Application of artificial neural networks in parametrical investigations of the energy flow and synchronization

Dąbrowski, A.; Jach, A.; Kapitaniak, T.

Artykuł - szczegóły

Tytuł artykułu

Application of artificial neural networks in parametrical investigations of the energy flow and synchronization

Autorzy

Dąbrowski A. , Jach A. , Kapitaniak T.

Treść / Zawartość

Pełne teksty:

httpwww_ptmts_org_pl2010-4-dabrowski-in.pdf

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Identyfikatory

Warianty tytułu

Aplikacje sztucznych sieci neuronowych w badaniach parametrycznych przepływu i synchronizacji energii

Języki publikacji

Abstrakty

Dynamics of nonlinear systems is a very complicated problem with many aspects to be recognized. Numerous methods are used to investigate such systems. Their careful analysis is connected with long-time simulations. Thus, there is great need for methods that would simplify these processes. In the paper, an application of Artificial Neural Networks (ANNs) supporting the recognition of the energy flow and the synchronization with use of Impact Maps is introduced. This connection applies an idea of the Energy Vector Space in the system with impacts. An energy flow direction change with the synchronization as a transitional state is shown. A new type of the index allowing one to control the system dynamic state is introduced. Results of the numerical simulations are used in the neural network teaching process. Results of a comparison of the straight impact map simulation and the neural network prediction are shown. Prediction of system parameters for the energy flow synchronization state with use of the neural network is presented.

Dynamika układów nieliniowych jest bardzo komplikowanymzagadnieniem z wieloma aspektami wciąż pozostającymi bez rozwiązania. Do badań takich układów stosuje się wiele różnych metod. Wnikliwa analiza związana jest najczęściej z bardzo czasochłonnymi symulacjami numerycznymi. Istnieje w związku z tym duże zapotrzebowanie na opracowanie metod upraszczających ten proces. W artykule pokazano zastosowanie sztucznych sieci neuronowych (ANN) wspomagających badania przepływu i synchronizacji energii. W badaniach zastosowano Mapy Uderzeń, będące efektem przedstawienia dynamiki układu z uderzeniami w przestrzeni energetyczno-wektorowej. Pokazano zmiany przepływu energii z przejściowym stanem synchronizacji. Wprowadzono nowy rodzaj parametru pozwalającego na określanie stanu dynamicznego układu z uderzeniami. Wyniki przeprowadzonych symulacji numerycznych zostały wykorzystane w procesie uczenia sztucznej sieci neuronowej. Przedstawiono następnie porównanie wyników symulacji i rozwiązania uzyskanego z sieci neuronowej oraz przewidywania parametrów układu, dla których występuje synchronizacja przepływu energii.

Słowa kluczowe

nonlinear dynamics chaos synchronization artificial neural networks

Wydawca

Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej

Czasopismo

Journal of Theoretical and Applied Mechanics

Rocznik

2010

Tom

Vol. 48 nr 4

Strony

871--896

Opis fizyczny

Bibliogr. 58 poz., rys.

Twórcy

autor

Dąbrowski A.

autor

Jach A.

autor

Kapitaniak T.

Technical University of Lodz, Division of Dynamics, Łódź, Poland, ar2de@p.lodz.pl

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Bibliografia

Identyfikator YADDA

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