|
|
Analysis of shape of random functions
Fürst, Matouš ; Nagy, Stanislav (advisor) ; Maciak, Matúš (referee)
Registration of functional data is a part of functional data analysis which focuses on the transformation of a sample of functions such that the shapes of these functions are aligned and undesired variation between them removed. This thesis describes the general theory of functional registration and compares two selected methods. These two methods are thoroughly described, with a focus on their theoretical properties. Moreover, a modification of one of the methods is proposed. A comparison is performed on both real and simulated datasets, and an extension for registration into multiple groups is utilized. 1
|
|
|
Optimization in energy problems
Fürst, Matouš ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
Title: Optimization in energy problems Author: Matouš Fürst Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis we present an optimization model of a semi-autonomous household, which aims to make energy management more efficient. The household is equipped with solar panels and an electric vehicle with a high-capacity battery. In the first part we summarize the basic properties of linear programming and two- stage stochastic linear programming. Subsequently, a two-stage stochastic linear program is formulated and solved in order to optimize the purchase, sale and storage of energy in the household during a single day. The program is formulated in two versions - with present and with departing vehicle. The final solution represents optimal decisions of the household and we discuss it with respect to the input data. In both versions the solution leads to a substantial reduction in costs compared to a household without a battery. Keywords: stochastic optimization, linear programming, domestic microgrid 1
|
|
|
Optimization in energy problems
Fürst, Matouš ; Kopa, Miloš (advisor) ; Lachout, Petr (referee)
Title: Optimization in energy problems Author: Matouš Fürst Department: Department of Probability and Mathematical Statistics Supervisor: doc. RNDr. Ing. Miloš Kopa, Ph.D., Department of Probability and Mathematical Statistics Abstract: In this thesis we present an optimization model of a semi-autonomous household, which aims to make energy management more efficient. The household is equipped with solar panels and an electric vehicle with a high-capacity battery. In the first part we summarize the basic properties of linear programming and two- stage stochastic linear programming. Subsequently, a two-stage stochastic linear program is formulated and solved in order to optimize the purchase, sale and storage of energy in the household during a single day. The program is formulated in two versions - with present and with departing vehicle. The final solution represents optimal decisions of the household and we discuss it with respect to the input data. In both versions the solution leads to a substantial reduction in costs compared to a household without a battery. Keywords: stochastic optimization, linear programming, domestic microgrid 1
|
guest ::
