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Local polynomial regression
Cigán, Martin ; Bašta, Milan (advisor) ; Maciak, Matúš (referee)
This thesis examines local polynomial regression. Local polynomial regression is one of non-parametric approach of data fitting. This particular method is based on repetition of fitting data using weighted least squares estimate of the parameters of the polynomial model. The aim of this thesis is therefore revision of some properties of the weighted least squares estimate used in linear regression model and introduction of the non-robust method of local polynomial regression. Some statistical properties of the local polynomial regression estimate are derived. Conditional bias and conditional variance of the local polynomial regression estimate are then approximated using Monte Carlo method and compared with theoretical results. Powered by TCPDF (www.tcpdf.org)
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Numerical solution of a stochastic model of a ball-type vibration absorber
Fischer, Cyril ; Náprstek, Jiří
The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplifcation, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect which can negatively influence efficiency of the absorber.
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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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Using LabVIEW to determine measurement uncertainty
Hoferková, Kateřina ; Štohl, Radek (referee) ; Šedivá, Soňa (advisor)
This bachelor thesis is focused on problematics of determining the measurement uncertainty. In the theoretical part of the thesis there is a theory of the procedure of determining the uncertainty of the measurement. The practical part of the thesis is focused on the realization of the program created in LabVIEW 2017. The bachelor thesis is about a determining the measurement uncertainty according to GUM, the standard uncertainty of type A, the standard uncertainty of type B, the combined uncertainty and the expanded uncertainty. The thesis is focused on determining the measurement uncertainty of direct measurements, indirect measurements and Monte Carlo method. The enclosed LabVIEW program enables to insert the data to determine the measurement uncertainty. The program determines the measurement uncertainty according to GUM and Monte Carlo method. The results of a calculation can be optionally saved to a file for an archiving.
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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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Using Artificial Neural Network Models to Assess Water Quality in Water Distribution Networks
Cuesta Cordoba, Gustavo Andres ; Tuhovčák, Ladislav (advisor)
A water distribution system (WDS) is based in a network of interconnected hydraulic components to transport the water directly to the customers. Water must be treated in a Water Treatment Plant (WTP) to provide safe drinking water to consumers, free from pathogenic and other undesirable organisms. The disinfection is an important aspect in achieving safe drinking water and preventing the spread of waterborne diseases. Chlorine is the most commonly used disinfectant in conventional water treatment processes because of its low cost, its capacity to deactivate bacteria, and because it ensures residual concentrations in WDS to prevent microbiological contamination. Chlorine residual concentration is affected by a phenomenon known as chlorine decay, which means that chlorine reacts with other components along the system and its concentration decrease. Chlorine is measured at the output of the WTP and also in several considered points within the WDS to control the water quality in the system. Simulation and modeling methods help to predict in an effective way the chlorine concentration in the WDS. The purpose of the thesis is to assess chlorine concentration in some strategic points within the WDS by using the historical measured data of some water quality parameters that influence chlorine decay. Recent investigations of the water quality have shown the need of the use of non-linear modeling for chlorine decay prediction. Chlorine decay in a pipeline is a complex phenomenon so it requires techniques that can provide reliable and efficient representation of the complexity of this behavior. Statistical models based on Artificial Neural Networks (ANN) have been found appropriated for the investigation and solution of problems related with non-linearity in the chlorine decay prediction offering advantages over more conventional modeling techniques. In this sense, this thesis uses a specific neural network application to solve the problem of forecasting the residual chlorine
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Risk Analysis in Transport Infrastructure Projects
Hašek, Jiří ; Holá, Michaela (referee) ; Hromádka, Vít (advisor)
The subject of the master’s thesis is a risk analysis in transport infrastructure projects. In the theoretical part, I deal with public sector, life cycle of the project, evaluation of public projects, conception of risk, clasification of risk, risk analysis and valuation of the risk. In the practical section I process risk analysis of the project in transport infrastucture.
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Uncertainty estimation of reservoir storage capacity in first stage of design preparation
Oulehla, Pavel ; Paseka, Stanislav (referee) ; Marton, Daniel (advisor)
The aim of the bachelor thesis is the estimation of reservoir storage capacity uncertainty. The input uncertainty is defined by the inaccuracy of the altitude geographic data. Using the appropriate altitude measuring and the estimated errors of the measurement, the change in the area – volumes curves is described as weel as its value of uncertainty. Afterwords the storage capacity loaded by batymetric curves uncertainty is calculated. Furthermore the uncertainty of the reservoir filling height has been quantified. For these kind of calculations the reservoir simulation model has been used, Monte Carlo method, to generate random values of the batygraphic curve has been used too. Expression of uncertainties when calculating the storage capacity can help to reduction risk of storage capacity failure, respectively reduction of water shortages during reservoirs operations during critical dry periods.
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A new method for the solution of the Schrödinger equation
Kocák, Jakub ; Uhlík, Filip (advisor) ; Demel, Ondřej (referee)
Title: A new method for the solution of the Schrödinger equation Author: Jakub Kocák Department: Department of Physical and Macromolecular Chemistry Supervisor: doc. RNDr. Filip Uhlík, Ph.D. Abstract: In this thesis we study method for the solution of time-independent Schrö- dinger equation for ground state. The wave function, interpreted as probability density, is represented by samples. In each iteration we applied approximant of imaginary time propagator. Acting of the operator is implemented by Monte Carlo simulation. Part of the thesis is dedicated to methods of energy calculation from samples of wave function: method based on estimation of value of wave function, method of convolution with heat kernel, method of averaged energy weighed by wave function and exponential de- cay method. The method for the solution was used to find ground state and energy for 6-dimensional harmonic oscillator, anharmonic 3-dimensional octic oscillator and hydrogen atom. Keywords: imaginary time propagation, Monte Carlo method, variational principle, ground state 1
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Tests of independence for multivariate data
Kudlík, Michal ; Omelka, Marek (advisor) ; Hlávka, Zdeněk (referee)
Title: Tests of independence for multivariate data Author: Bc. Michal Kudlík Department: Department of Probability and Mathematical Statistics Supervisor: Ing. Marek Omelka, PhD., Department of Probability and Mathema- tical Statistics Abstract: This thesis is an overview of tests of independence for multidimensi- onal data. The report includes tests on independence of categorical and conti- nuous random variables, tests assuming normal distribution of data, asymptotic nonparametric tests and permutation tests with application of the Monte Carlo method. This thesis shows the suitability of tests with properly chosen real data and checks significance level and compares the strength of the selected tests by simulation study while using appropriate statistical software. Based on the simu- lation study the thesis discusses an appropriateness of the use of different tests for different situations. Keywords: independence, permutation and asymptotic tests of independence, Monte Carlo method, simulation study 1
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