| Abstract [eng] |
Processes and random variables are often analyzed using mathematical models in various branches of science. Results of mathematical models are uncertain, but still they are applied in technology science, physics, biology, pharmacy and others. In this case the sampling of random variables is used for simulation and analysis. The first task of this work is to get familiar with Latin hypercube sampling method and its advantages, and to compare it with other commonly used sampling methods. Another task is become acquainted with uncertainty and sensitivity analysis as well as sampling, simulation and SimLab 2.2 software applications. The predator and prey model is the main object in this work. It is a complicated model, described by a system of differential equations. This system is solved using 4-step Runge-Kutta method. Parameters of predator and prey model are going to be dynamic (uncertain), generated using LHS, FAST and Sobolmethods. Different results appear after performing calculations for each set of uncertain parameters. Quantiles are going to be used to determine the limits of uncertainty. In order to find parameters, that can have the biggest influence to the uncertainty of results of this model the sensitivity analysis is performed and various sensitivity measures are comapared. The following methods of sensitivity analysis are used: Pearson and Spearman rank correlation, partial correlation and partial rank correlation coefficients, Fast and Sobol methods. |
