Documents published in Scipedia

• 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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• On Observer-Based Control of One-Sided Lipschitz ω-Tempered Fractional-Order Systems under Input Saturation

  S. Afli, A. Jmal, O. Naifar

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (4), 71

  
  

  Abstract

  This paper addresses the critical challenge of observer-based control for one-sided Lipschitz (OSL) nonlinear systems governed by tempered fractional-order dynamics under input saturation constraints. We introduce a novel stability framework combining ω-tempered Caputo derivatives with Mittag-Leffler stability theory, enabling significantly faster exponential error decay compared to classical fractional operators. The proposed methodology features three key innovations: (1) a tempered Mittag-Leffler stability theorem incorporating sector-bounded saturation nonlinearities, (2) linear matrix inequality (LMI) conditions accommodating arbitrary OSL constants (ρ∈ R), and (3) a Cone Complementary Linearization (CCL) algorithm resolving gain synthesis challenges in tempered fractional systems. Numerical validation demonstrates 62% faster convergence than classical fractional approaches while maintaining saturation constraints. The CCL algorithm provides guaranteed convergence with computational efficiency, overcoming initialization sensitivity through regularization techniques.OPEN ACCESS Received: 05/06/2025 Accepted: 15/08/2025 Published: 27/10/2025

  Abstract
  This paper addresses the critical challenge of observer-based control for one-sided Lipschitz (OSL) nonlinear systems governed by tempered fractional-order dynamics under [...]

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• Numerical Simulation, Physical Modeling and Plant Trial on the Slag Entrapment Behavior in a Four-Strand Tundish

  B. Qin, J. Zhang, J. Chen, C. Gao, X. Zuo, Q. Liu

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (4), 70

  
  

  Abstract

  The continuous casting process yields more than 96% crude steel worldwide. Numerical simulation and physical modeling were employed to investigate the slag entrainment behavior during the final casting stage in a four-strand continuous casting tundish. It is demonstrated that the numerical and physical modelling results agree well. Vortex formation in the final casting stage can be divided into four distinct stages: surface rotation, vortex generation, vortex development, and vortex penetration, with significant variations in critical slag entrainment depths observed among different outlets. Increasing casting speed increases slag entrainment risks, while employing vortex inhibitors could reduce the critical slag entrainment height by up to 29%. Through optimized casting termination procedures in a plant trial, the tundish residual depth decreased from 400 to 200 mm; The tail-end billet cleanliness significantly improved to reach a normal billet quality level in the end billet range of 2–3 m. This study provides theoretical and technical support for reducing slag entrainment defects and improving steel cleanliness in continuous casting.OPEN ACCESS Received: 15/05/2025 Accepted: 10/07/2025 Published: 27/10/2025

  Abstract
  The continuous casting process yields more than 96% crude steel worldwide. Numerical simulation and physical modeling were employed to investigate the slag entrainment behavior [...]

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• A Comparative Analysis of the Boundary Condition Schemes for an Immersed Cylinder in a Water Stream with the Lattice Boltzmann Method

  F. Garzeri, I. Martins, L. Cabezas-Gómez

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (4), 69

  
  

  Abstract

  In this paper, we investigate the performance of different boundary condition (BC) schemes for curved walls within the framework of the Lattice Boltzmann Method (LBM). A canonical benchmark problem—the flow past a circular cylinder in a channel—is considered, with Reynolds numbers ranging from 50 to 300. While prior studies have examined similar configurations, this work provides a novel comparative analysis under realistic conditions—using dimensional LBM simulations with actual fluid properties and consumer-grade hardware, rather than idealized lattice units. Additionally, we introduce an in-house GPU-accelerated solver, enabling efficient high-fidelity simulations without reliance on specialized computational resources. Four wall boundary conditions—the standard bounce-back scheme, the non-equilibrium extrapolation scheme, the fictitious equilibrium scheme and a one-point scheme—are implemented and analyzed through their influence on the time-averaged drag coefficient of the cylinder. The results are compared against both experimental and Navier-Stokes-based numerical data to assess accuracy. Additionally, the study evaluates the relative impact of outlet BC selection on simulation fidelity. The findings show that all tested solid wall boundary schemes can produce reasonable predictions under suitable conditions. Furthermore, based on our results, the accuracy of LBM simulations is notably more sensitive to the choice of the outlet boundary condition when compared to the choice of the ones used at the immersed body.OPEN ACCESS Received: 08/05/2025 Accepted: 24/06/2025 Published: 27/10/2025

  Abstract
  In this paper, we investigate the performance of different boundary condition (BC) schemes for curved walls within the framework of the Lattice Boltzmann Method (LBM). A canonical [...]

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• Dynamic and Control in a Three-Variable Chemical Reaction Model

  M. Martinez, F. Chavarette

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (4), 68

  
  

  Abstract

  Chaotic behavior in nonlinear chemical systems presents significant challenges for stability and control, particularly in practical applications. This study investigates the suppression of chaos in a three-variable reaction system through an optimal linear feedback strategy, formulated via the solution of an algebraic Riccati equation. The proposed control approach effectively eliminates chaotic oscillations, guiding the system to equilibrium even under parameter uncertainties of up to 20%. Numerical simulations confirm that the control action maintains high robustness, ensuring convergence with minimal effort. The stabilization time for x

  Abstract
  Chaotic behavior in nonlinear chemical systems presents significant challenges for stability and control, particularly in practical applications. This study investigates the [...]

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• Optimum Analysis and Parameter Inference of a New Improved Adaptive Progressive Unit-Weibull Model Censoring with Two Physical Applications

  H. Mohammed, O. Abo-Kasem, A. Elshahhat

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (4), 67

  
  

  Abstract

  Recently, a new bounded version of the Weibull lifetime has been introduced, retaining the flexibility of the standard Weibull model while restricting it to the unit interval, making it particularly useful for betalike modeling in various fields. This paper investigates the improved adaptive Type-II progressively censored plan by applying it to the bounded unit Weibull distribution. From a frequentist perspective, both maximum likelihood and maximum product of spacings methods are used, along with appropriate approximate confidence intervals. Bayesian point estimates, along with Bayesian credible intervals, are obtained using classical procedures that involve Markov-Chain Monte Carlo sampling, with two separate posterior distributions based on the squared error loss. The proposed estimation frameworks encompass both distribution parameters and key reliability metrics, notably the reliability and failure rate functions. Extensive simulations are conducted to evaluate the accuracy and efficiency of the estimators under various censoring levels, sample sizes, and thresholds. To determine the optimal removal strategy under both frequentist estimation paradigms, several metrics are proposed. Additionally, the model is applied to two real-world datasets from engineering reliability; one contains core samples from petroleum reservoirs collected across four cross-sections, and the other pertains to the tensile strength of polyester fibers, illustrating its practical utility and flexibility in modeling. The novelty of this study lies in integrating the bounded support of the unit-Weibull model with an improved adaptive censoring scheme, providing enhanced robustness and adaptability in reliability analysis across different fields.OPEN ACCESS Received: 21/06/2025 Accepted: 19/08/2025 Published: 27/10/2025

  Abstract
  Recently, a new bounded version of the Weibull lifetime has been introduced, retaining the flexibility of the standard Weibull model while restricting it to the unit interval, [...]

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• Approximate Calculation of the Generalized Erdélyi-Kober Operator Using a Cubic Spline

  S. Karimov, E. Islamov, E. Shishkina

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (4), 66

  
  

  Abstract

  This article investigates the problem of approximating the generalized Erdélyi-Kober fractional operator (often referred to as the Lowndes operator) using cubic splines. A method based on cubic spline interpolation is proposed for approximating the operator on a non-uniform grid. The convergence rate of the proposed method is proven, and its stability is analyzed. Error bounds are established for functions in the class C4[0; b], providing a mathematical justification for the accuracy of the approximation. The efficiency of the method is validated through practical examples using test functions such as f (x)= x4.7and f (x)= cos x, with results presented in graphical and numerical forms. This approach ensures high accuracy and flexibility in computing fractional integrals, which is of significant importance for solving fractional models used in physics, engineering, and other sciences. The article also provides an overview of the role of the generalized Erdélyi-Kober operator in modern fractional calculus and its applications.OPEN ACCESS Received: 06/06/2025 Accepted: 08/09/2025 Published: 27/10/2025

  Abstract
  This article investigates the problem of approximating the generalized Erdélyi-Kober fractional operator (often referred to as the Lowndes operator) using cubic splines. [...]

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• Fundamental Mechanics and Precision Control of Optical Axis Stability and Parallelism in Multi-Sensor Electro-Optical Pods

  Z. Huang, S. Chi, L. Zhu

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (4), 65

  
  

  Abstract

  Modern electro-optical pods incorporatemulti-spectral sensors for reconnaissance, target acquisition, and laser designation, where sub-milliradian optical axis stability and inter-sensor parallelism are critical for mission success. This paper establishes a unified theoretical framework combining rigid-body kinematics and deformable body mechanics to develop a physics-based stability metric through screw theory formulation, expressing the optical axis dynamics as ˙O = [ω]×O+v, with thermo-mechanical constraints [ω]×O < ω, v < v for engineering implementation. A novel computational geometry method evaluates multi-sensor alignment errors by solving Ei = si − (si · ˆO) ˆO + JTT + Jgg, where JT and Jg represent thermal and gravitational Jacobians. The rigid-flexible coupling model with multi-point constraints (MPC) reveals thermal dominance (0.49 mrad IR sensor pitch displacement at 60◦C, 272× gravitational effect), material sensitivity (CTE mismatch contributing 68% of TV sensor’s azimuthal error), and cross-axis coupling (19% LD error amplification under thermal gradients). However, due to the limitations of current experimental conditions, the experimental validation ismainly carried out in controlled environments. The current experimental validation shows <5% deviation between predicted andmeasured parallelismerrors across −20◦C to 60◦C. In the future, we will supplement the evaluation of the robustness of the control method through existing simulation verifications (such as adding vibration and temperature disturbance models) in the “experimental discussion” or “prospect” section, and clarify the research plan for actual environment testing. The framework provides design guidelines for optimal sensor placement minimizing JT F, temperaturedependent calibration protocols, and 0.1 mrad allocable margin for manufacturing tolerances. This methodology advances electro-optical system engineering fromempirical tuning tomodel-driven optimization, demonstrating 0.12 mrad (3σ) stability in field tests under ISO 9022 environmental stress profiles, with key innovations including the first integration of Lie algebra kinematics with FEM-based deformation analysis for optical systems and physics-informed error budgeting separating thermal, mechanical, and alignment components.

  Abstract
  Modern electro-optical pods incorporatemulti-spectral sensors for reconnaissance, target acquisition, and laser designation, where sub-milliradian optical axis stability [...]

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• On Nonlinear Monge-Ampère Equations and Their Symmetry Classifications

  Z. Izgi, Ö. Avit, D. Baleanu, M. Yousif, M. Alharthi, P. Mohammed

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (4), 64

  
  

  Abstract

  The Monge-Ampère equation (MAE) plays a pivotal role across a broad spectrum of theoretical and applied sciences, with its solutions being essential for advancing various fields. This study explores all forms of the fully nonlinear MAE using Lie group transformations to reduce the equation into solvable forms. Analytical solutions are derived using ansatzbased methods, yielding novel and generalized results that enhance the existing body of knowledge. In particular, solutions for cases with diverse source functions and boundary conditions are obtained, addressing gaps in the literature. Stability of the solutions is studied through both analytical and numerical approaches. Comparisons with existing solutions demonstrate the efficiency and generality of the proposed methods. The results presented in this work are poised to impact numerous applications, providing a robust framework for further research on MAEs.OPEN ACCESS Received: 24/05/2025 Accepted: 07/08/2025 Published: 27/10/2025

  Abstract
  The Monge-Ampère equation (MAE) plays a pivotal role across a broad spectrum of theoretical and applied sciences, with its solutions being essential for advancing various [...]

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• RCS Simulation of Double S-Shaped Inlet with Radar Absorbing Materials Shedding Using Iterative Physical Optics with Impedance Boundary Condition

  X. Guo, X. Xia, Z. Zhao, M. Wu, Y. Liu

  Rev. int. métodos numér. cálc. diseño ing. (2025). Vol. 41, (4), 63

  
  

  Abstract

  The inlet of an aircraft engine is a primary contributor to the aircraft’s forward electromagnetic scattering. S-shaped inlet and radar absorbing materials (RAM) coatings have been widely adopted as effective measures to reduce forward radar cross section (RCS). To investigate the influence of RAM shedding on the RCS reduction efficiency, the electromagnetic scattering characteristics of the inlet under five different shedding probabilities were calculated using the iterative physical optics (IPO) combined with impedance boundary condition (IBC). Numerical simulation results demonstrate that the forward RCS of the S-shaped inlets increases monotonically with shedding probability. In the yaw plane, intact non-magnetic RAM exhibits better RCS reduction efficiency (RRE) than that in the pitch plane across all scenarios. Specifically, at a shedding probability of 0.7, the remaining non-magnetic RAM maintains an RRE exceeding 40% in the pitch plane. Collectively, these results suggest that recoating the nonmagnetic RAM is recommended when the shedding probability exceeds 0.7 in either detection plane to sustain critical stealth performance.OPEN ACCESS Received: 20/05/2025 Accepted: 13/08/2025 Published: 27/10/2025

  Abstract
  The inlet of an aircraft engine is a primary contributor to the aircraft’s forward electromagnetic scattering. S-shaped inlet and radar absorbing materials (RAM) coatings [...]

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