Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería / International Journal of Numerical Methods for Calculation and Design in Engineering

RIMNI - An International Journal of Numerical Methods for Calculation and Design in Engineering (Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería) is a peer-reviewed Open Access journal, founded in 1985. RIMNI publishes articles written in Spanish and English. The journal's scope includes Computational and Numerical Models of Engineering Problems, Development and Application of Numerical Methods, Advances in Software, Computer Design Innovations, Soft Computing, Machine Learning, Artificial Intelligence, etc. RIMNI is an essential ... show more

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Robust Adaptive Neural Network Tracking Control for Quadrotor Unmanned Aerial Vehicle via Reinforcement Learning Strategy
B. Wang, K. Wu, Y. Wang, Z. Chu, K. Liu

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 96

Abstract
This paper proposes an adaptive event-triggered trajectory and attitude tracking control framework for quadrotor unmanned aerial vehicle (QUAV) with external disturbances. To handle unknown uncertainties in QUAV control system, we propose a dual neural network (NN) architecture: combining reinforcement learning with disturbance estimation for real-time disturbance compensation. Specifically, the Actor-NN generates compensation signals to offset uncertainties, while the Critic-NN dynamically evaluates control performance to adjust the learning process. A nonlinear neural network disturbance observer (NNDO) is incorporated to estimate the lumped total disturbances in real time. By combining backstepping control approach with event-triggered mechanism, the proposed control strategy achieves rigorous closed-loop stability with guaranteed exclusion of Zeno behavior. Experimental validation on QUAV demonstrates the effectiveness of the proposed scheme in balancing computational efficiency and control performance.OPEN ACCESS Received: 30/08/2025 Accepted: 12/12/2025
Abstract
This paper proposes an adaptive event-triggered trajectory and attitude tracking control framework for quadrotor unmanned aerial vehicle (QUAV) with external disturbances. [...]
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A HyAR Algorithm for Dynamic Order Approval in China Energy Railway Freight System
P. Wang, R. Liu, J. Pan, S. Ni, J. Geng

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 97

Abstract
As a heavy-haul railway, China Energy Railway mainly transports coal and has the characteristics of stable supply and large freight volume. The order approval process follows a centralized and unified model. This approach suffers from prolonged approval cycles, extended intervals between order submission and actual transportation (with submissions required a year in advance), and vague planned delivery times, making it difficult to meet clients’ demands for precise delivery timelines and the flexibility required for high-value scattered cargo orders. To stabilize long-term revenue for transport enterprises and enhance client satisfaction, this study introduces a client value coefficient and a delivery-time satisfaction function to evaluate order value. A dynamic order approval model for China Energy Railway freight services is constructed and solved using a deep reinforcement learning algorithm. Given the large volume of orders and the complexity of order requirements in China Energy Railway, which involve multiple auxiliary decision variables, some discrete decision variables are adjusted to continuous variables to accelerate model training. This adjustment is combined with the HyAR algorithm to enhance the training efficiency of intelligent agents. Finally, the model’s performance is tested using freight data from China Energy Railway in March 2024. Under constrained capacity conditions, the dynamic order approval model achieves 3.1% improvement in comprehensive revenue compared to static approval methods.OPEN ACCESS Received: 23/09/2025 Accepted: 24/11/2025
Abstract
As a heavy-haul railway, China Energy Railway mainly transports coal and has the characteristics of stable supply and large freight volume. The order approval process follows [...]
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Numerical Investigation of a Berthed Engineering Ship Subjected to Narrow-Gap Resonance
Z. Zhang, X. Pan, Z. Wang, W. Liu, H. Wu

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 98

Abstract
This paper investigates the hydrodynamic behavior of a berthed engineering ship using a potential model incorporating the damping lid method, which effectively mitigates the strong hydrodynamic interactions caused by narrow-gap resonance. First, the viscous correction approach is validated against experimental data. Then, the abrupt variations in the ship’s hydrodynamic characteristics at resonant frequencies are analyzed for different gap widths. Subsequently, by comparing the ship motion responses obtained from the response amplitude operators (RAOs) and the Cummins equation, the damping factors at specific frequencies are identified. Finally, under severe sea-state conditions, a safety assessment of the mooring system is performed. The results reveal that narrower gaps lead to stronger hydrodynamic interactions. Moreover, the predicted extreme load responses confirm that the mooring system is capable of ensuring the ship’s safety. This study provides useful insights for the design of berthed structures with narrow gaps.OPEN ACCESS Received: 30/09/2025 Accepted: 21/11/2025
Abstract
This paper investigates the hydrodynamic behavior of a berthed engineering ship using a potential model incorporating the damping lid method, which effectively mitigates the [...]
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A Bi-Dimensional Identification Model of Seismic Vulnerability and Intelligent Sensing Capability: A Case of Seoul
J. Zeng, J. Kang, D. Kim, H. Kim

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 99

Abstract
Seismic disasters pose increasingly complex risks to large metropolitan areas. Identifying spatial disparities between seismic vulnerability and governance capacity has become a critical issue for enhancing urban resilience. This study proposes a bi-dimensional identification model integrating seismic vulnerability and intelligent sensing capability, using the 25 districts of Seoul as a case. A comprehensive three-level indicator system of seismic vulnerability was developed. Simultaneously, the spatial density of S-DoT sensors, representing the city’s intelligent sensing infrastructure, was adopted as a proxy for district-level sensing capability. Methodologically, spatial data processing was conducted using ArcGIS Pro, while Z-score standardization and K-means clustering were performed in Python. To ensure the scientific rigor of the numerical model, a multi-scenario sensitivity analysis was conducted to evaluate the impact of multicollinearity among indicators. The clustering stability was further validated through the Adjusted Rand Index (ARI) and centroid shift metrics, and cross-checked with hierarchical clustering, confirming consistent typological structures. The results identified three types: (1) high vulnerability–low sensing, (2) moderate to low vulnerability–high sensing, and (3) moderate to low vulnerability–low sensing. These types exhibited distinct spatial clustering patterns and imply differentiated governance priorities and responses. The primary contribution of this research lies in introducing a spatially coupled model that integrates intelligent sensing into seismic vulnerability assessment. This approach moves beyond traditional static, one-dimensional frameworks, offering improved visual interpretability and decision support. The findings offer insights for resilienceoriented governance in Seoul and other high-density cities.OPEN ACCESS Received: 11/10/2025 Accepted: 20/01/2026
Abstract
Seismic disasters pose increasingly complex risks to large metropolitan areas. Identifying spatial disparities between seismic vulnerability and governance capacity has become [...]
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Hybrid AI-Quantum Computational Framework for Efficient Eddy Current Repulsion Force Simulation
Z. Zhaoming, Y. Ryu, W. Li, J. Wang

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 100

Abstract
Eddy current repulsion forces are essential to the operation of magnetic levitation, electromagnetic braking, and wireless power transfer systems, yet their accurate simulation remains computationally intensive due to the complexity of Maxwell’s equations and the need for fine-resolution meshing in transient, high-frequency domains. This paper presents a hybrid AI-Quantum computational framework that accelerates eddy current simulation by combining adaptive meshing via Physics-Informed Neural Networks for adaptive meshing, quantum-assisted solvers (HarrowHassidim-Lloyd algorithm and Variational Quantum Eigensolver) for selected finite element subdomains, and GPU-accelerated finite element methods, and reduced-order modeling based on Proper Orthogonal Decomposition and Quantum Autoencoders. The framework selectively routes well-conditioned sparse subblocks to quantum solvers while retaining classical GPU-based methods elsewhere. Validation across three representative applications—electromagnetic braking, magnetic levitation, and wireless power transfer—demonstrates that the hybrid solver maintains accuracy within 5%–8% of full FEM results while reducing computational cost by 1.3×–2× speedup in the tested scenarios. These results confirm the feasibility of integrating AI and near-term quantum computing into electromagnetic simulation workflows and provide guidance on complexity, resource requirements, and scalability.OPEN ACCESS Received: 14/10/2025 Accepted: 22/12/2025
Abstract
Eddy current repulsion forces are essential to the operation of magnetic levitation, electromagnetic braking, and wireless power transfer systems, yet their accurate simulation [...]
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Actuator Fault-Tolerant Containment Control for Fractional Multi-UAVs with Input Saturation and Communication Delays
J. Du, H. Louati, M. Iqbal, M. Almazah, A. Smerat, S. Hilali

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 101

Abstract
In this paper, the issue of distributed containment control for multiple Unmanned Aerial Vehicles (UAVs) is discussed using a fractional-order model with convenient limitations. A new event-based finite-time slidingmode control algorithm is proposed to enable the follower UAVs to converge to the convex hull spanned by a set of dynamic leaders. The suggested approach is immune to actuator failure, input constraint, timevarying communication delays, as well as exogenous stochastic disturbances. Memory effects present in UAV dynamics are reflected in the control law since fractional calculus is involved in calculations. The eventtriggering mechanism is configured to reduce the communication burden and ensure stability and performance. The convergence is verified carefully in finite time via Lyapunov techniques and the fractional stability of systems. It is ascertained that the proposed control scheme is highly effective and robust, as demonstrated by numerical simulations. The numerical simulations demonstrate that the proposed fractional-order fault-tolerant containment controllers achieve rapid convergence, with the average follower tracking error reducing below 0.02 within 5 s, and the multi-UAV formation remaining stable under stochastic disturbances and input saturation. These results highlight the effectiveness and robustness of the proposed strategies in maintaining desired containment performance across all agents.OPEN ACCESS Received: 09/11/2025 Accepted: 04/01/2026
Abstract
In this paper, the issue of distributed containment control for multiple Unmanned Aerial Vehicles (UAVs) is discussed using a fractional-order model with convenient limitations. [...]
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Neural Network-Based Resilient Consensus Control of Nonlinear Multi-Agent Systems under Stochastic Disturbances and Cyber-Physical Attacks
J. Du, M. Zahid, A. Niazi, H. Louati, N. Iqbal, M. Almazah

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 102

Abstract
For nonlinear multi-agent systems (MASs) vulnerable to stochastic disturbances and cyber-physical attacks on both sensors and actuators, this paper proposes an adaptive self-triggered consensus control framework based on neural networks. By using a decentralized leader-follower eventtriggered strategy, the method avoids Zeno behavior and drastically reduces communication overhead by updating local state estimates only at designated triggering instants. An adaptive mechanism compensates for actuator attacks, and a neural network is integrated to approximate unknown nonlinear dynamics, thereby improving robustness against malicious attacks and uncertainties. To ensure stability, a lower bound on inter-event times is derived, and practical consensus is demonstrated using Lyapunov-Krasovskii analysis. Both homogeneous and heterogeneous MASs’ numerical simulations confirm that the technique guarantees bounded state convergence and reduces the impact of attacks.OPEN ACCESS Received: 22/11/2025 Accepted: 24/12/2025
Abstract
For nonlinear multi-agent systems (MASs) vulnerable to stochastic disturbances and cyber-physical attacks on both sensors and actuators, this paper proposes an adaptive self-triggered [...]
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Fault-Tolerant Control of FractionalOrder Multi-Agent Systems Using Interval Type-2 Fuzzy Logic and Adaptive Observers
Q. Hu, A. Niazi

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 103

Abstract
This study addresses the containment control challenge in heterogeneous, nonlinear fractional-order multi-agent systems (MASs) operating under uncertainties, actuator faults, unknown nonlinearities, and mixed timevarying delays, with the aim of ensuring stability and robust performance in realistic environments. A fully distributed adaptive observer is developed for each follower to estimate leader state information using only local neighbor data, and an interval type-2 fuzzy logic system is integrated into the adaptive control law to approximate unknown dynamics and compensate for actuator faults. Stability is established via a newly formulated fractional-order Lyapunov Krasovskii functional combined with inequality analysis, and the method’s effectiveness is verified through simulations on a fractional-order Lorenz-based MAS. Results show that the proposed approach achieves precise containment control despite actuator efficiency loss and bias faults, with an root-mean-square error (RMSE) of 0.028, a settling time of 1.2 s, and disturbance rejection within 0.8 s, outperforming classical Proportion, Integral, Differential (PID) and Type-1 fuzzy controllers. These findings demonstrate that the proposed framework not only enhances fault tolerance and tracking accuracy but is also computationally efficient, making it suitable for real-time applications such as UAV swarms, autonomous vehicles, and cooperative robotics.OPEN ACCESS Received: 12/11/2025 Accepted: 22/12/2025
Abstract
This study addresses the containment control challenge in heterogeneous, nonlinear fractional-order multi-agent systems (MASs) operating under uncertainties, actuator faults, [...]
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A Novel Modified Grasshopper Algorithm for State Estimation of Power System and Design of Renewable Energy Powered Shunt Active Power Filter
P. Balachandran, D. Sundaragiri, D. Sreenivasarao, S. Saheb, H. Subhadra, E. Madhukar, K. Srilakshmi

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 104

Abstract
In recent times, meta-heuristic optimization techniques have become indispensable for effectively solving complex engineering problems involving multiple objectives. The Grasshopper Optimization Algorithm (GOA) is a population-based approach inspired by the foraging behaviour of grasshopper swarms. However, the standard GOA may fail to escape sub-optimal solutions, as it does not account for the predator-prey strategy. To address this limitation, this study introduces a modified version of GOA, termed MGOA, which incorporates the predator-prey concept to enhance its ability to avoid local optima and achieve globally optimal solutions. The proposed MGOA is tested on two distinct electric power system challenges. The first optimization problem focuses on the optimal design of a solar system (SS) combined with an energy storage system (ESS) connected to DC bus of the shunt active power filter (SHAPF) to supply an EV charging station and harmonic loads to select filter and gain values of PID controller to minimize THD and maintain stable DC bus voltage (DCBV) to enhance the power quality (PQ) of local distribution network. In addition, to show the superiority of the MGOA, two different test cases were selected with varying loads and partial shading conditions in the solar system. The second optimization problem involves power system state estimation (SE). The goal of SE is realized by employing weighted least square (WELS) or weighted least absolute value (WELAV) criterions where the objective function is formed by minimizing the sum of squares of weighted deviations (SSWD), sum of absolute values of weighted deviations (SAVWD) of estimated measurements from actual measurements Finally, the results highlight the superior performance of MGOA when compared to traditional optimization methods such as Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). However, the proposed method reduces THD to 2.19% with 98% of successes rate with a lower DCBV settling time of 0.03 s while GOA, GA and PSO give that with 3.18%, 3.45%, 3.27% THD with 91%, 88% and 91% of successes rate with higher settling.OPEN ACCESS Received: 23/11/2025 Accepted: 03/02/2026
Abstract
In recent times, meta-heuristic optimization techniques have become indispensable for effectively solving complex engineering problems involving multiple objectives. The Grasshopper [...]
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Constant Voltage Constant Current Control for Stable Operation of DC–DC Converters in Multilevel Inverters
A. Elsaid, A. Ibrahim, P. Balachandran, M. Radz, S. Al-Bawri, M. Zainuri

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 105

Abstract
Multilevel inverters (MLIs) offer superior waveform quality, reduced harmonic distortion, and lower voltage stress compared to conventional twolevel converters. In such systems, the individual voltage levels are typically generated through DC-DC converters, where each level is produced for a specific duration by selectively connecting one or more DC sources. To generate lower voltage levels, some DC sources are temporarily disconnected, resulting in light-load or no-load conditions making the output of the DC-DC converters unstable. Most existing control strategies for DC-DC converters are designed to regulate the output voltage assuming a continuously connected load, which leads to instability when the converter operates at light or no-load conditions. To address this challenge, this paper employs a Constant Voltage Constant Current (CVCC) control method to ensure stable voltage generation for MLI voltage levels. The proposed method is benchmarked against Proportional–Integral (PI), Fuzzy Logic (FL), and Sliding Mode Control (SMC) techniques. Simulation results demonstrate that the proposed method achieves superior voltage stability, accuracy, and transient performance. The proposed method is used to generate three-level and seven-level voltage waveforms in the PLECS environment, and its real-time implementation further validates its effectiveness and practical applicability. The results confirm excellent voltage regulation, with capacitor voltage fluctuations remaining below 1 V (corresponding to only 0.33% of the nominal 300 V DC-link voltage, compared to the commonly accepted±5% tolerance).OPEN ACCESS Received: 06/12/2025 Accepted: 05/03/2026
Abstract
Multilevel inverters (MLIs) offer superior waveform quality, reduced harmonic distortion, and lower voltage stress compared to conventional twolevel converters. In such systems, [...]
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Mechanical Properties and Constitutive Modelling of UHPC with Ultra Fine Waste Glass Powder (UFWGP), Micro Silica, Fly Ash and Steel and Polypropylene Fibres
A. Ayub, A. Khan, S. Fareed

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 111

Abstract
Ultra-high-performance concrete (UHPC) offers superior mechanical performance but remains limited by high cement content, sustainability concerns, and the lack of reliable constitutive models capable of capturing its full stress–strain response including pre-peak and post-peak behaviour. This study presents an integrated experimental and constitutive modelling investigation of UHPC incorporating ultra-fine waste glass powder, micro silica, fly ash, and different fibre reinforcement. Two UHPC mix designs with a water-to-cementitious material ratio of 0.20 were developed, yielding 24 independent mixtures. Cement was partially replaced with 20% ultra-fine waste glass powder and combined with either micro silica or fly ash. Fibre reinforcement was introduced independently using 2% straight steel fibres and 1.5% crimped polypropylene fibres to evaluate flowability, viscosity, uniaxial compressive strength, modulus of elasticity, splitting tensile strength, flexural strength and drying shrinkage behaviour. Experimental results demonstrate that UHPC with micro silica, UFWGP and steel fibres, prepared following the ACI 239 R-18 mix design, achieved the highest 28 days compressive, splitting tensile and flexural strength of 144.8, 12.8 and 36.1 MPa, respectively. Steel fibre-reinforced mixes exhibited up to a 42% increase in compressive strength and significantly enhanced post-peak ductility compared to the control mix (without fibre). Crimped Polypropylene fibre-reinforced UHPC attained compressive strength up to 129.7 MPa, provided improved strain capacity, and effectively reduced drying shrinkage, highlighting their suitability for crack control and deformation mitigation. The incorporation of UFWGP consistently improved flowability, reduced viscosity, and enhanced mechanical performance, while fly ash improved rheological behaviour but resulted in lower earlyage strength compared to micro silica-based mixes. To capture the compressive response of UHPC, an elasto-damage model previously proposed by Khan and Zahra was reformulated by recalibrating the compression damage parameter (β) using experimentally derived and literature based compressive strength and elastic modulus. The proposed model reproduces both pre-peak and post-peak stress–strain behaviour, with prediction errors generally within ±7% of experimental results ranging from 72.4 to 148.5 MPa. The findings provide robust experimental evidence and a validated constitutive framework for the sustainable design and structural application of UHPC
Abstract
Ultra-high-performance concrete (UHPC) offers superior mechanical performance but remains limited by high cement content, sustainability concerns, and the lack of reliable [...]
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Computational Study of Thermal Performance of Shape-Dependent CNT/ Titanium Dioxide/Aluminum OxideSodium Alginate Hybrid Nanofluids for Solar Annular Collectors
M. Bhatti, T. Abbas, O. Bég, T. Bég

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 110

Abstract
Solar direct absorber collectors are increasingly deploying more complex working nanofluids to enhance thermal performance. Hybrid nanofluids with non-Newtonian base fluids offer great promise in this regard. Motivated by these developments, the present article examines theoretically and numerically the thermal convection in a ternary hybrid nanofluid comprising an incompressible non-Newtonian sodium alginate base fluid in the annular gap between a pair of infinite concentric cylinders, as a model of a solar annular collector system. Sodium alginate (C6H9NaO6)n exhibits distinctive thermophysical characteristics, including enhanced versatility and viscoelasticity, rendering it appropriate for solar energy applications when integrated with hybrid nanoparticles. The Reiner-Rivlin third-grade viscoelastic model is therefore deployed to simulate the non-Newtonian characteristics. Three categories of nanoparticles are featured in the hybrid nanofluid: Carbon nanotubes (CNTs), Titanium dioxide (TiO2), and Aluminum oxide (Al2O3). The nanoparticles are categorized by their specific shapes: Carbon nanotubes exhibit a cylindrical form, Titanium dioxide exhibits a spherical configuration, and Aluminum oxide takes on a platelet shape. The presence of hybrid nanofluids influences both the internal transport characteristics and the heat flux towards the curved boundary and the behavior of nanoparticles with varying shapes is also a critical factor. Both linear and quadratic convection, along with viscous dissipation and heat generation/absorption, are also taken into account. The transformed boundary value problem is solved numerically with a finite difference method. Validation of the computational scheme with previous studies is included. Graphical results are provided for the impact of all emerging parameters on transport characteristics. Nusselt number is observed to be elevated with higher Grashof number (thermal buoyancy parameter) and heat generation parameter, whereas this trend is reversed with larger volume fractions of nanoparticles (CNTs, TiO2, Al2O3) and greater values of the quadratic convection parameter. The larger volume fraction of CNTs, TiO2, and Al2O3 nanoparticles strongly modifies viscosity and suppresses velocity magnitudes. The skin friction profile shows an increasing trend, which is greatly influenced by the Grash of number, heat generation parameter, and third-grade fluid parameter. In contrast, the quadratic convection parameter and the introduction of nanoparticles (CNTs, TiO2, Al2O3) tend to reduce skin friction magnitudes
Abstract
Solar direct absorber collectors are increasingly deploying more complex working nanofluids to enhance thermal performance. Hybrid nanofluids with non-Newtonian base fluids [...]
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Integration of Renewable Energy Sources into Electrical Power Systems and Its Impact on Grid Stability
M. KAMAL, M. Kashif, A. Ahmad, H. Samkari, M. Allehyani, H. Mohamed

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 109

Abstract
The integration of renewable energy sources (RES) into electrical power systems introduces critical challenges to grid stability, including frequency deviation, voltage fluctuation, and reduced transient performance. This study investigates the impact of increasing RES penetration (15%, 30%, 45%, and 60%) on grid stability using the IEEE 39-bus benchmark system. A coordinated mitigation framework integrating battery energy storage systems (BESS), synthetic inertia, and advanced inverter-based controls is proposed and evaluated. Simulation results demonstrate that at 60% RES penetration without mitigation, the frequency nadir declines to 49.32 Hz, the rate of change of frequency (RoCoF) increases to 1.82 Hz/s, voltage deviations exceed 9.3%, and the critical clearing time (CCT) reduces to 180 ms, indicating significant stability deterioration. The proposed mitigation strategy improves these metrics to 49.76 Hz, 0.94 Hz/s, 4.6%, and 260 ms, respectively, representing improvements of+0.44 Hz, –48.4%, –50.5%, and+44.4%. Benchmarking against recent literature confirms the superior performance of the coordinated approach. These findings provide quantitative guidance for grid planners and operators to maintain reliable operation under high renewable penetration scenarios.OPEN ACCESS Received: 19/01/2026 Accepted: 28/02/2026
Abstract
The integration of renewable energy sources (RES) into electrical power systems introduces critical challenges to grid stability, including frequency deviation, voltage fluctuation, [...]
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Robust Adaptive Consensus Control of Fractional-Order Multi-Agent Systems Using BBO-Optimized Type-2 Fuzzy Neural Networks
P. Yu, H. Rauf, M. Arab, S. Trabelsi

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 108

Abstract
The consensus control problem to be discussed in this paper is concerned with nonlinear multi-agent systems with unknown dynamics, unknown fractions, time-varying delays, and input saturation limits. In order to address these difficulties, an adaptive control system is established, incorporating a recurrent general type-2 fuzzy neural network (RGT2FNN) with a biogeography-based optimization (BBO) algorithm. The RGT2FNN is used to model nonlinear functions that are not known offline, and the BBO algorithm also optimizes the parameters of the fuzzy network and performs offline identification of the fractional order by minimizing multi-step model prediction error. In order to make the model more resistant to modeling uncertainties, time-varying delays, and actuator saturation effects, a LMI-based compensator is proposed to ensure the stability of the closed-loop. Lyapunov analysis guarantees the boundedness of consensus errors. The simulation findings prove that the suggested methodology can attain an accurate consensus tracking and strong performance when the uncertainties are harsh, the delays may change with time, and the limits of input saturation are taken into account.OPEN ACCESS Received: 06/01/2026 Accepted: 16/03/2026
Abstract
The consensus control problem to be discussed in this paper is concerned with nonlinear multi-agent systems with unknown dynamics, unknown fractions, time-varying delays, [...]
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Advanced Numerical Treatment of Newell Whitehead Segel Equation Using the Method of Lines with Third-Order Finite Difference Approximations
M. Hamza, M. Yaseeen, S. Trabelsi, M. Arab

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 107

Abstract
The Newell-Whitehead-Segel equation (NWSE) is a foundational nonlinear model for understanding pattern development and bifurcation in a variety of physical and engineering systems, such as Rayleigh-Bénard convection, material microstructure evolution, and nanostructure selfassembly. This study proposes a strong high-order numerical technique for solving the NWSE that combines the Method of Lines with thirdorder finite difference approximations for spatial derivatives. The spatial discretization transforms the governing partial differential equation into a system of ordinary differential equations, which are then integrated in time using the standard fourth-order Runge-Kutta technique. A thorough stability and convergence analysis is carried out to determine the theoretical validity of the proposed method. Numerous numerical studies show that the approach is highly accurate, stable, and computationally advantageous across a number of examples of testing. This work makes a novel contribution by constructing third-order one-sided finite-difference stencils at the boundaries, which ensure high-order accuracy while successfully implementing Dirichlet boundary conditions and avoiding precision loss near domain boundaries. The suggested numerical framework is a reliable and effective tool for describing challenging pattern-forming systems, as well as precisely parametric studies for design and control applications in engineering and scientific studies.OPEN ACCESS Received: 01/01/2026 Accepted: 27/02/2026
Abstract
The Newell-Whitehead-Segel equation (NWSE) is a foundational nonlinear model for understanding pattern development and bifurcation in a variety of physical and engineering [...]
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Research on Heat Transfer Law of Drilling Fluid Mixed with Low Temperature Phase Change Materials
M. Li, X. Song, H. Wang, J. Wang, Z. Song, Y. Chen

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 106

Abstract
During the drilling process of deep and ultra-deep wells, the hightemperature wellbore environment seriously affects drilling safety and efficiency. Traditional circulating cooling methods are limited by insufficient heat exchange capacity. Therefore, this paper proposes a new active wellbore temperature control technology for drilling fluids based on the endothermic mechanism of ice crystal phase change, and builds a physical simulation experimental system to conduct a study on the influence of multiple parameters. In the experiment, pre-cooled ice crystals were added to the drilling fluid, and the influence of factors such as ice crystal size, concentration, flow rate, initial temperature of the hot fluid, viscosity of the drilling fluid, and initial temperature on the cooling performance was systematically investigated. The results show that increasing the ice crystal size and concentration can significantly improve the heat exchange effect; appropriately increasing the flow rate is beneficial to enhancing heat transfer; the higher the temperature of the hot fluid, the greater the absolute cooling amplitude, but the increase in viscosity and the initial temperature of the drilling fluid weaken the cooling effect. This study provides an experimental basis and technical support for the design and engineering application of ice crystal-type functionalized drilling fluids.OPEN ACCESS Received: 23/12/2025 Accepted: 12/03/2026
Abstract
During the drilling process of deep and ultra-deep wells, the hightemperature wellbore environment seriously affects drilling safety and efficiency. Traditional circulating [...]
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Hierarchical Convolutional Neural Network for Emotion Recognition Using EEG and Facial Expressions
M. Shafiq, S. Awan, T. Kamal

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 112

Abstract
Emotion recognition is crucial for advancing human–computer interaction (HCI) by enabling systems to interpret complex affective states. While Electroencephalogram (EEG) signals provide direct insights into neural activity, facial expressions offer external emotional cues. However, unimodal systems often struggle with robustness and generalization across diverse subjects. This study presents a Hierarchical Convolutional Neural Network (HCNN) framework that integrates EEG and facial expressions through multi-level convolutional feature extraction and featurelevel fusion. The proposed model combines deep hierarchical representations with handcrafted temporal–frequency and texture-based descriptors to form a unified feature vector. Experiments on the MAHNOB-HCI and DEAP datasets show that the HCNN achieves accuracies of 91.40% and 88.09%, outperforming CNN-, LSTM-, and SVM-based methods. The results demonstrate the model’s ability to effectively capture complementary cross-modal correlations while reducing feature redundancy and computational complexity. The HCNN framework shows great promise for real-time emotion recognition applications, offering a scalable, interpretable, and data-efficient solution for multimodal emotion recognition in next-generation HCI systems.
Abstract
Emotion recognition is crucial for advancing human–computer interaction (HCI) by enabling systems to interpret complex affective states. While Electroencephalogram (EEG) [...]
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Flexible Power Supply and Distribution Based on FDN for Photovoltaic Tobacco Logistics Warehouses
T. Gui, G. Zhang, K. Zhang, J. Cui

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 113

Abstract
Industrial plants should implement sophisticated renewable-energy-based distribution systems to guarantee a continuous and reliable power supply and enhanced operational efficiency under varying loading conditions. A Flexible Power Supply and Distribution System (FPSDS) utilize the concept of Flexible Distribution Networks (FDN) for photovoltaic-contracted tobacco warehouse facilities. The integrated power system connects PV panels to a multi-port bidirectional DC-DC converter, which operates with a BESS and a full-bridge PWM inverter to provide bi-directional energy management and increased power reliability. The system achieves enhancement by integrating three control mechanisms, which include DLD for real-time energy distribution, IPR for loss minimization and Multi-Agent Deep Reinforcement Learning (MADRL) for adaptive system optimisation. The system manages dynamic voltage and power regimes and current movements through predictive behaviour prediction, which utilizes Model Predictive Control (MPC). Simulation results demonstrate enhanced electric power management that leads to better voltage systems alongside lower transmission losses and superior peak demand control. Such a solution enables both real-time capabilities and scalability benefits while enhancing operational durability and suits warehouses with energetic systems that function dynamically. The research creates a smart solution to incorporate renewable power sources within logistics operations that builds sustainable energy frameworks for decentralizing power systems. The proposed system introduces an integrated control framework combining Dynamic Load Distribution, Intelligent Power Routing, and Multi-Agent Deep Reinforcement Learning within an FDN for photovoltaic-integrated warehouses. The approach demonstrates a 15–20% reduction in transmission losses, a 12–18% increase in overall energy efficiency, and improved voltage stability by maintaining deviations within 5%. These results confirm the novelty of this research in achieving adaptive, intelligent, and scalable power distribution for logistics facilities.
Abstract
Industrial plants should implement sophisticated renewable-energy-based distribution systems to guarantee a continuous and reliable power supply and enhanced operational efficiency [...]
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Dynamic Variational Autoencoder Regressor for Soft Sensor Modeling
H. Wu, P. Zhang, S. Tian, Z. Chen

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 114

Abstract
Due to the dynamics of industrial production, it is a great challenge to learn robust feature representations from industrial process data for building an accurate soft sensor model. The traditional variational autoencoder (VAE) can learn robust features that can adapt to the dynamic process better, but cannot be directly applied in soft sensor modeling. Therefore, a novel regression-based dynamic VAE (REGDVAE) is introduced in this paper. Firstly, the encoder of the DVAE, which is constructed by the graph attention and the convolutional neural networks, is utilized to obtain the robust spatio-temporal features. The decoder of the DVAE is responsible for reconstructing the input data via transposed convolution. Secondly, the Transformer is employed to capture the dynamic associations between the robust spatio-temporal features and corresponding outputs. Moreover, with the purpose of guaranteeing the confidence of the proposed method, the Gaussian loss function is used as the optimization target of the REG-DVAE to enhance the confidence of each predicted value. The proposed REG-DVAE is implemented in a real-world melt index modeling of the polypropylene production process. The results show that compared with other baseline methods, the REG-DVAE not only can achieve the best performance, but also can provide a confidence interval, which greatly enhances the credibility of the prediction results.
Abstract
Due to the dynamics of industrial production, it is a great challenge to learn robust feature representations from industrial process data for building an accurate soft sensor [...]
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IMA: An Interpretable Machine Learning Framework Based on Large-Scale Anonymous Evaluations to Decode the Black Box of Student-Supervisor Mentorships
Y. Gao, W. Jin, Y. Nan, Y. Ma, B. Zhao, Z. Zhang

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 115

Abstract
Student-supervisor relationships (SSR) play a central role in postgraduate training, academic development, and research well-being. In the context of the rapid expansion of Chinese graduate education, understanding mentorship quality has become increasingly important for both educational governance and student development. However, prior SSR studies have often relied on small-scale surveys, context-specific qualitative evidence, or linear analytical approaches, which limits their ability to capture heterogeneous, non-linear, and system-level patterns across institutions and disciplines. To address this gap, we propose Interpretable Mentorship Analytics (IMA), a scalable analytical framework built on large-scale anonymous student evaluations. First, we construct a multi-platform dataset of anonymous supervisor evaluations and transform unstructured review text into structured mentorship indicators through a preprocessing and LLM-assisted feature engineering pipeline. Second, we employ gradient-boosting models, including XGBoost, LightGBM, and Gradient Boosting, to model the relationship between mentorship-related features and overall evaluation outcomes. Third, we apply explainable machine learning methods, particularly SHAP and LIME, to identify global feature importance, local decision patterns, and non-linear interactions among mentorship dimensions. The results show that IMA can effectively uncover the key drivers of mentorship satisfaction, especially the central role of teacher-student relationship quality, while also revealing substantial heterogeneity across regions, institution types, and disciplines. By combining large-scale anonymous evaluations with interpretable predictive modeling, this study provides a transparent and data-driven framework for evaluations with interpretable predictive modeling, this study provides a transparent and data-driven framework for understanding SSR and offers empirical evidence for improving postgraduate supervision and educational policy.
Abstract
Student-supervisor relationships (SSR) play a central role in postgraduate training, academic development, and research well-being. In the context of the rapid expansion of [...]
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CARE-FSP: A Cost-Aware and Resource-Efficient Hybrid RSO–SFO Framework for Fog-Based IoT Service Placement
H. Merouani, S. Bendib, H. Moumen, L. Guezouli

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 116

Abstract
sup>Efficient service placement is a critical challenge in large-scale Internet of Things (IoT) environments, where fog computing must balance deployment cost and resource utilization under heterogeneous and dynamic conditions. To address this challenge, this paper proposes a hybrid metaheuristic approach that combines Rat Swarm Optimization (RSO) and Sunflower Optimization (SFO), leveraging the strong global exploration capability of RSO and the efficient local exploitation behavior of SFO. The proposed RSO–SFO framework integrates both strategies within a unified fitness function designed to minimize deployment cost while ensuring efficient allocation of fog resources. Extensive simulation results demonstrate that the proposed hybrid algorithm consistently outperforms state-of-the-art optimization techniques, including Grey Wolf Optimization (GWO), Particle Swarm Optimization (PSO), and the standalone RSO and SFO methods. Specifically, the RSO–SFO approach achieves a fitness improvement of 45.38%, reduces deployment costs by 43.71%, and maintains a high average resource utilization of 78.83%. These results confirm the effectiveness and robustness of the proposed hybrid strategy for optimal service placement in fog-based IoT environments.
Abstract
sup>Efficient service placement is a critical challenge in large-scale Internet of Things (IoT) environments, where fog computing must balance deployment cost and resource [...]
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Hybrid Fractional Coupled Systems with Generalized Caputo Derivatives
D. Alhwikem, M. Awadalla

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 117

Abstract
This paper establishes a comprehensive theoretical framework for a novel coupled system of nonlinear hybrid fractional differential equations involving generalized Caputo derivatives. The system’s hybrid nature, coupled with the generality of the fractional operators, allows for modeling complex interdependent processes with memory effects that cannot be adequately captured by existing models. Using Krasnoselskii’s fixed point theorem, we prove the existence of at least one solution under explicit coupling conditions. Under appropriate Lipschitz conditions, we establish uniqueness via Banach’s contraction principle, deriving a quantitative condition involving the fractional orders, generalization parameters, and Lipschitz constants. We also conduct a rigorous analysis of Ulam-Hyers and Ulam-Hyers-Rassias stability, obtaining explicit stability constants that provide quantitative bounds on how perturbations in the input affect the solution. The theoretical results are validated through three carefully constructed numerical examples with explicit parameter values demonstrating existence, uniqueness, and Ulam-Hyers stability. A parameter sensitivity analysis confirms the robustness of the uniqueness condition across variations in fractional orders, generalization parameters, and interval lengths. The paper concludes with a discussion of limitations and directions for future research, including extensions to higher fractional orders, delay and impulsive effects, and numerical methods.
Abstract
This paper establishes a comprehensive theoretical framework for a novel coupled system of nonlinear hybrid fractional differential equations involving generalized Caputo [...]
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