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
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
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
Joseph Hart, Bart van Bloemen Waanders
Summary: Inverse problems constrained by partial differential equations (PDEs) are critical in model development and calibration. Reducing parameter dimension by fixing auxiliary parameters and using PDE-constrained optimization is a common approach. However, HDSA is not always suitable for ill-posed inverse problems. This article introduces novel approaches based on likelihood informed subspaces and a posteriori updates to enable HDSA in such cases.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2023)
Article
Mathematics, Applied
Vu Huu Nhu
Summary: This paper discusses the Levenberg-Marquardt method for solving ill-posed inverse problems in Banach spaces with general regularization terms. The findings show that the method performs well in dealing with specific problems.
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
Shanshan Tong, Wei Wang, Chaofeng Dong
Summary: A data-driven type Kaczmarz method with uniformly convex constraints is proposed for solving ill-posed problems. By learning an operator from training data, a data-driven term is constructed to improve the reconstruction accuracy. The introduced convex penalty, including L1 and total variation, recovers special features of the solutions and removes artifacts when data information is not close to the true solution. The method is validated through numerical experiments on linear and nonlinear problems.
APPLIED NUMERICAL MATHEMATICS
(2023)
Article
Computer Science, Artificial Intelligence
Guangyu Gao, Bo Han, Zhenwu Fu, Shanshan Tong
Summary: We propose a new iterative regularization method that combines classical iterative regularization format and Data-Driven approach for solving inverse problems in Hilbert spaces. The method utilizes convex functions as penalty terms to capture the special feature of solutions. We apply the two-point gradient acceleration strategy based on homotopy perturbation method to the iterative scheme, which achieves satisfactory acceleration effect. Convergence analysis is provided under standard assumptions, and numerical experiments demonstrate the effectiveness and acceleration effect of our method.
SIAM JOURNAL ON IMAGING SCIENCES
(2023)
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
Alessandro Buccini, Marco Donatelli, Lothar Reichel
Summary: This work considers the theoretical and computational aspects of a recent paper (Buccini et al., 2021) that aimed to relax convergence conditions in a previous work by Donatelli and Hanke, making their iterative method applicable to a wider range of problems. Although the presented analysis is correct, it does not establish the superiority of the iterative method. The authors describe a slight modification of the analysis that demonstrates the superiority and allows for discussion of algorithm behavior with varying parameters.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Ruixue Gu, Zhenwu Fu, Bo Han, Hongsun Fu
Summary: In this paper, a heuristic stopping rule for the inexact Newton regularization method is proposed. The method combines Landweber iteration and a strong convex function as the penalty term. Unlike prior and posterior stopping rules, the proposed heuristic rule is purely data driven and does not require knowledge of the noise level. The convergence analysis and numerical simulations demonstrate the effectiveness of the heuristic rule.
Article
Mathematics, Applied
Weike Chang, Nicola D'Ascenzo, Qingguo Xie
Summary: Iterated Tikhonov regularization methods provide an effective regularization approach for solving ill-posed problems, and improve convergence efficiency and accuracy by introducing relaxation parameters and early stopping rules.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Jonas Latz
Summary: Inverse problems involve blending mathematical models with observational data, and are fundamental in many scientific and engineering disciplines. These problems are typically ill-posed, but can be approached through methodologies such as the variational and Bayesian approach. In this study, the concept of well-posedness is simplified and generalized, with conditions that are significantly weaker than previous assumptions.
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
Alessandro Buccini, Marco Donatelli, Lothar Reichel, Wei-Hong Zhang
Summary: This article discusses an iterative regularization method based on iterated Tikhonov regularization for solving ill-posed inverse problems, particularly in image restoration. The method requires the approximating operator to be spectrally equivalent to the original operator, but a modification is proposed to relax this demand, resulting in good performance in various computed experiments.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2021)
Article
Engineering, Multidisciplinary
Chandler B. Smith, Eric M. Hernandez
INVERSE PROBLEMS IN SCIENCE AND ENGINEERING
(2019)
Article
Engineering, Civil
Eric Hernandez, Milad Roohi, David Rosowsky
EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS
(2018)
Article
Construction & Building Technology
Milad Roohi, Eric M. Hernandez, David Rosowsky
STRUCTURAL CONTROL & HEALTH MONITORING
(2019)
Article
Engineering, Mechanical
Eric M. Hernandez
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2019)
Article
Engineering, Mechanical
Chandler B. Smith, Eric M. Hernandez
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2019)
Article
Engineering, Civil
Milad Roohi, Eric M. Hernandez
JOURNAL OF CIVIL STRUCTURAL HEALTH MONITORING
(2020)
Article
Engineering, Multidisciplinary
Laurence A. Clarfeld, Paul D. H. Hines, Eric M. Hernandez, Margaret J. Eppstein
IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING
(2020)
Article
Biophysics
Benjamin LeBlanc, Eric M. Hernandez, Ryan S. McGinnis, Reed D. Gurchiek
Summary: This study proposes a new state-input-parameter estimation framework to continuously estimate the vertical ground reaction force waveform during running outside of laboratory environments. By simulating a runner's motion model and using Kalman filters for estimation, personalized metrics of vertical ground reaction force could be monitored for potential biofeedback applications. The results of this study demonstrate a high level of consistency between the estimates produced by the framework and measurements from instrumented treadmills.
JOURNAL OF BIOMECHANICS
(2021)
Article
Engineering, Mechanical
Milad Roohi, Eric M. Hernandez, David Rosowsky
Summary: The authors propose a seismic monitoring framework for instrumented buildings that uses dissipated energy for damage detection and localization. The framework employs a nonlinear model-based state observer to estimate seismic response and is validated using data from the Van Nuys hotel testbed. Results demonstrate the accuracy and capability of the framework in real-world instrumented buildings.
JOURNAL OF ENGINEERING MECHANICS
(2021)
Article
Engineering, Mechanical
Milad Roohi, Kalil Erazo, David Rosowsky, Eric M. Hernandez
Summary: This paper introduces a model-based observer for state estimation in nonlinear hysteretic structural systems, designed to be physically realizable as a nonlinear structural model and offer good performance in real-world applications.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Engineering, Civil
John E. Lens, Mandar M. Dewoolkar, Eric M. Hernandez
Summary: This study conducted quantitative analysis on typical multiple span bridges in low-to-moderate seismic hazard regions of the Central and Eastern United States. The research results indicate a low likelihood of significant seismic damage to these bridges overall, but certain bridge features may require specific analysis.
EARTHQUAKE SPECTRA
(2021)
Article
Engineering, Mechanical
Chandler B. Smith, Eric M. Hernandez
Summary: This paper investigates the ability of l(1)-norm regularized inverse methods to quantify sparse damage and finds that sparsity alone is insufficient for solving the inverse problem that involves significant changes in both mass and stiffness. By incorporating a nonnegative constraint with sparsity, physically meaningful solutions can be obtained when damage is defined by local reductions to stiffness and mass.
JOURNAL OF ENGINEERING MECHANICS
(2022)
Article
Engineering, Civil
Reza Filizadeh, Eric Hernandez, David Rosowsky
Summary: Explicit multihazard analysis of structures has received attention due to its importance in assessing the effects of multiple hazards on structures, especially bridges. This paper explored the damage scenarios and performance criteria that require an explicit multihazard analysis for overpass bridges in the US. The analysis focused on seismic, scour, and corrosion hazards, assuming seismic hazard as dominant. The study used a probabilistic methodology to model time-dependent damage processes, considering uncertainties associated with earthquake occurrence and intensity, corrosion initiation time and rate, and stream flow intensity. The findings indicated that the combined effect of multiple hazards becomes important in evaluating low-probability damage events during the life of the structure.
ASCE-ASME JOURNAL OF RISK AND UNCERTAINTY IN ENGINEERING SYSTEMS PART A-CIVIL ENGINEERING
(2023)
Proceedings Paper
Engineering, Electrical & Electronic
Laurence A. Clarfeld, Margaret J. Eppstein, Paul D. H. Hines, Eric M. Hernandez
2018 POWER SYSTEMS COMPUTATION CONFERENCE (PSCC)
(2018)
Article
Engineering, Mechanical
Xuanen Kan, Yanjun Lu, Fan Zhang, Weipeng Hu
Summary: A blade disk system is crucial for the energy conversion efficiency of turbomachinery, but differences between blades can result in localized vibration. This study develops an approximate symplectic method to simulate vibration localization in a mistuned bladed disk system and reveals the influences of initial positive pressure, contact angle, and surface roughness on the strength of vibration localization.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Zimeng Liu, Cheng Chang, Haodong Hu, Hui Ma, Kaigang Yuan, Xin Li, Xiaojian Zhao, Zhike Peng
Summary: Considering the calculation efficiency and accuracy of meshing characteristics of gear pair with tooth root crack fault, a parametric model of cracked spur gear is established by simplifying the crack propagation path. The LTCA method is used to calculate the time-varying meshing stiffness and transmission error, and the results are verified by finite element method. The study also proposes a crack area share index to measure the degree of crack fault and determines the application range of simplified crack propagation path.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Rongjian Sun, Conggan Ma, Nic Zhang, Chuyo Kaku, Yu Zhang, Qirui Hou
Summary: This paper proposes a novel forward calculation method (FCM) for calculating anisotropic material parameters (AMPs) of the motor stator assembly, considering structural discontinuities and composite material properties. The method is based on multi-scale theory and decouples the multi-scale equations to describe the equivalence and equivalence preconditions of AMPs of two scale models. The effectiveness of this method is verified by modal experiments.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Hao Zhang, Jiangcen Ke
Summary: This research introduces an intelligent scheduling system framework to optimize the ship lock schedule of the Three Gorges Hub. By analyzing navigational rules, operational characteristics, and existing problems, a mixed-integer nonlinear programming model is formulated with multiple objectives and constraints, and a hybrid intelligent algorithm is constructed for optimization.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Jingjing He, Xizhong Wu, Xuefei Guan
Summary: A sensitivity and reliability enhanced ultrasonic method has been developed in this study to monitor and predict stress loss in pre-stressed multi-layer structures. The method leverages the potential breathing effect of porous cushion materials in the structures to increase the sensitivity of the signal feature to stress loss. Experimental investigations show that the proposed method offers improved accuracy, reliability, and sensitivity to stress change.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Benyamin Hosseiny, Jalal Amini, Hossein Aghababaei
Summary: This paper presents a method for monitoring sub-second or sub-minute displacements using GBSAR signals, which employs spectral estimation to achieve multi-dimensional target detection. It improves the processing of MIMO radar data and enables high-resolution fast displacement monitoring from GBSAR signals.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Xianze Li, Hao Su, Ling Xiang, Qingtao Yao, Aijun Hu
Summary: This paper proposes a novel method for bearing fault identification, which can accurately identify faults with few samples under complex working conditions. The method is based on a Transformer meta-learning model, and the final result is determined by the weighted voting of multiple models.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Xiaomeng Li, Yi Wang, Guangyao Zhang, Baoping Tang, Yi Qin
Summary: Inspired by chaos fractal theory and slowly varying damage dynamics theory, this paper proposes a new health monitoring indicator for vibration signals of rotating machinery, which can effectively monitor the mechanical condition under both cyclo-stationary and variable operating conditions.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Hao Wang, Songye Zhu
Summary: This paper extends the latching mechanism to vibration control to improve energy dissipation efficiency. An innovative semi-active latched mass damper (LMD) is proposed, and different latching control strategies are tested and evaluated. The latching control can optimize the phase lag between control force and structural response, and provide an innovative solution to improve damper effectiveness and develop adaptive semi-active dampers.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Menghao Ping, Xinyu Jia, Costas Papadimitriou, Xu Han, Chao Jiang, Wang-Ji Yan
Summary: Identification of non-Gaussian processes is a challenging task in engineering problems. This article presents an improved orthogonal series expansion method to convert the identification of non-Gaussian processes into a finite number of non-Gaussian coefficients. The uncertainty of these coefficients is quantified using polynomial chaos expansion. The proposed method is applicable to both stationary and nonstationary non-Gaussian processes and has been validated through simulated data and real-world applications.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Lei Li, Wei Yang, Dongfa Li, Jianxin Han, Wenming Zhang
Summary: The frequency locking phenomenon induced by modal coupling can effectively overcome the dependence of peak frequency on driving strength in nonlinear resonant systems and improve the stability of peak frequency. This study proposes the double frequencies locking phenomenon in a three degrees of freedom (3-DOF) magnetic coupled resonant system driven by piezoelectricity. Experimental and theoretical investigations confirm the occurrence of first frequency locking and the subsequent switching to second frequency locking with the increase of driving force. Furthermore, a mass sensing scheme for double analytes is proposed based on the double frequencies locking phenomenon.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Kai Ma, Jingtao Du, Yang Liu, Ximing Chen
Summary: This study explores the feasibility of using nonlinear energy sinks (NES) as replacements for traditional linear tuned mass dampers (TMD) in practical engineering applications, specifically in diesel engine crankshafts. The results show that NES provides better vibration attenuation for the crankshaft compared to TMD under different operating conditions.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Wentao Xu, Li Cheng, Shuaihao Lei, Lei Yu, Weixuan Jiao
Summary: In this study, a high-precision hydraulic mechanical stand and a vertical mixed-flow pumping station device were used to conduct research on cavitation signals of mixed-flow pumps. By analyzing the water pressure pulsation signal, it was found that the power spectrum density method is more sensitive and capable of extracting characteristics compared to traditional time-frequency domain analysis. This has significant implications for the identification and prevention of cavitation in mixed-flow pump machinery.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Xiaodong Chen, Kang Tai, Huifeng Tan, Zhimin Xie
Summary: This paper addresses the issue of parasitic motion in microgripper jaws and its impact on clamping accuracy, and proposes a symmetrically stressed parallelogram mechanism as a solution. Through mechanical modeling and experimental validation, the effectiveness of this method is demonstrated.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)
Article
Engineering, Mechanical
Zhifeng Shi, Gang Zhang, Jing Liu, Xinbin Li, Yajun Xu, Changfeng Yan
Summary: This study provides useful guidance for early bearing fault detection and diagnosis by investigating the effects of crack inclination and propagation direction on the vibration characteristics of bearings.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2024)