Determination of the Electrical Radius ka of a Circular Cylindrical Scatterer from the Scattered Field

1971 ◽  
Vol 49 (7) ◽  
pp. 804-819 ◽  
Author(s):  
W. M. Boerner ◽  
F. H. Vandenberghe ◽  
M. A. K. Hamid
Keyword(s):  
Inverse Problem ◽  
Scattered Field ◽  
Measurement Techniques ◽  
Optimization Procedure ◽  
Cylindrical Wave ◽  
Matrix Inversion ◽  
Nonsingular Matrix ◽  
Double Precision ◽  
Scattering Geometry ◽  
Expansion Coefficients

The inverse problem of scattering for a circular cylindrical scattering geometry is considered. The transverse far field components are related to the Fourier coefficients of the circular cylindrical wave expansion in terms of the scattered field matrix. The associated determinant which describes the scattering geometry is formulated in closed form. To achieve nonsingular matrix inversion, a novel, determinate optimization procedure for the measurement aspect angles is derived and proved. Measurement techniques or experimental results are not presented. Yet, it is shown analytically that the unknown expansion coefficients can be recovered with standard double precision matrix inversion techniques to the degree of accuracy dictated only by any suitable measurement technique. Assuming the required set of expansion coefficients {an}TM and/or {bn}TE is found, it is shown that the electrical radius ka of the scatterer can be determined from four contiguous expansion coefficients in the TM as well as the mixed TM–TE cases. Only the TE case is an exception for which a more elaborate formulation exists. The relationships between contiguous expansion coefficients of both electric and magnetic type are relevant to the general cylindrical inverse problem, since the electrical radius can be directly recovered from the scattered field data. Furthermore, the scattered field can be uniquely expressed in terms of only one set of expansion coefficients associated with either the electric or magnetic vector wave functions.

On the Inverse Problem of Scattering from a Perfectly Conducting Elliptic Cylinder

1972 ◽  
Vol 50 (17) ◽  
pp. 1987-1992 ◽  
Author(s):  
F. H. Vandenberghe ◽  
W. M. Boerner
Keyword(s):  
Inverse Problem ◽  
Electromagnetic Scattering ◽  
Scattered Field ◽  
Low Frequency ◽  
Elliptic Cylinder ◽  
Cylindrical Wave ◽  
Wave Functions ◽  
Principal Axes ◽  
Expansion Coefficients ◽  
Model Technique

The inverse problem of electromagnetic scattering from a perfectly conducting elliptic cylinder for the low-frequency case is considered. The approach is based on the model technique presented in Boerner and Vandenberghe, conjecturing that the salient features of the scatterer can be determined from the far scattered field via matrix inversion. This follows the low-frequency formulation of the scattered field as given by Udagawa and Miyazaki rather than from an expansion in the elliptic cylindrical wave functions. It is then shown that the characteristic parameters of the ellipse, i.e. the principal axes a′ and b′ and the numerical eccentricity ε, can be directly recovered from the expansion coefficients associated with circular cylindrical wave functions, as is presented in Udagawa and Miyazaki.

Determination of the Electrical Radius ka of a Spherical Scatterer from the Scattered Field

1971 ◽  
Vol 49 (11) ◽  
pp. 1507-1535 ◽  
Author(s):  
W. M. Boerner ◽  
F. H. Vandenberghe
Keyword(s):  
Inverse Problem ◽  
Closed Form ◽  
Scattered Field ◽  
Closed Form Solution ◽  
Form Solution ◽  
Vector Wave ◽  
Wave Expansion ◽  
Spherical Scatterer ◽  
Expansion Coefficients ◽  
Spherical Vector

The inverse problem of scattering for a spherical vector scattering geometry is considered. The transverse scattered field components are related to the expansion coefficients of Hansen's vector wave expansion in terms of the scattered field matrix. This matrix needs to be inverted to obtain the unknown expansion coefficients which are required to recover the shape of the target in question. Since the particular properties of the spherical vector wave expansion may cause highly instable matrix inversion, an analytical, closed form solution of the determinant associated with the scattered field matrix was sought. For vector scattering geometries representing the mth degree multipole cases such closed form solutions for the associated determinant of truncated order 2N are derived, using a novel complementary series expansion for the employed forms of the associated Legendre's functions of the first kind. A novel determinate optimization procedure is presented which enables the specification of the optimal distribution of measurement aspect angles within any given finite measurement cone of the unit sphere of directions. The closed form solution for nonsymmetrical vector scattering geometries is presented in Appendix III only for the value N = 3 (m = 0 and 1) employing properties of quadratic forms as derived in Appendix II. It is then shown that the electrical radius ka of a perfectly conducting spherical scatterer can be directly recovered from a finite number of contiguous expansion coefficients similar to the cylindrical case presented in Boerner, Vandenberghe, and Hamid. Furthermore, relationships between contiguous expansion coefficients of both electric and magnetic type result, which are relevant to the general inverse problem since the scattered field can be uniquely expressed in terms of only one set of expansion coefficients associated with either the electric or magnetic vector wave functions.

An Inverse Problem for the Mechanical Characterization of Steels From the Taylor Test

2010 ◽  
Author(s):  
C. Hernandez ◽  
A. Maranon ◽  
I. A. Ashcroft ◽  
J. P. Casas-Rodriguez
Keyword(s):  
Inverse Problem ◽  
Material Characterization ◽  
Impact Test ◽  
Kinematic Hardening ◽  
Optimization Procedure ◽  
Material Model ◽  
Hardening Material ◽  
Final Shape ◽  
Taylor Impact ◽  
Taylor Impact Test

Material characterization procedures are often complicated processes. In particular, dynamic material characterization usually requires many complicated and expensive tests. One of the tools used to characterize the behavior of materials under dynamic loading is the Taylor impact test. In this experiment, a flat-ended cylinder of initial uniform cross-sectional area is fired at a rigid target. The terminal geometry of the deformed cylinder is used to determine the material strength at different strain rates. This paper presents the formulation and solution of a first class inverse problem for the identification of the kinematic hardening material model from a Taylor impact test of a steel cylinder. The inverse problem is formulated as an optimization procedure for the determination of the optimal set of the model constants. The input parameter of the procedure is the final shape of a Taylor impact test specimen, in terms of central geometric moments, at a given impact velocity. The output parameters are the material model constants, which are determined by fitting the final shape of a numerically simulated Taylor specimen to the final shape of the experimental specimen. This optimization procedure is performed by a real-coded genetic algorithm. The paper includes a numerical example of the characterization procedure for a steel 1018 Taylor specimen of 8 mm diameter and 20 mm length, impacted at a velocity of 250 m/s. This simulation demonstrates the performance of the algorithm and the ability to estimate the kinematic hardening material model constants.

scholarly journals Approximate Bayesian framework for 3D reconstruction in a volumetric PIV/PTV measurement

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Sayantan Bhattacharya ◽  
Ilias Bilionis ◽  
Pavlos Vlachos
Keyword(s):  
Inverse Problem ◽  
3D Reconstruction ◽  
Velocity Measurement ◽  
Tracer Particle ◽  
Measurement Techniques ◽  
Local Maximum ◽  
Position Estimation ◽  
Map Estimation ◽  
Reconstruction Methods ◽  
Particle Images

Non-invasive flow velocity measurement techniques like volumetric Particle Image Velocimetry (PIV) (Elsinga et al., 2006; Adrian and Westerweel, 2011) and Particle Tracking Velocimetry (PTV) (Maas, Gruen and Papantoniou, 1993) use multi-camera projections of tracer particle motion to resolve three-dimensional flow structures. A key step in the measurement chain involves reconstructing the 3D intensity field (PIV) or particle positions (PTV) given the projected images and known camera correspondence. Due to limited number of camera-views the projected particle images are non-unique making the inverse problem of volumetric reconstruction underdetermined. Moreover, higher particle concentration (>0.05 ppp) increases erroneous reconstructions or “ghost” particles and decreases reconstruction accuracy. Current reconstruction methods either use voxel-based representation for intensity reconstruction (e.g. MART (Elsinga et al., 2006)) or a particle-based approach (e.g. IPR (Wieneke, 2013)) for 3D position estimation. The former method is computationally intensive and has a lesser positional accuracy due to stretched shape of the reconstructed particle along the line of sight. The latter compromises triangulation accuracy (Maas, Gruen and Papantoniou, 1993) due to overlapping particle images for higher particle concentrations. Thus, each method has its own challenges and the error in 3D reconstruction significantly affects the accuracy of the velocity measurement. Though, other methods like maximum-a-posteriori (MAP) estimation have been previously developed (Levitan and Herman, 1987; Bouman and Sauer, 1996) for computed Tomography data, it has not been explored for PIV/ PTV 3D reconstruction. Here, we use a MAP estimation framework to model and solve the inverse problem. The cost function is optimized using a stochastic gradient ascent (SGA) algorithm. Such an optimization can converge to a better local maximum and also use smaller image patches for efficient iterations.

scholarly journals Optimization of shot peen forming patterns to achieve complex target shapes the inverse problem

2021 ◽  
Author(s):  
Hong Yan Miao ◽  
Martin levesque ◽  
Frederick Gosselin
Keyword(s):  
Inverse Problem ◽  
Optimization Procedure ◽  
Spherical Shape ◽  
Forming Process ◽  
Peen Forming ◽  
Out Of Plane ◽  
Order Of Magnitude ◽  
Complex Target ◽  
Wing Skin ◽  
Relative Differences

The inverse problem of determining how to shot peen a plate such that it deforms into a desired target shape is a challenge in the peen forming industry. While peening thick plates uniformly on one side results in a spherical shape, with the same curvature in all directions, complex peening patterns are required to form other shapes, such as cylinders and saddles found on fuselages and wing skin panels. In this study, we present an optimization procedure to automatically compute shot peening patterns. This procedure relies on an idealized model of the peen forming process, where the effect of the treatment is modeled by in-plane expansion of the peened areas, and on an off-the-shelf optimization algorithm. For validation purposes, we peen formed three 305 X 305 X 4.9 mm and two 762 X 762 X 4.9mm 2024--T3 aluminium alloy plates into cylindrical and saddle shapes using the same peening treatment. The obtained shapes qualitatively match simulations. For 305 X 305 X 4.9mm plates, the relative differences had the same distribution and were of the same order of magnitude as initial out-of-plane deviations measured on the as-received plates.

scholarly journals Rubber Stiffness Optimization for Floor Vibration Attenuation of a Light Bus Based on Matrix Inversion TPA

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Hui Shi ◽  
Wenku Shi ◽  
Changhai Yang ◽  
Guozheng Liu ◽  
Zhaomeng Fan ◽  
...  
Keyword(s):  
Natural Frequencies ◽  
Optimization Procedure ◽  
Matrix Inversion ◽  
Vibration Test ◽  
Transfer Path ◽  
Stiffness Optimization ◽  
Market Competitiveness ◽  
Vibration Attenuation ◽  
The Matrix ◽  
Floor Vibration

The NVH characteristics of light buses are a very important performance for market competitiveness. To solve the serious floor vibration of a light bus at speed of 60 km/h and 90 km/h, we first derive the matrix inversion TPA (MITPA) method, and then transfer path contribution is analyzed by applying matrix inversion TPA with TPA model establishment, operational vibration test, and FRF measurement. Next, the energy decoupling rate of the powertrain mount system (PMS) is optimized by rubber stiffness optimization based on the path contribution analysis taking both amplitude and phase into consideration. The optimized natural frequencies and energy decoupling rate indicate that energy decoupling rate (EDR) of each DoF of the powertrain mount system is improved. Finally, to verify the optimization effect, this paper implements an operational vibration test with optimized mount installed. The results indicate that floor vibration of postoptimization is improved significantly compared with that of preoptimization. This paper offers a method for engineers to improve vibration problem of vehicle by combining experimental TPA for identification of dominant paths with optimization procedure.

scholarly journals Diffraction of Transient Cylindrical Waves by a Rigid Oscillating Strip

2020 ◽  
Vol 10 (10) ◽  
pp. 3568
Author(s):  
Amer Bilal Mann ◽  
Muhammad Ramzan ◽  
Imran Fareed Nizami ◽  
Seifedine Kadry ◽  
Yunyoung Nam ◽  
...  
Keyword(s):  
Mathematical Analysis ◽  
Wave Diffraction ◽  
Scattered Field ◽  
Integral Transforms ◽  
Cylindrical Wave ◽  
Steepest Descent ◽  
Cylindrical Waves ◽  
Cylindrical Source ◽  
Method Of Steepest Descent

This investigation portrays the transient cylindrical wave diffraction by an oscillating strip. Mathematical analysis of the problem is carried out with the help of an integral transforms and the Wiener–Hopf technique. Using far zone approximation, the scattered field is evaluated by the method of steepest descent. This study takes into consideration the transient cylindrical source and an oscillating strip such that both the source and a scatterer have different oscillating frequencies ω 1 ′ and ω 0 ′ , respectively. The situation under consideration is well supported by graphical results showing the effects of emerging parameters.

CLASSIFICATION OF OBJECTS IN AN ACOUSTIC WAVEGUIDE BY INVERSION OF THE FARFIELD DATA

2006 ◽  
Vol 14 (02) ◽  
pp. 185-199 ◽  
Author(s):  
DOO-SUNG LEE ◽  
R. P. GILBERT ◽  
NOAM ZEEV
Keyword(s):  
Inverse Problem ◽  
Analytical Solution ◽  
Least Squares ◽  
Scattered Field ◽  
Body Problem ◽  
Acoustic Fields ◽  
Parallel Plates ◽  
Tangent Sphere ◽  
Unknown Object

In this paper we investigate the unknown body problem in a waveguide. The Rayleigh conjecture states that every point on an illuminated body radiates sound from that point as if the point lies on its tangent sphere. This conjecture is the cornerstone of the intersecting canonical body approximation ICBA for solving the unknown body inverse problem. Therefore, the use of the ICBA requires that an analytical solution be known exterior to the sphere in the waveguide, which leads us to analytically compute the exterior solution for a sphere between two parallel plates. A least-squares matching of theoretical acoustic fields against the measured, scattered field permits a reconstruction of the unknown object.

scholarly journals Multipole Theory and Algorithms for Target Support Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Edwin A. Marengo
Keyword(s):  
Inverse Problem ◽  
Helmholtz Equation ◽  
Inverse Scattering ◽  
Scattered Field ◽  
Source Region ◽  
Multipole Expansion ◽  
Source Regions ◽  
Support Estimation

The inverse problem of estimating the smallest region of localization (minimum source region) of a source or scatterer that can produce a given radiation or scattered field is investigated with the help of the multipole expansion. The results are derived in the framework of the scalar Helmholtz equation. The proposed approach allows the estimation of possibly nonconvex minimum source regions. The derived method is illustrated with an example relevant to inverse scattering.

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