Differential Evolution approach and parameter estimation of chaotic
Shemyakin, Vladimir (2012)
Diplomityö
Shemyakin, Vladimir
2012
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe2012112610040
https://urn.fi/URN:NBN:fi-fe2012112610040
Tiivistelmä
Parameter estimation still remains a challenge in many important applications.
There is a need to develop methods that utilize achievements in modern
computational systems with growing capabilities. Owing to this fact
different kinds of Evolutionary Algorithms are becoming an especially perspective
field of research. The main aim of this thesis is to explore theoretical
aspects of a specific type of Evolutionary Algorithms class, the Differential
Evolution (DE) method, and implement this algorithm as codes capable to
solve a large range of problems. Matlab, a numerical computing environment provided by MathWorks inc., has been utilized for this purpose. Our implementation
empirically demonstrates the benefits of a stochastic optimizers
with respect to deterministic optimizers in case of stochastic and chaotic
problems. Furthermore, the advanced features of Differential Evolution are
discussed as well as taken into account in the Matlab realization. Test "toycase"
examples are presented in order to show advantages and disadvantages
caused by additional aspects involved in extensions of the basic algorithm.
Another aim of this paper is to apply the DE approach to the parameter
estimation problem of the system exhibiting chaotic behavior, where the
well-known Lorenz system with specific set of parameter values is taken as
an example. Finally, the DE approach for estimation of chaotic dynamics
is compared to the Ensemble prediction and parameter estimation system
(EPPES) approach which was recently proposed as a possible solution for
similar problems.
There is a need to develop methods that utilize achievements in modern
computational systems with growing capabilities. Owing to this fact
different kinds of Evolutionary Algorithms are becoming an especially perspective
field of research. The main aim of this thesis is to explore theoretical
aspects of a specific type of Evolutionary Algorithms class, the Differential
Evolution (DE) method, and implement this algorithm as codes capable to
solve a large range of problems. Matlab, a numerical computing environment provided by MathWorks inc., has been utilized for this purpose. Our implementation
empirically demonstrates the benefits of a stochastic optimizers
with respect to deterministic optimizers in case of stochastic and chaotic
problems. Furthermore, the advanced features of Differential Evolution are
discussed as well as taken into account in the Matlab realization. Test "toycase"
examples are presented in order to show advantages and disadvantages
caused by additional aspects involved in extensions of the basic algorithm.
Another aim of this paper is to apply the DE approach to the parameter
estimation problem of the system exhibiting chaotic behavior, where the
well-known Lorenz system with specific set of parameter values is taken as
an example. Finally, the DE approach for estimation of chaotic dynamics
is compared to the Ensemble prediction and parameter estimation system
(EPPES) approach which was recently proposed as a possible solution for
similar problems.