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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Adaptive Power Splitting Strategies for Smart Microgrids with Enhancing Energy Efficiency and Resilience through Dynamic Load Management
A. Shaher, Z. Mushtaq, G. Abbas, H. Alwadie, M. Irfan, H. Murtaza, A. Shaheen, S. dawsari

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 41

Abstract
The integration of a renewable energy distributed generation into microgrids poses a significant constraint in the way power is managed, further so due to the natural variability in renewable generation and the variability in the load demands. To address these issues, this paper introduces a novel approach to the Spider Swarm Optimization (SSO) algorithm, the Dynamic LoadAdaptive Power Splitting (DLAPS) strategy, to enable real-time adaptive power sharing and enhance system resilience. Unlike the classical methods of power allocation that are static, according to which the power is divided between sources of renewable energy and storage systems, and between these sources and critical loads, the DLAPS-SSO applies the idea of a machine learning based predictive model to predict the power and dynamically optimize power allocation between the sources of renewable energy and storage systems and the sources and the critical loads. The model provides a multi-objective optimization framework that aims to minimize power losses and grid frequency variations, and to maximize the system’s resilience to disturbances, including disconnection from the grid, component malfunctions, and the availability of renewable energy sources. The comparison of simulation results with those of the Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) methods shows that the energy efficiency of the DLAPS-SSO increases by 15%–20%, and the amount of power losses across various load profiles decreases by 30%–35%. Moreover, the proposed solution offers 60% faster recovery time in case of grid disconnection, maintains 65.9% of the critical load in case of component failure, and provides 40%–50% less resilience than state-of-the-art techniques. The analysis of seasons and real data shows that there is stability of the behavior with the increase of efficiency (18%–22% during winter, and 23%–25% during summer), and the ability of the suggested approach to be robust when changing plant configuration/operation. Integration of optimization of dynamic load management and adaptive power splitting will spur microgrid control strategies and offer a viable strategy to stabilize the grid, reduce operation costs, and enable sustainable changes in energy transformations. The results demonstrate the essential role of bio-inspired optimization and reactivity in the next generation of smart grids.
Abstract
The integration of a renewable energy distributed generation into microgrids poses a significant constraint in the way power is managed, further so due to the natural variability [...]
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Advanced Computational Study of Nonlinear Time-Fractional Newell-Whitehead-Segel Equation with Caputo-Fabrizio Derivative Using B-Spline Techniques
M. Shafique, M. Yaseeen, S. Trabelsi, M. Balti

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 42

Abstract
This study presents numerical solutions for the time-fractional NewellWhitehead-Segel (NWS) equation with a Caputo-Fabrizio derivative. Spatial derivatives are discretized using three B-splines-cubic, cubic trigonometric and extended cubic B-splines-while temporal discretization is handled by a finite difference scheme. The proposed schemes are rigorously analyzed for stability and convergence. Their performance is evaluated in terms of accuracy and computational efficiency. Numerical experiments confirm the effectiveness of these techniques in capturing the dynamics of the fractional NWS equation. Each B-spline variant demonstrates unique strengths, highlighting the flexibility of B-spline approaches for solving fractional differential equations with nonlocal, memory-dependent operators. These results affirm the reliability and robustness of B-spline-based methods for such problems, paving the way for future advancements in this area.OPEN ACCESS Received: 23/08/2025 Accepted: 08/12/2025
Abstract
This study presents numerical solutions for the time-fractional NewellWhitehead-Segel (NWS) equation with a Caputo-Fabrizio derivative. Spatial derivatives are discretized [...]
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Multisensor Fault Diagnosis Leveraging Reinforced Evidential Jensen-Alpha Divergence under Dempster-Shafer Theory
Z. Liu, J. Liao, L. Wang, Y. Huang, K. Liu, H. Dhumras, W. Mbasso

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 53

Abstract
Uncertainty and conflicting information are pervasive in artificial intelligence (AI)-driven engineering systems, especially in multisensor fault diagnosis. Dempster-Shafer theory (DST) has garnered significant interest across various fields as it provides a powerful framework for modeling uncertainty. However, despite its advantages, the application of Dempster’s rule can lead to paradoxical outcomes when it encounters highly conflicting evidence. To address this limitation, this paper first presents a new evidential Jensen-alpha divergence (EJ AD) to quantify the discrepancy between the evidence items based on DST. Furthermore, an advanced version, the reinforced evidential Jensen-alpha divergence (REJ AD) is developed, which takes into account the quantity of potential propositions. We demonstrate thatREJ ADcan be transformed into various divergences such as the χ2divergence, Jensen-Shannon divergence, Hellinger distance, and arithmetic-geometric divergence under certain conditions. Also, we show the key properties ofREJ AD, including non-negativity, non-degeneracy and symmetry. Additionally, we design a new multisensor fault diagnosis method utilizingREJ ADand belief entropy. The superior performance of the proposed method is tested in three distinct fault diagnosis cases, and analysis shows robust performance across a range of its key parameter α, offering a computationally feasible, scalable and interpretable solution for AI-based decision-making in real-world engineering applications.OPEN ACCESS Received: 15/10/2025 Accepted: 17/11/2025
Abstract
Uncertainty and conflicting information are pervasive in artificial intelligence (AI)-driven engineering systems, especially in multisensor fault diagnosis. Dempster-Shafer [...]
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Computational Investigation of Fractal-Fractional Nonlinear Viscoelastic Fluids Using Local Radial Basis Function Method
H. Ahmad

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 54

Abstract
Fractal-fractional derivatives generalize both traditional and fractional differentiation approaches by integrating memory effects with fractal properties. This mathematical framework is especially valuable for describing complex systems in which conventional continuum mechanics becomes inadequate, particularly in scenarios involving porous or discontinuous structures. This research investigates the behavior of a non-linearWalter’s-B fluid subjected to time-varying thermal and concentration conditions. Beyond the extended derivative formulation, the analysis incorporates phenomena including first-order chemical reactions, radiative heat transfer, Joule heating, Soret effect, and viscous dissipation. Thesystem is also subjected to a transverse magnetic field with magnitude B0.The fluidmodel is initially formulated through traditional constitutive equations and subsequently generalized using a fractal-fractional operator. Solutions to this extendedmodel are computed employing ameshfree numerical approach utilizing localized radial basis functions (LRBF), which eliminates the requirement for structured grids and improves precision when addressing intricate geometries.The computational outcomes, displayed through graphical representations, illustrate how the fractional and fractal parameters influence the rheological characteristics of the Walter’s-B fluid. These findings establish that adjusting these parameters enables retrieval of classical, fractional, and fractal formulations as particular instances within this comprehensive mathematical structure.
Abstract
Fractal-fractional derivatives generalize both traditional and fractional differentiation approaches by integrating memory effects with fractal properties. This mathematical [...]
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How Can an Appropriate CFD Model be Developed for Turbulent Flow in Rough Pipes?: Evidence from Friction Factor Prediction
K. Boonsamer, B. Temsiriphan, P. Thongnoi, S. Areerat, E. Bumrungthaichaichan, S. Wattananusorn

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 55

Abstract
This paper answers the question: “How can an appropriate turbulent rough pipe flow computational fluid dynamics (CFD) model be developed?” The Reynolds-averaged Navier-Stokes equations with the standard k-epsilon turbulence model and scalable wall functions were solved to obtain Fanning friction factors and mean velocity profiles in inflectional and monotonic rough pipes. CFD models with near-wall grid sizes from four dimensionless wall distances and two roughness treatment approaches were simulated. Eight roughness Reynolds numbers, covering the lower end of the transitionally rough regime through the fully rough regime, were studied for each roughness type. Appropriate roughness and turbulence model constants for turbulent rough pipe flows in the transitionally rough regime were determined. For model validation, the predicted mean axial velocity profiles for Reynolds numbers of 5 × 104and 5 × 105exhibited good agreement with the reference experimental data. A total of 208 CFD simulations (32 from our previous works and 176 from the present study) were analyzed. Finally, based on comparisons between predicted Fanning friction factors and established correlations, appropriate CFD models for turbulent flows in inflectional and monotonic rough pipes were identified. Suitable CFD models for accurately predicting mean velocity profiles at roughness Reynolds numbers below 11.225 were also obtained, although with the caution that improved mean velocity prediction may reduce Fanning friction factor accuracy. Furthermore, the present CFD work provides essential guidance for extending simulations to other rough surface types and rough-wall flow situations.OPEN ACCESS Received: 25/11/2025 Accepted: 30/12/2025
Abstract
This paper answers the question: “How can an appropriate turbulent rough pipe flow computational fluid dynamics (CFD) model be developed?” The Reynolds-averaged [...]
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Applications of Artificial Intelligence in Bridge Structural Health Monitoring: A Systematic Review of the Last Decade
B. Silva, L. Vega, Y. Huaricallo

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 56

Abstract
Bridges are critical components of transportation networks whose structural integrity is often threatened by aging, environmental loads, and insufficient maintenance. Structural Health Monitoring (SHM) supported by Artificial Intelligence (AI) offers a transformative approach to early damage detection, predictive maintenance, and operational safety. This study presents a systematic literature review, conducted in accordance with PRISMA 2020 guidelines, on the application of AI algorithms to bridge SHM between 2015 and 2025. A total of 70 peer reviewed articles were analyzed, covering diverse geographic contexts, structural types, and sensing technologies. The review categorizes studies by AI technique (ANN, CNN, LSTM, SVM, hybrid models, and emerging methods such as Transformers and Graph Neural Networks), sensor architecture (accelerometers, fiber optic sensors, UAV based imaging, IoT modules), and performance metrics. Results indicate that convolutional and recurrent neural networks achieve detection accuracies above 95% and R2values exceeding 0.90 in displacement prediction, while hybrid approaches combining deep learning with traditional classifiers enhance robustness. Sensor integration with IoT and multimodal data fusion improves detection sensitivity, with correlation values above 0.99 in some cases. However, over 90% of studies lack robust cross validation, real world deployment, or standardized performance reporting, limiting replicability. This review highlights current trends, technical challenges, and research opportunities, including the need for interoperable sensor– algorithm platforms, explainable AI models, and broader implementation in developing regions. By consolidating existing knowledge, the study provides a technical reference for researchers, practitioners, and policymakers aiming to implement intelligent, predictive, and resource efficient bridge SHM systems.OPEN ACCESS Received: 27/08/2025 Accepted: 13/11/2025
Abstract
Bridges are critical components of transportation networks whose structural integrity is often threatened by aging, environmental loads, and insufficient maintenance. Structural [...]
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Smart Sensors and Artificial Intelligence for Urban Water Networks: A Systematic Literature Review (2015–2025)
N. Cruz, A. Cuba, Y. Huaricallo

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 57

Abstract
Efficient management of urban drinking water networks is challenged by population growth, rising consumption, and leakage-related losses. This study presents a Systematic Literature Review (SLR) following the PRISMA protocol, covering research published between 2015 and 2025 on smart sensors and advanced techniques for leak detection and consumption optimization. From 788 initial records, 40 studies met the inclusion criteria. Findings indicate that acoustic, pressure, fiber-optic, and hybrid sensing enable real-time monitoring and accurate leak localization, with typical error margins between±1% and ±5%, depending on sensor type and hydraulic conditions. A marked shift toward artificial intelligence (AI) and machine learning is observed for optimal sensor placement, event classification, and prediction, achieving >95% accuracy. The cost analysis reveals a direct relationship between technological sophistication and required investment. Overall, integrating smart sensors with AI provides a promising pathway toward more sustainable, efficient, and resilient urban water management.OPEN ACCESS Received: 06/09/2025 Accepted: 30/10/2025 The search strategy was constructed using combinations of keywords and Boolean operators, adjusted for each database to ensure consistency and reproducibility. The searches targeted titles, abstracts, and
Abstract
Efficient management of urban drinking water networks is challenged by population growth, rising consumption, and leakage-related losses. This study presents a Systematic [...]
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Monitoring Techniques for Structural Health of Roads Using Emerging Technologies: A Systematic Re-View of the Last Five Years
A. Quezada, Y. Huaricallo

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 58

Abstract
This systematic review examines the most recent techniques used to monitor the structural health of roadways, with a special focus on emerging technologies applied over the past five years. The progressive deterioration of road networks and the limitations of traditional inspection methods have driven the development of more precise, automated, and efficient solutions. The technologies analyzed include LiDAR laser scanning, drones equipped with computer vision, visual sensors, mobile cameras, ground-penetrating radar (GPR), and unmanned aerial vehicles (UAVs). Each technique was assessed based on its accuracy and the type of pavement distress it can identify, such as cracks, potholes, and surface deformations. The findings indicate that these tools enhance the efficiency and safety of inspections, enabling real-time data collection. Additionally, there is a growing trend toward the integration of artificial intelligence algorithms to automate data analysis. However, data heterogeneity and the need for cross-domain model adaptation may affect performance and scalability in large-scale or multi-source scenarios. Overall, this study provides an updated perspective on the application of emerging technologies in road infrastructure management, contributing to the development of innovative strategies for sustainable and intelligent roadway maintenance.OPEN ACCESS Received: 09/09/2025 Accepted: 09/12/2025 The search strategy was designed based on the PICOC framework, using the following Figure 1: Most frequent and trending
Abstract
This systematic review examines the most recent techniques used to monitor the structural health of roadways, with a special focus on emerging technologies applied over the [...]
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Integrability, Conservation Laws by Variational Analysis and Lump Solitons for (2+1) Fourth-Order Biharmonic Equations with Quantum Field Applications
B. Alqurashi, A. Raza

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 59

Abstract
We study the integrability via conservation laws and discuss the nonlinearity of the fourth-order biharmonic equations in (2+ 1) dimensions related to quantum field models based on the potential functions h(u). Lie symmetry reduction is performed, and the forms of the invariant solutions are presented, including travelling wave solutions. Variational analysis has been performed based on the various potential functions h(u). Corresponding Euler-Lagrange equations and conservation laws are investigated by Noether’s theorem and presented in the form of conserved vectors. The obtained conserved flows define energy, momentum and flow dynamics supporting the system integrability. Furthermore, detailed lump and breather solutions are presented for each potential h(u) using Bilinear forms illustrating various localized and oscillatory field characteristics.OPEN ACCESS Received: 08/11/2025 Accepted: 17/12/2025
Abstract
We study the integrability via conservation laws and discuss the nonlinearity of the fourth-order biharmonic equations in (2+ 1) dimensions related to quantum field models [...]
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On a Class of Hybrid Langevin Inclusions Involving Two Generalized Fractional Derivatives
A. Lachouri, M. Arab

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 60

Abstract
In this paper, we study the existence of solutions for a hybrid Langevin inclusion involving a combination of φ-Hilfer and φ-Caputo fractional derivatives. To this end, we construct a new operator derived from the integral solution of the given boundary value inclusion problem and subsequently apply the hypotheses of Dhage’s fixed point theorem to this fractional operator. Finally, to support our theoretical findings, an illustrative example is provided.OPEN ACCESS Received: 13/11/2025 Accepted: 20/01/2026
Abstract
In this paper, we study the existence of solutions for a hybrid Langevin inclusion involving a combination of φ-Hilfer and φ-Caputo fractional derivatives. To this [...]
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