A Study on Data-Driven Identification and Representation of Nonlinear Dynamical Systems with a Physics-Integrated Deep Learning Approach: Koopman Operators and Nonlinear Normal Modes
Document Type
Conference Proceeding
Publication Date
7-29-2022
Department
Department of Mechanical Engineering-Engineering Mechanics
Abstract
In this study, we investigate the performance of data-driven Koopman operator and nonlinear normal mode (NNM) on predictive modeling of nonlinear dynamical systems using a physics-constrained deep learning approach. Two physics-constrained deep autoencoders are proposed: one to identify eigenfunction of Koopman operator and the other to identify nonlinear modal transformation function of NNMs, respectively, from the response data only. Koopman operator aims to linearize nonlinear dynamics at the cost of infinite dimensions, while NNM aims to capture invariance properties of dynamics with the same dimension as original system. We conduct numerical study on nonlinear systems with various levels of nonlinearity and observe that NNM representation has higher accuracy than Koopman autoencoder with same dimension of feature coordinates.
Publication Title
Conference Proceedings of the Society for Experimental Mechanics Series
ISBN
9783031040856
Recommended Citation
Rostamijavanani, A.,
Li, S.,
&
Yang, Y.
(2022).
A Study on Data-Driven Identification and Representation of Nonlinear Dynamical Systems with a Physics-Integrated Deep Learning Approach: Koopman Operators and Nonlinear Normal Modes.
Conference Proceedings of the Society for Experimental Mechanics Series, 227-228.
http://doi.org/10.1007/978-3-031-04086-3_30
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/16309