A Machine Learning Approach for Minimal Coordinate Multibody Simulation

Abstract

Over the years, a wide range of generalized coordinates have been proposed to describe the motion of rigid and flexible multibody systems. Depending on the type of formulation, a different equation structure is obtained for the model. Most formulations rely on a redundant number of Degrees Of Freedom (DOFs) and some associated constraints, leading to a set of Differential-Algebraic Equations (DAEs) to model the system dynamics. On the other hand, the 'Minimal Coordinate' formulation describes the dynamics through a minimal amount of DOFs and leads to a system of Ordinary Differential Equations (ODEs). For many applications, this ODE structure is an important benefit, as it enables a natural integration for state-estimation and model-based control. The backside of this approach is that it is generally not-straightforward to find a minimal number of parameters to unequivocally describe the system configurations, especially for complex mechanisms. In this work, a machine learning approach based on Auto-Encoders is proposed to find a non-linear transformation that leads to a minimal parameterization of the motion. It is shown that such non-linear transformation can be used to project into minimal coordinates while its inverse permits to perform the simulation in the reduced dimension and re-obtain the original coordinates.

Deep learning for model order reduction of multibody systems to minimal coordinates

“…Lately a particular neural network architecture, the autoencoder, has showed promising results in manifold learning and non-linear dimensionality reduction [25,26] and has been successfully applied to the learning of (lowdimensional) dynamical systems [27][28][29]. Its combination in a Model Order Reduction (MOR) scheme has been introduced in [30] while an application to multibody dynamics has been first proposed in [31].…”

Deep learning of multibody minimal coordinates for state and input estimation with Kalman filtering

“…In this work, a model order reduction approach based on deep learning presented in [14,15,16] is exploited to obtain the minimal coordinate mapping and reduce a multibody model from redundant to minimal coordinates. The non-linear mapping from redundant to minimal coordinates is approximated with a neural network.…”