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1

Analysis of selected methodological problems regarding the examination of traffic events at road intersections

Metelski A.

Archiwum Motoryzacji

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2018

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Vol. 82, nr 4

77--85

EN

The planning of statistical examining of population within the scope of undesirable events at road intersections with three-colour traffic lights has been discussed. In particular, the problems have been raised that are related to the analysing how the installation of countdown timers showing the time left to a change in the traffic lights signal affects the traffic flow. Attention has been focused on selected research process elements that concern the preliminary works, examination proper, and statistical inference, without describing the types and engineering designs of the displays used and without dealing with the legal aspects. Selected literature items related to the subject matter touched upon have been analysed, with pointing out the practices that either might be desirable or might arouse some reservations. In the part concerning the preliminary works, such issues as the sample selection method, sample size, and selection of the variables under analysis have been discussed. As regards the examination proper, some elements of the information acquisition process have been considered in both the subject-related and object-related aspects. When discussing the statistical inference, some limitations have been pointed out that affect the conclusions drawn from the examination of statistically non-representative samples and some acceptable methods of the analysis of empirical data have been mentioned. The article has been concluded with a brief recapitulation.

2

Identification of source function using the numerical methods

Metelski A., Lara S., Pawlak E.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2006

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Vol. 5, nr 1

148-153

EN

In the paper the inverse heat conduction problem is discussed. The energy equation contains the term determining the capacity of volumetric internal heat sources q(x) (x is a geometrical coordinate) and this parameter is identified. The solution of inverse problem bases on the least square criterion in which the sensitivity coefficients are introduced. In the final part of paper the examples concerning 1D and 2D problems are shown.

3

Identification of solidification model parameters

Mochnacki B., Metelski A., Siedlecki J.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2006

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Vol. 5, nr 1

170-175

EN

In the paper the parametric inverse problem [1, 2] concerning the identification of latent heat is considered. This parameter appears in the energy equation in the source term if the one domain approach is taken into account [4]. The identification of latent heat is possible under the condition that one disposes the additional information concerning the temperature field in the casting domain (cooling curves at the selected set of points). In order to solve the problem the algorithm using the sensitivity coefficients and least squares criterion has been used. The numerical example is presented in the final part of the paper.

4

Identification of solidification model parameters

Metelski A., Siedlecki J.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2005

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z. 86

67-70

EN

In the paper the parametric inverse problem concerning the identification of substitute thermal capacity is considered. This parameter (controlling the solidification process) appears in the energy equation if the one domain approach is taken into account. The identification of thermal capacity is possible under the condition that one disposes the additional information concerning the temperature field in the casting domain (cooling curves at the selected set of points). In order to solve the problem the algorithm using the sensitivity coefficients and least squares criterion has been used. The numerical example is presented in the final part of the paper.

5

Identification of an unknown source term in a heat equation using sensitivity coefficients

Metelski A.

Zeszyty Naukowe. Mechanika / Politechnika Opolska

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2005

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z. 85

39-46

EN

This paper concerns the numerical techniques for the solution of non-linear one-dimensional parabolic inverse heat conduction problem (IHCP). The discrete approximation of the problem is based on the finite element method (FEM). These techniques are presented for the identification of unknown temperature-dependent source function. The main idea for obtaining the solution of a given partial differential equation is to approximate the unknown function by polynomial. Approach of proposed method is to determine optimal parameter values so as to minimize an error functional based on the overspecified data. A numerical example is presented.

PL

Artykuł dotyczy metod numerycznych w rozwiązywaniu nieliniowego, jednowymiarowego, parabolicznego odwrotnego zadania przewodnictwa cieplnego. Dyskretyzacja obszaru została dokonana na bazie metody elementów skończonych. Prezentowane techniki posłużyły do identyfikacji nieznanej funkcji źródła, zależnej od temperatury, przy założeniu, że jest ona wielomianem stopnia drugiego. Główną ideą proponowanej metody jest wyznaczenie optymalnych wartości współczynników funkcyjnych w celu zminimalizowania błędu funkcjonału jakości. Artykuł kończy przykład numeryczny.

6

Identification of internal heat source capacity in the heterogeneous domain

Mochnacki B., Metelski A.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

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2005

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Vol. 4, nr 1

182-187

EN

The heterogeneous domain Ωbeing the composition of two domains (Ω1, Ω2) is considered. It is assumed that in the first domain Ω1 the internal volumetric heat sources act. On the basis of knowledge of heating (cooling) curves at the selected set of Ω2 the capacity of internal heat sources in Ω1 is identified. The inverse problem formulated in this way is interesting from the practical point of view. For example, a such situation takes place during the casting solidification. The evolution of latent heat in the casting domain causes that in Ω1 the internal heat sources appear, while in the mould domain this component of energy equation is equal to 0. Additionally the measurements of temperature in the mould are essentially simpler from the technical view-point. In the paper the theoretical base of the problem and the examples of numerical realization are discussed.

7

Estimation of nuclei density in solidifying casting using the Kolmogorov theory

Majchrzak E., Dziewoński M., Metelski A.

Archiwum Odlewnictwa

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2005

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R. 5, nr 15

253--258

EN

In the paper the solidification process in the micro-macro scale is analyzed. The mathematical model of heat transfer in the domain considered bases on the Mehl-Johnson-Avrami-Kolmogorov theory. The capacity of internal heat source resulting from the latent heat evolution is, among others, the function of nuclei density. This parameter is estimated using the methods of inverse problem solution. The additional information necessary in order to identify the unknown parameter results from the cooling curves at the selected points from casting domain. On the stage of numerical algorithm construction the least squares criterion containing the sensitivity coefficients is applied. The solution has been obtained using the boundary element method.

PL

W artykule analizowano proces krzepnięcia w skali mikro-makro. Model matematyczny przepływu ciepła w obszarze bazuje na teorii Mehla-Johnsona-Avrami-Kołmogorowa. Wydajność wewnętrznych źródeł ciepła związana z wydzielaniem się ciepła krzepnięcia jest zależna między innymi od gęstości zarodków. Oszacowanie tego parametru uzyskano rozwiązując zadanie odwrotne, w którym wykorzystano dodatkową informację dotyczącą przebiegu krzywych stygnięcia w kilku punktach odlewu. Algorytm bazuje na kryterium najmniejszych kwadratów, w którym występują tzw. współczynniki wrażliwości.