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1

Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

Gurgul Daniel, Burbelko Andriy, Wiktor Tomasz

Journal of Casting & Materials Engineering

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2021

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Vol. 5, no. 4

53--60

EN

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section. The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

2

Analysis of Proportional Scopes on Probability Density Functions of Random Chords of Spherical Particles

Gurgul D.

Archives of Foundry Engineering

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2021

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Vol. 21, iss. 4

61--66

EN

The paper presents an experimental confirmation of the fact that if a three-dimensional volume does not contain spherical particles with particular size, the Probability Density Function (PDF1) of half-chord lengths has proportional ranges. This fact has been deduced in work [1] during the derivation process of the Probability Density Function (PDF3) that maps the particle radii on the basis of data (PDF1) collected from flat cross-sections. The experiment has been executed virtually by using a simple computer program written in the C++11 language. The computer generation of particles allowed imposing various kinds of known PDF3 and the ranges in which the particles could not be created. Next, the virtual nodules have been used to produce sets of chords that served as input data to create histograms that approximated the continuous PDF1. Having such histograms, it was possible to reveal proportional scopes of the PDF1. The proportional dependencies occurred in the same ranges where the nodules had not been generated.

3

Analysis of Spherical Particles Size Distribution – Theoretical Basis

Gurgul D., Burbelko A., Wiktor T.

Archives of Foundry Engineering

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2018

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Vol. 18, iss. 1

29--34

EN

The determination of the form of a probability density function (PDF3) of diameters for nodular particles by using a probability density function (PDF2), which form is empirically estimated from cross-sections of these nodules in a metallographic specimen, can be regarded as a special case of Wicksell's corpuscle problem (WCP). The estimation of the PDF3 for the nodular particles provides information about the kinetics of these particles nucleation, and so about the kinetics of their growth. This information is essential for building more accurate mathematical models of the alloy crystallization. In the paper there are presented two derivations of the methods used for the estimation of the PDF3 form. The first method bases on diameters received from a planar cross-section. The second one uses also data from the planar cross-section but not the diameters only chords. Both methods provide practical rules for the analysis of the empirical diameters’ and chord’s size distribution and allow to estimate the mean value of the external surface area of the particles.

4

Theory of the Stereological Analysis of Spheroid Size Distribution – Validation of the Equations

Gurgul D., Burbelko A., Wiktor T.

Archives of Foundry Engineering

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2017

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Vol. 17, iss. 4

67--72

EN

The paper presents validation tests for method which is used for the evaluation of the statistical distribution parameters for 3D particles’ diameters. The tested method, as source data, uses chord sets which are registered from a random cutting plane placed inside a sample space. In the sample space, there were individually generated three sets containing 3D virtual spheres. Each set had different Cumulative Distribution Function (CDF3) of the sphere diameters, namely: constant radius, normal distribution and bimodal distribution as a superposition of two normal distributions. It has been shown that having only a chord set it is possible, by using the tested method, to calculate the mean value of the outer sphere areas. For the sets of data, a chord method generates quite large errors for around 10% of the smallest nodules in the analysed population. With the increase of the nodule radii, the estimation errors decrease. The tested method may be applied to foundry issues e.g. for the estimation of gas pore sizes in castings or for the estimation of nodule graphite sizes in ductile cast iron.

5

Wspomaganie decyzji wykonawcy o udziale w przetargu z wykorzystaniem liniowej analizy dyskryminacyjnej

Leśniak A.

Materiały Budowlane

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2016

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nr 6

97--98, 101

PL

Odpowiednia selekcja przetargów, do których startuje przedsiębiorstwo budowlane, jest ważna w aspekcie jego wyników finansowych oraz kreowania jego pozycji na rynku. Aby pomóc wykonawcy, opracowuje się modele wspomagające podejmowanie przez niego decyzji. W artykule zaproponowano model klasyfikacyjny, który generuje odpowiedź w formie zalecenia przystąpienia do przetargu bądź rezygnacji z udziału. Do budowy modelu wykorzystano liniową analizę dyskryminacyjną oraz bazę danych z 88 przetargów, w których brali udział wykonawcy uczestniczący w badaniach. Model osiągnął dobrą jakość działania i prawidłowo sklasyfikował 86,36% przypadków, a pole pod krzywą ROC (współczynnik AUC) wyniosło 0,92057. Świadczy to o możliwości wykorzystania go w praktyce.

EN

An appropriate selection of tenders in which a company wishes to participate is vital for the business’s market position. To enhance the decision making process and increase its effectiveness, models facilitating the process have been developed. The present paper proposes a bidding model based on a linear discriminant analysis. The proposed classifying model generates the answer in the form of a recommendation for joininga tender or resigning from it. The construction of the model involved a database consisting of 88 evaluated tenders that the contractors taking part in the study participated in. The model was successful in correctly classifying 86,36% of cases, and the area below the ROC curve (the AUC index) amounted to 0,92057. The results obtained prove that the model can be implemented in practice.

6

Ocena pracy dźwigara zadaszenia Hali Blanika w Gdańsku

Żółtowski K., Binczyk M., Kalitowski P.

Materiały Budowlane

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2016

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nr 7

100--102

PL

W artykule przedstawiono kompleksowe sprawdzenie nośności stalowej konstrukcji zadaszenia Hali Leszka Blanika w Gdańsku. Dokonano oceny wpływu otworów dużej średnicy w środnikach dźwigara na jego nośność. Oszacowano nośność nietypowego, zginanego styku doczołowego łączącego elementy dwuteowe klasy 4. Obliczenia wykonano na podstawie norm i analiz modeli MES.

EN

The paper presents profound verification of a load capacity for the roof in the Leszek Blanik sport hall in Gdansk. An influence of significant-diameter holes in the web on a load capacity of a girder was evaluated. A bending resistance of an untypical butt joint which connects I-sections in class 4 was assessed. Calculations were done on the basis of design codes and additional, non-linear FEM analysis.

7

Analysis of heart rate variability as a predictor of mortality in cardiovascular patients of intensive care unit

Moridani M. K., Setarehdan S. K., Nasrabadi A. M., Hajinasrollah E.

Biocybernetics and Biomedical Engineering

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2015

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Vol. 35, no. 4

217--226

EN

Objective: Dynamic changes of heart rate variability (HRV) reflect autonomic dysfunction in cardiac disease. Some studies suggest the role of HRV in predicting intensive care unit (ICU) mortality. The main object of this study was analyzing the HRV to design an algorithm to predict mortality risk. Methods: We evaluated 80 cardiovascular ICU patients (45 males and 45 females), ranging from 45 to 70 years. Common time and frequency domain analysis, non-linear Poincaré plot and recurrence quantification analysis (RQA) were used to study the HRV in two episodes. The episodes include 8–4 h before death, and 4 h before death to death. Independent sample t-test was used as statistical analysis. Results: Statistical analysis indicates that frequency domain and Poincaré parameters such as LF/HF and SD2/SD1 show changes in transition to death episode (p < 0.05). Moreover, Lmean, vmax and RT measures showed meaningful changes (p < 0.01) in closer segments to the death. Conclusions: Analysis of physiological variables shows that there are significant differences in RQA measures in episodes close to death. These changes can be interpreted as more stability and determinism behavior of HRV in episodes close to death. RQA parameters can be used together with HRV parameters for description and prediction of mortality risk in ICU patients.

8

A survey of various FE models with conceptual diagrams for linear analysis

Radwańska M.

Computer Assisted Mechanics and Engineering Sciences

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2006

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Vol. 13, No. 2

209-233

EN

In the paper a general survey of existing finite element (FE) models is presented using a conceptual description in diagram form, which was initiated in paper [1]. The analysis is focused on the description of FE models, which is uniform in its concept but specific for each FE type. All FE models are associated with certain variational principles (and their stationarity conditions) in their original or modified versions. The diagrams are used to visualize the equations which are satisfied inside an individual FE and on interelement boundaries. The use of conceptual diagrams is very convenient in the presentation of finite element method (FEM), it simplifies the understanding and teaching of this method.