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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Comparison with Different Bayesian and non-Bayesian Estimation Techniques for the Compound Rayleigh Exponential Distribution with Actuarial Measures and Applications
I. Alkhairy, H. Alsuhabi

Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. Online First, 75

Abstract
Many lifetime analysis, such as engineering, biology, survival, actuarial and medical sciences, heavily rely on the two-parameter compound Rayleigh exponential distribution, which is well-known in statistical theory. Because of their ability to successfully handle small sample sizes and involve prior knowledge, Bayesian techniques are crucial for estimating the parameters of the compound Rayleigh exponential distribution. This study presents the estimation of the compound Rayleigh exponential distribution unknown parameters using Bayesian and non-Bayesian estimation techniques, including maximum likelihood estimation, maximum product spacing, least square estimator, weighted least square estimator, Cramer-Von-Mise estimator, Anderson-Darling estimator, and Bayesian techniques with informative and non-informative priors based on different loss functions. Additionally, we used several methods to obtain the confidence intervals for the unknown parameters, such as the approximate and Bootstrap methods. The effectiveness of these estimators is evaluated through a Monte Carlo simulation study. Furthermore, we are committed to investigating three widely recognized risk metrics: the value at risk, the tail value at risk, and the tail variance premium. These findings are helpful for actuarial risk researchers who depend on risk measurement fitting when evaluating Bayesian tools for effectively modeling actuarial sciences. Finally, different applications taken from several areas are examined to illustrate the practical usefulness of the compound Rayleigh exponential distribution. Using various model selection criteria, the introduced model is contrasted with that of several well-known distributions. Our empirical findings indicate that the suggested model has superior goodness-of-fit to the other models examined.
Abstract
Many lifetime analysis, such as engineering, biology, survival, actuarial and medical sciences, heavily rely on the two-parameter compound Rayleigh exponential distribution, [...]
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Study on the Annular Pressure Prediction Method for Ultra-Deep Well Hydraulic Lift Dual-Gradient Drilling
Y. Chen, J. Yuan, K. Liu, J. Zhu, M. Li, H. Wang, Y. Li

Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. Online First, 86

Abstract
With the ongoing advancement of oil and gas exploration into deep and ultra-deep formations in China, precise wellbore pressure control under complex geological conditions has become a critical technical challenge for safe drilling operations. To overcome the limitations of existing dual-gradient drilling (DGD) technologies—particularly their poor applicability and limited pressure regulation capability in land-based drilling—this study introduces an innovative hydraulic-lift dual-gradient drilling annular flow model, tailored for ultra-deep vertical wells. The model accounts for solid–liquid phase separation flow characteristics and the hydraulic-lift effect of downhole dual-gradient pumps. The Stability Enhancing Two-Step (SETS) method is employed to solve the strongly nonlinear, coupled governing equations, significantly improving computational stability and efficiency. Experimental validation reveals that the model’s predicted pressure distribution closely matches measured data, with a maximum average error of only 16.4%, confirming the model’s accuracy and applicability. Additionally, this study systematically analyzes the impact of key parameters—such as drilling fluid flow rate, viscosity, lift pump speed, and the number of pump sections—on bottomhole pressure regulation, providing valuable insights into their influence on annular pressure behavior. The findings offer a solid theoretical foundation for optimizing drilling parameters and ensuring safe, efficient drilling in ultra-deep wells under challenging geological conditions.OPEN ACCESS Received: 16/07/2025 Accepted: 19/08/2025
Abstract
With the ongoing advancement of oil and gas exploration into deep and ultra-deep formations in China, precise wellbore pressure control under complex geological conditions [...]
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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. (2025). Vol. Online First, 87

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
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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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. Online First, 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. Online First, 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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Research on Correction Method for Pipe-Soil p-y Curves in Submarine Silty Clay-Sand Gas Hydrate Formations
H. Diao, Y. Xia, B. Wu, F. Ban, L. Fu, H. Yang, K. Wang, A. He, X. Wang, P. Fu, H. Wang, C. Li, S. Deng

Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. Online First, 88

Abstract
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.
Abstract
The development of marine natural gas hydrates faces complex geomechanical challenges. Argillaceous silty hydrate reservoirs, due to their weak cementation and low permeability, [...]
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