Two-step B-splines regularization method for solving an ill-posed problem of impact-force reconstruction

2006 ◽  
Vol 297 (1-2) ◽  
pp. 200-214 ◽  
Author(s):  
Fergyanto E. Gunawan ◽  
Hiroomi Homma ◽  
Yasuhiro Kanto
Keyword(s):  
Regularization Method ◽  
Impact Force ◽  
B Splines ◽  
Force Reconstruction ◽  
Ill Posed

scholarly journals Wavelet deconvolution technique for impact force reconstruction: mutual deconvolution approach

2021 ◽  
Vol 3 (SI2) ◽  
pp. first
Author(s):  
Hai Tran ◽  
Tat-Hien Le
Keyword(s):  
Indirect Method ◽  
Impact Force ◽  
Impulse Response Function ◽  
Reconstruction Process ◽  
Deconvolution Technique ◽  
Force Reconstruction ◽  
History Of ◽  
Ill Posed ◽  
And Shifts ◽  
Large Magnification

In the field of impact engineering, one of the most concerned issues is how to exactly know the history of impact force which often difficult or impossible to be measured directly. In reality, information of impact force apply to structure can be identified by means of indirect method from using information of corresponding output responses measured on structure. Namely, by using the output responses (caused by the unknown impact force) such as acceleration, displacement, or strain, etc. in cooperation with the impulse response function, the profile of unknown impact force can be rebuilt. A such indirect method is well known as impact force reconstruction or impact force deconvolution technique. Unfortunately, a simple deconvolution technique for reconstructing impact force has often encountered difficulty due to the ill-posed nature of inversion. Deconvolution technique thus often results in unexpected reconstruction of impact force with the influences of unavoidable errors which is often magnified to a large value in reconstructed result. This large magnification of errors dominates profile of desired impact force. Although there have been some regularization methods in order to improve this ill-posed problem so far, most of these regularizations are considered in the whole-time domain, and this may make the reconstruction inefficient and inaccurate because impact force is normally limited to some portions of impact duration. This work is concerned with the development of deconvolution technique using wavelets transform. Based on the advantages of wavelets (i.e., localized in time and the possibility to be analyzed at different scales and shifts), the mutual reconstruction process is proposed and formulated by considering different scales of wavelets. The experiment is conducted to verify the proposed technique. Results demonstrated the robustness of the present technique when reconstructing impact force with more stability and higher accuracy.

Sparse deconvolution for the large-scale ill-posed inverse problem of impact force reconstruction

2017 ◽  
Vol 83 ◽  
pp. 93-115 ◽  
Author(s):  
Baijie Qiao ◽  
Xingwu Zhang ◽  
Jiawei Gao ◽  
Ruonan Liu ◽  
Xuefeng Chen
Keyword(s):  
Inverse Problem ◽  
Large Scale ◽  
Impact Force ◽  
Force Reconstruction ◽  
Ill Posed

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

scholarly journals Impact force reconstruction and localization using nonconvex overlapping group sparsity

2022 ◽  
Vol 162 ◽  
pp. 107983
Author(s):  
Junjiang Liu ◽  
Baijie Qiao ◽  
Yuanchang Chen ◽  
Yuda Zhu ◽  
Weifeng He ◽  
...  
Keyword(s):  
Impact Force ◽  
Group Sparsity ◽  
Overlapping Group Sparsity ◽  
Force Reconstruction

scholarly journals Heating source localization in a reduced time

2016 ◽  
Vol 26 (3) ◽  
pp. 623-640 ◽  
Author(s):  
Sara Beddiaf ◽  
Laurent Autrique ◽  
Laetitia Perez ◽  
Jean-Claude Jolly
Keyword(s):  
Heat Conduction ◽  
Source Localization ◽  
Conjugate Gradient ◽  
Regularization Method ◽  
Three Dimensional ◽  
Gradient Algorithm ◽  
Iterative Regularization ◽  
Heating Source ◽  
Ill Posed ◽  
Reduced Time

Abstract Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this end, several configurations are detailed and effects of noisy observations are investigated.

scholarly journals Two-Parameter Regularization Method for a Nonlinear Backward Heat Problem with a Conformable Derivative

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Vu Ho ◽  
Donal O’Regan ◽  
Hoa Ngo Van
Keyword(s):  
Integral Equation ◽  
Regularization Method ◽  
Time Variable ◽  
Conformable Derivative ◽  
Heat Problem ◽  
Regularization Parameters ◽  
Ill Posed ◽  
Parameter Regularization ◽  
Two Parameter ◽  
Backward Heat Problem

In this paper, we consider the nonlinear inverse-time heat problem with a conformable derivative concerning the time variable. This problem is severely ill posed. A new method on the modified integral equation based on two regularization parameters is proposed to regularize this problem. Numerical results are presented to illustrate the efficiency of the proposed method.

An enhanced sparse regularization method for impact force identification

2019 ◽  
Vol 126 ◽  
pp. 341-367 ◽  
Author(s):  
Baijie Qiao ◽  
Junjiang Liu ◽  
Jinxin Liu ◽  
Zhibo Yang ◽  
Xuefeng Chen
Keyword(s):  
Regularization Method ◽  
Impact Force ◽  
Sparse Regularization ◽  
Force Identification
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