Publication: Analytical Aspects and Practical Pitfalls in Technical Applications of AD
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Analytical Aspects and Practical Pitfalls in Technical Applications of AD

- incollection -
 

Author(s)
Florian Dignath , Peter Eberhard , Axel Fritz

Published in
Automatic Differentiation of Algorithms: From Simulation to Optimization

Editor(s)
George Corliss, Christèle Faure, Andreas Griewank, Laurent Hascoët, Uwe Naumann

Year
2002

Publisher
Springer

Abstract
We apply ad to three technical problems from multibody dynamics, vehicle dynamics and finite element material modeling. The multibody dynamics application investigates threshold and maximum-value optimization criteria in direct representation using ad for the sensitivity analysis. Secondly, an adaptive cruise controller of a vehicle convoy is optimized with respect to control error and control effort. Two experimental cars equipped with state-of-the-art sensors and actuators are used to verify the designed controllers. Since the engine voltage of the actuator is restricted to ± 10 V, there are non-differentiable points in the time trajectory, but ad techniques can still be used. Thirdly, ad is used for the evaluation of constitutive relations for hyperelastic materials. Some important continuum mechanical quantities correspond to the first and second derivatives of the scalar stored energy function with respect to the strain tensor. These quantities can be derived analytically using complicated analysis but it is fascinating that with minimal preparation and only few mathematical insight exactly the same values can also be computed using ad methods.

Cross-References
Corliss2002ADo

BibTeX
@INCOLLECTION{
         Dignath2002AAa,
       author = "Florian Dignath and Peter Eberhard and Axel Fritz",
       title = "Analytical Aspects and Practical Pitfalls in Technical Applications of {AD}",
       pages = "131--136",
       chapter = "14",
       crossref = "Corliss2002ADo",
       booktitle = "Automatic Differentiation of Algorithms: From Simulation to Optimization",
       year = "2002",
       editor = "George Corliss and Christ{\`e}le Faure and Andreas Griewank and Laurent
         Hasco{\"e}t and Uwe Naumann",
       series = "Computer and Information Science",
       publisher = "Springer",
       address = "New York, NY",
       abstract = "We apply AD to three technical problems from multibody dynamics, vehicle dynamics
         and finite element material modeling. The multibody dynamics application investigates threshold and
         maximum-value optimization criteria in direct representation using AD for the sensitivity analysis.
         Secondly, an adaptive cruise controller of a vehicle convoy is optimized with respect to control
         error and control effort. Two experimental cars equipped with state-of-the-art sensors and actuators
         are used to verify the designed controllers. Since the engine voltage of the actuator is restricted
         to $\pm 10$ V, there are non-differentiable points in the time trajectory, but AD techniques
         can still be used. Thirdly, AD is used for the evaluation of constitutive relations for hyperelastic
         materials. Some important continuum mechanical quantities correspond to the first and second
         derivatives of the scalar stored energy function with respect to the strain tensor. These quantities
         can be derived analytically using complicated analysis but it is fascinating that with minimal
         preparation and only few mathematical insight exactly the same values can also be computed using AD
         methods.",
       referred = "[Klein2002DMf]."
}


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