Orienting Body Coordinate Frames Using Karhunen-Loe`ve Expansion for More Effective Structural Simplification

Abstract

Previous work by the authors developed a junction-inactivity-based structural simplification technique for bondgraph 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-Loe`ve 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 conclusion is that the Karhunen-Loe`ve expansion complements well the junction-inactivity-based structural simplification technique when multibody dynamics are involved in the system.