Colloquiam: Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería

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

Jesús Sánchez Pinedo — Tue, 09 Dec 2025 10:06:13 +0100

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

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

Jesús Sánchez Pinedo — Fri, 19 Dec 2025 09:59:33 +0100

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

Adaptive Federated Fault Diagnosis Framework for Wind Turbine Reliability

Jesús Sánchez Pinedo — Fri, 19 Dec 2025 09:50:33 +0100

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

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

Jesús Sánchez Pinedo — Fri, 19 Dec 2025 09:48:23 +0100

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

Bearing Fault Diagnosis Based on AVMD and HPO-DBN

Jesús Sánchez Pinedo — Fri, 19 Dec 2025 09:45:24 +0100

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

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

Jesús Sánchez Pinedo — Fri, 19 Dec 2025 09:44:34 +0100

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

Research on Correction Method for Pipe-Soil p-y Curves in Submarine Silty Clay-Sand Gas Hydrate Formations

Jesús Sánchez Pinedo — Fri, 19 Dec 2025 09:41:34 +0100

The development of marine natural gas hydrates faces complex geomechanical challenges. Argillaceous silty hydrate reservoirs, due to their weak cementation and low permeability, have significantly different mechanical properties from those of general reservoirs. Based on the self-developed triaxial seepage experimental platform for hydrates, this paper systematically carried out triaxial compression experiments of argillaceous silt hydrate sediments, focusing on simulating the insitu temperature and pressure conditions of the formation, analyzing the influences of saturation, temperature and confining pressure on mechanical properties, and comparing them with the experimental results of sandy hydrate sediments. The experimental results show that due to the weak cementation effect of kaolin and methane hydrate, the failure mode of argillaceous silt hydrate is manifested as compression and dispersion, while sandy hydrate presents the traditional core compression failure characteristics. The peak strength of the stress-strain curve of argillaceous silt hydrate is lower than that of sandy hydrate, and the strain softening characteristic is more significant. The experimental results were calculated through MATLAB programming, and it was obtained that the cohesion and internal friction Angle of the argillaceous silt hydrate increased with saturation higher than those of the sandy hydrate. The pipe-soil coupling numerical simulation based on ABAQUS reveals that the initial stiffness and plastic deformation response of the p-y curve in the argillaceous silty hydrate formation are essentially different from those in the traditional API sandy soil model. By comparing the numerical simulation results of sandy properties and argillaceous silty hydrate, a two-parameter correction model for argillaceous silty strata was proposed. The cementation factor related to mass abundance and the displacement correction term were introduced. The error analysis indicated that the correction method was significantly superior to the API specification. Studies show that the mechanical properties of hydrates need to be evaluated independently, and the correction method provides a theoretical basis for the safety design of deep water well engineering.

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

Scipedia content — Mon, 29 Dec 2025 15:38:34 +0100

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

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

Jesús Sánchez Pinedo — Wed, 07 Jan 2026 11:22:23 +0100

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

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

Jesús Sánchez Pinedo — Wed, 07 Jan 2026 11:19:23 +0100

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

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

Jesús Sánchez Pinedo — Wed, 07 Jan 2026 11:18:23 +0100

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