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

Abstract

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. We also post the files needed to build and reproduce our experiment in a public repository.