Learning Data-Driven Model of Damped Coupled Oscillators from System Impulse Response

Published

October 28, 2022

Author(s)

Jacob Fabro, Gregory W. Vogl, Yongzhi Qu, Reese Eischens

Abstract

Data-driven modeling of dynamical systems has drawn much research attention recently, with the goal of approximating the underlying governing rules of a dynamical system with data-driven differential equations. Many real-world dynamical systems can be modeled as coupled oscillators, such as chemical reactors, ecological systems, integrated circuits, and mechanical systems. In those systems, the response can be described by coupled differential equations in which multi-dimensional state variables describe the timeevolution. However, in practice, the full set of state variables is often difficult or expensive to measure. This paper shows an attempt to develop a data-driven model for damped coupled oscillators from a mixed-mode response signal using neural differential equations. The univariate time-series data of the impulse response is first resampled into a multi-variate time-delayed embedding. A singular value decomposition is then applied to find the dominant orthogonal basis (oscillator modes). The decoupled modes are then modeled with parameterized neural differential equations. The unknown parameters can be learned from a segment of historical data. The proposed methodology is validated using impact testing data of an end mill in a machine tool spindle. The results demonstrate that the proposed method can effectively model damped coupled oscillators.

Proceedings Title

Proceedings of the Annual Conference of the Prognostics and Health Management Society 2022

Volume

41

Issue

1

Conference Dates

November 1-4, 2022

Conference Location

Nashville, TN, US

Conference Title

14th Annual Conference of the Prognostics and Health Management Society

Pub Type

Conferences

Download Paper

https://doi.org/10.36001/phmconf.2022.v14i1.3204

Local Download

Citation

Fabro, J. , Vogl, G. , Qu, Y. and Eischens, R. (2022), Learning Data-Driven Model of Damped Coupled Oscillators from System Impulse Response, Proceedings of the Annual Conference of the Prognostics and Health Management Society 2022, Nashville, TN, US, [online], https://doi.org/10.36001/phmconf.2022.v14i1.3204, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=935029 (Accessed October 9, 2025)