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Lundengård, K., Rancic, M., Javor, V. & Silvestrov, S. (2019). Electrostatic discharge currents representation using the analytically extended function with P peaks by interpolation on a D-optimal design. Facta Universitatis Series: Electronics and Energetics, 32(1), 25-49
Open this publication in new window or tab >>Electrostatic discharge currents representation using the analytically extended function with P peaks by interpolation on a D-optimal design
2019 (English)In: Facta Universitatis Series: Electronics and Energetics, ISSN 0353-3670, Vol. 32, no 1, p. 25-49Article in journal (Refereed) Published
Abstract [en]

In this paper the Analytically Extended Function (AEF) with p peaks is used for representation of the electrostatic discharge (ESD) currents and lightning discharge currents. The fitting to data is achieved by interpolation of certain data points. In order to minimize unstable behaviour, the exponents of the AEF are chosen from a certain arithmetic sequence and the interpolated points are chosen according to a D-optimal design. The method is illustrated using several examples of currents taken from standards and measurements.

Place, publisher, year, edition, pages
UNIV NIS, 2019
Keywords
Analytically extended function, electrostatic discharge (ESD) current, lightning discharge current, D-optimal design
National Category
Computational Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-42695 (URN)10.2298/FUEE1901025L (DOI)000457549900002 ()
Available from: 2019-02-15 Created: 2019-02-15 Last updated: 2019-06-24
Lundengård, K. (2019). Extreme points of the Vandermonde determinant and phenomenological modelling with power exponential functions. (Doctoral dissertation). Västerås: Mälardalen University
Open this publication in new window or tab >>Extreme points of the Vandermonde determinant and phenomenological modelling with power exponential functions
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis discusses two topics, finding the extreme points of the Vandermonde determinant on various surfaces and phenomenological modelling using power-exponential functions. The relation between these two problems is that they are both related to methods for curve-fitting. Two applications of the mathematical models and methods are also discuss, modelling of electrostatic discharge currents for use in electromagnetic compatibility and modelling of mortality rates for humans. Both the construction and evaluation of models is discussed.

In the first chapter the basic theory for later chapters is introduced. First the Vandermonde matrix, a matrix whose rows (or columns) consists of monomials of sequential powers, its history, some of its properties are discussed. Next some considerations and typical methods for a common class of curve fitting problems are presented, as well as how to analyse and evaluate the resulting fit. In preparation for the later parts of the thesis the topics of electromagnetic compatibility and mortality rate modelling are briefly introduced.

The second chapter discusses some techniques for finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids and cylinders. The discussion focuses on low dimensions but some results are given for arbitrary (finite) dimensions.

In the third chapter a particular model called the p-peaked Analytically Extended Function (AEF) is introduced and fitted to data taken either from a standard for electromagnetic compatibility or experimental measurements. The discussion here is entirely focused on currents that appear in lightning discharge currents or electrostatic discharges.

The fourth chapter consists of a comparison of several different methods for modelling mortality rates, including a model constructed in a similar way to the AEF found in the second chapter. The models are compared with respect to how well they can be fitted to estimated mortality rate for several countries and several years and the results when using the fitted models for mortality rate forecasting is also compared.

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2019
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 293
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-44579 (URN)978-91-7485-431-2 (ISBN)
Public defence
2019-09-26, Delta, Mälardalens högskola, Västerås, 13:15 (English)
Opponent
Supervisors
Available from: 2019-06-24 Created: 2019-06-24 Last updated: 2019-07-03Bibliographically approved
Javor, V., Lundengård, K., Rancic, M. & Silvestrov, S. (2018). Electrostatic discharge currents and their derivatives' approximation by piecewise power-exponential functions. Turkish Journal of Electrical Engineering and Computer Sciences, 26(2), 1093-1102
Open this publication in new window or tab >>Electrostatic discharge currents and their derivatives' approximation by piecewise power-exponential functions
2018 (English)In: Turkish Journal of Electrical Engineering and Computer Sciences, ISSN 1300-0632, E-ISSN 1303-6203, Vol. 26, no 2, p. 1093-1102Article in journal (Refereed) Published
Abstract [en]

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.

Keywords
Electrostatic discharge currents, N-peaked analytically extended function, Marquardt least-squares method, power-exponential function
National Category
Computational Mathematics Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-36536 (URN)10.3906/elk-1707-95 (DOI)000428723200037 ()2-s2.0-85044990579 (Scopus ID)
Available from: 2017-09-28 Created: 2017-09-28 Last updated: 2018-12-17Bibliographically approved
Javor, V., Lundengård, K. & Rancic, M. (2018). Modeling of Artificially-Triggered Lightning Currents by Multi-Peaked Analytically Extended Functions. Paper presented at “Theoretical Electrical Engineering (ISTET 2016), Ilmenau, Germany” special issue. Compel, 37(4), 1354-1365
Open this publication in new window or tab >>Modeling of Artificially-Triggered Lightning Currents by Multi-Peaked Analytically Extended Functions
2018 (English)In: Compel, ISSN 0332-1649, Vol. 37, no 4, p. 1354-1365Article in journal (Refereed) Published
Abstract [en]

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.

National Category
Computational Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-36586 (URN)10.1108/COMPEL-09-2017-0380 (DOI)000447495900005 ()2-s2.0-85053032203 (Scopus ID)
Conference
“Theoretical Electrical Engineering (ISTET 2016), Ilmenau, Germany” special issue
Available from: 2017-09-30 Created: 2017-09-30 Last updated: 2018-12-17Bibliographically approved
Lundengård, K., Österberg, J. & Silvestrov, S. (2018). Optimization of the Determinant of the Vandermonde Matrix and Related Matrices. Methodology and Computing in Applied Probability, 20(4), 1417-1428
Open this publication in new window or tab >>Optimization of the Determinant of the Vandermonde Matrix and Related Matrices
2018 (English)In: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 20, no 4, p. 1417-1428Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
SPRINGER, 2018
Keywords
Vandermonde determinant, Optimization, Grobner basis, Orthogonal polynomials, Ellipsoid, Optimal experiment design, Homogeneous polynomials, 33C45, 11C20, 15B99, 08B99
National Category
Computational Mathematics Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-41818 (URN)10.1007/s11009-017-9595-y (DOI)000449431800019 ()2-s2.0-85033696033 (Scopus ID)
Available from: 2018-12-27 Created: 2018-12-27 Last updated: 2019-06-24Bibliographically approved
Javor, V., Lundengård, K., Rancic, M. & Silvestrov, S. (2017). Analytical Representation of Measured Lightning Currents and Its Application to Electromagnetic Field Estimation. IEEE transactions on electromagnetic compatibility (Print), 60(5), 1415-1426
Open this publication in new window or tab >>Analytical Representation of Measured Lightning Currents and Its Application to Electromagnetic Field Estimation
2017 (English)In: IEEE transactions on electromagnetic compatibility (Print), ISSN 0018-9375, E-ISSN 1558-187X, ISSN 0018-9375, Vol. 60, no 5, p. 1415-1426Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
IEEE, 2017
Keywords
Lightning measurement and modeling, natural and man-made electromagnetic noise, near-field modeling and measurements
National Category
Computational Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-38039 (URN)10.1109/TEMC.2017.2768549 (DOI)000438903100033 ()2-s2.0-85038364781 (Scopus ID)
Note

Paper has been published:

online december 2017

print october 2018

Available from: 2018-01-15 Created: 2018-01-15 Last updated: 2018-10-01Bibliographically approved
Javor, V., Lundengård, K., Rancic, M. & Silvestrov, S. (2017). Application of Genetic Algorithm to Estimation of Function Parameters in Lightning Currents Approximations. International Journal of Antennas and Propagation, 2017, Article ID 4937943.
Open this publication in new window or tab >>Application of Genetic Algorithm to Estimation of Function Parameters in Lightning Currents Approximations
2017 (English)In: International Journal of Antennas and Propagation, ISSN 1687-5869, E-ISSN 1687-5877, Vol. 2017, article id 4937943Article in journal (Refereed) Published
Abstract [en]

Genetic algorithm (GA) is applied for the estimation of two-peaked analytically extended function (2P-AEF) parameters in this paper. 2P-AEF is used for approximation of measured and typical lightning discharge currents. Lightning discharge channel is often modeled as thin-wire vertical antenna at perfectly conducting ground. Engineering lightning stroke models assume that the current along that channel is related to the channel-base current which may be measured at the instrumented tall towers and in triggered lightning experiments. Mathematical modeling of lightning currents is important in verification of lightning strokes models based on simultaneously measured electromagnetic fields at various distances, so as in lightning protection studies, computation of lightning induced effects and simulation of overvoltages in power systems. Typical lightning discharge currents of the first positive, first negative, and subsequent negative strokes are defined by IEC 62305 Standard based on comprehensive measurements. Parameters of 2P-AEF’s approximation of the typical negative first stroke current are determined by GA and compared to approximations obtained by other functions. Measured currents at Monte San Salvatore in Switzerland, at Morro de Cachimbo Station in Brazil, and in rocket-triggered lightning experiments at Camp Blanding in Florida are approximated by 2P-AEFs, and good agreement with experimentally measured waveshapes is obtained.

National Category
Computational Mathematics Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-36530 (URN)10.1155/2017/4937943 (DOI)000410335700001 ()2-s2.0-85029809348 (Scopus ID)
Available from: 2017-09-28 Created: 2017-09-28 Last updated: 2017-10-05Bibliographically approved
Lundengård, K., Ogutu, C., Silvestrov, S., Ni, Y. & Weke, P. (2017). Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases. In: Sivasundaram, S (Ed.), AIP Conference Proceedings: . Paper presented at 11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, 4 July 2016 through 8 July 2016 (pp. 020094-1-020094-7). American Institute of Physics (AIP), 1798, Article ID 020094.
Open this publication in new window or tab >>Construction of moment-matching multinomial lattices using Vandermonde matrices and Gröbner bases
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2017 (English)In: AIP Conference Proceedings / [ed] Sivasundaram, S, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020094-1-020094-7, article id 020094Conference paper, Published paper (Refereed)
Abstract [en]

In order to describe and analyze the quantitative behavior of stochastic processes, such as the process followed by a financial asset, various discretization methods are used. One such set of methods are lattice models where a time interval is divided into equal time steps and the rate of change for the process is restricted to a particular set of values in each time step. The well-known binomial- and trinomial models are the most commonly used in applications, although several kinds of higher order models have also been examined. Here we will examine various ways of designing higher order lattice schemes with different node placements in order to guarantee moment-matching with the process. 

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2017
National Category
Mathematics Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-35007 (URN)10.1063/1.4972686 (DOI)000399203000094 ()2-s2.0-85013643900 (Scopus ID)9780735414648 (ISBN)
Conference
11th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences, ICNPAA 2016, 4 July 2016 through 8 July 2016
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2017-03-09 Created: 2017-03-09 Last updated: 2017-09-01Bibliographically approved
Lundengård, K., Rancic, M., Javor, V. & Silvestrov, S. (2017). Electrostatic discharge current modelling using multi-peaked analytically extended function. In: Proceedings of 2nd International Multidisciplinary Conference on Computer and Energy Science (SpliTech): . Paper presented at 2nd International Multidisciplinary Conference on Computer and Energy Science, SpliTech 2017; University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture (FESB)Split; Croatia; 12 July 2017 through 14 July 2017; (pp. 272-277). IEEE conference proceedings, Article ID 8019264.
Open this publication in new window or tab >>Electrostatic discharge current modelling using multi-peaked analytically extended function
2017 (English)In: Proceedings of 2nd International Multidisciplinary Conference on Computer and Energy Science (SpliTech), IEEE conference proceedings, 2017, p. 272-277, article id 8019264Conference paper, Published paper (Refereed)
Abstract [en]

In order to establish realistic requirements for ESD generators used in equipment and device testing, as well as to ensure and improve the repeatability of tests, an analytical expression of real electrostatic discharge (ESD) currents is sought for. It should be adoptable to various test levels, test set-ups and procedures, and also various ESD conditions (approach speeds, types of electrodes, relative arc length, humidity, etc). A mathematical function is necessary for computer simulation of such phenomena, for verification of test generators and for improving standard waveshape definition.

Place, publisher, year, edition, pages
IEEE conference proceedings, 2017
Keywords
Electrostatic discharges, IEC Standards, Mathematical model, Discharges (electric), Current measurement, Lightning
National Category
Computational Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-36532 (URN)000426982300050 ()2-s2.0-85030838106 (Scopus ID)978-953-290-071-2 (ISBN)
Conference
2nd International Multidisciplinary Conference on Computer and Energy Science, SpliTech 2017; University of Split, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture (FESB)Split; Croatia; 12 July 2017 through 14 July 2017;
Available from: 2017-09-28 Created: 2017-09-28 Last updated: 2018-04-05Bibliographically approved
Lundengård, K., Rancic, M., Javor, V. & Silvestrov, S. (2017). Electrostatic Discharge Currents Representation using the Multi-Peaked Analytically Extended Function by Interpolation on a D-Optimal Design. In: : . Paper presented at The 2017 IEEE International Symposium on Electromagnetic Compatibility, Signal and Power Integrity, Washington, USA, August 7-11, 2017 (pp. 25-30). , Article ID 8077985.
Open this publication in new window or tab >>Electrostatic Discharge Currents Representation using the Multi-Peaked Analytically Extended Function by Interpolation on a D-Optimal Design
2017 (English)Conference paper, Published paper (Refereed)
Abstract [en]

Multi-peaked analytically extended function (AEF), previously applied by the authors to modelling of lightning discharge currents, is used in this paper for representation of the electrostatic discharge (ESD) currents. The fitting to data is achieved by interpolation of certain data points. In order to minimize unstable behaviour, the exponents of the AEF are chosen from a certain arithmetic sequence and the interpolated points are chosen according to a D-optimal design. ESD currents’ modelling is illustrated through two examples: one corresponding to an approximation of the IEC Standard 61000-4-2 waveshape, and the other to representation of some measured ESD current. 

National Category
Computational Mathematics Other Electrical Engineering, Electronic Engineering, Information Engineering
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-36533 (URN)10.1109/ISEMC.2017.8077985 (DOI)000428753300006 ()2-s2.0-85039159873 (Scopus ID)978-1-5386-2231-5 (ISBN)978-1-5386-2229-2 (ISBN)
Conference
The 2017 IEEE International Symposium on Electromagnetic Compatibility, Signal and Power Integrity, Washington, USA, August 7-11, 2017
Available from: 2017-09-28 Created: 2019-06-24 Last updated: 2018-04-18Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-3204-617X

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