Global Complex Roots and Poles Finding Algorithm Based on Phase Analysis for Propagation and Radiation Problems

Kowalczyk, Piotr

doi:10.1109/tap.2018.2869213

Cited by 33 publications

(16 citation statements)

References 31 publications

(58 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Region 4 was divided into 2 subregions containing respectively: a hole (0 ≤ r ≤ g) and conductive material (g ≤ r ≤ b). Complex eigenvalues u of this region and the corresponding coefficients v = (u 2j ω μ 4 μ 0 σ 4 ) 1/2 were calculated with the expression: Equation ( 8) can be solved utilising any method of finding complex roots of a complex function [20][21][22][23].…”

Section: Methodsmentioning

confidence: 99%

Locating Defects in Conductive Materials Using the Eddy Current Model of the Filamentary Coil

Tytko

2021

J Nondestruct Eval

View full text Add to dashboard Cite

This article presents an innovative technique for detecting flaws in conductive materials by using an ideal filamentary coil. To characterize such a coil accurately and explicitly, it is sufficient to be in possession of merely two parameters: the radius of the circle within which all the turns are located and the distance of the coil from the tested surface. The mathematical model derived using the truncated region eigenfunction expansion method enables the calculation of the changes in the components of the filamentary coil impedance that are the result of positioning the coil close to the conductive material with a hole. Because of this, the air-cored coil model can be replaced with a much simpler filamentary coil model. This solution makes it is possible to detect various types of holes (internal, surface, subsurface or through) occurring in both multilayer magnetic and non-magnetic materials. The derived results were verified by means of measurements and numerical calculations based on the finite element method. Very good agreement was observed in both cases. The paper contains the source code implemented in Matlab, which is used to for calculations.

show abstract

Section: Methodsmentioning

confidence: 99%

Locating Defects in Conductive Materials Using the Eddy Current Model of the Filamentary Coil

Tytko

2021

J Nondestruct Eval

View full text Add to dashboard Cite

show abstract

“…The candidate-region contour contains discrete samples; hence, Cauchy's argument principle is used in its discretized version. That is, discrete Cauchy's argument principle (DCAP) is used [22]. The existence of zero/pole inside the unit circle is confirmed by the counterclockwise summation of quadrant differences along a path between the nodes around a candidate region.…”

Section: Complex-function Phase Analysismentioning

confidence: 99%

“…In (22) and (23), v i and v i are, respectively, current and previous velocities of the ith particle. The variables p i and p g are, respectively, the best coordinates found so far by an individual particle and the best coordinates found so far by a whole swarm.…”

Section: Mpso-wpa Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Testing Stability of Digital Filters Using Optimization Methods with Phase Analysis

Trofimowicz¹,

Stefański

2021

Energies

View full text Add to dashboard Cite

In this paper, novel methods for the evaluation of digital-filter stability are investigated. The methods are based on phase analysis of a complex function in the characteristic equation of a digital filter. It allows for evaluating stability when a characteristic equation is not based on a polynomial. The operation of these methods relies on sampling the unit circle on the complex plane and extracting the phase quadrant of a function value for each sample. By calculating function-phase quadrants, regions in the immediate vicinity of unstable roots (i.e., zeros), called candidate regions, are determined. In these regions, both real and imaginary parts of complex-function values change signs. Then, the candidate regions are explored. When the sizes of the candidate regions are reduced below an assumed accuracy, then filter instability is verified with the use of discrete Cauchy’s argument principle. Three different algorithms of the unit-circle sampling are benchmarked, i.e., global complex roots and poles finding (GRPF) algorithm, multimodal genetic algorithm with phase analysis (MGA-WPA), and multimodal particle swarm optimization with phase analysis (MPSO-WPA). The algorithms are compared in four benchmarks for integer- and fractional-order digital filters and systems. Each algorithm demonstrates slightly different properties. GRPF is very fast and efficient; however, it requires an initial number of nodes large enough to detect all the roots. MPSO-WPA prevents missing roots due to the usage of stochastic space exploration by subsequent swarms. MGA-WPA converges very effectively by generating a small number of individuals and by limiting the final population size. The conducted research leads to the conclusion that stochastic methods such as MGA-WPA and MPSO-WPA are more likely to detect system instability, especially when they are run multiple times. If the computing time is not vitally important for a user, MPSO-WPA is the right choice, because it significantly prevents missing roots.

show abstract

“…However, by treating β as a complex variable, we are able to apply methods of complex analysis; (A.22) is analytic everywhere except along a branch cut on the real axis. In order to calculate the dispersion relations presented in the main text, we applied the global complex roots and pole finding (GRPF) algorithm developed in [30].…”

Section: Appendix a Planar Waveguidementioning

confidence: 99%

ARRAW: anti-resonant reflecting acoustic waveguides

Schmidt¹,

O'Brien²,

Steel³

et al. 2020

New J. Phys.

View full text Add to dashboard Cite

Development of acoustic and optoacoustic on-chip technologies calls for new solutions to guiding, storing and interfacing acoustic and optical waves in integrated silicon-on-insulator systems. One of the biggest challenges in this field is to suppress the radiative dissipation of the propagating acoustic waves, while co-localizing the optical and acoustic fields in the same region of an integrated waveguide. Here we address this problem by introducing anti-resonant reflecting acoustic waveguides (ARRAWs)—mechanical analogues of the anti-resonant reflecting optical waveguides. We discuss the principles of anti-resonant guidance and establish guidelines for designing efficient ARRAWs. Finally, we demonstrate examples of the simplest silicon/silica ARRAW platforms that can simultaneously serve as near-IR optical waveguides, and support strong backward Brillouin scattering.

show abstract

Global Complex Roots and Poles Finding Algorithm Based on Phase Analysis for Propagation and Radiation Problems

Cited by 33 publications

References 31 publications

Locating Defects in Conductive Materials Using the Eddy Current Model of the Filamentary Coil

Locating Defects in Conductive Materials Using the Eddy Current Model of the Filamentary Coil

Testing Stability of Digital Filters Using Optimization Methods with Phase Analysis

ARRAW: anti-resonant reflecting acoustic waveguides

Contact Info

Product

Resources

About