Orienting body coordinate frames using Karhunen-Loeve expansion for more effective structural simplification
As part of an effort to create an automated modular modeling environment, previous work by the authors developed a junction-inactivity-based structural simplification technique that is particularly suitable for bond-graph models. The technique is highly sensitive to the orientation of the body coordinate frames in multibody systems: improper alignment of body coordinate frames may prohibit a significant simplification. This paper demonstrates how the Karhunen-Loeve expansion can be used to automatically detect the existence of and to find the transformation into body coordinate frames that render the bond graph of a multibody system more conducive to simplification. The proposed technique is demonstrated using the simple example of it 3D pendulum constrained to move in a plane, but is applicable to arbitrarily complex multibody dynamics problems. The conclusion is that the Karhunen-Loeve expansion successfully complements the junction-inactivity-based structural simplification technique when multibody dynamics are involved in the system, and thus significantly contributes to the development of art automated modular modeling environment. (C) 2007 Elsevier B.V. All rights reserved.
karhunen-loeve expansion modular modeling bond graphs model simplification activity junction elements