Identification of internal forces in free vibration of mechanical structures using Hamiltonian neural networks

Abstract

The inverse matrix method is used to identify internal forces in a machine structure to reduce noise and vibration of the machine. To apply the inverse matrix to the machine, it is necessary that the machine is physically divided into two segments at the position where the internal forces are to be identified, it takes a lot of times. On the other hand, the machine learning model called Hamiltonian Neural Networks (HNN) has been proposed to predict the motion of objects with considered the energy conservation law from experimental data of the entire structure. In this research, at first, we confirm characteristics of HNN from predicting the motion of objects with the common neural network, we called Baseline Neural Networks (BNN) and HNN, and then we confirm the accuracy of the identified internal forces using BNN and HNN. Applying BNN and HNN to two dynamics problems, it shows HNN accurately predicts the trajectory of the system considering the energy conservation law. Applied to a numerical spring-mass model to predict internal forces, HNN has been able to predict more accurately than the BNN. We also confirmed the number of data needed to obtain sufficient identification accuracy, since the number of data obtained by the experiment is limited. It was found that the number of data required increases rapidly as the number of degrees of freedom of the system increases.