Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

Stender, M; Oberst, S; Hoffmann, N

Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction

Stender, M Oberst, S

Hoffmann, N

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Publisher:: MDPI
Publication Type:: Journal Article
Citation:: Vibration, 2019, 2 (1), pp. 25 - 46
Issue Date:: 2019-01-10

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Field	Value	Language
dc.contributor.author	Stender, M	en_US
dc.contributor.author	Oberst, S https://orcid.org/0000-0002-1388-2749	en_US
dc.contributor.author	Hoffmann, N https://orcid.org/0000-0003-2074-3170	en_US
dc.date.issued	2019-01-10	en_US
dc.identifier.citation	Vibration, 2019, 2 (1), pp. 25 - 46	en_US
dc.identifier.issn	2571-631X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/129631
dc.description.abstract	<jats:p>Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for (a) describing the dynamics and (b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and nonlinearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and how to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of nonlinearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.</jats:p>	en_US
dc.language	en	en_US
dc.publisher	MDPI	en_US
dc.relation.ispartof	Vibration	en_US
dc.relation.isbasedon	10.3390/vibration2010002	en_US
dc.title	Recovery of Differential Equations from Impulse Response Time Series Data for Model Identification and Feature Extraction	en_US
dc.type	Journal Article
utslib.citation.volume	1	en_US
utslib.citation.volume	2	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	open_access
pubs.consider-herdc	true	en_US
pubs.issue	1	en_US
pubs.publication-status	Published online	en_US
pubs.volume	2	en_US

Abstract:

Time recordings of impulse-type oscillation responses are short and highly transient. These characteristics may complicate the usage of classical spectral signal processing techniques for (a) describing the dynamics and (b) deriving discriminative features from the data. However, common model identification and validation techniques mostly rely on steady-state recordings, characteristic spectral properties and non-transient behavior. In this work, a recent method, which allows reconstructing differential equations from time series data, is extended for higher degrees of automation. With special focus on short and strongly damped oscillations, an optimization procedure is proposed that fine-tunes the reconstructed dynamical models with respect to model simplicity and error reduction. This framework is analyzed with particular focus on the amount of information available to the reconstruction, noise contamination and nonlinearities contained in the time series input. Using the example of a mechanical oscillator, we illustrate how the optimized reconstruction method can be used to identify a suitable model and how to extract features from uni-variate and multivariate time series recordings in an engineering-compliant environment. Moreover, the determined minimal models allow for identifying the qualitative nature of the underlying dynamical systems as well as testing for the degree and strength of nonlinearity. The reconstructed differential equations would then be potentially available for classical numerical studies, such as bifurcation analysis. These results represent a physically interpretable enhancement of data-driven modeling approaches in structural dynamics.

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http://hdl.handle.net/10453/129631