Orienting body coordinate frames using Karhunen-Loève 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-Loève 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 a 3D pendulum constrained to move in a plane, but is applicable to arbitrarily complex multibody dynamics problems. The conclusion is that the Karhunen-Loève 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 an automated modular modeling environment.