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1

Tool to identify parameters of insulation system in electrical machines

Kulesz Barbara, Sikora Andrzej, Słota Damian

Przegląd Elektrotechniczny

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2022

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R. 98, nr 11

292--295

EN

The issue of the equivalent scheme parameter identification for the insulation system in an electrical machine is discussed in the paper. The presented method is based upon a recorded voltage waveform, and Artificial Bee Colony algorithm is used in calculations. A numerical example is presented.

PL

W artykule przedstawiono problem identyfikacji parametrów schematu zastępczego układu izolacyjnego maszyny elektrycznej. Zaproponowana metoda identyfikacji wykorzystuje zarejestrowane przebiegi napicia i algorytm roju pszczelego (Artificial Bee Colony Algorithm). Zamieszczono przykład obliczeniowy.

2

Matrix methods in evaluation of integrals

Wituła Roman, Słota Damian, Matlak Jarosław, Różański Michał

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 1

103--112

EN

The method of evaluating the integrals through use of the matrix inversion, presented here, was introduced by J.W. Rogers and then generalized by Matlak, Słota and Wituła. This method is still developed and one of its other possible applications is presented in this paper. This application concerns a new way of evaluating the integral ʃ sec2n+1 xdx on the basis of the discussed method. Additionally, many other applications of the obtained original recursive formula for this type of integral are given here. Some of them are used to generate the interesting identities for inverses of the central binomial coefficients and the trigonometric limits. The historical view is also presented as well as the connections between the received and previously known identities.

3

Symbolic description of the polynomial roots and their numerical implementation - better than in Mathematica software?

Hetmaniok Edyta, Słota Damian, Pleszczyński Mariusz, Wituła Roman, Różański Michał, Szczygieł Marcin

Annals of Computer Science and Information Systems

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2019

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Vol. 20

41--45

EN

This paper is a continuation of the discussion undertaken in one of our previous papers. We present in the current paper the corrected, and also given in a slightly changed form, Vandermonde formulae for the roots of some quintic polynomials considered in J.P. Tignol's monograph. The proofs of selected trigonometric identities from our previous paper are given and some new identities have been generated by the occasion, which also can be used for testing our Langrange algorithm for the case of cubic polynomials. Moreover, we present here the decomposition of polynomials belonging to some two-parameter family of polynomials related to the Chebyshev polynomials of the first kind.

4

Application of the immune algorithm IRM for solving the inverse problem of metal alloy solidification including the shrinkage phenomenon

Zielonka Adam, Hetmaniok Edyta, Słota Damian

Computer Methods in Materials Science

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2018

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Vol. 18, No. 1

1--10

EN

In the paper the mathematical model of the inverse one-dimensional problem of binary alloy solidification, with the material shrinkage phenomenon taken into account, is defined. The process is described by using the model of solidification in the temperature interval, whereas the shrinkage of material is modeled basing on the mass balance equation. The inverse problem consists in reconstruction of the heat transfer coefficient on the boundary of the casting mould separating the cast from the environment. Lack of this data is compensated by the measurements of temperature in the control point located inside the mould. The method of solving the investigated problem is based on two procedures: the implicit scheme of finite difference method supplemented by the procedure of correcting the field of temperature in the vicinity of liquidus and solidus curves and the immune optimization algorithm IRM.