Validated Modeling of Mechanical Systems with SmartMOBILE: Improvement of Performance by ValEncIA-IVP

Authors:
Ekaterina Auer;Andreas Rauh;Eberhard P. Hofer;Wolfram Luther
Affiliations:
Faculty of Engineering, IIIS, University of Duisburg-Essen, Duisburg, Germany D-47048;Institute of Measurement, Control, and Microtechnology, University of Ulm, Ulm, Germany D-89069;Institute of Measurement, Control, and Microtechnology, University of Ulm, Ulm, Germany D-89069;Faculty of Engineering, IIIS, University of Duisburg-Essen, Duisburg, Germany D-47048
Venue:
Reliable Implementation of Real Number Algorithms: Theory and Practice
Year:
2008

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Abstract

Computer simulations of real life processes can generate erroneous results, in many cases due to the use of finite precision arithmetic. To ensure correctness of the results obtained with the help of a computer, various kinds of validating arithmetic and algorithms were developed. Their purpose is to provide bounds in which the exact result is guaranteed to be contained. Verified modeling of kinematics and dynamics of multibody systems is a challenging application field for such methods, largely because of possible overestimation of the guaranteed bounds, leading to meaningless results.In this paper, we discuss approaches to validated modeling of multibody systems and present a template-based tool SmartMOBILE, which features the possibility to choose an appropriate kind of arithmetic according to the modeling task. We consider different strategies for obtaining tight state enclosures in SmartMOBILEincluding improvements in the underlying data types (Taylor models), modeling elements (rotation error reduction), and focus on enhancement through the choice of initial value problem solvers (ValEncIA-IVP).