System Partitioning and Physical-Domain Model Reduction Through
Assessment of Bond Graph Junction Structure
D.G. Rideout
J.L. Stein
Automated Modeling Laboratory
University of Michigan
Ann Arbor, MI, USA 48109-2121
Phone: +1 734 763-7388, Fax: +1 734 764-4256, E-mail: drideout@umich.edu, stein@umich.edu
L.S. Louca
Dept. of Mechanical and Manufacturing Engineering
University of Cyprus
Nicosia 1678, Cyprus
Phone: +357 22 892279, Fax: +357 22 892254, E-mail: lslouca@ucy.ac.cy
Abstract - This paper proposes a technique to
quantitatively and systematically search for
decoupling among dynamic elements of a bond graph
model, and partition models in which decoupling is
found. The method can increase the efficiency and
accuracy of simulation-based design by improving
physical-domain model reduction and preventing the
use of inappropriate decoupling assumptions.
A full model is first generated using the bond graph
formalism. The relative contributions of the terms of
the generalized Kirchoff loop and node equations are
computed by calculating and comparing an aggregate
measure of the power flow through the individual
bonds connected to each 1- and 0-junction. Negligible
aggregate bond power at a junction represents an
unnecessary constraint term. Such bonds are replaced
by a source modulated by the output of that junction.
If separate bond graphs joined by modulating signals
result, then the model can be partitioned into driving
and driven subsystems. While the algorithm is not
restricted to bond graph representations of system
models, the formalism is shown to greatly facilitate its
implementation and heighten the physical insight
gained thereby.
The algorithm is demonstrated for a slider-crank
mechanism. The case study illustrates that decoupling
can be found without the modeler relying on a priori
assumptions, and that the computation speed and ease
of use of the model increase after partitioning. The
validity of decoupling assumptions can be tracked as
the design and environment change.
I. INTRODUCTION
The role of computer simulation in engineering design
continues to increase as companies strive to gain
competitive advantage by reducing the time required to
move from concept to final product. As model
complexity increases in step with advances in computer
technology, the engineer remains well served to use
“proper models” - simulation models with sufficient
predictive ability but minimum complexity.
Proper Modeling [Wilson and Stein, 1995] has been
defined as the systematic determination of the model of
minimal complexity that a) satisfies the modeling
objectives and b) retains physically meaningful variables
for design. Techniques compatible with the proper
modeling philosophy should be systematic and
algorithmic, minimizing the need for a domain expert to
override the algorithms and leverage his or her experience
and intuition to generate the optimally reduced model.
The techniques are to be applicable to hybrid models
comprised of electrical, hydraulic, thermal, and multibody
mechanical components. To ensure that underlying
assumptions remain valid throughout the process, the
required complexity of the model should be reevaluated as
the system parameters and environment change.
In addition to eliminating unnecessary complexity from a
full model, the modeler may wish to systematically
determine if boundaries or partitions exist in the model
that allow application of model reduction techniques to
two or more simpler submodels. A priori assumptions of
one-way coupling within a system are often made to
achieve the latter goal. As an example, consider a highfidelity
half-car model subject to small road undulations.
For a suitably smooth road, the pitch motions will not
affect the prediction of the longitudinal velocity and the
vehicle can be approximated as a point mass. The
longitudinal dynamic outputs may then be used to drive a
pitch model that predicts the time response of the sprung
mass rotation and suspension components [Louca et al.,
2001]. This reduction becomes questionable when
rougher road inputs excite pitch motions more vigorously.
The intuition of the analyst may allow him or her to
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