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Uncertainty Calculation by the Monte Carlo Method
Kósa, Valentin ; Šedivá, Soňa (referee) ; Havlíková, Marie (advisor)
This bachelor’s diploma thesis deals with the measurement inaccuracies. Various types of uncertainty, methods, their specifications and ways of their recording are described. Next, Monte Carlo method and its application are introduced to the reader. Next, both methods described are applied: calculation of accuracy using uncertainty – GUM method and calculation of accuracy using Monte Carlo method. The methods are applied in measurements of DC current at resistive load with different meters.
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Measurement uncertainties determined by the Monte Carlo method
Krejčí, Roman ; Havlíková, Marie (referee) ; Šedivá, Soňa (advisor)
This bachelor thesis deals with the determination of the uncertainties of direct and indirect measurements. It focused on the uncertainty calculation by Monte Carlo method and GUM uncertainty framework. The practical part deals with the determination of uncertainties indirect measurement of resistance Ohm’s method. The calculated uncertainties are compared on the basis of the influence of the method, accuracy used devices and the temperature.
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Depletion calculation of VVER 1000 reactor fuel using KENO code
Janošek, Radek ; Katovský, Karel (referee) ; Novotný, Filip (advisor)
The introduction to operational nuclear reactors focusing on light-water pressurized reactor VVER 1000 is in the beginning of this Master´s thesis. This thesis covers basic technology of VVER 1000 reactor with focus on reactor core and nuclear fuel TVSA-T. A significant part of the thesis deal with basic concepts of nuclear safety and its methods. The main goal is to create a model of VVER 1000 reactor, which can be used in nuclear burn-up calculations using KENO code. Therefore a part of this thesis deals with explanation of statistical Monte Carlo method and the KENO code.
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Uncertainty of Indirect Measurement Determined by Monte Carlo Method
Novotný, Marek ; Havlíková, Marie (referee) ; Šedivá, Soňa (advisor)
This bachelor's thesis deals with determination of uncertainty in measurement, primarily with regard to the indirect measurement. There is theoretically analyzed and practically implemented calculate the uncertainty coefficient ent - speed multiple hole probe Annubar 485 in two ways. The first way is to calculate the uncertainty of the classical met-hod and the second one is the uncertainty using the Monte Carlo.
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Determination of the functional volumes of the reservoir considering input data uncertainties
Paseka, Stanislav ; Doležal, Petr (referee) ; Szolgay,, Ján (referee) ; Marton, Daniel (advisor)
Damaging changes and interventions in the water cycle in our landscape caused mainly in the last century together with uncertainties from climate change are the cause of more frequent occurrences of hydrological extremes. In Hydrology, the most urgent problem is that the values of the long-term mean flows are decreasing in rivers as well as the yield of groundwater sources, but on the other hand, we cannot forget to the problem of extreme floods. In these consequences developing methods and tools to uncertainty analysis of the reservoir yield and of the reservoir flood protection is very important, useful and desired. The main aim was to determine the functional volumes of the reservoir considering input data measurement uncertainties and to quantify them and was explained how uncertainty took into account in results. The active storage capacity was determined from the historical series of monthly flows that were affected by uncertainties, next were applied on water evaporation, seepage losses of the dam and morphological volume-area curves. The simulation-optimization reservoir model was developed and temporal reliability as reservoir yield performance measures was applied. This model will extend the existing UNCE_RESERVOIR software. The flood capacity was determined from random flood wave variations were obtained by repeatedly generating uncertainty on the flood hydrograph. Software was developed based on the modified Klemes method, which was able to transform flood waves. The measurement uncertainties of data inputs were created using Monte Carlo method in both softwares. By connecting two softwares, the functional volumes of the reservoir under conditions of measurement uncertainties were complexly determined. The case study was applied to the real water reservoir, in the Morava River Basin. The result will be whether the dam is resistant to the current conditions, or the optimal design of the functional volumes of reservoir under conditions uncertainties.
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Approximations in Stochastic Optimization and Their Applications
Mrázková, Eva ; Horová, Ivana (referee) ; Štěpánek, Petr (referee) ; Karpíšek, Zdeněk (advisor)
Mnoho inženýrských úloh vede na optimalizační modely s~omezeními ve tvaru obyčejných (ODR) nebo parciálních (PDR) diferenciálních rovnic, přičemž jsou v praxi často některé parametry neurčité. V práci jsou uvažovány tři inženýrské problémy týkající se optimalizace vibrací a optimálního návrhu rozměrů nosníku. Neurčitost je v nich zahrnuta ve formě náhodného zatížení nebo náhodného Youngova modulu. Je zde ukázáno, že dvoustupňové stochastické programování nabízí slibný přístup k řešení úloh daného typu. Odpovídající matematické modely, zahrnující ODR nebo PDR omezení, neurčité parametry a více kritérií, vedou na (vícekriteriální) stochastické nelineární optimalizační modely. Dále je dokázáno, pro jaký typ úloh je nutné použít stochastické programování (EO reformulace), a kdy naopak stačí řešit jednodušší deterministickou úlohu (EV reformulace), což má v praxi význam z hlediska výpočetní náročnosti. Jsou navržena výpočetní schémata zahrnující diskretizační metody pro náhodné proměnné a ODR nebo PDR omezení. Matematické modely odvozené pomocí těchto aproximací jsou implementovány a řešeny v softwaru GAMS. Kvalita řešení je určena na základě intervalových odhadů "optimality gapu" spočtených pomocí metody Monte Carlo. Parametrická analýza vícekriteriálního modelu vede na výpočet "efficient frontier". Jsou studovány možnosti aproximace modelu zahrnujícího pravděpodobnostní členy související se spolehlivostí pomocí smíšeného celočíselného nelineárního programování a reformulace pomocí penalizační funkce. Dále je vzhledem k budoucím možnostem paralelních výpočtů rozsáhlých inženýrských úloh implementován a testován PHA algoritmus. Výsledky ukazují, že lze tento algoritmus použít, i když nejsou splněny matematické podmínky zaručující konvergenci. Na závěr je pro deterministickou verzi jedné z úloh porovnána metoda konečných diferencí s metodou konečných prvků za použití softwarů GAMS a ANSYS se zcela srovnatelnými výsledky.
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Programs for calculating measurement uncertainty using Monte Carlo method
Novotný, Marek ; Havlíková, Marie (referee) ; Šedivá, Soňa (advisor)
The thesis deals with establishing uncertainties of indirect measurements. It focuses primarily on random number generators in software enabling the calculation of mea-surement uncertainties using Monte Carlo. Then it focuses on the uncertainty calculati-on indirect measurement as the Monte Carlo method and the classical numerical met-hod. The practical part deals with the verification of randomness generators numbers contained in various softwares. It also deals with the determination of uncertainties indi-rect current measurements by both above-mentioned methods and then comparing and evaluating the values achieved.
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Uncertainty of Measurement Estimation of Mean Monthly Flows Values of the Selected Hydrometric Station at the Svitava River Catchment Area
Paseka, Stanislav ; Janál,, Petr (referee) ; Marton, Daniel (advisor)
Currently, a sizes of the time series elements of average monthly flows uncertainty are not taken into account in more detail and it does not know the estimation of their sizes. The above mentioned fact could ultimately affected the design and operation of large open water reservoirs. This bachelor's thesis deals with the uncertainty of measurement estimation of the mean monthly flows which have derived in the measuring profile Prostřední Poříčí in the Křetínka river in the Svitava river basin. Evaluation is done using a measured values of water level stages and a stage-discharge relation curve. The basis for design of uncertainty affected stage-discharge curves and water lavel stages the Monte Carl method is used. The outcome values of random flows are further evaluated using the statistical methods in the form of the statistical characteristics and presented as uncertainties of mean monthly flows.
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Proposal of modernizing the Mesing instrument to calibrate the gauge blocks over 100 mm
Sokl, Antonín ; Jankových, Róbert (referee) ; Šrámek, Jan (advisor)
The aim of this thesis, which deals with the modernization of the Zeiss/Tesa device, which is designed to calibrate the gauge blocks, is to provide a detailed analysis of the current state of the art of this instrument and to search for gauge blocks calibration requirements. The introductory part of the thesis is devoted to the definition of basic metrological concepts and terms. One of the separate chapters contains a elaborate description of the Zeiss/Tesa device and the possibilities of its modernization. A qualified estimation of the measurement uncertainty is determined in the practical part of the thesis and a simulation of the measurement uncertainty is performed using the Monte Carlo method. The final chapter contains the technical documentation of the proposed modernization.
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