Adjoint sensitivity analysis of multibody system equations in state-space representation obtained by QR decomposition

Citation
11th ECCOMAS Thematic Conference on Multibody Dynamics (MULTIBODY 2023)
Contribution to Conference
11th ECCOMAS Thematic Conference on Multibody Dynamics 2023  
Publisher Link
https://multibody2023.tecnico.ulisboa.pt/~multibody2023.daemon/prog_MULTIBODY_WEB/MULTIBODY2023_PAPERS/ID_223_548_eccomas2023_full_paper.pdf
Publisher
IDMEC
ISBN
978-989-53599-3-6
Peer Reviewed
true
The paper is on applying the adjoint variable method in the sensitivity analysis of multibody systems, which are formulated in state-space representation using a QR decomposition. The Jacobian of the state equations, which is necessary to develop the adjoint dynamics, is derived. Moreover, an analytical way to determine the derivatives of the QR matrices with respect to the redundant position variables is presented, which avoids costly finite differences or differentiation of the direct QR algorithm. The developed method is tested by a spring torsional pendulum found in previous contributions to the subject. The obtained gradient is more precise compared to numerical differentiation using forward differences. Also, providing the analytical Jacobian of the state equations turns out to be beneficial regarding both the gradient accuracy and computational times.
Subjects
adjoint sensitivity analysis
multibody systems
QR decomposition
state-space respresentation
DDC Class
004: Computer Sciences
620: Engineering