Documents published in Scipedia

• Enhancing Wind Power Forecasting Using Hybrid Multi-Head Attention and 1-Dimensional Convolutional Neural Networks

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

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 32

  
  

  Abstract

  The accurate forecasting of wind power plays a veritable part in integrating renewable energy from wind turbines into power grids. Wind power, being a highly volatile mode of energy generation owing to temporal variations and complex weather patterns, renders reliable predictions essential for energy management and grid stability. In order to tackle this, we propose a hybrid Multi-Head Attention and 1D-Convolutional Neural Network (MHA-CNN) architecture that combines attention mechanisms and convolutional layers to capture both long-term dependencies and localized features in time-series data from a Supervisory Control and Data Acquisition (SCADA) system. The model effectively improves forecasting performance by attaining an R2score of 99.42 for hour-ahead and 96.52 for day-ahead predictions on a 50,540-sample, 10-min SCADA dataset using 5-fold chronological cross-validation, outperforming traditional methods without any manual feature engineering. The proposed method is also evaluated across multiple scenarios to assess the robustness of the proposed approach.OPEN ACCESS Received: 01/10/2025 Accepted: 10/11/2025 Published: 23/01/2026

  Abstract
  The accurate forecasting of wind power plays a veritable part in integrating renewable energy from wind turbines into power grids. Wind power, being a highly volatile mode [...]

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• Tuning Curvature in Quadratic Regression via Caputo Fractional Derivatives: Theory and Applications

  Y. Tandogdu, S. Ilgaz, M. Awadalla, Y. Yameni

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 30

  
  

  Abstract

  Classical regression can only examine the relation between response and predictor variables based on integer order calculus theory. What happens when non integer order calculus is considered is a field where a vast spectrum of studies can be undertaken. The purpose of this study introduces a novel fractional-order quadratic regression model grounded in the Caputo derivative framework, addressing the limitation and the rigidity of classical polynomial regression in adapting to the intrinsic curvature of data. The core innovation is the use of the fractional order ν as a tunable parameter for curvature-sensitive optimization. Our main contributions are fourfold: First, we establish a fundamental theoretical pillar by proving that the second-order Caputo derivative preserves the curvature direction of quadratic functions, enabling a principled optimization framework. Second, we rigorously demonstrate the model’s robustness by proving the existence and uniqueness of solutions via Banach’s fixed point theorem and establishing stability bounds through a fractional Grönwall inequality. Third, we develop a practical methodology to identify an optimal fractional order ν that minimizes the error-to-explained-variation ratio (SSE/SSR). Finally, we validate the framework on four diverse real-world datasets from air quality, soil science, education, and meteorology. The proposed model consistently outperforms classical quadratic regression, achieving a reduction in the SSE/SSR ratio by up to 21% in specific cases. The proposed method yields more efficient models with either lower estimation error or higher correlation coefficients, positioning Caputo fractional quadratic regression as a powerful and theoretically sound alternative for modeling cases where quadratic regression is considered appropriate.OPEN ACCESS Received: 10/09/2025 Accepted: 05/11/2025 Published: 23/01/2026

  Abstract
  Classical regression can only examine the relation between response and predictor variables based on integer order calculus theory. What happens when non integer order calculus [...]

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• Investigation of Compensated Foundation SettlementMechanism Based on FEM-DEM Coupling Method

  X. Zhang, L. Lv, M. Xu, G. Mei

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 39

  
  

  Abstract

  The application of compensated foundations is common in engineering, but significant settlements often occur during the application process. A foundation pit model supported by a rigid retaining wall was established based on the Finite Element Method-Discrete Element Method (FEMDEM), and a cantilevered layer-by-layer excavation process was simulated. A rolling resistance linear model was used to simulate the sand, while a variable particle size method was adopted to establish the foundation model. It is shown that during the excavation process of the foundation pit, the stress of the sand at the pit bottom gradually decreases, and the displacement of the soil changes gradually fromsettlement to uplift as one moves frombehind the retaining wall to the bottomof the foundation pit. Moreover, theporosityof the sandat thepit bottomgradually increases.As a result, the strength of the uplifted sand at the pit bottomdecreases due to over-excavation during the foundation pit excavation stage. The uplifted sand is finally excavated during the site leveling stage, resulting in a further decrease in the strength of the sand at the pit bottom. Finally, an inverted arch bottom plate structure is proposed to mitigate the over-excavation settlement of the compensated foundation.

  Abstract
  The application of compensated foundations is common in engineering, but significant settlements often occur during the application process. A foundation pit model supported [...]

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• A New Scalable Hybrid Model Approach of High-Dimensional Time Series Forecasting Applications

  N. Yaqoob, F. Alghamdi, A. Aloufi, R. Jabeen, A. Zaka

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 29

  
  

  Abstract

  This study introduces a Lasso–Prophet hybrid framework developed to deal with the limitations and gap of Facebook’s Prophet model. The approach begins with Prophet’s decomposition of a time series into its fundamental components trend, seasonality, and holiday effects, and then applies Lasso regression to the residuals to capture additional structural patterns that fail to capture by the base model. This layered methodology boosts predictive accuracy by enabling the model to learn both systematic and irregular variations within temporal data by incorporating Lasso’s feature selection capability, the framework efficiently handles highdimensional datasets, retaining only the most informative predictors. The outcome is a hybrid model which achieves an optimal balance among interpretability, scalability, sparsity, and forecasting precision. Validation on simulated high-feature datasets and real-world electricity consumption data demonstrates that the Lasso–Prophet hybrid consistently outperforms the Prophet and other baseline models.OPEN ACCESS Received: 31/08/2025 Accepted: 17/11/2025 Published: 23/01/2026

  Abstract
  This study introduces a Lasso–Prophet hybrid framework developed to deal with the limitations and gap of Facebook’s Prophet model. The approach begins with Prophet’s [...]

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• Qualitative Analysis of Nonlinear Systems Involving Hadamard-Type Fractional Derivatives with Nonlocal Boundary Conditions and Stability Properties

  M. Manigandan, M. Awadalla, R. Shanthi, S. Trabelsi

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 27

  
  

  Abstract

  This paper establishes a comprehensive analysis of a coupled system of nonlinear Hadamard-type fractional differential equations subject to generalized nonlocal integral boundary conditions. The distinct logarithmic kernel of the Hadamard derivative makes this framework particularly suitable for modeling scale-invariant processes and ultraslow diffusion phenomena. The existence and uniqueness of solutions are rigorously investigated using fixed point theory: Banach’s contraction principle ensures uniqueness, while the Leray-Schauder nonlinear alternative guarantees existence under more general growth conditions. Furthermore, the system is proven to be Ulam-Hyers stable, ensuring that approximate solutions remain close to exact solutions, which is crucial for the robustness of the model in practical applications. The theoretical findings are effectively validated through two detailed numerical examples, demonstrating the applicability of the established results to different classes of nonlinearities.OPEN ACCESS Received: 22/08/2025 Accepted: 03/11/2025 Published: 23/01/2026

  Abstract
  This paper establishes a comprehensive analysis of a coupled system of nonlinear Hadamard-type fractional differential equations subject to generalized nonlocal integral boundary [...]

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• Solving the Sine-Gordon Equation: A Novel Numerical Approach Using Cubic B-Splines and the Method of Lines

  I. Ashraf, M. Yaseeen, S. Trabelsi, M. Balti

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 28

  
  

  Abstract

  This work explores a numerical approach to solving the sine-Gordon equation using the method of lines combined with cubic B-spline interpolation. The sine-Gordon equation, a nonlinear partial differential equation, arises in various fields of physics and engineering, describing phenomena such as solitons in non-linear optics and magnetic flux lines in superconductors. In our approach the method of lines is used to discretize the spatial derivatives, thereby converting the partial differential equation into a system of ordinary differential equations. These ordinary differential equations are then solved numerically using standard techniques, specifically the Runge-Kutta method of order 4. Cubic B-spline interpolation is employed to approximate the spatial derivative, ensuring efficient and precise computation of the solution. A comprehensive stability analysis reveals that our scheme requires the time step conditiont1.53 h for numerical stability. Theoretical convergence analysis demonstrates that the method achieves O(h2)spatial convergence and O( t4)temporal convergence, resulting in an overall error bound of O(h2+ t4 ). These theoretical predictions are strongly supported by numerical experiments, where empirical convergence rates closely match the theoretical values. To validate the numerical scheme, the results are compared with existing solutions. Our findings demonstrate the accuracy and computational efficiency of the proposed method, highlighting its potential as a valuable tool for studying the dynamics and behavior of systems governed by the sine-Gordon equation.OPEN ACCESS Received: 29/08/2025 Accepted: 05/11/2025 Published: 23/01/2026

  Abstract
  This work explores a numerical approach to solving the sine-Gordon equation using the method of lines combined with cubic B-spline interpolation. The sine-Gordon equation, [...]

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• Combining Copula Theory and Machine Learning for Prediction of Ground Vibrations Induced by Tunnel Blasting

  Y. Cao, R. Ma, L. Zhang, X. Du, W. Liu, Q. Gao

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 26

  
  

  Abstract

  To effectively predict and control the peak particle velocity (PPV) induced by tunnel blasting, this study investigates the Qinhuangdao Jiaoshan Tunnel as a case study. This study first proposes an Improved Particle Swarm Optimization (IPSO) algorithm through theoretical derivation. Building upon IPSO, a further enhanced algorithm, termed CIPSO, is developed by integrating a dependency model derived from Copula theory. The CIPSO algorithm is then employed to optimize a Support Vector Regression (SVR) model, establishing the final CIPSO-SVR prediction framework. Copula theory was employed to quantify the correlation between PPV and surface cumulative settlement (S). A regularization term incorporating Kullback-Leibler (KL) divergence was then embedded into the SVR objective function. The Hyperparameters of the CIPSO-SVR model were optimized using fixed-step rolling cross-validation. The model’s predictive performance was rigorously compared against CIPSO-optimized Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM) models, as well as against SVR, CNN, and LSTM models optimized by the Grey Wolf Optimizer (GWO) and Moth-Flame Optimization (MFO) algorithms. The results show that the CIPSO-SVR model achieves superior accuracy and robustness on the test set (R2= 0.9569) in predicting PPV compared to the alternative models. Crucially, the model effectively captures the inherent nonlinear relationships of complex engineering problems, even with small-sample data.OPEN ACCESS Received: 18/08/2025 Accepted: 17/10/2025 Published: 23/01/2026

  Abstract
  To effectively predict and control the peak particle velocity (PPV) induced by tunnel blasting, this study investigates the Qinhuangdao Jiaoshan Tunnel as a case study. This [...]

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• Bearing Fault Diagnosis Based on AVMD and HPO-DBN

  X. Sha, F. Qian

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 25

  
  

  Abstract

  To overcome difficulties such as non-stationary vibrations, highdimensional feature redundancy, and mode selection issues that may arise during signal decomposition in bearing fault diagnosis. We propose an adaptive method called Adaptive Variational Mode Decomposition (AVMD) for extracting time-frequency domain characteristics from the bearing vibration displacement signals to the maximum extent possible. Next, the ReliefF algorithm is employed to select desired features, and an autoencoder is used to reduce the selected features dimensionally. Furthermore, because the Hunter-Prey Optimisation (HPO) algorithm can balance multiple objectives during the search process by utilising the concepts of hunter and prey to generate a better solution set, incorporating this algorithm into the Deep Belief Network (DBN) establishes an HPO-DBN fault diagnosis model. Subsequently, we validate the proposed method using both public datasets and field compressor data. Moreover, we compare the results with those obtained from the Support Vector Machine (SVM). The findings indicate that this approach enhances the bearing fault identification rate, thus supporting predictive maintenance of bearings.OPEN ACCESS Received: 13/08/2025 Accepted: 16/10/2025 Published: 23/01/2026

  Abstract
  To overcome difficulties such as non-stationary vibrations, highdimensional feature redundancy, and mode selection issues that may arise during signal decomposition in bearing [...]

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• Comparative Study of Fuzzy Logic, P&O, Incremental Conductance, and Artificial Neural Network MPPT Methods in Fluctuating Irradiance

  K. BOUJAGHAMA, N. Khaldi, R. Markazi, L. Amhaimar

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 24

  
  

  Abstract

  Photovoltaic (PV) energy is among the renewable and clean energies which are been widely used in recent years worldwide. To ensure optimal energy extraction under dynamic irradiance and temperature conditions, improving the efficiency of PV systems requires advanced Maximum Power Point Tracking (MPPT) techniques. To identify the most suitable technique that can be implemented practically, we conduct a comparative study in this paper between MPPT algorithms, namely Incremental Conductance (INC), Perturb and Observe (P&O), Fuzzy Logic (FL), and Artificial Neural Network (ANN). Using MATLAB/Simulink, our study was conducted under the same operating conditions, with a focus on efficiency, statistical analysis of robustness, and computational complexity. Our results show that the FL controller delivered the best overall performance, whose effectiveness depends on the accuracy of the rule base and scaling factors. It is characterized by a mean efficiency of 97.17%, a rapid response of 0.0585 s, minimal steady-state oscillations, and strong adaptability to environmental variations. The ANN-based approach achieves a mean efficiency of 94.91% and exhibits high performance at medium to high irradiance levels. However, its efficiency decreases significantly at low irradiance, resulting in reduced stability and increased deviation. INC and P&O achieve mean efficiencies of 95.20% and 95.15%, respectively. Moreover, due to their low computational cost, both techniques can be easily implemented. However, under rapidly changing conditions, they exhibit slower dynamics and more pronounced oscillations around the maximum power point, resulting in less stability.OPEN ACCESS Received: 01/08/2025 Accepted: 14/10/2025 Published: 23/01/2026

  Abstract
  Photovoltaic (PV) energy is among the renewable and clean energies which are been widely used in recent years worldwide. To ensure optimal energy extraction under dynamic [...]

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• Reliability Modeling Using Weibull Distribution in Partially Accelerated Life Tests with Unified Hybrid Censoring: White Organic LEDs and Micro-Droplet Applications

  O. Alqasem, M. Nassar, M. Elwahab, A. Elshahhat

  Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. 42, (1), 22

  
  

  Abstract

  Accelerated life testing has become essential in modern reliability assessment, particularly for high-reliability products where traditional testing is often impractical due to time constraints. This study introduces a comprehensive framework for reliability analysis using Weibull-based partially accelerated life tests under a unified hybrid censoring scheme. Assuming lifetimes follow a Weibull distribution, we provide both classical and Bayesian estimation procedures to estimate core quantities, shape, scale, and the acceleration factor, alongside reliability metrics at normal operating conditions. The inferential framework encompasses point estimation along with uncertainty quantification, using both approximate confidence intervals and Bayesian credible intervals derived from Markov Chain Monte Carlo methods. A comprehensive Monte Carlo simulation study evaluates the performance of various methods in terms of mean squared error, interval coverage, and average interval width across a range of censoring patterns. The results provide actionable insights and practical recommendations for selecting appropriate methods and designing future studies under different censoring scenarios. The proposed methodology is further illustrated through two real-world case studies: the reliability of white organic light-emitting diodes and the lifetime of micro-droplets in ambient environments. These examples highlight the method’s flexibility and practical relevance in both engineering and biomedical reliability applications.OPEN ACCESS Received: 31/07/2025 Accepted: 10/09/2025 Published: 23/01/2026

  Abstract
  Accelerated life testing has become essential in modern reliability assessment, particularly for high-reliability products where traditional testing is often impractical due [...]

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