Article
Mathematics, Applied
Qingsong Wang, Zehui Liu, Chunfeng Cui, Deren Han
Summary: This paper proposes inertial accelerated SGD methods for the subproblems in CP decomposition. Two methods for block index selection are considered: stochastic manner with replacement and randomly permuted order without replacement. The proposed algorithms are proven to have global convergence and convergence rate, and numerical experiments demonstrate their superiority over existing methods.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Geological
M. Jeffery, J. Huang, S. Fityus, A. Giacomini, O. Buzzi
Summary: The paper introduces a new multiscale approach using random field theory to generate synthetic 3D surfaces with controlled distribution of asperity heights and gradients. The approach was successfully validated with 25 input seed traces from 5 different natural surfaces. This rigorous multiscale approach is essential for applying the recently developed stochastic method to predict the shear strength of large in situ discontinuities.
INTERNATIONAL JOURNAL OF ROCK MECHANICS AND MINING SCIENCES
(2021)
Article
Materials Science, Multidisciplinary
Behrad Koohbor, Nicholas Pagliocca, George Youssef
Summary: This study quantitatively characterized the micro-to-macro transition length scale in polymeric foams using an experimental-statistical approach, showing that this transition is a function of material density.
MECHANICS OF MATERIALS
(2021)
Article
Engineering, Mechanical
Zhibao Zheng, Marcos Valdebenito, Michael Beer, Udo Nackenhorst
Summary: This paper focuses on the simulation of random fields on random domains, which is an important problem in topology optimization and multiphase material analysis. The authors propose the stochastic Karhunen-Loeve expansion (SKLE) as an extension of the classical Karhunen-Loeve expansion (KLE) to solve this issue. They present three numerical algorithms, including an extended Monte Carlo simulation (MCS), a domain transformation-based method, and a reduced-order method, to efficiently solve the stochastic integral equations in the SKLE. Numerical examples demonstrate the effectiveness of the proposed methods.
PROBABILISTIC ENGINEERING MECHANICS
(2023)
Article
Computer Science, Information Systems
En Zhang, Zihao Nie, Qiang Yang, Yiqiao Wang, Dong Liu, Sang-Woon Jeon, Jun Zhang
Summary: Facing complex large-scale optimization problems, most existing optimization algorithms lose their effectiveness. In order to effectively solve this type of problem, we propose a heterogeneous cognitive learning particle swarm optimization algorithm (HCLPSO). Unlike most particle swarm optimization algorithms, HCLPSO partitions particles into superior and inferior categories based on their fitness and treats them differently. With the collaboration of two learning mechanisms, HCLPSO can effectively explore the search space and exploit the found optimal zones to find optimal solutions.
INFORMATION SCIENCES
(2023)
Article
Engineering, Multidisciplinary
Yiran Wang, Eric Chung, Shubin Fu
Summary: In this paper, a local-global multiscale method is proposed for highly heterogeneous stochastic groundwater flow problems. The method combines the reduced basis method and the generalized multiscale finite element method to achieve computational efficiency. The authors provide rigorous analysis and extensive numerical examples to demonstrate the accuracy and efficiency of the method.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Engineering, Mechanical
Mohammad Aramfard, Francisco Perez-Rafols, Lucia Nicola
Summary: A seamless 2D dual-scale computational scheme has been developed to study contact problems, combining an atomistic domain for contact interaction description and an elastic continuum domain. The innovative scheme is validated against full atomistic simulations and used to investigate the effect of adhesion on scratching processes.
TRIBOLOGY INTERNATIONAL
(2022)
Article
Computer Science, Interdisciplinary Applications
Yashar Mehmani, Nicola Castelletto, Hamdi A. Tchelepi
Summary: This study introduces a pore-level multiscale method that efficiently approximates direct numerical simulation with controllable accuracy for predicting the elastic response of solid media containing cracks or defects.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mechanics
A. Ciampaglia
Summary: This paper proposes a statistical inverse method to calibrate micromechanical material parameters by predicting the mechanical response of composite laminates using macro-scale experiments and 3D reconstruction. Glass fiber reinforced epoxy laminates have been analyzed with Computer Tomography (CT) and then the material 3D microstructure reconstructed. Tensile tests were performed and the homogenized response of the composite was computed using the reconstructed volume.
COMPOSITE STRUCTURES
(2023)
Article
Engineering, Electrical & Electronic
Clemence Prevost, Konstantin Usevich, Martin Haardt, Pierre Comon, David Brie
Summary: This paper proposes a theoretical performance analysis method for reconstruction problems, which are formulated as coupled canonical polyadic decompositions of two low-resolution tensor observations. A particular case of fully coupled tensors is studied, and two probabilistic scenarios are introduced. By deriving the constrained Cramer-Rao bounds for the parameters and the mean-squared error of the reconstructed tensor, it is shown that the maximum likelihood estimators can reach the bounds even in challenging cases.
Article
Mathematics, Interdisciplinary Applications
Tobias Kaiser, Joris J. C. Remmers, Marc G. D. Geers
Summary: Computational multiscale methods rely on accurate representation of microscale morphology and its constituents for quality prediction, which makes the formulations computationally demanding. This study explores the applicability of an adaptive wavelet-based collocation approach, deriving wavelet-based scale-bridging relations and a mapping algorithm. In-depth analysis of elementary problems in multiscale mechanics and analytical solutions are used to assess the accuracy of simulation results.
COMPUTATIONAL MECHANICS
(2022)
Article
Engineering, Mechanical
Marco Behrendt, Matthias G. R. Faes, Marcos A. Valdebenito, Michael Beer
Summary: In engineering, the modelling of environmental processes is essential for designing structures safely and determining the reliability of existing structures. This work focuses on situations where data is limited and it is not feasible to derive reliable statistics. The proposed approach uses a radial basis function network to generate basis functions that enclose the data, resulting in an interval-based power spectral density (PSD) function. The applicability of this imprecise PSD model is demonstrated with recorded earthquake ground motions.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2023)
Article
Mathematics, Applied
Xiaofei Guan, Lijian Jiang, Yajun Wang
Summary: In this article, a multiscale method is introduced for elasticity problems in random media. The method utilizes variable separation and ensemble techniques to construct an efficient reduced model, which is applied to elastic deformation and wave propagation. Numerical results demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics
Jie Wang
Summary: This paper presents several error bounds for the solution sets of generalized polynomial complementarity problems (GPCPs) with explicit exponents. By leveraging the state-of-art results in error bounds for polynomial systems, a much improved error bound result for the solution set of GPCPs is established based on exploring intrinsic sparsity through tensor decomposition.
LINEAR & MULTILINEAR ALGEBRA
(2022)
Article
Mathematics, Applied
S. Z. Feng, Q. J. Sun, X. Han, Atilla Incecik, Z. X. Li
Summary: This paper proposes two efficient algorithms based on the stable nodal integration method (SNIM) to address the material and spatial uncertainties in the stochastic electric field problem. Random variables/fields are used to describe the uncertainties, and a generalized stochastic perturbation-SNIM (GS-SNIM) method is developed for random-variable scenarios, while a random field-SNIM (RF-SNIM) method is developed for random-field scenarios. Numerical examples are studied to verify the accuracy and efficiency of the proposed methods, and the results demonstrate their capability in solving different uncertainties and reducing computational cost.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Anatoliy Malyarenko, Martin Ostoja-Starzewski
JOURNAL OF ELASTICITY
(2017)
Article
Physics, Applied
Anatoliy Malyarenko, Martin Ostoja-Starzewski
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2017)
Article
Physics, Mathematical
Nikolai Leonenko, Anatoliy Malyarenko
JOURNAL OF STATISTICAL PHYSICS
(2017)
Article
Statistics & Probability
Chunsheng Ma, Anatoliy Malyarenko
JOURNAL OF THEORETICAL PROBABILITY
(2020)
Article
Mechanics
Anatoliy Malyarenko, Martin Ostoja-Starzewski
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
(2020)
Article
Statistics & Probability
Tarik Faouzi, Emilio Porcu, Igor Kondrashuk, Anatoliy Malyarenko
Summary: This paper investigates the spectral properties of the Dagum family, including finite properties, asymptotic properties, and closed-form expressions of the spectral density. Understanding these properties is important for the application of the Dagum model in random field modelling.
JOURNAL OF APPLIED PROBABILITY
(2022)
Article
Mathematics, Applied
Anatoliy Malyarenko, Martin Ostoja-Starzewski
Summary: This paper investigates a type of random fields that take values in a linear space and are mean-square continuous, wide-sense homogeneous, and isotropic. The paper identifies a set of such fields whose values are symmetric and positive-definite dyadics, and outlines a strategy for simulating them.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
Anatoliy Malyarenko, Yuliya Mishura, Kostiantyn Ralchenko, Sergiy Shklyar
Summary: This paper focuses on studying the properties of entropy in relation to the Hurst index, which represents fractional Gaussian noise. Due to the difficulty of analytically studying the behavior of the determinant of the covariance matrix as a function of the Hurst index in high dimensions, simple alternative entropy functionals are also examined. The asymptotic behavior of the normalized entropy (entropy rate) is investigated for both the entropy and the alternative functionals.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2023)
Article
Statistics & Probability
Betuel Canhanga, Anatoliy Malyarenko, Ying Ni, Milica Rancic, Sergei Silvestrov
COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
(2018)
Article
Statistics & Probability
A. Malyarenko
THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS
(2017)
Proceedings Paper
Computer Science, Theory & Methods
Andrejs Matvejevs, Jegors Fjodorovs, Anatoliy Malyarenko
Proceedings Paper
Mathematics, Applied
Ying Ni, Betuel Canhanga, Anatoliy Malyarenko, Sergei Silvestrov
ICNPAA 2016 WORLD CONGRESS: 11TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES
(2017)
Proceedings Paper
Mathematics, Applied
Anatoliy Malyarenko
ICNPAA 2016 WORLD CONGRESS: 11TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES
(2017)
Proceedings Paper
Mathematics, Applied
Betuel Canhanga, Ying Ni, Milica Rancic, Anatoliy Malyarenko, Sergei Silvestrov
ICNPAA 2016 WORLD CONGRESS: 11TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES
(2017)
Article
Engineering, Multidisciplinary
Tohya Kanahama, Motohiro Sato
Summary: This study theoretically explains the effect of initial deflection and initial slope on self-buckling characteristics of heavy columns and proposes a formula characterizing the self-buckling problem. The results show that the greatest height is proportional to the 2/3 power of radius, and the formula can potentially predict the height of tree-like natural structures.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2024)
Article
Engineering, Multidisciplinary
Aps Selvadurai, Alexander P. Suvorov
Summary: This paper examines the torsion of a solid cylinder made of a fluid-saturated porous medium with a hyperelastic porous skeleton. It analyzes the mechanics of the twisted cylinder in both short-term and long-term behaviors, using numerical solutions and the ABAQUSTM finite element code.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2024)
Article
Engineering, Multidisciplinary
S. Kanaun
Summary: This study focuses on spherical radially transverse isotropic heterogeneous inclusions in homogeneous isotropic conductive host media. The volume integral equation for the field in the medium with an isolated inclusion subjected to a constant external field is solved using Mellin-transform technique. The method allows revealing tensor structure of the solution with precision to one scalar function of radial coordinate. The study also investigates the influence of neutral inclusions and conductivity coefficients on the effective conductivity of the composite material.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2024)
Article
Engineering, Multidisciplinary
Marinos Kattis, Vassilis Tsitsos, Vassilis Karatzaferis
Summary: The proposed model utilizes continuum mechanics to describe the mechanical behavior of a weakened interface between materials with microstructure, simulating the weakened interface using a surface elastic medium adhering on either side with bulk elastic continua. The model is able to investigate the effect of a weakened interface on stress concentration around inhomogeneities embedded in an unbounded matrix of Cosserat materials.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2024)
Article
Engineering, Multidisciplinary
Shixiang Zhao, Yu. V. Petrov, Yuyi Zhang, G. A. Volkov, Zejian Xu, Fenglei Huang
Summary: This paper theoretically studies the thermal softening related to stress relaxation using the incubation time approach and examines the temperature-time correspondence. The developed relaxation model of plasticity (RP model) is analyzed and compared with other constitutive models and artificial neural networks. The advantages and disadvantages of different models are discussed, and the differences between the ANN model and other constitutive models are examined.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2024)
Article
Engineering, Multidisciplinary
Ivan I. Argatov, Federico J. Sabina
Summary: This study models a seismic metabarrier as a cluster of single-degree-of-freedom resonator units and considers the scattering effects on pulsed Rayleigh waves caused by the vertical displacements of the resonators and the normal contact forces. The variation of the amplitude reduction factor due to the model parameters variation is studied in detail.
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE
(2024)
