A Weighted Dynamic Inverse Problem for electroencephalographic current density reconstruction

2013 ◽  
Author(s):  
E. Giraldo ◽  
J. S. Castano-Candamil ◽  
G. Castellanos-Dominguez
Keyword(s):  
Inverse Problem ◽  
Current Density ◽  
Dynamic Inverse ◽  
Dynamic Inverse Problem

scholarly journals Dynamic inverse problem for Jacobi matrices

2019 ◽  
Vol 13 (3) ◽  
pp. 431-447 ◽  
Author(s):  
Alexandr Mikhaylov ◽  
◽  
Victor Mikhaylov ◽  
Keyword(s):  
Inverse Problem ◽  
Jacobi Matrices ◽  
Dynamic Inverse ◽  
Dynamic Inverse Problem

scholarly journals Dynamic inverse problem solution using a kalman filter smoother for neuronal activity estimation

TecnoLógicas ◽  
2011 ◽  
pp. 33 ◽  
Author(s):  
Eduardo Giraldo-Suárez ◽  
Jorge I. Padilla-Buriticá ◽  
César G. Castellanos-Domínguez
Keyword(s):  
Inverse Problem ◽  
Kalman Filter ◽  
Neuronal Activity ◽  
Problem Solution ◽  
Inverse Problem Solution ◽  
Dynamic Inverse ◽  
Activity Estimation ◽  
Dynamic Inverse Problem

En este artículo se presenta un método de estimación de la actividad neuronal sobre el cerebro usando un filtro de Kalman con suavizado, que tiene en cuenta en la solución del problema inverso, la variabilidad dinámica de la serie de tiempo. Este método es aplicado sobre un modelo realista de la cabeza, calculado con elementos finitos de frontera. Se presenta un análisis comparativo entre diferentes métodos de estimación y el método propuesto sobre señales EEG simuladas para diferentes condiciones de relación señal a ruido. La solución del problema inverso se hace utilizando computación de alto desempeño y se presenta una evaluación delcosto computacional para cada método. Como resultado, el filtro de Kalman con suavizado presenta un mejor desempeño en la tarea de estimación comparado con la solución estática regularizada, y la solución dinámica sin suavizado.

scholarly journals On an application of the Boundary control method to classical moment problems.

2021 ◽  
Vol 2092 (1) ◽  
pp. 012002
Author(s):  
A S Mikhaylov ◽  
V S Mikhaylov
Keyword(s):  
Dynamical System ◽  
Inverse Problem ◽  
Boundary Control ◽  
Control Method ◽  
Jacobi Matrices ◽  
Moment Problems ◽  
Control Approach ◽  
Boundary Control Method ◽  
Dynamic Inverse ◽  
Dynamic Inverse Problem

Abstract We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach to a dynamic inverse problem for a dynamical system with discrete time associated with Jacobi matrices. We show that the solution of corresponding truncated moment problems is equivalent to solving some generalized spectral problems.

scholarly journals Inverse Problem Solution and Regularization Parameter Selection for Current Distribution Reconstruction in Switching Arcs by Inverting Magnetic Fields

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jinlong Dong ◽  
Guogang Zhang ◽  
Zhiqiang Zhang ◽  
Yingsan Geng ◽  
Jianhua Wang
Keyword(s):  
Inverse Problem ◽  
Density Distribution ◽  
Current Density ◽  
Cross Validation ◽  
Regularization Parameter ◽  
Current Density Distribution ◽  
Optimality Criteria ◽  
Parameter Selection ◽  
Selection Strategies ◽  
Regularization Parameter Selection

Current density distribution in electric arcs inside low voltage circuit breakers is a crucial parameter for us to understand the complex physical behavior during the arcing process. In this paper, we investigate the inverse problem of reconstructing the current density distribution in arcs by inverting the magnetic fields. A simplified 2D arc chamber is considered. The aim of this paper is the computational side of the regularization method, regularization parameter selection strategies, and the estimation of systematic error. To address the ill-posedness of the inverse problem, Tikhonov regularization is analyzed, with the regularization parameter chosen by Morozov’s discrepancy principle, the L-curve, the generalized cross-validation, and the quasi-optimality criteria. The provided range of regularization parameter selection strategies is much wider than in the previous works. Effects of several features on the performance of these criteria have been investigated, including the signal-to-noise ratio, dimension of measurement space, and the measurement distance. The numerical simulations show that the generalized cross-validation and quasi-optimality criteria provide a more satisfactory performance on the robustness and accuracy. Moreover, an optimal measurement distance can be expected when using a planner sensor array to perform magnetic measurements.

scholarly journals Application of Whitney elements for the reconstruction of electric arc current density in low-voltage circuit breakers

2019 ◽  
Vol 38 (3) ◽  
pp. 1036-1047 ◽  
Author(s):  
Jinlong Dong ◽  
Luca Di Rienzo ◽  
Olivier Chadebec ◽  
Jianhua Wang
Keyword(s):  
Inverse Problem ◽  
Current Density ◽  
Vector Potential ◽  
Low Voltage ◽  
Electric Arc ◽  
Electric Vector ◽  
Common Mode ◽  
Content Type ◽  
Edge Elements ◽  
Arc Current

Purpose This paper aims to present the mathematical formulations of a magnetic inverse problem for the electric arc current density reconstruction in a simplified arc chamber of a low-voltage circuit breaker. Design/methodology/approach Considering that electric arc current density is a zero divergence vector field, the inverse problem can be solved in Whitney space W2 in terms of electric current density J with the zero divergence condition as a constraint or can be solved in Whitney space W1 in terms of electric vector potential T where the zero divergence condition naturally holds. Moreover, the tree gauging condition is applied to ensure a unique solution when solving for the vector potential in space W1. Tikhonov regularization is used to treat the ill-posedness of the inverse problem complemented with L-curve method for the selection of regularization parameters. A common mode approach is proposed, which solves for the reduced electric vector potential representing the internal current loops instead of solving for the total electric vector potential. The proposed inversion approaches are numerically tested starting from simulated magnetic field values. Findings With the common mode approach, the reconstruction of current density is significantly improved for both formulations using face elements in space W2 and using edge elements in space W1. When solving the inverse problem in space W1, the choice of the regularization operator has a key role to obtain a good reconstruction, where the discrete curl operator is a good option. The standard Tikhonov regularization obtains a good reconstruction with J-formulation, but fails in the case of T-formulation. The use of edge elements requires a tree-cotree gauging to ensure the uniqueness of T. Moreover, additional efforts have to be taken to find an optimal regularization operator and an optimal tree when using edge elements. In conclusion, the J-formulation is to be preferred. Originality/value The proposed approaches are able to reconstruct the three-dimensional electric arc current density from its magnetic field in a non-intrusive manner. The formulations enable us to incorporate a priori knowledge of the unknown current density into the solution of the inverse problem, including the zero divergence condition and the boundary conditions. A common mode approach is proposed, which can significantly improve the current density reconstruction.

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