Documents published in Scipedia

• 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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• 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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• An Integrated IVHFS and DEMATEL-ANP Framework for Competitive Intelligence Evaluation in Smart Factories

  W. Lo, M. Li, D. Huang, C. Yang, W. Deng, S. Li

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 40

  
  

  Abstract

  In the era of big data, the ability to evaluate high-quality and actionable competitive intelligence (CI) has become essential for smart factories to support data-driven decision-making and maintain technological and operational advantages. However, the highly dynamic and complex nature of the smart manufacturing environment introduces considerable uncertainty, hesitation, and interdependencies among evaluation indicators, posing significant challenges to traditional decision-making frameworks. To address these issues, this study proposes an integrated framework that combines interval-valued hesitant fuzzy sets (IVHFS) with the decision-making trial and evaluation laboratory-analytic network process (DEMATEL-ANP). IVHFS is employed to capture the ambiguity and hesitation inherent in expert judgments, enabling a more flexible and realistic representation of evaluation inputs. Subsequently, the DEMATEL-ANP approach is used to uncover the causal relationships among CI indicators and to construct a network-based weighting structure that reflects their interdependencies. A case study in a smart factory is conducted to validate the practicality and effectiveness of the proposed framework, and a sensitivity analysis confirmed its stability.OPEN ACCESS Received: 04/08/2025 Accepted: 28/10/2025 Published: 23/01/2026

  Abstract
  In the era of big data, the ability to evaluate high-quality and actionable competitive intelligence (CI) has become essential for smart factories to support data-driven decision-making [...]

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• Biological Solitons in Biomembranes: Analytical Solutions of a Boussinesq-Type Equation with Amplitude-Dependent Nonlinearity

  F. Abbas, A. Raza, F. Zaman, S. Baloch

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 38

  
  

  Abstract

  Boussinesq-type equations (BTE) emerge in various fields of fluid and solid mechanics, particularly where nonlinearities and dispersion are considered. Boussinesq-type equations are used to model wave effects in biomembranes, particularly longitudinal waves. They can account for nonlinear and dispersive effects that are important for characteristic wave behavior in biomembranes, composed of lipids, with distinct nonlinear effects. This provides a realistic description of longitudinal mechanical waves in nerve membranes. In this research, we investigate the Boussinesq-type equation that describes the waves in biomembranes with amplitude-dependent nonlinearities, using the Khater method (KM) and the Jacobi elliptic function method (JEFM). In addition to producing generic biological answers, the proposed methods allow the analysis of single wave solutions. These methods make it easier to derive solutions for solitary waves, which occur in a variety of forms, including bell, antibell, periodic, anti-kink and kink solitons. Each of these waves has a wide range of possible applications in biomathematics. Some of the findings are displayed as contour, 2D, and 3D graphics with particular parameter values applied under the specified conditions in order to highlight the important propagation properties. To the best of our knowledge, the biological solitons of the considered model have not been reported by using the proposed techniques in the literature. These results provide new theoretical insights into wave phenomena in biomembranes and may contribute to biological physics and nonlinear science.OPEN ACCESS Received: 04/11/2025 Accepted: 15/12/2025 Published: 23/01/2026

  Abstract
  Boussinesq-type equations (BTE) emerge in various fields of fluid and solid mechanics, particularly where nonlinearities and dispersion are considered. Boussinesq-type equations [...]

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• Fractional-Order Resilient Control for UAV–USV Cooperation under Actuator Constraints, Signal Attacks, and Wind Gusts

  Y. Qiao, S. Asghar, M. Arab, M. Awadalla, S. Trabelsi, A. Niazi

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 37

  
  

  Abstract

  The paper presents a resilient dynamic adaptive event-triggered sliding mode control (DAET–SMC) framework for fractional-order delayed multi-agent systems under actuator saturation, stochastic disturbances, and cyber-attacks. Existing methods often fail to ensure containment and formation stability when multiple practical constraints coexist. The proposed approach leverages Riemann–Liouville fractional dynamics to capture system memory effects and integrates adaptive compensation to mitigate actuator faults, measurement attacks, and communication delays. Numerical simulations on a 16-agent network with one leader and fifteen followers show that all followers achieve containment within 20 s, with formation errors below 10−2m, while maintaining bounded control effort. Compared with conventional non-adaptive controllers, the proposed method demonstrates faster convergence, superior robustness, and resilience under combined disturbances, achieving up to 35% faster error convergence and maintaining control input within saturation limits. These results confirm the effectiveness of the DAET–SMC strategy for practical multi-agent coordination in uncertain and constrained environments.OPEN ACCESS Received: 30/10/2025 Accepted: 26/11/2025 Published: 23/01/2026

  Abstract
  The paper presents a resilient dynamic adaptive event-triggered sliding mode control (DAET–SMC) framework for fractional-order delayed multi-agent systems under actuator [...]

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• Robust Neutrosophic Ratio-Type Estimators Using REWLSE: A Simulation-Based Approach for Efficient Mean Estimation under Outlier-Contaminated Data

  K. Abuhasel

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 36

  
  

  Abstract

  The exact estimations of population mean under the influence of indeterminacy and data contamination are a long-standing issue in survey sampling. Traditional ratio-type estimators are highly sensitive to influential observations, and the neutrosophic methods that are currently used do not effectively describe robustness in the face of uncertainty. The current research constructs a generalized family of neutrosophic robust ratio-type estimators that are developed in the context of Robust and Efficient Weighted Least Square Estimation (REWLSE) framework. Bias and mean square error (MSE) expressions are analytically derived for Ordinary Least Squares (OLS) and REWLSE frameworks in order to allow extensive comparisons between theory and efficiency. Monte Carlo simulations on neutrosophic data are systematically used to study the finitesample behavior of proposed estimators, and an empirical evaluation of these estimators is done using actual temperature data. The simulation and empirical evidence have repeatedly shown that suggested REWLSEbased neutrosophic estimators have significant efficiencies, they remain highly resistant to outliers, and perform better than OLS-based ones. These results support the effectiveness of the suggested framework and highlight its potential to become a powerful and trustworthy alternative to population mean estimation in uncertain, imprecise, and contaminated data environments.OPEN ACCESS Received: 13/10/2025 Accepted: 12/11/2025 Published: 23/01/2026

  Abstract
  The exact estimations of population mean under the influence of indeterminacy and data contamination are a long-standing issue in survey sampling. Traditional ratio-type estimators [...]

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• Robust Finite Population Mean Estimation under Outlier Contamination Using Adaptive UK’s Redescending M-Estimation

  K. Abuhasel

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 35

  
  

  Abstract

  The efficient estimation of population parameters under non-ideal data conditions remains a critical challenge in survey sampling. Traditional estimators based on ordinary least squares (OLS) often yield unreliable results when datasets contain outliers or deviate from normality. This study introduces a new class of ratio-type estimators that incorporate population parameters such as the median and decile mean and are developed under both OLS and UK’s redescending M-estimation frameworks. To further enhance robustness, an adaptive variant of the UK’s redescending M-estimator is proposed, which automatically adjusts its tuning constant based on the degree of contamination. Analytical derivations of bias and mean square error (MSE) confirm the superiority of the proposed estimators over their OLS counterparts. Empirical validation using realworld socio-economic survey data and extensive simulation studies across varying sample sizes, outlier rates, and distributional forms demonstrate that the adaptive UK’s redescending estimator achieves substantial efficiency gains and reduced bias, even under high contamination levels. The results establish the adaptive redescending M-estimation approach as a robust and computationally efficient alternative for finite population mean estimation in the presence of outliers.OPEN ACCESS Received: 10/10/2025 Accepted: 03/11/2025 Published: 23/01/2026

  Abstract
  The efficient estimation of population parameters under non-ideal data conditions remains a critical challenge in survey sampling. Traditional estimators based on ordinary [...]

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• Enhancing Wind Turbine Reliability: A Hybrid State-Space and Generative Approach to SCADA-Based Fault Detection

  A. Shaher, N. Khan, Z. Mushtaq, A. Hassan, M. Irfan, H. Alwadie, S. Dawsari, S. Rahman

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 34

  
  

  Abstract

  Wind turbine reliability is essential for the renewable energy sector, as failures in key parts such as gearboxes and main bearings lead to more than $10 billion in downtime and maintenance costs each year. Supervisory control and data acquisition (SCADA) systems can monitor turbines using signals such as vibration, power output, and wind speed; however, applying machine learning to this data type is challenging due to the presence of unbalanced fault types and complex time patterns. Previous research has explored physics-informed deep learning, digital twins, and contrastive learning, achieving noteable fault detection accuracy. However, challenges remain in detecting rare faults, dealing with imbalanced data, combining data sources, and model generalization. This study presents StateSpaceNetWithGen (SS-Gen), a hybrid model integrating state-space modeling for temporal dynamics with generative augmentation for class imbalance. Tested on a 35,000-sample SCADA dataset (2018–2019), SS-Gen achieved high accuracy (≈1.00) and F1-score (≈1.00) on this specific dataset, improving by 33% over baselines. To further validate the strengths of the proposed method, the methodology is validated on a second dataset with different distribution. These results support more reliable and interpretable wind turbine health monitoring and move the field toward stronger physics-informed and federated machine learning solutions.OPEN ACCESS Received: 06/10/2025 Accepted: 19/11/2025 Published: 23/01/2026

  Abstract
  Wind turbine reliability is essential for the renewable energy sector, as failures in key parts such as gearboxes and main bearings lead to more than $10 billion in downtime [...]

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• Adaptive Federated Fault Diagnosis Framework for Wind Turbine Reliability

  M. Irfan, N. Khan, M. Abubakr, Z. Mushtaq, H. Alwadie, A. Shaher, S. dawsari, S. Rahman

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 31

  
  

  Abstract

  Wind turbine reliability is critical for sustainable energy production, yet fault diagnosis faces challenges due to data privacy concerns, heterogeneous operational conditions, and resource constraints in distributed wind farms. Traditional centralized Machine Learning (ML) approaches struggle with these issues, necessitating decentralized solutions. This study introduces the Adaptive Federated Fault Diagnosis (AF2D) framework, a novel Federated Learning (FL) approach for wind turbine fault diagnosis that ensures data privacy while addressing non-i.i.d. data distributions. Using a dataset of 35 uniaxial vibration recordings from six turbines at the University of Mustansiriyah, AF2D leverages two key modules: Adaptive Model Aggregation (AMA) and Lightweight Model Optimization (LMO). AMA employs Jensen-Shannon divergence and cosine similarity to adaptively aggregate local model updates, mitigating data heterogeneity, while LMO applies structured pruning (60% filter reduction) and 8bit quantization to enable deployment on resource-constrained SCADA systems. Results show AF2D achieves 91.3% accuracy (±1.2%, 95% confidence interval), a 3.5% improvement over FedAvg (87.8%± 1.4%), with statistical significance (p < 0.05), and outperforms state-of-the-art methods like Clustered FL (88.5%) and Privacy-Preserving FL (87.2%). LMO reduces inference time by 64.44% and memory usage by 53.71%, enhancing edge deployment feasibility. However, the small dataset raises overfitting risks, and scalability tests reveal a threefold communication cost increase (54.5 to 150.6 MB) for 18 clients, mitigated by proposed compression (30%–50% reduction) and asynchronous updates (20%–40% overhead reduction). Privacy is maintained with a differential privacy guarantee of= 1.0, though advanced techniques like secure multiparty computation could achieve <1. Despite limitations in severe fault detection and dataset diversity, AF2D demonstrates robust performance. Future work includes integrating multi-modal data (SCADA, vibration, environmental), testing real-time deployment, and expanding federated datasets to enhance generalizability and scalability.OPEN ACCESS Received: 11/09/2025 Accepted: 16/10/2025 Published: 23/01/2026

  Abstract
  Wind turbine reliability is critical for sustainable energy production, yet fault diagnosis faces challenges due to data privacy concerns, heterogeneous operational conditions, [...]

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• A Novel Sin Model SMEx with Application on COVID-19 and Precipitation Data

  A. Alrumayh, H. Khogeer

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 33

  
  

  Abstract

  The present study proposes a new and flexible trigonometric extension of the moment exponential distribution, termed the Sine Moment Exponential (SMEx) distribution, developed using the sine-G family of distributions. This model offers an attractive alternative to well-known lifetime distributions by providing enhanced flexibility for analyzing lifetime datasets that exhibit leptokurtic or platykurtic behavior. Several statistical properties of the SMEx distribution are derived, including its moments, quantile function, mean residual life, and order statistics. To assess its performance, five different estimation approaches are applied, including Anderson-Darling estimation, maximum likelihood estimation, Cramervon Mises estimation, ordinary least squares estimation, and weighted least squares estimation. A detailed Monte Carlo simulation study is utilized to illustrate the estimation behavior of these considered estimation procedures. In the end, two datasets associated with COVID-19 and precipitation are utilized to illustrate the applicability and flexibility of the proposed distribution. It is found that the proposed distribution efficiently analyzed these datasets as compared to competitive distributions.OPEN ACCESS Received: 06/10/2025 Accepted: 28/10/2025 Published: 23/01/2026

  Abstract
  The present study proposes a new and flexible trigonometric extension of the moment exponential distribution, termed the Sine Moment Exponential (SMEx) distribution, developed [...]

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