Abstract Among the proposed formulations for rigid multibody dynamics, the minimal coordinates approach permits to parametrize the system motion with the minimal amount of degrees of freedom without the need of additional constraints equations. This leads to a system of ordinary differential equations to describe the motion which enables a straightforward combination of the model with control or estimation algorithms. However, an explicit relation between the model full coordinates and a minimal number of parameters is not always available or easily obtainable, especially for spatial closed-loop mechanisms. In this work, we therefore propose to deploy deep learning to find an approximation of such motion mappings. More specifically, an autoencoder neural network architecture is exploited for the nonlinear dimensionality reduction from full to minimal coordinates. A novel neural-network training scheme is introduced, which exploits the multibody model dynamics information to optimize the decoder-function derivatives so that they represent the tangent space and the curvature of the minimal coordinates manifold. This scheme leads to an effective description of the motion manifold which can be used to express the dynamics in minimal coordinates. The approach is validated on two reference rigid body mechanisms.
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Deep learning for model order reduction of multibody systems to minimal coordinates
Semantic Scholar · Engineering · 2021
Abstract
Abstract Among the proposed formulations for rigid multibody dynamics, the minimal coordinates approach permits to parametrize the system motion with the minimal amount of degrees of freedom without the need of additional constraints equations. This leads to a system of ordinary differential equations to describe the motion which enables a straightforward combination of the model with control or estimation algorithms. However, an explicit relation between the model full coordinates and a minimal number of parameters is not always available or easily obtainable, especially for spatial closed-loop mechanisms. In this work, we therefore propose to deploy deep learning to find an approximation of such motion mappings. More specifically, an autoencoder neural network architecture is exploited for the nonlinear dimensionality reduction from full to minimal coordinates. A novel neural-network training scheme is introduced, which exploits the multibody model dynamics information to optimize the decoder-function derivatives so that they represent the tangent space and the curvature of the minimal coordinates manifold. This scheme leads to an effective description of the motion manifold which can be used to express the dynamics in minimal coordinates. The approach is validated on two reference rigid body mechanisms.