Publication: Adjoint Variable Method for the Sensitivity Analysis of Multibody Systems Interpreted as Continuous, Hybrid Form of Automatic Differentiation
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Adjoint Variable Method for the Sensitivity Analysis of Multibody Systems Interpreted as Continuous, Hybrid Form of Automatic Differentiation

- incollection -
 

Author(s)
Peter Eberhard

Published in
Computational Differentiation: Techniques, Applications, and Tools

Editor(s)
Martin Berz, Christian Bischof, George Corliss, Andreas Griewank

Year
1996

Publisher
SIAM

Abstract
The multibody system approach is widely used for analyzing the dynamic behavior of mechanical systems with large motions, and several programs are available for this task. However, there is still a lack of tools for synthesizing nonlinear dynamic systems systematically by using optimization methods. Because the system's time behavior and optimization criteria can be computed only by numerical time integration, an analytical, closed form solution is not available for complicated, nonlinear multibody systems. Modern approaches such as the adjoint variable method offer the design engineer valuable tools to calculate required gradients for these problems in a reliable and efficient way. We show that the adjoint variable approach, developed from variational calculus is similar to automatic differentiation techniques, developed from recursive application of the chain rule. A parallel implementation of the adjoint variable approach yields further improvements in the computation time.

Cross-References
Berz1996CDT

BibTeX
@INCOLLECTION{
         Eberhard1996AVM,
       author = "Peter Eberhard",
       editor = "Martin Berz and Christian Bischof and George Corliss and Andreas Griewank",
       title = "Adjoint Variable Method for the Sensitivity Analysis of Multibody Systems Interpreted
         as Continuous, Hybrid Form of Automatic Differentiation",
       booktitle = "Computational Differentiation: Techniques, Applications, and Tools",
       pages = "319--328",
       publisher = "SIAM",
       address = "Philadelphia, PA",
       key = "Eberhard1996AVM",
       crossref = "Berz1996CDT",
       abstract = "The multibody system approach is widely used for analyzing the dynamic behavior of
         mechanical systems with large motions, and several programs are available for this task. However,
         there is still a lack of tools for synthesizing nonlinear dynamic systems systematically by using
         optimization methods. Because the system's time behavior and optimization criteria can be
         computed only by numerical time integration, an analytical, closed form solution is not available
         for complicated, nonlinear multibody systems. Modern approaches such as the adjoint variable method
         offer the design engineer valuable tools to calculate required gradients for these problems in a
         reliable and efficient way. We show that the adjoint variable approach, developed from variational
         calculus is similar to automatic differentiation techniques, developed from recursive application of
         the chain rule. A parallel implementation of the adjoint variable approach yields further
         improvements in the computation time.",
       keywords = "Multibody systems, mechanical systems, ordinary differential equations, adjoint
         variable method, parallel sensitivities.",
       referred = "[Dignath2002AAa].",
       year = "1996"
}


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