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Electrostatic discharge currents representation using the analytically extended function with P peaks by interpolation on a D-optimal design
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0003-3204-617X
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0001-9635-0301
Univ Nis, Dept Power Engn, Fac Elect Engn, Nish, Serbia..
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0003-4554-6528
2019 (Engelska)Ingår i: Facta Universitatis Series: Electronics and Energetics, ISSN 0353-3670, Vol. 32, nr 1, s. 25-49Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
UNIV NIS , 2019. Vol. 32, nr 1, s. 25-49
Nyckelord [en]
Analytically extended function, electrostatic discharge (ESD) current, lightning discharge current, D-optimal design
Nationell ämneskategori
Beräkningsmatematik Elektroteknik och elektronik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-42695DOI: 10.2298/FUEE1901025LISI: 000457549900002OAI: oai:DiVA.org:mdh-42695DiVA, id: diva2:1289032
Tillgänglig från: 2019-02-15 Skapad: 2019-02-15 Senast uppdaterad: 2019-08-13Bibliografiskt granskad
Ingår i avhandling
1. Electrostatic Discharge Currents Representation using the Multi-Peaked Analytically Extended Function by Interpolation on a D-Optimal Design
Öppna denna publikation i ny flik eller fönster >>Electrostatic Discharge Currents Representation using the Multi-Peaked Analytically Extended Function by Interpolation on a D-Optimal Design
2017 (Engelska)Konferensbidrag, Publicerat paper (Refereegranskat)
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. 

Nationell ämneskategori
Beräkningsmatematik Annan elektroteknik och elektronik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
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)
Konferens
The 2017 IEEE International Symposium on Electromagnetic Compatibility, Signal and Power Integrity, Washington, USA, August 7-11, 2017
Tillgänglig från: 2017-09-28 Skapad: 2019-06-24 Senast uppdaterad: 2018-04-18Bibliografiskt granskad
2. Extreme points of the Vandermonde determinant and phenomenological modelling with power exponential functions
Öppna denna publikation i ny flik eller fönster >>Extreme points of the Vandermonde determinant and phenomenological modelling with power exponential functions
2019 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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 discussed, 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 and 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 of 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 originating from lightning 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 third 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.

Ort, förlag, år, upplaga, sidor
Västerås: Mälardalen University, 2019
Serie
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 293
Nationell ämneskategori
Matematik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-44579 (URN)978-91-7485-431-2 (ISBN)
Disputation
2019-09-26, Delta, Mälardalens högskola, Västerås, 13:15 (Engelska)
Opponent
Handledare
Tillgänglig från: 2019-06-24 Skapad: 2019-06-24 Senast uppdaterad: 2019-08-22Bibliografiskt granskad

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Förlagets fulltexthttp://casopisi.junis.ni.ac.rs/index.php/FUElectEnerg/article/view/4725/2863

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Lundengård, KarlRancic, MilicaSilvestrov, Sergei

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