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Recovery of differential equations from impulse response time series data for model identification and feature extraction
Citation Link: https://doi.org/10.15480/882.1991
Publikationstyp
Journal Article
Date Issued
2019-01-10
Sprache
English
Institut
TORE-DOI
Journal
Volume
2
Issue
1
Start Page
25
End Page
46
Citation
Vibration 2 (1): 25-46 (2019)
Publisher DOI
Publisher
Multidisciplinary Digital Publishing Institute
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.
Subjects
signal processing
sparse regression
system identification
impulse response
optimization
feature generation
structural dynamics
time series classification
DDC Class
500: Naturwissenschaften
530: Physik
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