Datum
2023-03-24Schlagwort
510 Mathematik 620 Ingenieurwissenschaften Neuronales NetzDuffing-OszillatorNichtlineare SchwingungMetadata
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Aufsatz
Data Driven prediction of forced nonlinear vibrations using stabilised Autoregressive Neural Networks
Zusammenfassung
In this work, we propose a novel approach to the data-driven prediction of vibration responses of nonlinear systems. The main idea is based on Autoregressive Neural Networks (ARNN) to model the nonlinear transfer behaviour between an external excitation and the system response. We propose an autoregressive network architecture with embedded symmetry using bias-free tanh activation and guarantee Input-to-State-Stability (ISS) by enforcing a special penalty term to the weights. The resulting training procedure is analysed for the example of a DUFFING oscillator with white noise excitation. In a BAYESian optimisation, it is found that beyond enforcing input-to-state-stability, the stabilising penalty term also decreases sensitivity with respect to other training parameters compared to other classical techniques. Furthermore, we show that the stabilised ARNN is able to give excellent approximations of the nonlinear response of the DUFFING oscillator for a wide range of excitation intensities. In contrast, linear models, such as autoregressive models with exogenous input (ARX) in time domain or linear transfer functions in frequency domain, will only find some linear approximation. In particular, by construction, they will not be able to capture nonlinear effects for arbitrary amplitudes and excitation levels.
Zitierform
In: Proceedings in applied mathematics and mechanics : PAMM Volume 22 / Issue 1 (2023-03-24) eissn:1617-7061Förderhinweis
Gefördert im Rahmen des Projekts DEALZitieren
@article{doi:10.17170/kobra-202304197837,
author={Westmeier, Tobias and Kreuter, Daniel and Bäuerle, Simon and Hetzler, Hartmut},
title={Data Driven prediction of forced nonlinear vibrations using stabilised Autoregressive Neural Networks},
journal={Proceedings in applied mathematics and mechanics : PAMM},
year={2023}
}
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2023-04-19T12:01:55Z 2023-04-19T12:01:55Z 2023-03-24 doi:10.17170/kobra-202304197837 http://hdl.handle.net/123456789/14597 Gefördert im Rahmen des Projekts DEAL eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ 510 620 Data Driven prediction of forced nonlinear vibrations using stabilised Autoregressive Neural Networks Aufsatz In this work, we propose a novel approach to the data-driven prediction of vibration responses of nonlinear systems. The main idea is based on Autoregressive Neural Networks (ARNN) to model the nonlinear transfer behaviour between an external excitation and the system response. We propose an autoregressive network architecture with embedded symmetry using bias-free tanh activation and guarantee Input-to-State-Stability (ISS) by enforcing a special penalty term to the weights. The resulting training procedure is analysed for the example of a DUFFING oscillator with white noise excitation. In a BAYESian optimisation, it is found that beyond enforcing input-to-state-stability, the stabilising penalty term also decreases sensitivity with respect to other training parameters compared to other classical techniques. Furthermore, we show that the stabilised ARNN is able to give excellent approximations of the nonlinear response of the DUFFING oscillator for a wide range of excitation intensities. In contrast, linear models, such as autoregressive models with exogenous input (ARX) in time domain or linear transfer functions in frequency domain, will only find some linear approximation. In particular, by construction, they will not be able to capture nonlinear effects for arbitrary amplitudes and excitation levels. open access Westmeier, Tobias Kreuter, Daniel Bäuerle, Simon Hetzler, Hartmut 6 Seiten doi:10.1002/pamm.202200318 Neuronales Netz Duffing-Oszillator Nichtlineare Schwingung publishedVersion eissn:1617-7061 Issue 1 Proceedings in applied mathematics and mechanics : PAMM Volume 22 false e202200318
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