Session: VIB-08-01 Vibration and Stability of Mechanical Systems and Machine Learning Applications to Vibrations and Dynamics

Paper Number: 74322

Start Time: August 19, 03:20 PM

74322 - Neural Network Ensemble With Embedded Hamiltonian Constraints for Modeling Nonlinear Structural Dynamics 

Data-driven machine learning models are sometimes useful for modeling complex structures based on empirical observations, bypassing the need to generate a physical model where the physics is not well known or otherwise readily model-able. However, one disadvantage of purely data-driven approaches is that they tend to perform poorly in regions outside the original training domain. To mitigate this limitation, physical knowledge about the structure can be embedded in the model architecture via the model topology or numerical constraints in the formulation. For large-scale systems, relevant physics, such as the system state matrices, may be expensive to compute. One way around this problem is to use scalar functionals, such as energy, to constrain the network to operate within physical bounds. We propose a neural network framework based on Hamiltonian mechanics to enforce a physics-informed structure to the model. The Hamiltonian framework allows us to relate the energy of the system to the measured quantities (e.g., accelerations) through the Euler-Lagrange equations of motion. The approach is demonstrated on simple exemplars, such as a two degree-of-freedom (DOF) damped oscillator with cubic nonlinearities. This presentation will discuss the potential applications for this framework in the context of data-driven physics-informed digital twins for real-time structural health monitoring.

Presenting Author: David A. Najera-Flores ATA Engineering

Authors:

David A. Najera-Flores ATA Engineering
Michael Todd University of California San Diego