## Przekształcenia statyczne i dynamiczne w modelowaniu sygnałów i układów wykorzystującym dane eksperymentalne

### Krystian Kubowicz

#### Abstract

The thesis deals with input preprocessing in signals and dynamic systems modelling which uses experimental data. What is considered is the need, neccessity and ways of input signal preprocessing in creation of neural models of dynamic systems. In the thesis it is shown that neural modelling of dynamic systems often requires the use of input signal preprocessing. Static as well as dynamic preprocessing is discussed. It is shown that in some situations it is not possible to create a model without an appropriate input signal preprocessing. The wiely used architecture with a series of unit delays may lead to the necessity of limitation of sampling period and/or the number of the delays. An architecture with all-pass filters instead of unit delays is proposed as a way of getting out of these limitations. An iterative algorithm is introduced in which the parameters of the all-pass filters are calculated. In every iteration the chosen parameter ensures that the relation of the obtained signal to the other signals is as close to the state of ortogonality as possible. The way how the algorithm works is illustrated by a numerical example. The notions of static and approximately static relationships between signals is defined. Based on these definitions four different indices of statics are introduced. They are used as a tool to determine whether a relationship between signals is approximately static. If the relationship is not approximately static then the indices show how far away from the state of statics is the given set of experimental data. Three of these indices are calculated based on the time values of the signals, while the fourth one uses mutliresolution analysis. Simulation examples are presented and discussed for all indices. It is shown how nonlinear transformations influence the spectrum of a signal. These results are used to develop a method which can be used to determine whether there exists a relationship between signals having a limited number of non-zero harmonic components.Diploma type | Doctor of Philosophy | ||||

Author |
Krystian Kubowicz (FoEE)
Krystian Kubowicz
| ||||

Title in Polish | Przekształcenia statyczne i dynamiczne w modelowaniu sygnałów i układów wykorzystującym dane eksperymentalne | ||||

Language | pl polski | ||||

Certifying Unit | Faculty of Electrical Engineering (FoEE) | ||||

Discipline | automation and robotics / (technology domain) / (technological sciences) | ||||

Start date | 12-05-2004 | ||||

Defense Date | 06-01-2010 | ||||

End date | 27-01-2010 | ||||

Supervisor |
Bartłomiej Beliczyński (FoEE / ICIE)
Bartłomiej Beliczyński
| ||||

Internal reviewers |
Andrzej Dzieliński (FoEE / ICIE)
Andrzej Dzieliński
| ||||

External reviewers |
Mirosław Świercz
Mirosław Świercz
| ||||

Pages | 122 | ||||

Keywords in English | xxx | ||||

Abstract in English | The thesis deals with input preprocessing in signals and dynamic systems modelling which uses experimental data. What is considered is the need, neccessity and ways of input signal preprocessing in creation of neural models of dynamic systems. In the thesis it is shown that neural modelling of dynamic systems often requires the use of input signal preprocessing. Static as well as dynamic preprocessing is discussed. It is shown that in some situations it is not possible to create a model without an appropriate input signal preprocessing. The wiely used architecture with a series of unit delays may lead to the necessity of limitation of sampling period and/or the number of the delays. An architecture with all-pass filters instead of unit delays is proposed as a way of getting out of these limitations. An iterative algorithm is introduced in which the parameters of the all-pass filters are calculated. In every iteration the chosen parameter ensures that the relation of the obtained signal to the other signals is as close to the state of ortogonality as possible. The way how the algorithm works is illustrated by a numerical example. The notions of static and approximately static relationships between signals is defined. Based on these definitions four different indices of statics are introduced. They are used as a tool to determine whether a relationship between signals is approximately static. If the relationship is not approximately static then the indices show how far away from the state of statics is the given set of experimental data. Three of these indices are calculated based on the time values of the signals, while the fourth one uses mutliresolution analysis. Simulation examples are presented and discussed for all indices. It is shown how nonlinear transformations influence the spectrum of a signal. These results are used to develop a method which can be used to determine whether there exists a relationship between signals having a limited number of non-zero harmonic components. | ||||

Thesis file |
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Citation count* | 5 (2020-09-18) |

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