An accelerated sequential subspace optimization method based on homotopy perturbation iteration for nonlinear ill-posed problems

2019 ◽  
Vol 35 (12) ◽  
pp. 125005 ◽  
Author(s):  
Shanshan Tong ◽  
Bo Han ◽  
Haie Long ◽  
Ruixue Gu
Keyword(s):  
Optimization Method ◽  
Homotopy Perturbation ◽  
Subspace Optimization ◽  
Ill Posed

scholarly journals Reconstruction of Electrical Impedance Tomography Using Fish School Search, Non-Blind Search, and Genetic Algorithm

2017 ◽  
Vol 8 (2) ◽  
pp. 17-33 ◽  
Author(s):  
Valter A. F. Barbosa ◽  
Reiga R. Ribeiro ◽  
Allan R. S. Feitosa ◽  
Victor L. B. A. Silva ◽  
Arthur D. D. Rocha ◽  
...  
Keyword(s):  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Imaging Technique ◽  
Optimization Method ◽  
Impedance Tomography ◽  
Circular Section ◽  
Fish School ◽  
Noninvasive Imaging Technique ◽  
Ill Posed ◽  
Blind Search

Electrical Impedance Tomography (EIT) is a noninvasive imaging technique that does not use ionizing radiation, with application both in environmental sciences and in health. Image reconstruction is performed by solving an inverse problem and ill-posed. Evolutionary Computation and Swarm Intelligence have become a source of methods for solving inverse problems. Fish School Search (FSS) is a promising search and optimization method, based on the dynamics of schools of fish. In this article the authors present a method for reconstruction of EIT images based on FSS and Non-Blind Search (NBS). The method was evaluated using numerical phantoms consisting of electrical conductivity images with subjects in the center, between the center and the edge and on the edge of a circular section, with meshes of 415 finite elements. The authors performed 20 simulations for each configuration. Results showed that both FSS and FSS-NBS were able to converge faster than genetic algorithms.

scholarly journals Application of He's Homotopy Perturbation Method for Cauchy Problem of Ill-Posed Nonlinear Diffusion Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Ali Zakeri ◽  
Azim Aminataei ◽  
Qodsiyeh Jannati
Keyword(s):  
Cauchy Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Nonlinear Diffusion ◽  
Homotopy Perturbation Method ◽  
Finite Interval ◽  
Nonlinear Diffusion Equation ◽  
Third Order ◽  
Homotopy Perturbation ◽  
Ill Posed

We consider a Cauchy problem of unidimensional nonlinear diffusion equation on finite interval. This problem is ill-posed and its approximate solution is unstable. We apply the He's homotopy perturbation method (HPM) and obtain the third-order asymptotic expansion. We show that if the conductivity term in diffusion equation has a specified condition, the above solution can be estimated. Finally, a numerical experiment is provided to illustrate the method.

scholarly journals Image Reconstruction Based on Homotopy Perturbation Inversion Method for Electrical Impedance Tomography

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jing Wang ◽  
Bo Han
Keyword(s):  
Image Reconstruction ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Perturbation Technique ◽  
Inversion Method ◽  
Impedance Tomography ◽  
Data Noise ◽  
Homotopy Perturbation ◽  
Ill Posed ◽  
Homotopy Perturbation Technique

The image reconstruction for electrical impedance tomography (EIT) mathematically is a typed nonlinear ill-posed inverse problem. In this paper, a novel iteration regularization scheme based on the homotopy perturbation technique, namely, homotopy perturbation inversion method, is applied to investigate the EIT image reconstruction problem. To verify the feasibility and effectiveness, simulations of image reconstruction have been performed in terms of considering different locations, sizes, and numbers of the inclusions, as well as robustness to data noise. Numerical results indicate that this method can overcome the numerical instability and is robust to data noise in the EIT image reconstruction. Moreover, compared with the classical Landweber iteration method, our approach improves the convergence rate. The results are promising.

An Inverse Method Using a Genetic Algorithm to Determine Spatial Temperature Distribution From Infrared Tranmissivity Measurements in a Gas

Volume 4 ◽  
2004 ◽  
Author(s):  
Keith A. Woodbury ◽  
Courtney Graham ◽  
John Baker ◽  
Charles Karr
Keyword(s):  
Genetic Algorithm ◽  
Temperature Distribution ◽  
Inverse Problems ◽  
Inverse Method ◽  
Biological Evolution ◽  
Optimization Method ◽  
Global Optimum ◽  
Simple Problem ◽  
Straight Line ◽  
Ill Posed

The ill-posed nature of inverse problems suggests that a solution be obtained through an optimization method. Genetic algorithms (GAs) effectively locate the global optimum, and are therefore an appealing technique to solve inverse problems. GAs mimic biological evolution, refining a set of solutions until the best solution is found. In this report, a genetic algorithm is developed and demonstrated based on a simple problem of determining the equation of a straight line. Then the GA is modified and implemented to estimate the temperature distribution in a gas based on the measured infrared tranmissivity distribution. The ulitimate task of this inverse method will be determination of the gas composition based on these transmissivity measurements.

scholarly journals Parameter Optimization Method for Identifying the Optimal Nonlinear Parameters of a Miniature Transducer with a Metal Membrane

2018 ◽  
Vol 8 (12) ◽  
pp. 2647 ◽  
Author(s):  
Yin-Cheng Jian ◽  
Yu-Ting Tsai ◽  
S. Pawar
Keyword(s):  
Numerical Simulation ◽  
Parameter Optimization ◽  
Optimization Method ◽  
Lumped Parameter Model ◽  
Displacement Sensor ◽  
Nonlinear Parameters ◽  
Metal Membrane ◽  
Lumped Parameter ◽  
Constrained Equation ◽  
Ill Posed

This study proposes a parameter optimization method for identifying the optimal nonlinear parameters of a miniature transducer with a metal membrane. Specifically, a nonlinear lumped parameter model (LPM) of a miniature transducer that accounts for predicted displacement in a manner that is consistent with the displacement measured by a high-precision capacitance micro-displacement sensor is proposed. To avoid application of the proposed optimization method to an ill-posed problem, this paper proposes a constrained equation that is derived from the relationships of nonlinear parameters. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is used to minimize the objective function in order to obtain an appropriate solution from the proposed nonlinear LPM. The numerical simulation results and a discussion of the experiments are presented. The numerical simulation verification demonstrated that the presented method can estimate the suitable nonlinear parameters for the displacement with errors. With regard to empirical verification, the empirical investigations showed that the proposed method could accurately assess the nonlinear parameters of a miniature transducer with a metal membrane.

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