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

  A. Anwar, N. Khan, Z. Mushtaq, A. Hassan, M. Irfan, H. Alwadie, S. dawsari, S. Rahman

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. Online First, 3

  
  

  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

  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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• 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. (2025). Vol. Online First, 2

  
  

  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

  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. (2025). Vol. Online First, 1

  
  

  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

  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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• 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. (2025). Vol. Online First, 95

  
  

  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

  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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• An Enhanced Pilot Aided Channel Estimation in XL-MIMO Communication Systems Using Bitterling Swallow Fish Optimization

  M. Kamal, S. Abideen, Y. Luo, A. Hussein, H. Samkari, M. Alleyani, T. Ma

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (4), 94

  
  

  Abstract

  The continuous evolution of 6th Generation (6G) wireless networks places Extremely Large-scale Multiple-Input Multiple-Output (XL-MIMO) schemes as a crucial enabler for ultra-reliable and high data rate communication. Channel estimation in XL-MIMO is crucial here because it allows the system to precisely recognize the wireless channel conditions between the transmitter and receiver, which is vital for enhancing signal processing, and resource allocation. Traditional pilot-aided channel estimation approaches face challenges, such as high error. Hence, this work proposes an innovative model called the Deep Kronecker Network-Bitterling Swallow Fish Optimization Algorithm (DKN-BSwaFOA) for pilot-aided channel estimation in XL-MIMO systems. Initially, the system model of XL-MIMO is contemplated. The pilot insertion is done at the transmitter, and the location of the pilot symbol is optimally selected using BSwaFOA. The signal is propagated over the hybrid field channel, where both farfield and near-field components coexist. At the receiver, the channel is estimated using DKN, which is trained using the proposed BSwaFOA. The experimental outcomes demonstrated that the DKN_BSwaFOA computed the minimum Root Mean Square Error (RMSE), Bit Error Rate (BER), and Mean Square Error (MSE) of 0.030, 0.002, and 0.001.OPEN ACCESS Received: 23/09/2025 Accepted: 11/11/2025

  Abstract
  The continuous evolution of 6th Generation (6G) wireless networks places Extremely Large-scale Multiple-Input Multiple-Output (XL-MIMO) schemes as a crucial enabler for ultra-reliable [...]

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• Entropy-Guided k-Core Pruning Balancing Redundancy Reduction and Information Preservation for Efficient CNN Compression

  Y. Yang, D. Jiang, X. Deng, L. Wang

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (4), 93

  
  

  Abstract

  Convolutional Neural Networks (CNNs) are widely used in computer vision, but their massive computational cost and parameter redundancy hinder deployment on resource-constrained devices (e.g., edge terminals). Existing filter pruning methods often struggle to balance two critical goals: aggressive redundancy reduction and effective preservation of taskcritical information—either leading to excessive accuracy loss or insufficient compression. To address this challenge, we are the first to jointly exploit k-core decomposition and information entropy in a unified pruning criterion, and we instantiate this idea in a novel graph–entropy collaborative framework that achieves Pareto-optimal compression-accuracy trade-offs. The key steps are as follows: First, we use perceptual hashing (pHash) to calculate the similarity of output feature maps between filters, then model each filter as a node in an undirected graph—edges are established only when filter similarity exceeds a predefined threshold, forming a “redundancy graph” that quantifies inter-filter redundancy. Second, kcore decomposition is applied to this graph to identify high-order redundant substructures, which helps locate redundant filters at the structural level. Finally, information entropy is introduced to evaluate the “informational value” of each node (filter) in the k-core: only filters with low redundancy and high information content are retained, ensuring minimal loss of critical features. Extensive experiments are conducted on CIFAR10 and CIFAR-100 datasets, using representative CNN architectures (VGGNet-16, ResNet-56/110, DenseNet-40). Specifically, VGGNet-16 achieves a 65.8% reduction in floating point operations (FLOPs) and an 88.8% reduction in parameters while experiencing only a 1.24% decrease in Top-1 accuracy. ResNet-56 attains a 50.1% reduction in FLOPs with a nearly imperceptible accuracy loss of 0.03%, markedly surpassing the Fire together wire together (FTWT) method which reduces FLOPs by 54% at the cost of a 1.38% accuracy decline. DenseNet-40 accomplishes a 76.5% FLOPs reduction with a 1.55% accuracy decrease, demonstrating the method’s strong applicability for high-intensity compression of densely connected networks. Furthermore, the method’s scalability is validated on the large-scale ImageNet dataset with ResNet-50, where it achieves a 73.65% FLOPs reduction with competitive accuracy, underscoring its practicality for real-world applications. These outcomes collectively affirm the effectiveness and broad applicability of the proposed graphentropy collaborative pruning framework.

  Abstract
  Convolutional Neural Networks (CNNs) are widely used in computer vision, but their massive computational cost and parameter redundancy hinder deployment on resource-constrained [...]

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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. (2025). Vol. Online First, 92

  
  

  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

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

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

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. Online First, 91

  
  

  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

  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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• Bearing Fault Diagnosis Based on AVMD and HPO-DBN

  X. Sha, F. Qian

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. Online First, 90

  
  

  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

  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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• Research on the Mechanical Characteristics and Structural Optimization of HighPressure Diaphragm Compressors in Hydrogen Refueling Stations under Service Conditions

  M. Li, L. An, W. Hu, Y. Hou, Z. Wang

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. Online First, 89

  
  

  Abstract

  To enhance the fatigue life and service safety of the diaphragm in high-pressure diaphragm compressors, this study investigated the realworld operating conditions of hydrogen refueling station diaphragm compressors. A refined finite element model of the gas cavity cover plate–diaphragm–oil cavity support plate assembly was established using Abaqus software. Static structural analysis, thermo-structural coupling analysis, and modal analysis were conducted to examine the stress distribution of the diaphragm assembly under extreme working conditions, the influence of bolt preload on the modal characteristics of the compressor, and the effect of diaphragm thickness on stress distribution and fatigue life. The research results indicate that air holes/passages and oil holes/passages significantly affect the stress distribution of the diaphragm. The high-stress areas of the diaphragm are mainly concentrated in the transition zone of the chamber and the overlapping area between the diaphragm and the air/oil passages. The temperature inside the diaphragm compressor’s membrane chamber significantly affects the stress level of the diaphragm. When the chamber temperature reaches 245°C, the maximum equivalent stress of the diaphragm reaches 1079 MPa. As the preload increases, the modal frequencies generally rise, with higher-order modes showing greater sensitivity to preload variations. Considering the stress level, fatigue life, and deflection performance of each diaphragm, the diaphragm thickness should be designed to be 0.4 mm. The finite element simulation model and research results proposed in this paper can provide a reference for the design improvement and selection of cavity types and diaphragms of diaphragm compressors in hydrogen refueling stations, as well as for the online health monitoring of hydrogen refueling stations.OPEN ACCESS Received: 31/07/2025 Accepted: 09/09/2025

  Abstract
  To enhance the fatigue life and service safety of the diaphragm in high-pressure diaphragm compressors, this study investigated the realworld operating conditions of hydrogen [...]

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