scholarly journals Numerical investigation of an inverse problem based on regularization method

2019 ◽  
Vol 13 (3) ◽  
pp. 193-199
Author(s):  
J. Damirchi ◽  
A. R. Yazdanian ◽  
T. R. Shamami ◽  
M. Hasanpour
Keyword(s):  
Inverse Problem ◽  
Numerical Investigation ◽  
Regularization Method

scholarly journals MFS fading regularization method for the identification of boundary conditions from partial elastic displacement field data

2018 ◽  
Author(s):  
L. Caillé ◽  
J L. Hanus ◽  
F. Delvare ◽  
N. Michaux-Leblonda
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Regularization Method ◽  
Synthetic Data ◽  
Fundamental Solutions ◽  
Image Correlation ◽  
Method Of Fundamental Solutions ◽  
Elastic Displacement ◽  
Isotropic Elasticity

A method is proposed to solve an inverse problem in twodimensional linear isotropic elasticity. The inverse problem consists of the determination of both the entire displacement field and the boundary conditions inaccessible to the measurement from the partial knowledge of the displacement field. The algorithm is based on a fading regularization method (FRM) and is numerically implemented using the method of fundamental solutions (MFS). The inverse technique is first validated with synthetic data and is then applied to the interpretation of experimental measurements obtained by digital image correlation (DIC).

scholarly journals Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source

2020 ◽  
Vol 28 (2) ◽  
pp. 211-235
Author(s):  
Tran Bao Ngoc ◽  
Nguyen Huy Tuan ◽  
Mokhtar Kirane
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Regularization Method ◽  
A Priori ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Nonlinear Source ◽  
Numerical Example ◽  
Ill Posed ◽  
Time Fractional Diffusion Equation

AbstractIn this paper, we consider an inverse problem for a time-fractional diffusion equation with a nonlinear source. We prove that the considered problem is ill-posed, i.e., the solution does not depend continuously on the data. The problem is ill-posed in the sense of Hadamard. Under some weak a priori assumptions on the sought solution, we propose a new regularization method for stabilizing the ill-posed problem. We also provide a numerical example to illustrate our results.

Solving the MEG Inverse Problem: A Robust Two-Way Regularization Method

Technometrics ◽  
2015 ◽  
Vol 57 (1) ◽  
pp. 123-137
Author(s):  
Siva Tian ◽  
Jianhua Z. Huang ◽  
Haipeng Shen
Keyword(s):  
Inverse Problem ◽  
Regularization Method ◽  
Meg Inverse Problem

scholarly journals SOLUTION OF THE PROBLEM OF COMPUTATIONAL STABILITY AND CONSISTENCY OF SAMPLE ESTIMATES OF THE CORRELATION MATRIX OF OBSERVATIONS BY THE METHOD OF DYNAMIC REGULARIZATION

2019 ◽  
Vol 26 ◽  
pp. 47-60
Author(s):  
V. SKACHKOV ◽  
Keyword(s):  
Inverse Problem ◽  
Regularization Method ◽  
Correlation Matrix ◽  
Regularization Parameter ◽  
A Priori ◽  
Computational Cost ◽  
Spectral Composition ◽  
Adaptive Antenna ◽  
Computational Stability ◽  
A Priori Uncertainty

The problem of forming sample estimates of the correlation matrix of observations that satisfy the criterion "computational stability – consistency" is considered. The variants in which the direct and inverse asymptotic forms of the correlation matrix of observations are approximated by various types of estimates formed from a sample of a fixed volume are investigated. The consistency of computationally stable estimates of the correlation matrix for their static regularization was analyzed. The contradiction inherent in the problem of regularization of the estimates with a fixed parameter is revealed. The dynamic regularization method as an alternative approach is proposed, which is based on the uniqueness theorem for solving the inverse problem with perturbed initial data. An optimal mean-square approximation algorithm has been developed for dynamic regularization of sample estimates of the correlation matrix of observations, using the law of monotonic decrease in the regularizing parameter with increasing sample size. An optimal dynamic regularization function was obtained for sample estimates of the correlation matrix under conditions of a priori uncertainty with respect to their spectral composition. The preference of this approach to the regularization of sample estimates of the correlation matrix under conditions of a priori uncertainty is proved, which allows to exclude the domain of computational instability from solving the inverse problem and obtain its solution in real time without involving prediction data and additional computational cost for finding the optimal value of the regularization parameter. The application of the dynamic regularization method is shown for solving the problem of detecting a signal at the output of an adaptive antenna array in a nondeterministic clutter and jamming environment. The results of a computational experiment that confirm the main conclusions are presented.

Approximate Evaluation of Exact Solutions of Measurements Inverse Problems

2014 ◽  
Vol 527 ◽  
pp. 326-331
Author(s):  
Yuri Menshikov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Exact Solutions ◽  
Regularization Method ◽  
Rolling Mill ◽  
Approximate Evaluation ◽  
Problem Identification ◽  
Main Hypothesis

The inverse problems of measurement are investigated in this paper. The main hypothesis was suggested for evaluation of exact solutions of such problems. For obtaining the steady evaluations of exact solutions of measurement's inverse problem the regularization method was used. Two practical inverse problems have been considered as examples: Krylov's inverse problem, identification of moment of technological resistance on rolling mill.

scholarly journals A New Method for Optimal Regularization Parameter Determination in the Inverse Problem of Load Identification

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Wei Gao ◽  
Kaiping Yu ◽  
Ying Wu
Keyword(s):  
Inverse Problem ◽  
Regularization Method ◽  
Cross Validation ◽  
Regularization Parameter ◽  
New Method ◽  
Parameter Determination ◽  
Load Identification ◽  
Noise Levels ◽  
Regularization Parameters ◽  
Curve Method

According to the regularization method in the inverse problem of load identification, a new method for determining the optimal regularization parameter is proposed. Firstly, quotient function (QF) is defined by utilizing the regularization parameter as a variable based on the least squares solution of the minimization problem. Secondly, the quotient function method (QFM) is proposed to select the optimal regularization parameter based on the quadratic programming theory. For employing the QFM, the characteristics of the values of QF with respect to the different regularization parameters are taken into consideration. Finally, numerical and experimental examples are utilized to validate the performance of the QFM. Furthermore, the Generalized Cross-Validation (GCV) method and theL-curve method are taken as the comparison methods. The results indicate that the proposed QFM is adaptive to different measuring points, noise levels, and types of dynamic load.

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