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1

Additive neural network approximation of multidimensional response surfaces for synthesis of eddy-current probes

Halchenko Volodymyr Ya., Trembovetska Ruslana, Tychkov Volodymyr, Sapogov Mykyta, Gromaszek Konrad, Smailova Saule, Luganskaya Saule

Przegląd Elektrotechniczny

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2021

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R. 97, nr 9

46--49

EN

A universal method for constructing multidimensional approximation models of surface eddy current probes with various structures of excitation systems is proposed. This method presupposes, firstly, the description of the eddy-current probe interaction with a testing object. Secondly, a computer design of the computational experiment based on quasi-random sequences with a minimum discrepancy is constructed. Thirdly, an approximation model is created using additive neural network regression and the assessment of the adequacy and information content of the obtained multivariate approximation model. The examples of approximation dependences of the eddy current density distribution are considered. Currents are generated by the uniform surface eddy current probes in the testing object. The results of reproduction of multidimensional response surfaces in the form of level lines are given. The lines were obtained on the basis of approximation models with an assessment of their quality using scatter diagrams. The value of the relative model error in the form of distribution histograms is presented.

PL

Zaproponowano uniwersalną metodę konstruowania wielowymiarowych modeli aproksymacyjnych powierzchniowych sond wiroprądowych o różnych strukturach układów wzbudzających. Metoda ta zakłada, po pierwsze, opis interakcji sondy wiroprądowej z obiektem badanym. Po drugie, konstruuje się komputerowy projekt eksperymentu obliczeniowego oparty na sekwencjach quasi-losowych o minimalnej rozbieżności. Po trzecie, tworzony jest model aproksymacyjny z wykorzystaniem addytywnej regresji sieci neuronowych oraz ocena adekwatności i zawartości informacyjnej otrzymanego wielowymiarowego modelu aproksymacyjnego. Rozważane są przykładowe zależności aproksymacyjne rozkładu gęstości prądów wirowych. Prądy generowane są przez jednolite powierzchniowe sondy wiroprądowe w badanym obiekcie. Podano wyniki odwzorowania wielowymiarowych powierzchni odpowiedzi w postaci linii poziomicowych. Linie te otrzymano na podstawie modeli aproksymacyjnych z oceną ich jakości za pomocą wykresów rozrzutu. Przedstawiono wartość błędu względnego modelu w postaci histogramów rozkładu.

2

On a characterization of exponential, Pearson and Pareto distributions via covariance and pseudo-covariance

Pawlas Piotr, Szynal Dominik

Demonstratio Mathematica

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2020

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Vol. 53, nr 1

285--291

EN

Properties of linear regression of order statistics and their functions are usually utilized for the characterization of distributions. In this paper, based on such statistics, the concept of Pearson covariance and the pseudo-covariance measure of dependence is used to characterize the exponential, Pearson and Pareto distributions.

3

Uniform Cross-entropy Clustering

Brzeski M., Spurek P.

Schedae Informaticae

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2016

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Vol. 25

117--126

EN

Robust mixture models approaches, which use non-normal distributions have recently been upgraded to accommodate data with fixed bounds. In this article we propose a new method based on uniform distributions and Cross- Entropy Clustering (CEC). We combine a simple density model with a clustering method which allows to treat groups separately and estimate parameters in each cluster individually. Consequently, we introduce an effective clustering algorithm which deals with non-normal data.

4

Analiza wpływu przypadków obciążenia śniegiem na nośność dachów płaskich z attykami

Siwiński J., Stolarski A.

Przegląd Budowlany

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2016

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R. 87, nr 2

24--29

PL

W pracy zawarto rozważania dotyczące stosowania przypadków normowych obciążenia śniegiem dachów płaskich z attykami według normy Eurokod 1. Przedstawiono sposób wyznaczania obciążeń śniegiem zgodny z normą PN-EN 1991–1-3:2005 wraz z późniejszymi zmianami. Przeprowadzono analizę porównawczą wytężenia stropodachów dla trzech przypadków obciążenia. Analizę porównawczą przeprowadzono numerycznie z wykorzystaniem oprogramowania systemowego ABC 6.15. Analizie poddano płaski stropodach, monolityczny, żelbetowy, krzyżowo-zbrojony. Przedstawiono wyniki momentów zginających dla trzech przypadków obciążenia śniegiem. W pracy odniesiono się również do typowych stosowanych w Polsce stropodachów prefabrykowanych typu TERIVA.

EN

The present work contains considerations related to application of norm cases, related to snow-load on flat roofs with attics, according to the provisions of the Eurocode 1 norm. The snow-load determination method has been presented. The method has been developed in line with the PN-EN 1991-1-3:2005 norm, along with the further amendments. In the further part of the article, the summarizes the comparative stress analysis for flat roofs, for three load cases. The analysis contained in the article has been carried out numerically, with the use of the ABC 6.15 software. A flat monolithic, ferro-concrete crossreinforced roof is the subject of that analysis. The work also presents the results for the bending momentum values, for three snow-load cases. The work also makes a reference to the typical TERIVA flat roofs that are widely and commonly applied in Poland.

5

Testowanie obserwacji istotnie odstępujących w próbach o rozkładzie jednostajnym

Dorozhovets M.

Mechanik

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2016

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R. 89, nr 11

1596--1599

PL

Przeanalizowano losowe nieskorelowane obserwacje na temat liczebności n, pobrane z populacji o rozkładzie jednostajnym w celu ujawnienia oraz eliminacji istotnie odstających obserwacji lub outlierów. Wyprowadzono wzory obliczania wartości krytycznych potrzebnych do testowania na zadanym poziomie istotności α jednej lub dwóch skrajnych obserwacji. Teoretyczne wyniki testowania skrajnych obserwacji zbadano metodą Monte-Carlo.

EN

In the article the random not correlated uniformly distributed observations in order to detect and eliminate significantly extreme observations or outliers is analyzed. The formulas for calculating critical values which are used to test for a given significant level α of the single or double extreme observations are presented. The theoretical results for testing extreme observations have been studied by Monte-Carlo.

6

On the factorization of the Haar measure on finite Coxeter groups

Urban R.

Probability and Mathematical Statistics

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2011

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Vol. 31, Fasc. 1

141--148

EN

Let W be a finite Coxeter group and let λW be the Haar measure on W; i.e., λW(ω) = |W|−1 for every ω ∈ W: We prove that there exist a symmetric set T ̸= W of generators of W consisting of elements of order not greater than 2 and a finite set of probability measures {μ1..., μk} with their supports in T such that their convolution product μ1 ∗ ...∗ μk = λW:

7

Scale free distribution of nodes in Euclidean graphs

Dominik A., Walczak Z., Wojciechowski J., Wojciechowski J.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2006

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z. 156

107-115

EN

In the paper we propose a new model of spatial distribution of nodes in graphs which can be represented in the Euclidean space. Such graphs appear in many areas of computer science, for instance wireless networks design, Traveling Salesman and Vehicle Routing Problems. We show analogies between scale-free and Euclidean graphs. Although the distribution of node's degrees in Euclidean graphs is not scale-free, the spatial distribution of node's follows the power law. We analyze distribution of population density in different continents, propose a model to generate such distributions and provide numerical experiments concerning its quality. Finally, the impact of our model on different NP-complete problems in Euclidean graphs is analyzed.

8

A characterization of uniform distribution

Chachulska J.

Bulletin of the Polish Academy of Sciences. Mathematics

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2005

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Vol. 53, no 2

207-220

EN

Is the Lebesgue measure on [0,1]2 a unique product measure on [0,1] 2 which is transformed again into a product measure on [0,1]2 by the mapping ψ(x, y) = (x, (x+y) mod 1))? Here a somewhat stronger version of this problem in a probabilistic framework is answered. It is shown that for independent and identically distributed random variables X and Y constancy of the conditional expectations of X+Y−I(X+Y>1) and its square given X identifies uniform distribution either absolutely continuous or discrete. No assumptions are imposed on the supports of the distributions of X and Y.

9

Watching steps of a grand tour implementation

Bartkowiak A., Szustalewicz A.

Machine Graphics and Vision

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1998

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Vol. 7, No. 3

655-680

EN

Bartkowiak and Szustalewicz, 1997 (B&Sz), have proposed an implementation of the grand tour algorithm designed specially to detect outliers in multivariate data. The algorithm work by performing a sequence of rotations and projections onto a specific 2D-plane (Π proj). This is equivalent to perform a series of rotations yielding transformed coordinates of the data: X(tr) = XA, with A being the rotation matrix, while X and X,sup>(tr) denote the data matrices before and after the rotation appropriately. A superimposed concentration ellipse indicates the outstanding points. We complement the paper of B&Sz by considering some details and variants of the implementation of the grand tour algorithm. In particular we watch the trajectories of the projected points. Our concern is the denseness of the watched projctions. We look at the trajectories of the projected point visible in the Π proj plane and the frequencies of thier appearing in various sectors of that plane. In the Appendix we present the derivation of the formula for the rotation matrix A employed in each step of the algorithm for obtaining the transformed data coordinates.