Data driven model identification methods have grown increasingly  
popular due to enhancements in measuring devices  
and data mining. They provide a useful approach for comparing  
the performance of a device to the simplified model that was  
used in the design phase. One of the modern, popular methods  
for model identification is Sparse Identification of Nonlinear Dynamics  
(SINDy). Although this approach has been widely investigated  
in the literature using mostly numerical models, its applicability  
and performance with physical systems is still a topic of  
current research. In this paper we extend SINDy to identify the  
mathematical model of a complicated physical experiment of a  
chaotic pendulum with a varying potential interaction. We also  
test the approach using a simulated model of a nonlinear, simple  
pendulum. The input to the approach is a time series, and estimates  
of its derivatives. While the standard approach in SINDy  
is to use the Total Variation Regularization (TVR) for derivative  
estimates, we show some caveats for using this route, and we  
benchmark the performance of TVR against other methods for  
derivative estimation. Our results show that the estimated model  
coefficients and their resulting fit are sensitive to the selection of  
the TVR parameters, and that most of the available derivative estimation  
methods are easier to tune than TVR. We also highlight  
other guidelines for utilizing SINDy to avoid overfitting, and we  
point out that the fitted model may not yield accurate results over  
long time scales. We test the performance of each method for noisy data sets and provide both experimental and simulation results.


Data Driven Model Identification for a Chaotic Pendulum With Variable Interaction Potential

Division / Sponsors: 
Design Engineering Division and Computers & Information In Engineering Division


Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2020/volume/83907

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