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Electrostatic Discharge Currents Representation using the Multi-Peaked Analytically Extended Function 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
University of Nis, Faculty of Electronic Eng., Serbia.
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)ORCID-id: 0000-0003-4554-6528
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. 

Ort, förlag, år, upplaga, sidor
2017. s. 25-30, artikel-id 8077985
Nationell ämneskategori
Beräkningsmatematik Annan elektroteknik och elektronik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
URN: urn:nbn:se:mdh:diva-36533DOI: 10.1109/ISEMC.2017.8077985ISI: 000428753300006Scopus ID: 2-s2.0-85039159873ISBN: 978-1-5386-2231-5 (digital)ISBN: 978-1-5386-2229-2 (tryckt)OAI: oai:DiVA.org:mdh-36533DiVA, id: diva2:1329412
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
Delarbeten
1. Optimization of the Wishart Joint Eigenvalue Probability Density Distribution Based on the Vandermonde Determinant.
Öppna denna publikation i ny flik eller fönster >>Optimization of the Wishart Joint Eigenvalue Probability Density Distribution Based on the Vandermonde Determinant.
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(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
Abstract [en]

A number of models from mathematics, physics, probability theory and statistics can be described in terms of Wishart matrices and their eigenvalues. The most prominent example being the Laguerre ensembles of the spectrum of Wishart matrix. We aim to express extreme points of the joint eigenvalue probability densitydistribution of a Wishart matrix using optimisation techniques for the Vandermondedeterminant over certain surfaces implicitly defined by univariate polynomials.

Nyckelord
Vandermonde determinant · Orthogonal Ensembles, Gaussian Ensembles, Wishart Ensembles, Eigenvalue Density optimization
Nationell ämneskategori
Sannolikhetsteori och statistik Matematisk analys
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-44568 (URN)
Tillgänglig från: 2019-06-24 Skapad: 2019-06-24 Senast uppdaterad: 2019-10-12Bibliografiskt granskad
2. Extreme points of the Vandermonde determinant on surfaces implicitly determined by a univariate polynomial
Öppna denna publikation i ny flik eller fönster >>Extreme points of the Vandermonde determinant on surfaces implicitly determined by a univariate polynomial
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(Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
Abstract [en]

In this paper some results on optimising the Vandermonde determinanton a few different surfaces defined by univariate polynomials are discussed. The coordinates of the extreme points are given as roots of polynomials. Applications in curve-fitting and electrostatics are also briefly discussed.

Nyckelord
Vandermonde Matrix, Vandermonde Determinant, Orthogonal Polynomials, n-Sphere, p-Norm, D-Optimal Design, Electrostatics
Nationell ämneskategori
Matematisk analys
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-44569 (URN)
Tillgänglig från: 2019-06-24 Skapad: 2019-06-24 Senast uppdaterad: 2019-10-12Bibliografiskt granskad
3. Optimization of the Determinant of the Vandermonde Matrix and Related Matrices
Öppna denna publikation i ny flik eller fönster >>Optimization of the Determinant of the Vandermonde Matrix and Related Matrices
2018 (Engelska)Ingår i: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 20, nr 4, s. 1417-1428Artikel i tidskrift (Refereegranskat) 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.

Ort, förlag, år, upplaga, sidor
SPRINGER, 2018
Nyckelord
Vandermonde determinant, Optimization, Grobner basis, Orthogonal polynomials, Ellipsoid, Optimal experiment design, Homogeneous polynomials, 33C45, 11C20, 15B99, 08B99
Nationell ämneskategori
Beräkningsmatematik Algebra och logik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-41818 (URN)10.1007/s11009-017-9595-y (DOI)000449431800019 ()2-s2.0-85033696033 (Scopus ID)
Tillgänglig från: 2018-12-27 Skapad: 2018-12-27 Senast uppdaterad: 2019-06-24Bibliografiskt granskad
4. Extreme points of the Vandermonde determinant on the sphere and some limits involving the generalized Vandermonde determinant
Öppna denna publikation i ny flik eller fönster >>Extreme points of the Vandermonde determinant on the sphere and some limits involving the generalized Vandermonde determinant
2013 (Engelska)Rapport (Övrigt vetenskapligt)
Abstract [en]

The values of the determinant of Vandermonde matrices with real elements are analyzed both visually and analytically over the unit sphere in various dimensions. For three dimensions some generalized Vandermonde matrices are analyzed visually. The extreme points of the ordinary Vandermonde determinant on finite-dimensional unit spheres are given as the roots of rescaled Hermite polynomials and a recursion relation is provided for the polynomial coefficients. Analytical expressions for these roots are also given for dimension three to seven. A transformation of the optimization problem is provided and some relations between the ordinary and generalized Vandermonde matrices involving limits are discussed.

Ort, förlag, år, upplaga, sidor
Mälardalen University, 2013. s. 28
Nyckelord
Vandermonde matrix, Determinants, Extreme points, Unit sphere, Generalized Vandermonde matrix
Nationell ämneskategori
Matematisk analys
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-23914 (URN)
Forskningsfinansiär
Vetenskapsrådet
Tillgänglig från: 2013-12-27 Skapad: 2013-12-21 Senast uppdaterad: 2019-06-24Bibliografiskt granskad
5. Modelling mortality rates using the powerexponential function
Öppna denna publikation i ny flik eller fönster >>Modelling mortality rates using the powerexponential function
2017 (Engelska)Ingår i: Booklet of abstracts of SPAS2017 - International Conference on Stochastic Processes and Algebraic Structures– From Theory Towards Applications, 2017Konferensbidrag, Muntlig presentation med publicerat abstract (Refereegranskat)
Abstract [en]

There are many models for the mortality rates of humans and other organisms. A phenomenon that complicates the modelling of human mortality rates is a rapid increase in mortality rate for young adults (in western Europe this is especially pronounced at the age of 25). We will examine models for mortality rates based on power-exponential functions, compare them to empirical data for mortality rates and other models.

Nationell ämneskategori
Sannolikhetsteori och statistik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-36534 (URN)
Konferens
SPAS2017 - International Conference on Stochastic Processes and Algebraic Structures– From Theory Towards Applications, Västerås and Stockholm, Sweden, October 4 – 6, 2017.
Tillgänglig från: 2017-09-28 Skapad: 2017-09-28 Senast uppdaterad: 2019-06-24Bibliografiskt granskad
6. Electrostatic discharge currents representation using the analytically extended function with P peaks by interpolation on a D-optimal design
Öppna denna publikation i ny flik eller fönster >>Electrostatic discharge currents representation using the analytically extended function with P peaks by interpolation on a D-optimal design
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
Nyckelord
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:nbn:se:mdh:diva-42695 (URN)10.2298/FUEE1901025L (DOI)000457549900002 ()
Tillgänglig från: 2019-02-15 Skapad: 2019-02-15 Senast uppdaterad: 2019-08-13Bibliografiskt granskad
7. On Some Properties of the Multi-Peaked Analytically Extended Function for Approximation of Lightning Discharge Currents
Öppna denna publikation i ny flik eller fönster >>On Some Properties of the Multi-Peaked Analytically Extended Function for Approximation of Lightning Discharge Currents
2016 (Engelska)Ingår i: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering, Series: Springer Proceedings in Mathematics & Statistics / [ed] Sergei Silvestrov, Milica Rančić, Heidelberg: Springer, 2016, s. 151-172Kapitel i bok, del av antologi (Refereegranskat)
Abstract [en]

According to experimental results for lightning discharge currents, they are classified in the IEC 62305 Standard into waveshapes representing the first positive, first and subsequent negative strokes, and long-strokes. These waveshapes, especially shot-term pulses, are approximated with a few mathematical functions in literature, in order to be used in lightning discharge models for calculations of electromagnetic field and lightning induced effects. An analytically extended function (AEF) is presented in this paper and used for lightning currents modeling. The basic properties of this function with a finite number of peaks are examined. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks as well as for the given charge transfer and specific energy is described. This framework is used to find parameters for some common single-peak wave-forms and some advantages and disadvantages of the approach are also discussed.

Ort, förlag, år, upplaga, sidor
Heidelberg: Springer, 2016
Serie
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009 ; 178
Nationell ämneskategori
Beräkningsmatematik Annan elektroteknik och elektronik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-33097 (URN)10.1007/978-3-319-42082-0_10 (DOI)2-s2.0-85015267484 (Scopus ID)978-3-319-42082-0 (ISBN)978-3-319-42081-3 (ISBN)
Tillgänglig från: 2016-09-08 Skapad: 2016-09-08 Senast uppdaterad: 2019-06-24Bibliografiskt granskad
8. Estimation of Parameters for the Multi-peaked AEF Current Functions
Öppna denna publikation i ny flik eller fönster >>Estimation of Parameters for the Multi-peaked AEF Current Functions
2017 (Engelska)Ingår i: Methodology and Computing in Applied Probability, ISSN 1387-5841, E-ISSN 1573-7713, Vol. 19, nr 4, s. 1107-1121Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

An examination of how the analytically extended function (AEF) can be used to approximate multi-peaked lightning current waveforms, is presented in the paper. A general framework for estimating the parameters of the AEF using the Marquardt least-squares method (MLSM) for a waveform with an arbitrary (finite) number of peaks is presented. This framework is used to find parameters for some common waveforms with a single peak, such as Standard IEC 62305 lightning currents. Illustration of fitting a p-peak AEF to recorded lightning current data is also presented.

Nyckelord
Analytically extended function, Electromagnetic compatibility, Lightning discharge, Marquardt least-squares method
Nationell ämneskategori
Beräkningsmatematik Annan elektroteknik och elektronik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-33096 (URN)10.1007/s11009-016-9501-z (DOI)000413792200007 ()2-s2.0-84973100963 (Scopus ID)
Konferens
15th Applied Stochastic Models and Data Analysis International Conference (ASMDA), Univ Piraeus, Piraeus, GREECE, JUN 30-JUL 04, 2015
Tillgänglig från: 2016-09-08 Skapad: 2016-09-08 Senast uppdaterad: 2019-06-24Bibliografiskt granskad
9. Application of a power-exponential function-based model to mortality rates forecasting
Öppna denna publikation i ny flik eller fönster >>Application of a power-exponential function-based model to mortality rates forecasting
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2019 (Engelska)Ingår i: Communications in Statistics: Case Studies, Data Analysis and Applications, E-ISSN 2373-7484, Vol. 5, nr 1, s. 3-10Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

There are many models for mortality rates. A well-known problem that complicates modeling of human mortality rates is the “accident hump” occurring in early adulthood. Here, two models of mortality rate based on power-exponential functions are presented and compared to a few other models. The models will be fitted to known data of measured death rates from several different countries using numerical techniques for curve-fitting with the nonlinear least-squares method. The properties of the model with respect to forecasting with the Lee–Carter method will be discussed.

Nyckelord
mortality rates modeling, power-exponential function, nonlinear curve fitting, Lee-Carter method
Nationell ämneskategori
Sannolikhetsteori och statistik Beräkningsmatematik
Forskningsämne
matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-41090 (URN)10.1080/23737484.2019.1578705 (DOI)2-s2.0-85080110292 (Scopus ID)978-618-5180-27-0 (ISBN)978-618-5180-29-4 (ISBN)
Konferens
SMTDA2018 International Conference and Demographics Workshop (12-15 June, 2018), Crete, Greece
Anmärkning

Originally presented at the SMTDA2018 conference.

Tillgänglig från: 2018-09-30 Skapad: 2018-09-30 Senast uppdaterad: 2020-03-12Bibliografiskt granskad

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