Wyniki wyszukiwania - BazTech

1

Determination of characteristic flow values downstream of the Racibórz Reservoir using Monte Carlo methods based on copula functions

Twaróg B.

Czasopismo Techniczne. Środowisko

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2015

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Y. 112, iss. 2-Ś

141--169

EN

This case study of the Racibórz reservoir discusses the application of a determination method of characteristic flow values below retention reservoirs. The study describes the selected theoretical foundations, the individual steps of the Monte Carlo (MC) method used to generate hypothetical flood wave hydrographs, and the results of simulations leading to the determination of characteristic flow values below retention reservoirs. The method is based on probability density functions for a multidimensional random variable obtained using copula link functions. The results of the analyses are represented in tables and graphs. The results of the simulation analysis are presented for comparison purposes, assuming a constant and a variable time for the hypothetical base flood elevation.

PL

W artykule zapresentowano aplikację określania wartości przepływów charakterystycznych poniżej zbiorników retencyjnych na przykładzie zbiornika Racibórz. Przedstawiono wybrane podstawy teoretyczne, poszczególne kroki metodyki, zastosowanie metody Monte Carlo (MC) do tworzenia hipotetycznych hydrogramów fal powodziowych oraz wyniki obliczeń symulacyjnych prowadzące do określenia wartości charakterystycznych przepływów poniżej zbiorników. U podstaw tej metody są funkcje gęstości prawdopodobieństwa wielowymiarowej zmiennej losowej budowanej z wykorzystaniem spinających funkcji copula. Wyniki analiz w artykule zostały przedstawione w postaci tabelarycznej i graficznej. Dla porównania przedstawione są wyniki analizy symulacyjnej przy założeniu stałego i zmiennego czasu podstawy hipotetycznej fali powodziowej.

2

Implementation of fast uniform random number generator on FPGA

Kozierski P., Lis M., Królikowski A.

Poznan University of Technology Academic Journals. Electrical Engineering

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2014

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No. 80

167--173

EN

The article presents approach to implementation of random number generator on FPGA unit. The objective was to select a generator with good properties (correlation values and matching of probability density function were taken into account). Design focused on logical elements so that the pseudo-random number generation time depend only on the electrical properties of the system. The results are positive, because the longest time determining the pseudorandom number was 16.7ns for the “slow model” of the FPGA and 7.3ns for “fast model”, while one clock cycle lasts 20ns.

3

Przetwarzanie liczb losowych o rozkładzie nierównomiernym na liczby losowe o rozkładzie równomiernym

Jessa M.

Pomiary Automatyka Kontrola

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2014

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R. 60, nr 7

453--455

PL

Podstawową wadą liczb losowych otrzymywanych sprzętowo jest ich nierównomierny rozkład. W rezultacie w ciągu wyjściowym liczba otrzymanych zer może się znacząco różnić od liczby jedynek. Sposobem na eliminację tej wady jest tzw. postprocessing. W artykule zaproponowano nową metodę postprocessingu, łatwą do zaimplementowania w każdym układzie cyfrowym. Stosując przekształcenia analityczne wykazano, że na wyjściu otrzymujemy liczby o rozkładzie równomiernym, niezależnie od postaci rozkładu liczb na wejściu. Metodę zilustrowano przykładem.

EN

Uniformly distributed random numbers play a key role in many fields of science. The basic disadvantage of random number generators is that the properties of a physical implementation differ from the theoretical expectations. Most sources of noise have a non-uniform distribution function, which eliminates them as a direct source of uniformly distributed random numbers. If the distribution is symmetric, we can use a threshold function, but this reduces the output bit rate and the output sequences are biased when the design is implemented in a real circuit. In this paper, there is proposed a novel method for producing uniformly distributed random numbers from non-uniformly distributed random numbers. The method uses an algorithm for improving the statistical quality of multiplicative congruential generators described in the literature. There is analytically shown that the bitwise exclusive-or sum of independent random numbers with non-uniform distribution provides, in the limit, numbers with uniform distribution. The proposed method also eliminates bias for constructions that use a threshold function and for sources with theoretically uniform distribution but implemented in real physical systems. Consequently, the set of systems that can be considered for use as sources of uniformly distributed random numbers is increased significantly to include practically all known sources of randomness. The method can be easily implemented in contemporary digital circuits.

4

Implementacja pakietu testów statystycznych do badania generatorów pseudolosowych w układzie programowalnym

Dąbal P., Pełka R.

Pomiary Automatyka Kontrola

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2014

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R. 60, nr 7

459--461

PL

W artykule przedstawiono projekt i wyniki badań eksperymentalnych mikrosystemu w układzie SoC Zynq (Xilinx) przeznaczonego do analizy statystycznej z użyciem pakietu NIST SP800-22 binarnych sekwencji pochodzących z implementowanych chaotycznych generatorów pseudolosowych. Omówiono sposób implementację pakiet testów NIST oraz wskazano potencjalne możliwości zrealizowania wybranych operacji sprzętowo. Kompletny system zajmuje 4% przerzutników i 19% bloków LUT dostępnych w układzie XC7Z020. Zastosowanie proponowanych mechanizmów pozwoliło na uzyskanie wydajności na poziomie 100 Mb/s.

EN

This paper presents the concept, design and experimental results of a SoCbased microsystem with Zynq device from Xilinx, for statistical testing of bit-streams from pseudo-random bit generators (PRBGs). In order to detect any symptoms of non-random behavior of PRBGs, we apply the commonly used statistical tests proposed by NIST as a standard package SP800-22. Five basic tests out of 15 tests from the NIST package have been converted from PC platform and adopted to specific embedded ARM architecture. Key elements of statistical analysis are performed by a dedicated analyzer implemented in programmable logic while the other functions are executed by an integrated dual-core processor. The complete microsystem uses 4% of flip-flops and 19% of LUTs available in the XC7Z020 SoC device. The operation of the microsystem has been optimized by assumption of fixed confidence level of statistical tests and constant data sample size equal to 220. Using these values we get the maximum throughput of data analysis at the level of 100 Mbps. The proposed system may be used for real-time analysis and tracing of pseudo-random binary sequences obtained from integrated PRBGs. This feature is an important improvement in statistical testing of high bit-rate data streams since conventional NIST tests running on the PC platform can be executed in the off-line mode only. Our further work will be focused on the implementation of some other tests from the NIST package and speedup techniques based on multiple bit analysis in a single clock cycle.

5

Parallel uniform random number generator in FPGA

Kozierski P., Lis M., Królikowski A.

Computer Applications in Electrical Engineering

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2014

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Vol. 12

399--406

EN

The article presents approach to implementation of random number generator in FPGA unit. The objective was to select a generator with good properties (correlation values and fidelity of probability density function were taken into account). During the design focused on logical elements so that the pseudo-random number generation time depend only on the electrical properties of the system. The results are positive, because the longest time determining the pseudorandom number was 16.7ns for the “slow model” of the FPGA and 7.3ns for “fast model”, while one clock cycle lasts 20ns. Additionally the parallel random number generator has been proposed, composed of 10 simple generator modules. After modules connecting, maximum time for generation of 10 random numbers was equal 41.0ns for the “slow model” and 16.6ns for the “fast model”.

6

Generator liczb losowych wykorzystujący mikrokontroler ATMEGA16

Ambroziak D., Dąbkowski M., Redlarski G.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

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2012

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Nr 31

23-26

PL

Istotę artykułu stanowi opis rozwiązania problemu dotyczącego syntezy generatorów liczb losowych: fizycznych oraz komputerowych - programowych, bazujących na układach scalonych wykorzystujących moduł mikrokontrolera serii Atmega16. Z tego względu we wstępie przedstawiono genezę, zastosowanie oraz rodzaje generatorów liczb losowych, natomiast w dalszej części artykułu opisano przykładowe generatory liczb quasi-losowych. Następnie zaprezentowano istotę podjętego problemu oraz propozycję jego rozwiązania. Na zakończenie przedstawiono krótkie podsumowanie oraz podano najważniejsze wnioski.

EN

The purpose of this publication is to provide a solution to the problem of synthesis of physical and computer random number generators based on a simple integrated circuit leveraging Atmega16 microcontroller. Article in the introduction presents the origins, application and types of random number generators. Later in this paper are presented examples of pseudorandom numbers generators. Another part of this publication is accurate to look at the problem and its solution method. Article ends with a summary presenting the final conclusions of this work.

7

Professor Ryszard Zieliński's contribution to Monte Carlo methods and random number generators. Uniform asymptotics in statistics

Niemiro W.

Mathematica Applicanda

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2012

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Vol. 40, No. 2

92--106

PL

The aim of the paper is to summarize contributions of Ryszard Zieliński to two important areas of research. First, we discuss his work related to Monte Carlo methods. Ryszard Zieliński was particularly interested in Monte Carlo optimization. About 10 of his papers concerned stochastic algorithms for seeking extrema. He examined methods related to stochastic approximation, random search and global optimization. We stress that Zielinski often considered computational problems from a statistical perspective. In several articles he explicitly indicated that optimization can be reformulated as a statistical estimation problem. We also discuss relation between the family of Simulated Annealing algorithms on the one hand and some procedures examined earlier by Ryszard Zieliński on the other. Another topic belonging to Monte Carlo methods, in which Ryszard Zieliński has achieved interesting results, is construction of random number generators and examination of their statistical properties. Zieliński proposed an aperiodic generator based on Weil sequences and showed how it can be efficiently implemented. Later he constructed an algorithm which uses several such generators and produces pseudo-random sequences with better statistical properties. The second area of Zieliński’s work discussed here is related to uniform limit theorems of mathematical statistics. We stress the methodological motivation behind the research in this direction. In Zieliński’s view, asymptotic results should hold uniformly with respect to the family of probability distributions under consideration. In his opinion, this requirement comes from the very nature of statistical models and the needs of practical applications. Zieliński examined uniform versions the Weak Law of Large Numbers, Strong Law of Large Numbers and Central Limit Theorem in several statistical models. Some results were rather unexpected. He also gave a necessary and sufficient condition for uniform consistency of sample quantiles. Two papers of Ryszard Zieliński were devoted to uniform consistency of smoothed versions of empirical cumulative distribution function. In one of them he proved a version of Dvoretzky-Kiefer-Wolfowitz inequality. The aim of the paper is to summarize contributions of Ryszard Zieliński to two important areas of research. First, we discuss his work related to Monte Carlo methods. Ryszard Zieliński was particularly interested in Monte Carlo optimization. About 10 of his papers concerned stochastic algorithms for seeking extrema. He examined methods related to stochastic approximation, random search and global optimization. We stress that Zielinski often considered computational problems from a statistical perspective. In several articles he explicitly indicated that optimization can be reformulated as a statistical estimation problem. We also discuss relation between the family of Simulated Annealing algorithms on the one hand and some procedures examined earlier by Ryszard Zieliński on the other. Another topic belonging to Monte Carlo methods, in which Ryszard Zieliński has achieved interesting results, is construction of random number generators and examination of their statistical properties. Zieliński proposed an aperiodic generator based on Weil sequences and showed how it can be efficiently implemented. Later he constructed an algorithm which uses several such generators and produces pseudo-random sequences with better statistical properties. The second area of Zieliński’s work discussed here is related to uniform limit theorems of mathematical statistics. We stress the methodological motivation behind the research in this direction. In Zieliński’s view, asymptotic results should hold uniformly with respect to the family of probability distributions under consideration. In his opinion, this requirement comes from the very nature of statistical models and the needs of practical applications. Zieliński examined uniform versions the Weak Law of Large Numbers, Strong Law of Large Numbers and Central Limit Theorem in several statistical models. Some results were rather unexpected. He also gave a necessary and sufficient condition for uniform consistency of sample quantiles. Two papers of Ryszard Zieliński were devoted to uniform consistency of smoothed versions of empirical cumulative distribution function. In one of them he proved a version of Dvoretzky-Kiefer-Wolfowitz inequality.

8

Losowość generatora TRNG zaimplementowanego w FPGA

Jessa M., Matuszewski Ł., Jaworski M.

Pomiary Automatyka Kontrola

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2011

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R. 57, nr 8

880-882

PL

Random Number Generator) zbudowanego z wielu niezależnych generatorów pierścieniowych zaimplementowanych w tym samym układzie FPGA. Wykorzystując nową metodę odróżniania losowości od pseudolosowości wykazano, że zmniejszenie częstotliwości próbkowania wyjścia generatora pierścieniowego może zwiększyć losowość ciągu wytwarzanego przez generator TRNG. Otrzymany wynik oznacza, że generator może dostarczyć ciągów losowych użytecznych w kryptografii z większą szybkością od tej obserwowanej dla większej częstotliwości próbkującej.

EN

One of the simplest sources of purely digital true random bit sequences is the ring oscillator with output sampled by a signal coming from a low-frequency quartz oscillator. Combining XOR bit streams produced by many such generators (see Fig. 1) can significantly improve the statistical properties of the output sequence. As it is shown in the literature, this statement is true for deterministic and non-deterministic sources of random numbers. In cryptography, a user needs sequences with very good statistical properties but originating from a non-deterministic system. Therefore a method for distinguishing pseudo and true randomness for sequences produced by a combined true random number generator (TRNG) is necessary. In this paper the authors show that even a small amount of true randomness, present in a single ring oscillator, accumulates as a function of the number of ring oscillators used to produce the output stream. There is experimentally proved that in a real field programmable gate array (FPGA), the amount of randomness offered by the generator of Fig. 2 can be greater for smaller sampling frequency. Fig. 3 illustrates the behaviour of parameter mmin introduced in [6] as a function of the number K of source generators for four sampling frequencies fL: 100 MHz, 150 MHz, 200 MHz, and 250 MHz. The basic result of this paper is the statement that the efficient bit rate of streams useful for cryptography can be greater for smaller sampling frequencies than that observed for greater sampling frequencies.

9

Generacja binarnych ciągów losowych w układzie Virtex-5

Jessa M., Jaworski M.

Pomiary Automatyka Kontrola

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2010

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R. 56, nr 7

681-684

PL

W pracy przedstawiono wyniki badań generatora losowego łączonego, zbudowanego z generatorów wykorzystujących generatory pierścieniowe. Wykazano, że po zaimplementowaniu generatora w układzie Virtex-5 ciągi wyjściowe spełniają wszystkie testy statystyczne z pakietu NIST 800-22. Rozważono trzy sposoby realizacji opóźnienia występującego w generatorze pierścieniowym: w postaci kaskady negatorów, kaskady przerzutników oraz za pomocą linii opóźniającej wbudowanej w układ Virtex-5. Przedstawiono ograniczenia wykorzystania proponowanego generatora w kryptografii.

EN

One of the simplest sources of purely digital true random bit sequences is a ring oscillator with output sampled by a signal from the low-frequency quartz oscillator (Fig. 1). The frequency fH is normally at least several times greater than the frequency fL. The same idea was used in the experiment conducted but there was assumed that the ring oscillators had frequencies , close to fL but not smaller than fL. The signal of frequency fL, common for all source generators, was produced by the quartz oscillator built into evaluation board ML505 containing Virtex-5 (Fig. 2). There was assumed that . The frequencies satisfy the condition . Generators that failed to satisfy this condition were reconstructed to meet this requirement, e.g., by changing the location of elements in the FPGA structure. Tables 1, 3, and 5 lists the results of NIST statistical testing for the realised generator composed of 40 source generators. The all tests were satisfactory independently of the hardware solution of the delay ?. In experiments there were considered three constructions for ?: a chain of inverters, a chain of latches and the delay line built into Virtex-5. The practical RNG demonstrates that the idea of combining modulo 2 of a finite number of source streams can be used to construct entirely digital, high-speed RNGs that pass all NIST statistical tests. The application of this type of generator to cryptography, considered in the last paragraph of this paper, although possible, requires further research.

10

Modele symulacyjne w zasosowaniach wojskowych. Cz. 1, Miejsce metod Monte Carlo w symulacjach numerycznych

Spustek H., Krakowski K.

Zeszyty Naukowe AON

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2004

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nr 2(55)

253-263

EN

The article presents the problem of applying computer simulation methods to military problems. Stochastic processes have been discussed, general information relating to the structure of random numbers generators has been given and the algorithm of Monte Carlo method has been described. The algorithm of Monte Carlo method has been presented in a descriptive version (12 steps reduced to 6 steps) and in a graphic way. Monte Carlo methods have been used in computer simulations for many years. Remembering them is to show how topical they are.