Article
Mathematics, Applied
A. Alqahtani, T. Mach, L. Reichel
Summary: This paper explores the feasibility of using the Chebfun package and a regularize-first approach to solve ill-posed problems numerically, which allows for a closer analysis-based solution rather than the traditional linear algebra-based method.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Min Zhong, Quoc Thong Le Gia, Ian Hugh Sloan
Summary: In this paper, we propose and analyze a support vector approach to approximately solve a severely ill-posed problem Au = f on the sphere. The approach adopts Vapnik's epsilon-intensive function as a regularization technique to reduce the error caused by noisy data. It is further extended to a multiscale algorithm by varying the support radius of the radial basis functions at each scale. The convergence of the multiscale support vector approach is discussed and strategies for choosing regularization parameters and cut-off parameters at each level are provided. Numerical examples are conducted to demonstrate the efficiency of the multiscale support vector approach.
JOURNAL OF SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Min Zhong, Wei Wang, Kai Zhu
Summary: We investigate the method of asymptotical regularization for solving nonlinear illposed problems F(x) = y in Hilbert spaces. A general uniformly convex functional has been embedded in the evolution equations which is allowed to be non-smooth, thus the algorithm can be applied for sparsity and discontinuity reconstruction. Assuming certain conditions concerning the nonlinear operator F and functional Theta, we establish the convergence and stability of the method.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Ye Zhang
Summary: Accelerated regularization algorithms for ill-posed problems have been a focus of research since the 1980s. This paper proposes a new class of regularization algorithms called AR(n), which can achieve optimal convergence rates with approximately the square root of the iterations required by benchmark methods. Unlike existing algorithms, AR(n) does not have a saturation restriction. Numerical experiments show that, for n <= 2, the practical acceleration capability of AR(n) matches the theoretical findings and exceeds existing regularization algorithms.
Article
Mathematics, Applied
O. Benchettou, A. H. Bentbib, A. Bouhamidi, K. Kreit
Summary: This study focuses on solving a class of tensorial ill-conditioned problems by formulating them as convex constrained minimization problems. The proposed approach introduces a new tensor degradation model and utilizes Tikhonov regularization to reduce the impact of noise in color image and video restoration. The tensor minimization problem is solved using the conditional gradient method. The Generalized Cross Validation method is adapted for appropriate selection of the regularization parameter in the tensorial model. Experimental results demonstrate the effectiveness of the proposed approach compared to classical methods.
APPLIED NUMERICAL MATHEMATICS
(2022)
Article
Mathematics, Applied
A. Alqahtani, R. Ramlau, L. Reichel
Summary: Linear ill-posed operator equations often appear in various fields of science and engineering. However, the presence of errors in the operator and data makes it challenging to compute an accurate approximate solution. In this paper, we propose a method that involves approximating the low-dimensional operators of the noisy operator using a continuous version of the Golub-Kahan bidiagonalization process. We then apply Tikhonov regularization to the obtained low-dimensional problem, with the regularization parameter determined by solving a low-dimensional nonlinear equation. Computed examples are provided to illustrate the theory presented in this paper.
Article
Mathematics, Applied
Guangxin Huang, Yuanyuan Liu, Feng Yin
Summary: This paper presents a new modified truncated randomized singular value decomposition (TR-MTRSVD) method for solving large Tikhonov regularization problems. Numerical examples demonstrate the effectiveness and efficiency of the proposed method in regularization.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2022)
Article
Mathematics, Applied
Ruixue Gu, Hongsun Fu, Bo Han
Summary: This paper generalizes inexact Newton regularization methods to solve nonlinear inverse problems and can handle various types of noise. The method has fast convergence through the inner scheme and accelerated version.
Article
Computer Science, Interdisciplinary Applications
Ce Huang, Li Wang, Minghui Fu, Zhong-Rong Lu, Yanmao Chen
Summary: This paper proposes a new iterative integration regularization method for robust solution of ill-posed inverse problems, which efficiently computes the integral through two methods and guarantees regularization effect.
ENGINEERING WITH COMPUTERS
(2021)
Article
Mathematics, Applied
Saknarin Channark, Poom Kumam, Juan Martinez-Moreno, Wachirapong Jirakitpuwapat
Summary: A new progressive and iterative approximation method called HSS-LSPIA is proposed in this paper to solve the problems of curves and surfaces approximation. The method includes two iterations with iterative difference vectors, providing an approximate optimal constant and convergence analysis. It is faster than other methods in terms of convergence speed.
Article
Mathematics, Applied
Shanshan Tong, Wei Wang, Bo Han
Summary: In this paper, a fast iterative algorithm based on the J-order homotopy perturbation method is proposed for solving the nonlinear ill-posed problem. The sequential subspace optimization technique is introduced to accelerate the convergence speed, and numerical experiments are conducted to demonstrate its effectiveness.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
Hong-Mei Song, Shi-Wei Wang, Guang-Xin Huang
Summary: This paper presents three types of tensor Conjugate-Gradient (tCG) methods based on the t-product between third-order tensors for solving large-scale linear discrete ill-posed problems. An automatic determination strategy of a suitable regularization parameter is proposed in the Fourier domain for the tCG method (A-tCG-FFT). Improved and preconditioned versions of the tCG method are also introduced. The effectiveness of the proposed tCG methods is demonstrated with several numerical examples in image and video restoration.
Article
Mathematics, Applied
Hong-Mei Song, Shi-Wei Wang, Guang-Xin Huang
Summary: This paper presents three types of tensor Conjugate-Gradient methods based on the t-product between third-order tensors, for solving large-scale linear discrete ill-posed problems. An automatic determination strategy and the discrepancy principle are proposed for determining suitable regularization parameters for the methods. Numerical examples in image and video restoration demonstrate the effectiveness of the proposed methods.
Article
Mathematics, Applied
Eric Chung, Kazufumi Ito, Masahiro Yamamoto
Summary: This paper proposes a least squares formulation for ill-posed inverse problems in partial differential equations, establishing the existence, uniqueness, and continuity of the inverse solution for noisy data in L-2. The method can be applied to a general class of non-linear inverse problems, and a stability analysis is developed. Numerical tests show the applicability and performance of the proposed method.
APPLICABLE ANALYSIS
(2022)
Article
Mathematics, Applied
Zhenping Li, Xiangtuan Xiong, Jun Li, Jiaqi Hou
Summary: This paper deals with the reconstruction problem of aperture in the plane from their diffraction patterns and proposes a quasi-boundary regularization method to stabilize the problem. The method has better approximation than classical methods in theory without noise.
Article
Engineering, Multidisciplinary
Dingcheng Zhang, Edward Stewart, Mani Entezami, Clive Roberts, Dejie Yu
Article
Engineering, Mechanical
Yiyuan Gao, Dejie Yu
MECHANISM AND MACHINE THEORY
(2020)
Article
Automation & Control Systems
Hui Yin, Ye-Hwa Chen, Dejie Yu
IEEE TRANSACTIONS ON CYBERNETICS
(2020)
Article
Physics, Applied
Tinggui Chen, Junrui Jiao, Dejie Yu
Summary: The GCM proposed in this study combines gradient and coiled structures to achieve enhanced broadband acoustic sensing, with the ability to amplify acoustic signals up to approximately 80 times over a wide frequency range. By coupling coiled structures, trapped and enhanced frequencies in the GCM can be reduced by nearly 43%. Experimental results demonstrate that GCM can enhance frequency-selective unknown signals and effectively recognize and recover harmonic signals from strong background noise.
JOURNAL OF PHYSICS D-APPLIED PHYSICS
(2021)
Article
Engineering, Multidisciplinary
Tinggui Chen, Junrui Jiao, Dejie Yu
Summary: The study proposes a method based on the gradient acoustic-grating metamaterial (GAGM) for detecting harmonic and periodic impulse signals more easily. Numerical and experimental investigations demonstrate that GAGM achieves acoustic rainbow trapping to spatially separate different frequency components. This work opens up new vistas for weak signals detection in various areas.
Article
Physics, Applied
Hongqing Dai, Baizhan Xia, Dejie Yu
Summary: Acoustic topological insulators enable non-contact particle manipulations, such as microparticle trapping and separation. Based on the SSH model, we can separate particles of the same size and density.
APPLIED PHYSICS LETTERS
(2021)
Article
Engineering, Electrical & Electronic
Tinggui Chen, Dejie Yu, Bo Wu, Baizhan Xia
Summary: A sensor based on acoustic metamaterials is proposed for detecting weak signals, utilizing a trapezoidal structure to enhance the acoustic pressure field and amplify pressure amplitudes by over 20 times around maximum gain frequencies, achieving broadband acoustic enhancement. Harmonic and periodic impulse signals are detected more easily, and experimental results show effective recovery of signals from background noise due to improved signal to noise ratios.
IEEE SENSORS JOURNAL
(2021)
Article
Materials Science, Multidisciplinary
Burigede Liu, Xingsheng Sun, Kaushik Bhattacharya, Michael Ortiz
Summary: The study develops an approach to quantify the overall uncertainty of material response without the need for integral calculations, utilizing the multiscale and hierarchical nature of material response. It effectively bounds uncertainties at different scales and provides a conservative estimate for the overall uncertainty of material behavior assessment.
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
(2021)
Article
Automation & Control Systems
Tinggui Chen, Dejie Yu
Summary: This article proposes a novel method to diagnose bearing faults using acoustic metamaterials, which enhances the resonance frequency band to extract fault features. Compared to conventional denoising techniques, this method shows superior performance in low signal to noise ratios.
IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS
(2022)
Article
Materials Science, Multidisciplinary
Nikola Kovachki, Burigede Liu, Xingsheng Sun, Hao Zhou, Kaushik Bhattacharya, Michael Ortiz, Andrew Stuart
Summary: In recent decades, various methods have been used to accelerate the development of materials targeted towards specific applications. The choice of a particular material system is based on the performance required for a specific application, which is optimized through processing. The structure is then designed by characterizing the material in detail and utilizing this information for system-level simulations and optimization.
MECHANICS OF MATERIALS
(2022)
Article
Acoustics
Tinggui Chen, Junrui Jiao, Dejie Yu
Summary: The detection and localization of acoustic signals are important in many areas, but achieving both high sensitivity and high directivity in an acoustic system remains a challenge. This study proposes a structure that combines phononic crystal point defects with four-sided Helmholtz resonators to enhance acoustics and enable directional sensing. The proposed structure surpasses the detection limit of conventional acoustic sensing systems and provides a new method for developing coupled acoustic sensing devices.
JOURNAL OF SOUND AND VIBRATION
(2022)
Article
Chemistry, Physical
Xingsheng Sun
Summary: This paper adopts a computational framework to study the ballistic performance of magnesium alloys, quantifying the effects of material uncertainties. It provides upper bounds and an ordering of uncertain parameters to improve ballistic performance and develop new material models.
Article
Physics, Applied
Guiju Duan, Shengjie Zheng, Jie Zhang, Zihan Jiang, Xianfeng Man, Dejie Yu, Baizhan Xia
Summary: This study reports the realization of a synthetic gauge field in acoustic Moire superlattices consisting of two superimposed periodic phononic crystals with mismatched lattice constants. The symmetric and antisymmetric Landau levels and interface states are observed in the acoustic Moire superlattices with the help of the synthetic gauge field. Sound pressure field distributions of Landau levels are experimentally measured and consistent with full-wave simulations. This study provides a simple way to generate synthetic gauge fields in phononics and expands the avenues for manipulating sound waves that were previously inaccessible in traditional periodic acoustic systems.
APPLIED PHYSICS LETTERS
(2023)
Article
Materials Science, Multidisciplinary
Xingsheng Sun, Burigede Liu
Summary: This paper investigates the optimal uncertainty bounds for systems with partially/imperfectly known input probability measures. The theory of Optimal Uncertainty Quantification is used to convert the task into a constraint optimization problem. The paper explores the use of machine learning, particularly deep neural networks, to tackle the difficulty of finding optimal uncertainty bounds.
MECHANICS OF MATERIALS
(2023)
Article
Computer Science, Artificial Intelligence
Yiyuan Gao, Dejie Yu
Summary: The study introduces an intelligent method using directed graphs for fault diagnosis, which improves diagnostic performance by constructing a directed and weighted k-nearest neighbor graph and measuring the similarity between samples using cosine distance. Experimental results show that the method is better than traditional convolutional neural networks and support vector machines in rolling bearing fault diagnosis.
ADVANCED ENGINEERING INFORMATICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Jose Pedro G. Carvalho, Denis E. C. Vargas, Breno P. Jacob, Beatriz S. L. P. Lima, Patricia H. Hallak, Afonso C. C. Lemonge
Summary: This paper formulates a multi-objective structural optimization problem and utilizes multiple evolutionary algorithms to solve it. By optimizing the grouping of structural members, the best truss structure can be found. After analyzing various benchmark problems, the study reveals the existence of competitive structural member configurations beyond symmetry-based groupings.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Se-Hyeon Kang, Hyun-Seok Kim, Seonho Cho
Summary: This paper investigates shape identification using peridynamic theory and gradient-based optimization. The particle-based and non-local characteristics of peridynamics allow for direct interface modeling, avoiding remeshing difficulties. The boundary of scatterers is parameterized using B-spline surfaces, and design sensitivity is obtained using an efficient adjoint variable method. The accuracy and efficiency of the proposed method are verified through numerical examples.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Laura Rio-Martin, A. Prieto
Summary: Any numerical procedure in mechanics requires selecting an appropriate constitutive model for the material. The common assumptions for linear wave propagation in viscoelastic materials include the standard linear solid, Maxwell, Kelvin-Voigt, and fractional derivative models. Typically, the intrinsic parameters of the mathematical model are estimated based on available experimental data to fit the mechanical response of the chosen constitutive law. However, this approach may suffer from the uncertainty of inadequate model selection. In this work, the mathematical modeling and selection of frequency-dependent constitutive laws for linear viscoelastic materials are solely performed based on experimental measurements without imposing any functional frequency dependence. This data-driven methodology involves solving an inverse problem for each frequency.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Pramod Kumar Gupta, Chandrabhan Singh
Summary: In this paper, a novel algorithm is developed to generate the geometrical model of coarse aggregate, and it is further applied in the generation of a finite element model for concrete. Through numerical simulation and comparison with existing literature, the effectiveness of the meso-model is verified.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Xiao Wang, Qingrui Yue, Xiaogang Liu
Summary: This study proposes a graph neural networks-based method to recover the missing connection information in crack meshes, and comparative analysis shows that the trained GraphSAGE outperforms other GNNs on triangular meshing task, revealing the potential of GNNs in restoring missing information.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Dhiraj S. Bombarde, Manish Agrawal, Sachin S. Gautam, Arup Nandy
Summary: The study introduces a novel twenty-seven node quadratic EAS element, addressing the underutilization of quadratic elements in existing 3D EAS elements. Additionally, a six-node wedge and an eighteen-node wedge EAS element are presented in the manuscript.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Hau T. Mai, Seunghye Lee, Joowon Kang, Jaehong Lee
Summary: In this work, an effective Damage-Informed Neural Network (DINN) is developed for pinpointing the position and extent of structural damage. By using a deep neural network and Bayesian optimization algorithm, the proposed method outperforms other algorithms in terms of accuracy and efficiency.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Qingsong Xiong, Qingzhao Kong, Haibei Xiong, Lijia Liao, Cheng Yuan
Summary: This study proposes a novel physics-informed deep 1D convolutional neural network (SSM-CNN) for enhanced seismic response modeling. By construing the differential nexus of state variables derived from the state-space representation of initial structural response, an innovative parameter-free physics-constrained mechanism is designed and embedded for performance enhancement. Experimental validations confirmed the effectiveness and superiority of physics-informed SSM-CNN in seismic response prediction.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
D. Herrero-Perez, S. G. Pico-Vicente
Summary: This work presents an efficient, flexible, and scalable strategy for implementing density-based topology optimization formulation in fail-safe structural design. The use of non-overlapping domain decomposition, adaptive mesh refinement, and computing buffers allows for successful evaluation of fault cases.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Xiangyang Cui, Gongcheng Peng, Qi Ran, Huan Zhang, She Li
Summary: A novel degenerated shell element called MITC4+R is developed, which eliminates various locking problems common to shell elements and significantly improves the computational efficiency. It is based on assumed natural strain method and introduces a physical stabilization term.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Shouyan Jiang, Wangtao Deng, Ean Tat Ooi, Liguo Sun, Chengbin Du
Summary: This study presents an innovative data-driven algorithm that combines the scaled boundary finite element method and a deep learning framework for identifying crack-like defects in large-scale structures. The proposed algorithm accurately determines the number, location, and depth of cracks and is robust to noise. It provides valuable insight into the detection and diagnosis of structural defects.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Shiqiang Qin, Jiacheng Feng, Jian Tang, Xuejin Huo, Yunlai Zhou, Fei Yang, Magd Abdel Wahab
Summary: This study assesses the condition of a CFST arch bridge using in-situ vibration measurements, finite element model updating, and an improved artificial fish swarm algorithm. The results indicate that the bridge has good dynamic performance, but track conditions need improvement before operation.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Md. Imrul Reza Shishir, Alireza Tabarraei
Summary: In this paper, a density-based topology optimization method using neural networks is proposed for designing multi-material domains under combined thermo-mechanical loading. The method achieves automatic sensitivity analysis and removes the need for other optimization algorithms. Experimental results show that the method can handle high-resolution re-sampling, resulting in more refined and smooth optimal topologies.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
Bartosz Sobczyk, Lukasz Pyrzowski, Mikolaj Miskiewicz
Summary: This paper describes the problems encountered during the analysis of the structural response of historic masonry railroad arch bridges. It focuses on the stiffness of the masonry arches, their strengths, and the estimation of railroad load intensity. The paper presents computational models created to efficiently describe the responses of the bridges under typical loading conditions and discusses the outcomes of nonlinear static analyses. The possible causes of the deterioration of the bridges' condition were identified through these analyses.
COMPUTERS & STRUCTURES
(2024)
Article
Computer Science, Interdisciplinary Applications
T. Koudelka, T. Krejci, J. Kruis
Summary: This paper presents a numerical model for the coupled hydro-mechanical behaviour of partially saturated soils, and demonstrates its effective application through a numerical example.
COMPUTERS & STRUCTURES
(2024)
