| 1. |
- Javor, Vesna, et al.
(författare)
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Analytical Representation of Measured Lightning Currents and Its Application to Electromagnetic Field Estimation
- 2018
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Ingår i: IEEE transactions on electromagnetic compatibility (Print). - : IEEE. - 0018-9375 .- 1558-187X. ; 60:5, s. 1415-1426
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Tidskriftsartikel (refereegranskat)abstract
- Lightning discharge currents waveshapes and their derivatives with multiple peaks are measured in artificially triggered lightning experiments and at instrumented tall towers. Such waveshapes are represented in this paper by the N-peaked analytically extended function (NP-AEF) and Marquardt least-squares method is applied for the estimation of its nonlinear parameters. Typical channel-base currents of the first negative, subsequent negative strokes, and positive strokes, based on comprehensive measurements by Berger et al. at Monte San Salvatore in Switzerland, are approximated by NP-AEFs and used in the computation of lightning electromagnetic fields. A new attenuation factor introducing nonlinear current attenuation along the channel is applied within the modified transmission line model (MTLSIN). A lightning return stroke is assumed to have a vertical discharge channel at the perfectly conducting ground. In order to validate this model, calculated lightning electromagnetic fields are compared with the typical, as measured by Lin et al. at various distances from the discharges. Lightning currents and their derivatives measured at the tall towers are also approximated by NP-AEFs. For the measured artificially triggered lightning currents, MTLSIN is applied for the calculation of their electromagnetic fields. These are compared with the measured fields of specific lightning strokes, so as to results of other models.
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| 2. |
- Javor, Vesna, et al.
(författare)
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Electrostatic discharge currents and their derivatives' approximation by piecewise power-exponential functions
- 2018
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Ingår i: Turkish Journal of Electrical Engineering and Computer Sciences. - : The Scientific and Technological Research Council of Turkey (TUBITAK-ULAKBIM) - DIGITAL COMMONS JOURNALS. - 1300-0632 .- 1303-6203. ; 26:2, s. 1093-1102
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Tidskriftsartikel (refereegranskat)abstract
- An analytically extended function based on power-exponential functions is used in this paper for approxi- mation of electrostatic discharge (ESD) currents and their derivatives. The Marquardt least-squares method (MLSM) is applied for obtaining nonlinear function parameters. IEC 61000-4-2 Standard ESD current is approximated, as well as some measured ESD currents' wave shapes. Power-exponential terms are extended at the local maxima and minima of the represented wave shape, so that this approximation is done from peak to peak. ESD current derivative is approxi- mated using the same procedure in order to obtain the continuous second order derivative of the current, as all piecewise functions are of differentiability class C1L . Currents and their derivatives are often measured in ESD experiments so that their analytical representation is needed for simulation of ESD phenomena, better definition of standard requirements, and computation of the transient fields and induced effects.
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| 3. |
- Javor, Vesna, et al.
(författare)
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Modeling of Artificially-Triggered Lightning Currents by Multi-Peaked Analytically Extended Functions
- 2018
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Ingår i: Compel. - : Emerald Group Publishing Limited. - 0332-1649. ; 37:4, s. 1354-1365
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Tidskriftsartikel (refereegranskat)abstract
- Purpose: This paper aims to present the approximation of lightning currents waveshapes by the multi-peaked analytically extended function (MP-AEF) for the experimentally measured channel-base currents in the artificially triggered lightning discharges. Modified transmission line model of lightning return strokes having the channel current both linearly decaying and sinusoidally changing with height (MTLSIN) is used to calculate the lightning electromagnetic field.Design/methodology/approach: MP-AEF’s parameters for the artificially triggered lightning channel-base currents are calculated by using Marquardt least squares method (MLSM). Lightning electromagnetic fields are calculated based on electromagnetic theory relations, thin-wire antenna model of the vertical lightning channel and the assumption of the perfectly conducting ground. MTLSIN model as an engineering model of lightning strokes is used to obtain the electric field results as these are simultaneously measured in rocket-triggered lightning experiments together with the channel-base currents. Findings: MP-AEF approximates multi-peaked pulse waveshapes. Some important function parameters are chosen prior to the approximation procedure, such as current peaks and the corresponding time moments of those peaks, which presents an advantage in comparison to other functions. The desired accuracy of approximation is obtained by choosing an adequate number of function terms. MLSM is used for the estimation of unknown parameters. Using MTLSIN model, the influence of the channel height and return stroke speed on the lightning electromagnetic field waveshape is analyzed in this paper. Research limitations/implications: MP-AEF may be used for approximation of various multi-peaked waveshapes. It has no errors in the points of maxima which is important for the lightning protection systems design. MTLSIN model may be validated by using simultaneously measured lightning electromagnetic fields at various distances from the channel and for channel heights estimated in the experiments. It is also possible to approximate measured current derivatives by MP-AEF and use them for further computation. Originality/value: MTLSIN model is proposed in this paper for the evaluation of lightning electromagnetic fields induced by artificially triggered lightning discharges. The procedure is based on the approximation of lightning channel-base currents by the multi-peaked analytically extended function previously proposed by the authors. This function may be used not only for representing lightning currents but also for other waveshapes as current derivatives, electric and magnetic fields and their derivatives, which are all important for the lightning protection design. MTLSIN gives lightning electromagnetic fields results which are in better agreement with measured fields than those obtained by other models from literature.
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| 4. |
- Lundengård, Karl, 1987-, et al.
(författare)
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Optimization of the Determinant of the Vandermonde Matrix and Related Matrices
- 2018
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Ingår i: Methodology and Computing in Applied Probability. - : Springer. - 1387-5841 .- 1573-7713. ; 20:4, s. 1417-1428
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Tidskriftsartikel (refereegranskat)abstract
- The value of the Vandermonde determinant is optimized over various surfaces, including the sphere, ellipsoid and torus. Lagrange multipliers are used to find a system of polynomial equations which give the local extreme points in its solutions. Using Grobner basis and other techniques the extreme points are given either explicitly or as roots of polynomials in one variable. The behavior of the Vandermonde determinant is also presented visually in some interesting cases.
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| 5. |
- Muhumuza, Asaph Keikara, 1975-, et al.
(författare)
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The Generalized Vandermonde Interpolation Polynomial Based on Divided Differences
- 2018
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Konferensbidrag (refereegranskat)abstract
- In this article, we will construct the divided differences interpolation polynomial based on the generalized Vandermonde determinant approach. Some results regarding the appropriateness for this method for curve-fitting and approximation will be discussed. The proposed interpolation technique will be tested by construction of approximative models based on experimental data.
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