Wyniki wyszukiwania - Biblioteka Nauki

1

A Novel Multimodal Probability Model for Cluster Analysis

100%

Yu J. , Yang M.-S. , Hao P.

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2011

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tom Vol. 111, nr 1

81-90

EN

Cluster analysis is a tool for data analysis. It is a method for finding clusters of a data set with most similarity in the same group and most dissimilarity between different groups. In general, there are two ways, mixture distributions and classification maximum likelihood method, to use probabilitymodels for cluster analysis. However, the corresponding probability distributions to most clustering algorithms such as fuzzy c-means, possibilistic c-means, mode-seeking methods, etc., have not yet been found. In this paper, we construct a multimodal probability distribution model and then present the relationships between many clustering algorithms and the proposed model via the maximum likelihood estimation. Moreover, we also give the theoretical properties of the proposed multimodal probability distribution.

2

Kernel Estimation of probability density function: properties and parameters optimization

100%

Jerzman B. , Kiciński W.

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2009

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tom Vol. 16, nr 1

85-105

EN

The article deals with the kernel estimation of the probability density function. The main subject of the research is the optimization of parameters of the estimator. In the particular case, the research focused on the estimation of the univariate, unimodal data representative for the normal distribution.

3

Metoda funkcji gęstości prawdopodobieństwa w problemie turbulencji

80%

Icha A.

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2012

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tom T. 12, nr 43

69-76

PL

W pracy rozważono statystyczny opis przepływów turbulentnych przy wykorzystaniu metody funkcji gęstości rozkładu prawdopodobieństwa charakterystyk przepływu. W szczególności otrzymano równanie ewolucyjne dla jednopunktowej funkcji gęstości prawdopodobieństwa pulsacji koncentracji dyfundującej substancji w zadanym polu prędkości cieczy. Rozważono bliżej przypadek statystycznie stacjonarnego i horyzontalnie jednorodnego przepływu turbulentnego, dla którego znaleziono ścisłe, zależne od dwóch parametrów, rozwiązanie zagadnienia dyfuzji, wyrażone przez 3-konfluentną funkcję Heuna.

EN

In the paper the use of probabiiity density functions metod to the statistical description of turbulent flows is considered. This formulation is less generał than the characteristic functionals approach, but primary in the relation to the Friedmann-Keller hierarchy equations. An evolution equation for single-point probability density function of pulsation of concentration of the diffusing substance in prescribed fluid velocity field, is derived. The case of statistical stationary and horizontal homogeneous turbulent flow is considered, for which an exact, new, two-parameter solution of diffusion problem in terms of Triconfluent Heun function, is obtained.

4

Models of bias of mean square value digital estimator for selected deterministic and random signals

70%

Lal-Jadziak J. , Sienkowski S.

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2008

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tom Vol. 15, nr 1

55-67

EN

The article presents the probability density functions as well as characteristic functions of selected periodic and random signals. On their basis, original models of the bias of the mean square value digital estimator have been designed. These models were employed in investigating estimation errors caused by analog to digital conversion and analog to digital conversion with a dither signal. Selected graphical model representations and their analyses are demonstrated. It has been shown that for a triangular probability density function random signal with the amplitude At = kq, k∈N \ {0}, mean square value reconstruction occurs on the basis of a signal quantized with the accuracy of Sheppard's correction. Whereas for periodic signals as well as for the sum of periodic and random signals, the δ component of bias due to the nonsatisfaction of the reconstruction condition is a suppressed oscillating function of the quotient of the amplitude A and the quantization step size q. It has been proved that by adding, prior to quantization, a triangular distribution random signal with zero mean and the amplitude At = kq (k = 1, 2, ...) in the mean square value measurement of any periodic signal, this bias component can be brought to zero.

5

Graphics processing units in acceleration of bandwidth selection for kernel density estimation

70%

Andrzejewski W. , Gramacki A. , Gramacki J.

International Journal of Applied Mathematics and Computer Science

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2013

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tom 23

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nr 4

869-885

EN

The Probability Density Function (PDF) is a key concept in statistics. Constructing the most adequate PDF from the observed data is still an important and interesting scientific problem, especially for large datasets. PDFs are often estimated using nonparametric data-driven methods. One of the most popular nonparametric method is the Kernel Density Estimator (KDE). However, a very serious drawback of using KDEs is the large number of calculations required to compute them, especially to find the optimal bandwidth parameter. In this paper we investigate the possibility of utilizing Graphics Processing Units (GPUs) to accelerate the finding of the bandwidth. The contribution of this paper is threefold: (a) we propose algorithmic optimization to one of bandwidth finding algorithms, (b) we propose efficient GPU versions of three bandwidth finding algorithms and (c) we experimentally compare three of our GPU implementations with the ones which utilize only CPUs. Our experiments show orders of magnitude improvements over CPU implementations of classical algorithms.

6

Modeling of polymer/clay nanocomposites by an iterative micromechanical approach

70%

Mohyeddin A. , Fereidoon A.

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2012

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tom Vol. 64, nr 6

541-554

EN

An iterative micromechanical method is presented in order to predict the elastic constants of composites and nanocomposites including arbitrarily oriented reinforcement particles. The proposed method is capable of introducing into the matrix any kind of heterogeneity based on its dimension, orientation, mechanical properties and volume fraction. The efficiency and convergence of solution method is studied by computing the elasticity tensor of a unidirectional particulate composite. It is then applied to model the elastic behavior of nylon-6/clay nanocomposite with taking into consideration the probability distribution of aspect ratio and orientation of effective particles. The results are validated by comparison with available experimental data.

7

Statistic characteristics of BFSK signal in the presence of Gaussian noise

60%

Stefanović M. , Krstić D. , Bandjur M. , Bandjur D.

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2007

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tom R. 83, nr 11

60-63

EN

In this paper we will consider the system for noncoherent demodulation of BFSK signal in the presence of Gaussian noise. We will derive the probability density function of BFSK receiver output signal and the joint probability density function of the output signal and its derivative in order to view the influence of the Gaussian noise and fading on the performances of the BFSK system.

PL

W artykule tym rozważa się system dla niekoherentnej demodulacji sygnału BFSK z szumem Gaussa. Wyprowadza się funkcję gęstości prawdopodobieństwa sygnału wyjściowego odbiornika BFSK oraz łączną funkcję gęstości prawdopodobieństwa sygnału wyjściowego i jej pochodnej w celu zbadania wpływu szumu Gaussa i zaniku sygnału na wydajność systemu BFSK.

8

Scale-based statistical analysis of sediment fluxes

60%

Campagnol J. , Radice A. , Ballio F.

Acta Geophysica

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2012

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tom Vol. 60, no. 6

1744-1777

EN

The flux of sediments over a line perpendicular to the main flow direction was measured during experiments of weak one-dimensional bed load. The standard definition of solid discharge through a boundary is a straightforward issue, yet the dependence of resulting values on the spatial and temporal scales used as a support for measurement is not. In this work, first- and second-order statistics of sediment transport rates were analyzed as scale-dependent quantities. The spatial scales used were significantly larger than the particle size, while the temporal scales covered a two-orders-of-magnitude range enabling the physical time scales of the single particles to be appreciated. In addition, the relationship between sediment fluxes, process intermittency and particle interarrival times was investigated. Proper knowledge of the scaledependence of statistical properties of sediment transport fluxes may allow for adequate design of measuring campaigns (both in the laboratory and field) and for sound interpretation of data from multiple sources.

9

A class of unbiased kernel estimates of a probability density function

60%

Rychlik T.

Applicationes Mathematicae

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1993-1995

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tom 22

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nr 4

485-497

EN

We propose a class of unbiased and strongly consistent nonparametric kernel estimates of a probability density function, based on a random choice of the sample size and the kernel function. The expected sample size can be arbitrarily small and mild conditions on the local behavior of the density function are imposed.

10

Probability Density Functions for Calculating Approximate Aggregates

60%

Gramacki J. , Gramacki A.

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2010

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tom Vol. 35, No. 4

223-240

EN

In the paper we show how one can use probability density function (PDF) for calculating approximate aggregates. The aggregates can be obtained very quickly and efficiently and there is no need to look through the large amount of data, as well as creating a sort of materialized aggregates (usually implemented as materialized views). Although the final results are only approximate, the method is extremely fast and can be successively used during initial phase of data exploration. We include simple experimental results which proof effectiveness of the method, especially if PDFs are typical, for example similar to Gaussian normal ones. If the PDFs differ from a normal distribution, one can consider making a proper preliminary transformation of the input variables or estimate PDFs by some nonparametric methods, for example using the so called kernel estimators. The later is used in the paper. To accelerate calculations, one can consider a usage of graphics processing unit (GPU). We point out this approach in the last section of the paper and give some preliminary results which are very promising.

11

Pseudo-Gaussian Density Functions for Gap Height Between Two Surfaces

60%

Wierzcholski K. C. , Nowakowska K.

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2010

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tom Vol. 18, nr 2

79-90

EN

The presented paper formulates the sequence of pseudo-Gaussian distributions where are presented the mathematical results of standard deviation and probability density function derivations for bio-and micro-bearing gap height on the basis of Mow, Dowson, Cwanek, Wierzcholski experimental results. The mathematical derivation of the optimum probability density functions and least standard deviation are illustrated in two cases. The first case relates to the height of the gap if vibration and unsteady load causes the random changes. The second case relates to the height of the gap if the asperities of the cartilage surface roughness cause the random changes. Author formulates one Theorem and some Corollaries where the sequence of pseudo-Gaussian-distributions are derived. The presented proof shows, that such sequence is convergent to the Gaussian distribution in infinity.

12

Analysis of Reliability and Stability of Bar Structures

57%

Radoń U. , Radoń U.

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13

Identification of characteristic length of microstructure for second order continuum multiscale model by Bayesian neural networks

51%

Kaczmarczyk Ł. , Waszczyszyn Z.

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2007

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tom Vol. 14, No. 2

183-196

EN

This-paper deals with the second-order CH of a heterogeneous material undergoing small displacements. Typically, in this approach an RVE of a heterogeneous material is investigated. A given discretized microstructure is determined a priori, without focusing on details of specific discretization techniques. Application of BNN as a tool for identification of characteristic length of a microstructure is discussed. An indentation test was analyzed under plane strain constraints for generating pseudo-experimental patterns by means of FEM. A single input of BNN was formulated due to the application of PCA. The BNN of structure 1-16-1 with sigmoid hidden neurons was designed. The Bayesian inference approach was applied to obtain pdf of the characteristic length. Numerical efficiency of the proposed approach is demonstrated in the paper.

14

A reactedness model for local extinction and reignition phenomena in turbulent jet diffusion flames

51%

Koutmos P. , Mavridis C.

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1999

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tom Vol. 6, No. 1

115-130

EN

An approach for modeling finite-rate chemistry effects such as local extinction and reignition in piloted diffusion flames of CO/H2/N2 or CH4 and air is presented. A partial equilibrium/two-scalar exponential PDF combustion model is combined with a 2D Large Eddy Simulation procedure employing an anisotropic subgrid eddy-viscosity and two equations for the subgrid scale turbulent kinetic and scalar energies. Statistical independence of tge PDF scalars is avoided and the required moments are obtained from an extended scale-similarity assumption. Extinction is accounted for by comparing the local Damkohler number against a 'critical' local limit related to the Gibson scalar scale and the reaction zone thickness. The post-extinction regime is modelled via a Lagrangian transport equation for a reactedness progress variable that follows a linear deterministic relaxation to its mean value (IEM). Comparisons between simulations and measurements suggested the ability of the method to calculate adequately the partal extinction and reignition phenomena observed in the experiments.

15

Reliability analysis of Misses truss

51%

Radoń U.

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2011

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tom Vol. 11, no 3

723-738

EN

The present study considers the problems of stability and reliability of truss structure susceptible to stability loss from the condition of node snapping. In the reliability analysis of structure, uncertain parameters, such us load magnitudes, the axial stiffness of bars, coordinate nodes are represented by random variables. Random variables are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier. In the current paper only the time independent component reliability analysis problems are considered. The Hasofer-Lind index in conjunction with transformation method in the FORM was used as a reliability measure.

PL

W niniejszej pracy rozważane są zagadnienia stateczności i niezawodności konstrukcji kratowej podatnej na utratę stateczności z warunku przeskoku węzła. Do określenia ścieżki równowagi konstrukcji wykorzystano metodę skalarnego parametru sztywności oraz metodę stałej długości łuku. W pracy jako zmienne losowe przyjęto obciążenie konstrukcji, sztywność osiową prętów, współrzędne węzłów. Rozkłady prawdopodobieństwa zmiennych losowych przyjmowane są spośród kilku, najczęściej stosowanych w praktyce. Rozpatrywany jest warunek nieprzekroczenia dopuszczalnego mnożnika obciążenia. W analizie niezawodności wykorzystano, jako miarę niezawodności wskaźnik Hasofera-Linda. Dokładność wyników otrzymywanych przy użyciu wskaźnika Hasofera-Linda jest wystarczająca dla potrzeb praktycznych i dlatego też zyskał on dużą popularność jako miara niezawodności, szczególnie w połączeniu z metodami transformacji wykorzystującymi pełną informację o rozkładach zmiennych losowych. Obliczenia probabilistyczne przeprowadzono stosując metodę FORM. Do obliczeń wykorzystano program do analizy niezawodności STAND zbudowany w IPPT PAN. Na podstawie przedstawionych wykresów i tabel możemy zauważyć, jak istotnym zagadnieniem w analizie niezawodności jest przyjęcie prawidłowego opisu stochastycznego. Niekompletne dane statystyczne oraz niewłaściwie przyjęte założenia dotyczące rozkładów prawdopodobieństwa oraz parametrów mogą prowadzić do poważnych różnic w ocenie bezpieczeństwa konstrukcji.

16

Bayesian neural networks for prediction of response spectra

41%

Waszczyszyn Z. , Słoński M.

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2006

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tom No. 7

343-361

EN

Standard artificial neural networks and Baycsian neural networks (BNNs) are briefly discussed on example of a simple feed-forward layered neural networks (FLNN). Main ideas of the Baycsian approach and basics of the applied BNNs are presented in short. A study case corresponds to prediction of Displacement Response Spectrum inside buildings at the basement level (DRSb). Data for network training and testing were adopted as DRS corresponding to the preprocessed accelerograms. They were taken from measurements in the Lcgnica-Gtogow Copperfield at monitored 5-storey buildings subjected to paraseismic excitations from explosives in nearby strip mines. Results of neural predictions by three NNs (standard FLNN trained by means of the conjugate gradient learning method, Simple Bayesian SBNN and Full Bayesian FBNN) are presented. The errors of predictions are on average on the level of 4% errors.

17

About the best measurand estimators of trapezoidal probability distributions

41%

Warsza Z. , Galovska M.

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2009

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tom R. 85, nr 5

86-91

EN

As introduction, the basic estimators of the measurand obtained from data sample of few basic types of probability density distributions - PDF are given. For trapezoidal PDF of symmetrical straight sides, in the range of ratio of upper and bottom bases 1 to 0.35 is found by Monte-Carlo method that the mid-range has the smaller standard deviation (SD) than the mean value. The best for the whole family of the linear trapeze PDF are two-component (2C) estimators as the linear form of the mean and mid-range values of the sample. Their coefficients are found, properties discussed and formulas of SD are given. Some conclusions for curvilinear trapeze also are included. The simplified 2C-estimator of coefficients equal 0.5 is proposed. For the simulated data sample the trapeze PDF is chosen by the criterion ?2, three estimators and their SD are calculated and the best one is selected.

PL

Na wstępie przedstawiono podstawowe estymatory mezurandu dla próbek o kilku głównych rozkładach prawdopodobieństwa (PDF). Dla symetrycznych trapezowych PDF o liniowych oraz o krzywoliniowych bokach, za pomocą symulacji metodą Monte-Carlo określono odchylenia standardowe różnych estymatorów jedno- i dwu-składnikowych. Dla stosunku podstaw trapezu ? od 1 (prostokąt) do 0,35 najdokładniejszy jest środek rozstępu, a poniżej 0,35 wartość średnia. Dla trapezu liniowego zaproponowano nowy dwuskładnikowy estymator o jednakowych współczynnikach 0,5. Dla przykładu danych o trapezowym rozkładzie wg kryterium ?2 obliczono wartości i odchylenia standardowe trzech estymatorów i wybrano najefektywniejszy z nich.