Publication: Performance of automatic differentiation tools in the dynamic simulation of multibody systems
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Performance of automatic differentiation tools in the dynamic simulation of multibody systems

- Article in a journal -
 

Area
Multibody Systems

Author(s)
Alfonso Callejo , Sri Hari Krishna Narayanan , de Jalon , Javier Garcia , Boyana Norris

Published in
Advances in Engineering Software

Year
2014

Abstract
Abstract Within the multibody systems literature, few attempts have been made to use automatic differentiation for solving forward multibody dynamics and evaluating its computational efficiency. The most relevant implementations are found in the sensitivity analysis field, but they rarely address automatic differentiation issues in depth. This paper presents a thorough analysis of automatic differentiation tools in the time integration of multibody systems. To that end, a penalty formulation is implemented. First, open-chain generalized positions and velocities are computed recursively, while using Cartesian coordinates to define local geometry. Second, the equations of motion are implicitly integrated by using the trapezoidal rule and a Newton–Raphson iteration. Third, velocity and acceleration projections are carried out to enforce kinematic constraints. For the computation of Newton–Raphson’s tangent matrix, instead of using numerical or analytical differentiation, automatic differentiation is implemented here. Specifically, the source-to-source transformation tool {ADIC2} and the operator overloading tool ADOL-C are employed, in both dense and sparse modes. The theoretical approach is backed with the numerical analysis of a 1-DOF spatial four-bar mechanism, three different configurations of a 15-DOF multiple four-bar linkage, and a 16-DOF coach maneuver. Numerical and automatic differentiation are compared in terms of their computational efficiency and accuracy. Overall, we provide a global perspective of the efficiency of automatic differentiation in the field of multibody system dynamics.

AD Tools
ADIC

BibTeX
@ARTICLE{
         Callejo2014Poa,
       title = "Performance of automatic differentiation tools in the dynamic simulation of multibody
         systems",
       journal = "Advances in Engineering Software",
       volume = "73",
       pages = "35--44",
       year = "2014",
       issn = "0965-9978",
       doi = "http://dx.doi.org/10.1016/j.advengsoft.2014.03.002",
       url = "http://www.sciencedirect.com/science/article/pii/S0965997814000477",
       author = "Callejo, Alfonso and Narayanan, Sri Hari Krishna and de Jalon, Javier Garcia and
         Norris, Boyana",
       abstract = "Abstract Within the multibody systems literature, few attempts have been made to
         use automatic differentiation for solving forward multibody dynamics and evaluating its
         computational efficiency. The most relevant implementations are found in the sensitivity analysis
         field, but they rarely address automatic differentiation issues in depth. This paper presents a
         thorough analysis of automatic differentiation tools in the time integration of multibody systems.
         To that end, a penalty formulation is implemented. First, open-chain generalized positions and
         velocities are computed recursively, while using Cartesian coordinates to define local geometry.
         Second, the equations of motion are implicitly integrated by using the trapezoidal rule and a
         Newton–Raphson iteration. Third, velocity and acceleration projections are carried out to
         enforce kinematic constraints. For the computation of Newton–Raphson’s tangent
         matrix, instead of using numerical or analytical differentiation, automatic differentiation is
         implemented here. Specifically, the source-to-source transformation tool \{ADIC2\} and the
         operator overloading tool ADOL-C are employed, in both dense and sparse modes. The theoretical
         approach is backed with the numerical analysis of a 1-DOF spatial four-bar mechanism, three
         different configurations of a 15-DOF multiple four-bar linkage, and a 16-DOF coach maneuver.
         Numerical and automatic differentiation are compared in terms of their computational efficiency and
         accuracy. Overall, we provide a global perspective of the efficiency of automatic differentiation in
         the field of multibody system dynamics.",
       ad_area = "Multibody Systems",
       ad_tools = "ADIC"
}


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