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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Hierarchical Convolutional Neural Network for Emotion Recognition Using EEG and Facial Expressions
M. Shafiq, S. Awan, T. Kamal

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 112

Abstract
Emotion recognition is crucial for advancing human–computer interaction (HCI) by enabling systems to interpret complex affective states. While Electroencephalogram (EEG) signals provide direct insights into neural activity, facial expressions offer external emotional cues. However, unimodal systems often struggle with robustness and generalization across diverse subjects. This study presents a Hierarchical Convolutional Neural Network (HCNN) framework that integrates EEG and facial expressions through multi-level convolutional feature extraction and featurelevel fusion. The proposed model combines deep hierarchical representations with handcrafted temporal–frequency and texture-based descriptors to form a unified feature vector. Experiments on the MAHNOB-HCI and DEAP datasets show that the HCNN achieves accuracies of 91.40% and 88.09%, outperforming CNN-, LSTM-, and SVM-based methods. The results demonstrate the model’s ability to effectively capture complementary cross-modal correlations while reducing feature redundancy and computational complexity. The HCNN framework shows great promise for real-time emotion recognition applications, offering a scalable, interpretable, and data-efficient solution for multimodal emotion recognition in next-generation HCI systems.
Abstract
Emotion recognition is crucial for advancing human–computer interaction (HCI) by enabling systems to interpret complex affective states. While Electroencephalogram (EEG) [...]
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Hybrid Fractional Coupled Systems with Generalized Caputo Derivatives
D. Alhwikem, M. Awadalla

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 117

Abstract
This paper establishes a comprehensive theoretical framework for a novel coupled system of nonlinear hybrid fractional differential equations involving generalized Caputo derivatives. The system’s hybrid nature, coupled with the generality of the fractional operators, allows for modeling complex interdependent processes with memory effects that cannot be adequately captured by existing models. Using Krasnoselskii’s fixed point theorem, we prove the existence of at least one solution under explicit coupling conditions. Under appropriate Lipschitz conditions, we establish uniqueness via Banach’s contraction principle, deriving a quantitative condition involving the fractional orders, generalization parameters, and Lipschitz constants. We also conduct a rigorous analysis of Ulam-Hyers and Ulam-Hyers-Rassias stability, obtaining explicit stability constants that provide quantitative bounds on how perturbations in the input affect the solution. The theoretical results are validated through three carefully constructed numerical examples with explicit parameter values demonstrating existence, uniqueness, and Ulam-Hyers stability. A parameter sensitivity analysis confirms the robustness of the uniqueness condition across variations in fractional orders, generalization parameters, and interval lengths. The paper concludes with a discussion of limitations and directions for future research, including extensions to higher fractional orders, delay and impulsive effects, and numerical methods.
Abstract
This paper establishes a comprehensive theoretical framework for a novel coupled system of nonlinear hybrid fractional differential equations involving generalized Caputo [...]
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Efficient Mean Estimation Using Repeated Measurements in PPS Sampling with Scientific Applications
M. Azeem, S. Hussain, N. Salahuddin, F. Idrees

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 128

Abstract
Research studies in many scientific disciplines need efficient estimation methods for estimating the parameters of quantitative variables, including, but not limited to, tensile strength, wind speeds, air quality, and temperature, etc. Statisticians employ a sampling design to get a random sample and estimate the population means based on the observed sample. If the units of a finite population have different selection probabilities, unequal probability methods of sample selection are used. The existing unequal probability sampling methods allocate probabilities proportional to size (PPS) to the population units by using a one-time measurement approach. Memory– type estimation methods, on the other hand, use multiple measurements and provide more precise estimates than the traditional estimators. This research study introduces a novel memory-type estimator using a PPS sampling design. Various properties of the suggested mean estimator are analyzed, and the efficiency conditions are derived. A few real-world data sets have been used from previous studies to evaluate the performance of the suggested and competing mean estimators. Our comparative study suggests that the suggested memory-based estimator performs much better than the competing estimators, which means that the suggested memory-type estimator is an appropriate estimator for application in real-life sample surveys.
Abstract
Research studies in many scientific disciplines need efficient estimation methods for estimating the parameters of quantitative variables, including, but not limited to, tensile [...]
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Enhancing Few-Shot Text Classification with Parameter-Efficient Tuning of Large Language Models
M. Zhao, Y. Sun, X. Fan, Y. Tian

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 129

Abstract
Traditional few-shot text classification models focus only on label prediction and cannot extract structured information such as entities or events, limiting their usefulness in real-world, semantics-driven tasks. They also rarely use external knowledge or parameter-efficient tuning, leading to shallow representations and weaker performance. To address this, this paper proposes a knowledge-aware multi-task framework that integrates few-shot classification with entity and event extraction. A single BERT encoder with IA3 adapters enables efficient tuning, while semantic triples extracted via spaCy and aligned with WordNet and ConceptNet are encoded using TransE. A BiLSTM captures sequential context and a softmax decoder performs token-level prediction. Experiments show strong results—97.97% accuracy, 98.00% precision, 97.95% recall, and 97.96% F1—surpassing state-of-the-art baselines. Ablation studies confirm the value of the knowledge-enhanced, multi-step design, demonstrating suitability for lowresource, knowledge-centric applications.
Abstract
Traditional few-shot text classification models focus only on label prediction and cannot extract structured information such as entities or events, limiting their usefulness [...]
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AI-IoMT Synergy: A Real-Time Framework for Automated Urinary Tract Infections (UTI) Detection Based on Urine Sediments
A. Ibrahim, M. Ahmed, I. Ame, C. Nwekwo, F. Hassan, S. Asir, S. Tackie, F. Al-Turjman, J. Idoko

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 130

Abstract
A Urinary Tract Infection (UTI) is characterized by an infection affecting the urinary system, including the kidneys, bladder, urethra, and ureters, with clinical presentations including pyelonephritis, cystitis, and urethritis. While conventional diagnostic methods such as urinalysis and urine culture and sensitivity (C&S) remain widely used, they are limited by subjectivity, time-intensive processing, susceptibility to contamination and risks of false-positive or false-negative results. This study proposes a comprehensive deep learning (DL) and Internet of Things (IoMT) framework to automate the real-time detection and classification of UTIs using microscopic urine sediment images. The study employed 2 datasets (A and B). Dataset A, a clinically acquired dataset, comprises of 3345 images (normal, erythrocytes, fungi and pus) and Dataset B, a publicly accessible data comprises of 5377 images and 26,419 cropped microscopic images corresponding to 7 classes (casts, crystals, erythrocytes leukocytes, epithelial cells, epithelial nuclei, mycetes). A two-stage classification approach was implemented: a binary task to distinguish urine sediments from normal cases, followed by a multiclass task (clinical data and online data) to identify the specific infection type. All images underwent pre-processing, including normalization, resizing, noise removal, and augmentation to enhance feature visibility and model generalizability. The data were partitioned into training (65%), validation (25%), and test (10%) sets. Six state-of-the-art DL architectures, including ResNet50-V2, ResNet101-V2, Inception-V3, XceptionV2, Inception-ResNet-V2, and VGG19 were fine-tuned using transfer learning and evaluated using accuracy, precision, recall, F1-score, and confusion matrices. The proposed models were uploaded to a website to enable realtime detection (accessible via this link: https://uticlassification.app/). The proposed pipeline demonstrated strong performance in both classification tasks, underscoring the potential of deep learning as a reliable, rapid, and reproducible tool for automated urine sediment identification in clinical practice.
Abstract
A Urinary Tract Infection (UTI) is characterized by an infection affecting the urinary system, including the kidneys, bladder, urethra, and ureters, with clinical presentations [...]
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Carbon-Aware Last-Mile Delivery Optimization using Sparrow search algorithm and graph neural network risk assessment
J. Xu, L. Yuan, X. Du

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 134

Abstract
With the advancement of global carbon neutrality strategies and explosive growth in e-commerce, urban last-mile delivery faces multiple challenges in balancing economic benefits, environmental impact, and risk management. Traditional optimization methods struggle to simultaneously address multi-objective trade-offs, network topological dependencies, and small-sample risk prediction problems. This study proposes a hybrid intelligent framework integrating an Improved Sparrow Search Algorithm (ISSA) with a Meta-Learning Graph Convolutional Network on Prototype Space (ML-GCNPS) for carbon-aware delivery optimization and risk assessment. ISSA-NSGA-III generates high-quality initial populations through Tent chaotic mapping, designs an adaptive periodic convergence factor to dynamically balance exploration and exploitation, and enhances global search capability by integrating Lévy flight with Elite Opposition-Based Learning (EOBL), achieving multi-objective collaborative optimization through embedding in the NSGA-III framework. ML-GCNPS designs a feature extraction network to extract discriminative features from multi-modal node data, explicitly models class centers through prototype space embedding to enhance small-sample generalization, constructs an adaptive Vertex-to-Edge (V2E) network to dynamically infer edge weights and capture risk propagation paths, and employs a two-layer graph convolutional architecture for sufficient information propagation. Experiments on the Kaggle Supply Chain Management dataset and Carbon Monitor risk dataset demonstrate that compared to standard SSA, ISSA-NSGA-III improves total cost, carbon emissions, and resource utilization by 14.0%, 14.2%, and 15.4%, respectively, with Pareto front quality improved by 28.5%. ML-GCNPS achieves an AUPRC of 0.850 (standard deviation 0.005) and a Macro Fl-Score of 0.850 (standard deviation 0.005) in 5-way 1-shot scenarios, reduces the False Negative Rate (FNR) to 0.080 (standard deviation 0.003), and achieves a Weighted Average Cost (WAC) of 45, significantly outperforming baseline methods such as ProtoNG and MAML-GNN (paired t-test, p less than 0.01 for AUPRC and FNR versus the second-best baseline GAT-FSL). Ablation experiments validate the necessity of the meta-learning framework, graph convolutional structure, V2E network, and prototype space embedding, while alternative design comparisons demonstrate the superiority of the technical choices. While the individual algorithmic components (Tent chaotic mapping, Lévy flight, EOBL, prototypical networks, and GCN) are established techniques, the principal contribution of this study líes in their systematic integration into a closed-loop optimization-assessment-feedback decision framework, where graph structure serves as an information bridge connecting delivery optimization with risk prediction. This study provides a teclmical solution for smart city logistics and offers theoretical basis and practica! guidance for sustainable delivery under carbon neutrality goals. All reported improvements over baseline methods are statistically significant across all evaluation metrics (paired t-test or Wilcoxon rank-sum test, p < 0.001
Abstract
With the advancement of global carbon neutrality strategies and explosive growth in e-commerce, urban last-mile delivery faces multiple challenges in balancing economic benefits, [...]
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Rainfall Trend Analysis and One-Dimensional Hydrodynamic Assessment of the Ganga River Basin Using HEC-RAS 6.3
G. Goswami, M. Alsubih, S. Islam, S. Basack, P. Borah

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 140

Abstract
This study integrates long-term rainfall trend analysis with one-dimensional hydrodynamic modelling to assess hydro-climatic variability and flood vulnerability along the selected stretch of the Ganga River near Farakka Barrage, eastern India. Daily gridded rainfall data for 1991–2025 were analyzed to identify trends and potential change points. The Mann–Kendall test, Sen’s slope estimator, Bias-Corrected Pre-Whitening, and Trend-Free Pre-Whitening were applied to account for serial correlation. The rainfall series showed an overall decreasing tendency, although statistical significance varied among the applied trend tests after pre-whitening. HEC-RAS 6.3 simulations showed increasing water surface elevation, velocity, and discharge under 25-, 50-, and 100-year design-flood scenarios. The findings indicate that flood risk in the study reach is shaped by both hydro-climatic variability and local hydraulic controls.
Abstract
This study integrates long-term rainfall trend analysis with one-dimensional hydrodynamic modelling to assess hydro-climatic variability and flood vulnerability along the [...]
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Multivalued Fixed Point Methods for Sequential Coupled Caputo-Type Fractional Differential Inclusions with Coupled Boundary Conditions
M. Arab, E. Krishnasamy, S. Trabelsi, M. MURUGESAN

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 153

Abstract
We study a coupled system of sequential Caputo-type fractional differential inclusions with two-point integral boundary conditions. Using fixed-point techniques for multivalued operators, existence results are established under Carathéodory-type and Lipschitz-type assumptions on the multifunctions. The obtained results extend several known solvability criteria for fractional differential inclusions with nonlocal boundary conditions. An example is included to illustrate the applicability of the theoretical results.
Abstract
We study a coupled system of sequential Caputo-type fractional differential inclusions with two-point integral boundary conditions. Using fixed-point techniques for multivalued [...]
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Dynamic Mechanisms and Multiparameter Control of Fracture-Induced Lost Circulation in Deep Wells—A Fluid-Solid Coupling Approach
P. Fu, Y. Guan, Q. He, J. Wang, B. Zheng

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 158

Abstract
Deep and ultra-deep well drilling in multi-scale fractured formations frequently encounters fracture-induced lost circulation, which restricts drilling efficiency and reservoir development. To address this problem, this paper establishes a dynamic finite element numerical model based on fluid-solid coupling theory, revealing the multi-physics coupling mechanism of fracture propagation and leakage channel evolution. The model fully considers the seepage-stress coupling effect during drilling fluid circulation, and quantitatively analyzes the influences of pump rate, fluid density, fluid viscosity, fracture geometric parameters, elastic modulus, Poisson’s ratio and in-situ stress on fracture aperture and fluid loss rate. The research results show that: pump rate and fluid density are positively correlated with loss rate and fracture aperture; fluid viscosity presents two-stage regulation characteristics, which is negatively correlated with leakage parameters at the fracture initiation stage and positively correlated in steady-state leakage stage; longer fracture length increases loss rate but reduces fracture aperture; elastic modulus, Poisson’s ratio and in-situ stress mainly affect the early leakage behavior, with little influence on steady-state stage. The proposed multi-parameter coupling control model can realize dynamic prediction of multi-fracture leakage in deep wells, and provides theoretical support for on-site anti-leakage and plugging work.
Abstract
Deep and ultra-deep well drilling in multi-scale fractured formations frequently encounters fracture-induced lost circulation, which restricts drilling efficiency and reservoir [...]
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A Robust Ensemble Learning Paradigm for Breast Cancer Diagnosis Based on Multi-Classifier Performance Optimization
A. Waqar, M. Abbass, Z. Mushtaq, M. Mariam, A. Iram, M. Taha, M. Jamil

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 157

Abstract
Breast cancer is among the major causes of cancer-related mortality in women, and early diagnosis is critical to improved survival. However, traditional diagnostic methods or standalone models often lack precision and have the potential to give false-negative results. This study aims to present a hyperparameter-tuned ensemble learning model for the classification of breast benign and malignant tumors based on the Wisconsin Breast Cancer (Original) dataset. Data quality was ensured through a series of preprocessing techniques: median imputation, Zscore standardization, and the Local Outlier Factor (LOF) noise reduction algorithm. The classical Machine Learning (ML) models (SVM, Random Forest (RF), XGBoost, Bagging) were compared with the Deep Learning models (VGG16 and DenseNet121). A hybridized soft-voting ensemble of the four classical classifiers (SVM, RF, XGBoost, and Bagging) was then constructed, and its hyperparameters were tuned with the OPTUNA framework using the Treestructured Parzen Estimator (TPE), a Bayesian optimization algorithm, over 30 trials. The results of the experiments demonstrated that the Ensemble + OPTUNA model performed with an accuracy of 99.25% and a recall of 1.00 for the malignant class compared to the individual models and recent state-of-the-art methods. This is an optimized ensemble for reliable and computationally stable performance. To enhance transparency and privacy-preserving validation in clinical settings, Explainable AI (XAI) will be incorporated into future research, while Federated Learning will be enhanced to better validate the model.
Abstract
Breast cancer is among the major causes of cancer-related mortality in women, and early diagnosis is critical to improved survival. However, traditional diagnostic methods [...]
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A Mixed-Integer Numerical Optimization Framework for Reliability-Driven Energy Storage System Configuration in Power Grids
M. KAMAL, H. Khan, T. Ma, H. Samkari, M. Allehyani, H. Mohamed

Rev. int. métodos numér. cálc. diseño ing. (2026). Vol. Online First, 159

Abstract
This paper introduces a numerical optimization model (mixed-integer) of reliability-based design of energy storage systems (ESS) in the highrenewable-based power grid. This is done by developing a mixed-integer nonlinear programming (MINLP) model that incorporates probabilistic reliability indices (Loss of Load Probability and Expected Energy Not Supplied) directly into the objective function and also optimizes ESS sizing, placement, and operational scheduling. An approach that is a hybrid solution strategy that incorporates outer approximation and metaheuristic enhancement is used to deal with non-convexities in reliability calculations and modelling of storage degradation. Convergence analysis demonstrates that the algorithm attains optimality gaps of less than 3.5% in 150 iterations, 18–22 times more efficient than standard solvers, computationally. It has been shown with a 320 MW peak load benchmark system based on the IEEE 118-bus topology under five operating conditions that the optimized ESS configuration saves Loss of Load Probability from 0.0214 to 0.0062 (71% improvement), as well as Expected Energy Not Supplied from 1245 to 358 MWh/year, and unnecessary ESS cycling is reduced by 29%. The framework provides system planners with a computationally manageable tool to optimally deploy ESS in a renewable-dominated grid.OPEN ACCESS Received: 12/03/2026 Accepted: 29/06/2026
Abstract
This paper introduces a numerical optimization model (mixed-integer) of reliability-based design of energy storage systems (ESS) in the highrenewable-based power grid. This [...]
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