scholarly journals NDF of Scattered Fields for Strip Geometries

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 202
Author(s):  
Ehsan Akbari Sekehravani ◽  
Giovanni Leone ◽  
Rocco Pierri
Keyword(s):  
Degrees Of Freedom ◽  
Plane Waves ◽  
Singular Value ◽  
Scattering Operator ◽  
Scattering Problems ◽  
First Order ◽  
Incident Plane ◽  
Minimum Number ◽  
Scattered Fields ◽  
Value Decomposition

Solving inverse scattering problems by numerical methods requires investigating the number of independent pieces of information that can be reconstructed stably. To this end, we address the evaluation of the Number of Degrees of Freedom (NDF) of far-zone scattered fields for some strip geometries under the first-order Born approximation. The analysis is performed by employing the Singular Value Decomposition (SVD) of the scattering operator in the two-dimensional scalar geometry of one or more strips illuminated by a TM polarized plane wave. It is known that investigating the scattering scene at different incident plane waves (multi-view configuration) enhances the NDF. Therefore we mean to examine the minimum number of incident plane waves providing the NDF of the scattered fields both by theoretical estimations and numerical verifications.

scholarly journals Efficient Computation of Wideband RCS Using Singular Value Decomposition Enhanced Improved Ultrawideband Characteristic Basis Function Method

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Wen-yan Nie ◽  
Zhong-gen Wang
Keyword(s):  
Singular Value Decomposition ◽  
Basis Function ◽  
Matrix Equation ◽  
Function Method ◽  
Plane Waves ◽  
Singular Value ◽  
Efficient Computation ◽  
Incident Plane ◽  
Filling Time ◽  
Value Decomposition

The singular value decomposition (SVD) enhanced improved ultrawideband characteristic basis function method (IUCBFM) is proposed to efficiently analyze the wideband scattering problems. In the conventional IUCBFM, the SVD is only applied to reduce the linear dependency among the characteristic basis functions (CBFs) due to the overestimation of incident plane waves. However, the increase in the size of the targets under analysis will require a large number of incident plane waves and it will become very time-consuming to solve such numbers of the matrix equation. In this paper, the excitation matrix is compressed by using the SVD in order to reduce both the number of matrix equation solutions and the number of CBFs compared with the traditional IUCBFM. Furthermore, the dimensions of the reduced matrix and the reduced matrix filling time are significantly reduced. Numerical results demonstrate that the proposed method is accurate and efficient.

scholarly journals Resolution of Born Scattering in Curve Geometries: Aspect-Limited Observations and Excitations

Electronics ◽  
2021 ◽  
Vol 10 (24) ◽  
pp. 3089
Author(s):  
Ehsan Akbari Sekehravani ◽  
Giovanni Leone ◽  
Rocco Pierri
Keyword(s):  
Degrees Of Freedom ◽  
Plane Waves ◽  
Single Frequency ◽  
Limited Data ◽  
Scattering Problems ◽  
Approximation Accuracy ◽  
Imaging Results ◽  
Exact Evaluation ◽  
Spread Function ◽  
Scattered Fields

In inverse scattering problems, the most accurate possible imaging results require plane waves impinging from all directions and scattered fields observed in all observation directions around the object. Since this full information is infrequently available in actual applications, this paper is concerned with the mathematical analysis and numerical simulations to estimate the achievable resolution in object reconstruction from the knowledge of the scattered far-field when limited data are available at a single frequency. The investigation focuses on evaluating the Number of Degrees of Freedom (NDF) and the Point Spread Function (PSF), which accounts for reconstructing a point-like unknown and depends on the NDF. The discussion concerns objects belonging to curve geometries, in this case, circumference and square scatterers. In addition, since the exact evaluation of the PSF can only be accomplished numerically, an approximated closed-form evaluation is introduced and compared with the exact one. The approximation accuracy of the PSF is verified by numerical results, at least within its main lobe region, which is the most critical as far as the resolution discussion is concerned. The main result of the analysis is the space variance of the PSF for the considered geometries, showing that the resolution is different over the investigation domain. Finally, two numerical applications of the PSF concept are shown, and their relevance in the presence of noisy data is outlined.

Ultra-wideband characteristic basis function method merging the secondary level characteristic basis functions for rapid computation of wideband radar cross section problems from conducting targets

2020 ◽  
pp. 1-10
Author(s):  
Zhong-Gen Wang ◽  
Jun-Wen Mu ◽  
Wen-Yan Nie
Keyword(s):  
Basis Function ◽  
Function Method ◽  
Secondary Level ◽  
Singular Value ◽  
Basis Functions ◽  
Ultra Wideband ◽  
Scattering Problems ◽  
Wideband Radar ◽  
Value Decomposition ◽  
A Current

In this paper, a merged ultra-wideband characteristic basis function method (MUCBFM) is presented for high-precision analysis of wideband scattering problems. Unlike existing singular value decomposition (SVD) enhanced improved ultra-wideband characteristic basis function method (SVD-IUCBFM), the MUCBFM reduces the number of characteristic basis functions (CBFs) necessary to express a current distribution. This reduction is achieved by combining primary CBFs (PCBFs) with the secondary level CBFs (SCBFs) to form a single merged ultra-wideband characteristic basis function (MUCBF). As the MUCBF incorporates the effects of PCBFs and SCBFs, the accuracy does not change significantly compared to that obtained by the SVD-IUCBFM. Furthermore, the efficiencies of constructing the CBFs and filling the reduced matrix are improved. Numerical examples verify and demonstrate that the proposed method is credible both in terms of accuracy and efficiency.

Reciprocity-Based Singular Value Decomposition for Inverse Kinematic Analysis of the Metamorphic Multifingered Hand

2012 ◽  
Vol 4 (3) ◽  
Author(s):  
Lei Cui ◽  
Jian S. Dai
Keyword(s):  
Singular Value Decomposition ◽  
Degrees Of Freedom ◽  
Singular Values ◽  
Analytical Form ◽  
Inverse Kinematic ◽  
Singular Value ◽  
Robotic Hand ◽  
Value Analysis ◽  
Constraint Equations ◽  
Value Decomposition

With a new type of multifingered hands that raise a new philosophy in the construction and study of a multifingered hand, this paper is a follow-on study of the kinematics of the metamorphic multifingered hand based on finger constraint equations. The finger constraint equations lead to a comprehensive mathematical model of the hand with a reconfigurable palm which integrates all finger motions with the additional palm motion. Singular values of the partitioned Jacobian matrix in their analytical form are derived and applied to obtaining analytical solution to inverse kinematics of a complete robotic hand. The paper for the first time solves this integrated motion and the multifingered hand model with the singular value decomposition and extra degrees of freedom are examined with the singular value analysis to avoid the singularities. The work identifies finger displacement and velocity with effect from the articulated palm and presents a new way of analyzing a multifingered robotic hand.

COUPLED SINGULAR VALUE DECOMPOSITION OF A CROSS-COVARIANCE MATRIX

2010 ◽  
Vol 20 (04) ◽  
pp. 293-318 ◽  
Author(s):  
ALEXANDER KAISER ◽  
WOLFRAM SCHENCK ◽  
RALF MÖLLER
Keyword(s):  
Singular Value Decomposition ◽  
Covariance Matrix ◽  
Order Approximation ◽  
Singular Value ◽  
Singular Vectors ◽  
First Order ◽  
Learning Rules ◽  
Cross Covariance ◽  
First Order Approximation ◽  
Value Decomposition

We derive coupled on-line learning rules for the singular value decomposition (SVD) of a cross-covariance matrix. In coupled SVD rules, the singular value is estimated alongside the singular vectors, and the effective learning rates for the singular vector rules are influenced by the singular value estimates. In addition, we use a first-order approximation of Gram-Schmidt orthonormalization as decorrelation method for the estimation of multiple singular vectors and singular values. Experiments on synthetic data show that coupled learning rules converge faster than Hebbian learning rules and that the first-order approximation of Gram-Schmidt orthonormalization produces more precise estimates and better orthonormality than the standard deflation method.

scholarly journals A necessary condition ensuring the strong hyperbolicity of first-order systems

2019 ◽  
Vol 16 (01) ◽  
pp. 193-221
Author(s):  
Fernando Abalos
Keyword(s):  
Evolution Equations ◽  
Sufficient Conditions ◽  
Singular Values ◽  
Singular Value ◽  
Necessary Condition ◽  
Finite Conductivity ◽  
Charged Fluids ◽  
First Order ◽  
Value Decomposition ◽  
Necessary And Sufficient

We study strong hyperbolicity of first-order partial differential equations for systems with differential constraints. In these cases, the number of equations is larger than the unknown fields, therefore, the standard Kreiss necessary and sufficient conditions of strong hyperbolicity do not directly apply. To deal with this problem, one introduces a new tensor, called a reduction, which selects a subset of equations with the aim of using them as evolution equations for the unknown. If that tensor leads to a strongly hyperbolic system we call it a hyperbolizer. There might exist many of them or none. A question arises on whether a given system admits any hyperbolization at all. To sort-out this issue, we look for a condition on the system, such that, if it is satisfied, there is no hyperbolic reduction. To that purpose we look at the singular value decomposition of the whole system and study certain one parameter families ([Formula: see text]) of perturbations of the principal symbol. We look for the perturbed singular values around the vanishing ones and show that if they behave as [Formula: see text], with [Formula: see text], then there does not exist any hyperbolizer. In addition, we further notice that the validity or failure of this condition can be established in a simple and invariant way. Finally, we apply the theory to examples in physics, such as Force-Free Electrodynamics in Euler potentials form and charged fluids with finite conductivity. We find that they do not admit any hyperbolization.

Sign in / Sign up

Export Citation Format

Share Document