Machete, R. L. (2007) Modelling a MooreSpiegel Electronic Circuit: the imperfect model scenario. PhD thesis, University of Oxford.

PDF
55MB 
Abstract
The goal of this thesis is to investigate model imperfection in the context of forecasting. We focus on an electronic circuit built in a laboratory and then enclosed to reduce environmental effects. The nondimensionalised model equations, obtained by applying Kirchhoff’s current and voltage laws, are the MooreSpiegel Equations [47], but they exhibit a large disparity with the circuit. At parameter values used in the circuit, they yield a periodic trajectory whilst the circuit exhibits chaotic behaviour. Therefore, alternative models for the circuit are sought.
The models we consider are local and global prediction models constructed from data. We acknowledge that all our models have errors and then seek to quantify how these errors are distributed across the circuit attractor. To this end, qpling times of initial uncertainties are computed for the various models. A qpling time is the time for an initial uncertainty to increase by a factor of q [67], where q is a real number. Whereas it is expected that different models should have different qpling time distributions, it is found that the diversity in our models can be increased by constructing them in different coordinate spaces.
To forecast the future dynamics of the circuit using any of the models, we make probabilistic forecasts [8]. The question of how to choose the spread of the initial ensemble is addressed by the use of skill scores [8, 9]. Finally, the diversity in our models is exploited by combining probabilistic forecasts from them so as to minimise some skill score. It is found that the skill of combined notsogood models can be increased by combining
them as discussed in this thesis.
Item Type:  Thesis (PhD) 

Subjects:  D  G > Dynamical systems and ergodic theory O  Z > Ordinary differential equations 
Research Groups:  Oxford Centre for Industrial and Applied Mathematics 
ID Code:  850 
Deposited By:  Eprints Administrator 
Deposited On:  19 Nov 2009 16:49 
Last Modified:  29 May 2015 18:32 
Repository Staff Only: item control page