management. However, it is challenging in practice. Terminal-voltage sensitivity becomes weak in open-circuit-voltage (OCV) plateau regions. Model uncertainty also persists at practical sampling periods. To tackle this issue, this paper proposes a discrete-time, model-based SoC estimation framework. This framework combines a dual-polarization equivalent-circuit model with a tuning-light sliding-mode observer. It is specifically designed for digitally sampled battery management systems. The modeling stage includes: (i) a discrete-time DP representation suitable for embedded use, (ii) a shape-preserving PCHIP reconstruction of the OCV–SoC curve and its derivative, and (iii) an effective-slope regularization mechanism that maintains non-vanishing output sensitivity even in flat OCV regions. On top of this structure, a boundary-layer SMO is developed with output-error shaping, model-driven gain scaling, and simple bias-compensation terms based on integral correction and leaky Coulomb counting. A discrete-time Lyapunov analysis is conducted directly on the surface dynamics. This analysis shows finite-time reaching to the boundary layer and a practical limit on the steady-state error that depends on the sampling period, disturbance level, and boundary-layer width. Numerical tests on a DP model identified from experimental data indicate that the proposed method achieves SoC accuracy similar to a switching-gain adaptive SMO. The results confirm the benefits of a model-centric design. The discrete-time formulation and convergence proof, which do not depend on high sampling rates, provide robustness advantages over traditional sliding-mode methods. The proposed method also performs better than a tuned EKF in plateau regions, requiring much less tuning effort.

16 February 2026

Dual-polarization (DP) equivalent-circuit model of the lithium-ion cell, including a nonlinear open-circuit voltage source, ohmic resistance and two RC branches representing fast and slow polarization dynamics.

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New Technological Solutions, Research Methods, Simulation and Analytical Models That Support the Development of Modern Transport Systems
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New Technological Solutions, Research Methods, Simulation and Analytical Models That Support the Development of Modern Transport Systems

Editors: Tomasz Nowakowski, Artur Kierzkowski, Agnieszka A. Tubis, Franciszek Restel, Tomasz Kisiel, Anna Jodejko-Pietruczuk, Mateusz Zaja̧c

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Modelling - ISSN 2673-3951